Calculation method of limit support force of tunnel excavation face based on overall analysis method

Abstract

The application discloses a tunnel excavation face limit support force calculation method based on a whole analysis method, and comprises the following steps: step 1: a limit support force calculation model of an excavation face is proposed based on the whole analysis method; step 2: according to the theoretical model, a calculation formula of the limit support force of a shield excavation face is derived; and step 3: a corresponding loose zone model of a shield tunnel damage is proposed, wherein the model comprises a shallow-buried shield tunnel damage model and a deep-buried shield tunnel damage model. The whole analysis method is applied to the excavation face stability problem, and a calculation model of the excavation face stability is established. According to the tunnel deep and shallow burying, an elliptic cylinder-type general arch model considering the soil arching effect is established. The limit support force obtained by the application presents a consistent development trend with the numerical simulation and the existing theoretical results. In addition, the calculation time of the analytical solution is far less than the calculation time of the numerical simulation, and a new idea is provided for the design of the limit support force of the excavation face.

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering technology, and in particular to a method for calculating the ultimate support force of a tunnel excavation face based on the overall analysis method. Background Technology

[0002] Shield tunneling boasts numerous construction advantages and has become the preferred method for subway construction. However, its widespread use often presents challenges related to the stability of the excavation face (Ding et al. 2019; Khezri et al. 2015; Klotz et al. 2006; Patil et al. 2018). The stability of the excavation face is related to the magnitude of the support force. If the support force is too small, active failure of the shield excavation face will occur (Li et al. 2019; Li et al. 2020; Zhang et al. 2022); if it is too large, passive failure will occur (Li et al. 2022; Mollon et al. 2011; Zhang et al. 2019). Appropriate excavation face support force is crucial for tunnel safety.

[0003] Over the past few decades, the stability of the tunnel boring machine (TBM) excavation face has attracted considerable attention from scholars both domestically and internationally. The main research methods include laboratory experiments, numerical simulations, and theoretical studies. Laboratory experiments, which can consider many complex factors and realistically reproduce ground disturbances and instability development, have been widely used in excavation face stability problems. Model tests under 1g conditions (Berthoz et al. 2012; Kirsch 2010; Lü et al. 2018; Takano et al. 2006b) and centrifuge tests (Chambon and Corte 1994; Chen et al. 2018; Idinger et al. 2011; Soranzo et al. 2015) are the most important research methods. Numerical simulations can simulate various complex working conditions. Their calculation process and results are easy to monitor, and the simulation cost is low, making them widely used in various research studies. The main research focuses on the finite difference method (Li et al. 2022; Li et al. 2020; Zhang et al. 2020; Zhang et al. 2022), the finite element method (Fan et al. 2020; Han et al. 2021; Qiu et al. 2022; Ukritchon et al. 2017), and the discrete element method (Chenet et al. 2011; Saadat and Taheri 2019; Wang et al. 2018; Zhang et al. 2011). Theoretical research is extensive in the study of excavation face stability, including limit analysis methods (Leca and Dormieux 1990; Li et al. 2022; Mollon et al. 2011; Soubra 2008; Zhang et al. 2020; Zhang et al. 2022) and limit equilibrium methods.

[0004] The limit equilibrium method was first used to analyze slope stability. Its principle is simple and calculations are convenient, and it is now widely used in calculating the stability of tunnel excavation faces. Horn (Horn 1961) first proposed the three-dimensional wedge model, which was subsequently improved by other scholars. Jancsecz et al. (Jancsecz and Steiner 1994) established a three-dimensional wedge-prism limit equilibrium model based on Horn's work (Horn 1961). Kraus (Krause 1987) used the limit equilibrium method to analyze the shear force on the sliding surface of the wedge, obtaining the ultimate support force of the excavation face under different conditions. Broere (Broere 1998) extended the three-dimensional wedge model to multi-layered soils, providing a theoretical basis for predicting the ultimate support pressure of tunnel excavation faces in multi-layered soil strata. Anagnostou (Anagnostou 2012) obtained the ultimate support force of the excavation face by performing stress analysis on cross-sections of a three-dimensional wedge, and the results were in good agreement with numerical simulation and model test results. Anagnostou et al. (1994) applied seepage force to a wedge model and calculated the ultimate support force. Lu et al. (2017) considered the influence of seepage force on the failure mode, modified the wedge model, and calculated the ultimate support pressure under seepage conditions. Perazzelli et al. (2017) extended the seepage model to the tunnel excavation face problem under anchor reinforcement.

[0005] Numerous scholars have obtained fruitful conclusions using the limit equilibrium method. However, in limit equilibrium studies, it is often assumed that the slip surface failure is planar or a logarithmic spiral surface, while the actual failure line is not a simple straight line or spiral (Kamata and Mashimo 2003; MASHIMO et al. 1999; Zhang et al. 2015; Zhang et al. 2022). When the slip surface is assumed to be planar, there is also no consensus on the value of its fracture angle (Chambon and Corte 1994; Chen et al. 2019; Chen et al. 2014; Cheng et al. 2021; Dziuban et al. 2018; Kirsch 2010; Liu et al. 2018; Lü et al. 2018; Qin 2005; Tang et al. 2013). Zheng et al. (Zheng and Tham 2009; Zheng and Zhou 2008) proposed an unstripped method, also known as the global analysis method, for solving slope stability. This method uses Newton's method with three-moment equilibrium, achieving a large and rapid convergence range and high computational accuracy. The slip surface can be planar or curved, making it applicable to various types of slip surfaces. Sun et al. (Sun et al. 2016) combined the global analysis method and the Morgenstern-Price method to obtain an expression for the normal stress distribution on the slip surface and established the equilibrium equations for the slope sliding body. Zhang et al. (Zhang et al. 2018) used the global analysis method to reinforce slopes with anti-slide piles and determined the location of the critical slip surface. The global analysis method is mainly used in slopes, where normal or tangential forces are directly applied to the outer contour of the slope. Unlike limit analysis or limit equilibrium methods, it cannot consider the influence of the surrounding rock failure zone above the excavation face. Summary of the Invention

[0006] The purpose of this invention is to design a calculation method for the ultimate support force of tunnel excavation faces based on the global analysis method, in order to solve the problems mentioned in the background art. The global analysis method is applied to the stability problem of excavation faces, and a calculation model for excavation face stability is established. Based on the tunnel depth, an elliptical cylinder-Push arch-like model considering the soil arching effect is established. The ultimate support force obtained by the model of this invention shows a relatively consistent development trend with numerical simulation and existing theoretical results. Moreover, the calculation time of the analytical solution is much shorter than that of the numerical simulation, providing a new approach for the design of the ultimate support force of excavation faces.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for calculating the ultimate support force of a tunnel excavation face based on the overall analysis method, comprising the following steps:

[0008] Step 1: Propose a calculation model for the ultimate support force of the excavation face based on the overall analysis method;

[0009] Step 2: Based on the theoretical model, derive the calculation formula for the ultimate support force of the shield tunneling face;

[0010] Step 3: Propose a loosening zone model corresponding to the failure of a shield tunnel, which includes a shallow-buried shield tunnel failure model and a deep-buried shield tunnel failure model; and establish a calculation model of the major principal stress arch using a major principal stress rotation arc.

