Longitudinal slope non-uniform rectangular tunnel surface support pressure calculation method

Abstract

The invention belongs to the technical field of tunnel construction, and relates to a longitudinal slope non-uniform rectangular tunnel surface support pressure calculation method, which comprises the following steps: adjusting an included angle between a wedge and a working surface in a six-block silo-wedge model based on the gradient of a tunnel to be tunneled to obtain an upslope optimization model; on the basis of a stress system of the rectangular pyramid wedge-shaped body and the triangular prism wedge-shaped body in the tunneling process, a mechanical equation of the rectangular pyramid wedge-shaped body in the tunneling process and a mechanical equation of the triangular prism wedge-shaped body in the tunneling process are constructed, and then a critical support pressure control equation representing the working face stability in the tunneling process is obtained; constructing a support pressure equation of the soil cabin partition plate by utilizing a stress balance principle of a soil cabin soil body along a tunneling slope direction; and calculating the supporting pressure of the soil cabin partition plate in real time by utilizing a supporting pressure equation of the soil cabin partition plate based on the tunneling gradient, the burial depth, the working face width, the working face height and the wedge-shaped body sliding face inclination angle in the tunneling process so as to judge whether the working face is stable in the tunneling process of the to-be-tunneled tunnel.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel construction, in particular to a method for calculating the support pressure of a rectangular tunnel surface with non-uniform longitudinal slope. Background Art

[0002] In order to ensure construction safety and improve construction efficiency during tunnel construction, a model is often constructed to simulate the soil damage area to simulate the mechanical behavior and failure mode of the soil during tunnel construction. By analyzing the force acting on the model during excavation, a support force equation acting on the model during excavation is constructed. This support force equation is used as the soil compartment diaphragm support force equation on the shield machine during actual construction. Based on this equation, the support force of the soil compartment diaphragm during excavation can be calculated in real time. When operating the shield machine for excavation, engineers can adjust the excavation parameters to ensure that the support force of the soil compartment diaphragm can reach the support force level that maintains soil stability, thereby preventing soil instability during construction, ensuring the stability of the tunnel during construction, and reducing safety hazards caused by insufficient support.

[0003] The existing models for simulating soil damage areas during tunnel construction include the six-block silo-wedge model and the uphill silo-wedge model. Figure 1 The figure shows a schematic diagram of the six-block silo-wedge model. Figure 2 Shown is a schematic diagram of the uphill silo-wedge model. The two models share the following similarities when simulating tunnel excavation faces: 1. In terms of structural characteristics, both use a silo-wedge composite structure, with the upper prism representing the overlying soil at the top of the rectangular tunnel, extending to the surface to form a three-dimensional soil slip surface; 2. In terms of geometric parameters, both models have the same excavation face geometry and the same slider bottom inclination angle, resulting in similar sliding surface mechanical mechanisms. The differences between the two are as follows: 1. In the six-block silo-wedge model, the lower triangular prism wedge (ii) is subjected to the soil chamber pressure, the pressure provided by the soil above, and the friction on the left and right quadrangular pyramid wedges (i and iii) and the inclined surface. The quadrangular pyramid wedges (i and iii) are subjected to the soil chamber pressure, the pressure of the overlying soil provided by the upper prism, the friction resistance on the outer contact surface, the inner contact surface and the bottom inclined surface, and their own weight. In the uphill silo-wedge model, the lower wedge is subjected to the support pressure, the vertical pressure on the top of the wedge, the normal force on the sliding surface and the corresponding friction resistance, the friction resistance on the two side surfaces, and the wedge's own weight.

[0004] Based on the above analysis, it can be seen that the uphill silo-wedge model cannot consider the non-uniform distribution of support pressure on the excavation face. It simplifies the lower wedge into a single rigid block, resulting in the neglect of frictional resistance between areas with different support pressures. Therefore, it is difficult to accurately simulate the support force required for different areas of soil damage during construction. In addition, it is also impossible to accurately calculate the support force of the shield machine's soil compartment partition during actual construction. Therefore, it cannot provide an accurate reference for adjusting the excavation parameters during excavation and it is difficult to ensure the stability of the tunnel during excavation. The six-block silo-wedge model assumes that the construction tunnel is a horizontal tunnel when it is constructed. Therefore, when constructing the model, the wedge is set flush with the working face. As a result, the model can only consider the soil stress and damage in the horizontal direction when simulating the excavation process. However, in actual construction, tunnels often have a certain slope due to terrain and route planning. If the six-block silo-wedge model is directly used to simulate the excavation process, it is difficult to accurately simulate the actual stress conditions under the influence of slope, making it difficult to construct an accurate wedge support force equation, which in turn affects the support of the soil compartment partition during actual construction. In addition, during the construction of a sloped tunnel, the support force in the soil compartment partition force system is not completely equal to the support force during model simulation due to the tunnel slope. Instead, it is affected by the component of the soil compartment partition's deadweight along the tunnel slope. Therefore, the existing six-block silo-wedge model can only be used to obtain the support force required during horizontal tunnel excavation, but cannot accurately obtain the support force required to maintain soil stability during slope tunnel excavation. As a result, it cannot provide an accurate reference for adjusting the excavation parameters during the excavation process, making it difficult to ensure the stability of the tunnel during excavation.

[0005] In summary, the existing tunnel excavation methods cannot accurately obtain the support force required to maintain soil stability during the excavation of a sloped tunnel, and thus cannot avoid the problem of soil instability during the construction of a sloped tunnel. Summary of the Invention

[0006] To this end, the technical problem to be solved by the present invention is to overcome the problem that the tunnel excavation method in the existing technology cannot accurately obtain the support force required to maintain soil stability during the excavation of a sloped tunnel, and thus cannot avoid the problem of soil instability during the construction of a sloped tunnel.

[0007] To solve the above technical problems, the present invention provides a method for calculating the support pressure of a rectangular tunnel face with non-uniform longitudinal slope, comprising:

[0008] Based on the slope of the tunnel to be excavated, the angle between the wedge and the working surface in the six-block silo-wedge model used to simulate the tunnel soil failure area is adjusted to obtain the upslope optimization model of the tunnel to be excavated.

[0009] Based on the force system of the quadrangular pyramid wedge and triangular prism wedge in the upslope optimization model during the excavation process, the mechanical equations of the quadrangular pyramid wedge and the triangular prism wedge during the excavation process are constructed;

[0010] Based on the mechanical equations of a quadrangular pyramid wedge and a triangular prism wedge during tunneling, the critical support pressure control equation that characterizes the stability of the working face during tunneling is obtained.

[0011] Using the force balance principle of the soil in the upslope optimization model along the excavation slope during excavation, the support pressure equation for the soil compartment diaphragm was constructed based on the soil deadweight and the support pressure equation acting on the wedge during excavation.

[0012] The support pressure equation of the soil compartment diaphragm is used to calculate the support pressure of the soil compartment diaphragm in real time based on the excavation slope, burial depth, working face width, height and inclination angle of the wedge sliding surface during the excavation process. This is used to determine whether the working face is stable during the excavation of the tunnel to be excavated, and thus adjust the excavation parameters.

