## 2 Methods
### Comparison of Computed Results with Field-Measured Results  
[PERSON] [26] analysed the load-settlement characteristics of a single pile and pile groups in overconsolidated clay using field tests and adopted closed-mouthed steel pipe piles with a diameter of 273 mm, a wall thickness of 9.3 mm, and a pile length of 13.1 m. The pile was jacked into the overconsolidated clay by static load and the pile groups were 9-pile by \(3\times 3\) and the centre-to-centre spacing is \(S\) = 3\(D\), where \(D\) is the diameter of the pile. The two single piles were located at a distance of 3.7m from the center of the pile groups. As the interaction between the pile group and pile cap in clay is low [27], in this analysis, the group pile stage was a rigid high pile cap and the cap was without contact with the soil. We compared these test results with the results of the back-analysis  
Figure 4: Comparison of results in terms of normalised stiffness vs. pile slenderness ratio ([PERSON] [24] and [PERSON] et al. [25]). Figure 5: Comparison of results between the present method and the elastic approximate methods under different load levels ([PERSON] and [PERSON] [7]). (**a**) \(L\)/\(D\) = 20; (**b**) \(L\)/\(D\) = 50.  
method in this paper for the load-settlement characteristics of the single pile. The pile group load-settlement characteristics of the 4-pile subgroup (pile marked 1), the 5-pile subgroup (piles marked 2 and 3), and the 9-pile group, are shown in Figure 6b. [PERSON] et al. [28] presented the exploration data of the field test and the soil shear modulus, and [PERSON] [8] selected the parameters of the soil shear model of the field test, assuming that the soil shear modulus linearly increased, whereas the surface was taken at \(G=47.9\mathrm{MN/m^{2}}\) and the bottom of the pile was \(G=151\mathrm{MN/m^{2}}\). In this paper, the back-analysis method also adopts a similar method, taking the surface soil without a drainage shear strength of 47.9 \(\mathrm{kN/m^{2}}\), the pile bottom increased linearly to 239 \(\mathrm{kN/m^{2}}\). At the same time, it is assumed that the Poisson's ratio of the soil, \(\upsilon\), was assumed to be 0.5, the \(R_{\zeta}\) was 0.9, the ultimate end-bearing pressure was 2.15 \(\mathrm{MN/m^{2}}\) (i.e., \(q_{tilt}=9C_{u}\)), and the single pile is the same as the middle soil parameters of the group piles consisting of the 4-pile subgroup, the 5-pile subgroup, and the 9-pile group. Figure 7 shows the results of the predicted \(K_{si}(z)\) and \(\tau_{f}(z)\) profiles for the single reference pile determined by the back-analysis method as proposed in the previous section. It is obvious that both the predicted \(K_{si}(z)\) and \(\tau_{f}(z)\) profiles varied rather non-uniformly but with an increasing trend in relation to depth. The variability of \(K_{si}(z)\) and \(\tau_{f}(z)\) was highly correlated to the variation of Afterberg's limits and the natural water content of the soils with depth. In fact, the variability of \(K_{si}(z)\) and \(\tau_{f}(z)\) could be used to delineate the natural stratification of the soil layers in the field. Thus, the soil conditions around the reference piles could be clearly reflected by the \(K_{si}(z)\) and \(\tau_{f}(z)\) profiles (i.e., the \(a\) and \(b\) parameters) as determined by the proposed back-analysis method. These back-calculated \(K_{si}(z)\) and \(\tau(z)\) profiles were used for a comparative study as discussed in the following sections. Furthermore, for illustration purposes, the average trend of \(\overline{K}_{si}\) and \(\overline{\tau}_{f}\) in relation to depth was determined by linear regression analysis on the actual back-calculated \(K_{si}(z)\) and \(\tau_{f}(z)\) profiles.