LOAD TRANSFER AND DEFORMATION ANALYSES OF PILED-RAFT FOUNDATION IN TAIPEI METROPOLITAN
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1 798 Journal of Marine cience and Technolog, Vol. 24, No. 4, pp (216) DOI:.6119/JMT LOAD TRANFER AND DEFORMATION ANALYE OF PILED-RAFT FOUNDATION IN TAIPEI METROPOLITAN Der-Gue Lin 1, Wen-Tsung Liu 2, and Jui-hing hou 3 Ke words: piled-raft foundation, load-carring ratio of the raft, FLA 3D, settlement. ABTRAT Piled-raft sstems are often suitable for foundations of highrise buildings to increase the bearing capacit and reduce the ecessive settlement of foundations. However, the conventional design of the piled-raft foundation commonl ignores the bearing effect of the raft. A parametric stud on the piled-raft foundation performance including the bearing effect for tpical Taipei ubsoil is investigated using 3D FDM program, FLA 3D. Input parameters of the parametric stud are back calculated from a series of static pile loading tests implemented on the jobsite of TIF (Taipei International Financial orporation or Taipei 1). Parametric stud results show that the loadcarring ratio of the raft depends on the number of piles of the pile group and the level of loading applied to the piled-raft foundation. This also shows that the raft of the piled-raft foundation is capable of sharing load. In addition, the settlement, differential settlement and bending moment of the piled-raft foundation are also discussed in this article. I. INTRODUTION The possibilit of using a piled-raft foundation to support superstructures as an economical alternative to the conventional piled foundation is gaining popularit in recent ears. The design of piled-raft foundations reuires analses considering the load transferring mechanisms between pile, soil and raft (Poulos et al., 1997). Three tpes of analses developed for the piled-raft foundation are commonl used: (1) simplified calculation methods simplifications on modeling the pile, Paper submitted 8/17/; revised 1/8/16; accepted 3//16. Author for correspondence: Jui-hing hou ( dglin@dragon.nchu.edu.tw). 1 Department of oil and Water conservation, National hung-hsing Universit, Taichung, Taiwan, R.O.. 2 Department of ivil Engineering, Kao-Yuan Universit, Kaohsiung, Taiwan, R.O.. 3 inotech Engineering onsultants, Taipei, Taiwan, R.O.. soil and raft interactions (Poulos and Davis, 198; Randolph, 1983 and 1994); (2) approimate computer-based analses using strip on springs approach (Poulos, 1991) or plate on springs approach (lanc and Randolph, 1993; Poulos, 1994); and (3) more rigorous computer-based methods - boundar element methods, 3-D FEM (Oh et al., 29; Lee et al., 2; Poulos et al., 211; Karim et al., 213; Nguen et al., 214) or 3-D FDM (omodromos et al., 29). In order to mimic the actual field conditions, 3-D FEM or 3-D FDM analses are desirable. 3-D FEM usuall reuires a large amount of computer storage and time but 3-D FDM on the other hand is memor and simulation time efficient with practicall acceptable accurac. The present stud chooses 3-D FDM (FLA 3D) as the prime software for the analsis of the piled-raft foundation. In the conventional design of the piled-raft foundation and the design practice in Taiwan, the contribution of load carring b the raft is usuall ignored. However, recent studies on real case histories and full scale pile group tests (Liang et al., 23; Lee et al., 2; Long, 2) demonstrated that the raft can carr % to 7% of the total load. The present stud therefore attempts to assess the piled-raft foundation behavior and to broaden the understanding of the comple interaction between the piles, raft and soil via numerical simulations. First, pile load tests on the jobsite of TIF (Taipei International Financial orporation or Taipei 1) are modeled to calibrate input parameters of piles. econd, a parametric stud is performed to stud effects of the raft thickness, the number of piles and the loading level on the settlement, the bending moment and the load carring ratio of the raft for a tpical Taipei Metropolitan soil profile. II. PILE LOADING TET IMULATION As shown in Fig. 1, Taipei 1 onstruction Project (or Taipei 1) possesses a deep ecavation at Tower Zone and Podium Zone with total ecavation area of 2.2 m 9.14 m 21.7 m. A total of 58 bored piles were installed beneath the mat foundation of basement. In Taipei 1, five pile loading tests (three etension piles, P241, P335 and P532, and two compression piles, P39, P112) were performed. The testing piles
