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AN EFFICIENT MODIFIED ELLIPTIC CURVE DIGITAL SIGNATURE ALGORITHM Tilahun Kiros Department of Computer Science and Engineering MekelleInstitute of Technology and Kumudha Raimond Department of Electrical and Computer Engineering Addis Ababa University ABSTRACT Many digital signatures which are based on Elliptic Curves Cryptography (ECC) have been proposed. Among these digital signatures, the Elliptic Curve Digital Signature Algorithm (ECDSA) is the widely standardized one. However, the verification process of ECDSA is slower than the signature generation process. Hence, the main objective of this work is to study ECDSA in order to improve its execution time. The method of the improvement is focused on the mathematical relationships of the algorithm in a manner that its verification process can be efficient. As a result, without affecting the underlying mathematical problem the Elliptic Curve Discrete Logarithmic Problem (ECDLP) - a related efficient scheme is developed. The signature verification algorithm of the modified scheme is found to be faster than the verification process of ECDSA by 45%. Keywords: Digital signature, ECDSA algorithm, Elliptic curve cryptography, Scalar multiplication, Signature generation, Signature verification. As a result, algorithms and techniques have been introduced to offer a better security mechanism. Algorithms like Rivest-Shamir-Adleman (RSA) [1, 6, 8], Digital Signature Algorithm (DSA)[1, 15], Diffie-Hellman (DH) [1, 7], and Elliptic Curve Cryptography (ECC) based schemes [4, 10] - like the ECDSA - are a few of the known cryptographic systems that are being employed in various applications. However, among these known cryptographic systems, ECC is emerging as an attractive and better alternative to the public-key cryptosystems [11, 12, 13, 14, 17, 18, 23]. ECC offers equivalent security with smaller key sizes resulting in faster computations. The use of elliptic curves in modern public key cryptography was independently introduced by Neal Kobltiz and Victor Miller in 1985 [2, 3, 4]. Since then, a lot of researches have been conducted in order to challenge its security strength and find out efficient ways of implementing ECC based cryptosystems. ECC has got increasing attention by the research community, as it offers equivalent security but shorter key size when it is compared with previously known systems like RSA and Discrete Logarithm (DL) based cryptosystems. Though the confidence level of ECC is not equal to RSA as RSA has been around for above thirty years, it is widely believed that 160-bit ECC offers equivalent security of 1024-bit RSA. In general, ECC has better per-bit security, hence, suitable in constrained environments smart cards and hand-held devices. ECC has storage, power, and bandwidth requirements, improved performance [20]. and like less and INTRODUCTION With the advent of information technology, ensuring network and data communication security has become a crucial issue. Though the information technology provides us with various versatile tools for data manipulation and data storage, it is not without different facets of security attack. Thus, it is crucial to have tools that can insure the integrity of data, the confidentiality of data, and authenticity of any form of data communication. To meet the requirements of network and data communication security, the cryptography science plays a great role. A variety of researches and applications of cryptography are developed in parallel with the advancement of the IT facilities. The rest of the paper is organized as follows: section 2 presents related works of elliptic curve digital signature. Preliminaries on ECC and ECDSA are presented in section 3. The proposed modified scheme is described in section 4. Journal of EEA, Vol. 26, 2009 66 Tilahun Kiros and Kumudha Raimond Don B. Johnson, [12], has given an explanation of ECC suitability on high-security environment based on the underlying difficulty of ECDLP. It is explained that ECDLP is more difficult to solve than IFP and DLP [12] as currently known efficient algorithms to solve ECDLP are full exponential, whereas to solve IFP and DLP there are sub exponential algorithms. The article shown in [13], and the works discussed in [14] strengthened this idea. Moreover, in [13, 14], the suitability of ECC on smart cards is evidently explained, as ECC is more compact than RSA. Pietilainen [14] has compared ECC and RSA based on security, efficiency and space requirement by implementing both of them. In [22], the authors provide basic alternatives to resolve the implementation issues of ECC on constrained devices like cellular phones. They indicated that curves over GF (2m) are convenient for hardware implementation; whereas curves on GF (p) are suitable for software implementation. Finally, in [22], optimization of ECC based schemes is recommended as it is accepted as the next generation public-key cryptosystem. Many of the works that aimed at improving performance of ECC based schemes either concentrated on improving the underlying mathematical operations, or concentrated on implementation of specific curves on a specific hardware platform. Little is done in designing different digital signature algorithms which may have a better performance than the existing ones. In this work, after a thorough study of ECC based cryptosystems, areas of performance improvements of ECDSA has been examined. In ECDSA, the most expensive operation is the scalar multiplication or elliptic curve point multiplication. Another expensive operation is the modular inversion operation. Optimized techniques of scalar multiplication are given in [4, 16, 24]. Here, an attempt has been made to develop ECDSA related scheme in such a way that the number of elliptic curve point multiplications can be reduced during signature verification process. PRELIMINARIES Elliptic Curve Cryptography Elliptic curves for cryptography are defined over finite algebraic structures such as finite fields. Let s assume prime fields Fp of characteristics p > 3 [2, 4]. Such a curve is the set of geometric Section 5 presents alternative form of the proposed scheme. Performance comparison of elliptic curve digital signature and the proposed modified scheme is presented in section 6, while section 7 concludes the paper. RELATED WORKS Leading mathematicians and scientists have done a lot to ensure the robustness and correctness of many of the cryptographic schemes [9]. However, in [17], it is discussed that none of the mathematical problems like the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problem (ECDLP) are proven to be intractable. This article [17] underlines that it is based on our belief of their intractability that we rely on these algorithms, as no efficient algorithms are found to solve them. This article, [17], also assures that no sub-exponential algorithm is found to solve ECDLP. Rosner discusses the implementation of GF1 (2m) based curves on a reconfigurable hardware [11]. It is shown that for GF (2168), one point doubling operation takes 273 clock cycles. The work in [11] provides with some fundamental concepts for hardware implementation. The suitability of ECC based schemes for constrained devices and embedded systems is explained in [18]. Based on the per-bit security of ECC, this paper clarifies the advantage of ECC to achieve longer running battery operated devices with less heat, faster applications that consume less memory, and scaleable cryptographic applications. Moreover, the key-size comparison of ECC with RSA and DH based systems is given in [18]. In general, the advantage and performance comparison of ECC with RSA and DH schemes is provided in [12, 13, 14, 17, 18]. In [16], implementation of ECDSA on Advanced RISC Machines (ARM) processors for a curve on GF (2m) is done. It is concluded that by using certain machine and curve specific techniques, the ECDSA signature can be made faster and optimized [16]. Similar work is done in [21] for a curve on GF (p). ARM processor implementation of curve p-224 is discussed in [21]. According to [21], it is concluded that 129.28ms was taken to perform point multiplication over the curve p-224 for C-based implementation. And the time was less for assembly language based implementation. Finite fields with pn, for p a prime integer and n a positive integer are known as Galois Fields or GF. 1 Journal of EEA, Vol. 26, 2009 An Efficient Modified Elliptic Curve Digital Signature Algorithm solutions form P = ( x, y ) 67 to an equation of the following point. The parameter n is the order of the point P. P is the generator of the cyclic sub group P (Eq. (4)). The parameter h is known as cofactor. It is found as h = order ( E ( Fq )) , Where order (E(Fq)) is the number of elements in E(Fq). Given the public-private key pair (Q, d), and domain parameters, the ECDSA signature generation and verification can be formulated as shown in Algorithms (1) and (2), respectively. A hash function, H shown in line 4 of Algorithm (1), accepts a variable size message M as input and produces a fixed-size output, referred to as a hash code H(M) or a message digest [2]. Hash functions are used for data integrity in conjunction with digital signature schemes, where a message is typically hashed first, and then the hash value as the representative of the message is signed in place of the original message. The receiver authenticates the message by applying the hash function on the message and re-computes the hash value. Algorithm (1) ECDSA signature generation Given parameters q, a ,b, P, n and private key d, to sign a message m, A does the following 1. Select k Î [1, n - 1] . 2. Compute kP = ( x1 , y1 ) . 3. Compute r = x1 mod n . If r=0 then go to step 1. 4. Compute e = H (m) . 5. Compute s = k -1 ( e + dr ) mod n . If s=0 go to step 1. 6. Return(r, s). Algorithm (2) ECDSA signature verification To verify A s signature (r, s) on m, B uses parameters q, a, b, P, n, h, public key Q, message m and signature (r, s). 1. Verify that r and s are integers in the interval [1, n- 1]. If any verification fails then return ( Reject the signature ). 2. Compute e=H(m). 3. Compute w= s-1 mod n. 4. Compute u1 = ew mod n and u2 = rw mod n. 5. Compute X = u1P + u2Q. a. If X = O¥ then return ( Reject the signature ); 6. Take the x-coordinate of X as x1 and compute v = x1 mod n. 7. If v = r then return ( Accept the signature ); Else return ( Reject the signature ). n E : y 2 = x 3 + ax + b(mod p) (1) Where a and b are constants in Fp (p > 3) satisfying 4 a3 + 27 b2 0 (mod p ) . To have the points on is E to form a group, an extra point denoted by included. This extra point is called the point at infinity and can be formulated as = ( x, ¥) (2) The point at infinity is the identity element for the group law formulated as E = { p = ( x , y ) | x , y Î F p that solves (1)} È { } (3) This set of points form a group under a group operation which is conventionally written additively using the notation + [2]. The group forms an abelian group, [5], over which ECC is based and all operations are performed. Suppose the point P is in E(Fp), and suppose P has a prime order n, then, the cyclic additive subgroup of E(Fp ) generated by P is P = {O¥ , P, 2 P , 3P ,..., (n - 1) P}. (4) The prime p, the equation of the elliptic curve E, and the point P and its order n, are the public domain parameters. Furthermore, a randomly selected integer d from the interval [1, n-1] forms a private key. Multiplying P by the private key d, which is called scalar multiplication, will generate the corresponding public key Q, i.e. Q = dP. The pair (Q, d) forms the ECC public-private key pair with Q is the public key and d is the private key. The Elliptic Curve Digital Signature Algorithm (ECDSA) ECDSA is the elliptic curve analogue of DSA [4, 16, 19]. It was accepted by many standard organizations around 2000. Below, the ECDSA signature generation and the ECDSA signature verification algorithms are given. The algorithms are available in [4]. In ECC, there are a set of domain parameters denoted by D = (q , a, b, P, n, h). q represents the field order of the prime field Fq. The parameters are coefficients of the elliptic curve a, b Î Fq equation E. The parameter P Î E ( Fq ) is the base Journal of EEA, Vol. 26, 2009 68 Tilahun Kiros and Kumudha Raimond curve scalar multiplication operation. This work focuses on a possible way of minimizing the scalar multiplication operations. PROPOSED SCHEME Scalar multiplication dominates the execution time of ECC based schemes [4, 10]. In ECDSA, there are scalar multiplications in the signature generation and signature verification processes. In step 2 of algorithm (1) (ECDSA signature generation), the base point P is multiplied by the scalar or integer value k. Furthermore, in step 5 of algorithm (2) (ECDSA signature verification), the base point P is multiplied by an integer value u1 and the public key Q is multiplied by an integer value u2. As there are two scalar multiplications in the ECDSA verification algorithm, execution of the signature verification process needs a longer time than the signature generation process. So, attention is given to the verification process to examine if a scheme can be developed to minimize the execution time needed for signature verification of ECDSA. Observing algorithms (1), and (2), there is an important relationship between the signature generation and the signature verification. The elliptic curve point kP = (x1, y1) computed in the signature generation algorithm must be equal to the elliptic curve point X = (x1, y1) computed during signature verification. Thus, if these points are equal, one can declare that the signature is valid and the signature is indeed generated by the owner of the public key Q. Therefore, finding any mathematical relationship without impairing the underlying ECDLP problem so that the points kP = (x1, y1) and X = (x1, y1) can be equal, leads us to a new scheme. Based on this notion, an attempt is made to search for such mathematical relationships and, accordingly, the following scheme is proposed. Let the signature s is generated as Below a proof is given to show how the signature verification of ECDSA works. If a signature (r, s) on a message m was generated by A, then necessarily the following will be true as a result of Algorithm (1), step number 5: s º k -1 (e + dr )(mod n) (5) From Eq. (5), by the principles of modular arithmetic, we will obtain that k º s -1 (e + dr) º s -1e + s -1 rd (mod n) (6) However, in algorithm (2), step number 3, s -1 (mod n ) is represented by the parameter w as w º s -1 (mod n). Substituting s -1 (mod n ) in Eq.(6) by w , we will get k º we + wrd (mod n ) (7) But, in Algorithm (2), step number 4, we (mod n) is represented by u1 and wr (mod n ) is represented by u 2 . Thus, based on equation (7), k = u1 + u 2 d (mod n) (8) From the verification algorithm, we can see that X = u1 P + u 2 Q (9) However, the public key Q = dP, where d is a private key in the interval [1, n - 1} and P is the generator of the cyclic sub group P (Eq. (4)). Therefore, substituting Q in Eq. (9) by dP and using Eq. (8), we will obtain, X = u1 P + u 2 dP = (u1 + u 2 d ) P = kP (10) This proves that v = r. Because, X = kP indicates that the x-coordinate of kP, x1 , in Algorithm (1) step numbers 2 and 3, and the x-coordinate of X, x1 , in Algorithm (2) step number 6, are equal in essence. The ECDSA algorithm is involving modular inversion and the elliptic curve point multiplication operations (scalar multiplication) in the process of signature generation and signature verification. Both the modular inversion operation and scalar multiplication operation can have impact on the performance of the algorithm. In fact, the most time consuming operation in ECDSA is the elliptic s = e + k + d (mod n) (11) Where e is the hash value H(m) of a given message m, k the per message secret, and d the private key. Hence, k can be computed as k = s - e - d (mod n ) (12) As the elliptic curve point X = (x1, y1) must be equal to the elliptic curve point kP = (x1, y1) (see algorithms (1), and (2)), in the verification process, Journal of EEA, Vol. 26, 2009 u = k + d (mod n)). in ECDSA s signature verification process. n. Verify that r and s are integers in the interval [1. Compute e = H(m). Vol. d = ( s . (i. The prominent issue here is security considerations. If any verification fails then return ( Reject the signature ). guessing d and k from the relationship s = e + k + d (mod n ) is difficult as there are different values of d and k in [1. Whereas in the proposed one.Q. Both of the algorithms are compared for the underlying field size of 32-bit and 64 bit. P. Compute u = s . n and private key d. In this proposed scheme.1] . Similarly. there is only one scalar multiplication i. 5. Without the knowledge of k. the problem is intractable. u1P and u2Q (algorithm (2)). there are two elliptic curve point multiplications i.dP = (u . If X = O then return ( Reject the signature ). Compute s = e + k + d (mod n) . Basically. Compute X=uP . the following proof is given. 7.d ) P = (k + d . respectively. the execution time required to verify a signature is reduced almost by half when it is compared with the execution time required to verify a signature in ECDSA.b. Compute kP = ( x1 . 3. the adversary is required to recover d by brute search or by understanding the per message secret key k or by using currently known efficient algorithms. The results of the point multiplications are to be added. The reason is.e. In ECDSA. If u = 0 return ( Reject the signature ). there is one point addition operation (algorithm (4)).e )(mod n ) (13) 3. Compute u = ( s . Proof: If the signature (r. s) is indeed generated by the private key d holder using Eq.k . 6.Q = uP . y1) can be calculated based on the following steps. Compute e = H(m). d can be recovered as Algorithm (4) Proposed scheme signature verification 1. So. However.e(mod n). 4. it would be reasonable and expected that the execution time for signature verification to be reduced almost by half. there are Journal of EEA. Compute X = uP Q. Signature verification process of the proposed scheme was 48-57% faster than that of the ECDSA (see section 6). 1. To make it further clarified and to show that verification process holds. If r = 0 then go to step 1. P. h. message m and signature (r. uP. Algorithm (3) Proposed scheme signature generation Given domain parameters q. if the adversary learns the per message secret k. For this proposed scheme. 4. 2. a . In the verification process X must be computed as X = uP . then Eq. n-1] that can satisfy such relationship. (12) holds true. Select k Î [1. And this proves that X = kP. 6. there is one point addition operation. Take the x-coordinate of X as x1 and compute v = x1 mod n. A does the following 1. this proposed scheme is relied on the ECDLP. n . and hence. If the adversary can get an opportunity to know the value of a single message secret key k. s). n1]. Compute r = x1 mod n . 3.e. Thus.e)(mod n) . So. In fact. 8. the way signature is generated and verified in this scheme is different from that of the ECDSA. 2. If v = r then return ( Accept the signature ). from which it can be concluded that v = r is as intended. To verify A s signature (r. 2. s).An Efficient Modified Elliptic Curve Digital Signature Algorithm the point X = (x1.d ) P = kP 69 5. is this proposed scheme as secure as ECDSA? The security of ECDSA relies on the mathematical problem ECDLP. cryptographic schemes are designed to secure our on-line communication as well as stored information asset. 2009 . y1 ) . b. (11). Compute e = H (m) . 26. Currently known efficient algorithms to solve the ECDLP are fully exponential time algorithms. it is possible to recover d from k. s) on m. Furthermore. B uses domain parameters q. Return(r. If s = 0 or s = e then go to step 1. The signature generation and signature verification algorithms are formulated as shown in algorithms (3) and (4). public key Q.e. Else return ( Reject the signature ). to sign a message m. a. in the verification process u (algorithm (4)) can be computed as shown below Here. b) and (a . Vol..a ' )(b '-b ) -1 (mod n) u = s . the verifier will verify the signature as ( n .a ' ) P = (b '-b ) dP d = ( a . By the birth day paradox. there is one loophole so far discovered while designing the algorithm. Currently. This is the reason for the check s ¹ e in algorithm (3) and the check u ¹ 0 in algorithm (4). b Î [1. (14) Therefore. (18) In the verification process X can be calculated as X = uP .2533 n . So. However.a ' ) P = (b'-b )Q = (b'-b) dP. The impact of the message size on the execution time is negligible. three sample inputs are used for k and d. u = s .70 Tilahun Kiros and Kumudha Raimond the public key Q and n is the order of the base point. Such a result is very huge number.Q = 0 P .2 P. n .e(mod n) = 0 Then.dP = (er + k + d .. The laptop s processor is Intel Centrino with speed of 1.(n . 26. s) will be a valid signature. It has 256MB RAM. then by assigning s = e and PERFORMANCE COMPARISON OF ECDSA AND THE PROPOSED SCHEME UPON PRACTICAL IMPLEMENTATION To test the time taken to verify a signature or to generate a signature in ECDSA. the goal is to recover the private key d.Q = ( s . it can be seen that this proposed scheme can be as secure as ECDSA. (a . This occurrence is called collision [4]. b ) of integers modulo n such that [4] However. Thus. then adversaries could have been also successful in recovering d from the relationship u1 + u 2 d = k (see algorithm (2)) in ECDSA. n .5GHz. b. In the proposed variant of ECDSA. b ) is to select random integers a. -Q contains the coordinate pair ( xQ .d ) P = kP (15) (19) The method for finding the pairs (a.. b) and (a .1] for the equation s = e + k + d (mod n ) for a given values of s and e. v = x Q (mod n ) = r is as required. computing all the points P .er )(modn) P .1) = n 2 .is easier. If the adversary prepares his/her own message m and calculates the hash value e as e = H (m) . Rather than using this method.Q = -Q If such a guess would have been possible.er . the straight forward attack exhaustive search . The main idea of Pollard s rho algorithm is to find distinct pairs (a. it is not possible to guess the value of k or d.the signature pair (r. 2009 .d (mod n ) (17) aP + bQ = a ' P + b' Q. From the Eq.. the expected number of iterations before a collision is obtained is approximately pn / 2 » 1. All the algorithms are executed in a Dell laptop.er (mod n). and hence. aP + bQ) in a table until another point equal to aP + bQ is obtained for the second time [4]. the value of d can be recovered as ( a . by using this approach. the most known efficient algorithm to attack ECDLP is the Pollard s rho algorithm. from these arguments. Each of the algorithms has been run five times and then the time elapsed to execute the program at each run is registered. r = x Q (mod n). The complexity of this approach will be O ( n 2 ) . ALTERNATE FORM OF THE PROPOSED SCHEME An alternate form of the proposed scheme can be achieved by including the parameter r while computing s as shown below: s = er + k + d (mod n) (16) And k can be computed based on the following equation k = s . In signature verification.er .2n + 1 possible solutions in the interval [1.3 P. (14).y Q ) .where xQ is the x -coordinate of Journal of EEA.1] and store the triples (a. That is. X = uP .e (mod n) = e .1) P until the point Q is encountered. and in the proposed scheme.1) ´ ( n . cryptographic schemes should normally pass through a lot of evaluations by different mathematicians and computer scientists before they get employed in real world applications in order that their security can be assured. Cryptological Mathematics .83 48. two modular inversion operations available in ECDSA are eliminated in the proposed scheme. W. http:// crypto. It can be seen that the proposed scheme s signature verification process can run faster than the ECDSA s signature verification by about 4857%.64 67. Vanstone. The underlying field implementation was up to 192-bit size. REFERENCES [1] Menezes. W.pdf. 24-27.edu/~rivest/rsapaper.31 0. The Mathematical Association of America. Hellman. Potentially. we believe that the result will play a great role in enhancing the speed of ECC based digital signature schemes.19 0. 1-73. Algorithm ECDSA Proposed Scheme Difference in sec. time in sec The result is depicted in Table 2. A. Prentice Hall. 180281. V. pp. M. The test was performed for randomly selected specific sizes of the private key d and the one-time key k. [4] Hankerson. A Method for Obtaining Digital Signatures and Publickey Cryptosystems .39 0. (20) ECDSA' s Corresponding verif. pp. the execution time difference between corresponding value for ECDSA and proposed scheme is very large.318 0.pdf.52 46. http://theory.09 0. Adleman.54 144.93 Journal of EEA.80 71 In general. pp. 223-481. though the impact on its improvement is negligible as the underlying field size is increasing. D. Vol. 2004. R. The signature verification algorithm of the newly proposed scheme is found to be above 45% faster than the verification process of ECDSA. New Directions in Cryptography . proposed scheme For sample For sample For sample input 1 input 2 input 3 326432643264bit bit bit bit bit bit 0. Menezes. Van Oorschot. [5] Shoup.857/papers/diffie-hellman.93%. Shamir. Cambridge University Press. pp.92 51. ´100%. 1-61. As it can be observed from Table 1. For 32-bit field the overall average improvement is 48. S.77 51.17 0. 2005. Table 1: Average time taken to execute signature verification of ECDSA and the proposed scheme for each of the three sample inputs Average elapsed time to verify a signature (in seconds) ECDSA vs.33 0.28 51.lcs. 75-147.An Efficient Modified Elliptic Curve Digital Signature Algorithm The time taken to execute the ECDSA s and the proposed scheme s verification process is shown in Table 1.144 0. Vanstone.16 0. pp. For the 64-bit field the overall average improvement is 56.23 170. 1997. [7] Diffie. 1977. 2003. A Computational Introduction to Number Theory and Algebra (version 1) . 153-196. if further researches are conducted to examine its security strength. Handbook of Applied Cryptography . 305321.53 0. it is observed that above 45% performance improvement can be achieved for signature verification process.mit. S. pp.edu/ classes/6. This new scheme and ECDSA are implemented for comparison purposes. P. The corresponding average value is shown for each of the three sample inputs. 1976. 141-176.594 0. Only the average values are given to save space. CONCLUSION A related new scheme is proposed and developed. Cryptography and Network Security: Principles and Practice . [3] Stallings. 2000. Prentice Hall. Table 2: Average improvement in percentage for signature verification process ECDSA Sample input number 1 2 3 Sum Average Average improvement for verification process in percentage (%) Signature verification 32-bit 64-bit 46. 2004. [8] Rivest. 126.145 1. A.csail. CRC Press. A.55 0. 235-394. 26.165 0. [6] Lewand. This is as a result of reduced elliptic curve point multiplications.17 1. 139-199. Springer.28%.56 0. [2] Wenbo Mao.79 56. Guide to Elliptic Curve Cryptography . L. R. Moreover. 1-165.mit. Modern Cryptocraphy: Theory and Practice .148 1. For each sample input the improvement in percentage is calculated as Difference in Sec. 2009 . Johnson. Algorithms. M. 2005. F.orst.pdf.psu. RS Information Systems.de/imperia/md/content/texte/theses/ ms_mrosner. Implementing Elliptic Curve Cryptography .edu/papers/01Turan.ece.comms.ruhr-unibochum. et al.comms. 2004.edu/papers/01Tanik. M. http://www.certicom. The Elliptic Curve Digital Signature Algorithm (ECDSA) . S. Oregon State University. W. H. 1999. Rosner. 2006.susx. K. Future Resiliency and High Security Systems http://www.com/download/aid355/WP-enhancedSecurity. 2001.ist. 2001. vol. 1996. Master s Thesis.pdf. ECDSA Optimization for ARM Processors for a NIST Curve Over GF(2m) .gov/reports/2005/CR2005-213578. An Interoperability Consideration in Selecting Domain Parameters for Elliptic Curve Cryptography .scitech. Vol.h tml. J. pdf. Vanstone. 2000. http://www. Eddy.ac. 2001. 461-481. 104-120.fizSznipsuzSzDipp azSzdi.certicom. http://www. 2000.com/smart/rd/publicatio ns/pdf/JT01nafe. [22] Pietilainen. 2000.uk/fft/cry pto/EccWhite3.iki.com/download/aid322/CIC_Markt& Technik_ECC. 3. http://islab.uk/fft/cry pto ECCFut. Elliptic Curve Cryptography on Smart Cards . and et al. ECC. John Wiley & Sons. et al . http://intro. M. Turan. Manning Publications. [18] Krasner. Elliptic Curve Cryptosystems on Reconfigurable Hardware .pdf. pp.72 [9] Tilahun Kiros and Kumudha Raimond Bauer. Oregon State University. 26. P. http://gltrs. B. Master s Thesis . http://citeseer. Rosing.scitech. Springer-Verlag. 2009 .C. Certicom ECC Challenge . Springer.nasa. Elliptic Curve Cryptography: The next generation of wireless security .pdf. Compact Encoding of NonAdjacent Forms with Applications to Elliptic Curve Cryptography . Balasubramaniam. pp. Johnson.pdf. 200-210.com/download/aid27/ECDSA. [10] [19] [11] [20] [12] [21] [13] [14] [23] [15] [16] [24] [17] Journal of EEA. Joye. Issue 1. http://www.certicom.grc. Helsinki University of Technology. Decrypted Secrets: Methods and Maxims of Cryptology . Worcester Polytechnic Institute. Tanik. 2004. 2001.crypto. 14-43.gemplus.pdf. 8-43. 1998.pdf. http://security.ac. D. 2000.edu/cache/papers/cs/25 616/http:zSzzSzwww.oregonstate. ECDSA Optimizations on an ARM Processor for a NIST Curve Over GF(p) . D..certicom. Schneier. Inc.pdf. E.com/download/aid111/cert_ecc_challenge. H. pp. and Source Code in C . Applied Cryptography: Protocols.susx. http://www. Master s Thesis. The Elliptic Curve Cryptosystem . Master s Thesis.pdf. Using Elliptic Curve Cryptography (ECC) for Enhanced Embedded Security http://www.pdf/blake00elliptic. B. TRANSACTION ON CRYPTOLOGY.pdf. Implementation Issues in Elliptic Curve Based Cryptosystem . 2006. limited reliability. [2]. the performance is comparatively low in average delay because of computational complexity. and only local communication with a modest number of neighbors.9% . On the one hand. and it determines the lifetime of WSNs. and communicate with each other over short distances. Wireless sensor networks present tradeoffs in system design. The proposed solution performs better in energy consumption. in January 2003. WSNs were identified by Business Week as one of the most important and impactive technologies for the 21st century. energy efficiency has always been a key issue for sensor networks as sensor nodes must rely on small. [3]. For this reason. In September 1999. WSN algorithms and routing protocols should be selected in a manner which fulfills these energy requirements. with a performance gain of Network Lifetime 45.ENERGY AWARE GPSR ROUTING PROTOCOL IN A WSN Sayed Nouh Egyptian Consultant. and communicate. INTRODUCTION Wireless sensor networks [1] have inspired tremendous researches of interest since the mid1990s. nonrenewable batteries. On the other hand. However. On the other hand. Wireless sensor networks (WSNs) are composed of sensor nodes that must cooperate in performing specific functions.78. Key Words: Energy aware routing protocol. beaconing protocol is used to enable sensors to know their neighbors positions on demand. These limitations make WSNs unrealistic to rely on careful placement or uniform arrangement of sensors. 26. where this radio information is used to compute ranges. The era of WSNs is highly anticipated in the near future. perform data processing. they are well suited to perform event detection. Advancement in wireless communication and micro electro-mechanical systems (MEMSs) have enabled the development of low-cost. The one with low radio signal strength is shortest to the destination and is selected to forward data. Rather than using globally accessible expensive global positioning system (GPS) to localize each sensor. Also. which is clearly an important application of wireless sensor networks. N3 N4 D X N1 N2 Figure 1 Beacon s working principle Journal of EEA. the MIT's Technology Review stated that WSNs are one of the top ten emerging technologies. multifunctional. low power. Egyptian Embassy and Zewdu Geta Department of Electrical and Computer Engineering Addis Ababa University ABSTRACT Energy is the scarce resource in wireless sensor networks (WSNs). GPSR routing protocol. 2009 . Geographical routing protocol. This paper presents a solution to increase the lifetime of WSNs by decreasing their energy consumption. each node is likely to have limited power. tiny sensor nodes that can sense the environment. The proposed solution is based on incorporating energy information into Greedy Perimeter Stateless Routing Protocol (GPSR). The operation of beaconing protocol is based on the measure of received radio signal strength. In particular. with the ability of nodes to sense. Wireless Sensor Networks. the low cost of the nodes facilitates massive scale and highly parallel computation. Vol. process data. network lifetime and packet delivery ratio.69%. D D X Y Figure 2 Greedy forwarding example. The proposed algorithm and its implementation is described in Section 5. First. 