Study on Influence Mechanism of Tunnel Construction on Adjacent Pile Foundation and Resilience Assessment

Abstract

To guarantee the safety of tunnel construction and the continued use of nearby structures, it is crucial to accurately forecast the size and extent of the plastic region that may occur due to tunnel excavation, as well as examine the impact on resilience. In this paper, the influence mechanism of tunnel construction on adjacent pile foundation and resilience assessment is investigated. Firstly, the stratum deformation and stress induced by tunnel construction are derived based on the thin-walled theory considering the influence of tunnel structure stiffness. Moreover, the resilience assessment based on the characteristics of the stratum plastic region is proposed to describe the degree of disturbance caused by tunnel construction to the adjacent pile foundation. Then, a comparison with a numerical simulation is conducted to verify the correctness of the prediction method of the stratum plastic region proposed in this paper. Finally, parameter sensitivity analysis is carried out, which indicates that pile parameters, soil parameters, and different tunnel outline conditions have a great influence on the prediction results. In order to reasonably control the impact of tunnel construction on the surrounding environment, safety control techniques, including advance grouting reinforcement and grouting uplift, need to be carefully designed.

1. Introduction

As a consequence of the rapid growth of the economy and increasing urbanization, the construction of municipal highway tunnels will likely reach a new level of success. The shield method has supplanted conventional mining methods as the primary technology for tunnel construction. This is mostly due to the fact that it is highly automated, requires little labor, has a small impact on the environment, and does not disrupt ground infrastructure or traffic. Subway tunnels are required to be constructed in close proximity to the structural foundations that are already in place in many cities [1,2,3,4,5]. The amount of land that is available for farming and other uses diminishes in proportion to the amount of construction that is taking place in urban areas. Numerous towns have put in a significant amount of effort to develop their underground areas. Within the context of the process of constructing urban infrastructure, an increasing number of foundation pit projects and subway lines are being constructed. The use of pile foundations in urban construction is becoming increasingly widespread due to the fact that they do not settle to a significant degree and may be applied in a variety of contexts. On the other hand, there are a few technical issues that frequently arise during the construction of subways. The lack of available space and driving lanes is the root cause of these obstacles. When the tunnel is being constructed, the dirt in the surrounding area will dissipate the ground stress and migrate toward the excavation spot. This is something that will occur regardless of whether the shield tunneling approach or the New Austrian Tunnelling approach is utilized. Both the deformation of the neighboring pile foundation and the amount of force that is contained inside it will be impacted as a result of this. When it comes to engineering design and construction, one of the most challenging aspects is figuring out how to properly examine how the structure of a neighboring pile base and tunnel construction interact with one another. At this very moment, this is one of the most important issues that is being investigated. The strata deformation and stress that are caused by the construction of tunnels have been explored by researchers, as well as the impact that this construction has on the environment around it [6,7,8,9,10,11,12,13,14,15]. Bobet [6] proposed an analytical solution for shallow tunnel construction in saturated ground, considering various construction processes and soil conditions, with a focus on small ground deformations and excavation methods. Liu et al. [15] investigated the deformation of tail grouting in shield tunnelling settlement control using a new lab apparatus. They used X-ray diffraction and SEM to analyze deformation and strength, confirming its adaptability. It is possible that a plastic region will develop in the stratum prior to the provision of temporary support. This is because the stress redistribution that occurs in the stratum is produced by the interaction between the foundation load and the tunnel excavation. By accurately anticipating the size and extent of the plastic region that may occur that will result from tunnel excavation, it is essential to ensure that the construction of tunnels is carried out in a safe manner while also ensuring that neighboring buildings continue to operate normally. There are areas of scientific investigation that have practical applications, such as the measuring of resilience and the effects of tunnel building on pile bases that are located nearby. However, in the above literature on tunnel construction disturbance degree or potential plastic region, tunnel structures are considered to be rigid bodies (i.e., no deformation occurs), while tunnel structures in actual engineering will undergo certain elliptic deformation, which leads to certain deviations in the prediction results of models proposed in the existing literature.