[0013] Preferably, the process of constructing the mechanical equation of the quadrangular pyramid wedge during the excavation process includes:

[0014] The stress analysis of the pyramid wedge was conducted. Based on the principle of force balance of the pyramid wedge during excavation, the vertical load equation of the overlying soil column, the relationship equation between the normal force and friction resistance of the base sliding surface, the relationship equation between the normal force and friction resistance of the outer contact surface, the support pressure equation of the working face, and the deadweight load equation of the pyramid wedge were constructed.

[0015] Based on the bidirectional static equilibrium conditions, a bidirectional static equilibrium equation group is constructed for the mechanical equations of the tetrahedral wedge during the excavation process; the bidirectional static equilibrium equation group is solved to obtain the normal force equation and friction force equation of the inner contact surface of the tetrahedral wedge during the excavation process.

[0016] Preferably, the vertical load equation of the overlying soil column on the quadrangular pyramid wedge during the excavation process is expressed as:

[0017]

[0018] Where P1 represents the vertical load of the overlying soil column on the pyramid wedge during the excavation process; γ represents the soil bulk density; C represents the depth of the tunnel to be excavated; σ s represents the surface load; L represents the width of the working face of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge;

[0019] The relationship between the normal force and friction resistance of the base sliding surface is expressed as:

[0020]

[0021] Wherein, T1 represents the friction resistance of the base sliding surface; c represents the cohesion of the soil of the tunnel to be excavated; N1 represents the normal force of the base sliding surface; It represents the soil friction angle of the tunnel to be excavated;

[0022] The relationship equation between the normal force and friction resistance of the outer contact surface is expressed as:

[0023]

[0024]

[0025] Where, N3 represents the normal force of the outer contact surface; K0 represents the static earth pressure coefficient, σ z represents the vertical stress on the lateral sliding surface, σ z =γC+γz, where z represents the integral variable;

[0026] The support pressure equation of the working face is expressed as:

[0027]

[0028] Among them, S1 represents the support pressure of the working face; s1 represents the support pressure acting on the excavation surface of the quadrangular wedge during excavation. K a represents the active earth pressure coefficient,

[0029] The self-weight load equation of the quadrangular pyramid wedge is expressed as:

[0030]

[0031] Where G1 represents the deadweight load of the tetrahedral wedge; V1 represents the volume of the tetrahedral wedge;

[0032] The two-way static equilibrium equations are expressed as:

[0033]

[0034] Among them, T 21 represents the friction resistance of the inner contact surface of the quadrangular pyramid wedge during the excavation process; α represents the base angle of the mid-waist trapezoidal surface of the overlying soil part of the upslope optimization model;

[0035] The normal force equation of the inner contact surface of the quadrangular pyramid wedge during the excavation process is expressed as:

[0036] N 21 =(P1+G1)cosθ+S1sinθcosβ-S1sinβcosθ-N3cosαsinθ,

[0037] Among them, N 21 It represents the normal force on the inner contact surface of the quadrangular pyramid wedge during the excavation process;

[0038] The friction equation of the inner contact surface of the quadrangular pyramid wedge during the excavation process is expressed as:

[0039] T 21 =-P1sinθ-G1sinθ-N3cosαcosθ+T3sinα+T1+S1cosθcosβ+S1sinθsinβ.

[0040] Preferably, the process of constructing the mechanical equation of the triangular prism wedge during the excavation process includes:

[0041] The force analysis of the triangular prism wedge was conducted. Based on the force balance principle of the triangular prism wedge during the excavation process, the vertical stress equation of the overlying soil column, the relationship equation between the normal force and friction resistance of the base contact surface, the support reaction force equation of the working face, the normal force equation and friction resistance equation of the symmetrically distributed lateral contact surface, and the deadweight load equation of the triangular prism wedge were constructed.

[0042] A set of spatial equilibrium equations is constructed based on the normal force equation and friction force equation of the symmetrically distributed lateral contact surface; the normal force equation and friction force equation of the lateral contact surface of the triangular prism wedge during the excavation process are obtained by solving the spatial equilibrium equation.

[0043] Preferably, the vertical stress equation of the overlying soil column to which the triangular pyramid wedge is subjected during the excavation process is expressed as:

[0044] P2=σ v BDcosβ(cotθ+tanβ),

[0045] Where P2 represents the vertical stress of the overlying soil column on the triangular pyramid wedge during the excavation process; σ v represents the Terzaghi loosening earth pressure, R represents the ratio of the overlying soil volume to the lateral area, γ represents the soil bulk density, K0 represents the static earth pressure coefficient, c represents the soil cohesion of the tunnel to be excavated, represents the soil friction angle of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge;

[0046] The relationship equation between the normal force and friction resistance of the substrate contact surface is expressed as:

[0047]

[0048] Wherein, T2 represents the friction resistance of the substrate contact surface; N2 represents the normal force of the substrate contact surface;

[0049] The support reaction equation of the working face is expressed as:

[0050] S2=σ s2 BD,

[0051] Among them, S2 represents the support reaction force of the working face; σ s2 represents the critical support pressure;

[0052] The normal force equation and friction resistance equation for the symmetrically distributed lateral contact surface are expressed as:

[0053]

[0054] Among them, T 12 represents the friction resistance of the first lateral contact surface of the triangular prism wedge; T 32 Indicates the friction resistance of the second lateral contact surface of the triangular prism wedge; N 12 Represents the normal force on the first lateral contact surface of the triangular prism wedge; N 32 represents the normal force on the second lateral contact surface of the triangular prism wedge;

[0055] The self-weight load equation of the triangular prism wedge is expressed as:

[0056]

[0057] Where G2 represents the deadweight load of the triangular prism wedge; V2 represents the volume of the triangular prism wedge;

[0058] The spatial equilibrium equations are expressed as:

[0059]

[0060] The normal force equation of the lateral contact surface of the triangular prism wedge during the excavation process is expressed as:

[0061]

[0062] The friction equation of the lateral contact surface of the triangular prism wedge during the excavation process is expressed as:

[0063] N 12 =(P2+G2)cosθ+S2sinθcosβ-S2sinβcosθ.

[0064] Preferably, the critical support pressure control equation is expressed as:

[0065]

[0066] Among them, σ s2 represents the critical support pressure; γ represents the soil bulk density; C represents the depth of the tunnel to be excavated; σ s represents the surface load; L represents the width of the working face of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge; K0 represents the static earth pressure coefficient, c represents the soil cohesion of the tunnel to be excavated, K represents the soil friction angle of the tunnel to be excavated; a represents the active earth pressure coefficient, R represents the ratio of the overlying soil volume to the lateral area, α represents the base angle of the mid-waist trapezoidal surface in the overlying soil part of the upslope optimization model.

[0067] Preferably, the supporting pressure equation of the soil compartment diaphragm is expressed as:

[0068]

[0069] Among them, σ t0 represents the supporting pressure of the soil compartment partition; γ represents the soil bulk density; C represents the burial depth of the tunnel to be excavated; σ s represents the surface load; L represents the width of the working face of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge; K0 represents the static earth pressure coefficient, c represents the soil cohesion of the tunnel to be excavated, represents the soil friction angle of the tunnel to be excavated; K a represents the active earth pressure coefficient, R represents the ratio of the overlying soil volume to the lateral area, α represents the bottom angle of the medium waist trapezoidal surface of the overlying soil part of the upslope optimization model; η represents the inverse of the loose coefficient of the soil in the soil compartment, K represents the looseness coefficient of the soil in the soil compartment; w represents the thickness of the soil in the soil compartment.