2009 . The possible advantage is a much simplified routing protocol with significantly smaller or even non existing routing tables as physical location carries implicit information to which neighbor to forward a packet to. [5]. almost all applications of sensor networks require the flow of sensed data from multiple sources to a particular base station. with their destinations locations. sink. Flat routing In flat networks. These neighbors in turn reply to node X. Such redundancy needs to be exploited by the routing protocols to improve energy and bandwidth utilization. the locally optimal choice of next hop is the neighbor geographically closest to the packet s destination. such as data fusion and data forwarding. processing. Sensor networks are strictly dependent on their applications. GREEDY PERIMETER STATELESS ROUTING (GPSR) Greedy Forwarding Rule: in GPSR. ROUTING PROTOCOLS IN WSNS Routing in WSNs is a very challenging task due to the inherent characteristics that distinguish these networks from other wireless networks like cellular or mobile ad hoc networks. suppose node X has a packet intended to send to node D. sensor nodes typically play the same role and collaborate together to perform the sensing task. Forwarding in this region follows successively closer geographic hops. For example. higher energy nodes can be used to process and send the information while low-energy nodes can be used in monitoring the interested area and gathering data. Y is X s closest neighbor to D. The location of nodes may be available directly from a GPS system or by implementing some localization protocol. X receives a packet destined for D. N3. (path X à N4)). As a result. The path with received low signal strength is selected. [5]. Here. node X sends Beaconing signal to its neighbors. Simulation set-up and performance metrics are presented in Section 6. until the destination is reached. and the design requirements of a sensor network change with the applications. while Section 8 concludes the paper. The rest of the paper is organized as follows: Section 2 presents the different routing protocols in WSNs. The lack of a global identification due to the large number of nodes present in the network and their random placement. due to the large number of sensor nodes and because getting the data is often more important than knowing the specific identity of the source sending it. and N4). X Journal of EEA. greedy choice in choosing a packet s next hop. [4]. a forwarding node can make a locally optimal. and the arc with radius equal to the distance between Y and D is shown as the dashed arc about D. Finally. by their originator. X s radio range is denoted by the dotted circle about X. and energy efficiency. in order to achieve system scalability. as shown in Fig. packets are marked. Vol. they require careful resource management. since data collected by many sensors in a WSN are typically based on common phenomena. Sensor nodes are constrained in terms of energy. 26. network lifetime increment. Specifically. thus. to forward packet towards destination D. position awareness of sensor nodes is important since data collection is normally based on their location. make it hard to select a specific set of sensors to be queried. An example of greedy next-hop choice appears in Figure 2. Traditional IP-based protocols may not be applied to WSN. typical of many specific wireless sensor network (WSN) applications. 1. This means the creation of clusters with the assigning of special tasks to cluster heads. Section 7 discusses the results obtained. Section 4 presents related work on energy-efficient routing.2 Sayed Nouh and Zewdu Geta Hierarchical routing In a hierarchical architecture. Greedy Perimeter Stateless Routing Protocol is explained in Section 3. [5]. N2. if a node knows its radio neighbors positions. they are often much correlated and contain a lot of redundancy. Furthermore. Furthermore. (N1. Geographical Routing Geographical Routing protocol exploits information about the location of the sensors in order to forward data through the network in an energy-efficient way. and storage capacities. as shown in Fig. Active. as the distance between Y and D is less than that between D and any of X s other neighbors. The first one aims at forwarding the packets towards the target region and the second step is concerned with disseminating the packet within the region. which is not scalable and all nodes are active even though only a part of the network is queried. ASCENT has four state transitions: Test. which works with the following network setting: · A vast field is covered by a large number of homogeneous sensor nodes which communicate with each other through short range radios. 3. and therefore an improvement that has not been implemented is to inform the routing protocol of ASCENT s state changes so that traffic could be re-routed in advance. The network area is divided into fixed zones to form a virtual grid. so we are going to consider the remaining energy of nodes. This may cause some packet loss. With high mobility of nodes there is a high packet loss as nodes may leave the gird without replacing an active node which is the disadvantage of GAF. significant overall energy savings can be achieved by turning off an appropriate subset of the nodes without losing connectivity or network capacity. Advantage of Greedy forwarding protocol is its reliance only on knowledge of the forwarding node s immediate neighbors. Vol. GAF uses equal areas of square zones. For more details about GPSR s advantage and limitations refer to [6]. [7. 26. Geographic adaptive fidelity (GAF) is an energyaware location-based routing algorithm. in wireless sensor network (WSN) energy is a scarce resource. whose size is dependent on the required transmitting power and the communication direction. the GEAR protocol has a limitation. ASCENT does not work for low density nodes and behaves differently for a different routing protocol which is the limitations of this work. To do this. It can be classified as a data-centric algorithm with geographic information knowledge. GAF exploits the equivalence of all nodes inside the same zone by keeping at least one node per zone awake for a certain period of time and turning all the others in that zone into sleep state during that time. [8]. ASCENT depends on the routing protocol to quickly re-route traffic. we can reduce energy wastage. Geographic and Energy Aware Routing (GEAR) exploits geographic information while propagating queries only to appropriate regions [9]. Passive and Sleep. As nodes in sleep mode uses least amount of energy. PROPOSED ALGORITHM AND ITS IMPLEMENTATION The GPSR routing protocol does consider only the shortest distance to the destination during path selection. 2009 . This greedy forwarding process repeats until the packet reaches D. Active nodes stay awake all the time and perform multihop packet routing while the rest of the nodes remain passive and periodically check if they should become active. 3 Figure 3 Virtual grid formations in a GAF Adaptive Self-Configuring sEnsor Networks Topologies (ASCENT) adaptively elects active nodes from all nodes in the network. However. [8]. Hence. RELATED WORK ON ENERGY-EFFICIENT ROUTING The current work on energy-efficient routing assumes that all the nodes in the network are always available to route all packets. 8] based on the notion of connected dominating sets that reduce energy consumption precisely by periodically putting some nodes into sleep mode. The state required is negligible and dependent on the density of nodes in the wireless network. Assumptions This section presents the basic design of the Proposed Protocol. However. The network uses Journal of EEA. · Each sensor node is assumed to be aware of its own geographic location. There has been much work on topology control algorithms. The process of forwarding a packet to all the nodes in the target region consists of two steps. not the total number of destinations in the network. Long range data delivery is accomplished by forwarding data across multiple hops. since nodes consume power even in idle mode.Energy Aware GPSR Routing Protocol in A WSN forwards the packet to Y. In reality. energy for transmission & receiving and by making nodes that are not participating in communication to go into sleep mode. · ECi is the consumed energy of node i. · Target (source) node moves randomly. The second one is considering remaining energy of nodes in addition to the shortest path during path selection. the distance from a source node to the destination and the remaining energy level of neighbor nodes. Each sensor node has constrained battery energy. The proposed solution consists of two-step-solution. The active node consumes more amount of energy while idle node consumes lesser and sleep node consumes the least amount of energy. Minimum weight function contains two factors. Sour Sleeping Erfi Where · Eoi is the initial energy of node i. The minimum weight function Wi. Hence a good power saving algorithm should make the active number of nodes as little as possible [7]. Then in wireless sensor network (WSN) there are 3 states of a Node: · Active. 2009 . so that a packet (a data) reaching to a destination is in question. as shown in Figure 4.4 Sayed Nouh and Zewdu Geta beaconing algorithm localization method to estimate the locations of the individual nodes. Sleep and Idle. 26. In this section we will formally de ne how to calculate the value of minimum weight function and using this weight to evaluate the proposed protocol. the timer is reset and all the nodes in a grid are set to active mode. [10]. During a communication cycle. All other nodes will be in active mode and will participate in sending and receiving a packet. of neighbor node x(i) is defined as follows: Wi Where · Wi is the minimum weight value among the N neighbors of a source node · x(i) is the position of the ith neighbor node of a source node · d(x(i). At the end of the communication cycle. Step I If nodes are farther away from a sink node than source node. Proposed solution GPSR routing protocol uses Greedy Forwarding to route data to neighboring nodes which does not consider either remaining energy of nodes or the transmission energy. Acti Sin Figure 4 Proposed scheme Journal of EEA. we set a timer. they will enter Sleep mode to save energy and will stay till next communication. · After having been deployed. The first step is concerned with making nodes which are not participating in either sending or receiving to go into sleep mode. sensor and sink nodes remain stationary at their initial locations. Vol. Step II: Minimum weight function calculation Minimum weight function is an important key to make the routing decision by a source node to a destination.y) is the Eculidean distance between the ith neighbor node and the destination y · Erfi is the remaining energy factor Sens · The wireless communication channels are bidirectional. SIMULATION SETUP AND PERFORMANCE METRICS The proposed algorithm is implemented by J-Sim simulation.t). Vol. set node i into Sleep mode. 2009 . 5 represents the two step solution. Node=Source Is Y Mode = Minimum Weight Node=Source ? N Is a node has Neighbors Y N Mode=Perimeter Minimum Weight Forwarding Have left Max? Y N Apply Right Hand Rule for Perimeter forwarding N Is Node= Destination? Y Reset Time r.t) . Whereas our proposed algorithm uses Minimum Weight forwarding (shortest distance plus residual energy) instead of Greedy forwarding and Perimeter forwarding to come out of no neighbor problem until it reaches a destination. i . node i will go into sleep mode otherwise it will be active. T=0 END Figure 5 Flow chart The flow chart in Fig. where it first sets a timer to make nodes either sleep or active by calculating distance d (i.Energy Aware GPSR Routing Protocol in A WSN Start 5 Set Wakeup Timer T=1 Calculate d (i.t). If d (i. s) and d (i. · d(i. If the forwarding node is a destination.t) is the Euclidean distance of each node I to a Target (source) node t.s) >d(i. 26. t). As J-Sim have the following features: Journal of EEA. The original GPSR routing protocol uses Greedy forwarding when there is a neighbor node and Perimeter forwarding when the source node has no neighbor or when its neighbor s distance is shorter than itself to a destination.s) and d(i.s) is the Euclidean distance of each node i to a Sink node s and · d(i.s) > d(i. If d (i. wakeup timer (T) will be reset and all nodes become active and this process is repeated again. 36mW 0. · Node density.6 Sayed Nouh and Zewdu Geta Performance metrics Although different researchers propose different performance metrics to evaluate the performance of routing protocols. In our simulation up to 450 sensors are scattered over to a 350 × 350 m2 sensor eld. Average Energy Consumption: The average energy consumption is calculated across the entire topology. makes J-Sim a truly platform-independent and reusable environment. · Average Delay: It is defined as the average time difference between the moments of data packets received by the Sink node and the moments of data packets transmitted by the Source node.g. Then · As it is implemented in Java. · Only the public classes/methods/fields in Java can be accessed in the Tcl environment instead of exporting explicitly all classes/methods/fields like other simulators. It measures the average difference between the initial level of energy and the final level of energy that is left in each node. 26. Simulation setup To explore the results. ns-2. · It is a dual-language simulation environment like ns-2 in which classes are written in Java and scripts using Tcl/Java (Jacl). The simulation is done on different performance metrics. target (source) speed may represent a moving tank. It can also be the time for all nodes in the network to die. This metric defines the freshness of data packet.88mW 12. and percentage of number of node failures are varied during simulation. The implementation has the following assumptions: · The sensor nodes are deployed in a random manner. 2009 . In wireless sensor networks (WSN). The lifetime of the network under a given flow can be the time until the first battery drains-out (died) [12] Journal of EEA. Vol. the network is partitioning too. · J-Sim exhibits good scalability for the memory allocation to carry out simulation of length 1000 is at least two orders of magnitude lower than that in ns-2 [11].50mW 12. most of which are taken from white papers of commercial products vendors. When the number of dead nodes increases. the death of the first node seldom leads to the total failure of the network. e. to compare the performance of the proposed algorithm against the original GPSR routing protocol. N: number of packets · Network Lifetime (NL): This is one of the most important metrics to evaluate the energy efficiency of the routing protocols with respect to network partition. we conduct a detailed simulation using a J-Sim simulator.016mW Average Data Delivery Ratio: This represents the ratio between the number of data packets that are sent by the source and the number of data packets that are received by the sink. especially in those with densely distributed nodes. we use the following metrics for evaluating the efficiency of the proposed routing protocol. Table 1: Simulation parameters Variables Communication Rage Simulation Time Simulation Area Target node Speed Number of Nodes Node receiving power Node transmit Power Node Idle mode power Node Sleep mode power Values 15 m 200sec 350 x350 m2 10 m/s and 15m/s 450 14. Network Lifetime can be defined in the following ways It may be defined as the time taken for K% of the nodes in a network to die. Let Ei and Ef are the initial energy and final energy level of a node respectively and N is total number of nodes in the network. Other simulation parameters are listed in Table 1. 2009 .Energy Aware GPSR Routing Protocol in A WSN We adopt the third definition for the analysis of this work. SIMULATION RESULTS AND DISCUSSIONS We deploy the nodes in a region of size 350 x350 m2. Figures 6. 7 and 9. The number of nodes in the region is controlled by increasing nodes from 50 to 450 with step of 100. There are one sink node. Scenario-1: This Scenario follows parameters shown in Table 2. Vol. We consider two scenario designs. Table 2: Scenario 1 parameters Variables Target Speed Number of Nodes Sink Location Target Location Sensor Location Random Node Failure Scenario-1 Results: Values 10 m/s 450 (350. As the aim of our interest is to increase the lifetime of the network.5 seconds and sensing radius is 15m. Speed 10m/s) Figure 8 Average Delay (no Node Failure. Speed 10m/s) Journal of EEA. show that the proposed solution performs better in energy consumption and packet delivery ratio than the original GPSR protocol and hence the Network Lifetime is improved significantly.0) (150. Sensor nodes are deployed randomly. sink node is fixed at the lower right corner of the grid and Target (Source) node deployed at the center of grid and moves with a speed of 10 m/s. a node with less than 20% of its full battery capacity is considered as a dead node based on the definition in [2]. Speed 10m/s) Figure 9 Network Lifetime (no Node Failure. simulation time and node failures. the goal is achieved by considering residual energy in the proposed solution which reduces individual node failure and network Figure 6 Average Energy Consumption (no Node Failure. one target node and 450 sensor nodes in our simulation environment. All the experiments are conducted on a dual processor Intel 2. Speed 10m/s) Scenario-1: Discussion of Results Scenario 1 results. Each data point reported below is an average of 20 simulation runs. The simulation time is 200 seconds and the parameters are affected by the number of nodes used in the simulation. [13].66 GHz machine running Windows XP Professional with 2 GB RAM. Each target node generates stimuli every 1.150) and moves Randomized and stay static With no Failure 7 Figure 7 Average Packet Delivery Ratio (no Node Failure. 26. Here. Moreover. Table 3: Scenario 2 parameters Variables Target Speed Number of Nodes Sink Location Target Location Sensor Location Random Node Failure Scenario-2 Results: Values 15 m/s 450 ( 350. Speed 15m/s) Figure 13 Average Delay (15% Node Failure. making nodes which are not participating in transmission or receiving into sleep mode reduces overall node failures. As Fig. In scenario 2 as compared with scenario 1. Figs. and 12 show that the proposed solution performs better in energy consumption and packet delivery ratio than the original GPSR protocol and hence there is an improvement in Network Lifetime. i. 13 shows. The proposed algorithm uses a number of parameters to select a route than the original GPSR protocol.150) and moves Randomized and stay static 15% Failure Figure 11 Average Packet Delivery Ratio (15% Node Failure. This is because in scenario 2. Scenario-2: This Scenario follows parameters shown in Table 3. the average delay is low too. Speed 15m/s) Scenario-2: Discussion of Results Figure 10 Average Energy Consumption (15% Node Failure. the average energy consumption.e.8 Sayed Nouh and Zewdu Geta partition. 26. Speed 15m/s) Figure 12 Network Lifetime (15% Node Failure. Hence the number of node failure and energy wastage decreases. 2009 .0) (150. Vol. average packet delivery ratio and Network Life time is comparatively low. Speed 15m/s) The same is true for this scenario. the lifetime of the network increases. 11. The cause of the delay is due to computational complexity. Journal of EEA. Whereas Figure 8 shows that the average delay of the proposed solution is larger as compared to the original GPSR protocol because the proposed solution checks not only the shortest distance but also the residual energy and distance calculation to make nodes either in sleep or in active mode. 10. Adaptive Topology Control for Ad-hoc Sensor Networks: By Ya Xu.jsim. in to sleep mode. if not. [7] [5] 9 Protocols and Architectures in Wireless Sensor Networks: John Willey & Sons. Li. NJ: Prentice Hall. J. Further. 2005. Proceedings of MOBICOM. simulation software. CONCLUSIONS In this paper. [14] Metrics in Wireless Networks. 2005. Ltd. Estrin D. [2] [3] [4] Journal of EEA. April 2005. Department of Computer science and Electrical engineering University of Maryland. It considers only distance during packet routing. Inc. 2003. Rappaport. SPAN: An Energy-Efficient Coordination Algorithm for Topology Maintenance in Ad Hoc Wireless Networks: By Zhimin He. Switzerland. there is more energy consumption. Publication. Baltimore County. http://www. Localization in Sensor Networks. Jennifer C. 194 205. we compare the proposed solution with the original GPSR routing protocol using J-sim.9% to 78. July 2001. Wireless Communications: Principles and Practice: Upper Saddle River.e. Holger Karl and Andreas Willig.org/comparision. June 2002. we have studied GPSR routing protocol. Vol. Wei-Peng Chen. 2003. 2001. July 2001. which is a geographical routing protocol and uses a greedy forwarding whenever possible and perimeter forwarding. less number of nodes will be available for routing i. and Govindan R. and Sensor Networks: A John Wiley & Sons. due to node failure. Wireless Sensor Network Designs: John Wiley & Sons Ltd. [13] J-Sim: A Simulation and Emulation Environment for Wireless Sensor Networks. Anna Hac. A. (access date April 2... and Deborah E. the proposed solution increases the average delay due to high computational complexity.html (access date April 23. Lausanne. which are not participating in sending or receiving packets. REFERENCES [1] Mobile. Lu-Chuan Kung. there is a performance gained in average energy consumption. 2009 . ACM MOBIHOC. 26. T.Energy Aware GPSR Routing Protocol in A WSN target speed is more which incur routing over-head. [11] Comparing ns-2 with j-sim. Hou.jsim. http://www. GEAR: A Recursive Data Dissemination Protocol for Wireless Sensor Networks: by Yu Y. Ning Li.69%. In order to increase the lifetime of a network. R. we added energy information and making nodes. Aslam and D. 2009). Hung-Ying Tyan. A. Hyuk Lim. Massachusetts Institute of Technology. pp..Ananda. The simulation output indicates that. Jonathan Bachrach and Christopher Taylor.org/. 2006. Oct 1st. 2005. [12] Online Power-aware Routing in Wireless AdHoc Networks: Q. Wireless. John H. Rus. and Honghai Zhang. However. by Ahmed Sobeih. A Survey on Routing Protocols for Wireless Sensor Networks: Kemal Akkaya and Mohamed Younis. [6] [8] [9] [10] Modeling the Lifetime of Wireless Sensor Networks: Kewei sha and Weisong shi. To show the performance gained. Jacobson.Shorey. UCLA Computer Science Department Technical Report. 1996. 2009). average packet delivery ratio and network lifetime from 45. The ability to travel allows a Mobile Agent to move to a system that contains the object with which the agent wants to interact and then take advantage of being in the same host or network as the object. draws a conclusion. Denial of Service. Mobile Agent Systems can be roughly divided based on the programming language by which they are developed and use: Java and non Java based (using languages like C/C++ and scripting languages like Tc1/Tk).THREATS AND TRUSTED COUNTERMEASURES USING A SECURITY PROTOCOL IN THE AGENT SPACE Sayed Nouh Egyptian Consultant. an agent could attack another agent and a platform could launch an attack against its visiting agents. it has not been translated into a significant number of real-world applications due to a new dimensionality of security problem it brings along with it. An agent could attack a platform. The threats are identified and a modified mobile computing model is proposed to prevent some of the threats. Mobile Agents are promising paradigms for the design and implementation of distributed applications [1]. which can autonomously migrate between various nodes of a network and perform computation on behalf of a user [1]. Around 80% of Mobile Agent systems available today are built using Java. It has a unique ability to transport itself from one system in a network to another. Some researchers even claim that it is impossible to solve. But the last kind of attack. In section 2 the threats of hostile hosts towards a visiting agent is identified and some of the available countermeasures to those threats are presented. Malicious host problem. Keywords: Agents. The agent along with the Mobile Agent platform is called Mobile Agent System (MAS). In section 3 the proposed system design is explained. Hostile host threats These types of threats represent a class of threat. that has generated considerable excitement in the research community. These attacks are most difficult to be detected and prevented. section 5. Vol. Mobile Agents. Despite that. due to its inherent support to Mobile Agent programming. Aglets. 26. Mobile Agent technology is not entirely based on Mobile Agents only. Eavesdropping and Alteration of carried result. Section 4 presents the capability and performance of the proposition using a prototype developed and the last section. where the host compromises the agent. Trusted nodes. A prototype that realizes the concept is implemented using IBM s Mobile Agent platform. since the host has a full control of the agent s code and data. The first two attacks have their counter part in the traditional client server environment. there is another complementary component called Mobile Agent platform. is the most difficult of all attacks to solve. In this paper familiarization to Mobile Agent technology and threat of hostile host towards a visiting agent is given due diligence: Malicious host problem. SECURITY IN THE AGENT SPACE The security issues of MAS are of multidimensional. It provides appropriate execution environment and services to the Mobile Agents. INTRODUCTION A Mobile Agent can be thought of as a program. a platform launches an attack against its visiting agent. The hostile actions include: Masquerading. In this paper we will be looking into this attack (Malicious Host Problem). 2009 . The rest of the paper is organized as follows. Masquerading: An agent platform can masquerade as another agent platform in an attempt to deceive the Mobile Agent as to its true Journal of EEA. Egyptian Embassy and Tinbit Admassu Department of Electrical and Computer Engineering ABSTRACT Mobile Agent computing is a paradigm of distributed computing. while still creating a semantically equivalent version of a program. however. if any. The problem has more to do with the capability of a visiting agent to correctly identify and authenticate its executing host. it exposes its code. creating a safe heaven within hosts in the agent space. Denial of Service: When an agent arrives at an agent platform. may ignore agent s service requests. but the processor will not understand the program s function [4]. a number of countermeasures for malicious behavior of hosts towards a visiting agent have been proposed. by making it believe that all other shops have quoted a higher price. A mechanism that ensures the integrity of the agent needs to be in place [5]. Agents. In this scenario. Generally. Code Obfuscation: Code obfuscation is suggested by Hohl [2]. some of them are applicable. Alternation: Alteration threatens the integrity of the agent as a whole. It eliminates the deployment of the specialized hardware. the masquerading platform can harm both the visiting Agent and other Agent platforms [3. but still it is trusted that it neither has malicious behavior nor collaborate with other hostile hosts that perform some evil action on the agent. is the one in which the Mobile Agent simply need to trust its entertaining host . Accordingly. The threat of eavesdropping. Eavesdropping: The classical eavesdropping threat involves the interception and monitoring of secret communications. can be tricked by a malicious masquerading platform. introduce unacceptable delays for critical task or even terminate the agent without notification. Trusted Execution Environment: This method is a variation of the above method. which are waiting for a result from a non-responsive agent on malicious platform must be careful to avoid becoming deadlocked. kind of trust. It has been suggested by Sander and Tshudlin and tries to ensure the computation privacy of the agent in the untrusted host. secure tamper detecting and responding hardware to conventional computing systems. PROPOSED SYSTEM DESIGN The proposed countermeasure is based on trust. destination. based on policy enforcement or based on control and punishment. the countermeasures Journal of EEA. An agent can also become live locked if a malicious platform or programming error creates a situation in which some critical stage of the agent s task is unable to finish because more work is continuously created for it to do. The idea is to make the program behave like a black box [6]. Instead. Generally a trust that a Mobile Agent has on a particular host can be blind folded. is further exacerbated in Mobile Agent systems because the agent platform can not only monitor communications. 2009 . Vol. Trusted Hardware: This countermeasure tries to enforce the notion of trust between an agent and a host by physically adding. 26. while others have only of a theoretical significance. state and data to the platform. According to this proposition. but is continuously given task to perform and can never catch up or achieve its goal [3]. the host can do whatever it wants while giving services to the Mobile Agent. The resulting program will consist of instructions that a processor understands. A malicious platform. It protects the visiting agent from any possible attack that could be launched by the entertaining host [6]. it expects the platform to execute the agent s request faithfully and provide a fair allocation of resources. all the data it brings to the platform. The hardware encapsulates the entire environment in which the agent executes. functions will be encrypted such that their transformation can again be implemented as programs. and all the subsequent data generated on the platform [3. Countermeasures for malicious host threats Over years. 4]. Agent live lock differs from agent deadlock in that the live locked agent is not blocked or waiting for anything. a Mobile Agent entrusted with the task of finding the lowest price of a commodity by visiting various virtual shops. an algorithm called obfuscating algorithm will be used to mess up the code. A blind folded. but also can monitor every instruction executed by the agent. As an example. however. As already discussed earlier when an agent arrives at a given host. according to this method a set of trusted nodes needs to be setup in the agent space prior to any agent to host interactions [1]. Computing with Encrypted Functions: This method prohibits the executing host from learning anything substantial about the agent. while it is actually on it.5]. Thus.54 Sayed Nouh and Tinbit Admassu provide either detection or prevention mechanism to the visiting agent. Before we move on to describe the proposed countermeasure. No pre negotiation with hosts. These keys are used by the security protocol to protect the confidentiality and the integrity of parts of the Mobile Agent. In this setup it is mandatory that the home or owner of the Mobile Agent has a public-private key pair at its disposal. Vol. with a number of additional elements. in which the proposed countermeasure is taken into account. Although there is no contract signed it is not a blind folded trust as in the first case. Host#2 mobile agent mobile agent Host#1 mobile agent mobile agent CA Host#3 Home mobile agent Trusted Server m il ob ea ge nt mobile agent t Host#4 Host#n mobile agent mobile agent mob en ile ag Host#5 Figure 1 Proposed mobile computing model Journal of EEA. The proposed countermeasure uses a combination of the above two kinds of trusts. the Mobile Agent and the host have a prior contractual relationship in the form of policy. Mobile Agents are subjected to such kind of attacks because they are a lonely figure once sent to the agent space. Abstraction of the modification. Such kind of trust should work fine as long as the signing parties conform to their rights and obligations. Hence the proposition modifies the computing model of the mobile computation in order to address hostile host threats. Design guidelines The following points are used as guidelines when the proposition is being developed: · · · · Convenience to the owner of the agent. so that the Mobile Agent could retrieve this key while it is visiting hosts. Figure 1 shows an overview of the mobile computing model. based on to which nodes. 