KEY ISSUES IN THE ANALYSIS OF PILES IN LIQUEFYING SOILS

Transcription

1 4 th International Conference on Earthquake Geotechnical Engineering June 2-28, 27 KEY ISSUES IN THE ANALYSIS OF PILES IN LIQUEFYING SOILS Misko CUBRINOVSKI 1, Hayden BOWEN 1 ABSTRACT Two methods for analysis of iles in liquefying soils are discussed in this aer: an advanced method for dynamic analysis based on the effective stress rincile and a simlified analysis based on the seudo-static aroach. The former method aims at an accurate simulation of the comlex liquefaction rocess and soil-ile interaction while the latter is a design-oriented aroach that uses conventional engineering arameters and modelling for estimation of the maximum ile resonse. This aer discusses some key issues in the imlementation of these analysis methods with reference to the assumtions used in modelling the soil-ile interaction in liquefying soils. Keywords: Effective stress analysis, lateral sreading, liquefaction, ile, seudo-static analysis INTRODUCTION Behaviour of iles in liquefying soils is very comlex involving raid change in stiffness and strength of soils, large ground deformation and significant inertial loads from the suerstructure. A rigorous analysis simulating this rocess in detail, such as the seismic effective stress analysis, imoses high demands on the user in terms of required inut data and understanding of the adoted numerical rocedures. On the other hand, when using design-oriented analyses based on the seudo-static aroach, one encounters great difficulties in the selection of aroriate values for the arameters of the simlified analysis because nearly all arameters used in the simlified model are subject to large variation in the course of the ore ressure build-u and eventual liquefaction. Thus, the key issues in the analysis of iles are quite different for the advanced seismic effective stress analysis and simlified seudo-static analysis. This aer addresses some of the key issues in the alication of these two methods of analysis to iles in liquefying soils. SOIL PILE INTERACTION IN LIQUEFYING SOILS Soil-ile interaction in liquefying soils is a very intense dynamic rocess that involves significant changes in the soil characteristics and loads on ile over a short eriod of time during and immediately after the strong ground shaking. Some tyical features of the ground resonse and loads on iles in liquefying soils are illustrated in Figure 1. During the intense ground shaking in loose saturated sandy deosits, the excess ore water ressure raidly builds u until eventually it reaches the level of the effective overburden stress σ v ' and the soil liquefies. In the examle shown in Figure 1a from the 199 Kobe earthquake, the excess ore ressure reached the maximum level after only 6-7 seconds of intense shaking, and this was ractically the time over which the soil stiffness reduced from its initial value to nearly zero. The intense reduction in stiffness and strength of the soil was accomanied with equally raid increase in the ground deformation, as illustrated with the solid line in Figure 1b where horizontal ground dislacements within the liquefied layer are shown. Note the cyclic nature and relatively large amlitude of these dislacements. The eak dislacement of about 4 cm occurred just 1 Deartment of Civil Engineering, University of Canterbury, New Zealand, misko.cubrinovski@canterbury.ac.nz

2 before or at the time of develoment of comlete liquefaction in the layer and was accomanied with high ground accelerations of about.4g. During this hase of intense ground shaking and develoment of liquefaction, the iles were subjected to kinematic loads due to ground movement and inertial loads due to vibrations of the suerstructure. Both these loads are oscillatory in nature with magnitudes and satial distribution deendent on a number of factors including ground motion characteristics, soil density, resence of non-liquefied crust layer at the ground surface, and redominant eriods of the ground and suerstructure, among others. In sloing ground or backfills behind waterfront structures the liquefaction may result in unilateral ground dislacements due to lateral sreading, as indicated with the dashed line in Figure 1b. Lateral CYCLIC PHASE SPREADING PHASE Excess ore water ressure (kpa) 2 1 σ v ' (a) Horizontal dislacement (cm) Relative ground dislacements between GL-m and GL-16m Cyclic dislacement Sreading dislacement (b) Time (seconds) (c) Figure 1. Illustration of ground resonse in liquefying soils and effects on iles: (a) Excess ore water ressure; (b) Lateral ground dislacement; (c) loads on ile during the cyclic hase and lateral sreading

