ABSTRACT

This paper presents the three dimensional nonlinear finite element analysis of piled raft foundation which is under the application of uniformly distributed load. Load settlement curves of raft and piled raft foundation have been provided for different raft and pile stiffness. The increase in stiffness of pile has been found to increase the load carrying capacity of piled raft foundation and reducing overall settlement upto a limiting value of pile stiffness. There is a specific combination of stiffness of raft and pile in a piled raft foundation beyond which further increase in stiffness of raft and pile neither increases the load carrying capacity nor reduces settlement It has also been found that the pile of known stiffness is more effective in reducing the settlement of flexible raft than the stiff raft. The results obtained from the present 3D finite element model compares well with the result reported in the literature.

KEYWORDS: Analysis, Nonlinear, Settlement, Raft, Pile, Stiffness

INTRODUCTION

A piled raft foundation (Figure 1) is a new concept in which the total load coming from the superstructure is partly shared by the raft through contact with soil and the remaining load is shared by piles through skin friction. A piled raft foundation is economical compared to the pile foundation because piles in this case donot have to penetrate the full depth of clay layer but it can be terminated at higher elevations. Such piled raft foundation undergoes more settlement than the pile foundation and less settlement than the raft foundation. Piled raft foundations have been used successfully in Germany and other places where thick clay deposits exist over large depth [Franke (1991), Yamashita (1994)].

**Figure 1.** Raft and piled foundation

From the literature review it has been found that most of the analysis of piled raft consider linear elastic analysis [Butterfield and Banerjee (1971), Hain and Lee (1978), Kuwabara (1989), Poulos (1993)]. These papers provide useful information on load sharing between pile and raft. Few important references which report elasto-plastic finite element analysis are Liu and Novak (1991), Trochanis et.al (1991), Maharaj (1996), Maharaj (2003). In all these papers Drucker Prager Yield criteria has been used to idealise material nonlinearity of soil. Design alternatives for a piled raft have been reported by Cunha (2001) while design and applications of piled raft foundation have been reported by Poulos (2001).

Literarures reviewed above mention the need for understanding the the effect of raft and pile stiffness on the load settlement behaviour of piled raft foundation. In this paper the behaviour of piled raft foundation subjected to uniformly distributed load has been analysed by three dimensional nonlinear finite element method. The material nonlinearity of the soil medium has been idealised by Drucker-Prager Yield Criterion [Drucker and Prager(1952)]. The effect of raft and pile stiffness on load settlement behaviour of piled raft foundation has been studied.

FINITE ELEMENT FORMULATION

The raft, pile and the soil have been discretized into eight noded isoparametric brick elements. The raft and pile have been considered as linear elastic material. The soil has been modeled as Drucker-Prager (1952) elastoplastic medium The stiffness matrix and force vector for an element has been obtained from energy principle. The stiffness matrix and load vetor for the complete raft, pile and soil system has been obtained by assembling the stiffness matrix and load vector for all the elements. The nonlinear finite element equation obtained for the complete structure has been solved by Full Newton Raphson Iterative Procedure. The stiffness matrix, load vector for the eight noded brick element and its assembly, the derivation of elastoplastic constitutive matrix and the Full Newton Raphson Iterative Procedure considered in this analysis are same as discussed by the Author [Maharaj (2003)] and hence the description is not repeated here.

ANALYSIS OF PILED RAFT FOUNDATION

A piled raft foundation with 16 number of piles each of 48 metre length and size 0.4 m x 0.4 m and a square raft whose each side is equal to one third of the length of the pile and thickness equal to one fourth of one side of pile has been analysed in order to study the effect of raft and pile stiffness on load-settlement behaviour of piled raft foundation.

Finite Element Discretization

The finite element discretization of piled raft foundation have been shown in Figures 2(*a*) and 2(*b*). Only one forth of the raft has been considered in the analysis due to symmetry about both axes. The raft, pile and soil have been discretized as eight noded isoparametric brick elements as shown in Figures 2(*a*) and 2(*b*). In the finite element idealisation to fix the horizontal boundary of the soil block in the x and y directions, a range equal to half the width of raft has been considered from the edge of the raft. This zone of soil considered have been found suitable due to the small thickness of the raft.The depth of soil below the raft considered has been shown in Figure 2(*b*). The boundary conditions considered have been shown in Figures 2(*a*) and 2(*b*).

