# On the Comparison Between the Approximate And Precise Methods of Piled Raft Foundation Analysis

Abbasali Taghavi Ghalesari

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Abbasali Taghavi Ghalesari. On the Comparison Between the Approximate And Precise Methods of Piled Raft Foundation Analysis. Mechanics, Materials Science & Engineering Journal, 2016, 10.13140/RG.2.1.5128.7446. hal-01309183

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# On the Comparison Between the Approximate And Precise Methods of Piled Raft Foundation Analysis

Abbasali Taghavi Ghalesari

1 - Department of Civil Engineering, Babol Noshirvani University of Technology, Babol, Iran

<figure><img src="image_2.png" /></figure>

DOI 10.13140/RG.2.1.5128.7446

**Keywords:** piled raft foundation, soil-structure interaction, 3D FE method, approximate method.

**ABSTRACT.** Use of raft foundation to support heavy and tall building may provide the overall safety factor against design loads but the average and differential settlement could exceed the allowable value. On the other hand, utilizing pile group may be an expensive option. In this situation, use of composite pile group and raft foundation that called “Piled Raft Foundation” seems a suitable choice. This foundation is a composite geotechnical system of three bearing components: raft, pile group and soil. The applied load on the raft is transferred to the underlying soil by the contribution of raft and piles. Therefore, considering the interaction effect between the components is essential. It causes some complexities in predicting the behavior of piled rafts. Thus, on this basis, so many different methods were developed. In this study, a comparison between these different methods including approximate and precise methods are presented. Based on the results, a three-dimensional finite element analysis gives perfectly satisfactory results in the prediction of bearing and settlement behavior of piled rafts.

**Introduction.** In recent years, piled raft foundations have been widely used in practice to support heavy and high-rise buildings due to weight and rigidity of the superstructure. When a raft foundation provides the required bearing capacity but the settlement values exceed the allowable limits, an addition of fewer piles in comparison with pile groups could improve the settlement behaviour of the foundation.

The expression of piled raft foundations is in no manner new and has been explained by several authors, including Zeevaert [1], Davis and Poulos [2], Hooper [3], Sommer et al. [4] and Franke [5], among many others.

The mechanism of load transmission in piled raft foundation is so complicated. Thus, different methods from simplified methods to more rigorous methods were developed. In addition to laboratory tests and field studies such as centrifuge test, shaking table test and full-scale modelling, several empirical, analytical and numerical methods have been presented to predict the behaviour of piled rafts under static vertical to dynamic loads. A comparison between the results of different methods of piled raft analysis through some examples is considered in this study. The results of these methods were compared with the results of three-dimensional finite element method as a precise solution. The 3D FE method is capable for considering the interaction effect of the piled raft components.

**Analysis methods.**

**Approximation methods.** Hongladaromp et al. [6] presented an approach that considered the soil as an elastic continuum, the raft as a thin plate and the piles as springs. In this method, the interaction effects between the piles were ignored. Poulos [7] presented a program, GARP, based on finite difference method with the consideration of pile-raft interaction. The piles were allowed to reach their ultimate bearing capacities and a local bearing failure was allowed for the raft. A similar method was employed by Russo [8] which the piles and raft were modelled by a series of springs. Boussinesq's solution was used to calculate the soil displacements. For a single pile, load-settlement curve was assumed hyperbolic to consider the non-linearity of piles. Kitiyodom and Matsumoto [9] presented a method where the piles were modelled by elastic beam elements and the interaction between the
structural elements was estimated by Mindlin's solutions. The lateral and vertical resistances of piles were incorporated in this method. Poulos [10] presented program GASP where the raft was modelled by a strip and piles and soil by springs. Four different interactions between the pile and raft were considered.

**Simplified methods.** Poulos and Davis [11] presented an approach that can be adopted to estimate the load-settlement behaviour. This method is extended by Randolph [12] to estimate the load bearing of piles and raft. The Poulos-Davis-Randolph (PDR) method involves with the stiffness of pile group and raft. The pile-raft interaction factor, $\alpha_{cp}$ and the load carried by the piles, $P_{up}$ was computed. By using these factors and programming in mathematical program MATHCAD, a tri-linear load-settlement curve was developed and the calculation of average settlements and pile capacity mobilization was performed.

