The Responses of an End-Bearing Pile to Adjacent Multipropped Excavation: 3D Numerical Modelling

It is well recognised that superstructure load is transferred to surrounding soil through piled foundation. Consequently, the high stress regime (stress bulb) is generated surrounding of the pile. On the other hand, the excavation in the ground inevitably results in the ground movement due to induced-stress release. These excavations are sometimes inevitable to be constructed adjacent to existing piled foundations. This condition leads to a big challenge for engineers to assess and protect the integrity of piled foundation. This research presents three-dimensional coupled consolidation analyses (using clay hypoplastic constitutive model which takes account of small-strain stiffness) to investigate the responses of an end-bearing pile due to adjacent excavation at different depths in soft clay. The effects of excavation depths (i.e., formation level) relative to pile were investigated by simulating the excavation near the pile shaft (i.e., case S) and next to (case T). It was revealed that the maximum induced bending moment in the pile after completion of excavation in all the cases is much less than the pile bending moment capacity (i.e. 800 kNm). Comparing the induced deflection of the end-bearing pile in the case T, the pile deflection in case S is higher. Moreover the piles in cases of S and T were subjected to significant dragload due to negative skin friction.


Introduction
It is well recognised that a pile foundation transfers the load of superstructure to surrounding soil which is adjacent to pile shaft as well as underneath the piled foundation. Consequently, the high stress regime (stress bulb) is generated surrounding of the pile [1]. On the other hand, the excavation in the ground inevitably results in the ground movement due to induced-stress release [2]. To cope with transportation problems in congested cities in the world like Hong Kong, Shanghai, London etc, underground transportation systems (involving tunnels for metros, excavations of metro stations and basement to facilitate inhabitants in the buildings for parking) have been developed. These excavations are sometimes inevitable to be constructed adjacent to existing piled foundations. This condition leads to a big challenge for a geotechnical engineer to assess and protect the integrity of piled foundation.
Finno et al. [1] and Goh et al. [2] reported case studies in granular soil and Alluvium residual soil respectively. They demonstrated that lateral soil movements due to excavation can be detrimental to adjacent piles. In both the reported case studies, piles toe level was much deeper than the excavation level and they reported only the lateral behaviour of piles. Apart from field monitoring, a number of centrifuge tests were also conducted to investigate the response of single pile (Ong et al. [23]) and pile group in soft Kaolin clay (Ong et al. [24]). They concluded that the induced bending moment and lateral deflection of piles were highly influenced by distance from wall and pile head condition. In studies, lateral response of end bearing piles without initial applied load was reported. In reality, piled foundation in soft clay behave as floating pile group and subjected to initial applied load from superstructure. In the presence of initial applied load, soil surrounding the pile foundation experience higher stress level before the commencement of adjacent excavation. Leung et al. [10][11][12] conducted centrifuge tests to investigate the effects of an un-propped excavation on the behaviours of nearby single piles and pile groups in dry dense Toyoura sand. It was found that the distance from the pile to the retaining wall and pile head conditions had a large influence on the induced pile bending moment and lateral deflection. Ng et al. [21] reported the results of three centrifuge tests which were carried out to study the effects of a multi-propped deep excavation in-flight on the behaviour of single piles in dry Toyoura sand. Piles were laterally restrained in terms of rotation and deflection right at or above ground surface in the three different tests. It was concluded that lateral restraints imposed on the pile head have a significant influence on induced pile bending moment. Induced bending moment due to excavation can exceed the pile bending capacity. Poulos and Chen [25] developed design charts to compute the lateral behaviour of a single pile adjacent to deep excavation in soft ground. They performed two staged analysis considering plane strain conditions and linear elastic soil model. Similar work was conducted by Liyanapathirana and Nishanthan [14] using finite element method. In both these studies lateral response of single pile was investigated.
The settlement behaviour of pile and development of excess pore water pressure and consolidation settlement were not investigated. Korff et al [8] proposed an analytical method to investigate reduction of capacity and increase in settlement of a nearby pile during excavation. It was reported that pile settlement due to excavation depends on the percentages of end bearing and shaft friction of the pile, the soil movement pattern, and the distribution of the maximum shaft friction with depth. However, shaft resistance in these methods is calculated on the assumption that horizontal stress acting on the piles does not change during excavation. This assumption may not be valid and the pile settlement may be underestimated using the preceding methods, leading to a non-conservative prediction. Shakeel and Ng [28] carried out three-dimensional coupled consolidation analysis is conducted to gain insight into the response of a (2×2) floating pile group adjacent to deep excavation in soft clay. By using a validated finite element model, the influence of the excavation depth, pile length, pile group location from excavation, the supporting system stiffness, soil state and permeability, and working load are systematically studied. The analysis revealed that the maximum settlement occurs when the pile group is founded at the excavation level and at a distance of 0.75 times the excavation depth, although the induced bending moment is insignificant. In contrast to pile group settlement, tilting is significant when it gets closer to the wall and minimum at a distance of 0.75 times the excavation depth. Zhang et al. [27] carried out the finite element analyses considering soil of the hardening small strain (HSS) constitutive model to establish the excavation-induced pile behaviors by varying the depth of excavation, pile diameter, pile length, pile distance away from the excavation, pilehead fixity, unsupported depth of excavation and axial loadings exerted on the pile head. Soomro et al [26] conducted parametric study to investigate the responses of floating pile to adjacent excavation at different depths. They concluded that the pile responses to excavation depend upon formation level of the excavation as well as the embedded depth of the wall. With different wall depth in each case, the induced settlement, lateral displacement and bending moment in the pile at the same stage of the excavation was different in the three cases.
Most of previous studies focused on lateral response of the piled foundation to excavation. Besides this, the location of an excavation depth relative to a pile foundation has not been studied systematically. The effects of excavation on the behaviour of piles (i.e., induced settlement and axial forces along the pile length) were rarely reported.
It is well understood that the stress-strain relationship of soils is highly nonlinear even at very small strain. The stiffness of most soils decreases as strain increases and depends on the recent stress or strain history of the soil [2,3]. Owing to non-linear soil behaviour, an excavation can cause reduction in the stiffness of the ground. To obtain a satisfactory numerical model of single pile responses to excavation-induced stress relief, the analysis needs to take account of the small strain non-linearity of soil.
This study aims at systematically investigating the effects of different excavation depths on a floating and an endbearing pile. A three-dimensional coupled consolidation numerical parametric study was carried out to analyse the responses of the single piles to the excavations. Lateral displacement, bending moment, induced lateral forces and axial load distribution along the pile and stress changes during excavation are reported and discussed.

