Numerical study on stress paths in grounds reinforced with long and short CFG piles during adjacent rigid retaining wall movement

The commercial FE software ABAQUS was chosen to develop the finite element model. The model comprised structural (pile, raft and wall) and geotechnical (soil and cushion) parts that were modelled as elastic and elastic ideal plastic Mohr–Coulomb constitutive model, respectively. Even though Mohr–Coulomb model is not a state-of-the-art constitutive relation, it has widely been employed in FE analysis to describe the engineering characteristics of geotechnical materials while investigating the behaviour of composite piled raft foundations^{[6,10,43,44,45]} and performance of deep foundation pit excavations and/or their influence on the surrounding infrastructures.^[26,46,47] Figure 1 depicts the typical meshed geometry employed in the model. The retaining wall in each case was 10-m deep, whereas to avoid boundary effects, the homogeneously treated soil medium was made to be at least as five times wide as the breadth Br of the raft in the lateral extent and as deep as more than thrice the length of long pile vertically.

Figure 1

Considering computational expensiveness without compromising accuracy, the mesh density in the neighbourhood of structural members was made finer than that for other locations, with a gradual change to coarser mesh sizes. Each mesh part was discretised using an eight-node linear brick element with reduced integration and hourglass control (C3D8R). As the size of the model parts for the cushion, raft and soil increased as the number of piles in the composite foundation was increased, their corresponding mesh discretisation yielded different number of nodes. As a consequence, increasing the number of piles, say from 9 to 25, increased the number of nodes in the model assembly from 98,526 to 155,733. The surrounding vertical boundaries were modelled to restrain lateral displacements, while the bottom was set to constrain both horizontal and vertical displacements. The top surface boundary was set to be free in each direction. The boundary condition at the base of the wall was defined by a pin support to allow only rotation about its base, while its side, the boundary which was in direct contact with the retained soil mass behind the wall, was defined by establishing a contact surface algorithm characterised by the general surface-to-surface contact formulation. The analysis was initiated by generating K₀ geostatic stress field within the soil that produced very small deformation but in equilibrium stress field with gravity loading. This initial condition was followed by introducing sequentially the piles, cushion layer and raft by establishing surface-to-surface contacts along the interacting interfaces. The face of stiffer contacting part was set as master surface contact candidate, while a slave surface described the other contacting body’s surface. Penalty friction formulation was enforced for both tangential and normal behaviours, assuming 0.005 m limiting displacement for the elastic slip to develop full contact friction, as suggested by Miao et al.^[48] to overcome overestimation of pile bending moment.

The FE model employed in this study was compared with the results from an indoor experiment conducted using a model box of 1.6 m × 1.6 m × 2.5 m inner dimension, which was sufficient to ignore boundary effects. The apparatus was designed and developed by the Research Institute of Geotechnical Engineering at Zhengzhou University. The model test setup is shown schematically in Figure 2 and was composed of stationary side walls braced with square section RHS fame, movable front wall equipped with bottom roller and slideway, and dismountable 10 split-steel plates connected to the frame with high-strength bolts forming the rear wall. Displacement control screw rods were symmetrically located at the top, middle and lower levels of the right and left edges of the front wall to permit rotation/translation in a way similar to that used by other researchers such as Yang et al.^[49] Rectangular RHS steel reaction frame was positioned beside sidewalls.

Figure 2

The test was conducted on 2 × 2 (two long–two short) pile composite foundation. Instrumented hollow aluminium close-ended tubes of length 2100 and 1000 mm were used as long and short piles, respectively, considering the length similarity ratio (λ_L) of 3 to account for scale effect. The pile’s Young’s modulus was 72 GPa and was not emulated for scaling. The outer diameter and thickness of each pile were 100 and 3 mm, respectively. The roughness of pile shaft surface was established with knurling treatment and effectuated an interface angle of friction 27.3°. The spacing of the piles in model and prototype was three times the pile diameter, so that the area replacement ratio remained 0.087.