[0011] Step 4: Based on the two models proposed in Step 3, derive the formula for calculating vertical earth pressure;

[0012] Step 5: Combine the calculation formulas for the ultimate support force of the shield excavation face and the vertical earth pressure to obtain the ultimate support force of the excavation face.

[0013] In a preferred embodiment of the present invention, the specific process of step 1 is as follows:

[0014] Assume that the sliding failure zone Ω is a planar region bounded by the outer contour line NOM and the potential slip surface MN;

[0015] Assume that the normal stress on the slip surface follows a natural distribution, and the shear stress follows the Mohr-Coulomb criterion;

[0016] The external forces acting on the sliding failure zone include body forces, surface forces, and stresses. Body forces include the vertical gravity W and the horizontal seismic force q; surface forces include the normal force acting on the outer contour line. and tangential force

[0017] The model includes the shield support force σT and vertical earth pressure σV perpendicular to the outer contour line NOM, and the tangential force f parallel to NOM; the stresses are the normal stress σ(x) and shear stress τ(x) on the slip surface MN.

[0018] In a preferred embodiment of the present invention, the process of deriving the calculation formula for the ultimate support force of the shield excavation face in step 2 is as follows: take any three points where the sliding failure zones are not on the same straight line. If i = 1, 2, 3, the sum of the moments of the force system acting on the failure zone about these three points is 0, i.e.

[0019] ∫ S (Δx ci σdx+Δy ci σdy)+∫ S (Δx ci τdy-Δy ci τdx)+m ci =0 (1)

[0020] Where Δx ci and Δy ci It is a point on the slip surface MN. and The components to the point (x, y); m ci The active force acting on the sliding failure zone about the point The torque, that is:

[0021]

[0022] and These are the loads on the outer contour line NOM and the moments of the volumetric forces in the sliding failure zone about the center of moment, respectively:

[0023]

[0024]

[0025] To simplify the calculation, it is assumed that the volumetric forces in the sliding failure zone consist only of gravity and that seismic loads are not considered; in equation (4), (x gk y gk ) represents a subdomain Ω of the sliding failure zone Ω. k The centroid, w k =γ k A k Ω k The area of ​​the slip surface MN; assuming the slip surface MN satisfies the Mohr-Coulomb criterion, when the slip failure zone is in limit equilibrium, we have:

[0026]

[0027] In equation (5): F S For the safety factor, c e and f e The effective stress shear strength parameter is given, where u is the pore water pressure.

[0028] To describe the distribution of normal stress on the sliding surface MN, a differential slice FGHI with arc length dS is considered along the anti-slip direction of the sliding surface MN. The slice's self-weight and horizontal seismic force are d. w and d q The force increment between the vertical and horizontal bars is d. v and d h The horizontal and vertical components of the load acting on the outer contour line NOM on the block are df. x and df y ,Right now

[0029]

[0030] In equation (6): dx g and dy g Let HI be the arc length dS g Differentiating in the x and y directions, and projecting all force systems on the differential strip onto the normal direction of the sliding surface, we get:

[0031] σdS=dwcosα-dqsinα+df x sinα-df y cosα+dvcosα-dhsinα (7)

[0032] In equation (7), α is the angle between FG on the differential strip and the x-axis, and h is the height of the center JK of the strip FGHI;

[0033] σ=σ(x)=σ0+σ I (8)

[0034] σ0 and σ I Let MN be the normal stress on the slip surface caused by the external load and the inter-strip force on the slip failure zone, respectively; where:

[0035]

[0036] In equation (9) The effect of volumetric forces in the sliding failure zone on the normal stress MN on the slip surface; The effect of the outer contour line NOM on the normal stress of the slip surface MN;

[0037] The approximate formula for the normal stress of the slip surface is:

[0038] σ=σ0+f(x,a,b) (10)

[0039] f(x,a,b)=al a (x)+bl b (x) (11)

[0040] In equation (11), f(x, a, b) is the correction function for the normal stress of the slip surface, a and b are undetermined coefficients, and l a (x), l b (x) is:

[0041]

[0042] In formula (12) and These are the x-coordinates of the bottom N point and the top O point of the shield tunnel excavation face, respectively.

[0043] According to the simplification of various formulas, we can obtain:

[0044] g(σ T,a,b)=au1+bu2+u3+au4+bu5+u6+m ci =0 (13)

[0045] Equation (13) is about σ T The system of three quadratic equations with variables a and b can be simplified to obtain the ultimate support force σ at the excavation face. T .

[0046] In a preferred embodiment of the present invention, in step 3, the loosening area of ​​the shallow-buried shield tunnel failure model is an elliptical cylindrical loosening area that extends directly to the ground; the loosening area of ​​the deep-buried shield tunnel failure model can be divided into two parts: the lower part is elliptical cylindrical, and the upper part is a parabolic rotating object, which is an arched area formed by the parabola rotating around an axis, and is set as a Protodyakonov-like arch calculation model.

[0047] In a preferred embodiment of the present invention, the specific process of deriving the formula for calculating vertical earth pressure in step 4 is as follows: assuming the compressive stress σ exerted by the soil above the arched region on the soil below... vk Consider a micro-element above the adjacent arch-like soil body. The thickness of the micro-element is dh, the span is L, and the arch height is f. The earth pressure acting on the micro-element is equivalent to a uniformly distributed load q acting on the entire span.

[0048] Assuming the compressive stress σ exerted by the soil above the arched region on the soil below... vk Therefore, after the earth pressure redistribution through a similar arch, the vertical stress transmitted to the adjacent stationary soil on both sides is approximately: the weight of the upper soil γ(Ch) minus the vertical compressive stress σ. vk Therefore, the expression for the equivalent load q is:

[0049]

[0050] By employing a structure similar to an arch, the lateral thrust dF under a uniformly distributed load q can be obtained. h for:

[0051]

[0052] Therefore, the compressive stress of the soil after stress redistribution due to the combined action of vertical stress and self-weight is:

[0053]

[0054] During tunnel excavation, the relative sliding of the soil causes a significant deflection in the direction of the principal stresses, thus having a crucial impact on the collapse pressure at the tunnel excavation face. The effect of this deflection is primarily manifested in the lateral pressure coefficient Kh between the moving soil and adjacent soil masses, as well as the stress distribution pattern within the soil.

