A NUMERICAL STUDY OF PILED RAFT FOUNDATIONS

Transcription

1 Journal of the Chinese Institute of Engineers, Vol. 9, No. 6, pp (6) 191 Short Paper A NUMERICAL STUDY OF PILED RAFT FOUNDATIONS Der-Gue Lin and Zheng-Yi Feng* ABSTRACT This paper presents raft-pile-soil interaction for a verticall loaded fleible piled raft on laered subsoil using a two-dimensional finite difference numerical tool. The subsoil is modeled as a linear elastic material and the raft is modeled as a beam structure under plane strain. In addition, the piles are simulated b a series of pile elements considering the pile/soil interface behavior. In the simulations, the reuired input parameters of soil, pile and interface are determined b back analses of pile loading tests. Settlement, bending moment, both in pile and raft, as well as effects of raft fleibilit for vertical uniform loading in the subsoil were eamined. It is found that even though for vertical uniform loading, a relativel high bending moment ma be induced in the piles due to lateral displacement of the stressed subsoil. For the case of a piled raft placed over a soft cla laer at ground surface the contact pressure at the raft-soil interface is merel 4 ~ 6% of that developed in the unpiled raft. Nevertheless, the contact pressure ma reach 15 ~ 5% of that of the unpiled raft if the piled raft is resting on a sand laer at the ground surface. This implies that the loading carried b the pile group could be reduced b almost 1/4 of the design load and it could eventuall reduce the cost of pile group construction to a certain etent. Ke Words: pile, raft, numerical analsis (CI5). I. INTRODUCTION Previous studies of Bangkok subsoil had focused mostl on the behavior and performance of single piles. The stud of pile groups mostl focused on pile capacit and group settlement without considering the presence of the raft. This fact indicates the necessit of the analsis of a piled raft foundation in Bangkok subsoil. This stud introduces a simple numerical procedure using in-hand finite difference code for piled raft analsis with sufficient accurac. The piled raft sstem, at ground level, was assessed and the pile/ raft connection was assumed fied. From the analsis results, readers can obtain read-made estimation curves for a similar piled raft foundation design in practice. The comparativel high bending moment *Corresponding author. (Tel: et. ; Fa: ; tonfeng@dragon.nchu.edu.tw) The authors are with the Department of Soil and Water Conservation, National Chung-Hsing Universit, Taichung 4, Taiwan. in verticall loaded piles is noted. In addition, the load carr ratio between raft and piles is investigated for the possible configuration of a piled raft foundation from the stand point of economical design. II. NUMERICAL MODELING OF PILE LOADING TESTS AND PILED RAFT FOUNDATION 1. Finite Difference Model The geotechnical finite difference code, FLAC (FLAC, ), was applied for this stud. For piled raft foundation the soil and structure were discretized into soil element and structural element respectivel as shown in Fig. 1. The soil element size close to piles is 1 m m for stress concentration zone and m m for soil elements awa from piles. To avoid boundar effects the mesh should etend sufficientl beond the region of interest and eventuall the soil mass 9 m 9 m was discretized into 1,6 rectangular plane strain elements. The adopted domain size

2 19 Journal of the Chinese Institute of Engineers, Vol. 9, No. 6 (6) B r = 15 m = 15 m S z = m L p = 4 m -restraints E R, v R S = m Soft cla E 1, v 1 15 m 48 m Stiff cla E, v 15 m L p = 4 m Sand E, v Piles 1 m 45 m 45 m, -restraints - Tpical piled raft foundation Finite difference grid to represent piled raft foundation Fig. 1 Tpical finite difference discretization of piled raft sstem was judged to be sufficient to represent the soil bod in the numerical problem b detecting the convergence of numerical solutions for various geometric boundaries. The piles were discretized into 14 pile elements while the raft was discretized into beam elements. The boundar between the raft grid and the soil grid was modeled as an interface and discretized into interface elements. Similar finite difference models were separatel prepared for other cases of the piled raft foundation.. Structural Elements and Conversion of -D Problem to -D Plane Strain Model The beam elements of linear elastic behavior with two nodes and three degree of