[0070] Preferably, obtaining the support pressure equation of the soil compartment partition also includes solving the support pressure equation of the soil compartment partition based on extreme value theory to obtain the maximum support pressure of the soil compartment partition, and using the maximum support pressure of the soil compartment partition as the critical support pressure to ensure the stability of the working face during excavation.

[0071] The present invention also provides a device for calculating support pressure of a rectangular tunnel surface with non-uniform longitudinal slope, comprising:

[0072] A model optimization module is used to adjust the angle between the wedge and the working surface in the six-block silo-wedge model used to simulate the tunnel soil failure zone based on the slope of the tunnel to be excavated, thereby obtaining an optimized upslope model of the tunnel to be excavated;

[0073] The wedge mechanics equation construction module is used to construct the mechanics equations of the quadrangular pyramid wedge and the triangular prism wedge during the excavation process based on the force systems of the quadrangular pyramid wedge and the triangular prism wedge in the upslope optimization model during the excavation process;

[0074] A wedge support pressure equation construction module is used to derive the critical support pressure control equation that characterizes the stability of the working face during tunneling based on the mechanical equations of a quadrangular pyramid wedge and a triangular prism wedge during tunneling.

[0075] The module for constructing the support pressure equation for the soil compartment diaphragm is used to construct the support pressure equation for the soil compartment diaphragm based on the force balance principle of the soil compartment along the excavation slope during excavation in the upslope optimization model and the control equation for the soil compartment's deadweight and critical support pressure.

[0076] The excavation parameter adjustment module is used to use the support pressure equation of the soil compartment diaphragm based on the excavation slope, burial depth, working face width, height and inclination angle of the wedge sliding surface during the excavation process to calculate the soil compartment diaphragm support pressure in real time to determine whether the working face is stable during the excavation of the tunnel to be excavated, thereby adjusting the excavation parameters.

[0077] The present invention also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the above-mentioned method for calculating the support pressure of a rectangular tunnel face with a non-uniform longitudinal slope are implemented.

[0078] The method for calculating support pressure of rectangular tunnel surface with non-uniform longitudinal slope provided in this application has the following beneficial effects:

[0079] Taking into account the problem of uneven support pressure distribution in different areas of soil damage during tunnel excavation, this application selects a six-block silo-wedge model when simulating tunnel excavation. Furthermore, before performing a force analysis on the model, the angle between the wedge and the working surface in the model is first changed based on the slope of the tunnel to be excavated to obtain an uphill optimization model. At this time, the angle between the wedge and the working surface in the uphill optimization model is approximately equal to the slope of the tunnel to be excavated. Therefore, during the excavation process, both the force system of the tetrahedral wedge and the force system of the triangular prism wedge include the parameter of the tunnel slope. Therefore, the critical support pressure control equation obtained based on the mechanical equations of the tetrahedral wedge during the excavation process and the mechanical equations of the triangular prism wedge during the excavation process also considers the support force equation under the influence of the tunnel slope; further, if not Taking the tunnel slope into consideration, the support force of the soil compartment partition during actual construction is not much different from the support force of the wedge during model simulation, and there is no need to consider the influence of the gravity of the soil in the soil compartment itself. The present application utilizes the force balance principle of the soil in the soil compartment along the excavation slope direction during excavation, and based on the control equation of the soil compartment self-weight and critical support pressure, jointly constructs the support pressure equation of the soil compartment partition. The constructed support pressure equation takes into account the influence of the self-weight component of the soil in the soil compartment along the tunnel slope direction on the support pressure of the soil compartment partition, and can more accurately calculate the support pressure value of the soil compartment partition during the excavation of a tunnel with a slope, thereby providing a more accurate theoretical reference for the control of excavation parameters during the construction of a longitudinal slope tunnel, ensuring the stability of the tunnel soil during the construction of a longitudinal slope tunnel to the greatest extent, and ensuring construction safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings, wherein:

[0081] Figure 1 Schematic diagram of the six-block silo-wedge model provided for this application;

[0082] Figure 2 Schematic diagram of the uphill silo-wedge model provided for this application;

[0083] Figure 3 Flowchart of the method for calculating support pressure of rectangular tunnel face with non-uniform longitudinal slope provided for this application;

[0084] Figure 4 Schematic diagram of the uphill optimization model provided for this application;

[0085] Figure 5 Schematic diagram of the uphill excavation analysis model provided for this application;

[0086] Figure 6Schematic diagram of the force system during the excavation process of the quadrangular pyramid wedge provided in this application; wherein, Figure 6 (a) is the front view of the force system during the excavation of the quadrangular pyramid wedge. Figure 6 (b) is the rear view of the force system during the excavation of the quadrangular pyramid wedge;

[0087] Figure 7 Schematic diagram of the force system during the excavation process of the triangular prism wedge provided in this application; wherein, Figure 7 (a) is the front view of the force system during the excavation of the triangular prism wedge. Figure 7 (b) is the rear view of the force system during the excavation of the triangular prism wedge;

[0088] Figure 8 The schematic diagram of the force analysis during the excavation of the soil cabin provided for this application; wherein, Figure 8 (a) is a schematic diagram of the three-dimensional force analysis of the soil during the excavation process. Figure 8 (b) is a schematic diagram of the plane force analysis during the excavation of the soil in the soil cabin;

[0089] Figure 9 The side profile of the failure mode calculated for the upslope optimization model of this application and the existing upslope model; wherein, Figure 9 (a) is the side profile of the failure mode calculated by the upslope optimization model of this application and the existing upslope model under the first condition. Figure 9 (b) is the side profile of the failure mode calculated by the upslope optimization model of this application and the existing upslope model under the second condition. Figure 9 (c) is the side profile of the failure mode calculated by the upslope optimization model of this application and the existing upslope model under the third condition. Figure 9 (d) is the side profile of the failure mode calculated by the upslope optimization model of this application and the existing upslope model under the fourth condition. Figure 9 (e) is the side profile of the failure mode calculated by the upslope optimization model of this application and the existing upslope model under the fifth condition, Figure 9 (f) is the side profile of the failure mode calculated by the upslope optimization model of the present application and the existing upslope model under the sixth condition;

[0090] Figure 10 Schematic diagram comparing the uphill optimization model of the present application and the uphill ultimate support pressure solution obtained by the prior art under different conditions provided in the embodiments of the present application; wherein, Figure 10 (a) is a schematic diagram comparing the uphill optimization model of the present application and the uphill ultimate support pressure solution obtained by the prior art under the first condition. Figure 10(b) is a schematic diagram comparing the upslope optimization model of the present application and the upslope ultimate support pressure solution obtained by the prior art under the second condition;

[0091] Figure 11 The variation pattern of the side range of the wedge body under different slope angles β provided in the embodiment of the present application; wherein, Figure 11 (a) shows the variation of the side range of the wedge when the slope angle is 3%. Figure 11 (b) shows the variation of the side range of the wedge when the slope angle is 6%. Figure 11 (c) shows the variation of the side range of the wedge when the slope angle is 9%.

