ABSTRACT

Nonlinear finite element analyses have been done to see the effect of raft size and pile length on the load settlement behaviour of axisymmetric piled raft foundation. Analyses have been done by NLAXIFEM-Nonlinear axisymmetric finite element software. The piles in the piled raft foundation have been represented as an equivalent annulus of same volume. The raft, pile and soil have been discretized into four noded isoparametric finite elements. The soil has been modeled as Von Mises elastoplastic medium. The load carrying capacity of raft foundation is found to increase with increase in size of the raft. This increase is not proportional to the increase in size of the raft. The effect of pile of length even equal to the diameter of the raft is found to reduce settlement of raft foundation significantly and also to increase load carrying capacity. Such piles of smaller length can be used successfully as settlement reducing piles in a piled raft foundation. The range of settlement reduction varies from 0 to about 50 percent. For the same size of raft and length of pile , with proportional increase of the two has been found to increase the initial overlap of the two load settlement curves. The effect of increase in length of pile is to increase the load carrying capacity of piled raft foundation. For the same length of piles below raft, the improvement is more for smaller raft than that of the larger raft.

Keywords: Piled raft foundation, raft, settlement, load carrying capacity, pile

INTRODUCTION

In piled raft foundation the raft and piles both contribute in load sharing. The raft carry load through contact with soil while piles carry load through skin friction. Piled raft foundation is an economical foundation compared to pile foundation and undergoes lesser settlement than that of the raft foundation.

LITERATURE REVIEW

A good number of papers are available in literatures on raft and piled raft foundations. Here important literatures which is directly related to the present research are discussed. Tomono et al. (1987) presented a simple model consisting of a rigid circular raft and a single pile. Karpurapu and Bathurst (1988) have shown the application of coupled finite and infinite elements for linear elastic foundations. Madhav and Karmarker (1982) have reported the elasto-plastic settlement of rigid footing. Gandhi and Maharaj(1996)have found the load sharing between raft and pile in a piled raft foundation by three dimensional finite element method..Liu and Novak (1991)has mentioned the cap, pile and soil interaction by finite and infinite elements. Maharaj (1996) has presented the linear and nonlinear finite element analysis of raft and piled raft foundation. Maharaj(Ppr -0334 (2003).)has analysed square raft and piled raft foundation by nonlinear finite element method. Maharaj (2003) has reported the nonlinear finite element analysis of axisymmetric box foundation. Maharaj and Anshuman(2003) have analysed axisymmetric raft and piled raft foundation.

Hooper (1973), Franke (1991), Yamashita et al. (1994) have provided useful information on field investigation of piled raft foundation.

Based on literature review it is found that very few literatures are reported on axisymmetric raft and axisymmetric piled raft foundation. Very few literatiures are reported on nonlinear analysis of piled raft foundation under axisymmetric condition. The present research aims to analyse axisymmetric raft and piled raft foundation by nonlinear finite element method using AXINLFEM-Axisymmetric Nonlinear Finite Element Software developed by the First Author. The raft, pile and soil have been discretized as four noded isoparametric finite elements. The soil has been modeled as the well known and widely accepted Von-Mises elastoplastic medium. The nonlinear finite element equation has been solved by Modified Newton Raphson Iterative Procedure. Based on finite element analysis load-settlement curves have been produced for varying diameters of raft and length of pile.

FINITE ELEMENT FORMULATION

In this paper the raft, pile and soil have been discretised into four noded isoparametric finite elements. The material nonlinearity of soil has been modeled by Von-Mises Yield Criteria. The equilibrium equation for an element has been obtained from principle of minimum potential energy. The equilibrium equation for the complete structure has been obtained after assembling the equilibrium equations of all the elements in the structure. The nonlinear finite element equation has been solved by Modified Newton-Raphson Iterative Procedure. The stiffness matrix, load vector for the four noded isoparametric finite element and its assembly, the derivation of elastoplastic constitutive matrix considered in this analysis are same as discussed by the Author [ Maharaj (2003-xxx) ] and the Modified Newton-Raphson Iterative Procedure is same as discussed by the Author [Maharaj (2003-Ppr-0338] and hence the description is not given here. The only difference lies in the constitutive model considered which has been discussed below.

