Determination of Liquefaction Potentialof Soil Using (N1)60 by Numerical Modeling Method Gholam Moradi Assistant professor Department of Civil Engineering, University of Tabriz, Tabriz, Iran Email:
[email protected] Behnam Rahro Khatibi, Mehdi Hosseinzade Sutubadi Department of Civil Engineering, University of Tabriz, Tabriz, Iran Email:
[email protected] [email protected] ABSTRACT One of the important design considerations for structures situated on sand deposits is the potential for instability caused by the development of excess pore pressure as a result of earthquake loading. A build-up of excess pore pressure may lead to initial liquefaction. In the present study, an alluvium with saturated sand was simulated in FLAC software. Three types of soil mass with various primary condensation (loose, medium dense and dense) were used. Parameter (N1)60 was defined to the software as a main soil property to calculate the other soil parameters such as internal friction angle, relative density, etc. As dynamic loading, acceleration time histories of three earthquakes with various magnitudes (low, medium and high) were applied to the model. To examine pore water pressure variation in the soil mass during the earthquake loading, the parameter ru was defined for the software by a Fish function. ru is the pore water pressure ratio, which equals the pore water pressure increment divided by the primary effective stress in soil. The results showed that FLAC can identify the regions with liquefaction potential by calculation of generated excess pore pressure during earthquake loading. Time histories of ru showed that liquefaction potential in the soil mass changes with depth variations. KEYWORDS: Liquefaction Potential, FLAC, Standard Penetration Test, Pore Water Pressure Ratio, Dynamic Loading. INTRODUCTION When earthquake loading is applied to saturated sand deposits, pore water pressure in the soil starts to increase leading that the soil strength is lost. Liquefaction is the ultimate appearance of this phenomenon (Liyanathirana D.S. and Poulos H.G. 2002). At the initiation of soil - 407 - (2010) shows that the cusp catastrophe model can simulate increment of excess pore water pressure and occurrence of liquefaction due to earthquake loading. This model can predict pore water pressure increment and liquefaction potential. the effect of depth variation on liquefaction potential is studied by definition of time histories of ru in various points of the soil mass. the effects of pore water pressure with or without loss of pore water pressure can be obtained. some dynamic centrifuge model testing (Steedman et al. Therefore. Their numerical analysis was performed by FLAC software. Bund. THEORY AND PROCEDURE OF NUMERICAL MODELING For modeling the soil mass with liquefaction potential. Therefore. Field experience during past earthquakes (Youd et al.). the effective stress in the soil becomes zero and pore pressure in the soil becomes equal to the initial confining pressure of the soil mass. and recently. Although simplified methods (Seed and Idriss. (2010) show that numerical simulation of liquefaction can predict both excess pore water pressure and displacements of marine structures. 2010). 16 [2011]. With FLAC. Also. 1971) are available in calculating the liquefaction potential of a soil mass. To perform the simulation. The effect of soil densification and magnitude of earthquake loading (as a dynamic loading) in liquefaction potential of the soil and level (or depth) of liquefied regions in the soil mass is considered. also it can be calculate as a function of volumetric strain and other parameters can be defined by void ratio.Vol. Generally. Presented results by Jafarian et al. For this purpose. the generation of pore water pressure can be calculated by considering the irrecoverable volumetric strain on basic model Finn with dynamic option. In addition. During past earthquakes. implementation of numerical simulation is necessary for examination of liquefaction potential. it is necessary to implement a numerical simulation to obtain pore water pressures and shear stresses in the soil due to earthquake loading. D 408 liquefaction. the FLAC software is used. these methods can’t be applied to all earthquakes with the same accuracy. In this paper liquefaction potential of saturated sandy soil is studied. 2001) shows that liquefaction has generally occurred at depths less than 15 m. Therefore. 