[0055] The calculation equations for the arch calculation model with high principal stress are as follows:

[0056] By arbitrarily selecting a soil element along the trajectory line and performing a force analysis, the vertical stress σ can be obtained from the force equilibrium condition. v and horizontal stress σ h As shown in the following formula:

[0057] σ v =σ1sin 2 θ+σ3cos 2 θ (18)

[0058] σ h =σ1cos 2 θ+σ3sin 2 θ (19)

[0059] The average vertical earth pressure within the damaged area can be obtained:

[0060]

[0061] Define the vertical stress distribution coefficient m as:

[0062]

[0063] According to the Mohr-Coulomb criterion, the upward shear stress τ acting on the boundary of the infinitesimal element is:

[0064]

[0065] The lateral pressure coefficient K acting on the sliding surface can be obtained. h for:

[0066]

[0067] In equation (23), Where θ0 is the angle of the fracture surface;

[0068] Assume the overburden layer of the tunnel is homogeneous, cohesionless soil, satisfying the Mohr-Coulomb failure criterion; consider an infinitesimal element of thickness dz at any depth z above the ground within the height range of the elliptical arch. The element has width L, soil weight γ, internal friction angle φ, and Kh is the lateral pressure coefficient considering the deflection of the major principal stress direction. Solving for the vertical direction of the element, we obtain:

[0069]

[0070] When the burial depth is large, the soil failure zone does not extend to the surface. At this time, the soil arching effect mechanism, composed of a Protodyakonov-like arch and an elliptical cylinder, comes into play. The vertical stress at any depth z from the surface within the soil failure zone of the elliptical cylinder arch can be obtained as shown in equation (25):

[0071]

[0072] When the burial depth is shallow (i.e., h ≥ C, where C is the tunnel burial depth), the elliptical cylinder develops to the ground surface. At this time, the vertical earth pressure is as shown in equation (26):

[0073]

[0074] Equations (25) and (26) do not consider the cohesion of the soil. If it is cohesive soil, the cohesion of the soil needs to be considered when establishing the force equilibrium conditions of the soil element, and the differential equation is listed as follows:

[0075]

[0076] The vertical stress of cohesive soil at different depths is obtained by integration using the same steps as for non-cohesive soil, as shown in equations (28) and (29).

[0077]

[0078]

[0079] When C = h, the critical burial depth Hcr for the force transmission mechanism of soil arches in both deep and shallow burial forms can be obtained:

[0080]

[0081] In a preferred embodiment of the present invention, in step 5, the obtained vertical earth pressure calculation formula is substituted into equation (13), and the ultimate support force of the excavation face can be obtained by combining the MATLAB program.

[0082] Compared with existing technologies, this invention provides a method for calculating the ultimate support force of tunnel excavation faces based on the overall analysis method, which has the following advantages:

[0083] 1. This invention applies the overall analysis method to the problem of excavation face stability and establishes a calculation model for excavation face stability. Based on the tunnel's depth, an elliptical cylinder-Pushman arch model considering the soil arching effect is established. The ultimate support force obtained by this invention shows a relatively consistent development trend with numerical simulation and existing theoretical results. Furthermore, the calculation time of the analytical solution of this invention is much shorter than that of numerical simulation, providing a new approach for the design of the ultimate support force of the excavation face.

[0084] 2. When the tunnel is shallow, the ultimate support pressure increases with increasing depth. However, when the depth is deep or the soil friction angle is large, the ultimate support pressure is almost no longer affected by the depth. The error between the numerical simulation and the actual simulation is small when the tunnel diameter is small. As the diameter increases, the error gradually increases, indicating that the model proposed in this invention is on the safe side and has a certain safety margin. The numerical simulation results show good agreement when the internal friction angle and cohesion are large. Attached Figure Description

[0085] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0086] Figure 1 This is a schematic diagram of the ultimate support force calculation model in this invention;

[0087] Figure 2 This is a schematic diagram of the forces acting on the differential strip in this invention;

[0088] Figure 3 This is a schematic diagram of the shallow-buried tunnel failure model in this invention;

[0089] Figure 4 This is a schematic diagram of the deep-buried tunnel failure model in this invention;

[0090] Figure 5 This is a schematic diagram of the vertical earth pressure calculation model in this invention;

[0091] Figure 6 This is a schematic diagram of the Pu-style arch micro-element in this invention;

[0092] Figure 7 This is a schematic diagram of the calculation model for the arch with high principal stress in this invention;

[0093] Figure 8 This is a schematic diagram of soil equilibrium in the loosened zone of medium-cohesive soil in this invention;

[0094] Figure 9 This is a schematic diagram of the numerical model established in Comparative Example 1;

[0095] Figure 10 This is a schematic diagram illustrating the effect of the burial diameter ratio C / D on the ultimate support pressure in Comparative Example 1.

[0096] Figure 11 This is a schematic diagram illustrating the effect of diameter D on ultimate support pressure in Comparative Example 1.

[0097] Figure 12 This is a schematic diagram illustrating the effect of the internal friction angle φ on the ultimate support pressure in Comparative Example 1.

[0098] Figure 13 This is a schematic diagram illustrating the effect of cohesion c on ultimate support pressure in Comparative Example 1.

[0099] Figure 14 This is a schematic diagram illustrating the effect of the burial diameter ratio C / D on the ultimate support pressure in Comparative Example 2.

[0100] Figure 15 This is a schematic diagram illustrating the effect of diameter D on ultimate support pressure in Comparative Example 2.

[0101] Figure 16 This is a schematic diagram illustrating the effect of cohesion c on ultimate support pressure in Comparative Example 2.

[0102] Figure 17 This is a schematic diagram illustrating the effect of the internal friction angle φ on the ultimate support pressure in Comparative Example 2.

[0103] Figure 18 This is a schematic diagram showing the results at different fracture angles in Comparative Example 3.

[0104] Figure 19 This is a schematic diagram comparing Comparative Example 3 with existing theories and centrifuge experiments. Detailed Implementation

[0105] To better understand the purpose, structure, and function of this invention, the following detailed description, in conjunction with the accompanying drawings, provides a more comprehensive account of the calculation method for the ultimate support force of the tunnel excavation face based on the overall analysis method.

