IRJET- Effect of Soil- Structure Interaction on Response of Building Frame wit Piled-raft Foundation
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This document analyzes the effect of soil-structure interaction on the response of a three-story building frame supported by a piled-raft foundation. A finite element model is developed to model the frame, slab, beams, columns, piles, raft, and soil. Parametric studies are conducted to evaluate the effect of raft thickness and pile diameter on frame displacements. The key findings are that considering soil-structure interaction increases frame displacements compared to assuming a fixed base, and displacements decrease with increasing pile diameter and raft thickness due to improved soil resistance. Nonlinear soil behavior further reduces displacements compared to linear analysis.
![International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2290
Effect of Soil- Structure Interaction on Response of Building Frame wit
Piled-raft Foundation
R. Mahadev Swamy1 and Dr. S.A. Rasal2
1Associate Professor, Department of Civil Engineering, Shivajirao S. Jondhale College of Engineering and
Technology, Asangaon
2Assistant Professor, Department of Civil Engineering, Datta Meghe College of Engineering, Navi Mumbai-400708.
India.
--------------------------------------------------------------------****----------------------------------------------------------------------
Abstract: The effect of soil structure interaction on response of the three storeyed (G+2) building frame
supported on piled-raft foundation is reported in this paper. The three storeyed frame comprises of two bays and
columns of the frames are supported by a piled-raft. The pile is assumed to be embedded in the cohesive soil mass.
For the purpose of the analysis, simplified idealizations made in the theory of finite elements. The slab of the
frame is idealized as two dimensional plate elements, beams and columns of the superstructure frame and pile of
the sub-structure are idealized as the one dimensional bem-column elements. The soil mass is idealized by
equivalent springs. The effect of different raft thicknesses with uniform pile diameter is evaluated on the
response of superstructure through a parametric study. The response of the superstructure considered includes
the displacement of the frame.
Keywords: Pile-raft, soil modulus, raft thickness, displacement
1. Introduction
The type of foundation and its design is based on the magnitude of the loads on it and the type of founding strata which
supports it. If the founding stratum is within a reasonable depth, a shallow foundation in the form of raft is adequate.
However, if the material is weak, the loads need to be transferred down to capable strata by means of deeper basements or
piles. This is true, especially in case of multistoried building frames resting on weak sub soil strata where heavy structural
loads acting on the frames have to be transmitted safely below to the firm strata.
The analysis of piled-raft foundation is very challenging because the load in the piled-raft structures is transferred to the
soil not only by the interaction between the soil and the piles but also by the interaction between foundation structure and
superstructure. In this interaction, deformations in the soils are the key factor which will affect forces and deformation in
foundation and superstructure
In the past few decades, there has been an increasing recognition that the use of pile groups in conjunction with the raft
can lead to considerable economy without compromising the safety and performance of the foundation. Such a foundation
makes use of both the raft and the piles, and is referred to here as a pile-enhanced raft or a piled raft. The piled-raft concept
has also proven to be an economical way to improve the serviceability of foundation performance by reducing settlements
to acceptable levels. Although the piled-raft concept has been most notably applied to new construction involving high-rise
buildings it is also potentially useful for remedial works and moderate height structures.
Methods that have been used for the analysis range from simplified calculations to numerical methods such as the
boundary element method (Butterfield and Banerjee [1], Brown and Wiesner [2], Kuwabara [3], Mendonca and De Paiva
[4]) and the finite element method (Hooper [5], Ottaviani [6], Chow [7], Liu and Novak [8], Katzenbach and Reul [9],
Prakoso and Kulhawy [10], Reul and Randolph [11]). In early years because of the limited availability of computer memory
and processing speed, the use of numerical methods was confined to simple problems. In last three decades due to rapid
development in computer technologies, numerical methods such as full three dimensional finite element methods are
often used to solve the complex problems.