[0092] Figure 12 Different friction angles provided in the embodiments of this application The variation pattern of the side range of the wedge-shaped body below; Figure 12 (a) shows the variation of the side range of the wedge when the friction angle is 15°. Figure 12 (b) shows the variation of the side range of the wedge when the friction angle is 25°. Figure 12 (c) shows the variation of the side surface of the wedge when the friction angle is 35°;

[0093] Figure 13 The influence of the aspect ratio of the top pipe on the failure mode provided in the embodiment of the present application; wherein, Figure 13 (a) shows the effect of different jacking pipe aspect ratios on the failure mode when the friction angle is 15°. Figure 13 (b) shows the effect of different jacking pipe width-to-height ratios on the failure mode when the friction angle is 35°. Figure 13 (c) shows the effect of different jacking pipe width-to-height ratios on the failure mode when the slope angle is 3%. Figure 13 (d) shows the effect of different jacking pipe width-to-height ratios on the failure mode when the slope angle is 9%;

[0094] Figure 14 The surface load σ provided in the embodiment of this application s The impact on the lateral range of the wedge; among them, Figure 14 (a) shows the influence of different surface loads on the side range of the wedge when the slope angle is 3%. Figure 14 (b) shows the influence of different surface loads on the side range of the wedge when the slope angle is 6%. Figure 14 (c) shows the effect of different surface loads on the side range of the wedge when the slope angle is 9%;

[0095] Figure 15 The influence coefficient N of soil density on support pressure provided in the embodiment of this application is γ The law of change; among them, Figure 15(a) is the support pressure influence coefficient N under the first soil density γ The law of change, Figure 15 (b) is the support pressure influence coefficient N under the second soil density γ The law of change, Figure 15 (c) is the support pressure influence coefficient N under the third soil density γ The law of change, Figure 15 (d) is the support pressure influence coefficient N under the fourth soil density γ Laws of change;

[0096] Figure 16 The coefficient N of influence of soil cohesion on ultimate support pressure provided in the embodiment of this application is c Transformation law; among them, Figure 16 (a) is the first type of soil cohesion on the ultimate support pressure coefficient N c Transformation rules, Figure 16 (b) is the influence coefficient N of the second soil cohesion on the ultimate support pressure c Transformation rules, Figure 16 (c) is the influence coefficient N of the third type of soil cohesion on the ultimate support pressure c Transformation rules, Figure 16 (d) is the fourth soil cohesion on the ultimate support pressure coefficient N c Transformation rules;

[0097] Figure 17 The variation law of soil friction angle to ultimate support pressure provided in the embodiment of this application; wherein, Figure 17 (a) is the first type of soil friction angle variation law of the ultimate support pressure, Figure 17 (b) is the second type of soil friction angle and the change law of the ultimate support pressure. Figure 17 (c) in the figure is the variation law of the third soil friction angle on the ultimate support pressure. Figure 17 (d) shows the variation of the fourth type of soil friction angle to the ultimate support pressure;

[0098] Figure 18 The variation law of the ratio B / L of the area with smaller support pressure (block II) to the ultimate support pressure provided in the embodiment of this application; wherein, Figure 18 (a) shows the variation of B / L to the ultimate support pressure when the slope angle is 3%. Figure 18 (b) shows the variation of B / L to the ultimate support pressure when the slope angle is 9%;

[0099] Figure 19 A finite element model of a rectangular tunnel provided in an embodiment of the present application;

[0100] Figure 20 Provided in the embodiments of this application Figure 19 Schematic diagram of the mesh of the rectangular tunnel finite element model shown;

[0101] Figure 21 The support pressure ratio-displacement evolution curve of the typical uphill working condition provided in the embodiment of the present application;

[0102] Figure 22 The geometric shape comparison of the failure mode of the finite element model provided in the embodiment of the present application and the failure mode of the uphill theoretical model is as follows: Figure 22 shown; among them, Figure 22 (a) is a comparison of the geometric shapes of the failure modes of the first finite element model and the uphill theoretical model. Figure 22 (b) is a comparison of the geometric shapes of the failure mode of the second finite element model and the failure mode of the uphill theoretical model. Figure 22 (c) is a comparison of the geometric shapes of the failure modes of the third finite element model and the uphill theoretical model. Figure 22 (d) is the geometric comparison of the failure mode of the fourth finite element model and the failure mode of the uphill theoretical model. Figure 22 (e) is the geometric comparison of the failure mode of the fifth finite element model and the failure mode of the uphill theoretical model. Figure 22 (f) shows the geometric comparison of the failure mode of the sixth finite element model and the failure mode of the upslope theoretical model;

[0103] Figure 23 The uphill ultimate support pressure solution provided in the embodiment of the present application varies with the friction angle; wherein, Figure 23 (a) shows the variation of the upslope ultimate support pressure solution with the friction angle when C / D is 1. Figure 23 (b) shows the variation of the upslope ultimate support pressure solution with the friction angle when C / D is 2;

[0104] Figure 24 The influence of B / L on the ultimate support pressure of the rectangular tunnel excavation face under different uphill slopes provided in the embodiment of the present application; wherein, Figure 24 (a) shows the influence of B / L on the ultimate support pressure of rectangular tunnel excavation face when the slope angle is 0%. Figure 24 (b) shows the influence of B / L on the ultimate support pressure of rectangular tunnel excavation face when the slope angle is 3%. Figure 24 (c) shows the influence of B / L on the ultimate support pressure of rectangular tunnel excavation face when the slope angle is 6%. Figure 24 (d) shows the influence of B / L on the ultimate support pressure of rectangular tunnel excavation face when the slope angle is 9%;

[0105] Figure 25The embodiment of the present application provides an example of the influence of the uphill slope angle of the jacking pipe on the ultimate support pressure. DETAILED DESCRIPTION

[0106] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0107] See also Figure 3 , Figure 3 The figure shows a flow chart of the method for calculating the support pressure of a rectangular tunnel face with non-uniform longitudinal slope provided by this application. The method specifically includes:

[0108] S10: Based on the slope of the tunnel to be excavated, the angle between the wedge and the working surface in the six-block silo-wedge model used to simulate the tunnel soil failure area is adjusted to obtain an optimized upslope model of the tunnel to be excavated.

[0109] Specifically, the angle between the wedge part and the working surface in the six-block silo-wedge model is adjusted to be consistent with the slope of the tunnel to be excavated, and the following is obtained: Figure 4 The upslope optimization model for the tunnel to be excavated is shown. When simulating the tunneling process using this model, the force analysis of the wedge-shaped portion of the model takes into account the tunnel slope. Therefore, the model accounts for both the longitudinal slope and the uneven distribution of support pressure. The wedge in the lower portion of the model can be viewed as the excavation surface abkj rotated counterclockwise by β around the lower edge bk of the rectangular section. β is the slope of the rectangular pipe during upslope jacking.

