3D Numerical Modeling of Large Piled-Raft Foundation on Clayey Soils for Different Loadings and Pile-Raft Configurations

In order to understand the effect of pile spacing, S_p has been varied from 3 to 7 m, whereas for other parameters such as raft size (B_r), raft thickness (t_r), and pile diameter (d_p), standard value has been chosen from Table 3. As mentioned earlier, all the PRCs used in the present study consist of an applied load of 150 kPa and a total pile length of 1,470 m. The effect of S_p on W_avg for different PRCs and for different types of soil (soft clay and stiff clay) is shown in Figure 6(a) and 6(b), respectively.

Figure 6

It can be seen that for any PRC with any soil profile (soft clay or stiff clay), W_avg decreases as the S_p increases. However, the rate of decrease in W_avg is observed to be substantial in case of soft clay soil profile as compared to that of the stiff clay soil profile. Here, it should be noted that with an increase in the pile spacing (with constant number of piles), width of pile group B_g increases, which results in the increase in the area covered by the piles (A_g). As the area covered by the piles increases (A_g), piles get uniformly distributed under the entire area of the raft (A_r) and because of which the average settlement of the pile-raft decreases. In stiff clay, soil is relatively stiff than that of soft clay soil; thus, the rate of decrease in W_avg is minimum in stiff clay soil.

For any soil profile, W_avg is observed to be lower for PRC with UDL when compared to the PRC with EPL. Moreover, for soft clay soil profile, the difference in W_avg is significant at lower pile spacing than that at larger pile spacing. For example, at the 3-m pile spacing, the W_avg of PRC1(b) was 1,010 mm and of PRC2(b) was 1,220 mm. While at the 7-m pile spacing, the W_avg of PRC1(b) was 120 mm and of PRC2(b) was 180 mm.

At lower pile spacing (S_p = 3 m), piles were mainly concentrated near the center portion (B_g = 19 m) of the raft; however, the applied load (UDL or EPL) was acting over the entire raft. Because of which, at lower pile spacing, the difference in W_avg was significant than that of larger pile spacing (S_p = 7 m). Thus, for better prediction of average settlement, the actual loading encountered in the practice (i.e., point or concentrating load, UDL, and line load) should be simulated in the modeling of piled-raft foundation.

For pile-raft foundation rested on soft clay soil and stiff soil profile, PRC(b) or “W”-shaped PRC and PRC(c) or “V”-shaped PRC with larger pile spacing can be used effectively to reduce the W_avg, correspondingly (Fig. 6a and b). Thus, it can be concluded that the effectiveness of PRC depends on the condition of soil (soft or stiff) beneath the raft. Moreover, as per the codal requirement, the allowable maximum settlement of the raft foundation is 125 mm and the allowable differential settlement is 148.5 mm (0.0033*Br) (IS 1904-1986). Therefore, pile spacing should be selected in such way that the values of maximum settlement and differential settlement are within allowable limits.

As the pile spacing increases, the trends observed for differential settlement are opposite to that of average settlement trends. For any PRC with any soil profile, W_diff increases as the S_p increases (Fig. 7). In case of soft clay soil profile, the rate of increase in W_diff is more significant than that of stiff clay soil profile. As stated earlier, with the increase in S_p, piles get spread away from the center of the raft, which results in the increase in pile group area A_g and subsequent decrease in the center settlement W_center of the raft (because piles start behaving as individual element). However, the difference between center and corner settlement increases.

Figure 7

Moreover, for soft clay soil profile at larger pile spacing, the relative difference in W_diff is significant as that of stiff clay soil profile (Table 5). Alike W_avg, for any PRC with any soil profile, W_diff is observed to be lower for PRC with UDL as compared to the PRC with EPL. For example, at the 3-m pile spacing for soft clay soil profile, the W_avg of PRC1(b) is 25 mm, whereas for PRC2(b), it is 46 mm.

For any load configuration and any soil profile, PRC(c) or “V”-shaped PRC with lower S_p can be used effectively to reduce the W_diff (Fig. 7b). In PRC(c) or “V”-shaped PRC, longer piles cover the center part of the raft because of which differential settlement decreases. Here, it should be noted that for any PRC, the total pile length is equal to 1,470 m. So, it is suggested to use the longer piles at the center part of the raft to reduce the differential settlement effectively rather than providing the uniform pile length under the raft.

Among the several other parameters, pile length and pile spacing are considerably affecting the load carried by the piles in piled-raft foundation. The contribution of piles in piled raft needs to be estimated for economical and efficient design of piled-raft foundation. The effect of S_p on load-sharing coefficient (α_pr) for different piled-raft configurations and different soil profiles are shown in Figure 8.

