5.14 Seismic Analysis of Interlocking Block in Wall–Foundation–Soil System

Challenges, Opportunities and Solutions in Structural Engineeringand Construction – Ghafoori (ed.) © 2010 Taylor & Francis Group, London, ISBN 978-0-415-56809-8 Seismic analysis of interlocking block in wall–foundation–soil system M.S. Jaafar, F. Hejazi, A.A. Abang Ali & J. Noorzaei Universiti Putra Malaysia, Selangor, Malaysia ABSTRACT: An interlocking mortar less concrete masonry block is a innovative structural component for masonry building construction. In this study an attempt was made to analyse a special interlocking mortarless hollow concrete block system which was developed by the Housing Research Center of University Putra Malaysia. The system was subjected to earthquake loading using the finite element method. An analysis was conducted on the hollow block wall, foundation and soil interaction. For this purpose, a finite element program was developed to analyze the masonry system under earthquake excitation. In order to account for the dry joint contact between the blocks, foundation and soil mass, an interface element was used. The response of the mortarless block wall with respect to displacement, stress and acceleration subjected to earthquake was studied and the effect of applying dry interlocking joints for connection of the block on seismic response of the system investigated. 1 INTRODUCTION The complex interaction between block units, dry joint and grouting material (if any) has to be well An interlocking mortar less concrete masonry block understood under different stages of loading; i.e. building system was developed as a new structural elastic, inelastic and failure. component for masonry building construction. The For interlocking mortarless masonry system, a very interlocking mortar less block system will reduce con- limited number of FE analyses have been reported in struction time and cost of construction. Interlocking the literature (Oh 1994; Alpa et al. 1998). mortar less load bearing hollow block system is dif- However, the characteristics of dry joints under ferent from conventional mortared masonry system as seismic excitation, and their effect on the overall the mortar layers are eliminated and instead the block behavior of the interlocking mortarless wall— units are interconnected through interlocking protru- foundation—soil system, are still not well understood. sions and grooves. Numerous analytical models have This paper covers the analysis of a special interlock- been developed to simulate the behaviour of the dif- ing mortar less hollow concrete block system devel- ferent types of structural masonry systems using the oped by the Housing Research Center of Universiti finite element (FE) technique. Putra Malaysia, subjected to earthquake loads using Two main approaches have been employed in the finite element method, to study the effect of using dry masonry modelling depending on the type of the prob- interlocking joints for connection of blocks under seis- lem and the level of accuracy required. The macro- mic loading of the hollow block wall. The interface modeling approach intentionally makes no distinction element is used for modelling of these joints. Also an between units and joints but smears the effect of joints attempt was made to model the foundation and soil and through the formulation of a fictitious homogeneous a seismic analysis of overall system was carried out. and continuous material, equivalent to the actual one which is discrete and composite (Lotfi & Shing 1991; Cerioni & Doinda 1994; Zhuge et al. 1998). The alter- 2 PUTRA BLOCK BUILDING SYSTEM native micro-modeling approach analyzes the masonry material as a discontinuous assembly of blocks, con- The traditional masonry construction method which nected to each other by joints at their actual positions, requires the use of mortar is labor intensive, and hence the latter being simulated by appropriate constitutive slow, due to the presence of a large number of the mor- models of interface (Suwalski & Drysdale 1986; Ali & tar joints. Therefore, there have been several attempts Page 1988; Riddington & Noam 1994). An extensive to develop interlocking mortarless hollow blocks in critical review of the analytical models of differ- different parts of the world in the recent years. These ent masonry systems can be found in the literature blocks vary widely in dimension, shape and interlock- (Alwathaf et al. 2003). ing mechanism. In Malaysia, the Putra interlocking 351 2008). ⎧ T⎫ This building system as seen in Figure 1 consists of ⎪ ⎪u1 ⎪ ⎪ three types of blocks: Stretcher block. the pair of nodes 1–1. Corner block    ⎪⎪ ⎨v T ⎪ ⎪ ⎬ ua 1 0 −1 0 1 and Half block. (b) Corner block. (Thanoon cates top & bottom continuum respectively. Saleh Jaafar et al. v1T . 