A plain carbon structural steel plate (quality Q235B) of dimension 600 mm × 600 mm × 50 mm was used as a rigid raft according to the stiffness requirement suggested by Horikoshi and Randolph.^[50] Fine dry river sand of Zhengzhou city, China and standard sand with the grain size distribution presented in Figure 3 were used as a foundation soil and cushion layer, respectively, according to the test requirement in the Chinese specification (GB/T 50783-2012). The scale effect of particle size on ultimate skin friction was also cross checked, so that the ratio of pile diameter (d) to the average particle size of the soil (D50) was at least 30–50 according to Fioravante’s^[51] suggestion. The maximum and minimum dry densities of the analogous fine sand were 1.795 and 1.592 g/cm³, respectively. The cushion layer had a thickness of 50 mm. The bearing layer was prepared by pouring and tamping technique with the sand being freely dropped from the height of the model box by a conveyor belt. Once the fill was made to the level of the prescribed pile toe, the pile was positioned vertically and the next layer was continued to the final surface. After the final sand surface was levelled, soil pressure cells were placed at the specified locations before laying the cushion layer. The cushion layer was placed after the bounding steel frame was laid. Then, the loading plate was stationed on top of the cushion.

Figure 3

The vertical working load was applied using a hydraulic jack pressed against the top beam of the reaction frame, and a load cell was mounted between the jack and the beam. The model ground had then been rested for more than a week before the loading process was begun, in order to balance the stress state of the soil. The loading application was performed according to the Chinese technical specifications for building foundation inspection (JGJ340-2015), technical code for testing of building foundation piles (JGJ106-2014) and technical code for ground treatment of buildings (JGJ 79-2012).

The settlement of raft surface during the loading process was obtained from the reading taken by YHD series electronic strain-type displacement sensors. All the strain gauges attached to the pile body, displacement transducers and pressure sensors placed at the top soil surface between piles and on the head and tip of pile were connected to static digital data acquisition system to collect real-time data. Each earth pressure-measuring cell and load sensor was verified for repeatability through indoor calibration preceding the experiment to correct calibration coefficients and stress hysteresis effect.

Based on existing research works conducted with the same model box,^[13,14] the rotation of wall about the base required to attain active limit state resulted in the top of the wall to displace laterally an amount of ∆ = 10–15 mm (0.47%–0.75% of the wall height). Accordingly, this study used 10-mm horizontal movement of the wall top away from the foundation in 11 stages, with 0.5 mm at the beginning and 1.0 mm each for the remaining. Consequently, the displacement of the screw rods on the top was controlled manually to obtain 0.5 or 1.0 mm at each stage, according to the calibration of screw rode rotation to yield the same. After the data of each stage were stable, the next rotation was carried out. Since settlement occurred as wall rotation advanced, for this very reason, the applied load on the foundation was manually sustained to maintain the hydraulic jack pressure unchanged throughout the process.

In order to compare experimental and numerical results with each other, the FEA was performed on the same geometric configuration, but with the depth of the sand being twice the long piles’ length. Table 1 summarises the material parameters used to back analyse the experiment, while Figure 4 presents the load settlement before wall rotation and the load-sharing characteristics during wall rotation. It can be seen that the prediction from the numerical simulation was in agreement with the results from the experiment in terms of magnitude and trend. Thus, the behaviour of long–short pile composite foundation can reasonably be predicted following similar numerical simulation procedure for succeeding analyses.

Figure 4

The changes in the state of stress during the process of wall movement were examined with the mobilised stress path of the soil elements at different selected monitoring points. As depicted in Figure 5, the stress path for each observation point travelled downwards towards the K_f-line (except for point B), indicating a reduction in both lateral and vertical stresses during the subsequent wall movement. It is well known from the basic soil mechanics that with increase in the depth, the vertical stress of the soil mass increases. Subsequently, the stress state on the p–q plane for the soil element at the observation point A was much lower than that of the soil element at point B. The same was true for the upper soil elements C and E, as compared to their respective bottom points D and F.