Research Methodology
Three-dimensional finite element analysis was carried out to investigate the responses of an end-bearing pile to excavation-induced stress release. Figure 1 shows the flow chart which illustrates the step by step methodology adopted in this study.
With the prime objective of investigating the effects of the different excavation depths relative to an end-bearing pile, a three-dimensional coupled consolidation numerical parametric study was carried out. Two different final excavation depths (He) relative to the pile length (Lp) namely near the pile shaft (Case S), adjacent to the pile toe (Case T)) are taken in this parametric study. The final depth of the excavation (He) has been adopted as 12 m and 18 m in cases of S and T, respectively. The embedded length (Lp) and diameter (dp) of the pile are 18 m and 0.8 m, respectively. The modelled pile represents a cylindrical reinforced concrete (grade 40, reinforcement ratio = 1) with a bending moment capacity of 800 kNm.

Figure 2. Configuration of a typical numerical run representing case of S; (a) elevation view (b) plan view
The ratio of wall penetration depth to excavation depth is typically 0.5-2 in engineering practice [6,7], and thus a value of 0.5 is adopted in this study. The props are used to support the diaphragm wall with a vertical spacing of 3 m. The props are modelled as soft with axial rigidity of 81 × 10 3 kNm [7]. Horizontal spacing of props is 10 m.
It is worth noting that, in reality, high-rise buildings are unlikely to be built on a single pile. This hypothesised study is a more virtual case [4][5][6]. This simplification is made to understand the settlement and load transfer mechanism clearly. Figure. 1(b) illustrates the plan view of the configuration of the numerical simulation. The length of the excavation is 12 m. Due to symmetry, only half of the excavation was simulated. A monitoring section was selected at the transverse centreline of the excavation. Table 1 summarises numerical simulations conducted in this study.