freedom at each node are used to represent the raft structures where bending resistance is important. The pile elements are adopted to represent the behavior of the piles. The formulation for fleural behavior of the beam elements and pile elements can be found in the documentation of the FLAC program (FLAC, ). The pile element interacts with the surrounding soil through coupling springs at the pile/soil interface. Converting -D problems of regularl spaced piles into -D plane strain models involves averaging the effect of actual -D structures over the spacing in the out-of plane direction. Donovan et al. (1984) suggested that linear scaling of material properties is a simple but accurate enough wa of distributing the discrete effect of elements over the spacing in a regularl spaced pattern. Therefore, the spacing of piles along the out-of-plane direction, s, is used to scale the properties of pile elements. The scaled propert is found b dividing the actual propert b s. Conversel, the actual properties of elements after analsis, such as bending moment and forces, are obtained b multipling the scaled values b s. The strength and stiffness properties of the pile elements and pile/soil interfaces were scaled with spacing, s, in the out-of plane direction. The Young s modulus of piles used in this stud is E c = MPa. Therefore, E c is scaled b s ( m pile spacing) into 9. 1 MPa for actual input for Young s modulus of the piles.. Loading Condition and Configuration of Piled Raft Foundation The loading was chosen as being in the working range as encountered in Bangkok epresswa construction and buildings and a tpical vertical uniform working load,, of (kn/m ) was applied on the piled raft. The thickness of the raft was varied to investigate the effect of the relative stiffness of the raft on load transfer, load carr proportion and settlement of piled raft.

3 D. G. Lin and Z. Y. Feng: A Numerical Stud of Piled Raft Foundations 19 Table 1 Soil properties for numerical model Soil tpe Unit Estimated Depth Estimated Es weight ν s S (m) u SPT-N (MPa) (kn/m ) (kpa) Soft cla ~ Stiff cla 15 ~ Silt sand ~ Accordingl, piled rafts with different thicknesses ( =. m, 1m and 5 m) and dimensions (width length = = 15 m 15 m and m m) were investigated. Checks were also made on the piled raft foundation with regularl spaced piles and tpical piled raft configurations for analsis. Results are illustrated in Fig.. For pile spacing of m the pile configurations in piled rafts are 5 5, and 1 1 and the corresponding raft dimensions are 15 m 15 m, and m m. The connection between piles and raft is considered as rigid. The diameter of piles is 1. m and the length of piles is 4 m. 4. Soil Propert and Material Model E R, v R s E 1, v 1 E, v E, v E R, v R =., 1 or 5 m / E 1, v 1 E, v E, v / s The elastic modulus of three laers of Bangkok subsoil, E s, was estimated b undrained shear strength, S u, using E s = 5 S u for the soft cla laer and E s = 1, S u for the stiff cla laer while the elastic modulus of the silt sand laer was determined b SPT-N value using E s = 6, N (kpa). On the other hand, the elastic modulus for the piled raft foundation, E p, was calculated b E s = 15, (f c ) 1/ (kg/cm ) in which the compressive strength of concrete, f c is eual to 5 (kg/cm ). In this stud, Poisson s ratio, ν s, of Bangkok subsoil was obtained from previous studies and eperiments performed b the Asian Institute of Technolog and the subsoil was generalized into three laers for the numerical modeling of pile loading tests and piled raft foundations. The laering generalization adopted is similar to those of Honjo et al. (199). The three laers are predominantl classified into a soft cla laer of depth from ~ 15 m, a stiff cla of depth from 15 ~ m and silt sand for the remaining depth of ~ 6 m. It should be noted that the generalization of subsoils into three laers is not strictl accurate but it ma fairl represent the average condition of Bangkok subsoil. The soil properties of the tpical Bangkok subsoil are summarized in Table 1. In the numerical analsis, the soils were assumed to behave as linear elastic entities to properl represent the material behavior of the linear load-settlement curve of a static pile loading test with a small displacement level. Similarl, raft and pile were also simulated as elastic structure materials without plastic ielding. Fig. Tpical piled raft configurations for numerical analsis 5. Determination of Input Parameters of Coupling Springs A single pile loading test was performed at the Bangpa-in Pakret epresswa project in Thailand. The observed load-settlement curves and load-transfer curves etracted from the test data were used to calibrate the input parameters of coupling springs in this stud. To obtain the real responses of interface behavior, it is necessar to evaluate from a laborator test or perform a series of parametric studies. Beer (1985) indicated that for a joint in contact, shear stiffness (K s ) and normal stiffness (K n ) of interfaces are theoreticall infinite and in the analsis procedure large finite values have to be used. The values for K s and K n should be chosen in such a wa that the elastic slip and closing is negligible compared to the displacements of the elements adjacent to the joint. In this stud, the stiffness of coupling springs was initiall estimated from the elastic modulus of surrounding subsoil, E s, for the numerical simulation of a pile loading test. The load transfer curve was used for comparison and finall to obtain the optimum values of shear stiffness, K s and normal stiffness, K n. In summar, the values of K s and K n for the soil laers in the pile load test site were (.4 ~.8) E s and (1.5 ~.8) E s respectivel. For interface strength parameters, the cohesive strength parameter C s and C n of cla laer

4 194 Journal of the Chinese Institute of Engineers, Vol. 9, No. 6 (6) Table Input parameters of pile-soil interface and raft/soil interfaces Pile/soil K s φ s c s K n φ n c interface n (N/m ) ( ) (N/m) (N/m ) ( ) (N/m) (Soil tpe) Soft cla Stiff cla Silt sand Raft/soil K s φ s c s K n φ n c interface n (N/m ) ( ) (N/m) (N/m ) ( ) (N/m) (Soil tpe) Soft cla and frictional strength parameter φ s and φ n of sand laer of interface were estimated from the strength parameters c and φ of surrounding subsoil. The interface cohesive strength parameters for the sand laer and the interface frictional strength parameters for cla laers were ignored. The reuired input parameters of pile/ soil interface obtained from back analsis of the single pile loading test are summarized in Table. Note that the actual input parameters of pile/soil interface for K s, K n, C s, and C n should also be scaled b the pile spacing, s, for D plane strain analsis to simulate regularl spaced structural elements (FLAC, ). III. NUMERICAESULTS OF PILED RAFT FOUNDATION The responses of piled raft foundations of different configurations (supported b 5 5 piles with = 15 m 15 m and 1 1 piles with = m m) located at the ground level were investigated under a uniform vertical loading of = kpa. 1. Effect of Raft Stiffness on Settlement The settlement of the piled rafts of different dimensions ( = 15 m 15 m and m m) is shown in Fig. (a) and (b). Note that vertical settlements are denoted b negative values in this stud for consistenc with the numerical output. The induced settlement of the piled raft was epressed in terms of normalized distance, /, as an abscissa and normalized settlement, I = w i E s / (1 ν s ), as an ordinate in which w i is settlement at point i, E s is the Young s modulus of soft cla, ν s is the Poisson s ratio of the soft cla laer, is the uniforml distributed vertical loading at raft surface. As shown in Fig. (a) and (b), the thickness of the piled raft merel displas a minor effect on the normalized settlement in the case of the smaller raft dimensions of 15 m 15 m (5 5 piles). On the other hand, the differential settlement of a thin piled raft ( = 1 m) appears more prominent than that of a thick piled raft ( = 5 m) in the case of larger Normalized settlement w i E s / (1 v s ) Normalized settlement w i E s / (1 v s ) Normalized distance / = 1 m = 5 m dimension of m m (1 1 piles) as indicated in Fig. (b). Meanwhile, the thin piled raft (1 1 piles with = m m) freuentl shows a bowl-shaped settlement pattern at the piled area and larger differential settlement than the thick piled raft. It can be seen that the normalized settlement of the thin piled raft varies from -.74 (w i = 6. mm) at the raft edge to -.9 (w i = 45. mm) at raft center while the (a) s E v, Normalized distance / = 1 m = 5 m (b) / / s E, v 145 Fig. (a) Normalized settlement of piled raft with = 15 m 15 m (5 5 piles) or different raft thicknesses, raft edge-to-raft edge plot. (b) Normalized settlement of piled raft with dimensions = m m (1 1 piles), raft edge-to-raft center plot.