[0110] S20: Based on the force systems of the quadrangular pyramid wedge and triangular prism wedge in the upslope optimization model during the excavation process, the mechanical equations of the quadrangular pyramid wedge and the triangular prism wedge during the excavation process are constructed.

[0111] S30: Based on the mechanical equations of a quadrangular pyramid wedge and a triangular prism wedge during tunneling, the critical support pressure control equation that characterizes the stability of the working face during tunneling is obtained.

[0112] S40: Utilizing the principle of force balance of the soil in the soil compartment along the excavation slope during excavation, the support pressure equation of the soil compartment diaphragm is constructed based on the control equation of the soil compartment's deadweight and critical support pressure.

[0113] S50: The soil compartment diaphragm support pressure equation is used to calculate the soil compartment diaphragm support pressure in real time based on the excavation slope, burial depth, working face width, height and wedge sliding surface inclination during the excavation process to determine whether the working face is stable during the excavation of the tunnel to be excavated, thereby adjusting the excavation parameters.

[0114] Specifically, if Figure 5 The figure shows a schematic diagram of the uphill excavation analysis model provided by this application. As can be seen from the figure, the rectangular jacking pipe is advanced uphill with a slope β in a homogeneous isotropic stratum. Its structural parameter system includes the geometric dimensions L×D of the tunnel section to be excavated, the width w of the soil cabin structure, the thickness C of the top of the excavation face, and the uniformly distributed surface load σ. s The constitutive model of the stratum adopts the ideal elastic-plastic Mohr-Coulomb criterion, and defines the key physical and mechanical parameters of the soil as soil bulk density γ, effective cohesion c, friction angle Based on the assumption that the soil tank is completely filled, the force exerted by the soil tank partition on the soil is σ t0 , under normal excavation conditions, σ t0 Mainly used to resist the soil weight G soil and support pressure in front of the working face σ s2 .

[0115] Based on the above analysis, this application uses an uphill optimization model to construct the support pressure equation in front of the working face, and then conducts a force analysis on the soil in the soil compartment to obtain the support pressure equation of the soil compartment partition during uphill excavation, so as to calculate the support pressure of the soil compartment partition during excavation in real time.

[0116] First, this application follows the following basic assumptions when using the upslope optimization model to simulate excavation to construct a theoretical model of support pressure: 1. Soil uniformity assumption: the stratum material has homogeneous and isotropic characteristics, and equivalent weighted parameters are used to characterize the layered strata; 2. Failure mode assumption: the excavation surface failure zone is controlled by a kinematically allowed wedge-prism combination mechanism; 3. Constitutive relationship assumption: the soil is regarded as an ideal rigid-plastic medium, strictly obeying the Mohr-Coulomb strength criterion, and its shear strength is determined by the internal friction angle Cohesion c and bulk density γ are jointly determined; 4. Stress distribution assumption: the normal stress on the top surface and sliding surface of the wedge is uniformly distributed, and the lateral vertical stress follows the distribution law of static water and soil pressure.

[0117] Furthermore, the above-mentioned uphill optimization model is explained in detail:

[0118] 1. Geometric configuration of the upslope optimization model: The lower excavation disturbance zone is composed of a composite sliding system consisting of wedge-shaped blocks I, II, and III. The geometric parameter system includes: the inclination angle θ of the wedge sliding surface (the angle between the base of the triangular prism block II and the horizontal plane), the jacking slope β (reflecting the characteristics of the equipment propulsion trajectory), and the parameters of the isosceles trapezoid in the upper part of the model (the lower base is the working surface width L, the upper base is the width B of block II, and the base angle of the isosceles trapezoid is α). The upper covering area is composed of blocks IV, V, and VI, and the burial depth C is the key control parameter. Blocks IV and VI are triangular prisms, and block V is a quadrangular prism.

[0119] 2. Mechanical mechanism: Blocks I and III have mechanical symmetry, and a single-sided analysis domain can be established to characterize the entire system. There is a coupling effect of normal force (N1, N2) and friction resistance (F1, F2) at the contact interface between blocks I and II. When the support reaction force F2 is insufficient, the downward trend of block II triggers a chain reaction of instability in block I through the shear effect on the contact surface.

[0120] Furthermore, based on the above description, it can be seen that in the wedge-shaped body part of the uphill optimization model, the four-sided pyramid wedges I and III located on both sides of the triangular prism wedge II are completely symmetrical, and the forces they receive during the excavation process are also exactly the same. Therefore, this application conducts a force analysis on the four-sided pyramid wedges in the uphill optimization model to obtain their force system. This force analysis process is applicable to the four-sided pyramid wedges I and III. Figure 6 Schematic diagram of the force system during the excavation process of the quadrangular pyramid wedge provided in this application; wherein, Figure 6 (a) is the front view of the force system during the excavation of the quadrangular pyramid wedge. Figure 6 Figure (b) shows the rear view of the force system of the pyramid wedge during excavation. Force analysis reveals that the force system of the pyramid wedge during excavation includes the vertical load of the overlying soil column, the mechanical response of the base sliding surface, the mechanical response of the outer contact surface, the mechanical response of the inner contact surface, the working face support pressure, and the deadweight load. The specific mechanical equation construction process includes:

[0121] The stress analysis of the pyramid wedge was conducted. Based on the principle of force balance of the pyramid wedge during excavation, the vertical load equation of the overlying soil column, the relationship equation between the normal force and friction resistance of the base sliding surface, the relationship equation between the normal force and friction resistance of the outer contact surface, the support pressure equation of the working face, and the deadweight load equation of the pyramid wedge were constructed.

[0122] Based on the bidirectional static equilibrium conditions, a bidirectional static equilibrium equation group is constructed for the mechanical equations of the tetrahedral wedge during the excavation process; the bidirectional static equilibrium equation group is solved to obtain the normal force equation and friction force equation of the inner contact surface of the tetrahedral wedge during the excavation process.

[0123] Specifically, the vertical load equation of the overlying soil column on the quadrangular pyramid wedge during the excavation process is expressed as:

[0124]

[0125] Where P1 represents the vertical load of the overlying soil column on the pyramid wedge during the excavation process; γ represents the soil bulk density; C represents the depth of the tunnel to be excavated; σ srepresents the surface load; L represents the width of the working face of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge;

[0126] The relationship between the normal force and friction resistance of the base sliding surface is expressed as:

[0127]

[0128] Wherein, T1 represents the friction resistance of the base sliding surface; c represents the cohesion of the soil of the tunnel to be excavated; N1 represents the normal force of the base sliding surface; It represents the soil friction angle of the tunnel to be excavated;

[0129] The relationship equation between the normal force and friction resistance of the outer contact surface is expressed as:

[0130]

[0131]

[0132] Where, N3 represents the normal force of the outer contact surface; K0 represents the static earth pressure coefficient, σ z represents the vertical stress on the lateral sliding surface, σ z =γC+γz, where z represents the integral variable;

[0133] Specifically, refer to Figure 6 As shown, the parameter z represents the distance from a moving point on edge bb′ to b′.