2009 . 26. in the computer network. The last kind of trust is based on control and punishment. But it still uses control mechanism to punish the host if found guilty of misbehaviors. 55 The proposed countermeasure A closer look and evaluation of the various kinds of attacks launched by hostile hosts reveals that. In this case. the next section outlines the guidelines used to develop the countermeasure. The second kind of trust is based on policy enforcement. Here no prior policy needs to be signed between the two parties. using a Security Protocol. Ease of access of information gathered.Threats and Trusted Countermeasures. the public key is published to the world. Much like the case of trusted third parties a node is setup in the agent space to provide a different task to the Mobile Agent. the Mobile Agent is interacting: based on policy enforcement and based on control and punishment. The trust assumes that hosts are not by nature malicious and give them a chance to behave accordingly. (ii) Mobile Agent (MA). Each of these components are listed and defined as follow: (i) Home of the Mobile Agent. Journal of EEA. as web servers do not modify the web page they host. likewise in the proposed countermeasure at the center of each region there is a trusted server. Home of the Mobile Agent (Home): It is the computer running Mobile Agent platform and has sent the Mobile Agent to carry out a task on its behalf. If we look around a number of servers deployed in an internet work. within each region a node called trusted server is setup. At the end of its mission the Mobile Agent returns back to the trusted node and asks the corresponding ASE to hand it over the results it has been accumulating so far. The ETC has the obligation not to modify the content of our page without our permission. have to be agreed on terms of use. More specifically by the huge set of nodes that are set up to be visited by the Mobile Agent. creates its own ASE at the trusted node and uses it to store the partial information it retrieves from each hosts. These servers provide various services to the Mobile Agent while the agent is in the agent space. Let us take on the web servers as an example to highlight the similarity as well as the feasibility of the proposition. here also terms of use could be signed between the user of the Mobile Agent (home node) and the trusted server in the agent space in a form of policy enforcement. the ETC and the one who wants to get hosting service. (iii) Trusted Node (TS). when our page is being viewed by all around the world. The ETC once agreed on to host our page. creates a temporary storage element called active storage element (ASE). Unlike the original model of a unified agent space. The Mobile Agent supported by these third parties trusted nodes as well as the security protocol discussed later on should be able to avert some of the evil acts from hostile hosts. In either case all that is needed from our side is to pay the price. Hence trusted servers will not modify the Mobile Agent s content. It can also be defined as a computer As it can be seen from the Fig. In section to follow. hence the ETC should display our page as it is. In case of mobile communication systems. Web servers. These days we can develop our own web page and upload it to a web server for free. it is assumed that the agent space is divided into regions. Vol. carry back the result to its home as if it has been doing the job alone. The nodes and the trusted servers could be set up. mail servers and root Domain Name Services (DNS) servers are some to mention. the Mobile Agent first goes to the trusted node. (iv) Active Storage Element (ASE) and (v) Host. More specifically. Take Ethiopian Telecommunication Corporation (ETC). the arrows dictate that. by the Mobile Agent user community. It is such a similar concept that the proposition wants to exploit. sends the information it has retrieved from the corresponding host to be stored temporarily at ASE. 26. Let us take this argument a step further as it might seem less convincing in case of freely web hosting services. it provides web hosting service with the amount of fee to be paid depending on the size of file we want to upload as well as other features our page requests from their web server. Components of the proposed countermeasure Figure 1 depicting the overall view of the proposal shows that the countermeasure constitutes various components at various degree of multiplicity. at the center of each cell there is a transmitter and receiver. The trusted node accepts the information and stores it. 1. the proposal modifies the way by which the mobile computation is done. they all or at least at some point in their operation provide synonym. in a similar style as nodes of root Web servers. then moves to the first host to be visited. This has a strong implication on the feasibility of a trusted server set up in the agent space by a third party which could provide a processing service to the Mobile Agent without altering the data or code of the Mobile Agent. The concept of introducing a trusted server setup in a network handled by a third party is not new at all. It goes there. 2009 . Each Mobile Agent that has a trust relationship with this node does the same. The division of the agent space into regions is analogous to the cells in the mobile communication systems.56 Sayed Nouh and Tinbit Admassu Indeed the two parties. it provides all the necessary computational resources. Much like the terms of use signed between the above two parties. we will take a look at the main components of the proposal and how should the components interact according to the security protocol. But here the security protocol provides further protection to the Mobile Agent content at the trusted server. Host: It is a computer in the agent space running Mobile Agent platform and entertains any visiting Mobile Agent which would like to gather information from it. as any malicious host could not counterfeit the digitally signed destination object. This component is at the center of the controversy. The ABA accepts the list and forms a destination object. So the Mobile Agent avoids the possibility that it would be directed to visit other hosts by altering the list of paths it has carried from its home. as pointed out in the previous section it goes first to the Trusted Node. The security protocol also develops a mechanism that lets the user of the Mobile Agent to digitally sign the list of destinations it wants the Mobile Agent to visit. The application as a part of its mission packs a task into the Mobile Agent and sends it to the agent space. The security protocol alters what the Mobile Agent constitutes depending on where it is. It actively participates in the process of temporary information storage and handing over of all the information to the Mobile Agent. the MA verifies that it has the right unsigned destination object from which the address of the next node to be visited is determined and dispatches itself to that node. The host provides all the necessary resources for the agent to execute there. which could be hostile. but differs in the function it provides. It is there to provide support and service to the Mobile Agent while it is in the agent space. Trusted Nodes and Active Storage Element) should interact with each other as well as what are the needed tasks to be performed at each level. Active Storage Element: It is a temporary storage element that is created by each Mobile Agent. The ABA digitally signs the destination object and passes it to the MA which is programmed to perform the required task and The MA accepts the signed object. It is assumed that. at the trusted server. to give hostile hosts no chance of disclosure of information collected from previous hosts. The destination object includes the list of hosts to be visited. the address of the trusted server (TS) and the home. it digitally signs the destination object using its private key. Security protocol A security protocol that defines how the basic components of the system (Home. Trusted Node: It is similar in composition to the home of the Mobile Agent.The public key could be retrieved by the hosts from relevant authorities. After forming a destination object which contains the list of all hosts the Mobile Agent is going to visit. While the Mobile Agent is transiting between its home and trusted nodes the usual composition is deemed. Ø Ø Journal of EEA. using a Security Protocol. the home node has a public-private key pair (HPubKHPrvK). By using HPubK. 2009 . is developed. running a Mobile Agent based distributed application. step by step. Mobile Agent: As defined throughout this paper. it is a program that migrates from one node to another node in a computer network to accomplish a task given to it by its owner. The Mobile Agent after completing its task will eventually return to the home carrying the result. that is sent to visit nodes in the agent space. the security protocol in action and its effects on the components of the Mobile Agent system. At Home. then the destination object is passed down to the Mobile Agent. But when the agent is in the agent space visiting Ø 57 different nodes it has assumed to be composed of only the two out of the three components that is usually associated with: code and state. 26.Threats and Trusted Countermeasures. so as the whole system could stand against the possible hostile host threats. Vol. as shown in Fig. 2: Ø The user of the MA specifies the address of the list of hosts it wants to be visited using the Agent Based Application (ABA). The Mobile Agent upon its arrival at each and every host in the agent space verifies that it has a valid copy of the destination object before putting that object into use. Let us see. Trusted Server (TS) HPubK Ø Using this key. The MA passes down the necessary information to the ASE so it can effectively communicate with it.58 Home Sayed Nouh and Tinbit Admassu HPrvK MA HPubK MA TS Address TS Address Host #1 Address Host #2 Address MA Host #1 Address Host #2 Address Host #1 Address Host #2 Address Signed Host #n Address Address of nodes to be visited entered by the user Host #n Address TS Address Home Address Destination object formed from the addresses entered Host #n Address TS Address Home Address Destination object signed using HPrvK Signed Signed The MA goes to TS Signed Destination object passed to the MA Unsigning the Destination object using HPubK to get the next node to be visited Ø Figure 2 Security protocol at home At Trusted Server (TS). Vol. 2009 . the MA unsigns the digitally signed destination object and determines the next node to be visited. In this case it is the first host in the list and The MA Dispatches itself to that node. HPubK. creates its own Active Storage Element (ASE). The MA retrieves the public key of the home. 26. as shown in Fig. 3: Ø Ø The MA arrives at the TS. Ø Ø MA MA MA Signed Signed Signed The MA arrived from Home The MA goes to the first host ASE created by the MA to store information temporarily Important variables passed to ASE Unsigning the Destination object using HPubK to get the next node to be visited ASE ASE Figure 3 Security protocol at TS Journal of EEA. Encrypts the randomly generated symmetric key using the public key. it looks for the address of the next node to be visited. in its last leg of journey. SymK_i(Info_i).Threats and Trusted Countermeasures. Else if it is a trusted server. At ith host. Asks the host about the information it wants. 5: Ø Ø The MA arrives at the TS. as show in Fig. Ø 59 If the next node is another host it does the same task as indicated above. 4: Ø Ø Ø Ø Ø Ø Ø The MA arrives at the ith host. At Trusted Server. HPubK(SymK_i) and SymK_i(Info_i). SymK_i. as shown in Fig. Journal of EEA. HPubK. Host_i. to its ASE at the TS to be stored temporarily. It generates a random symmetric key. The MA retrieves the public key of the home. 2009 . Encrypts the information using the symmetric. In this case for sure it is the home node and The MA dispatches itself to its home. SymK_i and retireves the HPubK Unsigning the Destination object using HPubK to get the next node to be visited Sym K_i(Info_i) The M A retrieves the info it w anted and encrypts it using Sym K_i HPubK(SymK_i) SymK_i(Info_i) The M A encrypts SymK_i using HPubK and send these inform ation to ASE To TS Figure 4 Security protocol at the ith host. and takes these information. Info_i. Asks the corresponding ASE to hand it the overall information it has been accumulating so far (a pair of HPubK(SymK_i) and SymK_i(Info_i) retrieved from each host). After unsigning its destination object. using a Security Protocol. looks the address of the next node to be visited and dispatches itself to that node. the following set of actions follows. Vol. Sends both of these information. Ø Ø Host_i HPubK Info_i MA MA MA MA Signed Signed Signed Sig ne d The M A arrived from TS The M A goes to the node SymK_i SymK_i G enerates randomly sym metric key . HPubK(SymK_i). 26. The MA unsigns its destination object. the ABA does the following: MA HPubK(SymK_i) Signed HPubK(SymK_i) HPubK(SymK_i) SymK_i(Info_i) SymK_i(Info_i) SymK_i(Info_i) SymK_i(Info_i) SymK_i SymK_i SymK_i SymK_i SymK_i(Info_i) SymK_i(Info_i) SymK_i(Info_i) SymK_i(Info_i) Info_i Info_i Info_i Info_i The MA arrived from TS HPubK( SymK_i) HPubK( SymK_i) HPubK( SymK_i) HPubK( SymK_i) SymK_i( Info_i) SymK_i( Info_i) SymK_i( Info_i) SymK_i( Info_i) HPubK(SymK_i) The Home retrives the HPubK and decrypts the SymK_i The Home using each of the retrieved SymK_i decrypts the corresponding info_i The MA hands over the total info accumulated so far to Home and disposes itself then after MA Figure 6 Security protocol back at home Journal of EEA.60 Sayed Nouh and Tinbit Admassu Trusted S erver (TS ) H P ub K MA MA MA S ig n ed S ig n ed Sig ned The M A arrived from the l ast h ost HP ubK( S ym K _i) HP ubK( S ym K _i) HP ubK( S ym K _i) HP ubK( S ym K _i) Sym K _i( Info_i) Sym K _i( Info_i) Sym K _i( Info_i) Sym K _i( Info_i) HP ubK ( S ymK _i) HP ubK ( S ymK _i) HP ubK ( S ymK _i) HP ubK ( S ymK _i) S ym K_i( SInfo_i) ym K_i( SInfo_i) ym K_i( SInfo_i) ym K_i( Info_i) The M A returns back to ho m e The M A asks the AS E to handover th e total info accum ulated so far AS E gives to the M A the info Unsigni ng the D estin ation ob ject usin g HP ubK to get the next no de to be visited AS E H P ub K (S ym K_i) H P ub K (S ym K_i) H P ub K (S ym K_i) H P ub K (S ym K_i) S ym K_i(In fo _i) S ym K_i(In fo _i) S ym K_i(In fo _i) S ym K_i(In fo _i) AS E Figure 5 Security protocol back at TS At Home. The MA contains a pair of encrypted information. Vol. as shown in Fig. 6: Ø Ø The MA arrives back at home after doing the task assigned to it. 26. 2009 . Home HPrvK Ø Ø The MA hands the overall information to the ABA. For each pair of encrypted information retrieved from each host. Note that they are all in encrypted form. the following techniques and equipments are used: Two personal computers with 768MB and 512MB of RAM respectively. Vol.2:8001 Host#2 20. Computer A takes up the position of trusted server (TS) and computer B runs many host nodes simulated through various port numbers as well as the home node. SymK_i (Info_i). 2009 .1:8000 Computer B Home 20. 26. Proposed Mobile Agent: Proposed MA A Mobile Agent which is governed by the security protocol and hence performs mobile computation as pointed out in Section 4. a test environment is set up using the above mentioned computers as shown in Fig. Normal MA and DS MA) are given a similar task to carry out. RESULTS AND PERFORMANCE COMPARISON To access the capability and the cost of the proposed countermeasure.0. Normal Mobile Agent: Normal MA A Mobile Agent that performs mobile computation in the usual way. Decryption at home node and Displaying the plain text result to the user. which run Windows Server 2003 and a number of Mobile Agents (Proposed MA. SymK_i. N information retrieved will be encrypted by the corresponding N symmetric keys.0. HPubK (SymK_i) .0. Digitally Signed Mobile Agent: DSMA 61 A Mobile Agent that supports digital signing of the destination object while still performing computation in a way discussed in Section 3. The Fig. 8 shows analysis of the packet captured while the Normal MA and DS MA are in operation. This packet analyzer software is made to sniff into packets exchanged between the two computers as the various types of MA s do their job. DS MA and Normal MA) as described below. The N symmetric keys will be encrypted by the public key (RSA) of the home.2:4434 Host#1 20. Ethereal Network Packet Analyzer software is run on computer A.0. using a Security Protocol.0. Results: To measure the capability of the proposal towards eavesdropping threat.0.2:8002 Host#3 20. using its private key (HPrvK) to decrypt the encrypted symmetric key. Each of the above Mobile Agents (Proposed MA. using the decrypted symmetric key. Computer A TS 20. N symmetric random keys generated at each host. are used.Threats and Trusted Countermeasures.0. it decrypts the information which is encrypted using the same key.2:8003 Host#4 20. One ASE created at TS. Ø The ABA does the same process for each pair of information retrieved from every host the agent goes to collect information and At last the ABA displays the result to the user.0. Ø Security Protocol Summary: · For N hosts: o o o o o o o o N hosts addresses digitally signed by the home node.0. The encrypted N information and encrypted keys stored at the ASE. It is open source freely available packet analyzer software that can capture and store packets from a live network for further processing.0.0.2:8004 *** Figure 7 Test environment set up Journal of EEA. o First. Info_i.0. 7.4. o Second. Hence the security protocol provides the required confidentiality of the information while it is being stored at ASE. a similar test environment as in the above case is used. 26. it is planned to supply a wrong public key to the MA as the MA arrives there and is in the process of unsigning its digitally signed destination object. OS Version: 5. Each of the above Mobile Agents (Proposed MA. Specifically. This node is planned to behave maliciously towards the Proposed MA. Figure 9 shows analysis of the captured packet while the Proposed MA is in operation. As it can be seen from Fig. Normal and DS). Normal MA and DS MA) are given a similar task to carry out. 2009 . Hence any attempt of alteration of destination object will be detected by the MA. Journal of EEA. Vol. Computer B. This substantial amount of time is a price to pay to achieve the corresponding security. it is not possible to look into its content. not by a private key which corresponds to the public key supplied by the hostile node. But fortunately the MA cannot unsign the signed object using the public Figure 9 Captured packet analysis for Proposed MA Performance comparison: Performance Comparison: To measure the cost of the proposal. unlike the above case since the information is sent to the TS in encrypted form. To test the capability of the proposed countermeasure. This performance parameter is the average time in milliseconds (ms) each Mobile Agent requires to do the job. Figure 8 Captured packet analysis for DS MA and normal MA. except that all of the nodes are simulated in computer. Their performance is compared in terms of their average turn around time.2 seen at the bottom right corner of the window. A hostile node is introduced on a different port number in the same computer. Comparing the execution time of the Normal MA with the Proposed MA. towards Alteration threat. Generation of the keys. measured in milliseconds (ms). As it can be seen from the figure. This is because the destination object is signed by the private key of the home node. the Proposed MA needs approximately 4x more time. in either of the cases it is possible to eavesdrop what information is retrieved and exchanged at each host: OS Architecture: x86. after dispatched till it returns and handovers the result to the user.62 Sayed Nouh and Tinbit Admassu key just supplied. a similar test environment as above is used. As might be expected DS Mobile Agent takes in between of the two. 8. Figure 10 indicates just that for the three scenarios (Proposed. 25 132. India. verification of destination object at each visited host and at last collecting the results back to the Mobile Agent from the TS all add up to form a big turn around time. As the number of nodes to be visited is steadily increased. 168. MD 220899. It takes time only as it verifies that the destination object is valid copy on its arrival at each and every host. Lange. B. Dissertation. using a Security Protocol. 2002. Classification of Malicious Hosts Threats in Mobile Agent Computing. Australia. Altalayleh. and Brankovic. 26. The paper more specifically was an attempt to try to look in to a notoriously difficult task as pointed out by many researchers. encryption of partial information. Springer-Verlag Berlin Heidelberg 1998. Mobile Agent Security. Gaithersburg. C. Figure 11 compares the trend of the execution time for all Mobile Agent cases. 180 160 140 120 Time(ms) 63 CONCLUSION AND FUTURE WORK In this paper we have tried to address the issue of Mobile Agent security at the same time providing familiarization to the concept of Mobile Agents programming.IIT Bombay.Threats and Trusted Countermeasures. M. University of NewCastle. D. Mobile Objects and Mobile Agents: The Future of Distributed Computing. Dissertation. M. we notice that the turn around time increases. Jansen W. Tech.25 40 20 0 Normal MA DS MA Proposed MA Figure 10 Actual performance time comparisons between the three scenarios Comparing the performance time between DS MA and Proposed MA. This is tribute to the fact that there are more jobs to be done. India. 2009 . Secuirty Issues in Mobile Agents.25 100 80 60 39. University of South Africa. E. Pages 141-148. 450 400 350 300 [2] [3] [4] [5] [6] Normal MA DS MA Proposed MA Time(ms) 250 200 150 100 50 0 1 2 3 4 5 6 7 8 9 No of Nodes Figure 11 Performance time trend as the number of nodes visited increases Journal of EEA. 2002. REFERENCES [1] Rahula Jha. and Cloete. The counter measure proposed introduces the concept of setting up another home in the agent space as called home away from home for partial result storage and the separation and digital signing of the destination of the Mobile Agent. Mobile Agents for e-commerce. and Karygiannis T. National Institute of Standards and Technology. L. M. Encryption and others. Bierman. Vol. An Overview of Security Issues and Techniques in Mobile Agents. E. IIT Bombay. This is due to the fact that it (DS MA) does not carry out some of the functions the Proposed MA performs like: Generation of keys. Vijil E. Tech. An attempt has been made to avert some of the malicious host s threats by adopting a number of mechanisms to the way the original computation is made by the Mobile Agent. the DS MA needs less time. Proceedings of SAICSIT 2002. FiberBased Certificates of Authenticity. Intaglio Printing. This manual method is currently being used in Ethiopia at the banks. The other method is manual inspection. Though experts make right decisions based on their years of experience. Sometimes. The Patented Smart Money Counterfeit Detector Pen (Money Tester Pen) has revolutionized counterfeit detection. INTRODUCTION Currency counterfeiting is a common problem around the world. etc. However. Ultraviolet Fluorescence. Counterfeit currency identification. symbols. it is recommended that this device be used in conjunction with other identification methods. ultraviolet detector [7]. Ethiopian 100 birr is taken as a case study in this work.A CASE STUDY ON ETHIOPIAN BIRR NOTE Zewde Dinku and Kumudha Raimond Department of Electrical and Computer Engineering Addis Ababa University ABSTRACT Counterfeit notes came into circulation right from the time of existence of genuine notes. detecting using infrared beams [6] etc. This approach works by simply running the pen over the currency which required to be detected.COUNTERFEIT CURRENCY IDENTIFICATION SYSTEM . While no method of counterfeit identification is foolproof. So. Second-Line Inspection Methods and Smart Money Counterfeit Detector Pen (Money Tester Pen). These are more secure than visual methods. Apart from this work. all countries are trying to tackle as much as possible. or at least minimize the risk of counterfeiting by enforcing different measures and techniques [1]. This technique is widely used for US and Canadian notes [8]. and printers which highly contribute to the work of counterfeiting are easily available to counterfeiters to reproduce pictures. it is mandatory to automate the identification system. [2]. 26. there has been a surge in casual counterfeiting. continuity of lines and for the availability of watermarks which are unique to genuine bank notes. [8]. This work proposes and implements a Counterfeit Currency Identification System (CCIS) based on Cauchy Schwarz inequality algorithm. LITERATURE SURVEY A number of techniques like first line inspection methods. Since the advent of color photocopy machines and printers. lots of other detecting techniques are also patented such as barcode scanner [5]. So. Cauchy-schwarz inequality. So. because highly sophisticated devices such as photocopiers. Smart Money Counterfeit Pen is a very good option and will detect a great majority of non-genuine notes. there should be some technique that should help the banks and insurance companies to precisely identify the counterfeit currencies. Second line inspection methods are Isocheck/Isogram. First-line inspection methods are used on-the-spot by vendors and retailers to determine the authenticity of currency being exchanged. it is very difficult to discriminate the fake notes from the genuine ones by simply looking at the paper notes. but the additional security increases the cost at both the manufacturing and verification ends. but requires an extra device to perform the verification process. Few of the existing techniques are: First-Line Inspection Methods. Micro text Holograms and Kinegrams. The other method is by just looking at the suspicious bank notes against bright light to check for the alignment of symbols. First-line inspection methods are Varied-Density Watermarks. A second-line inspection method is one that cannot be verified by the naked eye alone. digital scanners. For more protection. digital cameras. it is however important to avoid any bias by humans. which is currently used in Ethiopia at the banks. Keywords: Banknote recognition. to avoid human errors. Journal of EEA. Color and Feature Analysis [9]. It needs additional means of identification using sophisticated currency identification hardware devices or machines. the main objective of this work is to identify and implement a suitable technique to correctly identify the counterfeit currencies. second line inspection methods and smart money counterfeit detector are being used in many countries to identify the genuine notes from the fake ones. Vol. A number of techniques like first line inspection methods. second line inspection methods are being used in different countries to tackle the counterfeiting problem. 2009 . logos. this algorithm is unable to recognize counterfeit banknotes and takes time for the learning process. The features that are pointed are considered as unique features of genuine 100 birr note by National Bank of Ethiopia (NBE). an algorithm is needed to address this problem of discriminating and identifying both genuine and counterfeit banknotes. Inductive learning rule-3 algorithm is used for the discrimination of the banknotes. it is very important to capture those invisible features also to automate the identification process. 3 points to the printing date in Ethiopian and Gregorian calendar. and Cauchy Schwarz inequality Algorithm. symbols and others. Since both CNN and Inductive learning rule-3 algorithms are used only for discriminating genuine currency notes and not for identifying and discriminating the counterfeit currencies. this work proposes Cauchy Schwarz inequality algorithm for the identification purpose. thereby slows down the processing speed compared to CNN and Cauchy Schwarz inequality algorithms. No. 1. and it is easy and cheap compared to CNN. But. Cauchy Schwarz inequality algorithm can be used for this purpose. 2 is exactly aligning with a similar circle at the overleaf while seeing against sunlight. The circle that is shown by No. 2 4 3 Figure 1 Genuine Note: Image obtained using digital Scanner The details of the features are: No. Figure 2 shows the corresponding image and the features that are pointed indicate the additional features of the genuine note. to classify a given banknote to a predefined class (designation) of banknotes. but it is complicated and expensive when compared to Cauchy-Schwarz. there are few more lines and watermarks which are visible only while seeing against sunlight. The system has been trained for back and front sides of 5 different Turkish banknotes. with the text denoting the denomination of the birr note.1 indicates thick bar consisting of logo of NBE. CAUCHY SCHWARZ INEQUALITY The Cauchy Schwarz inequality theorem is useful for measuring the similarity measure between two images. 2: The line looks discontinuous. Inductive Learning Rule-3 Algorithm. the phrase National Bank of Ethiopia is written in English and Amharic. but costly and more complicated. 2009 . The important requirement of the system is to distinguish the notes between genuine and fake based on the features of genuine note. different colors. Vol. No. The algorithm is explained elaborately in [10]. This algorithm saves memory space. No. it is used only for discriminating the genuine banknotes [4]. So. The images are taken by digital camera using UV light to acquire those invisible feature. and is not applicable for counterfeit currency discrimination and identification. countries have implemented and are implementing algorithms and enforcing different measures to discourage counterfeiters. This algorithm has been implemented to discriminate all denominations of Turkish banknotes. On this continuous line. 26. 4 shows a watermark of map of Ethiopia. So. Therefore. it is important to understand the distinguishing features of the genuine note. 1: A watermark of farmer plowing is seen on the white area while seeing against light. Apart from the techniques/methods mentioned above. The system also has been tested using 24 unseen examples and correctly classified all of them.74 Zewde Dinku and Kumudha Raimond ANALYSIS OF CCIS It is important to analyze the requirements of CCIS before designing the system. 1 Journal of EEA. Some of the algorithms are: Cellular Neural Network (CNN) Algorithm. The efficiency of the system has been found to be 100% [3]. i. Apart from the features shown in Fig. Bankers use those features also to check for an alignment of different symbols and for the continuity of lines available on the notes to identify the counterfeit currencies. Figure 1 shows the scanned image of genuine Ethiopian 100 birr note. CNN algorithm is efficient because of the use of CNN universal machine which is faster. None of these above mentioned techniques/ algorithms are implemented in Ethiopia for banknote identification at present.e. but it is continuous in light. No. Added to that. Due to the above stated reasons. it is very easy for the counterfeiters to duplicate the back side as it is in the original note. After filtering. The explanations of the block diagram corresponding to both the approaches are given below: Birr Note Image Approach I/ Approach II Image Pre-Processing. Cauchy Schwarz inequality algorithm is selected for this work to measure the similarity between the genuine and test images and to decide whether a given birr note is genuine or not. and comparing the images of genuine with that of fake ones using Cauchy Schwarz inequality algorithm. Some of the genuine birr notes are old and some of them are very old and torn. the birr note will be considered to be genuine . otherwise will be considered as suspicious or fake. the data must be transformed into a form useful for the selected algorithm. 2. Vol. Apart from the features mentioned in Fig. 600 dpi) and by digital Camera using UV light. Also. The fake birr notes are almost new. Enhancement and Normalization Image Pre-processing. Image Processing: The digital images (JPEG format) of both the genuine and fake 100 birr notes are taken using digital scanner (HP Scan jet 5100C. The notes are collected by taking into consideration the age of the notes and the dirt on the notes as criteria. The number of fake notes collected for this work is very limited as it is very difficult to get the fake notes (even the hole punched ones) from authorized body. Counterfeit Identification Technique/Algorithm: The image processed by the above steps will be given to a suitable CCI algorithm to identify the notes. and the background against which the images are taken. processing the images of these currencies. the pre-processing of an image involves creating a uniform background and converting the image into binary format. the features at the back side of the note overlap with the front side features.Counterfeit Currency Identification System . 