The idea of resilience has been widely used by academics to examine issues in the domains of engineering, ecology, and economics. By examining the resilience features of infrastructure, as demonstrated by the system’s functional time curve, researchers have assessed its resilience. Tierney and Bruneau [16] proposed that the area between the functional time curve and the initial functional time curve can serve as an indicator of infrastructure resilience, who also devised a resilience evaluation methodology. The resilience indicator was established by Attoh-Okine et al. [17] as the ratio of the area enclosed by the horizontal axis and the functional time curve following disruption to the area surrounded by the horizontal axis and the initial functional time curve. Cimelaro et al. [18] proposed three categories for evaluating the durability of medical networks following seismic catastrophes: trigonometric recovery, exponential recovery, and linear recovery. They also constructed a fundamental framework for disaster resilience. Ouyang et al. [19] separated the system’s functional time curve into three phases: the evaluation recovery period, the accumulation of losses, and the catastrophe preventive period. Turnquist and Vugrin took into account both the pre-disaster planning and post-disaster recovery investments. The analytical framework for resilience assessment, established by Francis and Bekera [20], consists of five components: system element verification, vulnerability evaluation, resilience goal setting, decision-maker thinking, and resilience capabilities. Ayyub conducted research on community resilience in the face of many disasters and put out a model of resilience that could be used for economic assessment [21]. Huang and Zhang [22] carried out a thorough examination of the engineering example of tunnel structural damage and developed a model appropriate for assessing the resilience of tunnel structures. A resilience evaluation approach for shield tunnel constructions under numerous perturbations was proposed by Lin et al. [23]. Lin et al. [24] proposed a resilience analysis model for shield tunnel linings that considers many stages of disturbance and recovery. A paradigm by Chen et al. [25] integrates post-seismic recovery, single-structure interrelationships, and seismic performance to quantitatively evaluate the seismic resilience of subway systems. Han et al. [26] introduced a resilience evaluation framework consisting of five steps. Their framework was designed to analyze the composite qualities and overall resilience of a structure formation system that is affected by nearby construction disruptions. However, the current research does not incorporate resilience design at the tunnel construction disturbance degree or potential plastic region.

To guarantee the safety of tunnel construction and the continued use of nearby structures, it is crucial to accurately forecast the size and extent of the plastic region that may be created during tunnel excavation, as well as examine the impact on structural resilience. In this paper, the influence mechanism of tunnel construction on adjacent pile foundation and resilience assessment is investigated. Firstly, the stratum deformation and stress induced by tunnel construction are derived based on the thin-walled theory considering the influence of tunnel structure stiffness. Moreover, the resilience assessment based on the characteristics of the stratum plastic region is proposed to describe the degree of disturbance caused by tunnel construction to adjacent pile foundation. Then, a comparison with the numerical simulation is conducted to verify the correctness of the prediction method of the stratum plastic region proposed in this paper. Finally, parameter sensitivity analyses are carried out.

2. Basic Framework of Stratum Plastic Region Prediction and Resilience Assessment

2.1. Theoretical Simplification of Practical Engineering Problems

This paper presents a simplified version of the engineering issue of tunneling through pile foundation, which is referred to as the plane strain problem. Figure 1 illustrates the theoretical simplification of engineering difficulties that are encountered in practice. In order to obtain the plastic region range of the stratum under the combined action of tunnel construction and piling load, the idea of superposition is applied, and the procedure of calculation is presented in Figure 2. To begin, the thin-walled theory is utilized to derive the stratum stress that is created by tunnel construction. This tension is derived by taking into consideration the impact of the tunnel structure’s stiffness. Additionally, the stratum stress that is generated by the pile foundation (i.e., pile shaft shear load and pile tip load) is superimposed on the stratum stress that is created by the building of the tunnel. Finally, the equation describing the envelope of the potential plastic region caused by tunnel building near a piling foundation is determined using the Mohr–Coulomb criteria.