2000) proposes a depth on the occurrence of liquefaction. piers. Furthermore. Numerical simulation performed by Shun-gun Li et al. liquefaction induced displacements have caused serious damages to marine structures (such as quay walls. breakwater. the prediction of liquefaction is the main concern for structures located in medium to high seismicity regions (Jafarian et al. an applicable constitutive model of saturated soils and a suitable formulation of numerical method for the two-phase coupled problem are required. an alluvium with saturated sand is simulated in FLAC software using Finn constitutive model. it is tried to simulate liquefaction phenomenon in FLAC using parameter (N1)60 as a main factor for soil parameters required to the software and identifying liquefiable regions in the soil mass. In Finn constitutive model. they can’t predict the pore pressure developed in the soil due to earthquake loading. The numerical simulation of liquefaction is essential in understanding the liquefaction mechanism. . it is assumed that void ratio is constant. Finn constitutive model is considered as default in FLAC that facilitates the ability of soil modeling in liquefaction states. equivalent linear method (Seed and Idriss 1969) and Finn constitutive method are used. The finite difference method for analysis of soil mass is used in FLAC. Also. etc. ) (3 3) U Using an empirical relationn between Dr and the norm malized standdard penetratiion test valuees (Boullanger 2004). Their propposed model is an equuation linking g the incremeent of the volumetric strainn per cycle off loading to the t shear straiin occurrred during th hat particular cycle. so Eq. (1).4/C1 in this case. a 1980)).. where γ is presum med to be thee “engineeringg” shear strainn: ∆? = ? (? ?−? ? )+ ? ? ?+? ? (1 1) w where C1. 16 [2011]. They supply the following fo emppirical equatiion that relatees the inncrement of volume decrrease. Definition D n of Soil Mass an nd Mesh Model A soil mass with w 30 meteers height annd 400 meterrs length is assumed a for the numericaal simulation. It is assumed thatt the bed of thhe soil mass is rock and both leftt and right boundaries of the model have h free-fieldd condition (Cundall ( et al. C3 and C4 aree constants. (5 5) C2 is then calcculated from C2 = 0. (1975) propossed an effective stress anallysis approacch. the mesh m model iss shown. B Byrne (1991) proposed p a modified m and simpler volum me change moodel with two parameters: ∆? ? ? ? = ? exp −? 2) (2 w where C1 and C2 are constaants with diff fferent interprretations from m those of Eqq. D 409 F Finn Constitutive Model M Martin et al.. Figure 1: The soil masss mesh .V Vol. Δεvd. ? = 7600(? . Parameter (N ( 1)60 is the main m factor of o numerical simulatiion in Finn Coonstitutive moodel in FLAC C. C2. γ. In manny cases. C2 = 0.7(? ) . to t the cyclicc shear-strainn amplitude. Bund. In Figu ure (1).4/C1. (N1)60: ? = 15(? ) (4 4) T Then: ? = 8. (2) innvolves only one o independent constant. 9 liquefaction happens. to introduce the soil condensation.Vol. the Boulanger formula (2004) is used. D 410 Then. the parameters of Finn model are defined by introducing (N1)60 for all the regions of soil mass.93. Previously. for determining the relative density (Dr) with (N1)60. parameter (N1)60 is used. values of (N1)60 equal to 8. if ru reaches a value greater than 0. For observation of the earthquake magnitude. But ru=1 is only theoretic definition for liquefaction occurrence.2g). Examination of Liquefaction Potential of Soil Mass with Various Condensations by Applying Karebass Earthquake As previously described. Also the quantity of (N1)60 is used to calculate the other soil parameters such as internal friction angle. if ru inclines to 1. (6): ?= 15. . it is experienced that liquefaction phenomenon occurred at ru=0. Therefore in this research.4 × (? ) + 18 (6) Finally. 16 [2011]. The relationship between these parameters with (N1)60 is defined to the software by a Fish function. Bund. special time histories are defined in some points of the mesh. acceleration time history of three earthquakes with low magnitude (Karebass earthquake with maximum acceleration 0. ru is the pore water pressure ratio. which equals the pore water pressure increment divided by the primary effective stress in soil. classification of soil regarding (Dr) and (N1)60 is denoted.15 and 25 are chosen. These time histories are defined to the software by a Fish function. According to Table (1) which is presented by Clayton et. Rayleigh damping is used for the model and relevant coefficients are given to the software. For observation of effective stress and pore water pressure variations. effective stress inclines to zero and liquefaction should occur. For example. The software calculates the values of C1 and C2 for all the regions of soil mass. average magnitude (San Fernando earthquake with maximum acceleration 0. the values of bulk modulus and water density and gravity are given to