2 1 Figure 2 Genuine Note: Image taken by digital camera using UV light The change in color is due to the UV light falling on the camera lens. 2009 . Only one side of the birr note is enough for the identification purpose. In the first approach. genuine and fake birr notes are collected for the testing purpose. New genuine note is used as a benchmark to compare against with any other sample note. Enhancement and Normalization: Generally. Data Collection: In this work. Further. images are obtained using digital camera and UV light. If the similarity value is greater than or equal to the threshold value. 26. The proposed CCIS is shown in Fig. IMPLEMENTATION PHASE The process of implementing the CCIS involves three basic steps: Collection of genuine and fake currencies. images are collected by scanning the genuine birr Journal of EEA. DESIGN OF CCIS Hence. digital camera used. Counterfeit Currency Identification Technique Figure 3 Proposed counterfeit currency identification system Birr Note Image: Two approaches are suggested for collecting the test images. the quality of the digital scanner. except the number of hole punches (hole punched by the bank in order to avoid the circulation) on the birr notes. This noise can be due to the dirt on the birr notes. this work concentrates only on the front side of the note. 3. there are other important features which can be noticed in the genuine note such as the quality of the paper and the texts written on the note which can be felt when rubbed with fingers (embossed features). Then the images should be filtered to reduce the noise. two approaches are proposed in this work: Approach I (image obtained using digital scanner) and Approach II (Image taken by digital camera using UV light). the bankers are verifying only the front side to discriminate the notes. A threshold value will be set after performing the counterfeit test with large number of samples.A Case Study on Ethiopian Birr Note 75 notes and in the second approach.1 and Fig. because there are no watermarks and invisible lines on the other side of the note. Since. the pixel values are normalized to take values between 0 and 1 .8148 Old fake note : better paper quality compared to test image No. Image Enhancement: The images of the birr notes (genuine and fake) should be filtered to reduce the noise.76 Zewde Dinku and Kumudha Raimond Table 1: Sample results of approach I No Test Images New genuine note Similarity Values Some of the lines. Also. dirty and lost some of the features of genuine note 3 0. The color of the image in this approach has changed due to the fact that the UV light passes through the notes while the images are taken. the test images in Table 1 and 2 are compared against the benchmark images shown in Fig. the similarity values are calculated between the benchmark note (new genuine) and other genuine and fake (new and old) birr notes. torn with much dirt and folding 4 0. In part II. image processing toolbox of MATLAB is used to create a uniform background. 1 1. Cauchy Schwarz inequality algorithm yields the similarity measure value between 0 and 1 . So. Counterfeit Identification Technique /Algorithm: Similarity measuring technique is implemented using Cauchy-Schwarz algorithm. Sample results of approach I and approach II are shown in Table 1 and 2 respectively. This filtering is done at different levels using MATLAB functions. 2009 . some of the features from the back side of the notes are overlapping with the front side features.7603 Journal of EEA. This may be due to the fact that the age and dirt on the old birr notes blocks the light to pass through the notes. The results of these approaches with their respective drawbacks (limitations) are given below.813 inches) and resolution (90 pixels/inch to 200 pixels/inch) of the images (JPEG images) are adjusted using Adobe Photoshope 7. In this work. However. In all these cases. 2 respectively. Image Pre-processing Stage: In part-I of this stage. 26. In this technique. This technique is applied to both the approaches.6 5 A number of tests are carried out. it is sufficient to make use of a twodimensional filter. 0.0 New genuine note: Noise added manually 2 0. the color of the old birr note has not changed much. Vol.9635 Old genuine note : aged. In this case. UV light is used as light source. Normalizing the pixel values: The pixel values of the images ranges from 0 to 255 . symbols and watermarks are visible only if the birr notes are seen against light sources.8573 Old genuine note : aged. A convenient property of filtering is that filtering a three-dimensional image with a two-dimensional filter which is equivalent to filtering each plane of the three-dimensional image individually with the same two-dimensional filter. 1 and Fig. linear filter which is a 2-dimensional filter has been used. the size (5.813 inches by 2. There are various types of noise removal techniques. lot of folding with poor paper quality Old fake note : better paper quality compared to test image 6 6 0.9293) than that of between genuine and fake ones which is lower (0.7318 1 1.7423 Old genuine note : aged. Vol. Finally.7362 5 0. hidden lines and symbols on the images taken by digital camera while these are invisible on the images obtained using digital scanner. aged.A Case Study on Ethiopian Birr Note 77 Old fake note : torn. dirty and lost all the features of genuine note 4 0.Counterfeit Currency Identification System .9721 I II Between Genuine notes 0. approach II is considered to be preferable compared to approach I for CCIS.7423).8836 As it can be seen from the above Table 3. 2009 . dirty and lost some of the features of genuine note 3 0. This interval between the genuine and the fake notes is higher in approach II than that in approach I. This is due to the visibility of some of the features such as watermarks.9293 Between Genuine and fake notes 0.9116 0.0 The following Table 3 depicts the average similarity measure value between the birr notes. This may be due to the change in color of the image and also due to the overlapping of the overleaf features with the front end features. In spite of capturing the important features in approach II.7578 0. the results of approach II are better than that of approach I. by considering the results obtained and the limitations of both the approaches. Journal of EEA. The average similarity measure value of approach II between genuine birr notes is higher (0. the similarity interval between the notes is not much higher than that of approach I. 26. Table 3: Average similarity values between the birr notes New genuine note: noise added manually Approaches 2 0.8904 Old genuine note : torn.7402 Old fake note : torn with lot of foldings Table 2: Sample results of approach II No Test Images New genuine note Similarity Values 6 0. IEEE International Conference on Image Processing (ICIP). Counterfeit Currency Detection Techniques. pp. 2002. 1994. the note is considered as suspicious or fake birr note . Turkey. When tested. Chua.oti.24232426.ac. Aksoy M. CONCLUSIONS The following conclusions have been drawn: · A methodology for identifying the fake Ethiopian 100 birr note has been proposed and implemented based on similarity measure and the results are found to be promising to distinguish the notes with a threshold of 0.. (Viewed as on 12 Nov 2009). and Soft Computational Intelligence in Management and Industrial Eng. L. FSSCIMIE 02. http://www. M. p. Method and apparatus for currency discrimination and counting. Banknote recognition using inductive learning. p. Counterfeit money detecting barcode scannerPatent US2003098350(A). 2003.80 (for this work) by considering the similarity measure values obtained for each test in both the approaches.oti. Sevkli. Vol. Detection of counterfeit currency . REFERENCES [1] Herley. Based on the values obtained in Table 3.. J.pdf (viewed as on 12 Nov 2009). International Conference on Fuzzy Syst. Detection and deterrence of counterfeiting of valuable documents. A. S. (viewed as on 12 Nov 2009). S.ed. http://www. Vol. http://www.uk/rbf/CVonline/ LOCAL_COPIES/AV0506/s0128541. C. it is observed that paper quality is playing a significant role. 1994. the birr note with similarity measure value above the threshold (0. 1998.80) is considered as genuine note otherwise. Third IEEE International Workshop on Cellular Neural Networks and their Applications. http://www.org/wiki/Cauchy%E2%80 %93Schwarz_inequality. 26. Vora.. T. stanbul Technical Univ. Optical Signal Processor for Anti-Counterfeiting and Security Systems.O.com/oti/patent/200803132008063252-US-A1 (viewed as on 12 Nov 2009). Roska. Novel Types of Analogic CNN Algorithms for Recognizing Bank-notes...1.oti.freepatentsonline. [5] [6] [7] [8] [9] [2] [10] Cauchy Schwarz inequality. 2004. Turkyilmaz. Javidi. L. pp.Patent US2008063252(A1).4. [3] Journal of EEA.122-128. folded and the dirty notes have less similarity compared to the new notes. http://en.com/oti/patent/199805265757001-US-A. · From the test cases.145-146. F. · From the fake note test cases. Horner. Vol.com/5295196..com/oti/patent/200305292003098350-US-A1 (viewed as on 12 Nov 2009). http://homepages. A. Yang.inf.wikipedia.ht ml. Declan McAleese. Werblin.Patent US5757001(A). aged.273-278. P. it is observed that torn. B. 2009 .78 Zewde Dinku and Kumudha Raimond [4] Zarandy.8. UV counterfeit currency detector . IEEE Conference Proceedings on Lasers and Electro-Optics Society Annual Meeting. the threshold value is set to 0. and high quality electric energy supply for Ethiopia and for sustainable qualified human power training for the sector have been recommended. Technical loss refers mainly to the electric energy lost on resistive effect of the electrical system (I2R) throughout the system and core losses on machines and control systems. Eq. Consorted efforts of Ethiopian universities and the sector players for sustainable. energy saving by efficiency improvement is more attractive. efficiency is defined as the ratio of output power from a system or equipment to the input power to the system or equipment. and welding transformers are estimated. technical and non-technical losses [2]. etc) . distribution and sales. electric energy efficiency improvement and search for renewable energy sources are some of the top agenda of the world and research themes of scholars. theft by some customers. . 2009 . It includes all forms of energy obtained from nuclear. Electric mittad. biomass. Technical loss. .. 26. The total energy a country uses to produce a dollar of Gross Domestic Product (GDP) for example can be used as the energy efficiency of a country [1]. 2. efficient. Vol. The investigation demonstrates that there is a possibility of electric energy saving which is at least equal to 10% of the present yearly generated electric energy. and the fast increase of energy demand in developing countries. etc. This is because of the carbon-dioxide emission and the resulting environmental deterioration. reliable.PRELIMINARY SURVEY ON ELECTRIC ENERGY EFFICIENCY IN ETHIOPIA:. 1. fossil fuel. Electric energy Efficiency with respect to the electric energy consumer can be defined as the ratio of the output of the consumer (in terms of product quantity or other form of energy) to the input electrical energy. Efficiency. transmission. Present trend in electrical engineering education. INTRODUCTION Energy efficiency In Engineering. However. Energy. h= Electric Energy Sold Electric Energy Generated (1) If a vertically integrated utility operator like Ethiopian Electric Power Corporation (EEPCo) is considered. h= Output (Pr oduct. because new conventional base load production sources Journal of EEA. In the consumer area the loss associated with the energy conversion devices like lamps. According to a study done in USA. Energy in this definition is not limited to electric energy. With respect to the Utility operator. that is the inclination of students towards electronics and computer engineering areas abandoning power engineering area and the resulting danger of shortage of qualified pool of engineers for employment in the energy sector have been demonstrated.AREAS OF INTERVENTION Mengesha Mamo Department of Electrical & Computer Engineering Addis Ababa University ABSTRACT In this paper the significance of electric energy efficiency improvement and major areas of loss in Ethiopia s electric power system are highlighted for further rigorous study. Major electric energy loss areas in the utility transmission and distribution systems and consumer premises are indicated. etc. efficiency applied to energy needs explanation. electric motors. Electric Energy Input in to the System (2) Why energy efficiency Today. Power factor. Mechanical Heat. In this article electric energy efficiency is defined with respect to the electric utility operator and the consumer. electric Mittad. Keywords: EEPCO.. electric energy efficiency is the ratio of electric energy sold by the utility operator to electric energy generated as shown in Eq. limited fossil fuels as energy source. the electric energy sold is total electric energy generated minus energy loss in the process of generation. Non-technical loss on the other hand accounts for energy utilized but not paid for due to measuring errors. There are two components of loss. 7]. UK 8% [5] [6]. EEPCO system and its customers systems to improve the electric energy efficiency. to have efficiency of 99% and the last transformer in the distribution to be 97% the overall efficiency of the transformers would be 95%. Older transformers have high loss or lower efficiency. One is loss in the lines while the other is loss in transformers. the industries. the step-down transformer at the distribution center. identification and quantification of sources of losses. USA about 6%.5%. development of new transformer core materials has resulted in high efficiency transformers.5 depending on the capacity. etc. EEPCO ELECTRICAL SYSTEM EFFICIENCY Energy losses along the way from the generation point up to utilization point is the main reason for low efficiency in electrical system. and the public as a whole. potentials of loss reduction at consumer premises and some efforts of Electrical and Computer Engineering Department (ECED) in this respect are discussed. indicates that there is a lot to be done in our system both in respect of the utility operator. low power factor. Europe average 6. This standard includes efficient transmission and distribution plus efficient utilization of energy.135 per kilowatt-hour while the saving cost through various improvements of efficiency is estimated to cost about $0. That is 5% energy loss on the three transformers overall. Since 1980s.46 Mengesha Mamo Technical loss in electric power system There are two main components of technical loss in transmission and distribution systems. 220 V) level. Common reasons for high electric energy loss on the line are low voltage level compared to the size and length of the conductor. This effort by the highly professional and developed country like USA. The transformer efficiency varies from 96 to 99. load unbalance in the phases. China 7%. the utility operator.073 to $0. which is two to four times. Introducing Energy Efficiency Resource Standard (EERS) USA plans to reduce its electric energy consumption by 15% in 2020 [3] [4]. Vol. load. the universities. 2009 . These are step-up transformer at the generator switch yard. EEPCo s and electric energy users systems and components modeling and analysis. design. what is generally the case. There are at least three transformers in a power system transmission from generation point up to the consumer premises. harmonics in the current and voltage. in Japan is 4%. In the following sections EEPCo present estimated efficiency. Pakistan 26% and Tanzania 25% [6. improper design or installation using inappropriate materials and components. including the loss on transformers and the line I2R loss.03 per kilowatt-hour [4]. and identification and recommendations on means of minimization of losses are what has to be done concertedly by stakeholders. A transmission and distribution loss. generate electricity at an estimated cost of $0. 26. sources of loss. step-down to low voltage (400 V. There are also high loss systems like that of India 31%. Figure 1 Electrical power system loss Journal of EEA. etc. In our EEPCo system. if we assume two of the three transformers in the chain. heat. The efficacy of incandescent lamp at present varies from 10 to about 25 Lumens/watt while the Compact Florescent Lamp (CFL) efficacy reaches around 75 Lumens/watt. becomes very small resulting in the compactness of the lamp. kinetic. For example. The intension is to make these as model and scale up for modeling and analysis of other similar transmission and distribution systems. If the lamps are to operate for fours hours per day. Due to the high frequency. This is true in European and American countries too. EEPCO s Electrical System Loss The current Electric Energy loss in EEPCo s system is about 18% of the electric energy generated [8]. The ECED of Addis Ababa University is encouraging the electrical power MSc students to work on real problems in EEPCo so that they come up with feasible solutions for improving the electric energy efficiency. We can save two-third of electric energy we are using for domestic lighting if we replace the incandescent lamps with CFLs. At present. and electronic outputs like audio. etc.2 GWH. video. Lighting 47 The electrical energy efficiency with respect to the consumer can easily be demonstrated by considering the electric lighting. from the efficiency level of USA. incandescent lamp is the most inefficient artificial light source as shown in Table 1.000 kWH (3 hours/day x 58. In Ethiopia almost in all domestic lightings. if we are able to reduce the system loss from 18% to 12% as a first stage.000 kW x 365days). Efforts by Electrical and Computer Engineering Department towards Improvement of Energy Efficiency There are some MSc students from EEPCo working on the modeling and analysis of major transmission lines like Koka to Diredawa and evaluation of main distribution system like BahirDar distribution system. European Union and Australian government are considering a ban on the import and sale of incandescent lamps in favor of CFL and other more efficient light sources. due to the relatively cheap initial cost and readily availability incandescent lamp is the first choice for domestic light source. 2009 . and secondary circuits in EEPCo s system need modeling. about 3.3 million customers at the moment [6]. The electric energy loss in transmission. ) and their contribution to the total electric energy loss. This saving which is equivalent to 6% of the yearly total energy generated. due to low power factor. However. 26. three times that of incandescent lamp. distribution. Vol. analysis. The analysis is expected to result in quantified performance of the system based on which appropriate decisions can be made. incandescent lamps are used. If one million of the customers are assumed to have two incandescent lamps of 40 Watts each replaced by two 11 Watts CFL. and transformer. Europe and Japan we can see that there is possibility of improvement in the efficiency of EEPCo s electrical energy system and save significant amount of energy. we would be able to have about 48 MW (~0.Preliminary Survey on Electric Energy Efficiency in Ethiopia. the current limiting inductor. However. Table 1: Efficacy of some electric lamps [10] Lamp type Incandescent Lamp Compact Fluorescent Lamp Fluorescent full size and U-tube Compact metal halide High pressure sodium lamp Low pressure sodium Efficacy.06x800MW) of electric power [9]. In CFLs the 50Hz.510.570 GWH. the total electric energy per year will be 83. ELECTRIC ENERGY EFFICIENCY AT CONSUMERS PREMISES At the point of use electric energy is basically changed to other form of energy like light. known as choke. However. That means a CFL gives light energy which is equal to three times that of incandescent lamp for the same electric energy consumed. Lumens/Watt 10 to 25 20 to 75 70 to 100 45 to 80 45 to 110 110 to 155 Journal of EEA. In other words efficiency of the system is 82%. EEPCO has about 1. 220V power supply is processed to supply the florescent with high frequency. and some measurements to quantify the level of each sources of loss (cable. is equal to 214. the power consumption reduces from 80 MW to 22 MW for the same light output if they are to operate at a time. It is possible to reduce the loss at least by half by proper design and material selection. EEPCO has taken an initiative to distribute CFL free of charge to its customers recently to relieve the power shortage pressure on it. Over sizing electric motors result in less efficient operation. the total electric energy consumption in a year can be calculated to be (3 kW x 52 weeks x 2 hours/week x 300. They also work at low power factor. Traditional methods of speed adjustment like inserting resistors in the rotor circuit and mechanical braking have excessive loss. Welding transformers Recently metal workshops using locally made welding transformers have increased all over the country. If we estimate the number of electric mittad in the country to be 300. work on efficiency of lighting can save more energy than what is estimated above. the government may need to take appropriate majors to encourage the import or local manufacturing of these high efficiency lamps at an affordable price for the household while discouraging the import and manufactory of low efficiency lamps. Journal of EEA. where the quality of light is not critical like street lightings need investigation to use the highest efficiency sodium lamps. This can be considered as significant awareness creation for energy efficiency issue. In the process.000 pcs. The authors have measured the loss of samples of the locally manufactured transformers to be on average 1 kW compared to 0. supplying the machine at a desired voltage level and frequency for best possible efficient conversion at a desired speed. Electric machines Electric machines are the main electric power loads in industry comprising up to 70% of electric energy in the processing and manufacturing industries. Some preliminary investigations demonstrate that the efficiency of injera baking can be improved by more than double using induction heating rather than resistor heating.000 [9]. The conversion efficiency can be improved by using power processors. the saving can be 46. Survey done by an MSc student in Electrical and Computer Engineering Department of Addis Ababa University has estimated the total number of locally produced welding generators in use to be about 60.2 GWH. Over sizing electric machine is another important point to be considered. the electric energy saving per year will be 10. Speed control of the electric machines and the driven units can be done by controlling the frequency and voltage of supply to the machine. Exterior lightings. If the electric energy consumption is halved. Electrical and computer engineering department is working on proper design and material selection to help the local manufacturers to improve the efficiency of the transformers. 26. In commercial buildings more than 25% electric energy is used for lighting. On average it consumes about 3 kW.000 mittads) 93. Therefore.23 kW of equivalent imported transformers. If 170 working days and about 2 hrs effective working hours are assumed per day. The department has filed a patent on induction mittad and is working on its further development. For the sustainability of energy saving through high efficiency light sources like CFL. the most widely used in the industry range from 78% to 94% when they operate at the rated power. Electric machines do convert the electric energy into mechanical energy. When they are partially loaded their efficiency drops much blow this range.48 Mengesha Mamo Work must be done in industries to audit their energy utilization and determine the quantified energy saving possible. In US 64% of total generated electric energy is said to be consumed by electric motors. It has demonstrated the energy saving possible at the national level and energy cost reduction to its customers. These transformers are not well designed and core material used is not the proper material for the required efficiency [12]. Research should be done on this indigenous equipment to improve efficiency. Vol. It uses resistor to convert electric energy to heat energy.80 GWH per year.60 GWH. The electric heat generated by the resistor is conducted to the plate made of clay. and each operate for two hours every week.000 to 80. 2009 . the heat transferred to the injera for baking is estimated to be very small while a huge amount of heat energy is lost to the environment [11]. Electric machines operate at their best efficiency when they are operated at their rating. The same holds for transformers. The efficiency of induction machines. Electric Mittad Important electric energy load in domestic use in Ethiopia is the electric Mittad. The electronic devices like computer and TV are also contributing to power factor reduction by introducing harmonics. 000.8 or 80% power factor (pf). the business community. In Fig. Table 2: Power-factor of some electric equipment Appliance Induction motors Arc welders Solenoids Induction heating equipment Small dry-pack transformers Fluorescent & HID lighting fixture ballasts Power Factor 55%-90% 50%-70% 20%-50% 60%-90% 30%-95% 40%-80% Economics of Electric Energy efficiency The approximate energy saving possible from the above exercises has been summarized in Table 3. where pf is the ratio of active power component current to the vector sum of the two. the active power component. 3(b). Figure 3 Electric motor power factor Power factor correction becomes more important in rural electrification where the distribution lines are relatively long. Journal of EEA.45 Birr/kWH (the average domestic charge rate). Vol. the yearly saving in Birr is more than 150. reducing power loss in the transmission and distribution 49 system due to the reactive power component current. The electric generator should supply the vector sum of the two that is 100 Amps. congestion of the transmission and distribution system line by the reactive component current. The cable from generator to the motor also carries the 80 Amps. Harmonic distortion results in power factor reduction. electric loss associated is critical. The power factor corrector solves four problems. 3 demonstrates the problem of reactive power. namely active power and reactive power.000. 2009 . socket outlets and dividers with the finding that there is a significant and alarming amount of these materials in Ethiopian market and in use [13]. The reactive power is required for proper functioning of the electrical equipments. reduction of voltage drop along the cable. Table 2 shows some electrical appliances and equipments requiring reactive power for proper operation with their approximate power factor. 3(a). the government bodies concerned with standards. The issue of substandard electrical materials and appliances require consorted effort of policy makers. In this case the electric generator is required to generate load current of only 80 Amps. the appliances and equipments are expected to increase the energy loss where ever they are used. Total of about 334. Similar survey has to be done on electric appliances. Recently electrical and computer engineering has made survey on electrical cables. Some details of capacitor bank selections for power factor correction are given in reference [14]. The electric motor is said to operate at 0. The line from generator to the motor carries 100 Amps. In Fig. Fig. 26. professional societies. Power factor Alternating current system has two types of power flow in electrical cables. EEPCOs yearly energy production in 2001 EC is about 3570 GWH. equipments and electronic devices. and the society as a whole. the reactive component current is supplied from capacitor bank. known as power factor compensator.Preliminary Survey on Electric Energy Efficiency in Ethiopia. Therefore. the electric motor draws 80 Amps for active power and 60 Amps for reactive power. relieving the generator from generating reactive power component current (instead it can generate additional 20 Amps active power current). If the electric energy is taken to be 0. Active power is the power which is converted to the useful power at the point of use while the reactive power is power in the energy storage elements like inductors and capacitors. Sub-Standard electric components In addition to the other disadvantages of substandard materials. Substandard materials.71 GWH energy saving is possible per year. the electric energy saving is about 10% of the yearly production. which is about 60% of the power generation of the whole sub-Saharan countries and about 80% of the southern African countries [16].12 per kWH.71 o o o o Inverter technologies for integrating power from renewable energy source with the grid system. If efficiency improvement of electric motors in industry and conservation of energy by using electric energy only when and where required are considered the energy saving can be multiple of the above exercise result. About 20 of these are expected to graduate in year 2002 EC. Ethiopia. 26. o Transmission (including high voltage DC) and distribution system modeling and analysis for increasing capacity and loss reduction. the trend in electrical engineering education is towards the electronics.94 and $3. Development of capacity to do contract research with ESKOM. Expatriate academic staffs.50 Mengesha Mamo The followings are the main areas the students have worked on in their independent project and thesis. 1 2 3 4 Intervention point Efficiency improvement from 18% to 12% Lighting (CFL) Electric Mittad Welding Transformer design improvement Sum GWH 214. ELECTRICAL POWER ENGINEERING EDUCATION Electrical power engineering in AAU With the advent of microelectronics and computer technologies.80 10. etc. There were no applicants for Electrical Power Engineering MSc program in AAU until some two years. This is a potential research topic to be done in our country. ESKOM is south-Africa s utility company generating 35 GW. 2009 . Journal of EEA. which were 25 students from EEPCo based on the postgraduate study and research agreement between AAU and EEPCo. Generation system control and automation. renewable energy technologies and power electronics and derives. computer engineering and communication engineering. o EEPCo has been supporting the Faculty by finance so that its students get diversified knowledge and skills at a required level.51 46. Electrical power engineering in USA and SouthAfrica The trend of electrical engineering education and the inclination of most students away from electrical power engineering have worried different electric utility operators and policy makers.20 334. SouthAfrica s ESKOM has introduced the so called Tertiary Education Support Program (TESP) in which it finances universities and research centers since 1980s to overcome the declining trend with the following specific benefits [15]. power factor and efficiency at the consumers premises Renewable energy technologies alternative electric energy source as an The cost to be paid for such saving requires rigorous evaluations and may include the electric power down-time cost at the country level during the critical power shortage like in year 2001 EC in our country. Table 3: Estimated possible energy saving No. Development of knowledge base of academic staff in the area. from EEPCo are working on their MSc thesis proposal at present. The largest admission to the electrical power engineering program was in 2000 EC. Survey on welding transformer efficiency and ways of improving efficiency Electric power quality. A study done in Nigeria on down-time cost has shown that the electric energy outage cost in that country varies between $0. transmission and distribution systems. There are only two graduates from the program until now. par-timers. Retention of academic staff in Electrical power area. The curriculum for Electrical Power Engineering masters program is a standard MSc program covering high-voltage engineering. Vol. and guest lecturers have been involved in the teaching EEPCo students.20 63. The first batches of electrical power engineering masters students. Development of students and potential pool of employees with an increased level of knowledge and skills. The competition is in efficiency. cost. Research and development (R and D) is investment by companies to continuously increase their competitiveness. 