3–3 and the tive displacement middle line nodes a. and the indices T and B indi- Centre (HRC) of Universiti Putra Malaysia. 2–2. the rela- Figure 2. Nc = (ξ + 1) u 2 2 = [N ] [T ] {δ} = [N ]δ {δ} (11) (5) v 352 . ⎪ ua ⎪ ⎪ ⎪ ⎪ ⎪ mulation of the interface element are presented herein: ⎪ ⎪ va ⎪⎪ ⎪ ⎪ ⎪ ⎪     ⎪ ⎨ ⎪ ⎬ u Na 0 Nb 0 Nc 0 u b x= Ni xi (1) = v 0 Na 0 Nb 0 Nc ⎪ ⎪ vb ⎪⎪  ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ u ⎪ ⎪ y= ⎪ ⎪ c ⎪ Ni yi (2) ⎩ v ⎪ ⎭ c  u= Ni ui (3) (9)    v= Ni νi u (4) = [N ]2∗6 {}6∗1 (10) v Where Na . Nc are the shape function at nodes as follows: By substituting Equation 8 into Equation 10 to get the following equation: 1 1   Na = ξ(ξ − 1). relationship can be expressed as. b. Also it can be write: (b) (c) ua = u1T − u1B and va = v1T − v1B Figure 1. (a) Stretcher block . v1B . Nb = (1 − ξ 2 ). uc = u3T − u3B and vc = v3T − v3B mortar less load bearing hollow concrete block system u1T . Thanoon et al. it also eliminates the need for steel reinforcement and therefore is very effective = [T ] {δa } (7) in reducing both cost and time of construction. c are defined by the same ⎧ ⎫ coordinates respectively. u1B . is sandwiched between two continuums. Brief descriptions on the for. (c) Half ub = u2T − u2B and vb = v2T − v2B (6) block. 2006. as shown in As in the case of isoparametric elements. The above et al. but is capable of withstanding the ver. are the nodal displacements has been developed recently by the Housing Research in x and y directions. c 3 INTERFACE ELEMENT {} = {a b c }T = [T ]6∗12 {δ}12∗1 (8) A typical curved parabolic interface element which Here again [T] is transfer matrix. Nb . (a) Figure 2. Parabolic interface element. Similar expression can be written for b . u2T · · · etc. {a } = = va 0 1 0 −1 ⎪ ⎪u1 ⎪ B ⎪ The Putra block building system does not require ⎪ ⎪ ⎪ the mortar layer. 2004. ⎩ B⎪ ⎭ v1 tical and horizontal loads. (a) 8-noded elements used for modelling of hol. the wall was modelled without consid- face characteristics of the dry joint and bond between ering the interlocking joints between prisms and the blocks Figure 3-b. Geometry of considered wall. and v are the displacements in the local co-ordinate ξ and η directions respectively. The two models prepared to investigate the effec- 4 FINITE ELEMENT MODEL tiveness of the interlocking system for connecting the block prisms are as follow: In the present study the hollow prisms modelled using an eight-node isoparametric element to simulate the 4. this analysis was carried out under static Foundation loading with self weight of blocks and loads coming Hollow Interface & from the roof and the resulting stresses were treated Block Soil as initial stresses which were then imposed on the structure during seismic analysis. respectively. (t) is the thickness of the ele- ment and [B] is the strain–displacement matrix of the 5m 5m 3m 5m 5m joint.  [K] = [Bi ]T [Di ] [Bi ] ds (13) Table 1. 5 RESULTS AND DISCUSSION low block prism. foundation and soil written as: system. foundation and soil properties. An eight-node isoparametric ele.3 2000 τ Soil 5e4 0. [R] is a rotation matrix and transfers global strains to local strains.2 Model 2 Figure 4 shows the finite element model of the wall- foundation—soil system. 4.3 2000   Foundation 1.3m εt 1 u 1 =  = [R] [Nδ ] {δ} = [Bi ] {δ} (12) εn t v t 5m   where u . (a) (b) (c) Figure 3. and Knn are the shear and normal stiffness between wall and foundation. The stiffness matrix of the interface element can be Figure 4.1 Model 1 masonry constituents Figure 3-a and six-node isopara- metric interface element of zero to model the inter. (b) 6-noded elements used for modelling of the interface. [Di ] is the Modulus of Poisson’s Density elasticity matrix for the joint and ds is a small length elasticity (kN/m2 ) ratio (kg/m3 ) of the joint and Wall 1. Wall. As explained earlier. foundation and soil are summarized in Table 