Tests on Model Piled Rafts in Sand: Measured Settlements Compared with Finite Element Predictions

Piled rafts are commonly installed to support heavy structures and are usually designed with the aid of computer software such as PLAXIS 3D, which overcomes limitations of simple older methods such as Poulos (2001). Of great importance are the interactions within piled rafts, which according to Lee and Chung (2005), are intertwined but are categorised as: (1) pile–soil–pile interaction and (2) cap–soil–pile interaction. These interactions govern the loaded behaviour of piled rafts and are strongly influenced by the installation technique, manner of loading, structural properties, dimensions and ground properties. Non consideration of the aforementioned interaction effects can lead to serious over-estimation of the raft stiffness, hence under-estimation of total and differential settlements.

Lee and Chung (2005) suggested that a piled raft is subject to two conflicting effects; the unfavorable settlement inducing effect and the favorable settlement reducing effect, which is due to increase in lateral stress in the surrounding soil as a consequence of driving a cluster of piles. The findings from the study showed that the favorable effect is governing for wider pile spacing, whilst the unfavorable effect prevails for narrower spacing of piles. For piles spacing of 5D, the bearing capacity of the raft was found to increase substantially, with pile driving effects increasing the raft capacity whereas applied vertical pile loads decreased the raft capacity. One might argue that the two opposite effects observed in the case study should nullify each other so that the piled raft has roughly the same capacity as the un-piled raft.

Conde de Freitas et al. (2015) used three dimensional finite element to analyse data from Lee and Chung’s (2005) load tests on small-scale single piles and 3 × 3 model sized piled rafts driven into sand of varying density. The piles were well instrumented and had different configurations, i.e. ground-contacting versus floating pile caps, various pile–pile spacing and overlap of cap from edge piles. They investigated the simultaneous effects of pile driving and group interaction on the densification of the sand, hence load capacity of the piled rafts. The findings from the numerical analysis agreed well with the experimental results and showed that the maximum improvement in sand density occurred for surface contacting piled rafts in which the pile spacing was 3D (where D = pile diameter). It was also found that densification was more pronounced for loose sand than dense sand and that, for pile spacing greater than 3D, differences in initial sand density did not affect the extent to which the pile installation enhanced the sand density.

Even prior to the works of Butterfield and Banerjee (1971), it was recognized that the cap–soil–pile interaction is a particularly influential mechanism controlling load capacity and that incorporating piles with a raft foundation can significantly increase the stiffness of the foundation, hence act as a settlement reducer. Among the simplest analytical methods of accounting for cap–soil–pile interaction is that of Randolph (1983), which defines an average interaction factor α_cp between the pile and cap as follows: in which r_m is the radius of influence of the piles, r_c is the effective radius of the element of pile cap associated with each pile and r_o is the pile radius. For a piled raft having n piles r_c is calculated such that nπr_c² = actual area of the pile cap. The overall stiffness k_f of the piled raft is then defined by: where k_c and k_p are the stiffness of cap and piles respectively, both of which may be evaluated in a conventional way. The ratio of load P_c supported by cap to the total load (P_c + P_p) carried by the piled raft is given by:

To assess the beneficial effects of incorporating piles beneath a raft foundation as opposed to raft only or piles with floating cap, an opportunity is taken in this paper to test small-scale piled rafts installed in sand with floating as well as surface-contacting caps. The piles are formed with different pile–pile spacing and tests are also conducted for cap-only (non-piled raft) cases. There are three research hypotheses to be tested or verified: (a) piled raft capacity increases with increasing pile–pile spacing and (b) a piled raft has an enhanced capacity compared to both a non piled raft and a single pile, (c) a piled raft with surface contacting cap has greater capacity and settlement resistance compared to all other cases. Along with the laboratory tests and finite element work, the above analytical methods (Eqs. 1–3) have been applied to ground-contacting piled rafts in order to assess the relative contribution of pile cap to total load resistance of piled rafts.

Figure 4 illustrates the equipment used in the testing program; a linear variable differential transformer (LVDT) and strain gauges at the top and bottom of two diagonally positioned piles were connected to a data logger to measure settlement and calculate axial loads in the piles respectively. In addition, a manually pumped hydraulic jack applied the vertical loads to the pile cap against a rigid reaction beam, whilst a load cell measured the actual applied loads to a precision of 10 N displayed on a load transducer.

The testing program entailed incremental loading of: (1) pure cap (un-piled raft), (2) single pile, (3) piled raft with cap not in contact with the soil (free standing), (4) piled raft with surface contacting cap. The length to diameter ratio of the piles (L/D) was 180/8 equating to 22.5; while the distance between the base of the piles and the rigid base of the container was considered sufficiently large to discount interaction between the two, following the guidelines in Nguyen et al. (2012). Model piles were fabricated with different spacing of piles in them (3D, 5D and 8D where D = pile diameter). The choice of 8D maximum spacing was based on the observation by Chen et al. (1997) that group interaction can still occur at spacing as large as 7.5D. Finally, the pile raft was placed on the soil and jacked to the predetermined level allowing 8 mm clearance between the cap and soil. Upon failure, the piled raft was jacked further until contact between the cap and soil was fully established. The load was then released; whilst the LVDT, strain gauges, and load transducer were reset to allow measurements for the surface contacting piled rafts. The loads were applied with the hand pump in a controlled and gradual manner until a reasonable decrement in settlement was reflected. Measurements were only recorded after the load and settlement stabilized. As the test progressed, the settlement for a given load also increased to a point where it was considered better to monitor load increments. Figure 5 shows the pile installation process.

