## 4 Conclusions  
In this paper, based on the simplified nonlinear load transfer functions for pile shaft and pile load as derived by [PERSON] and [PERSON] [20,21], analyses were conducted to understand the behaviours of the pile groups in a nonhomogeneous soil medium and of various sizes. This method is suitable for pile groups embedded in any layered soil. The accuracy of the method based on the proposed load-transfer function was verified by comparisons with the more rigorous boundary integral solution reported by [PERSON] and [PERSON][7] and with [PERSON] and [PERSON]'s [24] results for pile groups in linear elastic homogeneous soils. Field pile load test results for the single pile and the pile groups as described by [PERSON] [26] were also referenced for the verification of the proposed method. Reasonable agreements were obtained for all cases. Furthermore, through systemic parametric studies, the following conclusions can be drawn:  
1. The soil-pile interface parameters \(a\) and \(b\) as described by [PERSON] and [PERSON] [20,21] can be obtained using the back-analysis method proposed in this paper. Both parameters bear strong physical relationships with the stratigraphy of the soils. It is shown through field tests that the approach accurately computes the load-settlement behaviours of the single pile and the pile groups. 2. The proposed method is an efficient method for the nonlinear analysis of large pile groups, which makes the method ideally suited to small computers. There is no requirement for a computer with a large storage capacity. 3. There are significant differences between the single pile and the pile groups' behaviours. However, there are two primary factors affecting the overall behaviours of the pile groups, which are the number of piles in the pile groups and the pile slenderness ratio, _L/D_. 4. Contrary to the behaviour of the long slender single piles, the soil located at the pile base plays an important role in the load-transfer mechanism of large pile groups. Due to the increasing amount of shaft interactions in large pile groups, the overall shaft resistance of pile groups is significantly reduced, and a larger proportion of the pile load is transferred to the base of the pile groups, especially under lower load levels (30-50%). From a conventional design point of view, one often designs a pile group based on single pile behaviour or a single pile test. This could sometimes be misleading since the load-transfer mechanism of the single pile differs from that of the pile groups. 5. For small pile groups, the load transfer behaviours are similar to the behaviours of single piles but for larger pile groups, such behaviours are similar to an equivalent rigid block foundation. Figure 18: Normalised pile stiffness with different pile group span ratios. When the pile slenderness ratio increases, the load distributions for the individual piles in the pile groups become more uniform and the normalised group stiffness becomes smaller. * Under a normal pile spacing ratio, \(S\)/\(D\), of 2 to 6, the shaft interaction factor is significant and it has some effects on the overall behaviours of the pile groups. Beyond this range, the interaction effects become quite small and the overall behaviours of the pile group are similar to those of isolated single piles. Data curation, H.L. ; investigation, H.L. and Z.X. ; project administration, K.L. ; supervision, K.L. ; writing--original draft, H.L. ; writing--review & editing, Z.X. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China grant number [50978086 and 51178165]. In particular, the author would like to thank the editor for the careful editing and layout of this article, as well as for the reviewer's valuable comments and suggestions for this article. This paper has also been supported by the National Natural Science Foundation of China (grant No. 50978086 and 51178165). The authors declare no conflict of interest. List of Notations