Constitutive Model

In the finite element analysis the soil has been idealised as elastoplastic medium by Von-Mises yield criterion. The criterion may be expressed as

(1) |

Where *J*_{2} is the second invariant of deviatoric stress tensor and s_{y} is the yield stress of the material.

VALIDATION OF THE AXISYMMETRIC FE MODEL

Figure 1 shows the comparison of the results as obtained by the present analysis and that reported in literature. The two results are in good agreement.

**Figure 1.** Finite element discretization of piled raft foundation

FINITE ELEMENT ANALYSIS

Finite element analysis for axisymmetric raft and piled raft foundations have been performed by AXINLFEM. The results obtained from AXINLFEM have been found in good agreement with standard finite element software. In order to model the piles in a piled raft foundation, each concentric row of piles has been represented as an equivalent annulus of same volume. Finite element discretization for typical piled raft foundation with the surrounding soil and the soil strata below has been shown in Figure 2. The raft, pile and soil have been discretized into four noded isoparametric finite elements. The material nonlinearity of soil has been idealised by Von-Mises Yield Criteria. The zone of soil considered in the anaysis is of depth equal to 200 meter and radius equal to 5 times the diameter of the raft. This depth has been kept constant for all the analyses. The bottom nodes are completely fixed. All the nodes at axis of symmetry and at the radial boundary have been allowed to undergo only vertical translation. Uniformly distributed load considered in the analysis have been applied as concentrated load on the respective nodes on the foundation.

**Figure 2.** Finite element discretization of piled raft foundation

Varying Parameters and Material Properties

Diameters of raft: 10, 20 and 30 meters

Length of piles : 10, 20 and 30 meters

Diameter of piles : 0.4 metre

Thickness of the raft: 1.0 metre

Elastic modulus of raft (Ec): 20000000 kN/m^{2} (20 GPa)

Poisson’s ratio for raft (n_{c}): 0.3

An undrained (f = 0) analysis is performed here using the following total-stress soil parameters

Modulus of soil (E_{s}): 22000 kN/m^{2} (22 MPa)

"Cohesion" (i.e., the undrained shear strength) of soil (*c*_{u}) = 55.0 kN/m^{2}

Poisson’s ratio for soil (n_{s}): 0.45

RESULTS AND DISCUSSIONS

Figure 3 shows the effect of size of raft on the load settlement behaviour of raft foundation. The load settlement curve for each of the raft is seen to be nonlinear. The curves also show that the rafts reach to their ultimate load carrying capacities. For the same load applied the raft with smallest diameter undergoes larger settlement than the raft of larger diameter. Also it can be seen that the smaller diameter raft has reached to its ultimate capacity at smaller settlement than that of the raft of larger diameter.

**Figure 3.** The effect of size of raft on load-settlement curves for raft foundation

Figure 4 shows the comparison of the load settlement curves of raft and piled raft foundations. Upto load of about 9340 kN and settlement 20.1 mm ,the load settlement behaviour of raft and piled raft foundation is same. Beyond this for the range of settlement the piled raft foundation carries more load than that of the raft. This is due to the fact that in piled raft foundation upto 1000 kN load the raft carries the complete load and the piles carry almost no load. Beyond this load with further settlement of piled raft, the piles start carrying the load. With futher settlement more load is transferred to the piles.

**Figure 4.** Comparison of load--settlement curves for raft and piled-raft foundation

Figure 5 shows the load settlement curves for raft and piled raft foundation. The two curves overlap upto about 45000 kN load and 40.5 mm settlement. Beyond this limit with further increase in settlement the load carried by piled raft foundation is more than that of the raft foundation. With increase in load the raft undergoes more settlement than that of the piled raft foundation.