[0106] like Figures 1-8 As shown, the calculation method for the ultimate support force of the tunnel excavation face based on the global analysis method includes the following steps:

[0107] Step 1: Propose a calculation model for the ultimate support force of the excavation face based on the overall analysis method;

[0108] Step 2: Based on the theoretical model, derive the calculation formula for the ultimate support force of the shield tunneling face;

[0109] Step 3: Propose a loosening zone model corresponding to the failure of a shield tunnel, which includes a shallow-buried shield tunnel failure model and a deep-buried shield tunnel failure model; and establish a calculation model of the major principal stress arch using a major principal stress rotation arc.

[0110] Step 4: Based on the two models proposed in Step 3, derive the formula for calculating vertical earth pressure;

[0111] Step 5: Combine the calculation formulas for the ultimate support force of the shield excavation face and the vertical earth pressure to obtain the ultimate support force of the excavation face.

[0112] Furthermore, the specific process of step 1 is as follows:

[0113] The calculation model for the ultimate support force of the excavation face based on the global analysis method (Zheng and Tham 2009) is as follows: Figure 1 As shown, the sliding failure zone Ω is assumed to be a planar region bounded by the outer contour line NOM and the potential slip surface MN. It is assumed that the normal stress on the slip surface follows a natural distribution, and the shear stress follows the Mohr-Coulomb criterion. The external forces acting on the sliding failure zone include body forces, surface forces, and stresses. Specifically: body forces include the vertical gravity W and the horizontal seismic force q; surface forces include the normal force acting on the outer contour line. and tangential force The model includes the shield support force σ perpendicular to the outer contour line NOM. T and vertical earth pressure σ V The tangential force f is parallel to NOM; the stresses are the normal stress σ(x) and shear stress τ(x) on the slip surface MN. The literature (Zheng and Tham 2009) defines normal stress as positive for compression and negative for tension. The positive direction of the outer contour line NOM is defined as follows: when moving along the outer contour line, the slip failure zone is located to the left of the outer contour line, and the shear stress is positive along the direction of the outer contour line and negative against the direction of the outer contour line.

[0114] Furthermore, in step 2, the process of deriving the calculation formula for the ultimate support force of the shield excavation face is as follows: take any three points where the sliding failure zones are not on the same straight line. If i = 1, 2, 3, the sum of the moments of the force system acting on the failure zone about these three points is 0, i.e.

[0115] ∫ S (Δx ci σdx+Δy ci σdy)+∫ S (Δx ci τdy-Δy ci τdx)+m ci =0 (1)

[0116] Where Δx ci and Δy ci It is a point on the slip surface MN. and The components to the point (x, y); m ci The active force acting on the sliding failure zone about the point The torque, that is:

[0117]

[0118] In formula (3) and These are the loads on the outer contour line NOM and the moments of the volumetric forces in the sliding failure zone about the center of moment, respectively:

[0119]

[0120]

[0121] To simplify the calculation, it is assumed that the volumetric forces in the sliding failure zone consist only of gravity and that seismic loads are not considered; in equation (4), (x gk y gk ) represents a subdomain Ω of the sliding failure zone Ω. k The centroid, w k =γ k A k Ω k The area of ​​the slip surface MN; assuming the slip surface MN satisfies the Mohr-Coulomb criterion, when the slip failure zone is in limit equilibrium, we have:

[0122]

[0123] In equation (5): F S For the safety factor, c e and f e The effective stress shear strength parameter is given, where u is the pore water pressure.

[0124] To describe the distribution of normal stress on the sliding surface MN, a differential strip FGHI with arc length dS is taken along the anti-slip direction of the sliding surface MN, as shown below. Figure 2 As shown, Figure 2 In the middle, d w and d q For the self-weight of the block and the horizontal seismic force; d v and d h For the force increment between vertical and horizontal bars; df x and df y The horizontal and vertical components of the load acting on the outer contour line NOM on the strip are, i.e.

[0125]

[0126] In equation (6): dx g and dy g Let HI be the arc length dS g Differentiating in the x and y directions, and projecting all force systems on the differential strip onto the normal direction of the sliding surface, we get:

[0127] σdS=dwcosα-dqsinα+dfx sinα-df y cosα+dvcosα-dhsinα (7)

[0128] In equation (7), α is the angle between FG on the differential strip and the x-axis, and h is the height of the center JK of the strip FGHI;

[0129] σ=σ(x)=σ0+σ I (8)

[0130] σ0 and σ I Let MN be the normal stress on the slip surface caused by the external load and the inter-strip force on the slip failure zone, respectively; where:

[0131]

[0132] In equation (9) The effect of volumetric forces in the sliding failure zone on the normal stress MN on the slip surface; The effect of the outer contour line NOM on the normal stress of the slip surface MN;

[0133] According to the literature (Zhang et al. 2018; Zheng and Tham 2009), the approximate formula for the normal stress of the slip surface is as follows:

[0134] σ=σ0+f(x,a,b) (10)

[0135] f(x,a,b)=al a (x)+bl b (x) (11)

[0136] In equation (11), f(x, a, b) is the correction function for the normal stress of the slip surface, a and b are undetermined coefficients, and l a (x), l b (x) is:

[0137]

[0138] In formula (12) and These are the x-coordinates of the bottom N point and the top O point of the shield tunnel excavation face, respectively.

[0139] According to the simplification of various formulas, we can obtain:

[0140] g(σ T ,a,b)=au1+bu2+u3+au4+bu5+u6+m ci =0 (13)

[0141] Equation (13) is about σ TThe system of three quadratic equations with variables a and b can be simplified to obtain the ultimate support force σ at the excavation face. T To solve for the ultimate support force at the shield excavation face in equation (13), the vertical earth pressure σ needs to be obtained beforehand. V ;

