Effects of excavation and construction sequence on behavior of existing pile groups

Figure 6 presents a 3D view of the finite-element mesh and boundary conditions employed in this analysis. The mesh width (x) was 24 m, and the mesh depth (z) was 45 m. The mesh length in the lateral direction (y) was 70 m in order to capture the influence zone of settlement trough nearby the excavation [29]. In addition, the boundaries were far enough away to prevent any restriction to the analysis. Mesh sensitivity analysis was carried out in order to determine a suitable mesh size. Fine mesh-size with a relative element size factor about (0.7) was chosen. Additionally, mesh becomes finer with a relative element size factor about (0.35) for the plates and embedded piles as large shear strain variations were expected. Moreover, the soil elements are relatively small near the excavation and gradually increase in size as they move away from it to maintain a logical balance between the results accuracy and computational cost. Based on a numerical parametric analysis, the mesh refinement degree was chosen by the criterion that the variation of computed pile group settlement was less than 10% if size of the current mesh was halved. Therefore, a good balance has been achieved between analyzing costs and accuracy. Vertical loads from the new building were applied as uniformly distributed axial loads on a 1.0 m thick concrete raft. The uniformly distributed axial load was applied on the raft and increased gradually from 50 kN/m² to 200 kN/m². Soil elements in the mesh were the 10-node tetrahedral elements. The tetrahedral soil elements provided a second-order interpolation of displacements. Moreover, the 10-node tetrahedral element can be crossed by the pile at any place. In addition, 6-node plate element was employed to model behavior of the pile cap, diaphragm wall, and raft of the new building in the excavated area. Moreover, soil-wall interaction was simulated using 12-node interface elements. The interface element consists of a pair of nodes to ensure that it is compatible with the 6-noded triangular side of plate element or soil element [26]. Three degrees of freedom (ux, uy, uz) are available for translation in each node in the interface element and differential displacements can occur. Struts were simulated in the analysis using fixed end anchor elements. The fixed end anchors were considered to be point elements in PLAXIS 3D. Embedded piles with 3-node line elements, which are available in PLAXIS 3D were employed to simulate the bored piles. The embedded piles interact with soil by means of special interface elements and behave like volume piles. To reduce effects of the undesirable mesh-dependent, specific volume around the embedded pile based on the pile diameter (elastic zone) is assumed in the analysis. Embedded pile model is capable of modeling the soil-pile interaction under lateral load and able to reproduce behavior of laterally loaded pile with rough shaft surface in numerical analysis [30]. Estimation of pile group behavior by employing the current embedded pile model was described by [31]. Moreover, validation and formulation of the embedded pile element can be found in [26, 32, 33]. These validation studies show a reasonable agreement with the calculations and field measurements for bored piles. The details about the elements and interface properties can be found in [26]. In total, mesh in Test G1 consisted of 33,727 nodes and 19,450 soil elements with average element size about 3.19 m. The model bottom boundary was fixed by pin supports in all directions, while roller supports restrained soil deformations in directions normal to vertical planes. However, the model top surface was free in all directions. Ground water level was initially at the ground surface, which developed a hydrostatic initial pore-water pressure profile. Free drainage was permitted on the mesh top boundary only. A multi-stage excavation with final depth of 15 m was modeled in the numerical analysis. During the excavation process, the water table inside the excavation pit was lowered to the excavation level with each stage. In this study, excavation was sufficiently slow that the flow field reached a steady-state situation in every excavation step. Moreover, the same steady state water pressure was developed on both passive and active sides below diaphragm wall. However, water pressure on the passive side was set to zero at the excavation level. This is a reasonable assumption for slow excavations in high permeable soils.

The hardening soil model with small-strain stiffness (HS Small), available in PLAXIS 3D, was used to simulate the nonlinear behavior of soil. The most important feature of this constitutive model is the difference between Young's modulus values under loading and unloading conditions. In addition, this soil model incorporates strain dependent stiffness modulus, simulating different soil reactions from small strains to large strains. Thus, the HS small model could significantly enhance the reliability of deep excavation analysis by providing more accurate displacements after each excavation stage[34, 35]. The soil parameters in Table 1 are derived from reference solution by [34, 36]. High quality experimental data are available for validation of berlin sand parameters. Comparing numerically simulated experimental data with real measured data allowed researchers to validate the soil parameters in the HS small model. Validation and verification of the Hs small model and soil parameters are available in [34]. In this study, the main interface parameter is the strength reduction factor (R_inter). The interface parameters can be obtained from the soil layer properties and the strength reduction factor by applying the following two equations:where c_i and ϕ_i are interface cohesion and friction angel, c_soil and ϕ_soil are effective cohesion and effective internal friction angel of the soil. An interface strength reduction factor (R_inter) of 0.95 gives a reasonable simulation of sand deformations [33].