Finite Element Mesh And Boundary Conditions
The finite element program Abaqus will be used in this study. The size of the mesh for each numerical runs will be taken as 50× 20×40 m as shown in Figure 3. Eight-noded hexahedral brick elements are used to model the soil, the pile and the diaphragm wall, while two-noded truss elements are adopted to model the props.
Roller and pin supports are applied to the vertical sides and the base of the mesh, respectively. Therefore, movements normal to the vertical boundaries and in all directions of the base are restrained. The water table is assumed to be at ground surface. Initially, the pore water pressure distribution is assumed to be hydrostatic. Free drainage is allowed at the top boundary of the mesh.
The pile-soil and wall-soil interface is modelled as zero thickness by using duplicate nodes. The interface is modelled by the Coulomb friction law, in which the interface friction coefficient () and limiting displacement (lim) are required as input parameters. A limiting shear displacement of 5 mm is assumed to achieve full mobilization of the interface friction equal to ×p', where p' is the normal effective stress between two contact surfaces and a typical value of for a bored pile of 0.35 is used in all analyses [9]. The excavation process will be simulated by deactivating soil elements inside excavation zone. In the meantime, the truss elements representing the props will be activated.

Constitutive Model And Model Parameters Used In Finite Element Analyze
The unique feature of basic hypoplastic model is to capture nonlinear behaviour within range of strain level of medium to large (due to monotonic loading) of granular material [15,16]. The basic model consists of five parameters ( ,   ,   ,  and ). The position and the slope of normal compression line in the space of ln(1 + ) versus ln ′ (where is the void ratio, and ′ is the mean effective stress) is representing by the parameters and   , respectively. The parameter   represents the slope of the isotropic unloading line in the same plane.  is the friction angle at critical state, and the parameter controls the large strain shear modulus. Mašín [17] further implemented the concept of intergranular strain to improve the basic hypoplastic model. To take into consideration of the strain and path dependency of soil stiffness, five additional parameters (required by intergranular strain) were included into the basic model. These five additional parameters are ,  , , and in which R is elastic range and  and  determine the rate of stiffness degradation. The remaining parameters and regulate the initial shear modulus, respectively. The hypoplastic clay model [15] with small strain stiffness has been implemented in the commercial finite element software package Abaqus through a user-defined subroutine.
The parameters (i. e. , ,   ,   and  ) for kaolin clay have been widely reported in the literature. Based on these four known parameters, the parameters which are r (i.e., controlling soil stiffness at medium to large-strain levels) and at small-strain levels (i.e, R,  r , , m T and m R ) were calibrated against existing experimental data of kaolin clay. The model parameters at small-strain and large-strain ranges are calibrated against the measured stress-strain relationships and the measured stiffness degradation curves in kaolin clay, respectively.
The coefficient of lateral earth pressure at rest, Ko is estimated by Jáky [14]'s equation: All model parameters for soft clay are summarised in Table 2. Since end-bearing piles are resting on hard stratum (i.e. rock). The rock was modelled as an elastic material. The modulus of elasticity and Poisson's ration of rock were taken as 70 GPa and 0.3, respectively [21].
The concrete pile, the diaphragm wall and the props were assumed to be linear elastic with Young's modulus of 35 GPa and Poisson's ratio of 0.25. The unit weight of concrete was assumed to be 24 kN/m 3 . The parameters for the rock and the piles and the diaphragm wall are summarised in Table 3.