5 D. G. Lin and Z. Y. Feng: A Numerical Stud of Piled Raft Foundations 195 thick piled raft shows almost identical values of normalized settlement from -.8 (w i = 4. mm) at the raft edge to -.87(w i = 41.9 mm) at the raft center. The thin piled rafts ehibit less settlement than thick piled rafts near the edge area for a / <.5. The effect of the raft stiffness is depicted in the Figs. 4(a) and (b) with relative raft stiffness, K R = 4E R (1 ν s ) /E s (1 ν R ) and normalized settlement, similar to the plots of Ta and Small (1997). The smbols E R, ν R and represent the Young s modulus, Poisson s ratio and thickness of the raft respectivel. It is seen that in Fig. 4(b) the settlement of the edge point (point 1) increases as the raft stiffness, K R, increases. Contrar to the edge point, the inner points (point, 4 and 5) of the raft show a decreasing trend in settlement as K R increases. Conclusivel, for K R > 1 the magnitudes of settlements along the transverse strip of raft can practicall be regarded as on the same level. Similarl, for K R <.1 the settlements of raft points merel displa slight variations with changing K R value whereas the settlements of the edge and inner points are distinctl different in magnitude. The region.1 < K R < 1 can be regarded as a transitional zone where the raft settlement ehibits sensitivit to the relative raft stiffness. Thione is also a matter of practical concern because most rafts lie in this range. For most reinforced concrete rafts in practice, the relative raft stiffness K R falls in the range.1 < K R < 1 and hence, it has implications on the practical design of the raft.. Effect of Raft Stiffness on Bending Moment Plane strain bending moments (M PS in kn-m/m) of the piled rafts were investigated in terms of normalized bending moment (M PS 1/ ) and normalized distance (/ ) for different raft thicknesses ( = 1 m and 5 m) and different raft dimensions ( = 15 m 15 m and m m). As illustrated in Figs. 5(a) and (b), the bending moment of the piled raft was investigated for a surface piled raft (supported b 5 5 and 1 1 piles at ground surface). It was observed that for all tpes of configuration the bending moment of a thick piled raft ( = 5 m) is higher than that of a thin piled raft ( = 1 m) and a larger raft ( = m m) displas much higher bending moment than a smaller raft ( =15 m 15 m). The bending moments of the piled rafts show sharp turnings at the pile points and it was shown that the bending moments sag at the pile points and peak at raft spans. The calculated bending moments are also compared with those of Ta and Small (1997) with fair agreement. The slight difference might be due to the differences in the degree of discretization and modeling discrepancies. The present analsis models the raft as a beam strip while Ta and Small (1997) considered it as a plate structure. Normalized settlement w i E s / (1 v s ) Normalized settlement w i E s / (1 v s ) Relative raft stiffness K R = 4E R (1 v s )t R /E s (1 v R )B R Fig Pile The thick piled raft ( = 5 m) induces higher normalized bending moment of.8 (or M PS = 6.8 kn-m/m) than the.18 (M PS = 65. kn-m/m) of the thin piled raft ( = 1 m) for a raft dimension = m m supported b 1 1 piles.. Contact Pressure at Piled Raft/Soil Interface The contact pressures at raft/soil interface were investigated for a piled raft with dimensions =15 m 15 m supported b 5 5 piles at ground surface under vertical uniform loading as shown in Fig. 6. The load transferred from the raft to soil is calculated from the contact pressure, σ v, induced at the raft/soil interface. An un-piled raft test is performed for comparison purposes. It is shown that the contact pressure of the piled raft is lower than that of the unpiled raft and is merel 4 ~ 6% of that developed in the unpiled rafts resting on the soft cla laer. (a) s E, v Relative raft stiffness K R = 4E R (1 v s ) /E s (1 v R ) (b) Pile Pile Pile / / s E, v 145 (a) Effect of raft stiffness on settlement of piled raft with dimension = 15 m 15 m (5 5 piles), raft edgeto-raft edge plot. (b) Effect of raft stiffness on settlemtn of piled raft with dimension = m m (1 1 piles), raft edge-to-raft center plot.