1. During the first step. εt and εn are the tangential and normal strains respectively at 5m the point.2 1500 [σ ] = = [Di ] {ε} (14) σn   Kss 0 [D] = (15) 0 Knn element has been used for modelling of connection where Kss. ment is also used for modelling of foundation and soil Figure 3-c. (c) 8-noded elements used for modelling of Both models were subjected to earthquake in the form foundation and soil. where [Bj ] is the strain displacement matrix.4285e7 0. the interface element was used for modeling of these joints. In this model. In this model an interface The wall was modelled by considering dry joints between blocks.4285e7 0. blocks directly connect to each others from their nodes. The strain at any point in the joint defined by the Wall local coordinate system: 5m Foundation Soil     0. of ground acceleration time series previously recorded 353 . The material properties for the modeling of the wall. 03 meters.5 0 -0.5 -1 0 5 10 15 20 Time (Sec) (a) – Model 1 Figure 5. and the displacement of the model (2) wall in X direction with the interlocking joints was less than the permis- sible amount. The displacement of model (2) in X direc. and for model (2) was 8 Mpa. Displacement of top node of the wall in X direc.5 1 0. (b) – Model 2 Figure 7. tion are plotted in Figures 6-a and 6-b respectively. It was clear from these figure that the amount of (b) – Model 2 displacement in Y direction was very small. Displacement of top node of the wall in Y direc- tion (m). so it is in an acceptable range imposed earthquake. dry joints for connecting the block prisms.15 g). The compressive strength of Putra block was about As seen in these figures maximum displacements of 23 Mpa. Maximum principal stress variation in the ele- ment at the bottom of the wall subjected to earthquake are plotted in figures (8-a) and (8-b) in model (1) and in Malaysia as shown in Figure 5 and the response model (2) wall respectively. The permissible displacement value for the horizon- tal movement of the wall was about 0. But the stresses in model (1). loading. Therefore the maximum Figure 6 shows the time history displacement of the principal stress was reduced to about 90% in model (2) top node of the wall in X direction during earthquake compared with model (1) due implementation of the excitation. The time history for principle stresses (S1) and (S2) at the nearest gauss point at the bottom of both model Figure 6. respectively. Earthquake acceleration record for Malaysia (PGA = 0. As seen in the figures of the wall was evaluated in terms of displacement. The minimum nominal stress almost 55% less than model (1) and it was shown that in model (1) was about 82 Mpa and in model (2) is 354 . pal stresses in the same element for Model (1) and The displacement of model (2) in X direction was model (2). Response of both models in the X direc. the maximum nominal stress in model (1) was 84 Mpa stresses and accelerations. permissible strength of block and will lead to failure. (a) – Model 1 the interlocking dry joints for connecting the block prisms can effectively reduce the horizontal displace- ment of the wall. therefore model (2) shows it can resist the models (1) and (2) were about 0.025 meters imposing earthquake because the stress was only respectively.06 and 0. Figure 7 shows the displacement of the top node of both models in the Y direction subjected to earthquake load. exceeds the It was seen that the interlocking dry joints for con. walls are shown in Figures 8 and 9 during earthquake tion (m). 2 Acceleration (m/s^2) 1. necting the block prisms can effectively reduced the Also Figure 9-a and 9-b show the minimum princi- horizontal displacement of the wall. 8 Mpa and less than the ultimate compression strength tion was almost 55% less than model (1) during the of the block of 23 Mpa. of stresses. are used for conventional masonry construction in Thus it is necessary to provide some additional low seismic area. Therefore from the results it was obvi- ous that the interlocking wall system was suitable for low earthquake area by just adding some strengthening system to resist the tensile stresses as mentioned above. The interlocking keys provided for the building connecting the blocks effectively reduce the amount system were able to integrate the blocks into a of minimum stress in the wall but again it is more than sturdy