[0134] The support pressure equation of the working face is expressed as:

[0135]

[0136] Among them, S1 represents the support pressure of the working face; s1 represents the support pressure acting on the excavation surface of the quadrangular wedge during excavation. K a represents the active earth pressure coefficient,

[0137] The self-weight load equation of the quadrangular pyramid wedge is expressed as:

[0138]

[0139] Where G1 represents the deadweight load of the tetrahedral wedge; V1 represents the volume of the tetrahedral wedge;

[0140] The two-way static equilibrium equations are expressed as:

[0141]

[0142] Among them, T 21 represents the friction resistance of the inner contact surface of the quadrangular pyramid wedge during the excavation process; α represents the base angle of the mid-waist trapezoidal surface of the overlying soil part of the upslope optimization model;

[0143] like Figure 4 As shown in Figure 2, the upper and lower surfaces of the overlying soil part located on the wedge in the upslope optimization model are both isosceles trapezoids (pnml and jfea), and the parameter α represents the base angle of pnml and jfea.

[0144] The normal force equation of the inner contact surface of the quadrangular pyramid wedge during the excavation process is expressed as:

[0145] N 21 =(P1+G1)cosθ+S1sinθcosβ-S1sinβcosθ-N3cosαsinθ,

[0146] Among them, N 21 It represents the normal force on the inner contact surface of the quadrangular pyramid wedge during the excavation process;

[0147] The friction equation of the inner contact surface of the quadrangular pyramid wedge during the excavation process is expressed as:

[0148] T 21 =-P1sinθ-G1sinθ-N3cosαcosθ+T3sinα+T1+S1cosθcosβ+S1sinθsinβ.

[0149] Furthermore, the present application performs a force analysis on the triangular prism wedge in the uphill optimization model to obtain its force system, such as Figure 7 The schematic diagram of the force system during the excavation of the triangular prism wedge provided in this application, wherein: Figure 7 (a) is the front view of the force system during the excavation of the triangular prism wedge. Figure 7 Figure (b) shows the force system of the triangular prism wedge during tunneling. Force analysis reveals that the force system of the triangular prism wedge during tunneling includes the vertical stress of the overlying soil due to the soil arching effect, the mechanical response of the base contact surface, the working face support reaction, the deadweight load, and the symmetrically distributed lateral contact force (i.e., the force between the triangular prism wedge and the four-sided pyramid wedges on both sides). The specific mechanical equation construction process includes:

[0150] The force analysis of the triangular prism wedge was conducted. Based on the force balance principle of the triangular prism wedge during the excavation process, the vertical stress equation of the overlying soil column, the relationship equation between the normal force and friction resistance of the base contact surface, the support reaction force equation of the working face, the normal force equation and friction resistance equation of the symmetrically distributed lateral contact surface, and the deadweight load equation of the triangular prism wedge were constructed.

[0151] A set of spatial equilibrium equations is constructed based on the normal force equation and friction force equation of the symmetrically distributed lateral contact surface; the normal force equation and friction force equation of the lateral contact surface of the triangular prism wedge during the excavation process are obtained by solving the spatial equilibrium equation.

[0152] Specifically, the vertical stress equation of the overlying soil column subjected to the triangular pyramid wedge during the excavation process is expressed as:

[0153] P2=σ v BDcosβ(cotθ+tanβ),

[0154] Where P2 represents the vertical stress of the overlying soil column on the triangular pyramid wedge during the excavation process; σ v represents the Terzaghi loosening earth pressure, R represents the ratio of the overlying soil volume to the lateral area, γ represents the soil bulk density, K0 represents the static earth pressure coefficient, c represents the soil cohesion of the tunnel to be excavated, represents the soil friction angle of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge;

[0155] The relationship equation between the normal force and friction resistance of the substrate contact surface is expressed as:

[0156]

[0157] Wherein, T2 represents the friction resistance of the substrate contact surface; N2 represents the normal force of the substrate contact surface;

[0158] The support reaction equation of the working face is expressed as:

[0159] S2=σ s2 BD,

[0160] Among them, S2 represents the support reaction force of the working face; σ s2 represents the critical support pressure;

[0161] The normal force equation and friction resistance equation for the symmetrically distributed lateral contact surface are expressed as:

[0162]

[0163] Among them, T 12 represents the friction resistance of the first lateral contact surface of the triangular prism wedge; T 32 Indicates the friction resistance of the second lateral contact surface of the triangular prism wedge; N 12 Represents the normal force on the first lateral contact surface of the triangular prism wedge; N 32 represents the normal force on the second lateral contact surface of the triangular prism wedge;

[0164] The self-weight load equation of the triangular prism wedge is expressed as:

[0165]

[0166] Where G2 represents the deadweight load of the triangular prism wedge; V2 represents the volume of the triangular prism wedge;

[0167] The spatial equilibrium equations are expressed as:

[0168]

[0169] The normal force equation of the lateral contact surface of the triangular prism wedge during the excavation process is expressed as:

[0170]

[0171] The friction equation of the lateral contact surface of the triangular prism wedge during the excavation process is expressed as:

[0172] N 12 =(P2+G2)cosθ+S2sinθcosβ-S2sinβcosθ.

[0173] Since there is an interaction force between the triangular prism wedge and the quadrangular pyramid wedge, a coupling analysis can be performed on the triangular prism wedge and the quadrangular pyramid wedge. The parameters are eliminated based on the mechanical coordination conditions of the contact surface between the two. The specific process is as follows:

[0174] 1. The normal force on the base contact surface of the triangular prism wedge and the normal force on the base sliding surface of the quadrangular pyramid wedge are coordinated, so the following equation holds:

[0175] (2S1+S2)(cosθcosβ+sinθsinβ)=[2(P1+G1)+P2+G2]sinθ+2N3cosαcosθ-2T1-

[0176] T2-2T3sinα,

[0177] 2. Perform simultaneous elimination of parameters based on the above equations to eliminate the intermediate variables N1 and N2.

[0178] Furthermore, based on the parameter relationship calculation in the above mechanical equation, the critical support pressure control equation that characterizes the stability of the working face can be obtained. This equation integrates the model geometric parameters (β, θ), material parameters and working parameters (C, D, w, B, L, σ s ), specifically, the critical support pressure control equation is expressed as:

[0179]

[0180] Among them, σ s2 represents the critical support pressure; γ represents the soil bulk density; C represents the depth of the tunnel to be excavated; σ s represents the surface load; L represents the width of the working face of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge; K0 represents the static earth pressure coefficient, c represents the soil cohesion of the tunnel to be excavated, represents the soil friction angle of the tunnel to be excavated; K a represents the active earth pressure coefficient, R represents the ratio of the overlying soil volume to the lateral area, α represents the base angle of the mid-waist trapezoidal surface in the overlying soil part of the upslope optimization model.