2 D.-G. Lin et al.: Load Transfer and Deformation Analses of Piled-Raft Foundation in Taipei Metropolitan Podium Zone P39 Podium Zone P112 P532 P241 Tower Zone P335 Unit: mm 736 compression pile: P241, P335, P532 etension pile: P39, P Podium Tower Fig. 1. Plan view of ecavation one and location of testing piles. were instrumented with strain gauges and rebar transducers to estimate the load distribution and deformation. In this article, comparisons between pile loading tests and numerical simulations for compression pile P241 and etension pile P112 are presented. The etension loading test of P39 was performed from April 19 to 21, 1999, with the maimum load of 2 MN (= 241 Ton) and the compression loading test of P241 loading test was performed from March 12 to 14, 1999, with the maimum load of 29.4 MN (3 Ton). The ATM D and ATM D were followed for the loading procedures of etension and compression loading tests respectivel. In the pile loading test simulation, the soil mass was modeled b soil block elements and the pile was modeled b pile structure elements with interface elements. oil parameters for numerical analses on Taipei 1 field site were determined b Lin and Woo (2, 25) based on 128 boring logs with high ualit field tests and laborator tests. The ground water table was set at 2 m below the ground surface. oil was modeled using Mohr-oulomb (M-) model and the pile was simulated using Linear Elastic (L-E) model. During pile loading tests, the loading was applied in a small increment and maintained at least for 2 hrs or for a settlement rate of pile head lower than.25 mm/hr to ensure the dissipation of pore water pressure. As a result, the simulation of pile loading tests was carried out b effective and drained analses. Input model parameters of soil and pile are listed in Table 1 including cohesion (c'), friction angle ( '), Poisson ratio ( '), Young s modulus (E'), dr unit weight ( d ) and dilation angle ( ). Interface elements simulate the normal and shear direction interactions of pile shaft with surrounding soil mass via shear coupling spring and normal coupling spring. Parameters of coupling spring are cohesion (c s & c n ), friction ( s & n ) and spring stiffness (k s & k n ). ubscript-s is for shear coupling spring and subscript-n is for normal coupling spring. In this stud, the interface parameters are adjusted based on Desai Table 1. Input model parameters of soil laers and the pile. Depth c E d oil laer (kpa) ( ) (MPa) (kn/m 3 ) ( ) ~2 m urfce fill ~23 m ilt cla ~32 m ilt cla ~41 m ilt sand ~ ilt gravel ~86 m andstone Test Pile Pile diameter = 1.5 m, Pile length = 72 m =.23, E = 335 MPa, d = 23.5 kn/m 3 Table 2. Parameters of interface elements. Pile Depth k s (MPa) k n (MPa) c s (kpa) c n (kpa) s ( ) n ( ) ~2 m ~23 m ~32 m ~41 m ~ ~8 m * k s = (4.9~25.8) G, k n = (.478~2) E, c s = (2/3) c, c n =.9 c and s = tan -1 [(2/3) tan ], n = tan -1 [(2/3) tan ] et al. (1984) to model the pile loading test. Then, the comparisons of load transfer and settlement curves between simulation and observation are made to obtain a set of values which can give the best curve fitting. The interface parameters are listed in Table 2. Fig. 2 shows the load-settlement curves at the pile top, the level of the basement and the pile tip. Results of numerical predictions and measurements of the compression pile (P241) are in a good agreement. Onl at the final loading increment, the numerical simulation underestimates about % at the pile head and 25% at the pile tip. Results of numerical predictions of the etension pile are deviated from the measured settlement. The settlement at the final loading stage is underestimated 53% at the pile head and 46% at the ecavation level. This deviation ma be caused b the etension tpe of loading, especiall in a high loading level, which is different from the compressive loading considered in the soil model. Figs. 3 and 4 present the load transfer curves under various loading levels. For the compression pile loading test (P dc = design load = 12, kn), predictions and measurements are almost identical at lower loading level (1.1 P dc and.55 P dc ). For the etension pile loading test (P de = design load=, kn), predictions and measurements are similar for a wide
3 8 Journal of Marine cience and Technolog, Vol. 24, No. 4 (216) Testing Load P ( 3 kn) Testing Load P ( 3 kn) Displacement δt, δe, δb (mm) P δt δe δb measurement (pile head δt) measurement (ecavation δe) measurement (ecavation δ b) (a) ompression Pile P241 Displacement δt, δe, δb (mm) P δt Fig. 2. Load-settlement curves of at different elevations. δe δb measurement (pile head δt) measurement (ecavation δe) measurement (ecavation δb) (b) Etension Pile P112 Depth (m) Load Transfer Q ( 3 kn) P Q measurement at kn at kn at kn at 6621 kn at kn at kn at kn at 6621 kn Fig. 3. Load transfer curves of compression pile P241 at different loading levels. Depth (m) Load Transfer Q ( 3 kn) measurement at 261 kn 3 at kn 35 at 423 kn 4 at 4169 kn 45 P at 261 kn 5 55 at kn Q 6 at 423 kn 65 at 4169 kn 7 Fig. 4. Load transfer curves of etension pile P112 at different loading levels.