6 196 Journal of the Chinese Institute of Engineers, Vol. 9, No. 6 (6) Normalized bending moment M PS 1/ Normalized distance / = 1m = 5m (a) E R, v R s E v, 1 54 Normalized contact pressure v / σ Fig. 6 Normalized distance / Unpiled raft Piled raft (assuming sand laer at surface) Piled raft (assuming stiff cla laer at surface) Piled raft (oringinal soft cla laer at surface) E R, v R s E v, 1 54 Comparison of contact pressure at raft-soil interface among piled rafts and unpiled raft, = 1 m, raft edge-to-raft edge plot Normalized bending moment M PS 1/ Fig Normalized distance / = 1m = 5m (b) / / s s E, v 145 (a) Bedning moment of piled raft with dimensions = 15 m 15 m (5 5 piles), raft edge-to-raft edge plot. (b) Bending moment in piled raft with dimensions = m m (1 1 piles), raft edge-to-raft center plot. Depth ratio of pile /L p Fig. 7 Normalized aial force P /P ave = 1 m Pile s E, v (a) Aial force distribution in pile structure of piled raft with diemensions = 15 m 15 m (5 5 piles), L p = 4 m, = kpa. This is due to the fact that a high proportion of the loading is transferred directl through the piles to the underneath bearing zone. To further investigate the influence of soil stiffness on contact pressure issues, the stiff cla and silt sand laers of Bangkok subsoil are fictitiousl assumed as surface laers for two additional analses. The two additional contact pressure results are also plotted in Fig. 6. For a piled raft resting on the stiff cla at ground surface, the contact pressure is increasing to 7 ~ 1% of that developed in the unpiled rafts resting on the soft cla laer. Moreover, for a piled raft resting on the sand laer at ground surface, the contact pressure is further increasing to 15 ~ 5% of that developed in the unpiled rafts. This implies that the loading carried b the pile group could be reduced b almost 1/4 of the design loading. Conseuentl, one-fourth of the cost of pile construction can be saved if the surface laer of soil stratum is a stiffer silt sand laer rather than a soft cla laer. From numerical results, it is indicated that the contact pressure and load carring ratio of a piled raft are similar in both cases of raft thickness of = 5 m and = 1. m. Eventuall, a summar conclusion can be made that the piled raft is capable of carring more loading and reducing the loading burden on the pile group to a certain etent, if the soil laer beneath the piled raft possesses sufficient stiffness. Nevertheless, the settlement of the piled raft should be carefull eamined if the compressibilit of soil laers appears significant. 4. Aial Force in Piles The aial forces of a pile in a pile group were calculated for a surface piled raft supported b 5 5 piles at ground surface under vertical uniform loading as shown in Fig. 7. The piled raft possesses dimensions of =15 m 15 m and a thickness of = 1 m. It is indicated that the outermost piles (pile-1) in the pile group take higher aial loads than the inner

7 D. G. Lin and Z. Y. Feng: A Numerical Stud of Piled Raft Foundations 197 piles (pile- and pile-5). The maimum normalized aial load carried b outermost piles can reach 1.5 P ave while it becomes.8 P ave at the inner piles. In which, the P ave value is an average loading defined b the total vertical load divided b the number of piles. This highlights the importance of the proper design of the outermost piles in the piled raft sstem. 