2.2. Stratum Stress and Displacement Caused by Tunnel Construction with Lining

The theoretical analytical model of the tunnel liner and ground is depicted in Figure 3. In this model, the cartesian coordinates x and y are considered, whereas the polar coordinates r and θ are considered elsewhere. In this equation, the variable h represents the buried depth of the tunnel, Ur and U_θ represent the radial and circumferential displacements of the soil, and σr, σ_θ, and τ_rθ represent the radial, circumferential, and shear stresses of the soil, appropriately. The liner thickness is denoted by the letter d. As far as the liner is concerned, the outer radius is denoted by r₁, whereas the inner radius is denoted by r₀. E_g and ν_g are the abbreviations for the elasticity modulus and Poisson’s ratio of the ground. E_l and ν_l are the elasticity modulus and Poisson’s ratio of the liner, respectively.

The boundary conditions involved in the problem are as follows:

$$\left\{\begin{array}{l}\tau {|}_{\theta =\pm \pi /2}=0\\ U_{\theta }{|}_{\theta =\pm \pi /2}=0\\ {\sigma }_r^{ground}{|}_{r=r_1}={\sigma }_r^{liner}{|}_{r=r_1}\\ {\tau }_r^{ground}{|}_{r=r_1}={\tau }_r^{liner}{|}_{r=r_1}=0\\ {\sigma }_y{|}_{r\to \infty }=-\gamma y=-\gamma (h-rsin\theta )\\ {\sigma }_x{|}_{r\to \infty }=k{\sigma }_y\end{array}\right.$$

(1)

Based on the thin-walled theory, the stress–displacement relationship of the liner and the stress–internal force relationship of the liner and the contact surface of the ground are as follows:

$${\displaystyle \frac{d^2{U}_{\theta }^{liner}}{d{\theta }^2}}+{\displaystyle \frac{d{U}_r^{liner}}{d\theta }}=-{\displaystyle \frac{C(1-{\nu }^2)}{E}}{r}_0{\tau }_{r\theta }^{liner}$$

(2)

$${\displaystyle \frac{d{U}_{\theta }^{liner}}{d\theta }}+U_r^{liner}+{\displaystyle \frac{C}{F}}({\displaystyle \frac{d^4{U}_r^{liner}}{d{\theta }^4}}+2{\displaystyle \frac{d^2{U}_r^{liner}}{d{\theta }^2}}+U_r^{liner})={\displaystyle \frac{C(1-{\nu }^2)}{E}}{r}_0{\sigma }_r^{liner}$$

(3)

$$\left\{\begin{array}{l}{r}_0{\displaystyle \frac{dT}{d\theta }}-{\displaystyle \frac{dM}{d\theta }}=-r_0^2{\tau }_{r\theta }^s\\ r_{0}T+{\displaystyle \frac{d^{2}M}{d{\theta }^2}}=r_0^2{\sigma }_r^s\end{array}\right.$$

(4)

where

$$\left\{\begin{array}{l}C={\displaystyle \frac{E_l{r}_0(1-{{\nu }_g}^2)}{E_g{A}_s(1-{{\nu }_l}^2)}}\\ F={\displaystyle \frac{E_l{r_0}^3(1-{{\nu }_g}^2)}{E_g{I}_s(1-{{\nu }_l}^2)}}\end{array}\right.$$

(5)

and A_S is the section area of the liner ring; I_S is the moment of inertia of the liner ring to the center of the circle, respectively.

In the analysis of tunnel deformation, the paper adopts nonuniform convergence (refer to Figure 4). This convergence is caused by three factors: uniform radial contraction u₀, which is caused by the volume of the tunnel surrounding rock stress, which causes changes in the tunnel size and shape; elliptic deformation u_d, which is caused by the partial stress of the rock surrounding the tunnel; and vertical displacement −Δu_y. In addition, two ratios are suggested in order to measure the elliptic deformation and vertical displacement in accordance with the uniform radial contraction. It is referred to as the elliptic ratio ρ_t, while the vertical settlement ratio is denoted by the symbol ρ_s, as rendered in Equations (6) and (7).

$${\rho }_t=u_t/u_0$$

(6)

$${\rho }_s=u_s/u_0$$

(7)

Corresponding mixed displacement outline conditions can be expressed as follows:

$$U_r^{ground}{|}_{r=r_0}-U_r^{liner}{|}_{r=r_0}=-u_0+u_t\cos 2\theta +u_s\sin \theta$$