4 D.-G. Lin et al.: Load Transfer and Deformation Analses of Piled-Raft Foundation in Taipei Metropolitan 36 m (,236,) (, 13 ne (,,9) 6, ) BR Zone V VI Zo ne Zone III II (,,9) (136,,9) = (X,Y,Z) 4 m division along boundar segment 4 (,,) (,,) 9 m (136,,) (236,,) X E1 v1 E2 v2 N = number of (,,) 236 (236,,9) IR ER vr Zone IV Y Zo Raft Zone VIII Zone I Z 36 m Zone VII 81 /4 (b) soil profile (a) unpiled-raft (one uarter) 236 m Fig. 5. Different ones for element sie consideration. /2 BR /2 Z Y X (c) 8 8 pile group ( = 2d) BR (a) Finite difference discretiation of piled-raft foundation (d) 5 5 pile group ( = 3d) M M Pile group 3 3 BR = 36 m = 36 m LP = (e) 3 3 pile group ( = 4.5d) (f) oordinate sstem of bending moment Fig. 7. Pile configurations. Piled raft (b) Raft slab (c) Piled-raft with pile group Fig. 6. Detailed FLA 3D grid. range of loading level (2.6~.42 Pde). However, the numerical modeling underestimates in the compression pile loading test and overestimates in the etension pile test at the depth of (and tone stratum). This deviation ma be resulted from the generalied soil profile adopted for numerical simulations in and tone stratum. Overall, FLA 3D analses can capture the deformation behavior of the pile fairl well. Therefore, above simulation procedures and parameters are considered justified and valid to use in the following parametric stud. III. PARAMETRI TUDY 1. Numerical Model The geometr model used in the parametric stud is shown in Fig. 5. The model consists of nine one blocks (Zone I~VIII and Zone Raft) with an area of 236 m 236 m 9 m. Fig. 6 shows the details of 3-D finite difference grid of the piled-raft foundation with 3 3 pile group. An unpiled-raft and three piled-raft foundations with identical raft dimension of BR = 36 m 36 m and various raft thickness (tr = 1 m, 2 m and 3 m) and various pile configurations were analed. The pile configurations are shown in Fig. 7 including 8 8 (pile spacing = 2 d = 4 m), 5 5 ( = 3 d = 6 m) and 3 3 ( = 4.5 d = 9 m) pile group with pile diameter d = 2 m, pile length Lp =. In the parametric stud, the soil mass and the pile were modeled followed the pile loading test simulation. The raft slab of the piled-raft foundation was modeled b shell structure elements with a linearl elastic material and no failure limit. Input parameters of the raft are the same as the pile. In addition, an idealied Taipei Metropolitan soil profile was used for analses. Input model properties are listed in Tables 2 and ettlement of Piled Raft Fig. 8 shows vertical displacement contours of the piledraft with 8 8 pile group and the unpiled-raft under a uniform loading of kpa. Both rafts deform in a bowl shaped settlement pattern same as observations from Poulos et al. (1997);
5 82 Journal of Marine cience and Technolog, Vol. 24, No. 4 (216) Table 3. Input parameters of soil laers and the piled-raft foundation. Depth oil laer c (kpa) ( ) E (MPa) d (kn/m 3 ) ( ) ~ ilt cla ~6 m andstone Raft Thickness 1 m, 2 m and 3 m; =.16, E = 335 MPa, d = 23.5 kn/m 3 Pile Diameter = 2 m Length = ; =.16, E = 335 MPa, d = 23.5 kn/m 3 (a) Piled-raft (pile group = 8 8) (b) Unpiled-raft Fig. 8. Vertical displacement contours under loading of kpa. Normalied ettlement, wies/br(1-vs2 ) Normalied Distance, /B R (a) trip-1 B R L R/4 Normalied ettlement, wies/br(1-vs2 ) Normalied Distance, /B R (b) trip-2 B R L R/4 Fig. 9. Normalied settlement of unpiled-raft at loading of kpa.