5. Bending Moment in Piles As shown in Fig. 8, for vertical uniform loading, as the pile group possesses a rigid connection with a thin raft ( = 1 m), the pile shaft at the elevations of pile/raft connection points, at the middle depth of the soft cla laer and at the transitions of soil laers ma all induce relativel high bending moments (M PL in kn-m/m). This implies heav reinforcements should be considered at the aforementioned pile elevations in structural design of the piled raft. It is worthwhile to emphasize again that even though the loading is vertical, it produces large bending moments in the piles due to lateral displacement of the stressed subsoil. The phenomenon is often neglected in design practice and ma lead to unsafe design. IV. CONCLUSIONS In this paper two-dimensional finite difference method with plane strain condition was applied to stud pile-raft-soil interaction in laered Bangkok subsoil. The analsis indicates that thick rafts induce higher bending moments than thin rafts. Meanwhile, the relative raft stiffness K R in the region.1 < K R < 1 (1 m < < 5 m) can be regarded as a transitional zone where the raft settlement ehibits high sensitivit to the raft thickness. Thione is also a matter of practical concern because most of the reinforced concrete piled rafts lie in this range. The normalized bending moment of a piled raft is generall lower than that of an unpiled raft. Similar to the unpiled raft, the thick piled raft ( = 5 m) induces higher bending moment than the thin piled raft ( = 1 m) for the case of raft dimension = m m supported b 1 1 piles. The maimum normalized aial load carried b outermost piles can reach 1.5 P ave while it is becomes.8 P ave at the inner piles for = 1 m. The induced maimum aial forces on a pile highlight the importance of the proper design of the outermost piles in the piled raft sstem. For vertical uniform loading, relativel high bending moment ma be induced in the piles due to lateral displacement of the stressed subsoil. Heavier reinforcements are then suggested for installation at those sections with high bending moments. Depth ratio of pile /L p Fig Normalized bending moment M PL /s = 1 m Pile The contact pressure developed in the raft-soil interface for a piled raft resting on a soft cla laer surface is insignificant (onl 4 ~ 6% of total loadings) and most of the loadings are carried b the piles. For the piled raft constructed over a stiffer soil laer, the contact pressure becomes 15 ~ 5% of the total loading. This implies that the loading carried b the pile group could be reduced b almost 1/4 of the design loading. REFERENCES Beer, G., 1985, An Isoparametric Joint/Interface Element for Finite Element Analsis, International Journal for Numerical Method in Engineering, Vol. 1, pp Donovan, K., Parisuau, W. G., and Cepak, M., 1984, Finite Element Approach to Cable Bolting in Steepl Dipping VCR Slopes, Geomechanics Application in Underground Hardrock Mining, pp. 65-9, Societ of Mining Engineers, New York, USA. FLAC,, Fast Lagrangian Analsis of Continua, User s Manual, Version 4., Itasca Consulting Group, Inc, Minneapolis, MN, USA. Honjo, Y., Limanhadi, B., and Liu, W. T., 199, Prediction of Single Pile Settlement Based on Inverse Analsis, Soil and foundations, Vol., No., pp Ta, L. D., and Small J. C., 1997, An Approimate Analsis of Raft and Piled Raft Foundations, Computer and Geotechnics, Vol., No., pp Manuscripeceived: Feb. 5, 5 Revision Received: Sep. 7, 5 and Accepted: Oct., 5 s E v, Bending moment distribution in pile structure of piled raft with dimensions = 15 m 15 m (5 5 piles), L p = 4 m, = kpa.