**Figure 2( a).**. Finite element discretization for piled raft foundation

(Top plane of discretized piled raft foundation)

**Figure 2( b).** Finite element discretization for piled raft foundation

(Front plane of discretized piled raft foundation)

Parameters Varied and Material properties

Based on the dimension of raft and above material properties relative stiffness parameters, raft supporting soil relative stiffness (*K*_{r}) and pile supporting soil relative stiffness (*K*_{p}) as reported by Hain and Lee (1978) have been calculated.

Relative stiffness of raft is defined as

(1) |

Where *L*_{R}, *B*_{R} and *t*_{R} are the length, breadth and thickness of raft. Other symbols retain the same meaning defined earlier.

The relative stiffness of pile is defined as

(2) |

The following table shows the relative stiffness parameters for raft and pile calculated based on equation (1) and (2).

**Table 1.** The relative stiffness parameters for raft and pile (see Eqs. 1 and 2)

Raft | Pile | ||

Raft ModulusE_{R} (GPa) |
Relative Stiffness of Raft ( K_{R}) |
Pile ModulusE_{P} (GPa) |
Relative Stiffness of Pile K_{P} |

2 | 0.00067 | 2 | 80 |

20 | 0.00670 | 20 | 800 |

200 | 0.06700 | 200 | 8000 |

2000 | 0.67000 | 2000 | 80000 |

Validation of 3D Finite Element Model

Figure 3 shows the comparison of load settlement curve for a single pile as obtained from the present analysis and that reported by Trochanis et. al (1991) under identical conditions. The results are in good agreement.

**Figure 3.** Validation of 3D FE model

RESULTS AND DISCUSSIONS

The Effect of Pile Stiffness on Load Settlement Curves of Piled Raft Foundation whose Raft is Flexible

Figure 4 shows the UDL (uniformly distributed load ) versus settlement curves for raft and piled raft foundation where raft is flexible (*K*_{r} = 0.00067). Keeping the raft stiffness same with increase in stiffness of pile, the load carrying capacity of piled raft foundation increases. This means that increase in stiffness of pile increases the load carrying capacity of piled raft . From the same curve it can be seen that there is an excellent reduction in settlement with increase in pile stiffness. The increase in load carrying capacity and reduction in settlement is upto a limiting stiffness of pile (*K*_{p} = 8000) beyond which further increase in pile stiffness is ineffective in increasing the load carrying capacity and in reducing settlement.

**Figure 4.** The effect of pile stiff ness on on load-settlement curves of piled raft foundation (flexible raft)

The Effect of Pile Stiffness on Load Settlement Curves of Piled Raft Foundation whose Raft is Stiff

Figure 5 shows the UDL versus settlement curve for raft and piled raft foundation where raft is stiff (*K*_{r}=0.67). Even in case of stiff raft increase in pile stiffness is effective in increasing the load carrying capacity and reducing the settlement of piled raft foundation.

The increase in load carrying capacity and reduction in settlement is up to a limiting stiffness of pile (*K*_{p} = ;8000) beyond which further increase in pile stiffness is ineffective in increasing the load carrying capacity and in reducing settlement. The increase in stiffness of raft increases its load carrying capacity and makes the raft more effective in reducing settlement (Figure 4 and Figure 5).

**Figure 5.** Effect of pile stiff ness on on load-settlement curves of piled raft foundation (stiff raft)

The Effect of Stiff Pile on Load Settlement Curves of Piled Raft Foundation whose Raft is Flexible and Stiff

Figure 6 shows the UDL versus settlement curve for raft and piled raft with different stiffness. It can be seen that stiffer raft (*K*_{r}=0.67) undergoes lesser settlement and is having more load carrying capacity than the flexible raft (*K*_{r}=0.00067). On the other hand the flexible raft (*K*_{r}=0.00067) undergoes more settlement than the stiff raft (*K*_{r}=0.67) and is having less load carrying capacity. In case of piled raft foundation, piled raft foundation with stiffer raft carries more load and reduces more overall settlement than the piled raft foundation with flexible raft. The same figure shows that pile with same stiffness reduces more settlement for flexible raft than for stiff raft even though the over all reduction is more for piled raft foundation with stiff raft than the piled raft foundation with flexible raft.