The foundation concept of piled rafts differs from traditional foundation design, where the loads are assumed to be carried
either by the raft or by the piles, considering the safety factors in each case. Several methods of analyzing piled rafts have
developed over the years include approximation methods, finite element method, boundary element method, combined
boundary element and finite element method, combined finite layer and finite element method; and variational approach.](https://image.slidesharecdn.com/irjet-v6i2456-190805083734/85/IRJET-Effect-of-Soil-Structure-Interaction-on-Response-of-Building-Frame-wit-Piled-raft-Foundation-1-320.jpg)
![International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2291
2. Brief Review of Literature
In recent years, a variety of approaches for analyzing the piled- raft foundation system as mentioned in the preceding
section have been developed over the years. All these approaches vary in the degree of sophistication of the formulations
amount and the type of input parameters required, assumptions made; and in the applicability to realistic pile-soil-raft
situations. Some of the significant studies are briefed approach wise in the subsequent paragraphs.
The approximation approach as presented by Chen et. al. [12] treated the raft as a thin plate, the piles as springs and the
soil as an elastic continuum; and further, the interaction effects between the piles were ignored. Randolph [13] presented a
method to compute the interaction between a single pile and a circular raft. Clancy and Randolph [14] employed a hybrid
method in which analytical solution was combined with the finite elements. The raft was modeled by two-dimensional thin
plate finite elements, the piles were modeled by one-dimensional rod finite elements and the soil response was calculated
by using an analytical solution. Poulos [15] employed a finite difference method for the raft with the consideration of the
interaction effects between the piles and raft. Kitiyodom and Matsumoto [16] developed a simplified method of numerical
analysis using a hybrid model in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil
is treated as springs.
The finite element method is one of the powerful tools for the analysis of the complex problems of piled raft. In order to
reduce the computational efforts, the problems are sometimes simplified to an axi-symmetric problem or a plane- strain
problem. Some of the noteworthy contributions using this method include those by Poulos et al. [17], and Sawant et al.
[18]. Some of the researchers analyzed the circular piled rafts while few of them, reported the performance of piled raft
foundation for a muti-storeyed building. Some of the analyses were carried out in the context of non-linear behaviour of
soil; few of them even used finite elements in conjunction with infinite elements. While some investigations considered
sandy soil, few of them considered the cohesive sub-soil. Even, a study considered layered soil. Some studies were carried
out using complete three-dimensional finite element analysis; few studies were carried out in the context of simplified
finite element models.
The boundary element method is a powerful tool that can be applied in engineering applications as only the boundary has
to be discretized which reduces the amount of computer memory and the time to solve the problem as compared to that in
finite element or finite difference method. This method provides a direct and accurate solution for the analysis. Moreover,
it is fast and requires a moderate amount of computer storage space. The method has been used by many researchers
(Brown and Wiesner [19], Kuwabara [20], Baziar et al. [21]) in the solution of the problem of piled raft embedded in
different types of soil. Different idealizations were made for modelling different components of the foundation in question.
Based on the afore-mentioned review of literature, the analysis of a piled raft is presented using a software programme
Build-Frame developed using FORTRAN 90. After assessing the accuracy of the programme in the context of simple
problems of structural engineering and soil- structure interaction and further, implementing it on the published work, the
said program is used in the present study. The present study aims at comparing the response of the piled-raft foundations
with non-interactive, linear interactive and nonlinear-interactive analysis. The response of the frame included the
displacement at each storey level of the frame along with the maximum positive and maximum negative bending moments
in the individual beams and columns. A parametric study is carried out to examine the effect piled-raft on static nonlinear
response with 0.5m thickness of the raft and 0.4 m pile diameter. The pile is assumed to be linear elastic throughout the
analysis and soil is modeled using von Mises yield criteria.
3. Problem Description
A 3-D three storeyed building frame resting on piled-raft foundation is considered for the study. The frame, 3 m high is 10
m 10 m in plan with each bay being, 5m 5m. The slab, 200 mm thick, is provided at top as well as at the floor level. The
slab at the top of the first, second and third storey is supported over 300 mm wide and 400 mm deep beams. The beams
are resting on columns of size 300 mm 300 mm. While dead load is considered according to the unit weight of the
materials of which the structural components of frame are made up of, for the purpose of the parametric study presented
here. The properties of the material for pile and pile cap are given in Table 1.
