As mentioned above, through model tests the impact of the pile length, pile diameter, the relative density of soil, number of piles, and pile configuration were investigated. The load sharing behavior of piled raft foundation is represented as ‘Piled-Raft Coefficient’ in this study as discussed earlier. The results obtained from the model tests were presented and discussed in the following sections.
Impact of pile length
The results showing the variation of the Piled-Raft coefficient with settlement for different pile lengths are presented in Fig. 5–7. Figure 5 shows the variation of the piled-raft coefficient for the raft with a single number of piles having a diameter of 10 mm, with varying lengths equal to 200 mm, 400 mm, and 600 mm (For Dr = 40%). It shows that Piled-Raft Coefficient decreases with the settlement of foundation up to the settlement level of about 20–30 mm. After this, no significant change in the coefficient can be observed and an asymptotic minimum value of piled raft coefficient is achieved. This shows that load shared by pile decreases with settlement and load shared by raft increases. In other terms, it can be said that at larger settlements the contribution of rafts increases. In piled-raft foundation, the first load gets transferred to the pile, because of this load sharing of the pile remains greater initially. With settlement contact of the raft with soil increases, this results in an increment of the load sharing by the raft. Cooke 1986, have also reported similar results. It can be further observed that the decrease in the piled-raft coefficient is greater for the smaller pile i.e. for the pile having a length equal to 20 mm. Decrease in the pile-raft coefficient with settlement gets reduced with an increase in the length of the pile. This shows that with the increase in the pile length load sharing by the raft decreases and pile increases. Pile contributes to load sharing by the end bearing resistance and surface friction. Due to an increase in the length of the pile, the magnitude of the surface friction gets increased. Because of this, the load shared by the pile increases with an increase in length.
In Fig. 6, a similar trend of the piled-raft coefficient can be observed for the foundation with the greater number of piles (N = 9) can be observed. For a single piled raft the minimum piled raft coefficient is increased three times from about 0.15 to 0.45 when the length of the pile changes from 200 mm to 600 mm. So, it can be noted that the impact of length of the pile on the load sharing behavior decreased when a greater number of piles were used under rafts. Similarly, in Fig. 7 for piled raft foundation with greater diameter, the minimum piled raft coefficient changes from about 0.35 to 0.45 when length changes from 200 mm to 600 mm. In this case, also the impact of pile length on the load sharing behavior of pile decreases when a pile of greater diameter was used. In both cases due to increment in the number of piles and diameter, surface friction and end bearing get increased. Due to this in both of the conditions (Fig. 6 and Fig. 7), greater load sharing by pile is shown even at lower length.
Impact of pile diameter
The impact of the diameter on the piled-raft coefficient can be understood by analyzing the results presented in Figs. 8 and 9. In Fig. 8 variation of piled-raft coefficient for the single piled-raft foundation with the relative density of soil equal to 40% is presented. It can be observed that the load shared by piles gets increased with increase in the diameter of the pile. Piled-raft coefficient corresponding to 20 mm settlement changes from 0.15 to 0.39 when diameter increases from 10 mm to 20 mm in the case when pile length is 200 mm as the diameter increases, the surface area of the pile increases, resulting in a heightened mobilization of friction on the surface. This, in turn, leads to an increased load borne by the pile. It can be further observed that for piled-raft foundations with pile length 600 mm, the Coefficient changes from 0.5 to 0.65 when diameter increases from 10 mm to 20 mm. This trend shows that the impact of diameter on load shared by piles decreases when the length of piles increases.
In Fig. 9 variation of the piled-raft coefficient is shown with the number of piles below the raft being equal to nine. At 20 mm settlement, the value of the piled-raft coefficient varies from 0.78 to 0.92 when the length of the piles was changed from 200 mm to 600 mm and the diameter of piles was changed from 10 mm to 20 mm. By comparing this result with the result of the pile-raft foundation with a single pile, it can be concluded that with greater numbers of piles the impact of diameter gets decreased. With greater numbers of piles end bearing and surface friction increases even for shorter piles (L = 200 mm). Because of this reason, the difference between the piled-sharing coefficient of piled-raft foundation with shorter and longer single piles is greater than the piled-raft foundation with the greater number of piles.