Elevated pile group was chosen to avoid soil-cap interaction and contribution of the cap in load carrying capacity. The elevated pile group reflects the worst-case scenario encountered in engineering practice. The piles were rigidly connected to a 1.0 m thick pile cap, and the cap was subjected to initial uniformly distributed load. For comparison purpose, all tests had the same pile cap thickness to avoid contribution of the cap rigidity in this study. The concrete used for the pile groups, diaphragm wall, and raft had a unit weight of 25 kN/m³. For all model groups, pile diameter (d_p) was 0.7 m and the pile cap projected 0.35 m beyond the face of the piles. In addition, pile load test was numerically simulated for pile group configuration in Test G3, The ultimate load-carrying capacity of pile group (i.e., failure load) was established to be 8293 kN, based on the failure criterion proposed by [37] for large diameter bored piles. By taking a safety factor (FOS) as 2.5, the initial applied load on the pile cap of four pile groups before excavation is 3317 kN. In the same way, the initial applied load on the pile cap of two and six pile groups before excavation are 1659 kN and 4976 kN, respectively. These loads are considered to ensure that each individual pile in all groups has the same head load prior to the excavation so that results could be compared. A realistic elastic modulus of 30 GPa was used in simulation of concrete diaphragm wall, pile cap, and raft. The excavation was supported by a 1.0 m thick diaphragm wall and many struts. The diaphragm wall, cap, and raft material behaviors were assumed to be linear elastic with Poisson’s ratio of 0.2. Steel pipes, having a thickness of 2.5 cm, outer diameter of 60 cm, and axial rigidity of EA = 9.03 × 10⁶ kN were used as struts.

In the current study, bottom-up excavation method was adopted. Staged construction provides an accurate simulation of various loading, construction and excavation processes. Firstly, the finite element model was established with the initial stress and boundary conditions with the at-rest earth pressure coefficient of 0.43. The K_o procedure considered only self-weight of the soil so that vertical stresses were generated in equilibrium with this soil self-weight without external loads. The numerical modeling procedures are summarized for the purpose of this research as follows:

Test G1 was performed with two bored piles arranged in one row parallel to the diaphragm wall at 3 m away from the diaphragm wall. In Test G2, two piles were arranged in one line perpendicular to the diaphragm wall with front and rear piles at 3.0 and 5.1 m away from the diaphragm wall, respectively. In both tests, the pile length was 12 m and the center-to-center pile spacing was three times of the pile diameter (d_p = 0.7 m). Figure 7 shows settlement of the pile group with advancement of the excavation. To obtain generalized results, pile group settlement (Δ) and excavation depth (H_e) are normalized by the pile diameter (d_p) and pile length (L_p), respectively. The normalized pile group settlement is presented in percentage. The general trend of the settlement is consistent with findings of [24]. For simplicity, only the results after excavation depth reaches 4.5, 7.5, 10.5, 13.5, and 15 m are included in the figure. The piles and diaphragm wall were wished-in-place, which means that pile behavior was closed to bored pile and installation effects were ignored. This assumption is suitable for structural elements that cause a limited disturbance of the surrounding soil during installation. Displacement is set to zero before the excavation begins. Hence, settlement due to initial working loads and diaphragm wall installation are not included in the presented results to exclude deformations before excavation. The pile group settlement is measured at center of the pile cap with reference to its original elevation. In test G1, settlement of the two piles with advancement of the excavation are essentially identical because of the symmetrical pile configuration. In both tests, variations of pile group settlement with excavation depth are similar. Upon completion of the excavation, settlements of 2.90% and 3.06% (d_p) are induced in the pile group in tests G1 and G2, respectively. It is thus concluded that, increasing of excavation depth leads to increasing pile group settlement at a rising rate. This is because soil stiffness and normal stress acting on pile shaft are significantly reduced with advancement the excavation. Moreover, this settlement is induced to maintain vertical load equilibrium.

Figure 8 shows variation of pile group tilting for different excavation depth. Tilting is represented in percentage and calculated by dividing the differential settlement between two edges of the pile cap by the horizontal distance between them. Tilting toward the excavation is regarded as positive and tilting away from the excavation is regarded as negative. Pile group tilting is a consequence of the side effects of the adjacent excavation. In Test G1, advancement of excavation induces totally negative pile group tilting. Initially, rear pile experiences lower settlement than those of front pile till H_e/L_p = 0.8 and then the rear pile experiences higher settlement than those of the front pile in Test G2. Upon completion of the excavation, a tilting of 0.12% is induced in the pile group in both tests. For both tests, the pile group tilting ranges from 0.001 to 0.118%, which not exceeds the allowable tilting of existing building (0.2% by [38, 39]). However, tilting caused an increased moment due to the eccentricity of the weight of the building. In addition, some structures experienced architectural and functional problems due to this tilting.