6 D.-G. Lin et al.: Load Transfer and Deformation Analses of Piled-Raft Foundation in Taipei Metropolitan 83 Normalied ettlement, wies/br(1-vs 2 ) Normalied ettlement, wies/br(1-vs 2 ) Normalied ettlement, wies/br(1-vs 2 ) Normalied ettlement, wies/br(1-vs 2 ) /2 Normalied Distance, /B R / L -.58 t R = 3 m 2 E 1 v 1 4 (a) trip-1 (Edge trip) Normalied Distance, /B R (b) trip-2 Normalied Distance, /B R (c) trip-3 Normalied Distance, /B R (d) trip-4 (entral trip) /2 /2 3 /2 /2 3 /2 /2 Fig.. Normalied settlement of piled-raft (8 8, = 2d) at loading of kpa. 3 L L L M M M M M M M M
7 84 Journal of Marine cience and Technolog, Vol. 24, No. 4 (216) Normalied Bending Moment M /BR 2 Normalied Distance, /B R (a) pile group 8 8, = 2d /2 /2 B R/2 3 L M M Normalied Bending Moment M /BR Normalied Distance, /B R (b) pile group 5 5, = 3d B R 4 M M Normalied Bending Moment M /BR Normalied Distance, /B R (c) pile group 3 3, = 4.5d B R Fig. 11. Normalied bending moment of central strip of piled-raft at loading of kpa. 3 M M omodromos et al. (29); Lee et al. (2) and Poulos et al. (211). Figs. 9 and show the normalied settlement of the unpiledraft and the piled-raft with 8 8 pile group at different raft locations. The normalied settlement is defined as (w i E s )/ ( B R (1- s 2 )) where w i is the settlement of the raft, E s is the Young s modulus of the soil, is the applied load and s is Poisson ratio of soil. Results show that piles can effectivel reduce the average and maimum settlements of the raft. Maimum settlements in center strip (strip-4) of the piled-raft (raft thickness 1 m to 3 m) are reduced b 32.3%, 28.5% and 26.2% respectivel comparing to the center strip (strip-2) of the unpiledraft. ame observations were found in previous studies (Long, 2; Karim et al., 213; Nguen et al., 213). Meanwhile, it is found that the differential settlement reduces as the raft thickness increases. The maimum differential settlement of the center strip of the raft is reduced about 5%. The same trend is also shown b several researches (Oh et al., 29;
8 D.-G. Lin et al.: Load Transfer and Deformation Analses of Piled-Raft Foundation in Taipei Metropolitan 85 Normalied Depth /Lp Normalied Bending 2 Moment M / s Pile 1 Pile 2 Pile 3 Pile 4 Normalied Depth /Lp Normalied Bending 2 Moment M / s Pile 5 Pile 6 Pile 7 Q Q R Q pi Q pi L 4 m Q pi /Q (Q pi /ΣQ pi ) B R/2 2 m L 2 m 4 m 4 m Fig. 13. Load carring ratio of piles at loading kpa (8 8 pile group, = 2d, d = 2 m, B R L R = 36 m 36 m, ). Normalied Depth /Lp Normalied Bending 2 Moment M / s Pile 8 Pile 9 Pile /2 /2 M M Fig. 12. Normalied bending moment of central strip of piled-raft at loading of kpa. Loading ratio of raft RR pile group 8 8 pile group 5 5 pile group Loading intensit Q (kn/m 2 ) Fig. 14. Load carring ratio of piled-raft for various loading intensit (). Rabiei, 29; El-Garh, 213). 3. Bending Moment of Piled Raft For all pile configurations (8 8, 5 5 and 3 3), the bending moment (M ) of the raft increases with the increase of the raft thickness as shown in Fig. 11. For the same raft thickness, the bending moment of the piled-raft decreases with the increase of the pile number. For the raft thickness of 3 m, the maimum normalied bending moments (M /B 2 R ) are 1.8, 1.63 and 1.71 for 8 8, 5 5 and 3 3 pile group respectivel. As compared with those developed in the unpiled-raft (1.52), onl the case of the piled-raft with 8 8 pile group reduces the raft bending moment effectivel. Fig. 12 presents the normalied bending moment distribution along the pile shaft under loading intensit of kpa (pile group 8 8, = 2d) acting on the piled-raft. The bending moment of the piles is affected b the settlement pattern of the raft. Because of the smmetric settlement pattern, the inner piles eperience less horiontal movements. Therefore, the bending moments on the inner piles (Pile 8, 9 and ) are less than on the outer piles (Pile 1, 2 and 5). For a single pile, the maimum bending moment occurs at the interface of the silt cla laer and sand stone bearing laer (GL - = Normalied Depth.6). It can be inferred that the pile segment at the transition one from the soft soil laer to the stiff bearing laer ma carr a higher bending moment. 