3 sreads tyically result in large ermanent dislacements of u to several meters in the down-sloe direction or towards waterways. Provided that driving shear stresses exist in the ground, lateral sreading may be initiated during the intense ore ressure build u, at the onset of liquefaction or after the develoment of comlete liquefaction. As comared to the cyclic hase of the resonse, ground dislacements are aroximately one order of magnitude bigger and inertial loads are relatively smaller during the lateral sreading, as illustrated schematically in Figure 1c. These large differences in liquefaction characteristics and loads on the ile between the cyclic hase and lateral sreading hase need to be accounted for in the analysis of iles. SEISMIC EFFECTIVE STRESS ANALYSIS The effective stress analysis ermits evaluation of seismic soil-ile interaction while considering the effects of excess ore water ressure and highly nonlinear stress-strain behaviour of soils in a rigorous dynamic analysis. This method basically aims at very detailed modelling of the comlex liquefaction rocess through the use of advanced numerical rocedures. In rincile, the effective stress analysis ermits simulation of the entire rocess of ore ressure develoment, onset of liquefaction and ostliquefaction behaviour including associated ground deformation and loads on iles during both cyclic hase and lateral sreading hase of the resonse. For these reasons, the seismic analysis based on the effective stress rincile has been established as one of the rimary tools for analysis of liquefaction roblems. Over the ast three decades, the alication of this analysis gradually has exanded from 1- D analyses of a level ground to more comlex 2-D analyses involving earth structures and soilstructure interaction roblems. Recently, attemts have been made to aly this method to a threedimensional analysis of large-deformation roblems, as described below. A comrehensive study on ile foundations in liquefiable soils has been recently carried out in Jaan, with a rincial objective to investigate the behaviour of iles in liquefying soils undergoing lateral sreading, from both exerimental and numerical viewoints. Within this roject, a series of shaketable exeriments on iles in liquefying soils undergoing lateral sreading was conducted at the Public Works Research Institute (PWRI), Tsukuba, Jaan (Tanimoto et al., 23). For all exeriments, Class- B redictions were made using two different constitutive models and numerical rocedures for 3-D effective stress analysis. The rincial objective of the numerical simulations was to assess the accuracy and caability of advanced 3-D effective stress analyses in redicting liquefaction-induced lateral flow and ile grou behaviour. Note that both methods of analysis have been extensively verified and have shown very good erformance in simulations of well-documented case histories, seismic centrifuge tests and large-scale shake table tests of liquefaction roblems (e.g., Cubrinovski et al., 1999; 21; Uzuoka et al. 22; 27). Various factors were varied in the aforementioned shake table exeriments such as the amlitude and direction of shaking (transverse, longitudinal and vertical), mass of the suerstructure and number and arrangement of iles. A tyical hysical model used in these tests is shown in Figure 2 consisting of a 3x3 ile foundation embedded in a liquefiable sand deosit, located in the vicinity of a sheet ile wall. By and large, the numerical redictions were in good agreement with the observations in the exeriment caturing the raid ore ressure build-u, develoment of liquefaction and subsequent ground flow around the foundation. In fact, the resonse of the foundation iles were very well redicted by both methods for all exeriments, as indicated in Figure 3a where comuted and measured horizontal dislacements at the ile head are shown for different tests. As indicated in Figure 3b, however, the analyses underestimated the dislacement of the sheet ile wall. It was found that the rediction of the large lateral movement of the sheet ile wall including instability in the backfills and foundation soils was the most difficult to accurately redict with the advanced seismic analyses. A number of issues are imortant when conducting a seismic effective stress analysis as above, but robably the most critical one is the erformance of the constitutive soil model, both in terms of its modelling caability and roer imlementation by the user. It is essential that the constitutive model