The models were tested with a variety of new building loads in order to investigate their influence. Effects of loading sequence of new building on settlement and tilting of the two-pile groups are plotted in Figs. 9 and 10. During construction of the new building in the excavated area, soil moves down. Accordingly, additional pile group settlement is induced, which is due to new building loads. Settlement of the pile group before new building construction is less than that induced after the construction. Upon completion of the new building construction (i.e., P_{new building} = 200 kN/m²), settlement in the existing pile group in Test G1 is about 3.87% (d_p). However, the settlement in Test G1 is about 2.90% (d_p) after completing the excavation. In Test G2, the pile group settlement increases by 8% (i.e., from 3.06 to 3.29% d_p) after applying vertical load of 50 kN/m² on raft of the new building. The settlement in Test G2 increases by 21% (i.e., from 3.29 to 3.97% d_p) when the new load increases from 50 kN/m² to 200 kN/m². This increase is due to the increased vertical soil movements. It infers that safety of the existing piled structures is significantly affected by the construction of new building in the excavated area. With reference to Figs. 8 and 10, it is inferred that the provision of new building reduces tilting in the pile cap. A closer examination at green field settlement and mechanism of soil shear failure can explain this phenomenon. The term “greenfield settlement” refers to settlement with absence of adjacent piles and building. Before applying new building load, adjacent piled structures significantly tilted away from the excavation (negative tilting) to follow the greenfield settlement at location of the pile group. Applying load of the new building forces the piled structures to slightly tilt toward the excavation (positive tilting) due to vertical soil movements and mechanism of soil shear failure. This explains why the negative tilting of the pile cap is reduced with the advancement of new building construction. Effect of this construction plays a key role in the tilting in both tests. After completion of new building construction, the pile cap tilting is about 0.094%, which is about 80% of that induced after completing the excavation in Tests G1. In the same manner, the pile cap tilting is about 0.088% after completion of new building construction, which is about 75% of that induced after completing the excavation in Tests G2.

Three model Tests, G3,G4, and G5 were performed to give a better insight in the response of a 2 × 2 pile group with 12 m pile length subjected to initial working load and adjacent to an excavation. To confirm results with different pile spacing, the effect of center-to-center pile spacing in a capped head four-pile group has been evaluated by performing these three tests. The front pair of piles were located at 3 m away from the diaphragm wall. In Test G3, the center-to-center pile spacing was three times of the pile diameter (d_p = 0.7 m). However, tests G4 and G5 were carried out with the same pile configuration as Test G3 except that the center-to-center pile spacing was 3.15 m in Test G4 and 4.2 m in Test G5. The normalized pile group settlement is plotted against the normalized excavation depth in Fig. 11. During the excavation, settlement of the pile group is very similar in Tests G4 and G5. However, settlement of the pile group in Test G3 is a little high than that of Tests G4 and G5.

Tilting of the pile cap in Tests G3, G4, and G5 is depicted in Fig. 12. Initially, pile cap tilting is positive and increases with the increase in excavation depth. Further advancement of excavation induces negative pile cap tilting in the three tests. In addition, tilting of the pile cap in Test G4 is very close to that of Test G3. Thus, increasing the center-to-center pile spacing from 3 to 4.5 of the pile diameter (d_p = 0.7 m) is insignificant on the pile cap tilting. Obviously, the pile group centroid shifts farther away from the diaphragm wall in test G5. Hence, the pile cap tilting in Tests G3 and G4 are significantly larger than that in Test G5 upon completion of the excavation. Based on the computed results, the maximum pile cap tilting decreases from 0.1 to 0.09% and from 0.09 to 0.05% when center-to-center pile spacing increases from 2.1 to 3.15 m and from 3.15 to 4.2 m, respectively. Some previous studies like [17, 29] found that the induced settlement increases with excavation depth. A similar general trend of pile settlement and tilting during the excavation are also observed in the present study.

Figure 13 shows the influence of new building load on settlements of the four-pile groups. The pile group settlement is exacerbated due to construction of the new building. For example, the pile group settlement in Test G3 increases by 5% (i.e., from 3.44 to 3.62% d_p) due to applying a vertical load of 50 kN/m² on the new building raft. This settlement increases by 6% and 20% when the load increases from 50 to 100 kN/m² and from 50 to 200 kN/m², respectively.

Figure 14 shows the effect of increase of new building load on the pile cap tilting. The figure clearly shows that the magnitude of pile cap tilting decreases with increasing new building load. The increase in the new building load to 100 kN/m² causes a decrease of pile cap tilting by 6% for Test G3, 8% for Test G4, and 12% Test G5 of that induced due to applying load of 50 kN/m². A further increase in the load to 200 kN/m² results in a decrease in tilting ranging from 15 to 33% of that induced after applying 100 kN/m².