2009 . A Masters Thesis. RECOMMENDATION The government. Vol. research and development in the energy sector for efficient. Government should allocate a certain percentage of gross domestic product (GDP). May 2007. 51 Improving energy efficiency can reduce new power plant generation requirements and can contribute to the effort being exerted to curb the energy shortage we are facing. Energy efficiency in the utilization process can also reduce the industries energy cost and improve their cost competitiveness in the global market. the energy sector players like EEPCO and higher education institutions have to work on policy framework to support the education. [2] CONCLUSION & RECOMMENDATION CONCLUSION This paper has demonstrated that there is a lot to be done to improve the electrical energy efficiency of our utility and industry. March 17th 2009. The chipset way of doing R&D for industries is to work with universities. 26. Recently. Discussion paper series No. Consorted Effort Requirement for Today s Competitive World Challenges In USA. REFERENCES [1] Estache. reliable. quality of product or service. the number of students in electrical power engineering area has been declining globally. It is generally expensive for industries to install and administer laboratories and employ highly qualified professionals to do research in-house for industries. and Dolores.S. Energy efficiency Resource Standard . A. London. etc.Preliminary Survey on Electric Energy Efficiency in Ethiopia. EEPCo and AAU have to strengthen their existing cooperation to produce solutions for local problems and become a successful/ideal model for university-industry linkage. It should be strengthened. 07/13. Had it been operating in USA. Power and Energy Engineering Workforce Collaborative. as compared to the computer and communication engineering students. November. Students who have worked on problems of a particular industry can also be employed by the industry and continue on working on the solution of the problem.5% of their revenue for research and development.al Are African Electricity Distribution Companies Efficient Evidence from South African Countries . Fritz J. AAU and EEPCo s agreement is a positive sign in this direction. The industries are required to cooperate with universities and come up with their problems and some finance. 2002. American Council for an Energy-efficient Economy. the U. Universities also have basic research facilities as part of laboratories of education. Millions of dollars has been allocated for the implementation of the plan. has developed a sweeping and detailed action plan. University postgraduate students guided by their professors can solve most problems. H. et. and encourage industries to allocate a certain percent of their revenue for research and development for sustainability of development and competitiveness of the products and services. and quality energy supply which is essential for sustainable economic and technological development of Ethiopia. reasonable and immediate actions to attract more young people to electric power engineering and to support the education system that will make them highlyqualified engineers [17]. The plan envisages to double the number of graduate and undergraduate electrical engineering students in USA calling upon industry. Department of Economics City University. government and educational institutions to take specific. College of Engineering and Technology Ohio University. We need to take appropriate action to secure pool of employees and researchers in electrical power engineering. [3] Journal of EEA. companies on average allocate 3. Non-Technical Losses in Electrical Power Systems . EEPCo should have expended more than 35 million Birr each year for research and development. led by the IEEE Power & Energy Society. In response to critical concerns about the power and energy engineering workforce and the education system that supports it. Power and Energy Engineering . AAU. D. 2008. Electrical and Computer Engineering. 2006. FoT. InHouse Generation of Electricity by Firms in Africa . International Journal of Electrical and Power Engineering. Onohaebi. AAU. U. October 2004. and Consensus recommendation for future federal climate legislation. O. [14] United States Department of Agriculture. [15] Faculty of Technology and Faculty of Business and Economics. February 2009. June 2008. 2009. 2009 . [13] Mengesha Mamo. [11] Senior Project by students advised by Getahun Mekuria. [5] [6] [7] [8] [9] [10] Egan. EEPCO webpage. Policy Research Working Paper 4913 The World Bank Africa Region. pp 25. EEPCO EEPCO s Strategic plan for the period of 1997 to 2002 EFY . [12] Tezarash Yohanes and Getachew Biru Performance Evaluation of Locally Made Welding Transformers . Paying the Price for Unreliable Power Supplies. AAU. an independent project report. 26. April 2009. [16] Vivien Foster Jevgenijs Steinbuks. McGraw Hill. The Application of Capacitors on Rural Electric Systems .eepco. Reengineering of Distribution lines for Power Loss Reduction-Bhiwandi Case Study . Vol. April 21.52 [4] Mengesha Mamo Reducing the cost of addressing climate change through energy efficiency . Induction mittad . July. WSEAS Transactions on Power Systems ISSN: 1790-5060. pp 421-431. Architectural Lighting Second edition.S. Electrical and Computer Engineering. Reduction of High Technical Power Loss Associated with the Nigerian 330KV Transmission Network . pp 154. M. FoT.gov. http://www. European Copper Institute. Rural Utilities Service Bulletin 1724D-112. June 2009.et [17] Workforce Collaborative Press Release. Substandard Materials in Ethiopian Market Proceeding of the second Scientific conference on Electrical Engineering. 2007. Journal of EEA. volume 1 of 2. pp 404 to 415. Shrirang Karandikar and Ashok Ghatol. Energy Efficiency in Transmission and Distribution the scope for energy saving in the EU through the use of energy-efficient electricity distribution transformers . December 1999. Needs Assessment and Curriculum Design for Graduate College At the Ethiopian Electric Power Corporation study Report . 2002. Sintayehu chala and Daniel Dilbie. 2009. August. S. RESEARCH SIGNIFICANCE The purpose of this paper is to present a new approach for the analytical proof of the equivalence between the relative design axial load and biaxial bending resistance of: i. where a is defined as the ratio of the solid to the gross cross sectional area. However. if the design yield strength of the reinforcement is taken to be equal to one. and (3) the resulting design yield strength of the reinforcement is in conformity with the transformation of the design compressive strength of concrete. Solid sections. Moreover the total amount of reinforcement in the transformed section can be replaced by the mechanical reinforcement ratio. the square cross section of unit-length side is used to calculate interaction diagrams for load eccentricities along axes parallel to the axes of symmetry and to a diagonal of a solid rectangular cross section for the derivation of approximate analytical expressions of the moment contours based on the ACI Code Specification [1] [2]. The results of the proof showed that the equivalence exists only if the design compressive strength of the concrete in the square cross section of unit-length side is equal to one for solid sections and 1/a for hollow rectangular sections. Square cross section. and amount of reinforcement the same as in the solid cross section.THE USE OF SQUARE CROSS SECTIONS OF UNIT-LENGTH SIDE FOR THE ANALYSIS OF RECTANGU LAR SOLID AND HOLLOW SECTIONS UNDER BIAXIALLY ECCENTRIC LOADS Girma Zerayohannes Department of Civil Engineering Addis Ababa University ABSTRACT This paper deals with the analytical proof of the equivalence between the relative design axial load and biaxial bending resistance of a solid and hollow rectangular section. Vol. Analytical proof of the equivalence between the dimensionless expressions for the solid rectangular section with four corner reinforcement and the ultimate bending moments and axial force of an equivalent square cross section of unit length-side is also provided in Ref [1]. Solid rectangular section with arbitrary reinforcement arrangement and the design axial load and biaxial bending resistance of the Journal of EEA. 2009 . provided that. Hollow section. provided that the design compressive strength of concrete used in the analysis of the latter is equal to 1/a. The new sets of compressive strengths and transformations of rectangular sections into square cross section of unit-length side have been shown to be matched with consistent transformations of the design yield strength of reinforcing bars. More recently. (2) the resulting rebar location and area of reinforcement is in conformity with the transformation of the rectangular cross-section into the square cross section of unit-length side. (1) the design compressive strength of the concrete in the square cross section of unit-length side is equal to one. Comparisons of cross section analysis results have shown the equivalence between the relative design axial load and biaxial bending resistance of a rectangular reinforced concrete section and the design axial load and biaxial bending resistance of an associated square cross section of unit-length side. locations of concrete fibre and rebar. and area of reinforcement. w. analytical proof for its justification is hardly available in the literature. INTRODUCTION The results of cross section analysis show that the relative design axial load and biaxial bending resistance of a solid rectangular reinforced concrete section is identical to the design axial load and biaxial bending resistance of an associated square cross section of unit-length side. 26. it can be shown that the relative values of the design axial load and biaxial bending resistance of a rectangular hollow section with solidity ratio a is identical to the design axial load and biaxial bending resistance of the corresponding square hollow section of unit-length side. and the design axial load and biaxial bending resistance of the associated square solid and hollow cross sections of unit-length side. concrete fibre locations. Keywords: Biaxial eccentric load. Keeping the transformation requirements in respect of rebar locations. 2009 . are the side lengths of the rectangular cross-section It can be seen from Eq. Same as in (i) and (ii). (4) to (6) would be identical to the required relative values of the design axial load and biaxial Journal of EEA. ii. area of reinforcement. 26. µRd y. and the design yield strength of reinforcing bars undergo consistent transformations as will be described in more detail in the following sections. locations of concrete fibre and rebar. Vol. In summary all rectangular sections with arbitrary side lengths b and h possess the same relative design axial load and biaxial bending resistances as that of the associated square cross section of unitlength side. The solutions are: b = 1. and µRd z of the original cross section directly. It is achieved through the transformation of the side lengths of the original cross section and the design compressive strength of concrete into unity. bending resistance of the original rectangular section. Rd. and MRd z are the design axial load and biaxial bending resistance of he rectangular cross section. but using net cross section for high strength concrete as recommended in modern building codes [3] [4]. h. and fcd. i. iii. h = 1.32 Girma Zerayohannes associated square cross section of unit length side. The resulting rebar location and area of reinforcement in the square cross section of unit-length side is in conformity with the coordinate and area transformation of the rectangular cross-section. Hollow rectangular section with arbitrary reinforcement arrangement and the design axial load and biaxial bending resistance of the associated square hollow cross section of unit length side. (1) to (3) that the design axial load and biaxial bending resistance of a different cross section whose side lengths and design compressive strength of concrete satisfy Eq. and fcd = 1. fcd b. (7) (1) m Rd y = (2) m Rd z = M Rd z f cd × h × b 2 (3) Thus given a rectangular reinforced concrete section with side lengths (b/h) and design compressive strength fcd. It is to be recognized that in the process. The resulting design yield strength of the reinforcement in the square cross section of unit-length side is in conformity with the transformation of the design compressive strength of concrete. The design values of the axial load and biaxial bending resistance of the transformed section will then give the relative design axial load and biaxial bending resistance Rd. MRd y. EQUIVALENCE BETWEEN THE RELATIVE DESIGN AXIAL LOAD AND BIAXIAL BENDING RESISTANCES OF A RECTANGULAR SECTION AND THE ASSOCIATED SQUARE CROSS SECTION OF UNIT-LENGTH SIDE Biaxial interaction diagrams for solid rectangular cross section made of reinforced concrete are presented in non-dimensional form as: n Rd = N Rd f cd × b × h M Rd y f cd × b × h 2 (4) (5) (6) f cd × h × b 2 = 1 Equation (4) to (6) represents a system of independent simultaneous equations in b. f cd × b × h = 1 f cd × b × h 2 = 1 ii. where. µRd z are the relative values of the design axial load and biaxial bending resistance of the rectangular cross section. The design compressive strength of the concrete fcd in the square cross section of unitlength side is equal to 1. µRd y. NRd. there is an alternative way of determining its relative values of the design axial load and biaxial bending resistance. provided that. iii. and h is the design compressive strength of concrete. Assuming that the cover in the rectangular section (Fig.5/ 0. As an example.The use of Square Cross Sections of Unit-Length Side for the Analysis COORDINATE TRANSFORMATION MATRIX Rectangular Solid Cross-Sections The transformation of a rectangular cross-section with side lengths b and h into a square cross section of unit-length side can be expressed in matrix form as: é1 b 0 ù ìb ü ì1ü ê 0 1 hú íh ý = í1ý ë ûî þ î þ 33 (8) Thus given a rectangular reinforced concrete section (Fig. provided that they satisfy the conditions of equal dimensionless cover in the y.(c h) þ (11) (9) é1 b 0 ù ì(b 2) . the coordinate of the location of the reinforcement in the transformed section is: ì0. 1(b)). will be used to determine the coordinates of any desired point in the associated square cross section of unit-length side (Fig.4þ h /h (12) h h y (b/2-b . 0.5þ Therefore equivalent square cross sections of unitlength side can be made to represent all rectangular sections regardless of their aspect ratios. h/2) z b (0. although it is not in accordance with the usual practice where equal absolute cover is provided in both directions.3ü í ý=í ý ' î0.5 .and z.5.5ü ý=í ý 2 þ î0.c þ î0. (8).e. (11). the rebar location in the positive quadrant in the square cross section of unit-length side is determined by the transformation given in Eq. as opposed to the symmetrical location of the reinforcement with equal y.5 .5 .(c h )þ î0. it can be shown that the coordinates of the location of the reinforcement in the transformed section is a function of the aspect ratio of the original rectangular section. the transformation matrix in Eq. in both directions. i.5 . This property is exploited in the preparation of biaxial interaction diagrams. (9) and (10) respectively. é1 b 0 ù ìb ê 0 1 h ú íh ë ûî 2 ü ì0.( h h) þ (10) Assuming further that c = 0.and z. Journal of EEA.c ' ü ì0.h þ î0. the coordinate of the corner concrete fibre and rebar locations in the positive quadrant. 2009 .directions. The result of the transformation shows that.(c ' b) ü ì0.(c ' b ) ü =í ý ê 0 1 húí 'ý ' ë û î( h 2) . On the other hand it can be observed from Eq. are determined in Eqs.5) (a) (b) Figure 1(a) Rectangular solid section.5 (h /h)) h b b h /h b /b z 1 b /b (b/2. the rebar are placed further apart in the direction of the larger dimension.b ' ü ì 0. h/2-h ) 1 y (0.2 × b and that the aspect ratio b/h = 0. Vol. b / b = h / h.5 (b /b). 1 (a)) is equal in both directions with b = h = c . and (b) Square cross section of unit-length side For a given size of concrete cover that can be expressed as a fraction of the length of one side of a rectangular cross section. 26.5 . h. The following example shows the differences observed in a square cross section of unit-length side when equal absolute cover is provided in the actual rectangular cross section instead of equal dimensionless cover.5 . é1 b 0 ù ì(b 2) .coordinates for the case of equal dimensionless cover. (10) that. the rebar location can be made independent of the aspect ratio by choosing equal dimensionless covers. 1(a)).(b ' b) ü =í ý ê 0 1 húí 'ý ' ë û î( h 2) . Thus the relative values of the design axial load and biaxial bending resistance of a rectangular hollow section with design compressive strength fcd can be determined by using a transformed square hollow section of unit length side with the corresponding design compressive strength of concrete equal to 1/a.5) and (0. 26. and µRd z. wb = wh = 0. which is the ratio of the wall thickness to the corresponding edge length.4 × b ü ì0.4. (13) to (15) that the design axial load and biaxial bending resistance of an associated rectangular hollow cross section whose side lengths and design compressive strength of concrete fcd satisfy Eq.5) (0. The solutions are: b = 1. 2009 . 0.5ü ý=í ý 2 þ î0. h.5. the hollow rectangular section has one additional parameter.4ü ê 0 1 h ú í0. and fcd = 1/a (19) (13) m Rd y = (14) m Rd z = (15) where.34 Rectangular Hollow Cross Sections Girma Zerayohannes f cd × a × b × h = 1 f cd × a × b × h 2 = 1 f cd × a × h × b 2 = 1 (16) (17) (18) Figure 2(a) and (b) show the actual rectangular hollow section with uniformly distributed reinforcement along the edges and the associated square hollow section of unit-length side respectively. a is the fraction of the solid part of the cross section which will be referred to as solidity ratio in short and the definitions of other variables are as in Eq. Moreover the solutions indicate that the coordinate transformation matrix for rectangular hollow sections is the same as that for rectangular solid cross section described in section 3. Compared to the solid rectangular section. 2(a) with b/ h = 2. (1) to (3).5þ (20) é1 b 0 ù ì0.4/0. of the original rectangular hollow section.4 × b. µRd y. é1 b 0 ù ìb ê 0 1 h ú íh ë ûî 2 ü ì0. and (b) Square cross section of unit-length side Biaxial interaction diagrams for hollow rectangular cross section made of reinforced concrete are presented in non-dimensional form as: n Rd = N Rd f cd × a × b × h M Rd y f cd × a × b × h 2 M Rd z f cd × a × h × b 2 Equation (16) to (18) represents a system of independent simultaneous equations in b. h = 1.3ý ë ûî þ î þ (21) Journal of EEA. Therefore for the example hollow cross-section shown in Fig.5/0. (16) to (18) would be identical to the required relative values of the design axial load and biaxial bending resistance Rd. (20) and (21).3) respectively as determined by the transformations shown in Eqs.2 × h.3 × h ý = í0. Vol. and fcd. It can be seen from Eq. 0.3 × h) wh h y wh wb (b/2.0. (0. 0.1.3) wh /h 1 y wh /h wb /b z 1 wb /b (b) (a) Figure 2(a) Rectangular hollow section. h/2) z b wb (0. the outer and inner corner points of the transformed concrete section in the positive quadrant have the coordinates (0. The use of Square Cross Sections of Unit-Length Side for the Analysis The locations of individual rebar in the square hollow section of unit-length side are also determined using the same transformation matrix. AREA AND STEEL STRENGTH TRANSFORMATION Rectangular solid sections The transformation of the rectangular cross section into the equivalent square cross section of unitlength side and the transformation of the design compressive strength of concrete fcd into unity have consequences on the magnitudes of cross sectional areas and material strengths that will be used in the transformed section. According to the solutions in Eq. (7), the gross cross sectional area b × h of a solid reinforced concrete section is transformed into the unit area, 1 × 1 = 1, while the design compressive strength of concrete fcd is transformed into unity. Therefore the transformation coefficients for areas and design strengths of materials are 1/(b × h) and 1/fcd respectively. Thus using the superscript u to designate the square cross section of unit-length side, the transformed area of reinforcement Asu , and design u yield strength of reinforcement f yd are: u f yd u f cd 35 (26) wu = r u × u Substituting f cd = 1 u w u = r u × f yd (27) u Substituting further for r u and f yd from Eqs. (25) and (23) wu = r × f yd f cd =w (28) Equation (28) indicates that under the transformation. is also invariant Finally from Eqs. (24), (25), and (28): Asu = w × f cd f yd (29) Asu = As b×h f yd f cd (22) u f yd = (23) Equation (29) gives the transformed area of steel in the square cross section of unit-length side in terms of the mechanical reinforcement ratio , the design compressive strength of the concrete, and yield strength of the reinforcement in the original cross section. This same amount of concrete area is to be deducted if the analysis would be based on net cross section. Usually analysis is based on gross cross sections as the use of net cross sections does not affect the result significantly. The effect of the displaced amount of concrete on the cross section capacity may however be significant if high strength of concrete is used requiring analysis on the basis of net cross section for high strength concrete [3] [4] . The transformed area of reinforcement Asu can also be expressed in terms of the transformed design u yield strength of reinforcement f yd as: Asu = w u f yd Further the geometric reinforcement ratio in the transformed section is: ru = u Asu b × hu u (24) u s (30) Substituting b = h = 1 and the expression for A from Eq. (22) u A r = s =r b×h u (25) Additional analytical advantage can be gained by u setting f yd = 1, because it allows the direct substitution of the reinforcement data by the mechanical reinforcement ratio . It is to be noted that this is not a consequence of the transformations discussed so far. It is rather an isolated action that allows the substitution of the amount of reinforcement Asu in the square cross section of unit-length side by , provided that u f yd =1. The direct use of w as reinforcement data Equation (25) indicates that the geometric reinforcement ratio is invariant under the transformation. Similarly the mechanical reinforcement ratio in the transformed section is: Journal of EEA, Vol. 26, 2009 36 Girma Zerayohannes Similarly the mechanical reinforcement ratio in the transformed section is: wu = r u × u Substituting f cd = 1 / a u f yd u f cd can be used advantageously in the calculation of biaxial interaction diagrams where it can be systematically varied to cover the practical range of the mechanical reinforcement ratio. Rectangular Hollow Sections The gross concrete area plus the hollow part of the cross section constitute the total area equal to b × h. According to the solutions in Eq. (19), this area is transformed into the unit area, 1 × 1 = 1, while the design compressive strength of concrete fcd is transformed into 1/a. Therefore the transformation coefficients for areas and design strengths of materials are 1/(b × h) and 1/(a × fcd) respectively. Using the superscript u to designate the square cross section of unit-length side, the transformed area of reinforcement Asu and design yield strength u of reinforcement f yd are: (36) u w u = a × r u × f yd (37) u Substituting further for r u and f yd from Eqs. (35) and (32) wu = r × f yd f cd =w (38) Equation (38) indicates that under the transformation. is also invariant Asu = u f yd = As b×h f yd Finally from Eqs. (34), (35), and (38): f Asu = a × w × cd f yd (31) (39) (32) a × f cd Similarly the transformed area of concrete Acu is: Acu = Ac a ×b×h = =a b×h b×h (33) Equation (39) gives the transformed area of steel in the square hollow section of unit-length side in terms of the solidity ratio, mechanical reinforcement ratio , design compressive strength of the concrete, and yield strength of the reinforcement in the original rectangular hollow section. This same amount of concrete area is to be deducted if the analysis would be based on net cross section. The transformed area of reinforcement Asu can also be expressed in terms of the transformed design u yield strength of reinforcement f yd as: Asu = w u f yd Since Eq. (33) can be rewritten as Acu = a × 1× 1 , it can be concluded that the solidity ratio does not change under the transformation. The geometric reinforcement transformed section is: ratio in the (40) ru = Asu a × bu × hu (34) Substituting bu = hu = 1 and the expression for Asu from Eq. (31) Thus the amount of reinforcement in the hollow square cross section of unit length side can be u replaced by by setting f yd = 1. CONCLUSIONS The following conclusions can be drawn from this study: 1. The relative values of the design axial load and biaxial bending resistance of a rectangular reinforced concrete section is identical to the design axial load and biaxial bending resistance of an associated square cross section of unit-length side, provided that the design ru = As =r a ×b×h (35) Equation (35) indicates that the geometric reinforcement ratio is invariant under the transformation. Journal of EEA, Vol. 26, 2009 The use of Square Cross Sections of Unit-Length Side for the Analysis u compressive strength of concrete f cd that is used in the analysis of the square cross section of unit-length side is equal to one and its rebar locations are in conformity with the transformation of the side lengths of the actual rectangular cross section. 37 ACKNOWLEDGMENTS The Author would like to express his deepest appreciation to the German Academic Exchange Service, DAAD, for sponsoring this study in the summer of 2008 at the Technical University of Kaiserslautern, Germany. Special thanks go to professor, Dr.-Ing. J. Schnell, Head of the Institute of Concrete Structures for supervising the work and providing me with suitable space and necessary equipments to carry out my study successfully. REFERENCES [1] Cedolin, L., Cusatis, G., Eccheli, S., Rovda, M., Capacity of Rectangular Cross Sections under Biaxially Eccentric Loads , ACI Structural Journal, April 2008, pp. 215-224. [2] ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (318R-05), American Concrete Institute, Farmington Hills, MI, 2005, 430 pp. [3] DIN 1045-1:2001-07, Tragwerke aus Beton, Stahlbeton und Spannbeton. Teil 1: Bemessung und Konstruktion. [4] Zilch, K., Jähring, A., Müller, A., Erläuterungen zu DIN 1045-1, Deutscher Ausschuss für Stahlbeton , Heft 525. Berlin: Beuth Verlag, 2003. [5] Zerayohannes, G., Bemmesungsdiagramme fuer Schiefe Biegung mit Laengskraft nach DIN 1045-1 : 2001-07, Schriftenreihe der Fachgebiete Baustofftechnologie und Bauschadenanalyse, Massivbau und Baukonstruktion und Stahlbau des Studienganges Bauingenieurwesen der Technischen Universitaet Kaiserslautern, Band 4, 2006, 270 pp. 2. Design axial load and biaxial bending resistance are calculated on the basis of net cross section for high strength concrete by deducting the amount of the transformed area of steel Au = w × f cd from the square cross s f yd section of unit-length side. The relative design axial load and biaxial bending resistance of a rectangular hollow reinforced concrete section with solidity ratio is identical to the design axial load and biaxial bending resistance of an associated square hollow section of unit-length side, provided that the design compressive strength of concrete, f cd that is used in the analysis of the square cross section of unit-length side is equal to 1/a, and its rebar locations are in conformity with the transformation of the side lengths of the actual rectangular hollow section. u 3. 4. Design axial load and biaxial bending resistance are calculated on the basis of net cross section for high strength concrete by deducting the amount of the transformed area of steel Au = a × w × f cd from the square s f yd hollow section of unit-length side. Journal of EEA, Vol. 26, 2009 38 Girma Zerayohannes Appendix-Verification Calculations of Axial Load and Biaxial Bending Resistance of Rectangular and Equivalent Square Cross Section of Unit Length-side Table 1: Input Data for the Calculation of a Typical Interaction Curve-Normal Strength Concrete Square cross section of unit length-side C12/15 up to C50/60; dimensionless cover = 0.1; nEd = -0.8, and w = 0.5 (4- corner reinforcement arrangement based on gross cross section) 2 1. -2.000 -3.500 .0000 .0000 2.000 1. -2.174 25.000 .0000 2.174 1.000 2 3 1 1 1 5 .5000 .5000 .0000 1 2 5 .4000 .4000 .125 w/4 3 -.8 1.0 1.0 0 0 0 fcd fyd Table 2: Analysis Result of the Square Cross Section of Unit-length Side Used as Coordinates for the Example Interaction Curve and Design Normal Load and Moment Resistances of the Actual Cross Section [5] Edy Edz -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 0.2409 0.2394 0.2377 0.2357 0.2335 0.231 0.2264 0.2213 0.2163 0.2114 0.2065 0.2017 0.1968 0.192 0.1871 0.1823 0.1774 0.1726 0.1677 0.1628 0.1578 0.1528 0.1478 0.1428 0.1376 0.1324 0.1272 0.1218 0.1164 0 0.0084 0.0166 0.0248 0.0328 0.0407 0.0481 0.0552 0.062 0.0687 0.0752 0.0815 0.0876 0.0936 0.0995 0.1052 0.1109 0.1164 0.1218 0.1272 0.1324 0.1376 0.1427 0.1478 0.1528 0.1578 0.1628 0.1677 0.1726 N -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 -2901.33 MEdy 698.9312 694.5792 689.6469 683.8443 677.4613 670.208 656.8619 642.0651 627.5584 613.3419 599.1253 585.1989 570.9824 557.056 542.8395 528.9131 514.6965 500.7701 486.5536 472.3371 457.8304 443.3237 428.8171 414.3104 399.2235 384.1365 369.0496 353.3824 337.7152 MEdz 0 12.1856 24.08107 35.97653 47.58187 59.04213 69.77707 80.0768 89.94133 99.6608 109.0901 118.2293 127.0784 135.7824 144.3413 152.6101 160.8789 168.8576 176.6912 184.5248 192.0683 199.6117 207.0101 214.4085 221.6619 228.9152 236.1685 243.2768 250.3851 Ru/R 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Journal of EEA, Vol. 26, 2009 004692 -.0843 95.174 1.33 -2901.2203 288.33 -2901.174 25.based on gross cross section (b/ h = 0.1823 0.8827 160.125 /4 3 -.000 434782.7579 305.000 3 3 1 1 1 5 .1871 0.004692 1 2 5 .1568 236.33 -2901.0000 2.5541 118.0876 0.1536 139.4656 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 39 Table 3: Example Input Data for Verification Calculation of the Actual Cross Section Actual cross section C20/25 .0248 0.0084 0 0.33 -2901.1803 199.3483 264.3104 214.000 2 3 1 1 1 5 .062 0.2065 0.4000 -.2264 0.2114 0.4000 -.33 -2901.8 -0.16213 24.33 -2901.7792 321.4587 218.2377 0.004692 .004692 -.95307 48.3 -2.5648 254.174 1.8 -0.6709 313.528 285.0000 .8 -0.5995 299.0936 0.0328 0.4197 278.200 .8 0.2163 0.5 (4corner reinforcement arrangement based on net cross section) 2 fcd 1.6827 271.0000 .33 -2901.8 -0.33 -2901.1.2357 0.4565 271.16373 71.8 -0.4000 -.33 -2901.4000 .000 -3. 26.4000 .4m/ 0.33 -2901.4000 -.5000 .0687 0.0752 0.000 .5000 .2896 349.8 -0.4000 .4309 335. dimensionless cover = 0.8235 347.8 -0.8 -0.8 -0.8m) 2 11333.33 -2901. 2009 .2335 0.2409 -2901.1600 .200 -2.0 1.4000 .500 .8.8 -0.2017 0.4912 292.104 338.0166 0.33 -2901.9221 344.000 .5627 306.2213 0.8 1.8 -0.33 -2901.7307 341.8 -0. -2.4000 . nEd = -0.33 -2901.3200 0.1052 0.8 -0.0481 0.1774 0.2000 .33 321.0 0 0 0 Journal of EEA.0000 2.0000 1 2 5 .174 25.2394 0.8 -0.1109 0.4085 0 0 0 fcd fyd Table 4: Input Data for the Calculation of a typical Interaction Curve-High Strength Concrete Square cross section of unit length-side C100/115.4000 -.231 0.0325 328.6 -2.33 -2901.The use of Square Cross Sections of Unit-Length Side for the Analysis -0.3216 179.0010426667 As/4 3 -2901.192 0.0815 0.1968 0.0407 0. -2. Vol.0000 2.0552 0.8 -0.4000 -.0000 4 1 1 .550 fyd 1.8 -0. and w = 0.0000 1.3712 0 257.0995 0.33 -2901.33 414. 584 1 -0.7056 928.1048 0.3872 1 -0.8 0.5184 832.1174 -13056 682.0251 0.859 317.8 0.8 0.8 0.8 0.8 0.8 0.5024 1 -0.0108 -13056 2017.0928 -13056 1017.9232 1 -0.2592 1 -0.1207 -13056 635.32 1 -0.995 363.0523 0.0576 1 -0.1142 -13056 727.472 1 -0.482 133.8 0.1589 -13056 71.0655 -13056 1368.328 1 Journal of EEA.8 0.0988 0.2848 980.8 0.131 -13056 490.1275 -13056 540.597 508.23 586.216 385.742 406.0686 0.0414 -13056 1664. 