4 a) Model: H14-1, H1-3 & H16-2 SHEET PILE FOOTING Coarse sand 4 Loose Toyoura sand (D r = 3%) PILE Loose T.S. (3%) 9cm Dense T.S. (9%) Figure 2. Schematic lot of hysical model used in the shake table test (a) Footing (ile head) (b) Sheet-ile wall Comuted dislacement (mm) Diana-J Liqca Comuted = Measured (2-D) Measured dislacement (mm) Comuted dislacement (cm) Diana-J Liqca 14-1 (2-D) Comuted = Measured Measured dislacement (cm) 16-3 Figure 3. Comarison between comuted and measured dislacements of footing and sheet ile rovides reasonably good accuracy in redicting the excess ore ressures and ground deformation in order to allow roer evaluation of the soil-ile interaction effects. The initial stress conditions and anticiated ground deformation attern are equally imortant for a correct rediction of ile behaviour. In the above study, for examle, detailed initial stress analyses were conducted in order to identify the initial stress in the soil deosit before the alication of shaking. Secific boundary conditions and soil-ile interfaces were also defined in order to allow develoment of large dislacements and deformation attern associated with lateral sreading. In fact, the latter was found to be one of the major reasons for the underestimation of sheet ile dislacements in the analyses. The aforementioned modelling issues together with inherent limitations of a articular numerical rocedure define the second critical issue in the alication of the seismic effective stress analysis. The comlexities associated with current constitutive soil models and numerical rocedures robably exlain why this analysis in site of the unaralleled caability has not found yet an adequate use in the engineering ractice.

5 PSEUDO-STATIC ANALYSIS Unlike the advanced effective stress analysis which aims at simulating the comlex soil-ile interaction as liquefaction develos through time, the seudo-static analysis aims at estimating the maximum ile resonse by using a relatively simle model and small number of engineering arameters. The key issue in such analysis is thus the selection of aroriate values for the arameters that reresent the soil conditions and loads at the time when the maximum resonse of the ile develos. As discussed in the revious sections, the liquefaction characteristics and lateral loads on iles vary significantly in the course of the develoment of liquefaction and are quite different between the cyclic hase and subsequent lateral sreading hase of the resonse. For this reason, the cyclic hase and lateral sreading hase have to be treated searately in the seudo-static analysis. A conventional beam-sring model allowing for stiffness and strength reduction in the liquefied layer, large movement of the liquefied soil, lateral soil ressure from the crust layer and lateral load on the ile due to inertial effects is shown in Figure 4. While this model generally ermits modelling of multile layers with different load-deformation sring roerties, in essence it distinguishes between three distinct layers: non-liquefiable crust layer at the ground surface, liquefiable layer and nonliquefiable base layer. As indicated in Figure 4, degraded stiffness and strength are used for the liquefied soil, and it is assumed that the crust layer moves as a rigid body on to of the liquefied soil. The characterization of nonlinear behaviour of the soil and ile shown in Figure is robably the simlest one that allows adequate treatment of nonlinear behaviour of the soil and ile. Here, the bilinear - relationshis for the soil are defined by an initial stiffness using the conventional subgrade reaction aroach and by an ultimate lateral soil ressure, max. The subgrade reaction coefficients k can be evaluated using emirical correlations based on the elastic moduli of the soil or SPT blow count while the ultimate lateral ressure for the non-liquefied layers can be estimated using a factored Rankine assive ressure, as described in Cubrinovski and Ishihara (24). a) Cross section b) Soil-ile model Uer foundation c) Numerical scheme U P U G Non-liquefied crust layer H 1 Lateral load Liquefied layer H 2 Degraded stiffness & strength Ground dislacement Pile Deformed ile Non-liquefied base layer H 3 Pile Soil sring Figure 4. Tyical FEM beam-sring model for seudo-static analysis of iles