(8)

Through the use of the equilibrium equation and the strain coordination equation, the general solution of the tunnel may be obtained. The concrete solution of a shallow buried tunnel can be derived by combining outline conditions with the solution. Using the Airy function Φ, the general solution may be expressed as follows:

$$\begin{array}{l}\mathsf{\Phi }=a_0\ln r+b_0{r}^2+c_0{r}^2\ln r+d_0{r}^2\theta +{a_0}^{\prime }\theta +{\displaystyle \frac{1}{2}}{a}_{1}r\theta \sin \theta +(b_1{r}^3+{a_1}^{\prime }{r}^{-1}+{b_1}^{\prime }r\ln r)\cos \theta \\ -{\displaystyle \frac{1}{2}}{c}_{1}r\theta \cos \theta +(d_1{r}^3+{c_1}^{\prime }{r}^{-1}+{d_1}^{\prime }r\ln r)\sin \theta +{\displaystyle \sum _{n=2}^{\infty }(a_n}{r}^n+b_n{r}^{n+2}+{a_n}^{\prime }{r}^{-n}+{b_n}^{\prime }{r}^{-n+2})\cos n\theta \\ +{\displaystyle \sum _{n=2}^{\infty }(c_n}{r}^n+d_n{r}^{n+2}+{c_n}^{\prime }{r}^{-n}+{d_n}^{\prime }{r}^{-n+2})\sin n\theta \end{array}$$

(9)

where the parameters (a_n b_nc_n, etc.) are determined by outline conditions.

When the symmetries of stress and displacement along the y-axis are taken into consideration, the general solution can be reduced as follows:

$$\begin{array}{l}\mathsf{\Phi }=a_0\ln r+b_0{r}^2+c_0{r}^2\ln r-{\displaystyle \frac{1}{2}}{c}_{1}r\theta \cos \theta +(d_1{r}^3+{c_1}^{\prime }{r}^{-1}+{d_1}^{\prime }r\ln r)\sin \theta \\ +(a_2{r}^2+b_2{r}^4+{a_2}^{\prime }{r}^{-2}+{b_2}^{\prime })\cos 2\theta +(c_3{r}^3+d_3{r}^5+{c_3}^{\prime }{r}^{-3}+{d_3}^{\prime }{r}^{-1})\sin 3\theta \end{array}$$

(10)

Furthermore, combined with the linear elastic stress–strain and strain–displacement relations, the ground stress and displacement can be calculated by the following:

$$\begin{array}{l}{\sigma }_r=a_0{r}^{-2}+2b_0+c_0+2c_0\ln r+(2d_{1}r-2{c_1}^{\prime }{r}^{-3}+c_1{r}^{-1}+{d_1}^{\prime }{r}^{-1})\sin \theta \\ -2(a_2+3{a_2}^{\prime }{r}^{-4}+2{b_2}^{\prime }{r}^{-2})\cos 2\theta -2(3c_{3}r+2d_3{r}^3+6{c_3}^{\prime }{r}^{-5}+5{d_3}^{\prime }{r}^{-3})\sin 3\theta \end{array}$$

(11)

$$\begin{array}{l}{\sigma }_{\theta }=-a_0{r}^{-2}+2b_0+3c_0+2c_0\ln r+(6d_{1}r+2{c_1}^{\prime }{r}^{-3}+{d_1}^{\prime }{r}^{-1})\sin \theta \\ +2(a_2+6b_2{r}^2+3{a_2}^{\prime }{r}^{-4})\cos 2\theta +2(3c_{3}r+10d_3{r}^3+6{c_3}^{\prime }{r}^{-5}+{d_3}^{\prime }{r}^{-3})\sin 3\theta \end{array}$$

(12)

$$\begin{array}{l}{\tau }_{r\theta }=-(2d_{1}r-2{c_1}^{\prime }{r}^{-3}+{d_1}^{\prime }{r}^{-1})\cos \theta +2(a_2+3b_2{r}^2-3{a_2}^{\prime }{r}^{-4}-{b_2}^{\prime }{r}^{-2})\sin 2\theta \\ -6(c_{3}r+2d_3{r}^3-2{c_3}^{\prime }{r}^{-5}-{d_3}^{\prime }{r}^{-3})\cos 3\theta \end{array}$$

(13)

Considering the outline conditions at infinity, and that the stress and displacement at R and infinity are single values, the above solutions can be simplified as follows:

$$\begin{array}{l}{\sigma }_r=-{\displaystyle \frac{\left(1+k\right)}{2}}\gamma h+a_0{r}^{-2}+\left\{{\displaystyle \frac{\left(3+k\right)}{4}}\gamma r-2{c_1}^{\prime }{r}^{-3}+c_1{r}^{-1}+{d_1}^{\prime }{r}^{-1}\right\}\sin \theta \\ +\left\{{\displaystyle \frac{\left(1-k\right)}{2}}\gamma h-6{a_2}^{\prime }{r}^{-4}-4{b_2}^{\prime }{r}^{-2}\right\}\cos 2\theta -\left\{{\displaystyle \frac{\left(1-k\right)}{4}}\gamma r+12{c_3}^{\prime }{r}^{-5}+10{d_3}^{\prime }{r}^{-3}\right\}\sin 3\theta \end{array}$$

(14)

$$\begin{array}{l}{\sigma }_{\theta }=-{\displaystyle \frac{\left(1+k\right)}{2}}\gamma h-a_0{r}^{-2}+\left\{{\displaystyle \frac{\left(1+3k\right)}{4}}\gamma r+2{c_1}^{\prime }{r}^{-3}+{d_1}^{\prime }{r}^{-1}\right\}\sin \theta \\ -\left\{{\displaystyle \frac{\left(1-k\right)}{2}}\gamma h-6{a_2}^{\prime }{r}^{-4}\right\}\cos 2\theta +\left\{{\displaystyle \frac{\left(1-k\right)}{4}}\gamma r+12{c_3}^{\prime }{r}^{-5}+2{d_3}^{\prime }{r}^{-3}\right\}\sin 3\theta \end{array}$$

(15)

$$\begin{array}{l}{\tau }_{r\theta }=\left\{{\displaystyle \frac{\left(1-k\right)}{4}}\gamma r+2{c_1}^{\prime }{r}^{-3}-{d_1}^{\prime }{r}^{-1}\right\}\cos \theta -\left\{{\displaystyle \frac{\left(1-k\right)}{2}}\gamma h+6{a_2}^{\prime }{r}^{-4}+2{b_2}^{\prime }{r}^{-2}\right\}\sin 2\theta \\ -\left\{{\displaystyle \frac{\left(1-k\right)}{4}}\gamma r-12{c_3}^{\prime }{r}^{-5}-6{d_3}^{\prime }{r}^{-3}\right\}\cos 3\theta \end{array}$$

(16)

Furthermore, considering that the shear stress at the interface between the ground and the liner is 0 and the stress–displacement relationship of the liner, the unknown parameters can be obtained:

$$\left\{\begin{array}{l}{a}_0={\displaystyle \frac{1}{2}}{\displaystyle \frac{CF(1-{\nu }^2)\gamma h\left(1+k\right)+2E\left(C+F\right)\frac{u_0}{r_0}}{\left(1+\nu \right)\left(C+F\right)+CF(1-{\nu }^2)}}{r_0}^2\\ c_1=-\gamma {r_0}^2\\ {c_1}^{\prime }={\displaystyle \frac{1}{8}}\left(k-{\displaystyle \frac{\nu }{1-\nu }}\right)\gamma {r_0}^4\\ {d_1}^{\prime }={\displaystyle \frac{1}{4}}{\displaystyle \frac{1-2\nu }{1-\nu }}\gamma {r_0}^2\\ {a_2}^{\prime }=-{\displaystyle \frac{1}{4}}{\displaystyle \frac{\left(F+6\right)\left(1-\nu \right)\gamma h\left(1-k\right)+\frac{6E{u}_d}{\left(1+\nu \right)r_0}}{\left(1-\nu \right)F+3\left(5-6\nu \right)}}{r_0}^4\\ {b_2}^{\prime }={\displaystyle \frac{1}{4}}{\displaystyle \frac{\left[2\left(1-\nu \right)F+3\right]\gamma h\left(1-k\right)+\frac{18E{u}_d}{\left(1+\nu \right)r_0}}{\left(1-\nu \right)F+3\left(5-6\nu \right)}}{r_0}^2\\ {c_3}^{\prime }={\displaystyle \frac{1}{12}}{\displaystyle \frac{\left(1-\nu \right)F+4\left(5-4\nu \right)}{\left(1-\nu \right)F+8\left(7-8\nu \right)}}\gamma \left(1-k\right){r_0}^6\\ {d_3}^{\prime }=-{\displaystyle \frac{1}{8}}{\displaystyle \frac{\left(1-\nu \right)F+8}{\left(1-\nu \right)F+8\left(7-8\nu \right)}}\gamma \left(1-k\right){r_0}^4\end{array}\right.$$

(17)

2.3. Resilience Assessment Based on the Characteristics of Stratum Plastic Region

In the above paper, the plastic region in the stratum surrounding the pile foundation caused by tunnel construction has been predicted through theoretical analysis. In this section, the assessment of resilience is conducted by considering the characteristics of the stratum plastic region. This method can effectively evaluate the resilience performance of the stratum and provide a new resilience evaluation method. The planned grade of resilience for the tunnel lining, as determined by the range of values of the resilience index R, is presented in

Table 1. Grade of resilience.

Grade	Description	Colour
High resilience	Two independent domains
Moderate resilience	Multiply connected region
Low resilience	Simply connected region

. This table illustrates the extent to which the excavation of a neighboring foundation pit affects the current shield tunnel lining. Generally, the degree of influence for high resilience is the lowest, followed by moderate resilience, and the highest degree of influence is observed for low resilience.

3. Parameter Sensitivity Analysis

3.1. Comparison and Verification with Numerical Simulation

The thin-walled theory is used to determine the stratum deformation and stress that are caused by tunnel construction. This theory takes into consideration the impact of the tunnel structure’s stiffness. In addition to this, the nonuniform convergence that occurs near the tunnel circumference is utilized. Moreover, the analytical method to describe the boundary of the plastic region is drawn by MATLAB software programming (R2023a version). To assess the accuracy of the proposed prediction approach for the stratum plastic region, this research conducts a comparison utilizing numerical simulation approaches (OptumG2). OptumG2 is a geotechnical analysis software that combines limit analysis and finite element analysis and can be analyzed using adaptive mesh encryption. The equation describing the envelope of the potential plastic region caused by tunnel building near a piling foundation is determined using the Mohr–Coulomb criteria. The results of this comparison are depicted in Figure 5. Under the identical parameters, the findings of the comparison demonstrate that the outline of the plastic region generated by the analytical prediction model is quite comparable to that which was acquired by the numerical simulation program. It should be pointed out that the derivation of the analytical solutions proposed in this paper is based on some assumed conditions, and that the comparison here is only qualitative, aiming at verifying the rationality of analytical solutions from the rule.

3.2. The Effects of Soil Parameters

A parameter sensitivity study was conducted to assess the extent to which changes in soil parameters, tunnel outline conditions, and piling parameters affect the prediction outcomes. The parameters of the prediction model are selected based on the information provided in

Table 2. Parameters used in parameter sensitivity analysis.

Parameters	Symbol	Value
Tunnel radius	R [m]	3
Depth of the tunnel	h [m]	10
Elasticity modulus of stratum	Eg [MPa]	50
Poisson’s ratio of stratum	νg	0.2
Elasticity modulus of liner	El [MPa]	25,000
Poisson’s ratio of liner	νl	0.2
Unit weight of stratum	γ [kN/m3]	16, 20, 24
Angle of internal friction of stratum	φ [°]	20, 25, 30
Cohesion of stratum	c [kPa]	20, 30, 40
Uniform radial contraction	u0 [cm]	6, 18, 24
Elliptic deformation	ud [cm]	1.5, 6, 12
Vertical displacement	−Δuy [cm]	0, 3, 6
Pile offset	dp [m]	6, 7, 8
Pile length	h0 [m]	7, 10, 13
Pile load	s, P [kN/m, kN]	75, 155; 150, 235; 225, 315

. The data values in Table 2 are selected by referring to the published relevant literature and the actual situation of the project [6,7,8,9,10,11,12,13,14,15].

Figure 6 indicates the effect law of the physical and mechanical parameters of stratum on the plastic region: (a) unit weight γ; (b) angle of internal friction φ; (c) cohesion c.

The impact of three distinct soil unit weight magnitudes (γ = 16 kN/m³, 20 kN/m³, and 24 kN/m³) on the outlines of the possible plastic regions is shown in Figure 6a. The plastic region’s tendency to alter as soil unit weight increases is indicated by the arrow direction. The findings show that when the soil unit weight grew, the potential plastic region’s limits somewhat shifted. The potential plastic region’s four corners stretch outward, while its midpoints on each side contract inward, indicating that as the soil unit weight increases, the prospective plastic region’s shape will progressively take on the form of a butterfly. Additionally, when the tunneling-induced potential plastic region expands, the two potential plastic regions near the tunnel and the pile merge.

Figure 6b illustrates the impact of three distinct soil cohesion magnitudes (c = 20 kPa, 30 kPa, and 40 kPa) on the limits of the possible plastic region. The impact of three distinct soil internal friction angle magnitudes (φ = 25°, 27.5°, and 30°) on the limits of the potential plastic region is shown in Figure 6c. The results show how similar the influence rules are to each other. Moreover, it is clear that when the soil’s cohesiveness or angle of internal friction increases, the potential plastic region’s four corners narrow inward, and its ranges significantly decrease. Stated differently, the occurrence of a possible plastic region shaped like a butterfly is noticeable even at low soil cohesion or internal friction angle values. It is important to note that the two tunneling-induced potential plastic regions surrounding the tunnel and the pile would merge if the soil parameters (angle of internal friction or cohesion) were high enough, but they would split apart otherwise.

Table 3. Grade of resilience for different soil parameters.

Unit Weight γ /kN/m3	Angle of Internal Friction φ /°	Cohesion c /kPa	Grade	Colour
16	25	30	High resilience
20	25	30	High resilience
24	25	30	Moderate resilience
20	20	30	Moderate resilience
20	25	30	Moderate resilience
20	30	30	High resilience
20	25	20	Moderate resilience
20	25	30	Moderate resilience
20	25	40	High resilience

shows the grade of resilience considering the physical and mechanical parameters of stratum on plastic region: (a) unit weight γ; (b) angle of internal friction φ; and (c) cohesion c. Basically, the estimated grade of resilience is inversely proportional to the area of the plastic region, that is, the higher the grade of resilience, the smaller the area of the plastic region.

3.3. The Effects of Different Tunnel Outline Conditions

Figure 7 renders the effect laws of tunnel outline conditions on plastic region: (a) uniform radial contraction u₀; (b) elliptic deformation u_d; and (c) vertical displacement −Δu_y.

Table 4. Grade of resilience for different tunnel outline conditions.

Uniform Radial Contraction u0 /cm	Elliptic Deformation ud /cm	Vertical Displacement −Δuy /cm	Grade	Colour
6	6	3	Moderate resilience
18	6	3	Moderate resilience
24	6	3	Moderate resilience
18	1.5	3	High resilience
18	6	3	High resilience
18	12	3	Moderate resilience
18	6	0	High resilience
18	6	3	High resilience
18	6	6	Moderate resilience

shows the corresponding grade of resilience.

Figure 7a illustrates the effect that three unique uniform convergence magnitudes (u₀ = 6 cm, 9 cm, and 12 cm) have on the borders of the potential plastic regions. These magnitudes are shown in the graphical representation. The observations suggest that the morphologies of the potential plastic zone change slightly and take on a butterfly-like appearance as the concentration of uniform convergence increases. Conversely, as the uniform convergence increases, the possible plastic region’s ranges greatly increase.

The impact of three distinct ovalization magnitudes (u_d = 1.5 cm, 3 cm, and 4.5 cm) on the edges of the possible plastic zones is depicted in Figure 7b. The ovalization is composed of these magnitudes. A vertical bone-shaped potential plastic region is formed, as evidenced by the observation that the potential plastic region’s left and right sides compress inward and its up and down sides extend outward. The fact that both sides of the potential plastic zone contract inward as ovalization grows serves as evidence for this.

Figure 7c shows an example of the impact of three distinct vertical translation magnitudes (Δu_y = 0 cm, −3 cm, and −6 cm) on the contours of the potential plastic zone created by tunneling. The form of the prospective plastic region appears to grow towards a fan shape since it is observed that when the vertical translation increases, the potential plastic region’s down side closes inward and its up side expands outward. This is a result of the potential plastic region’s upward expansion expanding outward. It should be noted that the uniform convergence of a tunnel mostly affects the range of the potential plastic zone, whereas ovalization of a tunnel primarily affects its shape. The vertical translation affects both the form and range of the possible plastic zone.

3.4. The Effects of the Pile Parameters

Figure 8 renders the effect laws of pile parameters on plastic region: (a) pile offset d_p; (b) pile length h₀; (c) pile load s, P. The findings render that the possible plastic regions close to the pile and the tunnel are related when the pile is positioned in such a way that it is near enough to the tunnel, where the pile tip’s depth is near the tunnel spring line and the pile loads are adequate. According to the grade of resilience displayed in

Table 5. Grade of resilience for different pile parameters.

Pile Offset dp /m	Pile Length h0 /m	Pile Load s, P /kN/m, kN	Grade	Colour
6	10	150, 235	Moderate resilience
7	10	150, 235	High resilience
8	10	150, 235	High resilience
7	7	150, 235	High resilience
7	10	150, 235	High resilience
7	13	150, 235	Moderate resilience
7	10	75, 155	Moderate resilience
7	10	150, 235	Moderate resilience
7	10	225, 315	Low resilience

, the matching grade of resilience is represented. When it comes down to it, the predicted grade of resilience is inversely proportional to the area of the plastic region. This means that the higher the grade of resilience, the smaller the area of the plastic region.

4. Conclusions

In this paper, the basic framework of the stratum plastic region prediction caused by tunnel construction with the lining adjacent to the pile foundation is constructed based on the idea of superposition. The main conclusions are as follows:

(1) The thin-walled theory is used to determine the stratum deformation and stress that are caused by tunnel construction. This theory takes into consideration the impact of the tunnel structure’s stiffness. In addition to this, the nonuniform convergence that occurs near the tunnel circumference is utilized. In order to determine whether or not the prediction approach of the stratum plastic region that is suggested in this research is accurate, a comparison using numerical simulation techniques is carried out.

(2) With the rise in unit weight γ, the four corners of the outline of the plastic region tend to expand, while the center of the outline tends to develop towards the inside of the tunnel. The outline range of the plastic region tends to decrease with the rise in cohesion c and the angle of internal friction φ. With the rise in the uniform radial contraction u₀, the range of the plastic region increases gradually. With the rise in the elliptic deformation u_d, the four corners of the outline of the plastic region hardly change, but the edges of the outline expand to the direction of the tunnel. As vertical displacement −Δu_y increases, the plastic region gradually increases. With the rise in pile offset, the plastic region gradually moves away from the tunnel. When the pile length grows, the outline of the plastic region increases gradually. As the pile load increases, the plastic region gradually increases.

(3) The resilience assessment based on the characteristics of the stratum plastic region is proposed to describe the degree of disturbance caused by tunnel construction to the adjacent pile foundation. Basically, the estimated grade of resilience is inversely proportional to the area of the plastic region, that is, the higher the grade of resilience, the smaller the area of the plastic region.

(4) In order to successfully reduce the negative effects that tunnel construction has on the surrounding environment, it is very necessary to rigorously establish safety control measures such as advance grouting reinforcement and grouting uplift.

However, the analytical method proposed in this paper also has some limitations, such as the inability to consider the elastoplastic formation process of the formation plastic zone. We will further consider these deficiencies in future studies.