[0181] Furthermore, if Figure 8 The figure shows a schematic diagram of the force analysis during the excavation of the soil cabin provided by this application; wherein, Figure 8 (a) is a schematic diagram of the three-dimensional force analysis of the soil during the excavation process. Figure 8 (b) is a schematic diagram of the plane force analysis during the excavation of the soil cabin; Figure 8 It can be seen from the figure that based on the force balance of the soil in the x′ direction, we can know:

[0182] P t0 =S2′+ηG soil xinβ,

[0183] Among them, S′2 and S2 are interaction forces, S′2=S2; η represents the inverse of the loose coefficient of the soil in the soil compartment, 0.74, K represents the looseness coefficient of the soil in the soil compartment. In the prior art, the looseness coefficient of shield slag is determined to be between 1.1 and 1.6 based on theory and experiments. In the embodiment of this application, the average value of 1.35 is taken for calculation; G soil Indicates the deadweight of the soil in the soil compartment;

[0184] G soil =γwDB,

[0185] Wherein, w represents the thickness of the soil in the soil compartment, which is 0.5m.

[0186] Then the supporting pressure equation of the soil compartment diaphragm can be expressed as:

[0187]

[0188] Among them, σ t0 represents the supporting pressure of the soil compartment partition; γ represents the soil bulk density; C represents the burial depth of the tunnel to be excavated; σ s represents the surface load; L represents the width of the working face of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge; K0 represents the static earth pressure coefficient, c represents the soil cohesion of the tunnel to be excavated, represents the soil friction angle of the tunnel to be excavated; K a represents the active earth pressure coefficient, R represents the ratio of the overlying soil volume to the lateral area, α represents the bottom angle of the medium waist trapezoidal surface of the overlying soil part of the upslope optimization model; η represents the inverse of the loose coefficient of the soil in the soil compartment, K represents the looseness coefficient of the soil in the soil compartment; w represents the thickness of the soil in the soil compartment.

[0189] The uniformly distributed support pressure σ t0 The dimensionless expression of is:

[0190]

[0191] in,

[0192]

[0193]

[0194]

[0195]

[0196]

[0197]

[0198] According to the uniformly distributed support pressure σ t0 From the dimensionless expression of , it can be seen that its mechanical response can be decomposed into three independent terms: 1) the self-weight effect term, which represents the contribution of the soil bulk density γ, which is expressed by the dimensionless parameter N γQuantify its influence weight; 2) Cohesion effect term, which reflects the reinforcement effect of soil cohesion c, through the dimensionless coefficient N c Achieve parameter normalization; 3) Load effect term, describing the surface load σ s The additional effect of Characterize its transfer efficiency.

[0199] Furthermore, obtaining the support pressure equation of the soil compartment partition also includes solving the support pressure equation of the soil compartment partition based on the extreme value theory to obtain the maximum support pressure of the soil compartment partition, and using the maximum support pressure of the soil compartment partition as the critical support pressure to ensure the stability of the working face during excavation.

[0200] Specifically, given the formation strength parameter Model parameters (C, D, L, B, β) and surface load (σ s ) condition, the critical support pressure σ t0 It can be expressed as a unary function of the slip angle θ. Based on the extreme value theory analysis, there exists a specific value of θ such that σ t0 The extreme state corresponds to the critical state of tunnel face instability. In engineering practice, σ t0 As a conservative threshold for support pressure design, when the actual support pressure > σ t0 When the tunnel face is stable, it can ensure the stability of the tunnel face.

[0201] This application also provides the support pressure equation obtained from the existing six-block silo-wedge model:

[0202]

[0203] s2=γDN γ -cN c ,

[0204] The difference between the existing support pressure equation and the support pressure equation obtained in this application is that the tunnel slope angle β is considered at various locations within the equation, and secondly, the soil deadweight term is considered. Finally, the surface load effect is considered.

[0205] In order to verify the scientific nature of the upslope optimization model provided in this application, the embodiment of this application also systematically compares the upslope optimization model with the existing model in two dimensions: the failure morphology evolution mechanism and the ultimate support strength response characteristics:

[0206] In order to analyze the parameter of the instability failure mode of the rectangular jacking tunneling face under upslope conditions, the rationality of the upslope optimization model was verified by comparing the geometric shape of the failure mode with the upslope silo-wedge model. The unified calculation parameters were γ = 19.8kN / m3, D = 6m, w = 0.5m, c / γD = 0, C / D = 1.0 to 2.0, L / D = 2.0, B / L = 0.4, β = 0% to 9%. Figure 9 The figure shows the side profile of the failure mode calculated by the upslope optimization model of the present application and the existing upslope model, wherein: Figure 9 (a) is the side profile of the failure mode calculated by the upslope optimization model of this application and the existing upslope model under the first condition. Figure 9 (b) is the side profile of the failure mode calculated by the upslope optimization model of this application and the existing upslope model under the second condition. Figure 9 (c) is the side profile of the failure mode calculated by the upslope optimization model of this application and the existing upslope model under the third condition. Figure 9 (d) is the side profile of the failure mode calculated by the upslope optimization model of this application and the existing upslope model under the fourth condition. Figure 9 (e) is the side profile of the failure mode calculated by the upslope optimization model of this application and the existing upslope model under the fifth condition, Figure 9 (f) in the figure is the side profile of the failure mode calculated by the uphill optimization model of the present application and the existing uphill model under the sixth condition. It can be seen from the figure that the instability range of the uphill optimization model of the present application is not much different from the instability range of the existing uphill model. Under the conditions of C / D=1, β=6%, their failure inclination angles only differ by 8.5%; from the comparison of Figures (a) to (c), it can be seen that the failure inclination angle θ increases with the increase of the slope angle β; it can also be found from the figure that the increase of C / D leads to a small increase in the failure inclination angle of the optimized model, while the failure inclination angle of the existing uphill model decreases significantly.

[0207] Furthermore, in order to study the influence of relevant parameters on the ultimate support pressure coefficient of the upslope rectangular tunnel excavation face, the rationality of the upslope optimization model was verified by comparing it with the upslope silo-wedge model solution. The unified calculation parameters were γ = 19.8 kN / m3, D = 6 m, w = 0.5 m, c / γD = 0, C / D=1.0~2.0, L / D=2.0, B / L=0.4, β=0%~9%. Figure 10 The figure shows a comparison diagram of the uphill optimization model of the present application and the uphill ultimate support pressure solution obtained by the prior art under different conditions provided in the embodiments of the present application, wherein: Figure 10 (a) is a schematic diagram comparing the uphill optimization model of the present application and the uphill ultimate support pressure solution obtained by the prior art under the first condition. Figure 10 (b) is a schematic diagram comparing the upslope ultimate support pressure solution obtained by the upslope optimization model of the present application and the prior art under the second condition. It can be seen from the figure that when other parameters are fixed, the ultimate support pressure increases with the internal friction angle. The increase of shows nonlinear attenuation characteristics, and its mechanical mechanism can be explained as follows: The value of soil shear strength parameter (c=0, ) is significantly enhanced, and the self-bearing capacity of the soil is strengthened, resulting in a corresponding reduction in the external support pressure required to maintain the stability of the excavation surface. Taking β = 6% as an example, the solution of this application The increase from 15° to 45° results in a decrease of about 68.5% in the ultimate support pressure, while the existing upslope solution decreases by about 75.5%, indicating that the existing solution is The sensitivity is higher than that of this application. Under the condition of β=9%, the difference between the solution of this application and the existing solution is about 21%, but as As the value of Under the condition of β=9%, the difference between the solution of this application and the existing solution is only about 5%. When C / D increases from 1.0 to 2.0, the existing uphill solution is slightly higher than the existing solution. The upslope optimization model has an obvious increasing trend with the increase of C / D, while the upslope optimization solution is almost not affected by the increase of C / D, which shows that the upslope optimization model is more suitable for shallow soil cover. The change pattern of is the same, which verifies the rationality of this application in evaluating the stability of the excavation face when the jacking pipe is jacked uphill.