4. Load-arring Ratio of Piled Raft Fig. 13 illustrates the loading mechanism of the piled-raft sstem and the loading distribution percentage carried b piles. A load carring ratio of piled-raft R R (= Q R /Q = (Q- Q pi )/Q) is introduced and calculated as shown in Fig. 14. In which, (Q) is the total loading carried b the piled-raft sstem whereas ( Q Pi ) and (Q R ) represent the loading portions carried b piles and the raft respectivel. Meanwhile, Fig. 13 also reveals that piles near the raft center carr a higher percentage of loading than those adjacent to the raft edge. However, pile load measurements of the Messe- Torhaus in Frankfurt presented in mall and Poulos (27) and numerical simulation results in Bourgeois et al. (212) show central piles carring a smaller loading than corner piles. One possible reason of this discrepanc could be the raft area which piles share the loading with. In this article, the distance from the edge of the raft to the center of the corner is 2d and that distance in mall and Poulos (27) and Bourgeois et al. (212) is 1d. Therefore, the raft area shares the loading for corner piles (Pile 1 to 4) is 6 m 6 m. Other piles (Pile 5 to ) onl have a raft area of 4 m 4 m sharing the loading. This area difference causes corner piles carring a smaller loading
9 86 Journal of Marine cience and Technolog, Vol. 24, No. 4 (216) than central piles. As shown in Fig. 14, for pile group 8 8, the raft shares 43.8% (= R R = Q R /Q) of the total vertical load (Q) for the loading intensit of 1, kpa while it appears 3.2%, % of total vertical load for 75 and 4 kn/m 2 with the raft thickness of 3 m. R R increases as the loading increases and the number of piles decreases. From previous studies, the load carring ratio of piled-raft varies from % to 7% depending on man factors such as the raft thickness, number of piles, pile length, configuration of piles, soil profile and loading level (Liang et al., 23; Lee et al., 2; El-Garh et al., 213). entrifuge test results of Lee et al. (2) show that R R increases as the settlement of the piled-raft increases (loading increases) or as the number of piles decreases. R R trends in this stud agree with above observations. IV. ONLUION The piled-raft sstem is commonl used as the foundation of the high-rise building. The conventional design of the piledraft foundation in Taiwan usuall ignores the contribution of the load carring b the raft. It makes engineers overdesign in the piled-raft foundation. This article attempts to understand the comple interaction between the piles, raft and soil via a pile load test simulation and a parametric stud using FLA 3D. The pile load test simulation analed pile load tests from Taipei 1 onstruction Project. In the simulation, soil laers were modeled using the M- soil model and the pile was modeled using pile structure elements with interface elements. imulation results indicate that FLA 3D can capture the deformation behavior of the pile fairl well. The parametric stud was performed using FLA 3D with the same procedures of the pile load test simulation and the idealied tpical Taipei Metropolitan soil profile. Parametric stud results show: (1) the piled-raft foundation reduces the settlement and the differential settlement of the raft; (2) the thicker raft reduces the settlement and the differential settlement of the raft; (3) onl the case of the piled-raft with 8 8 pile group reduces the raft bending moment; and (4) the raft can carr a higher percentage of loading when the loading increases and the number of piles decreases. Observations from the parametric stud indicate that ignoring the bearing capacit contribution of the raft results in overdesign in the conventional foundation design practice. In addition, assuming piles carring the same loading