26.1346 0.0414 0.648 953.0623 -13056 1408.152 1 -0.1275 0.933 468.944 294.8528 1 -0.2944 1 -0.0557 0.6688 1 -0.765 488.8256 809.0686 -13056 1329.304 724.8 0.5312 1 -0.111 0.8 0.645 191.338 219.1152 644.563 163.8 0.8288 766.8 0.8 0.8224 1 -0.131 0. Vol.8 0.152 70.0748 0.0557 -13056 1490.8 0.0048 1008.64 270.101 447.6816 878.0958 -13056 976.0779 0.0809 -13056 1172.0523 -13056 1532.9136 1 -0.0376 -13056 1710.1079 -13056 813.1174 0.576 1 -0.8 0.1635 -13056 0 1067.5888 625.8 0.6304 1 -0.1152 1 -0.0158 0.1422 0.598 35.8 0.656 0 1 -0.398 566.0055 -13056 2074.336 245.0655 0.3824 1 -0.059 0.808 1037.8 0.0205 -13056 1907.1207 0.0451 -13056 1618.8 0.9664 1 -0.7408 1 -0.8 0.8 0.8 0.8 0.0839 -13056 1133.1018 0.0717 0.8 0.062 605.0108 0.1018 -13056 895.8 0.8 0.0868 0.0487 0.4528 1 -0.8 0.8 0.2192 745.1142 0.0336 -13056 1757.5056 1 -0.269 427.299 1 -0.4128 1 -0.0898 -13056 1056.4976 1 -0.3712 1 -0.8272 787.0623 0.1545 0.0487 -13056 1575.0294 0.3408 1 -0.6992 1 -0.1344 1 -0.774 341.8 0.8464 902.0158 -13056 1961.1048 -13056 855.111 -13056 770.8 0.011 103.429 528.0779 -13056 1211.0958 0.6944 1 -0.8 0.4144 1 -0.8208 1 -0.608 1 -0.8 0.168 1 -0.8 0.124 0.0988 -13056 936.9296 1 -0.261 547.7984 1 -0.0055 0.6416 664. 2009 .1079 0.1383 -13056 383.1502 -13056 206.1346 -13056 438.0809 0.0717 -13056 1289.168 684.40 Girma Zerayohannes Table 5: Analysis Result of the Square Cross Section of Unit-length Side Used as Coordinates for the Example Interaction Curve and Design Normal Load and Moment Resistances of the Actual Cross Section [5] N MEdy MEdz Ru/R Edy Edz -0.0251 -13056 1856.9056 855.1635 0 -13056 2134.8 0.3888 704.0294 -13056 1805.0336 0.0898 0.8 0.2816 1 -0.8 0.8 0.0376 0.1424 1 -0.8 0 0.8 0.904 1 -0.824 1 -0.1422 -13056 327.0205 0.1589 0.5504 1 -0.8 0.1383 0.0839 0.6096 1 -0.124 -13056 588.8 0.1502 0.1461 -13056 267.0748 -13056 1250.1461 0.0868 -13056 1095.0928 0.8 0.8 0.2144 1 -0.0451 0.1545 -13056 141.059 -13056 1449. 1600 -. Vol.9664 0 0 0 fcd fyd Journal of EEA.1600 . 26.004692 -.3200 -.4m/ 0.200 .2000 .3200 -.004692 .004692 1 2 5 .1600 -.550 434782.The use of Square Cross Sections of Unit-Length Side for the Analysis 41 Table 6: Example Input Data for Verification Calculation of the Actual Cross Section-High Strength Concrete Actual cross section .1600 .004692 -. 2009 .0000 .004692 As /4 3 -13056.4000 .174 1.000 .000 3 3 1 1 1 5 .3200 -.200 -2. 936.1600 .3200 .61 -2.0000 4 1 1 .C100/115 (based on net cross section (b/ h = 0.174 25.8m) 2 51000 -2.0000 1.3200 -.1152 644.0000 2. 1500 .4500 -.0555555555555555 .4000 .0555555555555555 .0033886666565006667 -.4500 -.4000 -.0033886666565006667 .4000 -.5000 -.0000 2. 2009 .0033886666565006667 .0555555555555555 .0750 .185 .0.0000 -.0033886666565006667 .0000 .3000 . Ed = -0.4000 -.923076923 -2.4000 -.5000 .2666666667 -.4500 -.0000 .174 1.0033886666565006667 10 2 5 .4000 -.4500 .4000 .3750 -.2666666667 -.4000 .3000 .0555555555555555 .0033886666565006667 -.3000 .0033886666565006667 .1333333333 -.4500 .1500 -.0555555555555555 3 -.0750 -.0555555555555555 .52) .5000 .2250 -.1500 .4500 .0000 36 1 1 . Vol.0033886666565006667 .0033886666565006667 .1500 -.5000 .2250 .3750 .3000 .1333333333 -.4000 -.4000 -.0033886666565006667 .4000 -.000 .2250 .0 .3000 .4000 -.0033886666565006667 .0000 4 1 1 .2250 -.1500 .0033886666565006667 -.3750 . C100/115.4500 .4000 -.0555555555555555 .0000 .4000 .0000 .2666666667 -.0033886666565006667 .4500 .0033886666565006667 .4000 .3750 -.0033886666565006667 .1333333333 -.0033886666565006667 -.4500 .174 25. -2.0033886666565006667 -.20 -2.0000 -.0000 1.0555555555555555 .4000 -.0033886666565006667 .4000 -.0033886666565006667 -.4000 .0033886666565006667 -.5000 .5000 .0000 .0033886666565006667 .4000 -.4000 -.8 .5000 .0033886666565006667 .0033886666565006667 -.4000 -.0033886666565006667 .0033886666565006667 -.4000 -.2961538 0 0 0 = 2.0555555555555555 .4500 .2250 .4500 .0033886666565006667 .4000 -.3000 -.200 .4000 -. Ac = a × b × h.0033886666565006667 -.0750 .based on net cross section a × ( /36) × fcd/ fyd / 36 Journal of EEA.8 and 2 1.2.4000 -.4500 .4500 .0033886666565006667 -.4000 -.4000 -.2666666667 .550 1.4000 -.High strength concrete fcd fyd Square hollow section of unit-length side.4000 .0033886666565006667 .4000 -.3000 -.1333333333 -.0000 -.3000 .3000 .2666666667 -.4500 .42 Girma Zerayohannes Table 7: Input Data for the Calculation of a typical Interaction Curve for Rectangular Hollow Section (b/h = 2.0750 .4000 -.0000 .000 4 3 1 4 1 1 -.0750 -.0033886666565006667 -.4000 .3750 .0000 .4500 -.0033886666565006667 -.4000 -.0033886666565006667 -.5000 -.0033886666565006667 -.4000 -.0555555555555555 .4000 -.4500 .0000 -.0033886666565006667 . a = 0.0033886666565006667 -.0000 -.4000 -.4000 . wh/ h = wb/ h = 0.1333333333 .0000 -.4500 -.4500 -. 26.0033886666565006667 -. 07576923 0.59878 8802.6012 18880.7967 43921.3984 22929.3976 26377.6 25520.4763462 0.08846154 0.8024 13055.4024 24398.8 -0.8 -0.2012 9812.1230769 0.8 -0.1992308 0.59755 6670.01730769 0.1992 15167.8 -0.9951 32252.00016 10669.08134615 0.4032692 0.4938461 0.45 N -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 -42432 MEdy 26193.8 -0.2565385 0.8 -0.8 -0.1438462 0. 26.9992 20705.3636538 0.4008 29722.2219231 0.2078846 0.1632692 0.305 0.1726923 0.1042308 0.9996 17758.2036538 0.1905769 0.2126923 0.2049 16299.03326923 0.8 -0.2161538 0.1817308 0.0625 0.79984 4314.8 -0.02980769 0.99988 805.3457692 0.40286 7762.1976 11872.2004 17217.8 -0.3371154 0.0024 28886.1005769 0.8 -0.79959 5528.8 -0.5984 13219.8 -0.3348077 0.8 -0.99976 3529.8 -0.8 -0.2582692 0.20008 1580.3546154 0.19992 5120. Vol.185 0.79837 6109.1257692 0.198 11770.6008 47736 Ru /R 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Journal of EEA.1996 10801.4008 22807.1944231 0.39992 6630 8037.2675 0.5951 23806.1561539 0.5971 25265.2 13698.6008 16697.8 -0.7996 12250.2401923 0.04826923 0.The use of Square Cross Sections of Unit-Length Side for the Analysis 43 Table 8: Analysis Result of a Square Hollow Cross Section of Unit-length Side Used as Coordinates for the Example Interaction Curve and Design Normal Load and Moment Resistances of the Actual Cross Section [5].3903846 0.1935 45124.3984 34863.9976 40595.05673077 0.1463462 0.8 -0.4253846 0.06923077 0.3246154 0.9951 15259.04346154 0.59796 8282.8 -0.1536538 0.9992 20073.9976 14177.8 -0.01519231 0 0.0033 20216.1976 31415.2767308 0.6041 28050.2244231 0.8 -0.8 -0.3826923 0.8 -0.3121154 0.8 -0.1151923 0.8 -0.3203846 0.2644231 0.43 0.1361538 0.8 -0.8 -0.5967 18319.3286538 0.7976 21368.20245 7221.2016 36679.2405769 0.8 -0.09307692 0.2309615 0.00004 3009.2486538 0.4373077 0.2 15667.1992 19278.8 -0.3928846 0.1119231 0.59992 9384.4004 16177.2953846 0.2492308 0.8 -0.8 -0.3451923 0.2325 0. Ed Edy Edz -0.3784615 0.800122 0 MEdz 1835.4 23582.3148077 0.4446154 0.1984 42778.398 14677.3040385 0.8 -0.2859615 0.8 -0.8 -0.8 -0.8016 14188.2723077 0.2801923 0.3559616 0.4028846 0.5951 17319.1659615 0.8 -0.8 -0.598 19461.8 -0.4 9312.3730769 0.8 0.4041 33109.7992 30559.8012 11281. 2009 .4033 22052.3951 39575.1755769 0.8 -0.2 22072.2016 33986.2880769 0.1967 37617.3669231 0.7984 46389.2016 12739.40163 4936.00004 2305.5998 3672.1951 27213.3976 21134.8 -0.8024 24663.1336538 0.8 -0.2033 18308.4161538 0.9992 41677.4140384 0.8 -0.2961538 0.7976 10312.5951 35761.8 -0.46 0.6016 38576.8 -0. 3000 .7500 -.9000 -.4500 .4000 .006777333333333 .006777333333333 . 2009 .1333333333 -.0000 4 1 1 .0000 -.4000 -.000 .0000 .006777333333333 .006777333333333 10 2 5 As / 36 .006777333333333 .0000 .5000 .1500 -.3000 .006777333333333 .006777333333333 -.006777333333333 -.006777333333333 .9000 .4000 -.006777333333333 .4000 .006777333333333 .9000 .5000 .4000 -.174 1.4000 -.006777333333333 .0000 1.1500 .1500 .6000 -.006777333333333 .006777333333333 .2033 15259.0000 .3000 .2666666667 -.2666666667 -.006777333333333 -.5000 .8000 .9000 .4000 .006777333333333 .9000 -.9000 .3000 .0 m.006777333333333 .6000 .4000 .4000 -.006777333333333 .174 25.4000 -.1333333333 -.4000 -.2666666667 .6000 .000 -.006777333333333 3 -42432 18880.0 m. a = 0.52.61 -2.3000 .7500 .000 -.4000 -.4500 .006777333333333 -.4000 -.0000 -.8000 -.000 .0000 1.2666666667 -. h = 1.2666666667 -. Vol.006777333333333 -.9000 .006777333333333 .4000 -.6000 .006777333333333 -.4000 -.0000 -.006777333333333 -.4000 -.8000 -.1500 .006777333333333 -.4000 -.006777333333333 .000 fyd 434782.006777333333333 .006777333333333 -.4000 -.0000 2.1333333333 .1500 -.0000 -.1333333333 -.4000 .0000 36 1 1 As / 36 .9000 .200 .4000 -.8000 .44 Girma Zerayohannes Table 9: Example Input Data Verification of the Actual Cross Section Actual Cross Section.4000 -.4000 -.006777333333333 .9000 -.9000 .006777333333333 -.006777333333333 -.9000 .006777333333333 -.4500 -.6000 -. b = 2.0000 -.550 .200 -2.006777333333333 .9000 . wb/h=wh /h=0.2049 0 0 0 Journal of EEA.4500 -.20 C100/115 (based on net cross section) 2 fcd 51000 -2.006777333333333 .9000 .006777333333333 -.4000 -.3000 .000 4 3 1 4 1 1 -1.006777333333333 .9000 -.4000 .4000 -.0000 .4000 .0000 1.006777333333333 .3000 -.9000 .4000 -.006777333333333 .006777333333333 .4500 .006777333333333 .4000 -.9000 -.4000 -.006777333333333 -.9000 .4000 -.7500 -.006777333333333 .7500 .4000 -.006777333333333 -.006777333333333 -. 26.006777333333333 -.0000 -1.3000 -.006777333333333 .5000 .4000 -.1333333333 -.0000 .4000 -.7500 .3000 .9000 -. Vol. Finally. the subgrade is idealized as an elastic continuum of finite thickness. Thus. which replaces the subgrade by a mechanical analogy consisting of a single bed of closely spaced vertical springs acting independently of each other. In the second approach. 8. 3. 4. Winkler-type models. Shear interaction. w0 is the corresponding vertical deformation. Winkler's model has the well-known shortcoming of bringing about a vertical deformation of those springs alone that are located just under the loaded region. It only demands specifying a relationship between the vertical and horizontal normal stresses. Mathematically. mainly due to the simplicity of Winkler's model in practical applications and its long time familiarity among practical engineers. Both are consequences of the neglected vertical shear stresses that would have coupled the vertical deformations of neighboring points with each other so that continuity of displacement exists. Winkler model. However. Simplified continuum. mechanical models are developed that involve different combinations of spring beds and shear elements [3. 9]. Accordingly. Because of this. 26. INTRODUCTION The simplest representation of a foundation subgrade is in the form of the classical Winkler model. Winkler's model translates into p ( x. its usage has endured to this date. all the normal components of the stress tensor are taken into consideration. a generalized formulation for the classical singleparameter Winkler's subgrade model is presented. The models give consistently larger stiffness for the Winkler springs as compared to previously proposed similar continuum-based models that ignore the lateral stresses. It has also been pointed out that it is only if the shear stress components of the subgrade are taken into consideration that a multiparameter model evolves regardless of whether the lateral normal stresses are included. Keywords: Heterogeneous subgrade. Both approaches can be judiciously synthesized for the purpose of solving practical problems. Many current commercial softwares continued incorporating the model as a major feature of their programs for the purpose of Journal of EEA.y) in the foundation-soil interface area. Furthermore. in which p is the vertical contact pressure at an arbitrary point (x. 9]. and certain simplifying assumptions are made to reduce the mathematical work involved [3. 4. ks is the only quantity characterizing the subgrade material.WINKLER'S SINGLE-PARAMETER SUBGRADE MODEL FROM THE PERSPECTIVE OF AN IMPROVED APPROACH OF CONTINUUM -BASED SUBGRADE MODELING Asrat Worku Department of Civil Engineering Addis Ababa University ABSTRACT Based on an isotropic elastic continuum of thickness H overlying a rigid stratum. the effective stiffness per unit area of the multiple beds of springs of such a higher order model is exactly the same as the subgrade modulus of the corresponding single-parameter Winkler model presented in this work. y ) . whereas the shear stresses are intentionally dropped with the purpose of providing a useful perspective. the model implies that a point undergoes vertical deformation independently of other adjoining points [1. Reissner's simplified continuum. This shortcoming can be overcome by appropriately accounting for the shear stress components of the subgrade. The formulation takes into account the variation of the elasticity modulus with depth. 7]. the model entails a discontinuity of vertical deformation at the edges of the loaded area. two such different assumptions are made to obtain two new Winkler-type subgrade models with the corresponding closed-form relations for the subgrade modulus. y ) = k s w0 (x . In this formulation. with which Winkler's model and its associated coefficient of subgrade reaction can be viewed. whereby the mechanical-model parameters are quantified in terms of the elastic parameters of the continuum [3. In the first approach. 2009 .commonly referred to as the coefficient of subgrade reaction or simply as the subgrade modulus [1-7]. 5]. A number of attempts have been made in the past to incorporate the shear stresses following two different approaches. and ks is a proportionality constant representing contact pressure per unit deformation . he suggested empirical relations for converting ks values from field plate loading tests to ks values of actual foundations that decrease with increasing width. it is pointed out that an additional assumption is needed regarding the variation of the vertical shear stress components with depth. As a pioneer. 2009 .y) z Isotropic. It is shown that the resulting model is a single-parameter Winkler-type x p(x. 26. A number of both analytical and empirical relationships have been suggested in the past for estimating ks. 1. the subgrade is idealized as an isotropic elastic continuum of finite thickness H. the shear components are first intentionally omitted with the normal stress components alone accounted for in the formulation. Two such functions are employed in this work to come up with two correspondingly different sets of closed-form relations for the coefficient of subgrade reaction for constant as well as variable elasticity modulus. Heterogeneity with respect to subgrade rigidity is taken into consideration by assuming a variable elasticity modulus with depth. analysis and design of beams and plates on elastic foundations. Finally. heterogeneous elastic layer Journal of EEA. Vesi [11] later proposed a formula that depends on the rigidity of the beam itself in addition to its width and the elastic properties of the subgrade material. Here. this article attempts to provide some insight into this model and its associated coefficient of subgrade reaction from the perspective of continuum modeling. Terzaghi [10] identified the width of the foundation as the most important influencing factor of ks in addition to the elastic properties of the soil. For long beams. in which only the vertical normal stress components are taken into consideration. In order to clearly understand the influence of the soil shear stress on the form of the resulting mathematical model. Accordingly. Horvath [5] recently derived closed form relations for ks for constant and varying elasticity modulus of the subgrade. for which the coefficient of subgrade reaction can be evaluated from an analytical relation obtained in form of a definite integral. By taking advantage of this important analogy. Vol. In this technique. n H Figure 1 The subgrade idealized as an isotropic. heterogeneous elastic layer: E(z).12 Asrat Worku model. The choice of the functions relating the normal stresses is at the discretion of the user. Recognizing the enduring usage of Winkler's model in wide ranging applications of geotechnical engineering. a brief account of ways of incorporating the shear stress components of the elastic subgrade is presented with the details being presented in the companion paper [9]. Correlations with standard penetration blow counts were also suggested more recently [12]. Open functions of depth are introduced to relate the horizontal and vertical normal stress components. It is pointed out that a three-parameter mechanical model consisting of two beds of springs and a layer of shear element results also in a differential equation of similar form and order to that of the continuum. Based on a subgrade idealized as a simplified elastic continuum of finite thickness. it has been shown that the effective spring stiffness per unit area of the two beds of springs of the three-parameter mechanical model is nothing other than the coefficient of subgrade reaction of the single-parameter Winkler-type model established in the present work by excluding the shear stresses. These are compared with similar relations proposed in the past. A GENERALIZED FORMULATION OF WINKLER'S SUBGRADE MODULUS The subgrade is idealized as an isotropic elastic continuum of thickness H similar to Reissner s simplified continuum [8] as shown in Fig. It has been found that the resulting mathematical models are always second-order differential equations with constant coefficients regardless of the nature of this assumption. ks is the coefficient of subgrade reaction given by ks = 1 H where. through appropriately selected functions. the equilibrium equation for the vertical direction becomes s z. z ) = p ( x. 13 The function f1 in Eq. y )íê ò dz dz ý E (z ) ú z = H ò E (z ) þ û îë (8) t xy = t xz = t yz = 0 (1) With this assumption. 26.p( x. Applying the stress boundary condition at the surface and noting that compressive stresses are negative. (6) is a function of x and y. Substituting the resulting expression back in Eq. Eq. y . (11a) takes the simplified form of where E(z) is the elasticity modulus that may generally vary with depth. and c1 is a constant of integration. z = 1 s z -n (s x + s y ) E( z ) [ ] (5) It is evident from this result that it is always a Winkler-type single-parameter model that evolves for an elastic subgrade as far as the normal stress components alone are taken into account. y ) = . Applying the zero-displacement boundary condition at the interface with the rigid base. y ) + c1 E (z ) (6) ks = 1 H (11b) g ( z ) = 1 . Vol. (3) and (4) in Eq. these two unknowns are readily determined at once. because it is known that the problem is less sensitive to its variation. (6) one obtains the vertical displacement function as ìé g ( z ) ù g (z ) ü w( x. Thus. The primary aim is to study the influence of the normal stress components alone by intentionally excluding the shear effect. y ) = k s w0 (x. (5) and integrating. Equation (2) implies that sz is constant with respect to depth. of the surface in particular is obtained by evaluating Eq. y ) (10) s z (x. which depends only on the elastic properties of the subgrade and. y ) = p ( x. -p(x. so that H é g (z ) ù g (z ) w0 ( x. If the lateral normal stress components are neglected in addition to the vertical shear stresses. (7) reduces to unity and Eq. (8) at z=0. (7). s y = g y ( z )s z ò 0 g (z ) dz E (z ) (11a) (4) The generalized Hooke's law for the normal strain in the vertical direction is given by w. The Poisson ratio is assumed constant. y )ê ò dz ú = p ( x . The lateral normal stresses.p( x.y) is the vertical contact pressure at the surface. can be related to the vertical normal stress. y . y )ò dz (9) E (z ) ë E (z ) û z = 0 0 z= H (2) where the coma sign represents a derivative with respect to the symbol that follows. z ) = .Winkler's Single-Parameter Subgrade Model from the Perspective of The depth-wise heterogeneity is taken into account by assuming a variable elasticity modulus with depth. w0 . implicitly through g(z) of Eq.n g x (z ) + g y ( z ) [ ] 1 ò E ( z ) dz 0 (7) It will be shown in a later section that Eq. g(z) in Eq. sx and sy. y ) (3) where. sz. y )ò where. it follows that This equation is the relationship sought between the vertical surface displacement and the vertical surface pressure that can be written as p ( x. one obtains for the vertical displacement w(x.z = 0 The vertical displacement. gx(z) and gy(z). so that s x = g x (z )s z . 2009 . g (z ) dz + f1 ( x. respectively. (11a) provides a generalized analytical formulation for quantifying the coefficient of subgrade reaction. (11b) is a unified formulation of the closed-form relations Journal of EEA. Substituting Eqs. on the size and shape of the loaded region on the surface as was correctly pointed out by Terzaghi [10]. and B is a dimension-bound coefficient [6. According to Eq. This condition poses some difficulties in the evaluation of the integral in Eq. (13) and (12b). For reasons of mathematical convenience. THE ELASTICITY MODULUS FUNCTION. 2009 . For other values of b. the coefficient B takes the dimension of a stress. Soils. Since the other important function in the estimation of ks using Eq. the assumption is made that k x = k y = k 0 (the coefficient of lateral pressure for at rest condition) and it is noted that this coefficient can be expressed as k 0 = n (1 . (7) and this in turn in Eq. For b = 0.n . (12b) and (13) are further used in this work.2n 2 1 -n (17) In plane-strain problems. (11a). It may thus be expected that Eq. In both Eqs.n ) . are often referred to as Gibson soils [6. (12a) and (12b). then the factor a in Eq. WINKLER-TYPE CONTINUUM MODEL VARIANT I In the development of this particular model. Vol. (17) can give reasonable results for strip foundations and for rectangular foundations with large aspect ratios. For b = 1. 14]. The most commonly employed option is the power function of z given by E (z ) = Bz b (12a) where b is a positive dimensionless constant known as the non-homogeneity parameter. 13. Appropriate values of l can be easily obtained by matching plots of Eqs. two alternative forms of this function that lead to correspondingly two different Winkler-type models are discussed next. what it all demands to estimate the subgrade modulus is to select an appropriate function g(z) that relates the vertical and horizontal normal stresses with each other and to employ a suitable function E(z) for the variation of the elasticity modulus with depth if there is the need to do so. The following sections deal with these two functions. E(Z) (13) where E0 is the elasticity modulus at the surface (for z=0) and l is a non-negative quantity having the dimension of m-1. (12a) represents a homogenous elastic layer with a constant elasticity modulus. In this case. because it can be easily shown in this case that k x = k y = k 0 . B assumes correspondingly different dimensions. 26. (16) becomes dependent only on the Poisson and takes the form This alternative formulation enables the assignment of a non-zero elasticity modulus of E = E0 at z = 0. one obtains ks = 1 dz aò E (z ) 0 H (15) where a is a constant given by a = 1 . Eq. it is common to use b = 1 for clayey soils and b = 1/2 for granular soils [13]. (14) in Eq.14 Asrat Worku E ( z ) = E 0 e lz proposed by Horvath [5] for estimating the subgrade modulus. as a special case. the Young's moduli of which vary in accordance with Eq. 14]. The other form of variation of the elasticity modulus that found some usage in the past is the exponential function given by [13] a= 1 . (11a) at z = 0 when b = 1. (12a). (11a). Eq. B=E0. s y = k ys z (14) where kx and ky are constants that are presumed to be estimated from knowledge of lateral earth pressure theories. (12a) gives a zero value for the elasticity modulus at the surface (z = 0). Eq. Substituting Eq. (12a) represents a heterogeneous soil layer with a linearly varying elasticity modulus. A more suitable variant for such a case is the form s x = k xs z . (4) are assumed constant so that The depth-wise variation of E(z) can be taken into consideration in one of two different forms: a power function or an exponential function of z. Journal of EEA. The coefficient B takes in this case the dimensions of the coefficient of subgrade reaction. the assumption of k x = k 0 alone is sufficient. only the relations in Eqs. For the general case of a heterogeneous layer (b ¹ 0).n (k x + k y ) (16) E ( z ) = E 0 + Bz b (12b) If. the functions gx and gy in Eq. (11a) is g(z). 6 0. the functions gx(z) and gy(z) are taken as g x ( z ) = rx e-zz . (12b) and (13) in Eq. the constants rx and ry.5 nz.5 1 1. 15]. nz and nr represent the normal stresses in the vertical and radial directions. 2009 . and noting that r = rx+ry one obtains (22) For E(z)=E0elz: ks = E0 l a 1 . (22) leads to ks = E0 H nr 11 . These constants take the values rx = ry = 0.Winkler's Single-Parameter Subgrade Model from the Perspective of Stratum with Constant E The case of a homogenous stratum corresponds to B = 0 in Eq. 2. Evaluation of the integral in Eq. ï é æ E 0 + B H öù ç ÷ú ï 2a ê B H . With Eq.6 0.8 0. Based on observations of the trend in Fig.lH ks = H ( ) (20) ò 0 ( 1 1 -nre -zz dz E (z ) ) WINKLER-TYPE CONTINUUM MODEL VARIANT II This model is motivated by observations of plots of the depth-wise variation of the horizontal-tovertical normal stress ratio underneath uniformly loaded circular and square regions on the surface of 1. 26. (15) then yields ks = E0 aH 15 (18) both a layered and non-layered elastic half space as presented in Fig. respectively. (12b) and l = 0 in Eq.8 and z = 3. For E(z)=E0+Bzb: B ì . In this figure.2 0 -0. (15) and performing the respective integrals.2 1 Stratum with Constant E For a homogenous soil layer with a constant E =E0. (7). one obtains for the heterogeneous layer. Accordingly.s/b=0.6 nr/nz nr. (21) substituted in Eq. s is the radial coordinate according to the cylindrical coordinate system. this ratio can be represented by a decaying exponential function of z as shown in the figure for a typical vertical plane through the loaded region.5 4 4.8exp(-1. this further in Eq.e . the origin of which is located at the center of the circle. 2 [9].96/H for a typical vertical plane and are indicated in Fig.5 3 3.5 depth ratiio Figure 2 Plots of typical vertical and horizontal stresses and their ratios with depth for a circular region subjected to a uniformly distributed load together with the best-fitting curve for sr/sz [9] Journal of EEA.2 0 0. (13).E 0 lnç ÷ E0 ï ê è øú û î ë b =1 (21) (19) b= 1 2 where. evaluation of the integral in Eq. both of which give a constant modulus of elasticity. Vol. E = E0.9.4 0. depending on the type of E(z) used. (11a). ï æ E 0 + BH ö ïa lnç ÷ ç E ÷ ï è 0 ø ï ks = í B2 ï . b is the radius of the loaded circular region.98z/b) 2 2.e -zH zH (23) ( ) stress ratio 0.s/b=0. 2 [4. and the dimensionbound z can be established from best-fitting curves for the plots of the horizontal-to-vertical normal stress ratio. g y (z ) = rye -zz Stratum with Variable E Substituting Eqs. (13) for E(z) is much more convenient to evaluate the integral of Eq. This plot is referred to as New Variant I in the Fig.a parameter dependant on the soil Poisson ratio.(z + l ) 1 . the evaluation of the integral in Eq. (11b) or be retrieved from Eqs. respectively.e ) . (18) and (19). (12b) with b = 1 and b = 1/2 was used to account for the variation of E. (18) and (19) are derived using the same power function of z of Eq. (12b) for the variation of E. for a linearly varying E (i. 3 together with that of Horvath (1/a = 1). (22) leads to complicated expressions for the coefficient of subgrade reaction. ks takes the form ks = B ¥ é æ E + BH ö (. The cases of both constant and variable E were considered. (26) and (27). (12b). when a = 1 . the use of the exponential function of Eq. (12b). (10) and given by For Constant E (E = E0): For the general case of a heterogeneous stratum. the model presented in this work based on the power function of z for E gives always a Winkler-type subgrade model with a spring stiffness that is 1/a times the stiffness of the corresponding model of Horvath irrespective of how E varies with depth. (22) than using Eq. The foregoing two sections presented two different Winkler-type models together with the corresponding closed-form relations for ks based on two different forms of assumed lateral-to-vertical normal stress ratio distribution with depth. COMPARISON WITH SIMILAR PREVIOUS STUDIES A similar study by Horvath [5] employed the same simplified-continuum idealization of the subgrade. that the approach enables to develop as many such models as the number of different assumptions made. (18) and (19) are now normalized with respect to the respective moduli of Eqs. however. one obtains in both cases 1/a . Journal of EEA.E0 ln ç ç ÷ú E0 ï ê è øû î ë b =1 (26) [ ] It is also possible to use Eq. (24) is much simpler to use than Eq. For example. 2009 . of the models presented in this work. Equations (26) and (27) can be obtained directly from Eq. The plot of 1/a against n is provided in Fig. However.a case that corresponds to kx = ky = 0 or to a condition of zero lateral normal stresses. It is important to note.1)n+1 B n-1 . This yields E0 l (24) ks = lnr -lH -(z + l )H (1 . 26. If Eqs. Vol.16 Stratum with Variable E Asrat Worku The subgrade models obtained were all Winklertype similar to Eq. 3. The power function of z in Eq. Therefore. when b takes the respective values of 1 and1/2. but with only sz taken into account and all other stress components neglected. (25) and demands only selecting appropriate values of l that give variations of E(z) sufficiently closely matching with the power function.e b = 1). where k0 = n (1 -n ) is used for both kx and ky. It is to be noted that Eqs. Obviously.¥ (.1)n+1 B n-1 ù ÷ +nrB êe -zH å n lnç 0 å z nEn ú n ç E ÷ n=1 z (E0 + BH ) n =1 è 0 ø 0 ë û (27) 1 b= 2 (25) The expression for ks becomes even much more complicated in the case of b = 1/2. Eq.e k s = E0 H For Variable E (E = E0 +Bzb): B ì ï æ E0 + BH ö ï ln ç ÷ ÷ ï ç E0 ø ï è ks = í B2 ï æ E0 + B H öù ï é ÷ú ï 2 ê B H . 3 as New Variant II. (27) cannot be retrieved from Eq. so that the simplified expression on the right hand side is commonly employed [18]. Their model takes into account the shear interaction missing in the Winkler model. (23) by substituting r = 0 .2 0. in which they introduced displacement constraints to simplify the continuum. Vol. which shows that this second model presented based on a decaying exponential function for the lateral-to-vertical normal stress ratio also gives consistently larger spring stiffness that increases with increasing n.42). the value of the 12th root multiplied by 0. this relation simplifies to ks 1 = E0 H 1 . according to the authors for relatively shallow The plot of this relation is also given in Fig. which is widely used in practice. This implies that Vesi 's model underestimates deflections.4n (28b) In this equation. the latter case being applicable for a thick stratum or a half space. It can be seen from Fig. (23) can be normalized with respect to Eq. but not as large as in the first model. In the case of an assumed linear variation of the vertical displacement w(x. but becomes indeterminate at n = 0. 3 for the cases of H = B and H = 2B.3 that the plot for the case of H = B almost coincides with that of New Variant II.a case that corresponds once again to zero lateral normal stresses. Vlasov and Leontiev presented [1. because the exponential function used to represent the variation of E in this case is different from the power function used by Horvath [5]. Furthermore. 16] a subgrade model based on the continuum approach. elastic subgrade in terms of the rigidity of the foundation element. Equation (26) of Horvath can also be obtained from Eq.42). However. 26. (26) to get ks 1 = E0 H 1 .z) with respect to depth that is deemed reasonable. Vesi 's relation gives the highest estimate for the subgrade modulus for thick formations of most soils (n 0. and the elastic subgrade properties. Eq. This relation. 2009 . (24) by substituting r = 0. Vesi 's model gives at least double the magnitude of stiffness provided by the new Variant II model of this author for thick strata or a half space.Winkler's Single-Parameter Subgrade Model from the Perspective of 17 10 8 ks/(Eo/H) 6 4 2 0 0 0. whereas New Variant I gives the highest values for soft cohesive soils (n>0.nr 1 .6512 E0 B 4 E0 E0 » E f I f B 1 -n 2 B 1 -n 2 ( ) ( ) (29) (28a) ( ) Using the values of r and z suggested in Eq. which is expressed in terms of n. its size.3 Poisson ratio 0. is given by ks = 0. The plots of this expression normalized with respect to E0 /H are also given in Fig. Eq. EfIf is the foundation rigidity.5 0.65 is close to 1.0.the case of an incompressible fluid.5 . Similarly.e -zH zH Vesi [11] proposed an analytical relation for computing the modulus of the homogenous.6 Figure 3 Plots of the normalized subgrade modulus according to different models Figure 3 shows that the difference between the spring stiffness of the Winkler-type model New Variant I and the corresponding model of Horvath increases with increasing Poisson ratio for both the homogenous and heterogeneous cases. especially for foundations on thick strata. Journal of EEA. whereas the plot for the case of H = 2B is double that of the case of H = B. (21). For relatively large-sized foundations like rafts. The indeterminacy is attributed to the nature of the definition of k0 employed.1 Horvath New Variant I New Variant II Vesic (H=B) Vesic (H=2B) Vlasov 0.4 0. For all practical purposes. the stiffness of the substitute spring responsible for the tributary area A in a Winkler's foundation is given by K = ksA. which is identical to Horvath's result of Eq. but the difference dwindles fast with increasing width of the plate. Figure 4(b) is for a medium stiff clay with n = 0. f2 and c2 are determined from the boundary conditions. it is evident that the stiffness of such a uniaxial member is given by K = EA/H (Figs. Vesi 's subgrade modulus values are consistently larger than those given by the other three models. 