wall and can replace the mortar layers that tensile strength of the block. It was clear that the amount of minimum the test results from this investigation. Principal stress of bottom element of the wall—S2 (MPa). fail. Acceleration of top node of the wall in X direc- tion (m/s2 ). So the minimum stress in model (2) was of masonry materials. The acceleration was increased by about 50% in some time steps of load excitation (Earthquake accel- eration) on model (2) wall compared with that in model (1).06 Mpa. The tensile strength of the block was about successfully developed and includes the modelling 2. Principal stress of bottom element of the wall—S1 (MPa). Time series acceleration of the top node of response of the system. Figure 10. Figure 9. The finite element model of the mortar less block for connecting of the blocks leads to reduced stress in masonry wall-foundation-soil system has been the wall. the wall as shown in Figure 10-a subjected to earth- quake were plotted in Figure 10-b for model (1) and Figure 10-c for model (2) wall. From these plots it was obvious that the maximum acceleration was about 17 g for model (1) and 26 g for (a) – Model 1 model (2). Therefore. Maximum displacement of 355 . strengthening system such as reinforcement for increas. But in high intensity earthquake area this system is (b) – Model 2 not recommended. 3. As observed the use of interlocking dry joints for 2. Application of dry interlocking joints for con- ing the tensile strength of the wall to resist tensile necting the blocks effectively reduces the seismic stress. several conclu- stress is about 90% smaller than that in model (1) in sions can be drawn as follows: most time step of earthquake excitation. 6 CONCLUSIONS Based on the foregoing analysis and discussions on 8. mortarless dry joint and more than the tensile strength of the blocks and it would block-grout interface behaviour. the use of dry interlocking mechanism 1.1 Mpa. (a) Model 1 (a) – Model 1 (b) Model 2 (b) – Model 2 Figure 8. Strength correlation between individ-ual block. subjected to concentrated loads. Vol. Riddington JR. wall. pp. 2004. 1994. A.D. 1998. Monetto I. 86: 520–528. D. p. Thanoon. Malaysia through the Housing Research Center the capacity of concrete block walls. Noam NF. Finite element analysis of inter-locking mortarless Engineering. 114(8): 1761–84. 4. reinforcement need to be provided for this. Construction and Building Materials. W. Thanoon WAM. of IBS2003 conf. 1991. Structural Engineering. Waleed A. The maximum stress in the model (2) wall was less anism of interlocking mortarless block masonry system. Abang Abdul-lah Abang Ali. 122–35. Jaafar M. 356 . ASCE. Ahmed H. Amad M. Spon.. Influence of slenderness on ences. Ali. Coreroy J. Noorzaei J.R. and it was within an acceptable margin of com. Finite element predic-tion of ACKNOWLEDGMENTS masonry compressive strength. 1998. thesis. 18: 445–454. A finite element model for the tion. the tensile strength of the block. Suwalski P. Computer and Structures. Oh K. Journal of Construction and Building Materials. 1994.S. and hence some 2006. Cerioni R. Jaafar MS. 4th Canadian masonry symposium. Also the maximum and minimum principal nonlinear analysis ofreinforced and prestressed masonry stresses were reduced by about 90%. 52(1): 113–9. Mohd.. Journal of Computers and Alpa G.S. 492–498. 2003. Computer and Structures. Journal of Structural 2008. Abdul Kadir. Najm.A. The results show that the interlocking hollow block Lotfi H. pressive strength but the minimum stress exceeded Mohd Razali Abdulkadir. The financial support granted by the Academy of Sci. Alwathaf. hollow block masonry prism..M. Gambarotta L. Page AW. p. Alwathaf AH. 111–8. Doinda G. continuum modeling for the in-plane analysis of shear Zhuge Y. Saleh Jaafar. 20. Journal of on computer methods in structural masonry. In: Proceeding of the 4th international symposium dynamic analysis of unreinforced masonry. 53: 1291–306. Philadelphia: Drexel University. M. E & FN. Mohd. Abdulkadir MR. edged. Thambiratnam D. Thanoon.. 41: 413–25. Razali Abdulkadir. Nonlinear walls. prism and basic wall panel for load bear-ing interlocking mortarless hollow block masonry. In: Proceed-ing of of Universiti Putra Malaysia is gratefully acknowl. and Najm. In: Proc. 124(3): 270–7. 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