6 H f H 1 Surface layer M Y Footing U U G2 k 1 1-max H 2 Liquefied layer C φ Pile β k max Ground dislacement H 3 Base layer D o k 3 3-max Figure. Characterization of nonlinear behaviour and inut arameters of the model Key arameters in this model are the magnitude of lateral ground dislacement (U G2 ), ultimate lateral ressure from the crust layer ( 1-max ), and stiffness and strength reduction in the liquefied layer as reresented by the stiffness degradation factor β 2 and ultimate ressure 2-max resectively. Some guidance in the selection of the ultimate ressure from the crust layer and variation in the magnitude of lateral ground dislacement can be found in Cubrinovski at al. (27). Here, effects of the ultimate ressure form the liquefied soil are examined somewhat in detail. Cyclic Phase Assuming that the eak resonse of the ile during the cyclic hase occurs at or before the onset of liquefaction, which is a reasonable assumtion according to observations from exeriments and analyses, then the following reasoning can be alied to the analysis of iles: (i) The value of β 2 commonly varies within a relatively small range of values between 1/2 and 1/1; (ii) The magnitude of cyclic ground dislacements can be estimated reasonably well using simle rocedures analogue to those for evaluation of liquefaction triggering based on emirical SPT / CPT charts, as suggested by Tokimatsu and Asaka (1998) for examle; (iii) The relative dislacement between the soil and the ile is often less than that required for mobilizing the ultimate soil ressure from the crust and liquefied layers; (iv) In addition to the large kinematic loads due to lateral ground movement, the iles are subjected to significant inertial loads from the suerstructure. The above basically imlies that often the articular values of β 2, U G2 and 2-max are not critically imortant, but rather the key issue in the analysis of iles during the cyclic hase is how to combine the kinematic loads and inertial loads on the ile since the eak values of these oscillatory loads do not necessarily occur at the same time. Clear and simle rules for combining the ground dislacements and inertial loads from the suerstructure in the simlified seudo-static analysis have not been established yet, though some suggestions may be found in Tamura and Tokimatsu (2) and Liyanaathirana and Poulos (2). Lateral Sreading Phase In the lateral sreading hase, the otential variation in key arameters is much more significant and involves: (i) Variation in β 2 over relatively wide range of values between 1/1 and 1/; (ii) Large uncertainty in the magnitude of lateral dislacement and scatter in the estimates based on emirical correlations for lateral sreads; (iii) Relative dislacements between the soil and ile sufficiently large to mobilize the ultimate soil ressure from the crust layer and liquefied layer; (iv) Small contribution of inertial loads relative to the kinematic loads. Thus, in the case of lateral sreading, the values of 1- max, β 2, U G2 and 2-max involve great variation and uncertainty associated with the strength and stiffness of liquefying soils, ost-liquefaction sreading dislacements and ultimate ressure from the non-