2009 . In contrast. In the case of the medium stiff clay (Fig. Such plots for two representative types of thick subgrade material with Ik = 2 are given in Fig. Vlasov's subgrade modulus is the same as that of Horvath. Horvath's model give the least values of subgrade modulus that are independent of Poisson ratio. In the case of a variable E. for which n = 0. and plotted. Equating the two expressions then yields ks = E/H. Figure 4(a) is for a medium dense coarse sand. the following relation is obtained using the uniaxial Hooke's law for the vertical deformation of a typical soil column at the location (x. (26) for the case of constant E. (31) for the variation of E. it can be concluded that Horvath's subgrade moduli form the lower bound for the subgrade modulus values that can be estimated using different assumed functions of g(z) in Eq. the New Variant II. 5(a) and 5(b)). noting that sz=-p(x. Horvath's model. whereas Vesi 's model gives consistently higher values of ks only exceeded by the New Variant I model for soils with n>0. New Variant I gives a bit larger values of ks in comparison. 4(a)). B. With E ( z ) = E 0 + Bz b substituted in Eq. 6(b)): subgrade. 4(b)). where B is the width of the loaded area. 3 and 4. (30) is also included in Fig. y ) + c 2 E(z) (31) where. 3. This is a consequence of the omission of the lateral normal stresses in his highly simplified model. which are close to each other for all sizes of the plates in the case of the medium dense sand. In the case of a constant E. (31) gives expressions for ks identical to Eq. and Vlasov's model give practically identical values of ks for all sizes of the plate. and Vlasov's model give ks values. Vesi 's subgrade modulus fall in this case between values of New Variant I and II. This can be easily verified as follows for both the constant and the variable E.25 and E = 40MPa are taken. the New Variant II. which was also employed by Horvath [5]. INTERPRETATION USING A CLUSTER OF CONTIGUOUS SOIL COLUMNS Horvath's simplified subgrade [5] can be visualized as a medium made up of a cluster of contiguous short columns (no buckling) of each with a height of H and a cross sectional area of A that do not interact with each other at all and are behaving in a uniaxial state of strain. 26. y . 4. This shows that Horvath's subgrade can be idealized as a cluster of contiguous short soil columns that do not interact with each other in any manner. the thickness of the elastic subgrade stratum can be expressed as H = I z B . and Iz is an influence factor dependant on the relative width of the foundation with respect to the thickness of the subgrade (For a half space Iz = 2 is taken).42 Following Schmertmann's semi-analytical approach [15. whereas values of Vesi 's subgrade modulus for H = B are close to those of New Variant II. z ) = ò sz dz + f 2 ( x.18 Asrat Worku As could be observed from Eqs. with the difference from the rest increasing with decreasing plate width.45 and E = 50MPa. Based on the above comparison. These two models interchange positions at about n =0. Vol. New Variant I gives the largest of ks values for all foundation widths. the various relations for ks presented in the preceding sections can be expressed in terms of the foundation width. (27) for b = 1 and 1/2. Using this approach. On the other hand. and applying the boundary conditions at the two ends of the soil column.n 4 ( 2 ) (30) The normalized plot of Eq. w( x. (7). Eq. The plot shows ks increasing with increasing Poisson ratio. In the case of the medium dense sand (Fig. The largest estimates of ks are obtained from Vesi 's model for H = 2B and from the New Variant I. though at a very low rate.42. Journal of EEA. their model results in a subgrade modulus given by ks = E0 H 1 -n + 2n 3 . Horvath's model. y) (Fig.17] for estimating immediate (elastic) settlement.y) is constant with respect to depth. (26) and (27) and Figs. and Vlasov's model gives only slightly higher values of ks. 25 and E = 40MPa). This can be achieved with relative ease. Due to the propping-up effect of the lateral normal stresses.y) x z H sx sx+Dsx (a) (b) (c) Figure 5 (a) The elastic subgrade idealized as a cluster of closely spaced soil columns.45 and E = 50MPa) p(x. Both models are similar second order partial differential equations with constant coefficients given by [s z . One can finally draw the important conclusion that the use of any type of relationship between the vertical and the horizontal normal stresses and any Journal of EEA. the main difference being the use of the generalized three-dimensional Hooke's law because of the inclusion of the lateral normal stresses in these models. Thus. 2009 . Such comprehensive considerations result in more complex mathematical models of higher order for the subgrade. the present model gives consistently stiffer springs. coarse sand (n = 0. Vol. 26. The mathematical proof goes analogously.y) p(x.n (s x + s y ) E ( z) ] dz + f 3 + c3 (32) in which. the subgrade represented by the models presented in this work is equivalent to the same cluster of contiguous soil columns. but with interaction through the lateral normal stresses as shown in Fig. only if the shear stress components in the stress tensor are taken into account in the formulation of the subgrade model. (6) and its evaluation leads to the respective expressions for ks presented in the preceding sections for the different cases considered. The integral in Eq.Winkler's Single-Parameter Subgrade Model from the Perspective of 19 16000 14000 12000 Horvath New V ariant I New V ariat II Vesic Vlasov ks (kN/m3) 10000 8000 6000 4000 2000 0 ) 3 ^ m / N k ( s k 35000 30000 25000 20000 15000 10000 5000 0 Horvath New Variant I New Variant II Vesic Vlasov ) 3 ^ m / N k ( s k 60 (a) 0 10 20 30 B (m) 40 50 60 (b) 0 20 B (m) 40 Figure 4 Plots of subgrade modulus against foundation width for: (a) a medium dense. assumptions are made with regard to the depth-wise variation of the vertical shear stress components txz and tyz in addition to the assumptions already made with respect to the lateral normal stresses. (32) is identical to Eq. (b) a typical soil column without lateral normal stresses. w( x. but reasonable. (b) a medium stiff clay (n = 0. y. f3 and c3 are dependant on the boundary conditions. z ) = ò form of distribution of E(z) will always result in a Winkler-type subgrade as far as the shear components of the stress tensor are not taken into account. THE MISSING SHEAR INTERACTION A more complete representation of the interaction among the soil columns or the Winkler springs can be achieved. Two such models have been proposed by the author in the accompanying paper that are counterparts of the two Winkler-type models presented in this paper. 5(c). (c) a typical soil column propped up by lateral normal stresses In contrast to this. if simplifying. the paper provided closed-form relations for estimating the subgrade reaction for both constant and variable elasticity modulus. Of special interest here is the effective subgrade modulus. ke. y ) .4n )H E (37) Counterpart Model to Winkler-Type Variant II: c1 = a1 GH 2 E .20 Asrat Worku Counterpart Model to Winkler-Type Variant I: p(x. which is at the discretion of the user. (ku + kl ) gk Ñ2 p( x. (16). a2. y ) - Equations (36) and (37) for the effective subgrade modulus of the three-parameter Kerr mechanical model are identical to Eqs. A comparison with previously proposed simplified models shows some notable differences in the coefficient of subgrade reaction that generally decrease with decreasing Poisson ratio of the subgrade material and with increasing width of the foundation. respectively. E and G are the Young's modulus and the shear modulus of the homogenous subgrade. y ) (34) Through comparison of coefficients in Eqs. CONCLUSIONS The presented work shows that a Winkler-type model will always evolve for an elastic subgrade as far as the shear components of the stress tensor are omitted regardless of whether all or part of the normal stress components are taken into consideration. one can easily obtain the following expressions for ke for the two continuum-based models under consideration that take into account the shear interaction [9]: Journal of EEA. The constant coefficients c1 to c3 depend on the soil properties and are different for the two models: Counterpart Model to Winkler-Type Variant I: GH 2 E c1 = a . 12E H c3 = a 3 GH 3 (33c) In Eqs. 2009 . 26. and a3 are dependent on the Poisson ratio of the soil. Such a work has been completed recently and suggested the use of a calibrating factor Iz = 2. of the single-parameter Winkler's mechanical model. The variation with depth of the elasticity modulus is taken into consideration. the effective subgrade modulus can be expressed as ke = ku kl ku + kl (35) Inserting the relations for ku and kl in Eq. y ) (ku + kl ) 0 (ku + kl ) kl ku w0 ( x. (33a) and (34). which becomes more significant with increasing relative rigidity of the soil with respect to that of the foundation. 12E aH GH c3 = 3 ke = E aH (36) Counterpart Model to Winkler-Type Variant II: ke = (33b) (1 . y ) . Since the two spring beds in Kerr model are arranged in series. and H is the layer thickness. Equation (33a) is similar in form and order to the three-parameter mechanical model proposed by Kerr [7]. With the introduction of two such functions. A generalized analytical formulation in form of a definite integral for evaluating the coefficient of subgrade reaction is provided by accounting for all normal stresses. one overlying the other. (33b) and (33c). (18) and (23). one can easily express each of the three parameters of the Kerr mechanical model in terms of the known elastic soil properties and the layer thickness for both continuum-based models presented in Eq.8 to 3 for beams on elastic foundations. It is important to note that a complete subgrade model should take into account the shear interaction.c3Ñ 2 w0 (x. respectively. (33). y ) = gk ku Ñ2w ( x. It is only required too make a reasonable assumption on the function g(z) relating the normal stresses. Ñ is the Laplace operator. Similar studies for plates are underway. separated by a shear layer of parameter gk. and a is the same as defined in Eq. The coefficients a1.c1Ñ 2 p(x. Its governing differential equation is given by p(x. it is possible to calibrate the Winkler-type models so that they give results that are in good agreement with finite-element based models by conducting a numerical study.0. c2 = a2 . with corresponding subgrade moduli of ku and kl. c2 = . y ) = c 2 w0 (x. y ) (33a) where. Vol. This mechanical model consists of two beds of springs. With the introduction of H = IzB in the expressions derived for ks. (35). 1967. Journal of Geotechnical Engineering. A. Geotechnique. Cheung. N. Vesi . CGT-2002-2. REFERENCES [1] Selvadurai. and Leontiev. Plates. 1979. Beams and Plates on Elastic foundations: a review. 25 (80). E. ASCE. J. 1946. Hetényi. Das. Journal of Applied Mechanics. 2009 . Foundation Analysis and design. 1955. Horvath. 109 (12). Z. Advanced Soil Mechanics. 1958. A Note on Deflections of Plates on a Viscoelastic Foundation. 1997.. Beams. Horvath. 491-498. G. 1964. Journal of Soil mechanics and Foundation Division. 4. 1567-1587. Manhattan College. ASCE. Evaluation of Coefficients of Subgrade Reaction. M. Israel program for Scientific Translations. 17. and Booker. 35-53. Beams on Elastic Foundation. H. New York. 1970. 1996. Static Cone to Compute Static Settlement over Sand. Elsevier Scientific Publishing Company. Schmertmann. P. [11] [2] [13] [3] [14] [4] [16] [6] [17] [7] [18] [8] [9] Journal of EEA. School of Engineering. SM3. 1983. M. S. 26. 109 (12). E. Worku. John Wiley 2005. U. S. J. A. John Wiley. Journal of Geotechnical Engineering. 174182. Das. 297-326. EM2. S. F. New Subgrade Model Applied to Mat Foundations. A. 2002. Bowles. Kerr. 5. [12] [10] 21 Terzaghi. Journal of Engineering mechanics division. B. Reissner. Basic SSI Concepts and Applications Overview. R. Elastic Analysis of SoilFoundation Interaction.Winkler's Single-Parameter Subgrade Model from the Perspective of The work has also shown that the effective spring stiffness per unit area of higher order models remains the same as the subgrade modulus of the single-parameter Winkler's model as far as the way the normal stresses are considered remains the same regardless of the subgrade shear stresses. 87. J. L. [15] [5] Horvath. ASCE. Progress in Structural Engineering and Materials. Wang. S. New York. K. Y. 1983. 1591-1596. New York. ASME. Tham. Modulus of Subgrade reaction: New perspective. International Journal for Numerical and Analytical Methods in Geomechanics. ASCE. Report No. Journal of Applied Mechanics. Gibson. ASME. 1983. V. Vol. New York. 361-378. B. University of Michigan Press. PWS publishing Company. 1966. 144-145. McGraw-Hill Book Company. 1995. D. Vlasov. 58-67. Part i: Loading on arbitrarily Shaped areas. Elastic and Viscoelastic Foundation Models. and Shells on Elastic Foundations. R. 1011-1043. Principles of Foundation Engineering. Submitted for publication in Zede. Stark. 1961. R. S. H. 21. J. M. Some results Concerning Displacements and Stresses in a Nonhomogenous Elastic Half-space. Surface Displacements of a Non-homogenous Elastic Half-space Subjected to Uniform surface Tractions. Soil-Structure Interaction Research Project. 25 (80).. McGraw-Hill. J. Journal of Ethiopian Engineers and Architects. 7. Bending of Beams Resting on Isotropic Elastic solid. Ann Arbor. Jerusalem (translated from Russian). K. Fifth Edition. New Variants of Continuumbased Models for an Elastic Subgrade. Geotechnique. 96. E. Boston. A. J. passive or at-rest lateral earth pressure condition.8].7. three different combinations of assumptions are made with regard to the lateral normal and the vertical shear stress components resulting in three correspondingly different variants of subgrade models. Reissner model. Shear interaction. In contrast. A number of mechanical models have been proposed in the past having varying degrees of mathematical complexity and different numbers of model parameters [1-6]. The consequence of this assumption is that the vertical shear stress components become constant and the vertical normal stress component varies linearly with depth. whether one deals with active. Instead. The resulting differential equations are similar in form and order to a highorder model developed earlier by Reissner based on a number of simplifying assumptions. continuum-based subgrade models proposed in the past are relatively few in number. The works of Horvath are also based on the same assumption [3. Vol. 2009 . With the help of appropriately selected mechanical models. in which linear relationships are assumed between the normal stresses. All components of the stress tensor in the subgrade are taken into account. that involves The RSCM makes the simplifying assumption of zero in-plane stresses. Kerr model. but without neglecting any stress components. This assumption considerably simplifies the mathematical work needed in arriving at the mathematical model. 26. This second assumption is introduced as a reasonable approximation of the nonlinear variation of the shear stresses observed in plots of analytical results available in the literature [10]. the second assumption with respect to the vertical shear stresses is improved by assuming a bilinear depth-wise variation. The present work follows Reissner's approach. The assumptions are based on observation of available analytical results of stress distributions and on knowledge of lateral earth pressure theories. but with different coefficients dependant on Poisson ratio. isotropic elastic layer of thickness H overlying a firm stratum. a linear relationship between the horizontal and the vertical normal stress components is assumed. The other assumption in this model is a constant depth-wise variation of the vertical shear stress components. INTRODUCTION Subgrade models developed so far can be categorized into two classes: continuum-based and mechanical models. i. Vlasov and Leont'ev presented a relatively indirect application of the simplified continuum variational calculus [9]. Horvath used later on two modifications of Reissner model to study the behavior of mat foundations [3. Reasonable assumptions are made regarding the depth-wise variation of the vertical shear stress components and of the horizontal-to-vertical normal stress ratios to simplify mathematical work.4. it underestimates both the vertical stiffness of the subgrade and the inherent shear interaction rendering the model one of the most conservative. Mechanical models. whereas the first assumption in the first variant with respect to the horizontal normal stresses is maintained. Keywords: Continuum models.7]. s x = s y = t xy = 0 [8].e. Winkler model. In the first model variant. In the second model variant.4]. it has been shown that all of the new model variants consistently give larger effective vertical stiffness and larger shear interaction among the classical Winkler springs for the range of Poisson ratio of practical interest. Journal of EEA. These models range from the classical single-parameter Winkler model to the multi-parameter models of Rhines [3. This assumption has as its basis the classical theory of lateral earth pressure. which is a second-order differential equation with constant coefficients.7]. Reissner's simplified continuum model (RSCM) can be regarded as one of the pioneering works based on some direct simplifying assumptions [3. However. The subgrade is idealized as a homogenous.PROPOSED HIGHER ORDER CONTINUUM-BASED MODELS FOR AN ELASTIC SUBGRADE Asrat Worku Department of Civil Engineering Addis Ababa University ABSTRACT Three new variants of continuum-based models for an elastic subgrade are proposed. and the only non-zero normal stress component. x z Isotropic elastic stratum: E. which consists of a homogenous. The vertical shear stress components. txz and tyz. This assumption is made only for the sake of mathematical ease and in order to show that RSCM is a simplified form of this model variant. 26. sz. varies linearly with depth. The layer is characterized by its elastic parameters of Young's modulus. but exhibiting notable differences in their coefficients. s x and s y . The horizontal normal stresses. n [8]. the two remaining shear stress components. isotropic elastic layer of thickness H underlain by a rigid formation as shown in Fig 1. are assumed constant with depth. p(xy) In the RSCM. the three independent in-plane stress components are neglected (i. E. Simplifying assumptions with regard to the rest of the stress components are unnecessary. At the depth H. This assumption results in a linear depth-wise variation of the vertical normal stress. s x = k x s z and s y = k y s z . sz. Similar studies on beams and plates using various subgrade models that include the variants reported in this work are currently underway with the objective of corroborating the findings presented here based on theoretical considerations alone. In contrast. THE PROPOSED MODELS In all model variants proposed in this work.e. sx and sy. Interestingly. As a consequence. Specifying values for the coefficients in advance is not necessary for the derivation of the model. Knowledge of lateral earth pressure theories motivated this assumption and can be utilized to reasonably estimate the values of the coefficients kx and ky. Once again. For this purpose. become constant with respect to depth. txz and tyz. and Poisson's ratio. s x = s y = t xy = 0 ). s z . ii. Model variant 1 This model. all deformation components are assumed zero. sz. There is a trend of increasing interest in numerical and analytical studies of beams and plates on elastic foundations using such models [11-15]. Comparisons show that all of the new model variants brought about increases in the vertical stiffness of the subgrade and the shear interaction among the Winkler springs.e. Vol. are linearly related to the vertical normal stress. n Figure 1 The elastic soil layer of thickness H overlying a rigid stratum Journal of EEA. A synthesis of these models with equivalent mechanical models helps in interpreting the differences observed in the coefficients of the differential equations. plots of available analytical results of the normal stresses are used to support this assumption [10]. Numerical results found so far are encouraging. the Kerr mechanical model is used. The proposed three models differ from each other according to the assumptions made with regard to the depth-wise variation of the vertical shear stress components. and the ratio of the lateral normal stress components. t xz and t yz .2 Asrat Worku The difference between the stress tensors of the RSCM and the present model variants is as shown in the arrays below in accordance with the Cartesian coordinate system: RSCM æ 0 ç ç 0 çt è xz 0 0 t yz t xz ö ÷ t yz ÷ sz ÷ ø NewVariant s æs x ç çt xy çt è xz t xy sy t yz t xz ö ÷ t yz ÷ sz ÷ ø The third model variant is derived by maintaining the second assumption in the second variant with respect to the vertical shear stresses and introducing an exponentially decaying function to approximate the vertical variation of the ratio of the horizontal to the vertical normal stresses. referred to simply as Variant 1. to the vertical normal stress. the subgrade under consideration is similar to that of RSCM. It appears possible to calibrate these models so that they give results in excellent agreement with finiteelement based models. i. 2009 . is based on the following two basic assumptions: i. all of the three model variants result in differential equations similar in form and order to that of RSCM. no stress component is neglected in any of the models proposed in this work as shown in the array on the right-hand side. Winkler-type models are obviously recovered.4 s/b=0.2 0. y ) 3 3 to be equal to the lateral earth pressure coefficient for at rest condition. and the boundary conditions at the ground surface and at the interface with the rigid formation are utilized to derive the mathematical model.05 0 0 1 2 s/b=0. are assumed to vary with depth according to a bilinear relation. The vertical shear stress components. Vol. txz and tyz. 2009 . the coefficient a becomes unity. ii.8 s/b=1. then a in Eq. y ) 12 E H GH 2 Ñ w0 ( x. This assumption emanates from observation of plots of the stress components underneath a uniformly loaded circular region on the surface of an elastic half space.5 z/b 3 (a) 4 5 (b) Figure 2 (a) Plots of the vertical shear stress with depth for a circular region subjected to a uniformly distributed load. and k0 can also be expressed in terms of other soil properties like the strength parameters or the degree of consolidation. However. The resulting subgrade model relating the surface pressure p(x. referred to as Variant 2.n .n (k x + k y ) (2) For kx= ky=0 (or zero lateral normal stresses). the coefficients kx and ky can generally be selected different from k0. G is the shear modulus of the upper layer. as in Variant 1. 2(a) for different vertical planes. (1a) takes the form a= 1 .3 0. (1a) reduces to the form of RSCM [8] given by p ( x.5. Hooke's law for isotropic elastic materials. y ) = w0 ( x. and Eq. (3) becomes indeterminate.a ç ç 12 E ÷ a H è ø GH 2 Ñ w 0 (x . y) is given by æ GH 2 ö 2 ÷Ñ p(x. For n=0. The horizontal normal stresses. y ) 3 (1b) If the higher derivatives in Eqs. the details of which are presented in Appendix A. y ) = 1 E w0 ( x. (1a) and (1b) are dropped. sx and sy. These plots are prepared from tabular values provided by Das [10] citing the works of Ahlvin and Ullery and are given in Fig.0 s/b=1.Proposed Higher Order Continuum-Based Models for an Elastic Subgrade Pertinent stress equations.5. y ) . Model variant 2 This model.35 0. k0. is based on the following assumptions: i. y ) p ( x. and the coefficient a is given by the relation a = 1 . and noting that this coefficient can be expressed as k0 = n (1 -n ) . y) and the corresponding surface displacement w0(x.1 0. y ) GH 2 2 E Ñ p ( x.2n 2 1 -n (3) (1a) According to this relation. If the coefficients kx and ky are assumed 0.2 s/b=0. In this second order partial differential equation with constant coefficients.6 s/b=0. 26. Eq. strain-displacement relations.2 s/b=1. sz. (b) A qualitative plot of the influence factor I(z) Journal of EEA. a is always less than one tending to zero with n approaching 0. are linearly related to the vertical normal stress.25 z /q 0.15 0. 2009 . and V are constants. the normalized average depth. s y = ry e-zzs z (6) where rx. and I(z) is the depthdependant influence factor assumed to vary bilinearly. Model variant 3 In this variant. where sr is the radial normal stress and sz is the vertical normal Journal of EEA. 2(b) so established. one obtains the following relation for the subgrade model sought: æ GH 2 ö 2 1 E æ GH ö 2 p(x. If the higher derivatives in Eq. and b2 characterizing the two line segments of I(z) can be readily determined from the known coordinates of the three points in Fig. but exhibit differences in their coefficients. y-plane. 2(a) and in Horvath [7] suggest the use of the following bilinear variation for the vertical shear stress components with depth: t xz ( x. the origin of which is taken as the center of the circle. ry. y ) . 2(b). the first assumption of a linear relation between the normal stress components is replaced by the decaying exponential functions of the form: where t xz (x . (5b) with (1a) and (1b) shows that the three models are still similar in form. x1. then a can be determined from Eq. b1. The corresponding value of IH at this depth may be taken around 0. (5b) are dropped. the details of which are given in Appendix B. The thickness s x = rx e-zzs z .the origin. (2) for the first new variant. Vol. one obtains the same Winkler-type model as in Variant 1. the depth-wise variation of the vertical shear stresses shown in Fig. This assumption is motivated by observation of plots of s r s z for points directly below a circular region of diameter equal to the layer thickness on the surface of an elastic half space subjected to a uniformly distributed vertical load.22ç 3 ÷Ñ w0 (x. whereas the second assumption in Variant 2 of bilinear variation of the vertical shear stress components with depth is maintained. y ) abGx p HE Ñ 2 p(x. k0. ï =í if hH £ z £ H ï(a2 + b2 z )t xz ( x. beyond which the shear stress becomes negligibly small. at which the shear stresses assume peak values. Substituting these coefficients.1. the influence curve for the vertical shear stresses is fully defined and the various constants in the coefficients of Eq. Plots of shear stresses exhibiting a similar trend are also reported by Horvath for points beneath a loaded square region on the surface of a layered formation [7]. z ) = I ( z )t xz ( x. This assumption results in a quadratic variation of the vertical stress.4 Asrat Worku H may be taken as that. the peak and the lower-most point. y) ÷ è ø è ø In Fig. î (4) (5b) Comparison of Eq. All the curves in Fig. 2(a). which entirely ignores the shear stresses. as in the previous model. 26. continuity of deformation at the depth z = hH is taken into consideration.35a ç ç 12E ÷Ñ p(x. For thick elastic strata. The coefficient a is as defined in Eqs. As in Variant 1. In addition. y ). y ) Ñ w0 (x. A qualitative plot of I(z) is given in Fig. b is the radius of the loaded circular region and s is the radial coordinate in accordance with the cylindrical coordinate system. (5a) are provided in Appendix B. Furthermore.2. unlike the linear variation in Variant 1 and RSCM. If the coefficients kx and ky are assumed equal to the lateral earth pressure coefficient for at rest condition. because the two models differ from each other only in the depth-wise variation of the vertical shear stresses . An exception is the curve for points below the edge of the circle due to the discontinuity there. x2.a condition irrelevant in Winkler model. 2(b) . sz. y ). 2 for an elastic half space may be taken as sufficiently representative for most foundations. The coefficients a2. With the peak and the lower-most points in Fig. y ) . (2) for any value of n. may be taken as h = 0. The plots in both Fig. and x3 in Eq. all pertinent elasticity equations together with the boundary conditions are employed to derive the mathematical model. y ) gives the variation of txz in the horizontal x. y ) if 0 £ z £ hH ì(b1 z ) t xz ( x. and their peaks occur within a narrow band of z. y ) = E bGxw 2 w0 ( x. y ) = a H w0 (x. y ) aH H (5a) Where x p = x 1 x 3 and x w = x 2 x 3 . (5a) can be readily evaluated from the relations given in Appendix B. The coefficients b. y . 2(a) exhibit a similar trend. The corresponding mathematical model of the subgrade becomes p( x.6 in both cases.2. The trend suggests that the likelihood of the occurrence of other terms and other orders of derivatives is unlikely with further refinement of assumptions.1 and h=0. p(x. and V can be easily estimated. These plots also suggest the use of relations similar to Eq.19÷H 17.46 l 3. Vol. (6) for depths of up to around 0. 26. y ) Ñ p(x .72 l 22. lGk p (7a) Where k p = k 1 k 3 and k p = k 2 k 3 . y ) dE d lGk w 2 Ñ w0 (x. SYNTHESIS OF THE PROPOSED CONTINUUM-BASED MODELS WITH A PERTINENT MECHANICAL MODEL The synthesis of continuum-models with pertinent mechanical models provides a means of quantifying the mechanical model parameters from those of the continuum. 2009 .72l 66. Looking at the form and order of the governing differential equations of the subgrade models presented above. Horvath gave plots of the normal stresses for points below a vertically loaded square region of side length B on a layered half space [3]. (7a) can be readily evaluated in terms of the Poisson's ratio and the layer thickness H using the relations provided in Appendix C. and k3 in Eq.236+1. the coefficients in Eq.8e -3. 3. y ) = w0 ( x. (6) tallies excellently with the plots. y ) - (ku + kl ) gk Ñ2 p(x. Expressions for the coefficients l.7B. the most appropriate mechanical model for this purpose is the threeparameter Kerr model [4]. d. The resulting mathematical model takes the form E p ( x.404 )H n l = (0.96 z H s z The same bilinear depth-wise variation of the vertical shear stresses shown in Fig. Once again.0. y ) = (ku + kl ) kl ku w0 (x. ry.286 )H 2 n 1 d 1 n 2 1 æ 1 nd ö kp =ç HH+ H n + 0. It also provides a useful perspective to compare the continuum models with each other.Proposed Higher Order Continuum-Based Models for an Elastic Subgrade stress [10]. This model consists of two beds of springs with spring constants of ku and kl per unit area separated by a shear layer of parameter gk as shown in Fig. A recently published work of the author that generalizes the presented approach of subgrade modeling showed that the maximum order of the differential equation and its general form remain indeed unchanged [15]. All involve the functions p and w0 and their respective second derivatives. one obtains d = (1 . y ) d 2 5 One can note from the forgoing material that all the proposed continuum-based models have the same form and order as the RSCM.k u Ñ2 w0 (x.8 l q g ku kl Figure 3 The Kerr (or modified-Pasternak) mechanical model The governing differential equation of this model as derived by Kerr is given by [4] (7b) The coefficients in the brackets and in the expression for kw are dimensionless quantities and dependent only on the Poisson ratio that can be easily evaluated. especially for points directly below the loaded region. An exponential function of the type of Eq. y ) (ku + kl ) Equation (8) is similar in form and order to the equations of all continuum-based models presented Journal of EEA. Accordingly.15+ H2 H2 n + 17.71 è 23. Observation of the plots suggests the use of the following function: s x = s y = 0. k1. the differences in the coefficients of this and the previous mathematical models are to be noted on the coefficients. k2. y ) (8) g k . the details of which are described in Appendix C. Once the depth-wise variations of the lateral normal stresses and of the vertical shear stresses are known. (7a) are given in Appendix C.68 l ø k w = 1. 