Table 1. Pile-raft and soil properties for parametric study
Soil properties
Modulus of Elasticity, E
s
20000 kPa](https://image.slidesharecdn.com/irjet-v6i2456-190805083734/85/IRJET-Effect-of-Soil-Structure-Interaction-on-Response-of-Building-Frame-wit-Piled-raft-Foundation-2-320.jpg)
IRJET- Effect of Soil- Structure Interaction on Response of Building Frame wit Piled-raft Foundation
- 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2290 Effect of Soil- Structure Interaction on Response of Building Frame wit Piled-raft Foundation R. Mahadev Swamy1 and Dr. S.A. Rasal2 1Associate Professor, Department of Civil Engineering, Shivajirao S. Jondhale College of Engineering and Technology, Asangaon 2Assistant Professor, Department of Civil Engineering, Datta Meghe College of Engineering, Navi Mumbai-400708. India. --------------------------------------------------------------------****---------------------------------------------------------------------- Abstract: The effect of soil structure interaction on response of the three storeyed (G+2) building frame supported on piled-raft foundation is reported in this paper. The three storeyed frame comprises of two bays and columns of the frames are supported by a piled-raft. The pile is assumed to be embedded in the cohesive soil mass. For the purpose of the analysis, simplified idealizations made in the theory of finite elements. The slab of the frame is idealized as two dimensional plate elements, beams and columns of the superstructure frame and pile of the sub-structure are idealized as the one dimensional bem-column elements. The soil mass is idealized by equivalent springs. The effect of different raft thicknesses with uniform pile diameter is evaluated on the response of superstructure through a parametric study. The response of the superstructure considered includes the displacement of the frame. Keywords: Pile-raft, soil modulus, raft thickness, displacement 1. Introduction The type of foundation and its design is based on the magnitude of the loads on it and the type of founding strata which supports it. If the founding stratum is within a reasonable depth, a shallow foundation in the form of raft is adequate. However, if the material is weak, the loads need to be transferred down to capable strata by means of deeper basements or piles. This is true, especially in case of multistoried building frames resting on weak sub soil strata where heavy structural loads acting on the frames have to be transmitted safely below to the firm strata. The analysis of piled-raft foundation is very challenging because the load in the piled-raft structures is transferred to the soil not only by the interaction between the soil and the piles but also by the interaction between foundation structure and superstructure. In this interaction, deformations in the soils are the key factor which will affect forces and deformation in foundation and superstructure In the past few decades, there has been an increasing recognition that the use of pile groups in conjunction with the raft can lead to considerable economy without compromising the safety and performance of the foundation. Such a foundation makes use of both the raft and the piles, and is referred to here as a pile-enhanced raft or a piled raft. The piled-raft concept has also proven to be an economical way to improve the serviceability of foundation performance by reducing settlements to acceptable levels. Although the piled-raft concept has been most notably applied to new construction involving high-rise buildings it is also potentially useful for remedial works and moderate height structures. Methods that have been used for the analysis range from simplified calculations to numerical methods such as the boundary element method (Butterfield and Banerjee [1], Brown and Wiesner [2], Kuwabara [3], Mendonca and De Paiva [4]) and the finite element method (Hooper [5], Ottaviani [6], Chow [7], Liu and Novak [8], Katzenbach and Reul [9], Prakoso and Kulhawy [10], Reul and Randolph [11]). In early years because of the limited availability of computer memory and processing speed, the use of numerical methods was confined to simple problems. In last three decades due to rapid development in computer technologies, numerical methods such as full three dimensional finite element methods are often used to solve the complex problems. The foundation concept of piled rafts differs from traditional foundation design, where the loads are assumed to be carried either by the raft or by the piles, considering the safety factors in each case. Several methods of analyzing piled rafts have developed over the years include approximation methods, finite element method, boundary element method, combined boundary element and finite element method, combined finite layer and finite element method; and variational approach.