**Figure 6.** Effect of stiff pile on load-settlement curves of piled raft foundation (flexible and stiff mat)

The Effect of Varying Raft and Pile Stiffness on Load Settlement Curves of Piled Raft Foundation

Figure 7 shows the UDL versus settlement curve for piled raft foundation for three different raft and pile stiffness combinations. The first piled raft foundation consists flexible raft and flexible pile. Second consists flexible raft (stiffer than the first) and stiff pile. Third consists stiff raft and stiff pile. It can be seen that piled raft foundation with flexible raft and flexible pile undergoes more settlement and is having least load carrying capacity. Piled raft foundation with flexible raft (stiffer than the first) and stiff pile and piled raft foundation with stiff raft and stiff pile both undergo the same settlement and is having the same load carrying capacity. This is only possible if the over all stiffness of piled raft foundation become same in both cases.

**Figure 7.** The effect of varying raft and pile stiffness on load-settlement curves of piled raft foundation

CONCLUSIONS

The load settlement curves provided in this paper will help the designers and researcher in understanding the effect of raft and pile stiffness on piled raft foundation behaviour. The increase in stiffness of raft increases its load carrying capacity and hence helps the raft in undergoing lesser settlement. The increse in stiffness of pile is very effective in increasing the load carrying capacity and reducing settlement of piled raft foundation whose raft is flexible. This increse in stiffness of pile is also very effective in increasing the load carrying capacity and reducing settlement of piled raft foundation whose raft is stiff. There is a limiting value of pile stiffness beyond which further increase in stiffness doesnot help in increasing load carrying capacity and reducing settlement. It has also been found that the pile of known stiffness is more effective in reducing the settlement of flexible raft than the stiff raft. There is a specific combination of stiffness of raft and pile in a piled raft foundation beyond which further increase in stiffness of raft and pile neither increases the load carrying capacity nor reduces settlement. It is suggested that while going for design and construction of piled raft foundation, the limiting combination of stiffness of raft and pile must be considered.

ACKNOWLEDGEMENTS

The author wishes to thank Birla Institute of Technology and Science, Pilani, Rajasthan for providing computing facility. The author thanks his wife and loving sons Ashish and Manish for their sincere effort in preparing this paper. The author also thanks all the groups specially his Civil Engineering Group for their cooperation.

references

- Butterfield, R. and P. K. Banerjee (1971) The problem of pile group and pile cap interaction, Geotechnique, Vol.21, No.2, pp.135-142
- Cunha, R.P., H.G. Poulos and J. C. Small (2001) Investigation of design alternatives for a piled raft case history, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol.127, No.8, pp. 635-641
- Drucker D. C. and W. Prager (1952) Soil Mechanics and Plastic Analysis of Limit Design, Quart. Applied Mathematics, Vol.10, No.2
- Franke, E. (1991) Measurements beneath piled rafts, Key note lecture to the ENPC Conference on Deep Foundations, Paris, pp.1-28
- Hain, S. J. and I. K. Lee (1978) The analysis of flexible raft pile system, Geotechnique, Vol.28, No.1 pp.65-83
- Kuwabara, F. (1989) An elastic analysis for piled raft foundations in a homogeneous soil, Soils and Foundations, Vol.29, No.1, pp.82-92
- Liu. W. and M. Novak (1991) Soil-pile-cap static interaction analysis by finite and infinite elements, Canadian Geotechnical Journal,Vol.28, pp.771-783
- Maharaj, D. K. (1996) Application of elastic and elasto-plastic analysis for piled raft foundation, Ph.D. Thesis, IIT, Madras, Chennai
- Maharaj, D. K. (2003) Load-Settlement Behaviour of Piled Raft Foundation by Three Dimensional Nonlinear Finite Element Analysis, Electronic Journal of Geotechnical Engineering. Vol. 8, Bundle C, Paper 0334
- Poulos, H. G (1993) Piled raft in swelling or consolidating soils, Journal of Geotechnical Engineering, ASCE, Vol.119, No.2, pp.374-380
- Poulos, H. G. (2001) Piled raft foundations: Design and applications, Geotechnique, Vol.51, No.2, pp.95-113
- Trochanis, A. M., J. Bielak, and P. Christiano (1991) Three-dimensional nonlinear study of piles, Journal of Geotechnical Engineering, ASCE, Vol.117, No.3, pp.429-447
- Yamashita, K., M. Kakurai and T. Yamada (1994) Investigation of a piled raft foundation on stiff clay, XIII International Conference on Soil Mechanics and Foundation Engineering, New Delhi, India, pp.543-546

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