[0142] Numerous studies have shown that the soil arching effect must be considered when shield tunnels are buried at significant depths (Dewoolkar et al. 2007; Iglesia et al. 2014; Jun et al. 2011; Terzaghi 1943). The soil arching effect originated from Roberts' discovery of the "silo effect." Later, the renowned Russian mining scientist Protodyakonov proposed Protodyakonov's arch theory (Protodyakonov 1907), which has been widely applied in engineering. In 1943, Terzaghi (1936; Terzaghi 1943) confirmed the existence of the soil arching effect through movable gate tests. Terzaghi treated the soil slip surface failure model as a vertical plane and established a calculation model for vertical earth pressure (loose earth pressure). Numerous experiments have shown (Chambon and Corte 1994; Chen et al. 2013; Idinger et al. 2011; Kirsch 2010; Oblozinsky and Kuwano 2004; Takano et al. 2006a) that when the tunnel is shallow, the soil failure zone extends approximately vertically to the surface; once the tunnel reaches a certain depth, soil failure no longer extends to the surface. These studies suggest that Teszaky's loose earth pressure is no longer applicable in some excavation conditions. For the lateral earth pressure coefficient, Teszaky recommends a constant value of 1. Marston (Marston 1930) suggests using the active earth pressure coefficient K. a Calculations should be performed. Jaky (Jaky 1936), Pirapakaran et al. (Pirapakaran and Sivakugan 2007) suggested using the at-rest earth pressure coefficient K0 for calculations. Krynine (Krynine 1945) proposed that it is related to the internal friction coefficient of the soil layer and gave a calculation expression. This lateral earth pressure coefficient has been applied in subsequent studies (Coates (Coates 1966); Handy (Handy 1985)). Therefore, an appropriate lateral earth pressure coefficient should be selected for calculation based on the actual vertical earth pressure failure model to obtain the optimal method for calculating vertical earth pressure.

[0143] Furthermore, in step 3, in the shallow-buried shield tunnel failure model, the loosened area is an elliptical cylindrical loosened region that extends directly to the ground; in the deep-buried shield tunnel failure model, the loosened area can be divided into two parts: the lower part is an elliptical cylindrical shape, and the upper part is a rotating parabolic object. This rotating parabolic object is an arched region formed by the parabola rotating around an axis, which is set as a Protodyakonov-like arch calculation model.

[0144] Research results from model tests on the stability of the excavation face of shield tunnels in sandy soil strata (Chambon and Corte 1994; Chen et al. 2013; Idinger et al. 2011; Kirsch 2010; Oblozinsky and Kuwano 2004; Takano et al. 2006a) indicate that when the excavation face is under ultimate support, a nearly vertical banded shear strain concentration zone of a certain height will appear above the tunnel crown. If the tunnel depth is large, a potential loose collapse zone with an outer contour similar to a Protodyakonov pressure arch will appear above the banded area. Therefore, when the excavation face is under ultimate support, the soil arch above the tunnel crown does not exhibit a single form, but rather varies with the tunnel depth. Figure 3 and Figure 4 This is a model of the loosened zone corresponding to the failure of a shield tunnel. Figure 3 This is a failure model for a shallow-buried shield tunnel. The loosened area is a loosened region similar to an elliptical cylinder, which extends directly to the ground. Figure 4 For the failure model of a deeply buried shield tunnel, the loosened area can be divided into two parts: the lower part is an elliptical cylinder similar to that of a shallow-buried tunnel, and the upper part is a rotating parabolic body. This rotating body is an arched region formed by the rotation of a parabola around an axis, similar to the Protodyakonov arch model, and is set as a Protodyakonov-like arch calculation model.

[0145] Based on Protodyakov's assumption of pressure arches, the height h of the arch (Protodyakov 1907) and the height h2 of the elliptical cylinder (Wan et al. 2019) can be obtained.

[0146] Furthermore, in step 4, the specific process of deriving the formula for calculating vertical earth pressure is as follows: to calculate the compressive stress σ exerted by the soil above the arch on the soil below, the formula is... vk ( Figure 5 and Figure 6 As shown, consider a micro-element immediately above the soil mass adjacent to the arch-like structure. This micro-element has a thickness of dh, a span of L, and an arch height of f. The earth pressure acting on the micro-element is equivalent to a uniformly distributed load q acting over the entire span. It is assumed that the compressive stress σ exerted by the soil mass above the arch-like structure on the soil mass below is... vkTherefore, after the earth pressure redistribution through a similar arch, the vertical stress transmitted to the adjacent stationary soil on both sides is approximately: the weight of the upper soil γ(Ch) minus the vertical compressive stress σ. vk Therefore, the expression for the equivalent load q is:

[0147]

[0148] By employing the structural concept of an arch (Leontovich 1959; Wan et al. 2019), the lateral thrust dF under a uniformly distributed load q can be obtained. h for:

[0149]

[0150] Therefore, the compressive stress of the soil after stress redistribution due to the combined action of vertical stress and self-weight is:

[0151]

[0152] Calculation of lateral pressure coefficient:

[0153] The relative sliding of the soil causes a significant deflection in the direction of the principal stresses, thus having a substantial impact on the collapse pressure at the tunnel excavation face. The effect of this deflection in the direction of the principal stresses is primarily reflected in the lateral pressure coefficient K between the moving soil and adjacent soil masses. h And in terms of the stress distribution in the soil, this invention uses the major principal stress rotation arc (Chen et al. 2014; Wan et al. 2019) to establish a calculation model (such as...). Figure 7 As shown), its calculation equation is:

[0154]

[0155] By arbitrarily selecting a soil element along the trajectory line and performing a force analysis, the vertical stress σ can be obtained from the force equilibrium condition. v and horizontal stress σ h As shown in the following formula:

[0156] σ v =σ1sin 2 θ+σ3cos 2 θ (18)

[0157] σ h =σ1cos 2 θ+σ3sin 2 θ (19)

[0158] The average vertical earth pressure within the damaged area can be obtained:

[0159]

[0160] Define the vertical stress distribution coefficient m as:

[0161]

[0162] According to the Mohr-Coulomb criterion, the upward shear stress τ acting on the boundary of the infinitesimal element is:

[0163]

[0164] The lateral pressure coefficient K acting on the sliding surface can be obtained. h for:

[0165]

[0166] In equation (23), Where θ0 is the fracture surface angle; in their studies (Chen et al. 2014; Cheng et al. 2019; Qin 2005), the fracture angle was defined as... Calculations were performed. Experimental results from some scholars (Idinger et al. 2011; Lü et al. 2018) show that the fracture angle of loose sand tunnels is close to... Other scholars (Chambon and Corte 1994; Cheng et al. 2021; Dziuban et al. 2018; Kirsch 2010; Tang et al. 2013) obtained results through dense sand tests that were significantly greater than... They obtained the range of variation related to the internal friction angle. Referring to existing studies (Chambon and Corte 1994; Cheng et al. 2021; Dziuban et al. 2018), the range of values ​​for this fracture angle is often considered to be... Therefore, it is necessary to further study the value of the fracture angle in order to obtain a suitable ultimate support force for the excavation face.

