PileGroup Validation - Example 2. Linear analysis of 3 x 3 pile group under three-dimensional loading (Pirrello and Poulos 2014)

This example is from the analysis of a 3 x 3 pile group, as documented by Pirrello and Poulos (2014). The pile group consists of piles with a diameter of 0.5 m and an individual length of 15 m. The piles are arranged with a spacing of 2 m between each pile, both horizontally and vertically.

The material properties used in the analysis are as follows: each pile has a Young’s modulus of 30 GPa. For the surrounding soil, a uniform Young’s modulus value of 50 MPa is applied, with a Poisson’s ratio of 0.3. At the level of the pile toe, the Young’s modulus of the soil increases to 100 MPa. The pile-to-cap connection was rigid for all piles. The layout of the pile group is shown in the figure below with the loading.

Figure 2-1 Pile group layout for Example 2

The analysis method for this example is based on the linear analysis module of the PileGroup program where Randolph’s elastic solutions for single piles in homogeneous or Gibson-type soils are adopted. The method assumes small-strain, elastic soil response and provides closed-form solutions for pile head displacement, rotation, and stiffness under vertical, lateral, and moment loading. Figure 2-2 and Figure 2-3 show the axial and lateral stiffness input parameters, respectively.

Figure 2-2 Axial stiffness inputs for linear analysis mode

Figure 2-3 Lateral stiffness inputs for linear analysis mode

The figure below shows the three-dimensional view of this 3 x 3 pile group modelled in the PileGroup program.

Figure 2-4 Three-dimensional view of 3 x 3 pile group

The figure below shows the soil layer information, pile group and pile cap loads defined in the program. It shows the thickness values for all the layers and the pile lengths.

Figure 2-5 Soil layers, soil properties and pile cap loads defined for this example.

Figure 2-6 Pile deflections for Example 2

Figure 2-7 Pile moment for Example 2

Figure 2-6 shows the pile deflection results within the pile group from the analysis using the PileGroup program. Figure 2-7 shows the bending moment results within the pile group.

Table 2-1 presents a detailed comparison of the analysis results obtained from several different software programs. The values calculated by the PileGroup program show strong agreement with those produced by the PIGLET program. This alignment between results demonstrates that the PileGroup program delivers reliable output for the examined response parameters when benchmarked against established analysis tools.

The analysis results from three pile group analysis programs - CLAP (Coffey 2017), PIGLET, and REPUTE—displayed good consistency. This was evident in both the calculated (rigid) pile cap deflections and maximum loads within the pile group. However, it was observed that REPUTE tended to report higher maximum lateral loads and moments compared to the other two programs. This discrepancy is likely attributed to differences in the modeling approach, specifically the inclusion of shielding effects within the pile group under lateral loading, as discussed by Basile (2003).

Table 2-1 Comparison results for Example 2

References:

1. Coffey Geotechnics. (2017). CLAP (Combined Load Analysis of Piles) User’s Manual. Sydney, Australia.

2. Basile, F. (2003). Analysis and design of pile groups. In Numerical Analysis and Modelling in Geomechanics (J. W. Bull, ed.), Spon Press (Taylor & Francis Group), Oxford, Chapter 10, pp. 278–315.

3. Pirrello, S., and Poulos, H. G. (2014). “Comparison of four pile group analysis programs.” Advances in Foundation Engineering, Proceedings of the International Symposium on Advances in Foundation Engineering (ISAFE 2013), Singapore, Research Publishing Services, Singapore, 291–297.