7 liquefied crust layer at the ground surface. Detailed discussion on the modelling of the crust layer and selection of 1-max is given in a comanion aer resented at this conference whereas here the combined effects of arameters of the liquefied layer U G2, β 2 and 2-max are briefly illustrated through an alication of the analysis to a case study. STIFFNESS AND STRENGTH OF THE LIQUEFIED SOIL The ile foundation of twin bridges crossing the Avon River in Christchurch, New Zealand, was analysed using series of seismic effective stress and seudo-static analyses. Various combinations of loads and liquefaction characteristics including ile-grou and soil-structure interaction effects were considered in these analyses. The seudo-static analyses resented in this aer are used only to demonstrate the effects of the ultimate ressure from the liquefied layer on the ile resonse. Figure 6 shows the soil rofile and SPT blow count at the site including the adoted three-layer interretation of the deosit. The soils between 2. m and 17. m were considered liquefiable, with a dense silty sand base layer below 17. m deth. The water table was estimated at 2. m deth thus defining a non-liquefiable crust layer at the ground surface. The 1.2 m diameter reinforced concrete iles are rigidly connected to a ile ca and extend from 2. m to 23 m deth below ground level. The interaction in the liquefied layer can be treated in a simlified manner by an equivalent linear - relationshi, i.e. with no limiting soil ressure. Alternatively and more rigorously, a limit can be laced on the ressure exerted by the liquefied soil. One aroach in doing this is to use the residual strength of the liquefiable soil S u as defined by Seed and Harder (1991) using emirical correlation with the SPT blow count, as shown in Figure 7. Since the scatter of the data is quite significant for this correlation, it was adoted to use three different S u values in the seudo-static analysis corresonding to an uer bound (S u-ub ), best-fit (S u-bf ) and a lower bound value (S u-lb ) resectively. The urose of this arametric study was to examine the effects of the ultimate lateral ressure from the liquefied soil on the ile resonse. Figure 8 comaratively shows the comuted bending moments and ile dislacements for the analyses with different S u values. Note that an analysis using an equivalent linear - aroximation was also Figure 6. Soil rofile and SPT blow count at the investigated site

8 6 S u-ub S u-lb S u-ub S u (kpa) S u-bf Best-fit Uer bound 1 S u-lb Lower bound (N ) 1 6cs Figure 7. Residual strength (S u ) of sandy soils back-calculated from case histories (after Seed and Harder, 199) Deth (m) 1 1 Mc My Mu Su-lb Su-bf Su-ub Eq. Linear Deth (m) 2 2 Mu My Mc Bending moment (MN-m) Dislacement (m) Figure 8. Effects of ultimate ressure from the liquefied soil on the ile resonse 1 1 Alied ground dislacement Eq. Linear S u-ub S u-bf S u-lb conducted for comarison urose. By and large, the ile resonse decreases with decreasing ultimate ressure from the liquefied layer. Figure 9 shows the relative dislacement between the soil and the ile lotted together with the reference yield dislacement of the soil, for the three analysis cases with different S u values. Here, the shaded areas denote zones over which yielding occurs in the soil. In other words, throughout these deths, the ultimate soil ressure is alied to the ile. Note that the resultant load on the ile increases with increasing ultimate lateral ressure from the soil, with the largest resonse being observed when S u-ub was used as a limiting lateral soil ressure. The equivalent linear analysis overestimates the ile resonse and is not alicable in this case. The relative contributions of the crust and liquefied layers to the total ile also change with the value of S u. As the value of S u decreases the role of the liquefied layer diminishes.

9 S u-lb S u-bf S u-ub Deth (m) Relative dislacement, Yield dislacement, y Deth (m) y Dislacement (m) Dislacement (m) Dislacement (m) Figure 9. Effects of ultimate ressure from the liquefied soil on soil yielding Deth (m) y The reasoning behind lacing limits uon the ultimate ressure exerted from the liquefied soil is to avoid unrealistic loads being imosed in situations with very large ground dislacements. Figure 1 shows how the bending moment of the considered ile varies with different levels of ground dislacement, for an assumed value of β 2 = 1/. It can be seen that when limits are laced on the ultimate ressure, different levels of ground dislacement yield virtually the same resonse. This clearly demonstrates that for any given set of values for β 2 and 2-max there exists a threshold magnitude of lateral ground dislacement above which the ile resonse is ractically unaffected by the magnitude of ground dislacement. Hence, for many analysis cases, a secific determination of the magnitude of lateral sreading dislacement may not be needed. CONCLUDING REMARKS The effective stress analysis aims at detailed modelling of the comlex soil-ile interaction in liquefying soils, and hence, this analysis rocedure is quite comlex and burdened by the large number of arameters and exertise needed for its execution. Two critical issues in the seismic effective stress analysis are: (i) the erformance of the constitutive soil model, both in terms of its modelling caability and roer imlementation by the user, and (ii) details of numerical modelling including initial stress state, boundary conditions and ossible effects of the adoted numerical rocedures. Bending moment (MN-m) 1 1 Eq. Linear Su-ub Su-bf Ground dislacement.m 1m 2m 3m Figure 1. Effects of ultimate ressure from the liquefied soil on soil yielding Su-lb