[0167] Derivation of the formula for calculating vertical earth pressure:

[0168] Assuming the overburden soil layer is homogeneous and cohesive, satisfying the Mohr-Coulomb failure criterion; Figure 5 As shown, consider an infinitesimal element of thickness dz at an arbitrary depth z above the ground within the height range of the elliptical cylindrical arch. Its width is L, soil weight is γ, internal friction angle is φ, and Kh is the lateral pressure coefficient considering the deflection of the major principal stress direction. Solving for the vertical direction of the element, we obtain:

[0169]

[0170] When the burial depth is large, the soil failure zone does not extend to the surface. At this time, the soil arching effect mechanism, composed of a Protodyakonov-like arch and an elliptical cylinder, comes into play. The vertical stress at any depth z from the surface within the soil failure zone of the elliptical cylinder arch can be obtained as shown in equation (25):

[0171]

[0172] When the burial depth is shallow (i.e., h ≥ C, where C is the tunnel burial depth), the elliptical cylinder develops to the ground surface. At this time, the vertical earth pressure is as shown in equation (26):

[0173]

[0174] Equations (25) and (26) do not consider the cohesion of the soil. If it is cohesive soil, the cohesion of the soil needs to be considered when establishing the force equilibrium conditions of the soil element, such as... Figure 8 As shown, the differential equation is listed:

[0175]

[0176] The vertical stress of cohesive soil at different depths is obtained by integration using the same steps as for non-cohesive soil, as shown in equations (28) and (29).

[0177]

[0178]

[0179] When C = h, the critical burial depth Hcr for the force transmission mechanism of soil arches in both deep and shallow burial forms can be obtained:

[0180]

[0181] Furthermore, in step 5, the obtained vertical earth pressure calculation formula is substituted into equation (13), and the ultimate support force of the excavation face can be obtained by combining it with the MATLAB program.

[0182] Comparative Example 1

[0183] Numerical simulation is widely used in the study of tunnel excavation face stability (Li et al. 2022; Li et al. 2020; Qiu et al. 2022; Saadat and Taheri 2019; Zhang et al. 2020). The numerical model established in this invention is as follows: Figure 9 As shown, the tunnel diameter D, the depth-to-diameter ratio C / D, and the internal friction angle are discussed. The influence of cohesion *c* on the ultimate support force was investigated. The boundary conditions were as follows: the upper surface was a free boundary, the lateral boundaries were normally constrained, and the bottom was a fixed constraint. The Mohr-Coulomb failure criterion was adopted, and the unit weight γ was 18 kN / m³. 3 The elastic modulus is 20 MPa, the Poisson's ratio is 0.35, and there is no overload on the ground surface.

[0184] Shield tunneling is a gradual process. To focus on analyzing the stability of the tunnel excavation face, a simplified single-step excavation method is used to simulate the excavation process (excavation length 25m). Fixed constraints are applied to each node of the excavated tunnel to simulate tunnel support. Based on the needs of the problem analysis and considering the avoidance of unnecessary influences from boundaries, the model built in this invention is 50m long along the tunnel excavation direction; in the longitudinal direction of the tunnel, the distance from the model boundary to the outer contour of the tunnel is 3D (half of the model is selected for calculation); the distance from the bottom of the tunnel invert to the lower boundary of the model is 4D. When solving for the ultimate support force, a support force σ, the same as the original horizontal ground stress at the center point of the excavation face, is first applied. T Then, the support force is gradually reduced to obtain the relationship curve between the horizontal displacement of the center point of the excavation face and the support force. When the support force of the excavation face is reduced to a certain value, the horizontal displacement of the center point of the excavation face increases sharply. This support force value is the ultimate support force.

[0185] like Figures 10-13 As shown, the ultimate support force obtained by the method of this invention under different burial depths, diameters, internal friction angles, and cohesion factors (the fracture angle range is indicated above). Because the trend of change is linear, the fracture angle is selected. and A comparison of the two scenarios with the numerical simulation results reveals that both exhibit similar development trends as the influencing factors change. Figure 10 Comparing the results of this invention with numerical simulation results at different burial depths, it can be found that when other parameters are fixed, the ultimate support force first increases and then remains constant with the increase of burial depth, with a maximum error of 28.73%. The results are closer to those of numerical simulation. Figure 11 Comparing the results of this invention with numerical simulation results for different tunnel diameters, it can be found that when other parameters are fixed, the ultimate support force increases linearly with the increase of diameter. The results are closer to the numerical simulation. and The results are quite close. The error between the two is small when the tunnel diameter is small (minimum 13.37%). As the diameter increases, the error between the two gradually increases (maximum 19.36%), indicating that the calculation model proposed in this invention is biased towards safety and has a certain safety margin.

[0186] Figure 12By comparing the results of this invention with the numerical simulation results under different internal friction angles, it can be found that when other parameters are fixed, the ultimate support force decreases continuously with the increase of the internal friction angle. The error between the two is large when the internal friction angle is small, and small when the internal friction angle is greater than 20°. Figure 13 Comparing the results of this invention with numerical simulation results under different cohesion, it can be found that when other parameters are fixed, the ultimate support force decreases continuously with the increase of cohesion, showing a linear decrease. Similar to the results of the internal friction angle, the results of the two fracture angles are basically consistent. The error is larger when the cohesion is small (maximum 34.22%), and smaller when the cohesion is large.

[0187] Comparative Example 2

[0188] Figures 14-17 The ultimate support force obtained by the method of this invention (still selecting the fracture angle) under different burial depths, diameters, internal friction angles, and cohesion factors. and The results of this invention (in both cases) are compared with existing theoretical results (Anagnostou and Kovári 1994; Leca and Dormieux 1990; Mollon et al. 2009; Zhang et al. 2015). It can be found that, with changes in influencing factors, the results of this invention and existing theoretical results show a basically similar development trend. Figure 14 By comparing the results of this invention with existing theoretical results at different burial depths, it can be found that the results of this invention are consistent with the trend of the limit analysis method. Moreover, both this invention and the limit equilibrium method (Anagnostou and Kovári 1994) are greater than the limit analysis method, and are more inclined to safety. Figure 15 Comparing the results of this invention with existing theoretical results for different tunnel diameters, it can be found that when other parameters are fixed, the ultimate support force increases continuously with the increase of diameter, and all show a linear increase. The results of this invention are close to those of the limit analysis method (Leca and Dormieux 1990; Mollon et al. 2009), and are both smaller than those in the literature (Anagnostou and Kovári 1994; Zhang et al. 2015). Figure 16Comparing the results of this invention with existing theoretical results under different internal friction angles, it can be found that when other parameters are fixed, the ultimate support force decreases continuously with the increase of the internal friction angle. When the internal friction angle is small, the results of this invention are all smaller than those of other methods. When the internal friction angle is greater than 20°, the results of this invention are close to those of the limit analysis method (Leca and Dormieux 1990; Mollon et al. 2009; Zhang et al. 2015) and are all smaller than those of the limit equilibrium method (Anagnostou and Kovári 1994). The results of this invention show a smaller trend of change compared with other results. Figure 17 Comparing the results of this invention with existing theoretical results under different cohesion forces, it can be found that when other parameters are fixed, the ultimate support force decreases linearly with the increase of cohesion. When the cohesion is low, the results of this invention are lower than those of other methods; however, as the cohesion increases, the results of this invention gradually approach those in the literature (Zhang et al. 2015). Consistent with the influence of the internal friction angle, the results of this invention show a smaller trend of change compared to other results.

[0189] Comparative Example 3

[0190] like Figure 18 and Figure 19 The figure shows a comparison between the results of this invention and existing theoretical results (Anagnostou and Kovári 1994; Leca and Dormieux 1990; Li et al. 2020; Mollon et al. 2009; Soubra 2008) and centrifugation experiment results (Idinger et al. 2011). The prototype tunnel has D = 5m and γ = 15kN / m. 3 , When C / D = 1.5, the ultimate support force is 8.5 kPa. Figure 18 Different fracture angles are given Comparison of the lower limit support force and centrifuge results. It can be observed that as θ0 increases, the lower limit support force initially decreases slowly, then the rate of decrease gradually increases, and the fracture angle... and The values ​​between these ranges reach the results of the centrifugation test. When the rupture angle... At that time, the results of the present invention were slightly better than those of the centrifugation test, with a maximum error of [missing value]. 7.87% at the time. When the fracture angle When the error of the centrifuge test was within 5%, the results were consistent with the analysis in existing literature (Chambon and Corte 1994; Cheng et al. 2021; Dziuban et al. 2018), verifying the correctness of the results of this invention. Figure 19 The results show that the results of this invention are smaller than those of the limit equilibrium method (Anagnostou and Kovári 1994) and larger than those of the limit analysis (Leca and Dormieux 1990; Li et al. 2020; Mollon et al. 2009; Soubra 2008). The fracture angle of this invention is [value missing]. and At that time, the errors from the experimental results were 1.31% and 0.996%, respectively, which were closest to the centrifugation test results. The rupture angle was... When the value is greater than that of the centrifugation test, it is safer, which verifies that the destruction mechanism of the present invention has better accuracy and superiority.

[0191] To analyze the stability of the excavation face of a shield tunnel, this invention establishes a calculation model for the ultimate support force of the excavation face based on the overall analysis method and considering the influence of soil arching. Then, the results of this invention are compared with those obtained from existing theories, numerical simulations, and centrifuge tests. The comparison with existing theories and centrifuge tests verifies the effectiveness of this invention.

[0192] The main conclusions are as follows:

[0193] 1. This invention applies the holistic analysis method to the problem of excavation face stability, establishing a calculation model for excavation face stability. Based on the tunnel's depth, an elliptical cylinder-Przewalski's arch model considering the soil arching effect is established. The ultimate support force obtained by the model of this invention shows a relatively consistent development trend with numerical simulation and existing theoretical results. Furthermore, the computation time of the analytical solution of this invention is much shorter than that of numerical simulation. This method provides a new approach for the design of the ultimate support force of the excavation face.

[0194] 2. When the tunnel is shallow, the ultimate support pressure increases with increasing depth. However, when the depth is deep or the soil friction angle is large, the ultimate support pressure is almost no longer affected by the depth. The error between the numerical simulation and the actual simulation is small when the tunnel diameter is small. As the diameter increases, the error gradually increases (maximum 19.36%), indicating that the model proposed in this invention is on the safe side and has a certain safety margin. The numerical simulation results show good agreement when the internal friction angle and cohesion are large.

[0195] 3. Under varying burial depth, the results of this invention and the limit equilibrium method are both superior to those of the limit analysis method, indicating a greater degree of safety. Under varying diameter, the results of this invention show a similar trend to existing theories, exhibiting a linear increase. When the internal friction angle is greater than 20°, the results of this invention are closer to those of the limit analysis method, verifying the correctness of the results. When the cohesion is low, the results of this invention are lower than other methods; however, as the cohesion increases, the results become closer to those of the limit analysis method. Consistent with the influence of the internal friction angle, the results of this invention show a smaller trend of change compared to other results.

[0196] 4. Compared with other theoretical results, the results of this invention are closest to those of centrifugation experiments. When the rupture angle... At that time, the error compared to the centrifuge test was within 5%, and greater than that of the centrifuge test ( When the error is minimized to 1.31%, the method proposed in this invention is verified to be safe and accurate, and can provide a theoretical basis for similar projects.

[0197] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for calculating the ultimate support force of a tunnel excavation face based on the overall analysis method, characterized in that: Includes the following steps: Step 1: Propose a calculation model for the ultimate support force of the excavation face based on the overall analysis method; Step 2: Based on the theoretical model, derive the calculation formula for the ultimate support force of the shield tunneling face; Step 3: Propose a loosening zone model corresponding to the failure of a shield tunnel, which includes a shallow-buried shield tunnel failure model and a deep-buried shield tunnel failure model; and establish a calculation model of the major principal stress arch using a major principal stress rotation arc. Step 4: Based on the two models proposed in Step 3, derive the formula for calculating vertical earth pressure; Step 5: Combine the calculation formulas for the ultimate support force of the shield excavation face and the vertical earth pressure to obtain the ultimate support force of the excavation face; The specific process of step 1 is as follows: Assume that the sliding failure zone Ω is a planar region bounded by the outer contour line NOM and the potential slip surface MN; Assume that the normal stress on the slip surface follows a natural distribution, and the shear stress follows the Mohr-Coulomb criterion; The external forces acting on the sliding failure zone include body forces, surface forces, and stresses. Body forces include the vertical gravity W and the horizontal seismic force q; surface forces include the normal force acting on the outer contour line. and tangential force ; The model includes the shield support force σT and vertical earth pressure σV perpendicular to the outer contour line NOM, and the tangential force f parallel to NOM; the stresses are the normal stress σ(x) and shear stress τ(x) on the slip surface MN.