the program.42g) are used as dynamic loading for the soil mass. By use of this table.29g) and high magnitude (Bam earthquake with maximum acceleration 0. internal friction angle φ is defined by Eq.al (1993). EXAMINATION OF THE RESULTS To distinguish between liquefiable and non-liquefiable areas. parameter ru is defined. Theoretically. Next. relative density and also the required parameters for the model to calculate volumetric strains such as shear modulus and initial bulk modulus. It is defined to the software by a Fish function. Also. . Fig gure (2) show ws that increase of soil dennsity leads too decrease off liquefied areea and decrease of liq quefaction pottential in deepp area of the soil s mass. 16 [2011]. Figurre (2-C) show ws that reegion with liq quefaction pootential is only in depth off 12m from thhe surface andd the soil masss in deppth of 30m is not liqueffied at all. B-meddium dense saand. earthqquake (Kareb Figure 2: Maximum m values of ru in i different densities of thee soil inducedd by Karebbass earthquakke Inn Figure (2-A A).V Vol. G Generally. Figure (2-B) obviously o shoows that liqueefied area in depth of 30m m reduces andd only a smaall part of o it in that depth reaches thhe liquefactioon boundary. maxim mum values of o ru become smaller s (yelloow color).100 (N1)60 (blows/300mm m) 0–3 3–8 8 – 25 25 – 42 42 . Also A it showss that.9 and thherefore the sooil mass is liqquefied. F this figure shhows that loose sand is liqquefied in botth approximatte depthhs 12 and 30m m. in thee regions neaar the surface. the soil maass in two vaarious depths have experieenced maximuum increase in i pore water pressu ure. thhe maxim mum value off ru is more thhan 0. Furthermore. But in depth of 12m in thee soil mass. Bund. . D 411 Table 1: Rellationship bettween (N1)60 and a soil conddensation Cllassification Very V loose Loose Medium Dense Very V dense Dr (%) 0 – 15 15 – 35 35 – 65 65 – 85 85 . Accordinng to this figgure. C-dense sand).58 Figure (2) sh hows the maaximum valuees of ru in soil mass innduced by loow magnitudde bass) (A-loosee sand. the soil around the regions markked in blue is liqueffied and aroun nd the regionns marked in pink p is on thee boundary beetween liqueffiable and nonnliqueffiable areas. Bund. s induced by b San Figure 3: Maximum values of ru in different dennsities of the soil Fernanndo earthquakke Inn Figure (3-C C) the area with liquefaction potential in depth of 30m 3 reduces and maximum m liqueffaction potenttial is approxiimately in deppth of 12m. Examina ation of Liquefact L tion Pote ential of Soil S Mass s with Various s Conden nsations by Apply ying Bam m Earthquake Figure (4) show ws the maxim mum values of o ru in soil mass m induced by b medium hiigh earthquakke m) (A-loose san nd. In Figure (3-B B). 16 [2011]. the soil mass havee liquefactionn potential in both b depth off 12 and 30m. C-dense sannd). Figu ure (3-A) show ws that liqueffied area in depth of 30m is larger thann liquefied areea in deppth of 12m.. C-ddense sand). the area of o liqueffied region in n depth of 30m reduces annd liquefied region r obviouusly is seen. B-medium B dennse sand. On O contrary to t Figuree (3-B). On the otherr hand. D 412 Examina ation of Liquefact L tion Pote ential of Soil S Mass s with Variou us Conde ensations s by App plying Sa an Fernan ndo Earrthquake e Figure (3) sho ows the maximum valuess of ru in soiil mass inducced by mediuum magnitudde earthqquake (San Feernando) (A-lloose sand. by appplying the medium m magnnitude earthqquake on loosse sand. B-medium m dense sand. a deep areaa of soil masss has more liquefaction potential. (Bam Figgure 4: Maxim mum values of o ru in differeent densities of o the soil indduced by Bam m earthquake .V Vol. On O the contrarry to Figgure (2). -All figures show that maximum potential of liquefaction in the soil mass is between depths of 10 and 15m. 16 [2011].Comparing Figure (2) and Figure (3). effective stress and pore water pressure).Vol. only one specific region with liquefaction potential is seen. According to these figures. liquefaction potential decreases from bottom to top of the soil mass. several time histories are defined in various points of the model mesh to score variations of soil parameters during earthquake loading (such as ru. on the contrary to Figure (2) and Figure (3) in the soil mass with applied high magnitude earthquake. shallow regions of the soil mass have maximum liquefaction potential. larger area of the soil mass is in the liquefaction boundaries. D 413 According to Figure (4-A). From Figure (4-B) it is seen that by increasing the soil density.In Figure (2) and Figure (3) which are related to low and medium magnitude earthquakes