**Figure 5.** Comparison of load--settlement curves for raft and piled-raft foundation

Figure 6 shows the load settlement curve for the raft and piled raft foundation. The overlap of the two curves are upto 84727 kN of load and settlement 50.1 mm. For the range of settlement, the load carried by the piled raft foundation is more than that of the raft foundation.

**Figure 6.** Comparison of load--settlement curves for raft and piled-raft foundation

Figure 7 shows the comparison of the load settlement curves for piled raft foundation for different diameter of the raft and same length of pile. The load carrying capacity of the piled raft with smaller size of raft is least while that of the larger size of raft is maximum. For a given length of pile with proportional increase in size of the raft doesnot increase the load carrying capacity proportionately. The increase in size of raft from 10 to 20 meter shows a significant improvement in the load carrying capacity. When the raft size has been increased from 20 to 30 meter, there is overlap of the two curves in the initial portion showing that the two piled raft foundations carry almost the same load. Beyond 100000 kN load, the load carrying capacity of the piled raft foundation with 30 meter length of the pile is more than that of the piled raft foundation with 20 meter length of pile. This increase is not as good as when the raft size increases from 10 to 20 meter.

**Figure 7.** Load--settlement curves for piled-raft foundation for different diameter of rafts (l/d = 75, S/d = 5)

Figure 8 shows the effect of length of pile on the load settlement behaviour of piled raft foundation for which the raft diameter is 10 meter. There is significant improvement in the load carrying capacity of raft even when a pile of length equal to the diameter of raft is provided.

**Figure 8.** Effect of pile length on the load--settlement curve for piled-raft foundation (D = 10m)

When the length of pile has been increased three times the diameter of raft (L/d=75), better improvement in load carrying capacity of the raft foundation can be seen. In other words the effect of increase in length of pile is to increase the load carrying capacity of piled raft foundation. Initial portion of the curves for piled rafts with different lengths of piles show overlap which simply shows that most of the load is carried by raft and for early application of loading the two piles undergo same deformation. At higher settlement the load carried by piled raft foundation with pile of larger length carries more load than that with pile of smaller length.

Figure 9 shows the effect of pile length on the load settlement curves of piled raft foundation whose raft diameter is 20 meter. A significant improvement in load carrying capacity due to increase in length of pile can be seen in Figure 9.

**Figure 9.** Effect of pile length on the load--settlement curve for piled-raft foundations with varying L/d ratios

Comparison of figures 8 and 9 show that although the total load carrying capacity of piled raft foundation with larger diameter is more than that with smaller diameter, the improvement in increase in load carrying capacity with addition of same length of pile to the raft is more for smaller diameter of raft than the larger diameter of raft.

CONCLUSIONS

The load carrying capacity of raft foundation increases with increase in size of the raft. This increase is not proportional to the increase in size of the raft. Addition of pile of length even equal to the diameter of the raft reduces settlement of raft foundation significantly and also increases load carrying capacity. Hence smaller length piles equal to the diameter of the raft can be used successfully as settlement reducing piles in a piled raft foundation. This range of settlement reduction varies from 0 to about 50 percent. Keeping the size of raft and length of pile same, with proportional increase of the two has been found to increase the initial overlap of the two load settlement curves. For the same length of pile, the increase in size of raft increases the load carrying capacity of piled raft foundation. The proportional increase in size of raft doesnot increase the load carrying capacity proportionately. The effect of increase in length of pile is to increase the load carrying capacity of piled raft foundation. For the same length of piles below raft, the improvement is more for smaller raft than that of the larger raft. The results obtained from the finite element model compare well with the reported literature.

ACKNOWLEDGEMENTS

The authors wish to thank Birla Institute of Technology and Science, Pilani, Rajasthan for providing computing facility. The authors also thank all the groups specially Civil Engineering Group for their cooperation.

references

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