Figure 8

For any PRC with any soil profile, α_pr increases linearly (approximately) as the S_p increases. Also, a lower value of α_pr is observed for the PRC with UDL than that of PRC with EPL. In case of point loading, the load is concentrated at single points, whereas in later case, the load is uniformly distributed over the entire area. Moreover, earlier studies have also reported that the load carried by piles for concentrated loading were generally greater than those of uniform loading (Ghalesari and Choobbasti 2016; Lee et al 2010). It can be also observed from Figure 8(a) that at larger pile spacing (S_p = 6–7 m), α_pr in soft clay soil profile is relatively higher than stiff soil profile.

Thus, for uniform distributed load, the contribution of pile bearing obtained was less than that of the point load. Furthermore, the calculated number of piles required to carry the applied load will be more for UDL than that of EPL. However, the addition of more number of piles may result into unnecessarily over safe design. Therefore, for efficient and economical design of foundation, attention should be given to simulate the loading condition as close as possible in the modeling.

It is interesting to note that for any load configuration with any soil profile, PRC(b) or “W”-shaped PRC observed to be more effective in enhancing the α_pr. In “W”-shaped PRC, piles in center part of the raft are relatively lesser in length compared to those of other PRCs. In “W”-shaped PRC, maximum pile capacities have been mobilized (higher soil confinement because of the W shape arrangement) because of the shorter length of piles at the center part of the raft. Table 6 presents the load carried by piles in different PRCs at different pile spacings.

Normally, the raft foundation is designed for maximum bending moment and maximum shear force values. Thus in the present study, the maximum bending moment and maximum shear force values are taken into account. The effect of S_p on M_max for different PRCs and different soil profiles is presented in Figure 9. For any PRC with any soil profile, M_max is observed to increase with the increase in S_p. PRC with soft clay soil profile possesses lower M_max (Fig. 9a) as compared to stiff clay soil profile (Fig. 9b).

Figure 9

Also, for any PRC with any soil profile, M_max is observed to be lower for PRC with UDL as compared to the PRC with EPL. For example, at the 3-m pile spacing for soft clay soil profile, the M_max of PRC1(b) is 2,400 kN m, whereas for PRC2(b), it is 3,150 mm. For any load configuration and any soil profile, PRC(c) or “V”-shaped PRC was more effective in reducing the M_max.

The effect of S_p on τ_max for different PRCs and different soil profiles is presented in Figure 10. For any PRC with any soil profile, τ_max is observed to increase with the increase in S_p (except for PRC with S_p = 6 m and EPL). Because columns are located at 6-m spacing, the shear force decreases abruptly. PRC with soft clay soil profile possesses lower τ_max as compared to stiff clay soil profile (except S_p = 3 m). Also, for any PRC with any soil profile, τ_max is lower for PRC with UDL (except at S_p = 6 m) as compared to the PRC with EPL.

Figure 10

For any load configuration and any soil profile, PRC(c) or “V”-shaped PRC is more effective in reducing the τ_max. Therefore, for lower bending and shear force in piled raft, it is suggested to use longer length of piles at the center of raft and relatively smaller piles towards the edge of the raft. The comprehensive study on design and applications of piled raft foundations has been reported in the literature (Poulos 2001). The study showed that the maximum settlement of piled raft was marginally affected by uniform and concentrated loading, whereas the differential settlement and bending moment of raft were higher for concentrated loading (alike present study) and, the percentage loads carried by the piles were independent of the type of loading. The foundation design with minimum bending moment and minimum shear force may be more economical; therefore, in subsequent sections, PRC(c) or “V”-shaped PRC and more realistic loading LC2 or EPL has been selected and the effect of raft thickness is studied.

The behavior of piled raft is dependent on the flexibility or stiffness of the raft. In order to assess the flexibility/stiffness of the raft, raft-to-soil stiffness ratio (Viggiani 2001) has been used in the present study and is presented in Eqn. (4). (4)Krs=4×Er×(1−vs2)3×Es(1−vr2)×tr3Br3K_{{\rm{rs}}} = {{4 \times E_{\rm{r}} \times (1 - v_s^2 )} \over {3 \times E_{\rm{s}} (1 - v_r^2 )}} \times {{t_r^3 } \over {B_r^3 }} where E_r is the Young’s modulus of raft; v_s is the Poisson’s ratio of soil; E_s is the elastic modulus of soil, v_r is the Poisson’s ratio of raft; B_r is the width of the raft, and t_r is the thickness of raft.

Thus, it can be observed from Eqn. 4 that with the increases in raft thickness, raft-to-soil stiffness ratio also increases. Moreover, the K_rs = 0.001 indicates the perfectly flexible, K_rs value I the range of 0.001–1 indicates intermediate flexibility, and K_rs ≥ 1 indicates the perfectly stiff (Viggiani 2001). The calculated K_rs values for a raft thickness of 0.5, 1, 1.5, and 2 m are 0.0015, 0.0118, 0.0398, and 0.0943, respectively, for the present study. The raft with t_r = 0.5 m is comparatively more flexible than other raft thickness.

The effect of t_r on W_avg, and W_diff for PRC2(c) and different soil profiles has been presented in Figure 11a and 11b, respectively. It is interesting to note that, with the increase in t_r, W_avg also increases. The increase in W_avg is due to the increase in self weight of the raft as the t_r increases. The optimum design from static response of pile–raft interaction had been discussed and developed by Ghalesari et al. (2015). They also reported that the increase in raft thickness may increase the average settlement of piled rafts under uniform load.

Figure 11

Furthermore, as expected the increase in W_avg is observed to be substantial in case of soft clay soil profile (Fig. 11a). Usually, soft clay soils are susceptible for larger settlement because it possesses low undrained shear strength. For any soil profile, W_diff decreases as the t_r increases. With the increase in raft thickness, raft becomes stiffer, and because of this, W_diff also decreases. Moreover, the decrease is observed to be significant in soft clay soil profile at larger pile spacings of 6 and 7 m (Fig. 11b). For stiff soil, the increase in raft thickness has minimal effect (compared to soft clay soil profile) on differential settlement reduction, because the stiff soil is sufficiently strong so that thinner raft is also behaved as stiff raft (raft with lower thickness).

The combined effect of t_r and S_p on α_pr for PRC2(c) and different soil profiles is shown in Figure 12. It can be seen that with the increase in t_r from 0.5 to 1 m, α_pr increases significantly, and when the raft thickness exceeds beyond 1 m, the rate of increase in α_pr is observed to be minimal. For any t_r, α_pr is higher for the soft clay soil profile compared to that of stiff clay soil profile. Also, it can be noted that at S_p = 7 m, α_pr reaches the value equal to 1.

Figure 12

It indicates that the entire applied load has been carried by piles only. In the soft clay soil profile, raft–soil contact pressure is relatively lower than that of stiff clay soil profile. Thus, because of lower raft–soil contact pressure, the maximum capacities of piles are mobilized in soft clay soil profile.

The maximum bending moment and maximum shear force in raft are considerably affected by the raft thickness. Normally, raft of lower thickness is susceptible for larger differential settlement and substantial bending because of its flexibility, whereas comparatively thicker raft may be uneconomical because of the requirement of huge amount of concrete. Figure 13 shows the effect of t_r and S_p on M_max and τ_max for PRC2(c) and different soil profiles. For any soil profile, M_max increases as the t_r increases.

For any soil profile, M_max is lower at smaller t_r with S_p = 6 m and higher at greater t_r with S_p = 7 m (Fig. 13a). In comparison with M_max, τ_max decreases marginally as the t_r increases. It can also be observed that τ_max is lower for soft clay profile than that for stiff clay profile. This is due to the lower resistance offered by the soft clay soil profile as compared to the stiff clay soil profile. Thus, the raft thickness should be selected in such way that differential settlement should be within tolerable limit, and bending moment and shear force in the raft should be least so that the economical and efficient design of piled raft can be achieved.

Figure 13

In this section, the effect of pile spacing on the pile head settlement, pile axial load (Q_p), and maximum bending moment in piles (M_maxp) for center pile (P₁), edge pile (P₄₀), and corner pile (P₃₇) are presented and discussed. The effect of pile spacing on aforementioned behaviors of piles in soft clay soil profile has been considered in this section, and the results are presented. As expected, it can be seen from Figure 14 that center pile (P₁) settle more followed by edge pile (P₄₀) and then the corner pile (P₃₇), which settles lesser. Also, with the increases in S_p, the pile head settlement decreases significantly.

Figure 14

The effect of S_p on axial pile load Q_p for soft clay soil profile is shown in Figure 15(a). It can be seen that with the increase in S_p, the axial load carried by piles increases. Also it can be noted that the length of corner pile (P₃₇) is lesser compared to center pile (P₁); however, corner pile (P₃₇) carries maximum load followed by edge pile (P₄₀) and then center pile (P₁). The corner pile (P₃₇) bends because of lower confinement (relative to edge and center pile), and because of this, the axial load carried by corner pile is more than other piles (Fig. 15b). The effect of S_p on maximum bending moment of piles (M_maxp) is shown in Figure 16. Initially, with the increase in S_p from 3 to 4 m, M_maxp increases and then decreases as the S_p reaches to 4 m, thereafter M_maxp increases gradually. It can be seen that M_maxp is higher in corner pile (P₃₇) and lower in center pile (P₁).

Figure 15

Figure 16