Impact of relative density of soil
The variation of the piled-raft coefficient of piled-raft foundation with varying lengths supported by sand with the relative density of 40% and 70% are depicted in Fig. 10. The piled-raft coefficient is greater for the soil having a relative density is 40% than the soil with a relative density of 70%. This indicates that the increase in the relative density load shared by the raft increases for shorter (L = 200 mm) and longer piles (L = 600 mm). Similar types of variation were found when piles with larger diameters were used. In the case of dense soil, the significant contact gets mobilized even at the lower settlement level. Lee et al. (2015) have also shown similar behavior. During the test at lower relative density i.e. at Dr = 40%, no heaving was observed. But at higher relative density heaving in the surrounding soil was observed. A similar observation of heaving was reported by Roy and Chattopadhyay (2017).
Impact of number of piles and configuration of piles
In Fig. 11 the variation of piled-raft coefficient for different numbers of piles is presented. It shows that piled-raft foundations with a single pile have a piled-raft coefficient of around 0.35 at a settlement level of 20 mm. The case, when the number of piles increased to five and nine shows the piled raft coefficient around 0.7 and 0.8 at 20 mm settlement level. This indicates that the load shared by piles increases with an increase in the number of piles supporting the raft. Due to an increase in the number of piles surface friction increases, because of this load shared by pile increases.
Two types of configurations were used in this study for experimentation to understand the impact of configuration on the load sharing behavior of pile and raft. The details of the configuration are discussed earlier (Fig. 2 and Table 2). The impact of configuration on the piled-raft coefficient is presented in Fig. 12. It can be observed that the piled-raft coefficient in the case of configuration C3 is greater than configuration C4. It means load sharing by pile in the case of C3 is greater than C4. Load sharing by pile increases when piles are arranged nearer to the center of the piled-raft foundation. In configuration C3 the arrangement of piles is nearer to the center, while in configuration C4 the piles are distributed over the raft area. Because of this C3 performs better than C4. Similar behavior was reported by Cao et al. 2004.
Mathematical model
A mathematical model to predict the piled-raft coefficient is developed through multivariable linear regression analysis (MLRA) in this study. The equation was developed by the help of Microsoft excel. In MLRA set of independent and dependent variable were selected. Piled-raft coefficient was taken as dependent variable. Settlement of piled-raft foundation, number of piles, relative density, and diameter of pile, length of the pile and area distribution of pile under raft are considered as independent variable in analysis. A general expression for the developed model can be written as follows.
$$Y= {A}_{o}+{A}_{1}{X}_{1}+{\dots \dots \dots \dots \dots +A}_{n}{X}_{n}+ϵ$$
2
……….
Where, Y is dependent variable; Ai is Coefficient need to be find out and Xi is independent variable. ϵ indicates error. Different forms of models were considered during the analysis. Finalization of the model was done by trial and error method. The form of model with best prediction capability was finally selected. Data analysis tool of excel was used for trial and error process of MLRA. The prediction model of piled-raft coefficient obtained from the analysis can be presented as:
$${\alpha }_{PR}={S}^{0.25}*Log\left({N}_{p}\right)*\frac{1}{{D}_{r}}*D*Log\left(L\right)*{A}_{r}$$
3
………..
Here, αPR is piled-raft coefficient, S is settlement of foundation, Np is number of piles, Dr is relative density, D is diameter of piles, L is length of piles and Ar is area ratio of piles. From the analysis coefficient of determination, R2 came out to be 0.82. Figure 13 shows the comparison of observed and predicted value of piled-raft coefficient with settlement. It can be observed that the model can predict well. Figure 14 shows the scattered plot of the predicted and measured value of the piled-raft coefficient. It shows that the scattering is not much. It also shows that model is predicting the piled-raft coefficient in good manner.