When the raft satisfies the bearing requirements, piles as settlement reducer are designed. On this basis, Burland [13] developed a step-by-step method to calculate the settlement and bending moment of piled raft.

**Boundary element method.** The boundary element method is based on the discretization of the pile-raft system boundary. Thus, the set of equations to be solved have been decreased. In this method, the partial differential equations are transformed to integral equations. This method is employed by Butterfield and Banerjee [14] to investigate the behaviour of pile group with a rigid cap embedded in an elastic half-space. The interaction effect and soil response were considered by using Mindlin's solution. Franke et al [15] used boundary element method to study the behaviour of piled rafts in high-rise buildings resting on the Frankfurt clay. They also performed a field study on the behaviour of these foundations and the measurement of the foundation settlements was presented. El-Mossallamy [16] applied the program GAPR based on the boundary element method to study the behaviour of piled raft foundation in some cases.

**Finite element method.** The finite element method has become a popular and powerful method for studying the behaviour of piled raft foundation due to its realistic results. In this method, both the foundation components and soil should be discretized. Some simplifications such as plane strain and axisymmetric assumptions were made to reduce the computational attempts. One of the first studies using this method was presented by Hooper [3] for the analysis of Hyde Park Barracks. An axisymmetric model is used and the equivalent stiffness is introduced to consider the effect of superstructure stiffening effect. A step-by-step analysis based on this method was presented by Katzenbach and Reul [16], in which the piles were modelled by 3D isoparametric elements and the raft was modelled by shell elements. Prakoso and Kulhawy [18] used finite element program PLAXIS to investigate the piled raft performance with a plane strain model. The analyses include linear elastic and non-linear elastoplastic models. Recently, several authors [19-23] used 3D FE method to study the behaviour of piled raft foundation in different conditions.

**Combined boundary element and finite element method.** In this method, the finite element method for the analysis of the raft is combined with the boundary element method for the analysis of the piles and soil. One example of this method is the study of Poulos et al [24] using elastic-plastic model by combined boundary element and finite element method in some case histories.

**Variational method.** The principle of minimum potential energy is used in this method to analyse the foundation. The interface of raft and soil is the only parts to be discretized. Chow et al. [25] used this method for the analysis of vertically loaded piled raft foundation. The raft was modelled by a thin plate and the pile group was represented by a finite series. The elastic-perfectly plastic behaviour of pile and soil were assumed.

## Numerical analysis

**Finite element mesh and boundary condition.** In this paper, in order to compare the results of above-mentioned methods with the three-dimensional finite element method, the behaviour of the
piled raft was investigated by carrying out 3D numerical analyses. The soil and structural elements were discretized to 8-node linear elements. Figure 1 shows a typical finite element mesh used for comparison. Due to load and geometry symmetry, only one-quarter of the problem was modelled. Two symmetric plane and two horizontal fixities were used at lateral boundaries. The base of the model is constrained against translation in three directions. The geostatic stresses were produced to simulate the in-situ condition. Then, a uniform load is applied over the raft area. The long-term response of the soil is considered and so drained effective parameters of the soil were applied.

**Constitutive Modelling.** In this study, Mohr-Coulomb model was used to simulate the soil condition due to its simple and quick responses. In all analyses, average (constant) values of material properties were used for the soil. The structural elements of foundation were modelled with a linear elastic model because they have a great modulus of elasticity in comparison with the soil. At the pile-raft interface, thin-layer elements with the properties of soil material were used. The thickness of these elements were 0.1D (D=pile diameter) and a slip behaviour between them was assumed.

<figure><img src="image_3.png" /><figcaption>Fig. 1. Typical Finite Element mesh used for the numerical method.</figcaption></figure>

**Comparative results and discussion.** In order to investigate the above-mentioned methods and to compare the results of these methods, three typical examples were analyzed and the efficiency of these methods was evaluated.