- 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2291 2. Brief Review of Literature In recent years, a variety of approaches for analyzing the piled- raft foundation system as mentioned in the preceding section have been developed over the years. All these approaches vary in the degree of sophistication of the formulations amount and the type of input parameters required, assumptions made; and in the applicability to realistic pile-soil-raft situations. Some of the significant studies are briefed approach wise in the subsequent paragraphs. The approximation approach as presented by Chen et. al. [12] treated the raft as a thin plate, the piles as springs and the soil as an elastic continuum; and further, the interaction effects between the piles were ignored. Randolph [13] presented a method to compute the interaction between a single pile and a circular raft. Clancy and Randolph [14] employed a hybrid method in which analytical solution was combined with the finite elements. The raft was modeled by two-dimensional thin plate finite elements, the piles were modeled by one-dimensional rod finite elements and the soil response was calculated by using an analytical solution. Poulos [15] employed a finite difference method for the raft with the consideration of the interaction effects between the piles and raft. Kitiyodom and Matsumoto [16] developed a simplified method of numerical analysis using a hybrid model in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. The finite element method is one of the powerful tools for the analysis of the complex problems of piled raft. In order to reduce the computational efforts, the problems are sometimes simplified to an axi-symmetric problem or a plane- strain problem. Some of the noteworthy contributions using this method include those by Poulos et al. [17], and Sawant et al. [18]. Some of the researchers analyzed the circular piled rafts while few of them, reported the performance of piled raft foundation for a muti-storeyed building. Some of the analyses were carried out in the context of non-linear behaviour of soil; few of them even used finite elements in conjunction with infinite elements. While some investigations considered sandy soil, few of them considered the cohesive sub-soil. Even, a study considered layered soil. Some studies were carried out using complete three-dimensional finite element analysis; few studies were carried out in the context of simplified finite element models. The boundary element method is a powerful tool that can be applied in engineering applications as only the boundary has to be discretized which reduces the amount of computer memory and the time to solve the problem as compared to that in finite element or finite difference method. This method provides a direct and accurate solution for the analysis. Moreover, it is fast and requires a moderate amount of computer storage space. The method has been used by many researchers (Brown and Wiesner [19], Kuwabara [20], Baziar et al. [21]) in the solution of the problem of piled raft embedded in different types of soil. Different idealizations were made for modelling different components of the foundation in question. Based on the afore-mentioned review of literature, the analysis of a piled raft is presented using a software programme Build-Frame developed using FORTRAN 90. After assessing the accuracy of the programme in the context of simple problems of structural engineering and soil- structure interaction and further, implementing it on the published work, the said program is used in the present study. The present study aims at comparing the response of the piled-raft foundations with non-interactive, linear interactive and nonlinear-interactive analysis. The response of the frame included the displacement at each storey level of the frame along with the maximum positive and maximum negative bending moments in the individual beams and columns. A parametric study is carried out to examine the effect piled-raft on static nonlinear response with 0.5m thickness of the raft and 0.4 m pile diameter. The pile is assumed to be linear elastic throughout the analysis and soil is modeled using von Mises yield criteria. 3. Problem Description A 3-D three storeyed building frame resting on piled-raft foundation is considered for the study. The frame, 3 m high is 10 m 10 m in plan with each bay being, 5m 5m. The slab, 200 mm thick, is provided at top as well as at the floor level. The slab at the top of the first, second and third storey is supported over 300 mm wide and 400 mm deep beams. The beams are resting on columns of size 300 mm 300 mm. While dead load is considered according to the unit weight of the materials of which the structural components of frame are made up of, for the purpose of the parametric study presented here. The properties of the material for pile and pile cap are given in Table 1. Table 1. Pile-raft and soil properties for parametric study Soil properties Modulus of Elasticity, E s 20000 kPa
- 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2292 Poisson's ratio, s 0.4 Density, γs 18 kN/m3 Yield stress, σy 100 kPa Interface element Normal stiffness, Kn 1.0 × 10 6 kN/m 3 Tangential stiffness, Ks 1000 kN/m 3 Piled-raft properties Modulus of Elasticity, E p 25 GPa Poisson's ratio, p 0.2 Density, γp 25 kN/m3 (a) Building frame with fixed base-half symmetry (b) Building frame with piled-raft Fig.1 Building frame considered in the present study The schematic of the building frame with fixed base-half symmetry and piled-raft is shown in Fig. 1 (a) and (b). While dead load is considered according to unit weight of materials of which the structural components of frame are made up for the parametric study presented here, a lateral load of 1000 kN is assumed to act at joints of the frame. The analysis carried out in the context of linear behavior of soil is extended further to account for the non-linearity of the soil using von Mises yield criterion. 3.1 Effect of Pile Diameter on Storey Displacement The values of the horizontal displacement at each storey level of the frame with the pile spacing in respect of four diameters of the pile (400, 600, 800 and 1000mm) considered in the study is shown in Table 2. The corresponding percentage increase in displacement due to consideration of SSI (linear-interactive w.r.t. non-interactive, i.e., fixed base, and further, non-linear-interactive w.r.t. linear-interactive) is indicated in brackets in Table 2. Similarly, the variation in the storey displacement with storey height in respect of different raft thicknesses (2.05m, 0.5m, 0.75m, 1.0m, 1.25m and 1.50m) considered in the present investigations is shown in Fig. 6.2.