Strains monitored on the data logger were converted into equivalent forces and finally back into kilograms; the levels of accuracy ranged between 89 and 95%. Although these errors were recognized they were not expected to affect the primary function of the gauges which was to determine a percentage increase in capacity of piles below a cap relative to that without cap contact rather than actual loads.

PLAXIS 3-D finite element (FE) software was used to model each of the piled rafts (at spacing of 3D, 5D and 8D) and the non-piled raft. The structure consisted of a plate element to model the raft and embedded piles (beam elements). Values of the material parameters assigned for the raft and pile structures are presented in Table 2.

Perhaps the most influential soil parameter for settlement analysis is the deformation modulus of the sand. Obviously sand stiffness and elastic modulus E_s depends on the state of consistency and packing (density). Obrzud and Truty (2012) catalogued values of E_s from several references. They recommended, for well graded sand, baseline values of E_s = 30–80 MPa and E_s = 80–160 MPa for loose and medium dense states respectively. For dense states E_s could be 160–320 MPa. Therefore, for the present research, allowing for the densification caused by the piles, it seems reasonable to adopt upper and lower limits of E_s as 100 and 200 MPa respectively. As for Poisson’s ratio, ν, typical values adopted for sand are 0.2–0.3 but generally variations in this parameter do not have a significant effect on calculated settlement. More marked variations in the magnitude of ν and effect on settlement occur in clays, where it can be proved from elasticity theory that for ν = 0.5 the elastic settlement takes place without volume change.

To account for positive installation effects the at-rest earth pressure coefficient K_o was increased by 50% to arrive at the operational lateral stress coefficient, K. This assumption is based on the recommendation by Fleming et al (2009) that K/K_o for displacement piles in sand is typically 1.5 for low stress levels and averages 1.2 over the range of stresses up to the limiting skin friction state.

Figure 8 typifies the PLAXIS output of vertical displacements, at 500 N load, for the surface contacting piled raft with 8D pile spacing when soil Young’s modulus was E_s = 100 MPa. The output is a cross-section that runs through the centre of two piles of the piled raft and reveals that no significant interaction occurred between the stressed soil and the sand box, hence removing concerns about possible boundary effects. Several other color-schemed outputs were produced, although excluded here for brevity. Some of them displayed the settlement of soil at approximately half way down the piles and immediately below the raft. In general it was indicated that maximum settlements occurred as the pile dragged soil downwards during loading. As seen in Fig. 8, the constant dark colored area immediately beneath the cap implies that, throughout the test, the zone just below the rigid pile cap was consistently the location of maximum settlement (Fig. 9).

Figures 10, 11 and 12 compare the PLAXIS predicted load-settlement curves for piled raft (for 3D, 5D and 8D spacing) and non-piled raft with experimental results. It is seen that PLAXIS predictions have over-estimated the initial stiffness of the load-settlement curve and under-estimated the ultimate capacity. This is due to the possibility that the PLAXIS models have not taken full account of the additional settlement induced by the piles during installation and at working loads. However, PLAXIS has effectively accounted for the increase in bearing capacity with corresponding increases in pile spacing. The lower bound value of 100 MPa chosen for the Young’s modulus was half that of the upper bound estimate of 200 MPa. For PLAXIS models using a Young’s modulus of 100 MPa the settlement prediction was twice as great as that for corresponding loads pertaining to soil models of 200 MPa.

It can be seen from Fig. 12 that, in contrast to the piled rafts, the load capacity of the non-piled raft was grossly underestimated by the finite element method. Nevertheless, findings by Nguyen et al. (2012) also reveal large variations in the PLAXIS 3-D output in comparison to experimental data from geotechnical centrifuge tests. This reinforces the need for pile testing, as a means of obtaining reliable design information for working piles, for large construction projects or where the ground conditions present special challenges.

Application of the Randolph’s (1983) analytical Eqs. 1–3, discussed earlier, showed that the piled rafts tested here had a very high proportion (typically 55–85%) of total capacities contributed by the pile cap alone.

It is seen that these percentages are well within the range of load sharing ratios covered by the normalized plots in charts published by Fleming et al. (2009). Therefore this gives confidence that the results from the lab tests and are reasonable, as are the finite element results albeit for low loading ranges. Although these findings are from model scale piles installed sand, the practical implications for design are as follows:

Load tests were conducted on differently configured piled rafts, single piles and non-piled rafts installed in dry sand. In addition, the foundations were analyzed using the finite element program PLAXIS 3-D to predict the load-settlement response of the foundations. It was found that: