Figure 3 shows the load-displacement curves obtained for the CC3 and CF3 tests. Considering the displacement failure criteria (10% of pile diameter, i.e. 25 mm), the foundation ultimate capacity (Qult) of the systems CC3 and CF3 were defined as 188 and 122 kN, respectively, which corresponds to a reduction of approximately 35% in the load capacity of the defective system.
The results in Fig. 3 also show good agreement between experimental and numerical curves. The back-analyzed parameters used to adjust the numerical prediction were able to capture both foundation stiffness and geotechnical failure. The software graphical output (Fig. 4) shows the formation of passive lateral earth pressure wedges (along soil’s surface) for both leading and trailing piles in the final steps, close to the overall soil failure.
The horizontal displacement contour map in Fig. 4 shows that the leading pile sustained most of the mobilized horizontal reaction. The plot also shows the importance of a reliable characterization of the soil upper layers, since the horizontal displacements were confined to a soil depth equal to 5–6 times the pile diameter. Both aspects are in accordance with the findings of Reese and Van Impe (2001). A gaping zone in the back part of the trailing piles is also noticed, indicating the actual separation that takes place between the soil-pile interfaces as the system approaches geotechnical failure.
Once the model was calibrated, it was possible to estimate output system variables that could not be measured during the experimental program. Hence, the numerical predictions of the pressure mobilized at each pile’s base, the raft tilting, the raft-soil contact normal forces, and the unit horizontal subgrade force at the borehole’s surface.
3.1 Mobilized pressure at the pile base, raft tilting, and raft-soil contact normal forces
The results of the numerically computed pressure at each pile base (Pi) were normalized in relation to maximum unit bearing pressure at the tip of the respective pile (Pimax). The results are shown in Fig. 5, for increasing values of the applied horizontal load (Qh), from 20–100% of the horizontal failure load (Qult). The Qult value applied to the normalized Qh was the one obtained from the defective system (CF3), in which Qult = 122 kN.
Figure 5 shows that despite the presence of a damaged zone, the defective pile continued to absorb and transmit a percentage of vertical load to its base. The results show a migration of vertical load from the trailing piles (piles 2 and 3) to the leading one (pile 1) when the system is defective, due to its tilting. This phenomenon is very contrasting when compared to the intact case system, which indicated a different distribution of loads between leading and trailing piles, establishing a more homogeneous distribution than the defective system.
For both CC3 and CF3 systems, the Pimax values of the leading pile (P1max) were around 10 to 16 times the values for the piles 2 and 3 (P2max and P3max – the trailing ones); the latter, in turn, presented very similar values between them, even in the defective system.
To understand the reason of the load spread that occurred by the presence of the defective pile, the raft’s tilting at each loading stage has to be assessed. Figure 6a shows the numerically derived tilt angle (ψ), normalized to its maximum value (ψmax), developed at the system’s ultimate load stage. The results show a relation between tilting and load migration to the leading pile tip in both defective and intact systems. Indeed, the increase in foundation tilting when the CF3 system is submitted to a horizontal loading between 40% and 80% of Qult, explains the load migration from trailing piles to the leading one (Pile 1) – as depicted in Fig. 5.
It shall be noticed that the relative tilting was much greater for the defective system than for the intact one, which was already expected given the influence of the defective trailing pile. This greater tilting was responsible for almost zeroing the unit bearing pressure for trailing pile 3 in the defective system (Fig. 5). On the other hand, in the intact system, this same pile still carried vertical load until the latest loading level.
Figure 6b shows the raft-soil normal force (qrs i), acting in two opposite nodes at the raft soil interface (points T and L in Fig. 6b). The results are normalized in relation to its maximum value (qrs max), which was measured in point L of the intact system (CC3). The results show that the presence of the defective pile caused a large decrease in the contact normal forces acting in the leading pile region (CF3 – Point L), to approximately 40% of the value computed in the intact system. This aspect will reduce the contribution of the raft-soil interface to absorb horizontal loadings.
Another interesting aspect shown in Fig. 6b is the decrease of the qrs value acting at the point T (CC3 system), which occurs until approaching null values, at 60% of Qult. In the defective system, the same point showed negligible values of qrs during all stages of the horizontal loading. This behavior corroborates with a high tilt verified to the CF3 system (Fig. 6a), and shows the large impact that the defective pile can cause on the effectiveness of the use of the raft-soil interface to absorb horizontal loads – hence the design as a piled raft.
3.2 Unit Horizontal Subgrade Force at Borehole’s Surface
The pile’s shaft-soil interaction was analyzed using the unit horizontal subgrade (reaction) forces acting on both front and back surface positions of the borehole, at several depths of interest along with the pile’s depth. The unit horizontal subgrade force (qiwl) was normalized by its respective maximum value (qiwl max) developed throughout the analyzed loading stage.
Figure 7 shows the normalized horizontal subgrade forces for pile 1 (Fig. 7a), 2 (Fig. 7b), and 3 (Fig. 7c). The results were solely computed to the allowable displacement level (working condition), i.e., the horizontal load corresponding to a horizontal displacement level equal to 5% of the pile diameter (design assumption). In the plot, positive signs indicate compression forces in the same direction as the horizontal loading onto the raft, whereas a negative sign means compression forces acting in the opposite direction. In both cases, the unit subgrade reactions at both borehole’s front and back surface positions are originated from the passive earth pressure caused by the interaction between the piles and the surrounding soil.
The results show that the reaction subgrade forces tend to be higher at the front surface position for the first 2 m (8 times the pile diameter). From this depth onwards the subgrade reaction forces are greater at the back surface position, independently of the pile type (leading or trailing) and condition (intact or defective). Figure 7 also shows that depending on the pile type and on the analyzed pile depth, there was a tendency of increasing or decreasing the subgrade force when comparing the intact to the defective system case. For instance, pile 1 (leading) front surface position increased the (average) subgrade force in the pile’s top region (0 to 3 m) for the defective case, when compared to similar results in the intact case.
A reverse phenomenon (decrease) was noticed for a similar comparison in the case of the trailing pile 3 in the CF3 system. Again, this was related to the migration of load and new equilibrium stage that was accomplished by the simultaneous tilting of the raft (intact system) and tilting plus defective pile influence (defective system).
Similar to the unit base pressure, the defective trailing pile 2 continued to generate horizontal subgrade reaction forces on the surrounding borehole surface at working displacement level. Nevertheless, the effectiveness of this pile has decreased, as it generated a lower average subgrade force when compared to the same pile at the intact system condition. On the other hand, the horizontal subgrade forces distribution generated by the trailing pile 3 (intact) has not considerably change from the defective to the intact case.
At the back surface position, for both intact and defective systems, the horizontal subgrade force has zeroed for leading pile 1 and trailing pile 3, indicating the formation of a gap (as shown in Fig. 4), with total loss of contact between the pile’s shaft and the borehole’s surface.