- 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2293 Table 2 Effect of pile diameter on storey displacement for raft thickness 0.25 m. Pile diameter (mm) Raft thickness = 0.25 m Storey Height (m) 9.0 6.0 3.0 0.0 Analysis Displacement (mm) Non-interactive 363.99 294.9 162.53 0.0 400 Linear 412.23 (13.25 %) 324.25 (9.95 %) 198.11 (21.89 %) 11.02 (100 %) Nonlinear 411.02 (12.92 %) 333.45 (13.07 %) 185.60 (14.19 %) 12.23 (100 %) 600 Linear 409.81 (12.59 %) 319.01 (8.18 %) 190.20 (17.02 %) 10.87 (100 %) Nonlinear 395.24 (8.59 %) 322.46 (9.35 %) 175.25 (7.83 %) 12.12 (100 %) 800 Linear 402.42 (10.56 %) 302.22 (2.48 %) 181.78 (11.84 %) 10.56 (100 %) Nonlinear 388.25 (6.67 %) 312.45 (5.95 %) 171.25 (5.37 %) 12.03 (100 %) 1000 Linear 397.65 (9.25 %) 299.45 (1.54 %) 175.23 (7.81 %) 10.02 (100 %) Nonlinear 378.99 (4.12 %) 303.63 (2.96 %) 164.99 (1.51 %) 11.23 (100 %) The general trend observed for all the pile diameters considered in this investigation is that horizontal displacement at each storey level increases due to the effect of soil structure interaction (SSI). It is seen that the displacement at top of each storey is on higher side corresponding to four different pile diameters (400, 600, 800 and 1000 mm) considered in the present investigation when compared with the values of top displacement obtained in non-interactive analysis. The reduction in the displacement is attributed to the improved passive resistance of soil with higher pile diameter. The general trend observed for all the pile diameters considered in the investigation in respect of all the pile diameters is that horizontal displacement is more when the diameter is less and thereafter, decreases with higher value of pile diameter considered in present study. From the results of parametric study conducted on a specific building frame with piled-raft foundation of 0.25 m thickness, the displacement at each storey level is found to be very less (Non-interactive) when the column bases are assumed to be fixed and increase owing to interactive analysis, i.e., when the effect of soil-structure interaction is taken into account. The displacement is observed to be maximum at the top of the frame, i.e., third storey. The maximum value of top storey are found to be 412.23 mm, 409.81 mm, 402.42 mm and 397.65 in respect of various pile diameters considered in the present investigation for the pile diameters 400 mm, 600 mm, 800 mm and 1000 mm, respectively. The interactive analysis is found to increase the storey displacement in the range of 9.52 – 13.25 %, 1.54 – 9.95 %, and 7.81 – 21.89 %, respectively at first, second and third storey level. Further, it is seen that the increase in displacement due to consideration of SSI is prominent on the bottom storey for any pile diameters and with increase in the storey; the increase in displacement goes on decreasing. Similar trend is observed in respect all raft thickness considered in the present investigation.
- 5. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2294 (a) Pile diameter 400 mm (b) Pile diameter 600 mm (c) Pile diameter 800 mm (d) Pile diameter 1000 mm Fig 2: Effect of pile diameter on storey displacement for raft thickness 0.25 m. 4. Conclusions From the parametric study presented in this paper, following significant conclusions can be drawn: The effect of soil- structure interaction on each storey displacement of the frame is quite significant. Displacement is less for the conventional analysis and increases when nonlinearity of soil is considered. With increase in pile diameter, storey displacement decreases in respect of all pile dimeters considered in the study. A displacement for minimum raft thickness and higher value of soil modulus is on higher side. It is seen that the displacement at top of each storey is on higher side corresponding to four different pile diameters considered in the present investigation when compared with the values of top displacement obtained in non- interactive analysis All the same, the effect of soil-structure interaction (linear and nonlinear) is shown to be prominent on the response of the specific building frame considered and the type of foundation used in the present study.