Constitutive Model And Model Numerical Modelling Procedure
The numerical analysis modelling procedure for a typical case (i.e. case S) is summarized as follows: Step 1: Set up the initial boundary and initial stress conditions (i.e., static stress conditions with varying K0 =0.63).
Step 2: Activate the brick elements representing single pile (modeled as "wished-in-place").
Step 3: Apply the working load (determined from numerical pile load test) on the pile.
Step 4: Allow excess pore pressure, which generated in result of application of working load on the pile, to dissipate.
Step 5: Activate the brick elements representing the diaphragm wall. Figure 4 shows the lateral pile displacement induced due to excavation in both case S and T. The positive values of the pile deflection indicate the lateral movement of the pile towards excavation side. It can be seen from the figure that the pile head displaced away laterally from the excavation side in each case. Because the toe of the end-bearing pile is resting on the hard stratum, negligible movement of the pile toe of the end-bearing toe was induced due to excavation. Comparing the induced deflection of the end-bearing pile in the case T, the pile displacement in case S is higher than that in case T. This result can be ascribed to soil displacement due to excavation-induced stress release. The horizontal component of soil displacement vectors towards excavation in case S is slightly higher than that of case T. The maximum deflection induced at the pile head is approximately 15 mm (2.0% dp) in both cases. In contrast to end-bearing pile, Soomro et al [26] reported that the pile toe of the friction pile deflected towards the excavation side and the pile head displaced away from the excavation in both the cases. Furthermore the excavation-induced deflection profile reveals that the pile has rotated counter-clockwise about an axis perpendicular to the plane of the figure. The centre of rotation is approximately at Z/Lp=0.25 in both the cases. This is because of excavation-induced stress release and soil displacement (flow) towards excavation. The soil displaced towards excavation near the toe of the friction pile resulting in the movement of the toe in both cases. A similar pile deflection profile during an adjacent excavation of the friction pile was observed by Liyanapathirana and Nishanthan (2016). The maximum deflection of the pile after the completion of the excavation was computed as 40 (5.0% dp) and 32 mm (4.0% dp) in cases of S and T, respectively. It can be observed from the figure that there was no any bending moment observed at the head of the pile because of no any constraint at the pile head. However, significant bending moment could be induced at the head of the end-bearing pile if large pile head deflection induced due to excavation (discussed in previous section) is constrained. In case of S, the negative bending moment was induced along the upper portion of the pile (Z/Lp < 0.9). However, the portion of the pile near the pile toe was subjected to positive bending moment. This is because the pile was subjected to lateral force due to soil movement towards excavation and the constraint of movement of the pile toe (i.e. no any pile toe deflection as shown in Figure 3) in the hard stratum. The maximum negative and positive bending moment of 260 kNm and 350 kNm were computed at Z/Lp = 0.64 and the pile toe, respectively.

Induced Lateral Displacement in the Pile Due to Excavation
In case of T, the induced bending moment profile is similar to that in case of S. However, the maximum bending moment (of magnitude 125 kNm) induced at Z/Lp = 0.55 is smaller than that in case of T. This is because of the vertical component of displacement vector of soil due to deeper excavation in case of T is slightly higher than that in case of S.
Comparing the induced bending moments of floating reported by Soomro et al [26] and end-bearing piles in case of S, negative bending moment was induced along the entire pile length of both types of piles in case T. Moreover, the bending moment reduces as excavation became deeper in case of T (i.e. formation level He = 18 m). The reason for this bending profile of both the piles can be attributed to the embedded depth of the wall which makes the vertical component of the soil displacement vector higher than that of horizontal component in case of S. The maximum bending moment induced of 42 kNm at Z/Lp = 0.7 in floating pile.
It can be seen that the maximum induced bending moment of pile after completion of excavation in all the cases is much less than the pile bending moment capacity (i.e. 800 kNm). Therefore, the most critical issue to be considered in excavation-soil-pile problem is relatively large lateral displacement of the pile. This conclusion may not be applicable to scenarios in which the ground conditions or stiffness of excavation system (i.e. wall and prop stiffness) are different from those adopted in this study. It can be seen from the figure that the direction of soil displacement in retained side is towards excavation. As a result the upper part of the piles in both cases displaced towards excavation side (see Figure 3). Moreover, soil heave at excavation side in case of S. However, no heave is observed on excavation side in case of T. Consequently, the induced lateral deflection and bending moment in end-bearing pile profiles in case of T were similar to that in case of S but lesser magnitude.