The geometry and material properties used in the first example are shown in Table 1. This example is based on the study of Chow et al. [25] based on a variational method. A 3 × 3 pile group with the length of 20 m was under a square raft with the 6 m width and 0.5 m thickness. The soil is considered as a linear elastic material. The results of these two methods were presented in Table 2.
<table><caption>Table 1. Geometry and material properties of the first example.</caption><tr><td rowspan="4">Pile</td><td>Young's Modulus (E<sub>p</sub>)</td><td>35000 MPa</td></tr><tr><td>Length (L)</td><td>20 m</td></tr><tr><td>Radius (r<sub>0</sub>)</td><td>0.4</td></tr><tr><td>Spacing (S)</td><td>2 m</td></tr><tr><td rowspan="4">Raft</td><td>Young's Modulus (E<sub>r</sub>)</td><td>35000 MPa</td></tr><tr><td>Poisson's ratio (ν<sub>r</sub>)</td><td>0.3</td></tr><tr><td>Thickness (t<sub>r</sub>)</td><td>0.5 m</td></tr><tr><td>Width (B<sub>r</sub>)</td><td>6 m</td></tr><tr><td rowspan="2">Soil</td><td>Young's Modulus (E<sub>s</sub>)</td><td>280 MPa</td></tr><tr><td>Poisson's ratio (ν<sub>s</sub>)</td><td>0.4</td></tr><tr><td>Arrangement</td><td colspan="2">3×3</td></tr></table>

<table><caption>Table 2. Comparison of the results for the first example.</caption><thead><tr><td></td><td>S<sub>avg</sub> (mm)</td><td>Pile Load (%)</td></tr></thead><tbody><tr><td>Chow et al. [25]</td><td>8.02</td><td>75</td></tr><tr><td>Present study</td><td>8.16</td><td>79</td></tr></tbody></table>

The second example contains a 5 × 5 pile group with a square raft of 27 m width and 2 m thickness. The piles had 30 m length and were embedded in clay soil. The geometry of this case is shown in Figure 2.

<figure><img src="image_4.png" /><figcaption>Fig. 2. The geometry of considered case in the second example.</figcaption></figure>

This example had been analyzed by Poulos [7] (GARP program) and El-Mossallamy [16] (boundary element method). A comparison between the results of these analyses with 3D FE method presented in this study for raft, pile group and piled raft is shown in Figure 3. A good agreement between the results of different methods can be recognized. This agreement exists up to reaching the ultimate capacity of pile group. The ultimate pile group capacity, in this case, is defined as a summation of the ultimate capacities of the individual piles. The curves related to 3D FE method and boundary element method are approaching but they are larger than the simplified method. This is due to increasing the
horizontal effective stresses around the piles caused by the contribution of the raft contact and hence increasing the piles ultimate capacity. There is an agreement between the results of boundary element and the simplified methods in the high load ranges. In this case, finite element method underestimates the piled raft capacity and tends to be conservative.

<figure><img src="image_5.png" /><figcaption>Fig. 3. Load-settlement curve for (a) unpiled raft (b) pile group (c) piled raft</figcaption></figure>

The third example analyzed by 6 different mentioned methods where a 10 × 6 × 0.5 m raft is supported by a pile group containing 15 piles. Pile, raft and properties soil and load characteristics are shown in
Figure 4. Based on finite difference method employing FLAC2D, FLAC3D, plate on spring approximation method [7] using GARP5, simplified PDR method and strip on spring method using GASP [10], the load-settlement curve of Figure 5 is depicted to compare the results.

<figure><img src="image_6.png" /><figcaption>Fig. 4. Pile, raft and soil properties and load characteristics for the third example [26]</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 5. Comparison of various methods for load-settlement analysis with the present study</figcaption></figure>

As shown in Figure 5, in low load ranges, even the approximation and simplified methods are comparative with the numerical methods (3D FDM and FEM). The latter method gives a softer response than others when the load exceeds 12 MN. It is due to the progress of plastic zone development beneath the raft and so the increase of plastic deformations. However, FLAC2D overestimates the settlements because of the assumptions involved in plane strain modeling. Therefore, 2D plane strain modeling is conservative and cause misleading in the analysis especially when the raft is square.
Moreover, the results of 2D FE [18], approximation method [7], combined BEM and FEM [24], BEM [15] and measurement of Franke et al. [15] were compared with the present method (Figure 6) and a good agreement was observed.

<figure><img src="image_8.png" /><figcaption>Fig. 6. Comparison between the approximate, numerical methods and measurements</figcaption></figure>

**Summary.** In this study, a review of the available methods to consider the behavior of piled raft foundations was performed and a comparison between the results of these different methods with a three-dimensional finite element model is presented. For this purpose, three separate examples for different soil and foundation conditions were considered. Based on the results, analysis of piled raft with the presented 3D FE method gives good and comparative results for the assessment of the performance of foundation.

**References**

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