- 6. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 02 | Feb 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 2295 5. References 1. Butterfield, R. and Banerjee, P. K. (1971), “The problem of pile group - pile cap interaction”, Geotechnique, 21(2), 135-142 2. Brown, P. T. and Wiesner, T. J. (1975), “The behaviour of uniformly loaded piled strip footings”, Soils and Foundations, 15 (4), 13-21 3. Kuwabara, F. (1989), “An elastic analysis for piled raft foundations in a homogeneous soil”, Soils and Foundations, 29(1), 82-92 4. Mendonca, A. V. and De Paiva, J. B. (2003), “A Boundary element method for the static analysis of raft foundations on piles”, Engg. Analysis with Boundary Elements, 24, 237-247 5. Hooper, J. A. (1973), “Observations on the behaviour of a piled-raft foundation on London Clay”, Proc. Int, Jl. Civ. Eng., 55 (2), 855-877 6. Ottaviani, M. (1975), “Three-dimensional finite element analysis of vertically loaded pile groups”, Geotechnique, 25 (2), 159-174 7. Chow, Y. K. (1987), “Axial and lateral response of pile groups embedded in non-homogeneous soil”, Int. Jl. Num. Analyt. Meth. Geomech., (11) 6, 621-638 8. Liu, W, and Novak, M. (1991), “Soil-pile-cap static interaction analysis by finite and infinite elements”, Canadian Geotech. Jl., 28, 771-783 9. Katzenbach, R., Arslan, U. and Moormann, C. (2000), “Piled raft foundation projects in Germany”, Design Applications of Raft Foundation, Thomas Telford, 323-391 10. Prakoso, W. A. and Kulhawy, F. H. (2001), “Contribution to piled raft foundation design”, Jl. Geotech. and Geoenv. Engg., ASCE, 127(1), 17-24 11. Reul, O. and Randolph, M. F. (2003), “Piled rafts in over consolidated clay: Comparison of in- situ measurements and numerical analyses”, Geotechnique, 53(3), 301-315 12. Chen, K. S., Karasudhi, P. and Lee, S. L. (1974), “Force at a point in the interior of layered elastic half-space”, Int. Jl. Solids Struct., 10(11), 1179-1199 13. Randolph, M. F. (1983), “Design of piled raft foundations”, Proc. Int. Symposium on Recent Developments in Laboratory and Field Tests and Analysis of Geotechnical Problems, Bangkok, 525—537 14. Clancy, P. and Randolph, M. F. (1993), “An approximate analysis procedure for piled raft foundations”, Int. Jl. Num. and Analyt. Meth. in Geomech., 17(12), 849–869 15. Poulos H.G. (1994), “An approximate numerical analysis of piled raft interaction” Int. Jl. Num. and Analyt. Meth. in Geomech., 18 (2), 73–92 16. Kitiyodom, P. and Matsumoto, T. (2003), “A simplified analysis method for piled raft foundations in non- homogeneous Soils”, Int. Jl. Num. Analyt. Meth. in Geomech., 27(2), 88-109 17. Poulos, H.G., Badelow, F., Small, J.C., Moyes, P. (2006), “Economic foundation design for tall buildings”. Proc. 10th Int. Conf. on Piling and Deep Foundations, Amsterdam, 200-209 18. Sawant,V. A., Ladhane, K. and Pawar, S. (2012), “Parametric study of piled raft for three load-patterns”, Coupled System Mech.: An Int. Jl., 1(2), 115-131 19. Brown, P. T. and Wiesner, T. J. (1975), “The behaviour of uniformly loaded piled strip footings”, Soils and Foundations, 15 (4), 13-21 20. Kuwabara, F. (1989), “An elastic analysis for piled raft foundations in a homogeneous soil”, Soils and Foundations, 29(1), 82-92 21. Baziar, M. H., Ghorbani, A., Katzenbach, R. (2009), “Small-scale model test and three-dimensional analysis of piled -raft foundation on medium-dense sand”, Int. Jl. Civ. Eng., 7 (3), 170-175