10 The seudo-static analysis is a simle design-oriented aroach that uses conventional engineering arameters and modelling for estimation of the maximum ile resonse. Liquefaction characteristics and lateral loads on iles are quite different between the cyclic hase and subsequent lateral sreading hase of the resonse, and therefore, these two hases have to be treated searately in the seudostatic analysis. When evaluating the ile resonse during the cyclic hase, the key issue in the seudo-static analysis is how to combine the kinematic loads due to ground movement and inertial loads from the suerstructure. For the lateral sreading hase on the other hand, the combined effects of arameters of the crust layer and liquefied layer 1-max, U G2, β 2 and 2-max are imortant. It is imortant to note, however, that for an assumed stiffness and strength of the liquefied soil (set of values for β 2 and 2- max), there is a threshold lateral ground dislacement U G2 above which the ile resonse is ractically unaffected by the magnitude of ground dislacement. This simlifies the use of the seudo-static analysis and eliminates the need for an accurate estimate of the magnitude of lateral sreading dislacement. REFERENCES Cubrinovski, M., Ishihara, K. and Furukawazono, K. (1999). Analysis of full-scale tests on iles in deosits subjected to liquefaction, Proc. 2nd International Conference on Earthquake Geotechnical Engineering, Lisbon, Vol. 2, Cubrinovski, M., Ishihara, K. and Kijima, T. (21). Effects of liquefaction on seismic resonse of a storage tank on ile foundations, Proc. 4th Int. Conf. on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, San Diego, CD-ROM, 6.1. Cubrinovski, M. and Ishihara, K. (24). Simlified method for analysis of iles undergoing lateral sreading in liquefied soils, Soils and Foundations, Vol. 44, No. 2: Cubrinovski, M., Ishihara, K. and Poulos, H. (27). Pseudostatic analysis of iles subjected to lateral sreading, Secial Issue Bulletin of NZ Society for Earthquake Engineering (to be ublished). Liyanaathirana, D.S. and Poulos, H.G. (2). Pseudostatic aroach for seismic analysis of iles in liquefying soil. ASCE Journal of Geotechnical and Geoenvironmental Engineering, Vol. 131, No. 12: Seed, R.B. and Harder, L.F. (1991). SPT-based analysis of cyclic ore ressure generation and undrained residual strength, H. Bolton Seed Memorial Symosium Proc., Vol. 2: Tamura, S. and Tokimatsu, K. (2). Seismic earth ressure acting on embedded footing based on large-scale shaking table tests, ASCE Geotechnical Secial Publication 14: Tanimoto, S., Tamura, K. and Okamura, M. 23. Shaking table tests on earth ressures on a ile grou due to liquefaction-induced ground flow. Journal of Earthquake Engineering, Vol. 27, Paer No. 339 (in Jaanese). Tokimatsu, K. and Asaka, Y. (1998). Effects of liquefaction-induced ground dislacements on ile erformance in the 199 Hyogoken-Nambu earthquake, Secial Issue of Soils and Foundations, Setember 1998: Uzuoka, R., Sento, N., Yashima, A. and Zhang, F. (22). Three-dimensional effective stress analysis of a damaged grou-ile foundation adjacent to a quay wall. Journal of the Jaan Association for Earthquake Engineering, 2(2): 1-14 (in Jaanese). Uzuoka, R., Sento, Kazama, M., N., Yashima, A., Zhang, F. and Oka, F. (27). Three-dimensional numerical simulation of earthquake damage to grou-iles in liquefied ground. Soil Dynamics and Earthquake Engineering, 27():