2 is taken with IH =0. from which the constants rx. All pertinent elasticity equations together with the boundary and continuity conditions are employed to derive the mathematical model.6. g= .404 H n (12) These expressions show that Variant 3 predicts always a shear parameter much higher than Variant 1 and RSCM. kl = . has increased significantly to 2. With the introduction of the bilinear variation for the vertical shear stresses and the decaying exponential function for the ratio of the lateral to vertical normal stresses. 3 that are arranged in series: Kerr Parameters from RSCM ku = 4E 4E 4GH E . dkw -kp ( ) 1 E ke = 1. Equating the coefficients in Eq.33.14 . In contrast. Therefore. dkw -kp ) 2 kw g= lG. (12) can be determined from Eqs. k e = 1. Since the factor a is always less than unity for common values of Poisson ratio of soils. The shear parameter of Variant 2.0. the coefficients of the individual spring beds and the shear parameter can be easily evaluated.45 : E E E ku = 21. g = 0. Then. 2009 . This yields x p = -0.3 .25fold that of RSCM and Variant 1 irrespective of the Poisson ratio. The parameters from Variant 2 become clearer by introducing the pertinent relations for the bilinear variation of the vertical shear stress components.31. kl = . the shear parameter remained unchanged as could be expected. which are summarized below together with the effective stiffness coefficient established using the relation k e = k u k l (k u + k l ) for the springs in Fig. (11) give Journal of EEA.35 H and x w = -1. this gives: For n = 0. especially for soils with larger Poisson ratio. (8) with the corresponding coefficients in Eqs. Variant 2 predicts significantly higher stiffness and higher shear interaction of the subgrade as compared to RSCM.30GH Kerr Parameters from Variant 3 ku = kw E. kl = .xp aH (11) ( ) g = 1. Comparison of the relations in Eqs. xp a Hxw .6 Asrat Worku k u = 3. on the other hand.75 E E . ke = H 3H 9 H (13) (9) These relations show that even though the effective spring coefficient remains the same in both Variant 1 and Variant 2. Simultaneous solution of these equations yields different expressions for the mechanical model parameters. both the individual bed of springs and the effective spring of Variant 1 are always stiffer than that of RSCM. (5b) and (7a) provides in each case three equations. g= . the various constants in Eqs. which when inserted in Eqs.95GH H H H For n = 0. kp kl = ( kw E. k e = 1. (1a).7 .22 H H H Kerr Parameters from Variant 1 ku = 4E 4E 4GH E . ke = aH a 3H 9 aH (10) Kerr Parameters from Variant 2 ku = xw E xw E .3: E E E ku = 17. kl = 1. (7b). 26. (9) and (10) shows that the spring constants of Variant 1 are always 1/a times those of RSCM.30 . ke = Hxw . k l = 1. For two selected values of Poisson ratio.36 . kl = 1. 4 against Poisson ratio. and even larger than Variant 2 for Poisson ratio larger than about 0.22 . Plots of Kerr Parameters The three normalized Kerr parameters are plotted in Fig. because constant vertical shear stresses are either assumed or implied in both models. (1b).xp a ( ) 2 xw E g= bG. Vol. g = GH aH aH above. the individual spring beds are different. 6 0.8 0. Beams on Elastic Foundation. and Hermann L. the increase in the vertical stiffness is not as large as in the other two model variants.2 0 0 0. The RSCM consistently underestimates both the vertical stiffness and the inherent shear interaction of the subgrade. In the important range of Poisson ratio of soils. 26. M. The shear parameter of Variant 3 for n = 0. the following conclusions are drawn: 1. However. 0. Basic SSI Concepts and Applications Overview. Fletcher. Variant 2 and Variant 3 are promising alternatives to existing continuum subgrade models.4 0.5 0.2 0. CONCLUSIONS From the foregoing material. REFERENCES [1] 1.2 g/GH RSCM Variant 1 Variant 2 Variant 3 1 0. by combining the assumption of bilinear vertical shears with the assumption of an exponentially decaying vertical-to-horizontal normal stress ratio with depth.5 in Variant 3 is slow as compared to the rate of increase observed in Variants 1 and 2. No. The three parameters of the RSCM are all independent of Poisson ratio and always less than those of the new model variants.3 0. Soil-Structure 2. The highest shear interaction is achieved in Variant 3. University of Michigan Press. 97.6 1. Vol. Results of recently completed studies on beams using these models indicate that the new models. 1946. especially for large Poisson ratios. [3] Journal of EEA. Q.0 at n =0 to 1. [2] 2. Considering the reasonable assumptions they are based on.317n + 0.259 . 3. Journal of Engineering Mechanics. 2009 . This model is thus the most conservative of all. The increase in the normalized spring stiffness values from 1. Horvath. This variation can be approximated by g k /(GH ) = 2. R. Plots of shear parameter 1. 95-107 Hetényi.6 Figure 4: Plots of the normalized model parameters against Poisson ratio as predicted by different continuum-based models The following important observations can be made from these normalized plots within the common range of values of Poisson ratio: 4.25 at n=0.5 is more than threefold that of RSCM and Variant 1 and about 40% larger than that of Variant 2.4 1.4 0. 1971. Variant 3 represents the highest shear parameter of all that increases nearly linearly with increasing values of n. the stiffness does not become indeterminate at n = 0. in particular Variant 3. Ann Arbor. can be easily calibrated to give results in excellent agreement with finite-element based models. EM1.Proposed Higher Order Continuum-Based Models for an Elastic Subgrade 7 Furthermore. J. Elastic Foundation Representation of Continuum. This is due to the more realistic decaying exponential function used in Variant 3 for the normal stress ratios in lieu of a constant. D.1 Poisson ratio 3. S. ASCE.5. ASCE. Beams and Plates on Elastic foundations: a review. International Journal of Solids and structures. Bending of Beams on Three-Parameter Elastic Foundation. A. [9] [16] [10] Journal of EEA. O'Neill. S. 25 (80). N. 2006. Yin. E. 167-173. 144-145. 357-375. February 20-24. Manhattan College. 1983. L. 1. Tanahashi. D. Pasternak Model Formulation of Elastic Displacements in the Case of a Rigid Circular Foundation. Wang.. A. Journal of Applied Mechanics. Elsevier Scientific Publishing Company. 25 (80). Annual Conference of the GeoInstitute. 1983. P. 1966 (Translated from Russian.. A Note on Deflections of Plates on a Viscoelastic Foundation. Tanahashi. [4] Kerr. Horvath J. GeoFlorida 2010. 2000. New York. 491-498. John Wiley 2005. I. 5. Morfidis. M. V. 1960).. Vlasov.. New York. 174182. W. 109-118. ASCE. (Technical Note) Journal of Engineering Mechanics. 111. 5. 1964. Elsevier. [12] [5] [13] [6] [14] [7] [15] [8] Reissner. 8. Y. 2009 . 1979. ASME. [11] Avramidis.. N. 869-874. Progress in Structural Engineering and Materials. H. 664-679. ASCE. Journal of Applied Mechanics. Worku. American Society of Civil Engineers. Journal of Asian Architecture and Building Engineering. 44. 1985. K. H. Elastic Analysis of SoilFoundation Interaction.. 7. Z. Elastic and Viscoelastic Foundation Models. Das. and Shells on Elastic Foundations. 1958. Beams. Beam on Generalized Two-Parameter Foundation. New Subgrade Model Applied to Mat Foundations. 109 (12). K. B. CGT-2002-2. 2007. J. Selvadurai. A. 2002.8 Asrat Worku Interaction Research Project. ASME. Journal of Geotechnical Engineering. Japanese Geotechnical Society. S. Cheung. 6.. Formulas for an Infinitely Long Bernoulli-Euler Beam on the Pasternak Model. McGraw-Hill Book Company. H. Nogami T. Report No. Advanced Soil Mechanics. 15671587. Tham. accepted for presentation and publication. Journal of Engineering Mechanics. 43. E. Israel Program for Scientific Translations. 26. G. Jerusalem. Vol. H. 126. Leont'ev. 2010. 2004. Part I: A generalized Formulation of Continuum Models for Elastic Foundations. Soils and Foundations. Closed-Form Solution for Reinforced Timoshenko Beam on Elastic Foundation. Plates. New York. M. one obtains the following relations: ù a é Qz 2 w( x. y = 0 (A1) Assuming that the vertical shear stresses are constant with depth. x + t zy .PH (hH ) 24 6 2 (A13) b2 4 a 2 3 RhH 2 H + H + H . 26.2h ) s z = -Qz . y ) = w0 . z + t zx . y 3 6E 9 (A7) Finally.÷ H 2 + (P H .3]. y ) . x = t xz G v. (A8) above. one obtains Equation (A8) is the differential equation for Variant 1 given in Eq. This involves a relatively lengthy mathematical work. y ) = a H w0 ( x. (1a).3 Ñ w0 (x. y ) ÷ è ø (A8) s z .a 2 (hH ) (A16) Journal of EEA.n (k x + k y ) (A5) x3 = (b1 .pH ÷ H2 èa ø (A4) x2 = - b1 (hH )4 + hH + 1 (PhH .Proposed Higher Order Continuum-Based Models for an Elastic Subgrade APPENDICES Appendix A: Derivation of Model 1 Equation (1a) is derived following the same procedure as in Reissner s and Horvath s work [2.b2 ) (hH )2 + b2 H 2 + (1 . y = t zy G PhH = R b2 (hH )4 + a 2 (hH )3 + hH (hH )2 . (A2) in the combined stress-strain and strain-displacement equation for the vertical direction.b2 ) 2 (hH )2 . x 3 6E 2G aGH = w0.h )a H 2 2 2 (A12) Equation (A3) is now substituted in the combined equations of stress-strain and strain-displacement for the vertical shear stresses given by u. z + w. The stress equilibrium equation in the vertical direction is given by t xz = t yz 2G aGH w0. and s = k ys z . z + w. only the final forms of the coefficients are given below: b = (3 .b2 )h 2 H 3 + b2 H 3 + (1 . y ) . y p.a ç ç 12E ÷Ñ p( x.2h ) a2 H 2 6 6 2 (A9) (A3) x1 = b1 1ö H æ 4 H (hH ) + çh . Eqs. (A2) and (A7) are inserted in Eq. The resulting equations are solved for the shear stresses to yield PH = b2 3 a2 2 H + H + RhH H 6 2 (A15) RhH = (b1 . x p. integrating Eq.p (A2) Substituting Eq. and employing the stress boundary condition at the surface. and employing the displacement boundary conditions at the surface and at the bottom of the layer. (A1) with respect to z. For brevity reasons.PH H 24 6 2 (A6) PH = (A14) Equations (A6) are integrated with respect to z and the remaining displacement boundary conditions applied. Appendix B: Derivation of Model 2 Equation (5a) is derived in a similar manner as that of Eq. 2009 . (A1) and rearranged to obtain æ GH 2 ö 2 1 E GH 2 p(x. noting the assumption s = k xs z .PH ) h 24 b 2ø b è (A10) where Q= and 2 æE ö ç w0 . integrating with respect to x y z.PH ) 24b b (A11) a = 1 . except that the continuity condition of displacements at z = h H should be observed in addition to the boundary conditions. Vol.ê + pz ú Eë 2 û (b1 . Considering the relatively large value of z used for the best-fitting curve and the rather small value of the coefficient of e -zH . 2009 . a term involving the product of the quantity e and another negligibly small quantity is assumed zero. Only at one stage in the process of derivation of the model.a 2 (hH ) (A19) r = rx + ry (A20) (A28) a b PH = 2 H 2 + 2 H 3 + RhH H 2 6 PH = h a2 (hH )2 + b2 (hH )3 + RhHhH 2 6 (A21) Journal of EEA.2 ThH e -zhH ÷ .P ý h H ç lï z÷ 2 û z ï ø ë è î þ ö ænrb ö b1 æh4H4 nr 3b nr ç .b2 ) 2 (A27) (hH ) 2 .1 4 ÷ ç lz3 ÷ 2l ç 12 z 2 l z ø è ø è (A23) k3 = (b1 . 26. Only the final forms of the coefficients are given below for the sake of brevity: l= b1 é (hH )3 nr -zhH æ 2 2 2 2 ö ù nrb1 ç ÷ + e ê çh H + z hH + z 2 ÷ ú .PhH ç ÷ z úe z ÷ 2z ç z ø è ø ëz è û .2 e ê a 2 çhH + ÷ + RhH + ThH ú ý lï z zø 2 ë è ûï î þ Equation (7a) has also been derived analogously.PH H l 2 l èl ø ö æ nrb1d nr ö b1d æ h 4 H 4 nr 3b nrd nr ç ÷ ç + . in which the compatibility condition of displacements at z = h H is observed in addition to the boundary conditions. this approximation is easily justified.10 Appendix C: Derivation of Model 3 Asrat Worku k1 = ùü b2 dì ~ nr -zhH é æ 2ö ï ï ç ÷ í.ThH e-zhH ÷ + ç 1 +1÷hH . This involves a much more lengthy mathematical work. Vol.b2 ) 2 h 2 H 2 + a 2 H (1 .zH d ~ H2 d æd ö + ç PH + H ÷hH + PH .PhH .z 3 2ë 3 z è øû RhH ù -hzH é a2 æ 1 ö b2 æ 2 2 2 2ö -nr ê çhH + ÷ + çh H + hH + 2z ÷ + + PH .h ) + b2 2 H 2 (A24) ThH = h 2 H 2 + 4 6 hH + 2 z z (A25) (A17) nr d =Hz (A18) RhH 2 a b ~ PH = 2 H 3 + 2 H 4 + H 6 24 2 RhH a b ~ 3 4 PhH = 2 (h H ) + 2 (h H ) + (hH )2 6 24 2 (A26) RhH = (b1 .ç + ÷hH + 1 4 + 2 2l ç 12 z lz 3 z ÷ l z z ø è ø è (A22) é æ ù b 1 ì~ nr 2ö ~ü ï ï k2 = íPH .2 e-zhH êa2 çhH + ÷ + RhH + 2 ThH ú + PH H(1-h) . Mechanical and cement stabilizations were investigated in two subsequent phases. often within the same quarry and may be red. and this is further confirmed on the gravel road study. and investigation of a cinder gravel road. The aggregate impact test carried out on 23 samples using a modified procedure for weak aggregates resulted values ranging from 46 to 177 which indicate that the cinder gravel is weak. and traffic. optimum amount of fine soils that makes up the deficiency of fine particles of natural cinder gravels was found to be 12 %. and The addition of locally available clayey soil to make up for the deficiency of fine materials improves the compactability and stability of cinder gravels. Vol. In a joint research project between the Ethiopian Roads Authority and Transport and Road Research Laboratory (UK). Due to the weak nature of cinder particles. In the first phase. 7. Cement stabilization. compaction causes the breakdown of particles which improves both grading and strength properties. Mechanized stabilization. INTRODUCTION Natural gravels are abundant source of road building materials but do not always meet the quality requirements for bases and are frequently rejected in favour of expensive alternatives such as crushed stone. brown.STABILIZING CINDER GRAVELS FOR HEAVILY TRAFFICKED BASE COURSE Girma Berhanu Department of Civil Engineering Addis Ababa University ABSTRACT Investigation into the improvement of natural cinder gravels with the use of stabilization techniques was made using samples collected from quarry sites near Alemgena and Lake Chamo. Cinder gravel.0 MPa as specified in ERA and AACRA pavement design standards for heavily trafficked base course without adding fine soils is found to be 7 % cement. Nevertheless. shrinkage. · · Journal of EEA. the performance of cement stabilized cinder gravel should be investigated in a full-scale road experiment against cracking due to stresses induced by thermal. Changes in moisture content do not affect the properties of cinder gravels.5 m in diameter to sand and silt sizes. or black. laboratory investigation. According to the study. Optimum cement content. their rough vesicular surface. and their high porosity. natural cinder gravel samples without. Other characteristics features of cinder are their light weight. The results of the investigation indicated that the optimum amount of cement required to achieve the minimum UCS of 3. 5. and with 12% fine soils were stabilized with 3. · They vary in colour. this high cement requirement was reduced to 5% cement which is a practical value by mechanically stabilizing cinder gravel with 12 % of fine soils before cement stabilization. The main findings from the investigation include: · The importance of sampling below the weathered zone which can extend to a depth of two meters to obtain representative materials. Keywords: Base course. these alternatives are often not locally available and the transportation of large quantities in heavy vehicles is expensive and consequently large financial and environmental benefits can be achieved if the properties of locally available materials such as natural cinder gravels can be improved by stabilization techniques and used with confidence. 2009 . and 10% of cement by mass. In the second phase. The preliminary study [1] involved field surveys. 26. grey. a preliminary investigation on the location and engineering properties and a fullscale road experiment of cinder gravels were undertaken. the two most important factors that affect the engineering behaviour of cinder gravels are grading and the strength of the gravel particles. The particle sizes also vary from irregularly shaped lumps of 0. However. Natural cinder gravels are pyroclastic natural materials associated with recent volcanic activity. However. The particle size analysis carried out on 53 samples collected during the field survey indicated that the grading of natural cinder gravel is deficient in fine particles and do not satisfy the recommended grading limits for base course. in both cases the gradation is almost within the specification limits except that the samples are deficient in fines before compaction and coarse particles are finer than the desirable limits after compaction because cinder particles break down during compaction due to their weak strength.24 Girma Berhanu MATERIALS AND EXPERIMENTAL INVESTIGATIONS Sources and Descriptions of Materials In this study. The road-mix surfacing was. 26. 2009 . near Alemgena and Lake Chamo. The results of the gravel surfaced experimental sections showed that improved performance can be obtained by mechanically stabilizing cinder with plastic fines. In the presentation through out the paper. natural cinder gravel samples were investigated from two sites. however. Figure 1 depicts the gradation curves of the samples before and after compaction from both sites with desirable gradation specification limits specified for stabilised base materials in ERA_PDM and AACRA_PDRM. However. Both pavement design manuals used in Ethiopia. recommend the use of stabilized locally available natural gravels when the cost of importing quality aggregate is expensive and hauling distance is far away. The samples near Alemgena were obtained from the freshly dozed stoke pile to be used for the subbase construction of AlemgenaButajira Road while the samples from Lake Chamo were obtained from the quarry site which was used for the construction of unpaved roads in Arba Minch town. The findings from the surface dressed sections showed satisfactory performance of cinder gravels whether untreated or mechanically stabilized for use in base course for up to 440. These samples were prepared for various tests after repeated quartering using sample splitter riffle box and studied in laboratories at Addis Ababa and Arba Minch Universities. respectively. The gradation of cinder obtained from Alemgena is generally coarser than cinder from Lake Chamo. the samples are designated by Alemgena and Lake Chamo respectively. The results of the joint research work should be further taken up to investigate the potentials use of these abundantly available natural gravels in base course for heavily trafficked roads by improving their engineering properties. Vol. not found a satisfactory method of providing a bituminous surface for cinder gravel. The full-scale road experiment [2] was comprised of 20 different sections out of which six sections were gravel surfaced and the remaining 14 sections were bitumen surfaced.000 ESA when designed according to Road Note 31. the Ethiopian Roads Authority Pavement Design Manual (ERAPDM) [3] and the Addis Ababa City Roads Authority Pavement Design and Rehabilitation Manual (AACRA-PDRM) [4]. This paper presents the results of laboratory investigations made in improving the properties of cinder gravels by cement stabilization. a) Gradation before compaction b) Gradation after compaction Figure 1 Gradation of cinder gravel samples before and after modified compaction Journal of EEA. Table 2 shows the descriptive test results carried out on fine soil samples that were collected near the cinder gravel quarry sites for this purpose. 1 (a) that the gradation of cinder gravel is deficient of fines particles. and 5. put in plastic bag. labelled.5 mm and 10 mm.75 mm 6. materials < 10 mm OMC = 24.7 A-2-7(0) 100 86 45 10 39 30 9 2.7 A-2-4 (0) specimens for each percent of cement. After compaction. and 10 % cement by mass. The specimens were then removed from the mould carefully. Vol. unconfined compressive strength (UCS) test was conducted following ASTM Experimental Investigations In this study. After moist curing the specimens for 7. 14. The optimum moisture content pertaining to the maximum dry density for the range of cement content was determined according to ASTM D558.0 %. 7.8% OMC = 25.425 mm 0. but satisfies the requirements for subbase course materials. Two series of trail mixes of cement stabilized cinder gravel were prepared three Journal of EEA. 7. the specimens in the mould were placed in a plastic bag.26.75 mm 2.075 mm Liquid Limit Plastic Limit Plastic Index Specific gravity Soil classification Test Results Lake Alemgena Chamo 100 88 51 17 55 39. 26.5 mm and 10 mm. Compaction and CBR testes were carried out on trial mixes prepared by blending 10 to 15 % fine soils by mass with natural cinder gravel samples to determine the optimum amount of fine soils required to mechanically stabilize cinder gravel samples. The second series are mechanically stabilized cinder gravel samples (cinder gravels blended with optimum amount of fine soils) stabilised with 3. materials between 37. The cement used was Ordinary Portland Cement. and 37. materials > 4. Tests were conducted as soon as they were removed from the water bath. 5. and 10 % cement by mass.04. The first series of trail mixes are natural cinder gravel samples stabilized with 3.0 Test results Alemgena Lake Chamo 43 % 44 % 2. Curing was necessary to ensure that there is always adequate water for the hydration reaction to proceed and to avoid the possible dry shrinkage while the reactions are proceeding.75 mm 1.0 1.36 mm 0. The specimens were then compacted using the optimum moisture contents determined in the standard mould following the same procedure as that used for proctor density. 2009 .5 15. cement stabilization of cinder gravels with and without the addition of fine soils to compensate for the deficiency of fine materials were investigated.07 %. covered with wet cloth and kept in a humid room to cure for 24 to 48 hours.5%. At the end of the moist curing period the specimens were soaked in water for four hours.75 mm and. As underlined in the previous studies.5 3. materials between 10. 1. covered with wet cloth. fine soils obtained near the quarry sites were blended with cinder gravel samples in order to make up for the deficiency of fine materials before cement stabilization.89 materials > 4. materials < 4. The CBR value of the material is low for base course. one can clearly observe in Fig.Stabilizing Cinder Gravels for Heavily Trafficked Base Course Table 1: Descriptive test results of natural cinder gravels used for the study Type of test Los Angeles Abrasion Aggregate Impact Value Specific Gravity Water absorption Procter test CBR Desirable limits < 50 % < 35 % 2. and 28 days and soaking.5% MDD = 12. During this study.0 2. 5.08%.95 materials < 4. and kept in a humid room to moist cure until it was tested at the required curing period. 2.5 2.75 mm and. materials < 10 mm 8.55 kN/m3 MDD = 12.75 kN/m3 34 % 43 % 25 The descriptive test results in Table 1 shows that cinder gravel is a weak material and has high water absorption capacity because of its high porosity. Table 2: Descriptive test results of fine soils used for mechanical stabilization Type of test Gradation: % Passing 4. 0 MPa. 2009 . CBR is not recommended [5] to be used when the strength of stabilised materials is more than 3 times that of the unstabilised materials. In general.366 28 days 1.51 1.0 27.34 28 days 1.449 1.0 0 1 4.84 14 28 CBR (%) 78 94 - 5 27.0 UCS (MPa) 5. RESULTS AND DISCUSSION Stabilization of Natural Cinder Gravel with Cement Table 3 shows the CBR test results carried out on cement stabilized cinder.802 2.22 3.99 Alemgena 14 days 1.69 2.5 Alemgena MDD Age (kN/m3) (days) 7 13. As shown in Fig. The extensively used method to determine the relative response to cement stabilization and specify the strength of stabilised materials for pavement structure is UCS test.75 14 28 7 13.0 0.24 7 days 1.61 2.81 2. Vol.08 4. CBR tests were also carried out on trail mixes prepared with 3 and 5 % cement contents following ASTM D 1883-87. 2.72 1.0 Table 4: UCS test results of cement stabilized cinder gravel in MPa Cement by weight % 3 5 7 10 7 days 1. Table 4 shows the results of UCS tests carried out on cement stabilised cinder gravels with 7.0 3. and 28 days of curing period.082 3.80 14 28 7 13. the UCS test results clearly indicate that the strength of cement stabilised cinder shows a consistent trend of increase with both increase in stabilising cement and curing period.0 2. 26.17 Lake Chamo 14 days 1.324 3.801 2.33 1.033 4. This is because the strength of stabilised materials usually exceeds the limits of the CBR test procedure.49 1. which is the minimum strength requirement specified in ERA-PDM and AACRA-PDRM at 7% cement after 28 days of curing.0 0.90 14 28 CBR (%) 69 111 140 124 134 202 OMC (%) 26.31 1. It is not also widely used to specify stabilised materials for road construction.41 3.0 0 1 7 Days 14 Days 28 Days Lake Chamo 2 3 4 5 6 7 8 9 10 11 2 3 4 5 6 7 8 9 10 11 % Cement % Cement Figure 2 Variation of UCS with percentage of cement and curing period Journal of EEA.0 7 Days 14 Days 28 Days Alemgena UCS (MPa) 4.0 1.0 3.0 2.4 Lake Chamo MDD Age (kN/m3) (days) 7 13. stabilised cinder gravel attains 3.0 1. D1633-90 procedure. CBR test is used Table 3: CBR test results of cement stabilized cinder gravel Cement by weight % 3 OMC (%) 25.26 Girma Berhanu here to indicate the general response of cement stabilization in cinder gravels.113 5.12 1. 14. The CBR values have increased by two folds for 3% cement in 7 days and almost four folds for 3% in 14 days and for 5% in 7 days. According to the results obtained. In both cases.0 13. The plot of UCS in Figure 4 shows that the strength of cement stabilised cinder blended with 12% fine soils has increased compared with that of stabilised cinder without the addition of fine soils.Stabilizing Cinder Gravels for Heavily Trafficked Base Course Stabilization of Mechanically Stabilized Cinder with Cement Because cinder gravel is deficient in fine particles.3 13.55 34 25.30 13.70 40 26. Vol.32 Cinder + 14 % 28.4 13. 26. the results consistently indicate that MDD and CBR increase with increase in fine soils up to 12%. the amount of cement required to stabilise natural cinder gravel that satisfies the minimum strength requirement (as seen in Section 3. In this section.38 Cinder + 11 % 25.2 13. However.8 12. the minimum strength requirement specified in ERAPDM and AACRA-PDRM is attained at 5% of cement by mass.0 13. 27 This result indicates that the optimum amount of fine soil that makes up for the deficiency of fines in cinder gravel samples from both Alemgena and Lake Chamo areas is 12%.31 Cinder + 15 % 28.75 Cinder + 10 % 25.6 13.98 Cinder + 13 % 27. Mechanical Stabilization of Cinder Gravel Table 5 shows the compaction and CBR test results conducted on mechanically stabilised cinder gravel with 10 to 15% fine soils by mass to determine the optimum amount of fines.80 13.75 43 26. These are presented in subsequent subsections as mechanical stabilization and cement stabilization of cinder gravel below.8 13. 2009 . Accordingly.0 13. This optimum amount. was mixed with the cinder gravel samples in order to investigate the improvement in strength that can be obtained when mechanically stabilised cinder is stabilized with cement.00 13.40 Cinder + 12 % 25.72 40 - CBR (%) 43 47 50 58 47 46 - 14.8 13.80 45 28.50 12.2 9 50 40 30 Alemgena Lake Chamo 10 11 12 % Fine Soil 13 14 15 9 10 11 12 % Fine Soil 13 14 15 Figure 3 Variation of MDD and CBR with percentage of fine soil mixed with cinder Journal of EEA. Cement Stabilization of Cinder Gravel Blended with Fine Soils Table 6 and Table 7 show the CBR and UCS test results carried out on cement stabilized cinder gravel with 12% fine soils respectively.01 13. beyond 12%.2 MDD (kN/m3) Alemgena Lake Chamo 60 CBR (%) 14.88 56 27. the results of two series of tests: (a) to determine an optimum amount of fine soil required to compensate the deficiency of fines in cinder and (b) to investigate the cement stabilised cinder gravel blended with the optimum amount of fine soils determined are discussed.1) for heavily trafficked base course is generally high.70 43 28.00 13. these values decreased. 12% fine soils by mass.3 13. Table 5: Results of mechanical stabilization of cinder with fine soils Alemgena Lake Chamo Fine Soil by weight OMC MDD CBR OMC MDD (%) (kN/m3) (%) (%) (kN/m3) Cinder only 24. Figure 3 shows the plots of these results. 0 3. and relatively easy to dig with shovel or hand tools.0 1.0 5.0 3. 5.0 UCS (MPa) 4.0 0 Lake Chamo 7 Days 14 Days 28 Days 0 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 % Ce me nt % Ceme nt Figure 4 Variation of UCS with percentage of cement and curing period The percentage increase in strength gained by adding fine soils was evaluated as shown in Fig.63 3. As one can observe from the figure. 2009 . This clearly indicates that 5 % cement by mass is an optimum amount to stabilise cinder gravel with sufficient fines.0 Ale mgena 7 Days 6.126 4. their use for road construction is limited for the reason that they do not meet the specification requirements.59 3.21 2.69 2.0 MPa which is the % Increase in UCS 80 60 40 20 0 1 2 3 4 5 6 7 Lake Chamo 8 9 10 11 % Cement · Figure 5 Variation of increase in UCS with cement content Journal of EEA. the percentage increase in UCS gained as a result of adding fine soils has an increasing trend up to 5 % cement and then starts falling.027 28 days 2. In this investigation.40 4.73 1. rarely support any vegetation other than grasses.282 7 2.695 3. the following conclusions are made: · The gradation of cinder gravel samples lacked fine particles and 12 % of fine soil by mass was found to be optimum for making up this deficiency which confirms the results of previous studies.573 10 3.17 3.332 5.0 14 Days 28 Days UCS (MPa) 5.0 0.24 5.91 2. mechanical and cement stabilisation techniques were used to improve their properties so that they are used as base course materials for heavily trafficked roads.596 3. Vol.23 3.0 1. Based on the results obtained. Cement stabilised cinder gravels without the addition of fine soils require 7 % of cement by mass to attain a UCS of 3. 26.336 3.56 2.623 2. 100 Alemgena CONCLUSIONS Although cinder gravels occur extensively in Ethiopia.0 2.0 4.23 6.138 5 2.0 2.28 Girma Berhanu Table 6: CBR test results of mechanically stabilized cinder with cement Cement Alemgena Lake Chamo by weight CBR CBR Age (days) Age (days) % (%) (%) 7 63 7 122 3 14 74 14 28 172 28 7 71 7 5 14 112 14 28 213 28 Table 7: UCS test results of mechanically stabilized cinder with cement in MPa Cement Alemgena Lake Chamo by weigh 7 days 14 days 28 days 7 days 14 days % 3 1.27 4.934 4.0 0. shrinkage. Guide to Stabilization in Road Works". [4] Addis Ababa City Roads Authority. the feasibility of cement stabilised cinder gravels should be checked for every project versus expenses related to getting quality aggregate and hauling distance. [3] Ethiopian Roads Authority.Stabilizing Cinder Gravels for Heavily Trafficked Base Course minimum specified strength in ERA-PDM and AACRA-PDRM for a base course in heavily trafficked pavement structure. 26. 2009 . R. "The Location and Engineering Properties of Volcanic Cinder Gravels in Ethiopia". 2003. Robinson. 9th Regional Conference for Africa on Soil Mechnics and Foundation Engineering / Lagos. September 1987. 2002. "Pavement Design and Rehabilitation Manual". ACKNOWLOGMENT This investigation was carried out as students' final project at Addis Ababa and Arba Minch Universities. "Experimental Use of Cinder Gravels on Roads in Ethiopia". D. 5 % cement by mass is found to be optimum to achieve a UCS of 3. The Author wishes to thank all students who have been involved in this investigation. [5] National Association of Australian State Road Authorities. However.0 MPa. [2] Newil. "Pavement Design Manual Volume I: Flexible Pavements and Gravel Roads". 1986. and traffic. Moreover. a full-scale road experiment is necessary in order to study the performance of stabilised cinder gravels against the possible detrimental effects of cracking due to stresses induced by thermal. Seventh Regional Conference for Africa on Soil Mechanics and Foundation Engineering/Accra. and Kassaye Aklilu. The results obtained in this investigation ascertained that the properties of cinder gravel can be improved by stabilisation and used for heavily trafficked base course. minimum specified by ERA and AACRA for a base course in heavily trafficked pavement structure for cement stabilised materials. Journal of EEA. Vol. D. and Kassaye Aklilu. June 1980. Sydney. REFERENCES 29 [1] Newil.. · With the addition of the optimum amount of fine soils to make up for the deficiency of fine particles.