in the conventional foundation design practice is not true either. In the future piled-raft foundation project, it is recommended to use 3D numerical simulation help engineers understand the loading distribution mechanisms and optimie the foundation design. REFERENE Bourgeois, E., P. De Buhan and G. Hassen (212). ettlement analsis of piled-raft foundations b means of a multiphase model accounting for soil-pile interactions. omputers and Geotechnics 46, lanc, P. and M. F. Randolf (1993). An approimate analsis procedure for piled raft foundations. International journal for numerical methods in geomechanics 17, omodromos, E. M., M.. Papadopoulou and I. K. Renteperis (29). Pile foundation analsis and design using eperimental data and 3-D numerical analsis. omputers and Geotechnics 36(5), Desai,.., M. M. Zaman, J. G. Lightner and J. J. iriwardanej (1984). Thin-laer element for interfaces and joints. Int. J. for Numer. and Analt. Methods in Goemech 8, El-Garh, B., A. A. Galil, A. F. Youssef and M. A. Raia (213). Behavior of raft on settlement reducing piles: Eperimental model stud. Journal of Rock Mechanics and Geotechnical Engineering 5(5), Karim, H. H., M. R. AL-Qaiss and M. K. Hameedi (213). Numerical analsis of piled raft foundation on clae soil. Eng. & Tech. Journal 31(7) Part (A), Lee,. W., W. W. L. heang, W. M. wolfs and R. B. J. Brinkgreve (2). Modelling of piled rafts with different pile models. Proceedings of the 7 th European onference on Numerical Methods in Geotechnical Engineering. Trondheim, Norwa: R Press, Liang, F. Y., L. Z. hen and X. G. hi (23). Numerical analsis of composite piled raft with cushion subjected to vertical load. omputers and Geotechnics 3(6), Lin, D. G. and. M. Woo (2). Deformation analsis of Taipei International Financial enter deep ecavation project, technical report. Trinit Foundation Engineering onsultants o., LTD. Lin, D. G. and. M. Woo (25). Geotechnical analses of Taipei International Financial enter (Taipei 1) onstruction Project, 16 th International onference on oil Mechanics and Geotechnical Engineering, 13-16, eptember 12-16, 25, Osaka, Japan. Long, P. D. (2). Piled raft - a cost-effective foundation method for high-rises. Geotechnical Engineering 41(3), Nguen, D. D..,. B. Jo and D.. Kim (213). Design method of piled-raft foundations under vertical load considering interaction effects. omputers and Geotechnics 47, Nguen, D. D.., D.. Kim and. B. Jo (214). Parametric stud for optimal design of large piled raft foundations on sand. omputers and Geotechnics 55, Oh, E. Y. N., Q. M. Bui,. urarak and A.. Balasurbamaniam (29). Investigation of the Behavior of Piled Raft Foundations in and b Numerical Modeling. In The Nineteenth International Offshore and Polar Engineering onference. International ociet of Offshore and Polar Engineers. Poulos, H. G. (1991). Analsis of piled strip foundations. omputer methods and advances in geomechanics (1), Poulos, H. G. (1994). An approimate numerical analsis of pile-raft interaction. International Journal for Numerical and Analtical Methods in Geomechanics 18(2), Poulos, H. G. and E. H. Davis (198). Pile foundation analsis and design. John Wile and sons, New York. Poulos, H. G., J.. mall and H. how (211). Piled raft foundations for tall buildings. Geotechnical Engineering Journal of the EAG and AGEA 42(2), Poulos, H. G., J.. mall, L. D. Ta, J. inha and L. hen (1997). omparison of some methods for analsis of piled rafts. Proceedings of the 3 th ear smposium of the outheast Asian Geotechnical ociet 5, 1-6. Rabiei, M. (29). Parametric tud for Piled Raft Foundations. EJGE 14. Randolph, M. F. (1983). Design of piled raft foundations. ambridge Universit Engineering Department. Randolph, M. F., R. Dolwin and R. Beck (1994). Design of driven piles in sand. Geotechniue 44(3), mall, J.. and H. G. Poulos (27). Nonlinear analsis of piled raft foundations. Geotechnical pecial Publication GP8, AE, D Volume, GeoDenver, 1-9.
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