respectively. which are applied. In Figure (4-C) it is obviously seen that in depth of 12m there is maximum liquefaction potential. General Results From Above Figures . On the other hand. a specific region cannot be distinguished as an area with liquefaction potential. by comparison with previous corresponding figures. approximately all the regions of the soil mass by applying high magnitude earthquake is liquefied and on the contrary to Figure (2-A) and Figure (3-A). This range of depth is similar to results of Seed and Idriss method (1971). . Bund. . time history of ru in middle region of the soil mass in depth of 10 and 20m is studied. the area of liquefied region decreases in depth of 30m. shows no particular difference between liquefied region area. only one liquefied region is seen. when soil densification increases. In this figure on the contrary to previous figures.According to Figure (4). However. . the soil mass has maximum potential of liquefaction in two separated regions. For example in this section. It is due to the small difference between maximum accelerations of two earthquakes. The Effect of Depth Variations on Liquefaction Potential of Soil Mass To examine the modeling exactness. V Vol.. Bund. 16 [2011]. D 414 F Figure 5: Tim me history of ru in depth of 10m related to t dense soil induced by hiigh magnitudde earthhquake loadingg F Figure 6: Tim me history of ru in depth of 20m related to t dense soil induced by hiigh magnitudde earthhquake loadingg . value of ru after tenth second inclines to 0. When soil condensation becomes high. the liquefied region moves to the surface. two separated regions with liquefaction potential are seen in depth of 12 and 30m. Schema of variations of ru in depth of 10m is different from variations of ru in depth of 20m. On the other hand.87 and the soil mass is not liquefied in that point. minimum effective stress in depth of 20m is more than corresponding value in depth of 10m. The maximum value of ru in Figure (5) is 0. In figure (6). liquefaction potential decreases. in all types of the soils with various densities. value of ru after tenth second suddenly falls and it inclines to 0. 6. 1. the final value of ru is 0. D 415 Both of two figures show that the soil mass has experienced maximum value of ru in tenth second of earthquake loading.Vol. In depth of 10m. Results show that Finn constitutive model can calculate excess pore pressure during earthquake loading by measurement of irrecoverable volumetric strain. only one area with liquefaction potential is seen. Results show that variations slope of ru (or pore water pressure) in lower depth (10m) is more than variation slope of ru in higher depth (20m). the value of ru after tenth second suddenly falls and it inclines to constant value (0. In depth of 20m. . In all types of soils (with various densities) by applying high magnitude earthquake loading. if depth increases. value of ru after tenth second inclines to constant value (0. it means that soil mass in that point is liquefied.83) with lightly ascending slope. 4.93. the liquefied regions are specified. while maximum value of ru in figure (6) is 0. It shows that when depth increases. Generally. Maximum value and variations slope of ru in Figure (5) are more than corresponding values in figure (6). CONCLUSION Based on numerical results the following conclusion can be obtained. the soil mass near the surface reaches sooner to the liquefaction state. Bund. During earthquake loading. In the loose and medium dense sand with applied low and medium magnitude earthquake loading. By introducing ru as a liquefaction potential index. The volume of liquefied region located in approximate depth of 30m is less than volume of liquefied region in approximate depth of 12m. This result shows that the effect of high magnitude earthquake shows its effect in low depth of the soil mass.83) with lightly descending slope. liquefaction potential in low depth is more than liquefaction potential in high depth. On the other hand. 3. 2. In Figure (5). 5. It shows that liquefaction potential in low depth is more than liquefaction potential in high depth.83 with a lightly ascending slope. 16 [2011].83 after peak point. At both states.83 with lightly descending slope. less reduction occurs in effective stress and there will be less increase in ru as well. ASCE. 6. Div. Hansteen. 1991). and Vakili. and Idriss.B.” J. CA 95616-5924.. C. D. and Poulos H.M (1971) “Simplified procedure for evaluating soil liquefaction potential. Selnes (1980) “NESSI — Soil Structure Interaction. Conf. 1. Seed. Boulanger.” Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics (St. Jafarian. 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