Tests G6 and G7 were carried out with six piles in order to further examine the group effect by using a relatively great number of piles. Test G6 was performed with 2 × 3 capped piles (piles arranged in 2 rows parallel to the diaphragm wall), whereas test G7 was performed with 3 × 2 capped piles (piles arranged in 3 rows parallel to the diaphragm wall), See Figs. 4 and 5. The pile length was 12 m in both tests. In these two tests, front piles were located at 3.0 m away from the diaphragm wall and the center-to-center pile spacing was three times of the pile diameter (d_p = 0.7 m). Figure 15 illustrates settlement of the pile groups with advancement of the excavation in both tests. Generally speaking, Tests G6 and G7 have the same settlement of pile group at the start and the end of excavation, while a minor difference in the settlement is observed at 7.5, 10.5, and 13.5 m excavation depth. After completing the excavation works in both tests, the pile group settlements in Tests G6 and G7 are 3.68% (d_p) and 3.67% (d_p), respectively.

Figure 16 shows variations of pile cap tilting in Tests G6 and G7 for different excavation depth. These variations are similar in shape as clearly seen in the figure. As the excavation depth reaches 10.5 m the (i.e., H_e/L_p = 0.88), pile cap tilts away from the excavation and tilting is reversed in Test G7. Tilting becomes clearly noticeable upon completion of the excavation in both tests. The calculated pile cap tilting is about 0.11% and 0.10% in Tests G6 and G7, respectively.

The induced pile group settlements during construction of the new building are presented in Fig. 17. As expected, construction of the new building induces additional settlement in the existing pile groups. The pile group settlement increases as new building load goes up. This increase is due to larger vertical soil movements. Upon completion of new building construction (i.e., P_{new building} = 200 kN/m²), settlement in the existing pile groups in Tests G6 and G7 are about 4.64% (d_p) and 4.56% (d_p), respectively.

Figure 18 represents the pile cap tilting at different new building loads. Obviously, pile cap tilting is reduced because of the increase in load of new building in both tests. In test G7, the pile cap tilting decreases from 0.090 to 0.085% when the new building load increases from 50 to 100 kN/m². In the same way, the tilting decreases from 0.085 to 0.072% when the load increases from 100 to 200 kN/m², as shown in Fig. 18.

After all, it is apparent that maximum settlement of the pile group appears at the end of new building construction. However, maximum pile cap tilting appears at end of the excavation. Moreover, similar trend of the pile responses are also observed in all tests. The pile group settlement increases almost linearly with increasing load of the new building in all tests. In addition, tilting of the pile cap continuously decreases with increasing the new building load. Based on the simulated results except test G1, initially tilting is positive and further advancement of excavation induces negative pile cap tilting. This observation may be attributed to the interaction between rear and front piles in Tests from G2 to G7. Moreover, this tilting trend can be illustrated by closer look at the greenfield ground surface settlement (concave type settlement). Maximum surface settlement takes place at a distance away from the diaphragm wall in the concave type settlement. If the pile group is situated between the diaphragm wall and position of the maximum ground surface settlement, pile group is tilted away from the excavation (negative tilting) and rear piles experience higher soil movements. On the contrary, the presence of the pile group at larger distance from the wall provides pile cap tilting toward the excavation (positive tilting). For comparison purpose, pile group settlement and tilting at the end of excavation are plotted for different groups in Figs. 19 and 20, respectively. During the excavation works, magnitude of pile group settlement of the two piles is lower than that of the four and six piles. Loses in pile shaft resistance increases by increasing number of piles in a group during the adjacent excavation. So the magnitude of pile group settlement at end of the excavation can be reduced by decreasing number of capped piles due to increasing group effects. It can be noticed that, settlement of the pile group in Tests G6 and G7 is slightly higher than that in test G3. Thus, much larger soil deformations is induced by excavating adjacent to six-pile group. Front piles reduce the effects of excavation on the rear piles in Tests from G2 to G7. The maximum magnitudes of pile cap tilting is 0.118%, which is obtained after completing the excavation in Test G2. In test G6, tilting of the pile cap is slightly higher than that in test G3. It seems fair to suggest that low values of pile cap tilting can be obtained in the case of four piles with large center-to-center pile spacing as test G5.

Finally, a Comparison of pile group settlements after construction of the new building is presented in Fig. 21. To produce plastic equilibrium, vertical downward movement of the raft is observed after applying the load in the excavated area. Thus, the settlement of pile group increases when the magnitude of new building applied load increases. Tilting of the pile cap at end of the new building construction in all tests is shown in Fig. 22. The pile cap tilting in test G1 is greater than that in the other tests upon completion of the new building construction. It is indicated that, finishing construction of the new building (i.e., P_{new building} = 200 kN/m²) results in a decrease in pile cap tilting ranging from 20 to 40% of that induced before the construction, as shown in Figs. 20 and 22.