Load Transfer Mechanism along the Pile Due to Excavation
To explore load transfer mechanism along the piles due to adjacent excavation, the changes in axial load distribution and mobilised shaft resistance along the pile length are discussed in this section Figure 7 shows the axial load distribution along the normalised pile length (i.e. Z/Lp) below the ground surface after excavation in case of S and T. For reference, axial load distribution after application of the working load (before excavation) is included. Because of the toe of the end-bearing pile on hard stratum, 100% of the working load transferred to the toe of end-bearing pile. This means that zero shaft resistance were mobilised along the end-pile length.

Load Transfer Mechanism Along the Pile Due to Excavation
It can be seen from the figure that on the completion of the excavation, axial load distribution in the pile due to excavation altered significantly in each case. The axial load increased along the entire pile length. By inspecting the load distribution after excavation, it can be seen that negative shaft resistance along the entire pile length was mobilised in each case. This is because of the significant ground movement due to excavation (see Figure 5) and the pile toe resting on the hard stratum (due to which no any settlement induced). This suggests that the pile was subjected to "dragload" by the surrounding soil. This led to increase the end-bearing resistance increased significantly. Owing to the excavation, the en-bearing resistance increased to 42% and 57% in case of S and T, respectively. In contrast to changes in axial load distribution in floating piles due to excavation reported by Soomro et al [26], the load distribution along the end-bearing piles altered significantly in each case. The axial load increased along the entire pile length. By inspecting the load distribution after excavation, it can be seen that negative shaft resistance along the entire pile length was mobilised in each case. This is because of the significant ground movement due to excavation (see Fig. 8) and the pile toe resting on the hard stratum (due to which no any settlement induced). This suggests that the pile was subjected to "dragload" by the surrounding soil. This led to increase the end-bearing resistance increased significantly. Owing to the excavation, the en-bearing resistance increased to 42% and 57% in case of S and T, respectively.

Load Mobilised Shaft Resistance on Completion of Excavation
To substantiate the discussion in the previous section, the mobilised shaft resistance in the end-bearing piles after the application of the working load (i.e., before excavation) and excavation in cases of S and T is shown in Figure 8 Where ΔQ is the difference between the computed axial loads at two consecutive depths, ΔZ is the vertical distance between the two consecutive depths, and s is the perimeter of the pile.
It is seen that after applying a load, zero shaft resistance mobilised in the pile, as expected. Inspecting the mobilised shaft resistance changes in the due to excavation, it can be seen that the soil movement due to excavation caused negative skin friction (NSF) mobilization along the entire pile length in each of cases (i.e. S and T). This implies that the pile is 'dragged' down by the surrounding soil which settles due to excavation. This observation is because of the end-bearing pile resting on the hard stratum stopping to settle. However, the induced ground movement surrounding the pile dragged the pile down resulting NSF. This led to increase end-bearing resistance (see Figure 6) to maintain equilibrium of the pile after excavation. The maximum negative shaft resistance of 12.4 kPa was induced at the mid of the end-bearing pile (Z/Lp =0.5).

Conclusions
This study investigate the responses of a end-bearing pile due to different excavation depths in saturated soft Kaolin clay using 3D coupled consolidation analysis. The effects of excavation depths relative to pile were investigated by simulating the excavation near the pile shaft (i.e. case S) and next to toe (i.e. case T). Based on ground conditions, different configurations and method of excavation modelled, the following conclusions can be drawn  Negligible movement of the pile toe of the end-bearing toe was induced due to excavation. Because the toe of the pile is resting on the hard stratum. Comparing the induced deflection of the end-bearing pile in the case T, the pile deflection in case S is higher.
 The negative bending moment was induced along the entire pile length of both types of piles in case T). The maximum induced bending moment in both types of piles after completion of excavation in all the cases is much less than the pile bending moment capacity (i.e. 800 kNm).
 On the completion of the excavation, piles were subjected to significant dragload. The downward load transfer mechanism was observed in end-bearing pile resulting in the end-bearing resistance increment of 42% and 57% in case of S and T, respectively.