Figure 5

The behaviour of the stress path for point B in this analysis was seen to be different from others, which might have occurred as a result of the reaction stresses developing at the base of the wall. Accordingly, during advancement of the wall movement, a pattern of mean isotropic stress increment and decrease in deviatoric stress was seen until the completion of wall rotation.

When the stress change in observation point E was compared to that of C, its stress state underwent a complex path in the earlier stages of wall rotation. It increased first, but reverted back to follow almost the same trend with that of observation point C after a certain rotation in the later stages of wall rotation. The reason for this behaviour could be the shadowing and reinforcing effect of the front pile, so as in the earlier stage of wall rotation, the incidence of gap formation between the cushion and soil due to the wall movement reduced the stress borne by soil element C and the corresponding stress was transferred to the neighbouring stiffer material. This increased the stress received by the soil between piles. As the wall progression continued, the soil element E underwent a stress relief and followed the stress path trace of point C.

Generally, it is difficult to totally avoid excavation-induced soil displacements in which the soil elements migrate towards the pit along with the inward retaining wall movement. Such a phenomenon generates a change in the stress state in conjunction with principal stress axes’ rotation.^[39,40,53] As the wall movement in the current study altered the initial stress state of the soil, variations of the stresses during the process brought changes not only in the magnitude, but also in the direction of the principal stresses. Figure 6 presents the stress change evolution schematically on a 3D stress space of principal axes σ₁, σ₂ and σ₃. The observation stress point C was taken for a soil element adjacent to the composite foundation at a distance 3 m behind the wall. It is obvious from the stress path illustration that from the kick-off to completion of wall movement, the soil element underwent stress unloading owing to a drop in the percentage of vertical load sharing of the soil and reduction of lateral confinement as a result of wall movement-induced stress relief. This stress reduction occurrence was also associated with changes in the direction of the principal stresses, as can be seen from the projection on the σ₂–σ₃ plane. An excerpt on the stress state in terms of principal stress magnitude and orientation for the same soil element is given in Figure 7.

Figure 6

Figure 7

The 3D principal stress directions can easily be obtained using programs such as MATLAB without doing algebra to calculate the eigenvectors. It is to be reminded that during PSRs, direction changes alone can produce plastic deformations. So as to have safer designs, deformations associated with PSR should not be neglected, apart from change in principal stress magnitude.^[54] Accordingly, a constitutive relationship that could possibly capture the plastic deformations to a better accuracy is sought for a higher fidelity, which mostly exists as sophisticated and overly complex advanced models, rendering practical difficulty for model parameter characterisation. Nonetheless, previous studies have shown that irrespective of the type of model employed, fairly accurate excavation-engendered stress change behaviour can be obtained.^[38,40,46]

Figure 8 shows the effect of distance from the wall on the change of stress experienced by the soil element C. As can be seen from the illustration, the influence of wall rotation on relocation of the stress and interplay between the soil and pile becomes less significant, but is still accompanied by similar trend on the p–q plane as the distance from the wall is increased. That is, if the CFG composite foundation is located closer to the wall, the foundation soil element just near the top of the first raw of piles experiences a stress path in which q decreases due to confining stress relief and p reduces owing to the bearing capacity drop in the upper ground because of wall rotation-induced soil settlement. In the case of composite ground situated relatively far away from the wall, the monitoring point experiences a stress path with little disturbance from the lateral unloading and settlement effect of an adjacent retaining wall rotation.

Figure 8

Observation on the change of load-sharing proportion of the soil (e.g., see Figure 4b) during the process of wall movement indicated that the percentage in bearing capacity of the soil between piles for the composite foundation situated at 3 m distance away from the wall reduced from 67.03% to 59.52%, while the reduction for those placed at 5, 7.5 and 10 m was from 65.23% to 60.45%, 65.47% to 62.63% and 65.74% to 63.53%, respectively. As the distance from the wall is increased, the effect of wall movement disturbance on the load-sharing proportion of the reinforced ground gradually diminishes. As the main intention of composite foundation is to bring the soil between piles to participate in sharing a certain amount of the applied foundation load, the influence of wall movement-induced disturbance should be carefully analysed to maintain the integrity and stability of existing on service CFG pile composite foundation located in close proximity to the wall.