2. The method for calculating the ultimate support force of a tunnel excavation face based on the overall analysis method according to claim 1, characterized in that: In step 2, the process of deriving the calculation formula for the ultimate support force of the shield excavation face is as follows: take any 3 points where the sliding failure zone is not on the same straight line ( , ), i=1, 2, 3, the sum of the moments of the force system acting on the failure zone about these 3 points is 0, that is （1）； in and It is a point on the slip surface MN. and The component that reaches the point (x, y); The active force acting on the sliding failure zone about point ( , The torque of ), that is: （2）； and These are the loads on the outer contour line NOM and the moments of the volumetric forces in the sliding failure zone about the center of moment, respectively: （3）； （4）； Assuming the volumetric forces in the sliding failure zone consist only of gravity and seismic loads are not considered; in equation (4), ( , ) represents a subdomain Ω of the sliding failure zone Ω. k The centroid; assuming the slip surface MN satisfies the Mohr-Coulomb criterion, when the slip failure zone is in limit equilibrium, we have: （5）； In equation (5): F S For the safety factor, c e and f e The effective stress shear strength parameter is given, where u is the pore water pressure. To describe the distribution of normal stress on the sliding surface MN, a differential slice FGHI with arc length dS is considered along the anti-slip direction of the sliding surface MN. The slice's self-weight and horizontal seismic force are d. w and d q The force increment between the vertical and horizontal bars is d. v and d h The horizontal and vertical components of the load acting on the outer contour line NOM on the block are df. x and df y ,Right now ， （6）； In equation (6): dx g and dy g Let HI be the arc length dS g Differentiating in the x and y directions, and projecting all force systems on the differential strip onto the normal direction of the sliding surface, we get: （7）； In equation (7), α is the angle between FG on the differential strip and the x-axis, and h is the height of the center JK of the strip FGHI; （8）； and Let MN be the normal stress on the slip surface caused by the external load and the inter-strip force on the slip failure zone, respectively; where: （9）； In equation (9) The effect of volumetric forces in the sliding failure zone on the normal stress MN on the slip surface; The effect of the outer contour line NOM on the normal stress of the slip surface MN; The approximate formula for the normal stress of the slip surface is: （10）； （11）； In equation (11), f(x, a, b) is the correction function for the normal stress of the slip surface, a and b are undetermined coefficients, and l a (x), l b (x) is: ， （12）； In equation (12) and These are the x-coordinates of the bottom N point and the top O point of the shield tunnel excavation face, respectively. According to the simplification of various formulas, we can obtain: （13）； Equation (13) is about σ T By simplifying the three quadratic equations in variables a and b, we can obtain the ultimate support force σ at the excavation face. T .

3. The method for calculating the ultimate support force of a tunnel excavation face based on the overall analysis method according to claim 2, characterized in that: In step 3, the loosening area of ​​the shallow-buried shield tunnel failure model is an elliptical cylindrical loosening area that extends directly to the ground; the loosening area of ​​the deep-buried shield tunnel failure model is divided into two parts: the lower part is elliptical cylindrical, and the upper part is a rotating parabolic object. This rotating parabolic object is an arched area formed by the parabola rotating around an axis, which is set as a Protodyakonov-like arch calculation model.

4. The method for calculating the ultimate support force of a tunnel excavation face based on the overall analysis method according to claim 3, characterized in that: In step 4, the specific process of deriving the formula for calculating vertical earth pressure is as follows: Assuming the compressive stress σ exerted by the soil above the arched region on the soil below... vk Consider a micro-element above the adjacent arch-like soil body. The thickness of the micro-element is dh, the span is L, and the arch height is f. The earth pressure acting on the micro-element is equivalent to a uniformly distributed load q acting on the entire span. Assuming the compressive stress σ exerted by the soil above the arched region on the soil below... vk Therefore, after the earth pressure redistribution through a similar arch, the vertical stress transmitted to the adjacent stationary soil on both sides is approximately: the weight of the upper soil γ(Ch) minus the vertical compressive stress σ. vk Therefore, the equivalent load q 等效 The expression is: （14）； Lateral thrust dF under uniformly distributed load q h for: （15）； Therefore, the compressive stress of the soil after stress redistribution due to the combined action of vertical stress and self-weight is: （16）； During tunnel excavation, the relative sliding of the soil causes a significant deflection in the direction of the principal stress of the soil, which has a significant impact on the collapse pressure at the tunnel excavation face. The impact of the deflection of the direction of the principal stress of the soil is mainly reflected in the lateral pressure coefficient Kh between the moving soil and adjacent different soils, as well as the stress distribution pattern in the soil. The calculation equations for the arch calculation model with high principal stress are as follows: ; By arbitrarily selecting a soil element along the trajectory line and performing a force analysis, the vertical stress σ can be obtained from the force equilibrium condition. v and horizontal stress σ h As shown in the following formula: （18）； （19）； Obtain the average vertical earth pressure within the damaged area: （20）； Define the vertical stress distribution coefficient m as: （21）； According to the Mohr-Coulomb criterion, the upward shear stress τ acting on the boundary of the infinitesimal element is: （22）； The lateral pressure coefficient K acting on the sliding surface can be obtained. h for: （23）； In equation (23), Where θ0 is the angle of the fracture surface; Assuming the overburden layer of the tunnel is homogeneous, cohesionless soil satisfying the Mohr-Coulomb failure criterion; considering an infinitesimal element of thickness dz at an arbitrary depth z above the ground within the height range of the elliptical arch; with span L, soil weight γ, internal friction angle φ, and Kh being the lateral pressure coefficient considering the deflection of the major principal stress direction; solving for the vertical direction of the element yields: （24）； When the burial depth is large, the soil failure zone does not extend to the surface; at this time, the soil arching effect mechanism, composed of a Protodyakonov-like arch and an elliptical cylinder, comes into play; the vertical stress at any depth z from the surface within the elliptical cylinder arch soil failure zone is shown below: （25）； When the burial depth is shallow, i.e., h ≥ C, where C is the tunnel burial depth, the elliptical cylinder develops to the ground surface; at this time, the vertical earth pressure is as follows: （26）； Equations (25) and (26) do not consider the cohesion of the soil. If it is cohesive soil, the cohesion of the soil needs to be considered when establishing the force equilibrium conditions of the soil element. The differential equation is as follows: （27）； The vertical stress at both shallow and deep burial depths in cohesive soil is obtained by integration using the same steps as for non-cohesive soil, as shown below: （28）； （29）； When C=h, the critical burial depth H is obtained for the force transmission mechanism of soil arches in both deep and shallow burial forms. cr : （30）。 5. The method for calculating the ultimate support force of a tunnel excavation face based on the overall analysis method according to claim 4, characterized in that: In step 5, the obtained vertical earth pressure calculation formula is substituted into equation (13), and the ultimate support force of the excavation face can be obtained by combining it with the MATLAB program.

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