Figure 9 shows a comparison of the change of stress states in a soil element C for the composite foundations with different number of piles throughout the whole model simulation process. As it is well understood from the vertical load-carrying characteristics of CFG pile composite foundation, the percentage vertical load borne by the soil between piles decreases as the number of piles increases.^[43,55,56] In line with this, the stress invariants for the monitoring element in the composite foundation with 25 piles were smaller than that of the group with nine piles. Accordingly, as shown in Figure 9, the mean isotropic state of stress for the stress element C on the p–q plane for the group with nine piles was higher for the applied working load. At a first glance, it is noticeable that the stress invariants decrease in both cases with identical stress paths directed downwards during the progression of the wall, but the state of stress at the end of wall movement for the smaller pile groups is much smaller.

Figure 9

Nevertheless, commensurate with dependency of pile responses on the position in the group and the shaft load it transfers to the surrounding soil, the change in stress state for soil elements at C and E at the outer and middle elements, respectively, during the advancement of wall rotation differs. Figure 10 gives a comparison of the change of stress in a soil element at the middle section of the composite foundation with different number of piles. It obviously shows that the state of stress at the beginning of the wall rotation is somehow disturbed, but manifests itself differently in each case.

Figure 10

For the group with nine piles, the stress reduction in the beginning stage of wall movement reverted back to increase as the wall movement proceeded to an amount of 25 × 10⁻⁴ rad, in order to adjust the effect of soil movement. However, as the wall movement proceeded further, the slip surface continued to enclose the stress point, which led to subsequent unloading. On the contrary, due to shadowing and reinforcing effect as well as depending on how far the location of the stress point under consideration was away from the wall, the stress state of the observation point kept increasing throughout the process. The rate of increase in mean isotropic stress and the deviatoric stress increased as the wall movement increased. Even though the upper load received by the soil decreased, the lateral stress of the soil increased as the load being transferred to the front piles redistributed to the inner piles and was further distributed to the surrounding soil. This feature can also be observed from the variation of the pile head load depicted in Figure 11.

Figure 11

It is also worthy to note from Figure 11 that before commencing wall rotation, the corner pile had carried the highest pile head load compared to the central (or inner) pile(s), akin to other previous studies.^[10,45,57] As the wall movement advanced, the change in the pile head load depended on the particular position of piles in the group. In other words, the pile–soil interaction and load-carrying mechanism of internal (central), lateral (edge) and corner piles were influenced by the overlap zones of shearing resistance; this mechanical behaviour has also garnered the attention to use dissimilar piles for practical purposes of reducing differential settlement in connected pile rafts. ^[58,59,60] In the composite foundation with 25 long and short piles, the percentage of load sharing of the soil dropped from 56.54% to 53.16%, indicating that the bearing capacity loss of the soil is attributable to wall rotation, which is transmitted proportionally to the piles.

It is well known in soil mechanics that proper description of the settlement and volume change characteristics of a soil under a certain stress condition depends on the capability to portray the soil’s non-linear behaviour and stiffness decay in low strain range. It is also common to capture the distortion component of the soil compressibility (settlement) using Hooke’s law employing the tangent modulus.^[61] Accordingly, many scholars used the compression modulus of the soil to estimate the settlement and deformation behaviour of CFG pile composite ground.^[62,63,64]

On the other hand, the soil displacement field during excavation is influenced by the stiffness of the retained soil.^[65] Both vertical deformation and lateral deformation of the natural ground are affected by the stiffness of the soil, which in turn depends on the stress level. Consequently, the necessity of considering the unloading strength of soil in excavation-induced deformation analysis is frequently discussed by scholars and the proposal to employ it during analysis is highly encouraged due to the fact that failure could occur under small strain as the retaining wall deflects.^[39,66] To better understand the initial stress condition change for various stiffness during such unloading instances arising from engineering operations, the stress path followed under different elastic modulus of the analogous soil was compared for the monitoring point C, as depicted in Figure 12.

Figure 12

It is evident from Figure 12 that the smaller the elastic modulus of the soil, the smaller are the stress invariants, as the piles share much of the applied pressure. This encourages the soil to share smaller proportion of the imposed load which gets little disturbance. Whereas for the piles embedded in a soil of higher stiffness, the upper soil proportionally bears higher load and the disturbance from the wall movement relatively affects the stress state of the soil largely during the progression of the wall movement. This is because of the reduction of the soil stress received beneath the cushion due to the soil displacement occurring as the wall movement proceeds.

Several researchers have discussed about the effect of cover ratio on the settlement and load-sharing characteristic of composite pile foundation under vertical loading in which the area replacement ratio was varied by either changing the pile diameter (or its head)^[45,56,67] or by provision of pile cap.^[68,69] The analyses in the current study reveal that keeping the intensity of the imposed raft load the same, but allowing the cover area ratio of the piles to increase by reducing the spacing of pile makes the stress path in a group with nine piles to follow a similar trend to what is portrayed in Figure 5, but with lower soil stress at smaller pile spacing. This feature is not reproduced and depicted here again to avoid redundancy and for space brevity. The behaviour of smaller percentage of load shared by the soil as the clearance between the piles decreases is a well-known mechanical behaviour of CFG pile composite foundation. Provoking wall rotation only decreases the stress invariants, keeping the trend almost similar, in an attempt to equilibrate the soil stress release from imposed soil movement. The relative higher stiffness of the piles with respect to the soil dictates more load to be drawn to the piles as the elastic modulus of the soil decreases. The result of the analysis showed that for the replacement ratios of 3.14, 4.91 and 8.73%, the overall upper soil load-bearing proportion lowered from 45.25% to 37.17%, 55.32% to 47.83% and 67.02% to 59.52%, respectively, due to the effect of wall movement. Similarly, when the working load was changed while the pile area cover ratio was kept constant, the trend of the stress path experienced by the soil elements under consideration followed almost similar trace as that of Figure 5, but with a higher state of stress due to increases in stress invariants. The pattern is also not repeated here to avoid redundancy of similar behaviours. However, it is worth noting that with increased working load, the load carried by the pile increases and the percentage proportion shared by the soil decreases.

When it comes to monitoring the points taken underneath the tip of the pile, the stress path ascends with wall movement progression unlike those stress points in the upper part close to the shaft. This is demonstrated in Figure 13. As each pile carries different amount of vertical load depending on the location of the pile in the group (refer also Figure 11), they transmit different amounts of stress to their surrounding soil layer. It can be observed that the amount of stress increase appearing on the stress state for the soil element underneath the piles in the first and second pile raw differed depending on the length of the piles. It was larger below the long pile in the second raw as compared to that felt by the soil element beneath the long pile in the first raw, but was vice versa for the soil elements below short piles.

Figure 13

The load deformation characteristics can also be articulated in terms of change in volumetric strain ε_v expressed against the corresponding deviatoric stress tensor √J₂ on soil specimens tested under different stress paths.

Figure 14 portrays the shear stress √J₂ – volumetric strain ε_v variations as the wall movement proceeded for soil elements surrounding the upper pile section and below the pile tip of the composite foundation located at 3 m away from the wall. It indicates that the volume change behaviour within the treated ground depends on the location of the soil element under consideration. The demonstration suggests that the state of stress at each wall rotation stage impacts the deformation pattern of the soil. Intuitively, it could be anticipated to find larger stain in the X-axis (direction normal to the wall) near the top section. So is the strains increment in the other directions, but not as large as the strain in the X-axis. The combined effect of these strains determines the dilation behaviour of the soil upon loading and unloading; in fact, reasonably accurate real behaviour could judiciously be found implementing sophisticated constitutive models that are capable of reflecting the non-linear soil responses. The stress relief and redistribution among the piles are more pronounced within the influence range around the wall.

Figure 14