[0208] Furthermore, in order to conduct parameter analysis on the failure mode of the longitudinal rectangular jacking pipe uphill excavation, the unified calculation parameters are γ=19.8kN / m3,D=6m,w=0.5m,c / γD=0, C / D=1.0~2.0, L / D=1.0~2.0, B / L=0.4~0.7, β=3%~9%, σ s =0~45kPa. Table 1 shows the wedge failure inclination angle θ along with the friction angle. The variation of slope angle β, jacking depth ratio C / D and the ratio of B / L of the area with smaller support pressure (block II). For cohesionless soil (c / γD=0), under certain conditions of β and C / D, The change trend of the failure angle θ shows that the wedge slip surface gradually becomes steeper, that is, the increase in the shear strength of the soil leads to a contraction of the unstable area. Under the conditions of β=6%,C / D=1.0,B / L=0.4, The increase from 15° to 45° results in a decrease in the failure angle of about 15.93°. When it is fixed, in the uphill excavation of the jacking pipe (β>0), the increase of the slope angle β makes θ gradually larger, that is, the unstable area is shrinking. The different changes in the failure angle in the uphill indicate that the corresponding failure modes are different, and will directly affect the change law of the support pressure. Table 1 also shows the influence of the tunnel depth ratio C / D on the failure mode of the excavation face. The influence of C / D on the failure mode is relatively small. Whether it is B / L=0.4 or B / L=0.7, the θ value when C / D=2.0 is larger than the value when C / D=1.0. The change is first less than and then greater than, but the relationship changes at the junction The value increases with the increase of B / L, which indirectly shows that B / L is a parameter that has a great influence on the failure angle θ.

[0209] Table 1 (γ=19.8kN / m 3 ,D=6m,w=0.5m,L / D=2.0,c / γD=0,σ s =0kPa)

[0210]

[0211] like Figure 11 The variation pattern of the side range of the wedge body under different slope angles β provided in the embodiment of the present application; wherein, Figure 11 (a) shows the variation of the side range of the wedge when the slope angle is 3%. Figure 11 (b) shows the variation of the side range of the wedge when the slope angle is 6%. Figure 11 (c) in the figure shows the variation of the side range of the wedge when the slope angle is 9%. Figure 12 Shown are different friction angles provided by the embodiments of this application The variation pattern of the side range of the wedge-shaped body below; Figure 12 (a) shows the variation of the side range of the wedge when the friction angle is 15°. Figure 12 (b) shows the variation of the side range of the wedge when the friction angle is 25°. Figure 12 (c) in the figure shows the variation of the side range of the wedge when the friction angle is 35°. Figure 11 As shown in the figure, the change of β still has a certain influence on the transformation of the failure angle. With the change of the tunneling posture of the pipe jacking machine, the area of ​​the overall unstable region increases but is not obvious. The overall performance is horizontal movement to the left. The distance that the left line of the unstable region moves to the left is slightly greater than the distance that the right line moves to the left.

[0212] from Figure 12 As shown in (a), it can be clearly seen that as the shear strength of the soil continues to increase, the unstable area gradually shrinks, and the corresponding surface failure length continues to decrease. Figure 12(a), (b), (c) found that the failure mode The sensitivity of the wedge failure angle θ is greater than β. The increase of increases, and from the spacing between the vertical lines of different colors in the figure, it can be concluded that the rate of increase increases with When the slope increases from 15° to 25°, the failure angle increases by about 6°; when it increases from 25° to 35°, the failure angle increases by about 5°; when it increases from 35° to 45°, the failure angle increases by about 4°.

[0213] Table 2 shows the variation of the wedge failure angle θ with the width-to-height ratio L / D of the jacking pipe. When other conditions are constant, the failure angle θ gradually decreases with the continuous increase of the L / D of the jacking pipe excavation section. Under the conditions of B / L = 0.7 and β = 3%, the L / D ratio is doubled, resulting in a decrease of θ by 8.4%. The decrease of θ means that the inclination angle of the wedge block is closer to the slope foot of the traditional model, that is, At the same time, it is shown that the optimization model is more suitable for large-section rectangular jacking pipes.

[0214] Table 2 (γ=19.8kN / m 3 ,D=6m,w=0.5m,C / D=1.0,c / γD=0,σ s =0kPa)

[0215]

[0216] Figure 13 The influence of the aspect ratio of the top pipe on the failure mode provided in the embodiment of the present application; wherein, Figure 13 (a) shows the effect of different jacking pipe aspect ratios on the failure mode when the friction angle is 15°. Figure 13 (b) shows the effect of different jacking pipe width-to-height ratios on the failure mode when the friction angle is 35°. Figure 13 (c) shows the effect of different jacking pipe width-to-height ratios on the failure mode when the slope angle is 3%. Figure 13 (d) shows the effect of different jacking pipe width-to-height ratios on the failure mode when the slope angle is 9%. It can be seen that at different friction angles Under the conditions of different slope angles β, the increase of L / D leads to the expansion of the unstable area, and the overall change of the failure mode is obvious. Figure 13 As can be seen from (a) and (b) in Figure 2, compared with L / D, the failure mode is Greater sensitivity to change; Figure 13 As can be seen from (c) and (d) in Figure 3, the failure mode is more sensitive to the change of L / D than β.

[0217] Table 3 shows the wedge failure inclination angle θ with the surface load σ sWhen other conditions are fixed, the failure angle θ changes with σ s decreases with the increase of surface load σ, which means that the instability area decreases with the increase of surface load σ s expanded with the increase of .

[0218] Table 3 (γ=19.8kN / m3, D=6m, w=0.5m, L / D=2.0, c / γD=0)

[0219]

[0220] Figure 14 The surface load σ provided in the embodiment of this application s The impact on the lateral range of the wedge; among them, Figure 14 (a) shows the influence of different surface loads on the side range of the wedge when the slope angle is 3%. Figure 14 (b) shows the influence of different surface loads on the side range of the wedge when the slope angle is 6%. Figure 14 (c) shows the influence of different surface loads on the side range of the wedge when the slope angle is 9%. Figure 14 As shown in the figure, it can be seen that with the surface load σ s As the pressure increases, the unstable area tends to expand slightly, and the corresponding surface damage length also increases.

[0221] Furthermore, in order to study the influence of relevant parameters on the ultimate support pressure coefficient of the upslope rectangular tunnel excavation face, the calculation parameters are determined to be γ = 19.8kN / m3, D = 6m, w = 0.5m, c / γD = 0, C / D=1.0~2.0, L / D=1.0~2.0, B / L=0.4~0.7, β=3%~9%, σ s =0kPa. Figure 15 The influence coefficient N of soil density on support pressure provided in the embodiment of this application is γ The law of change; among them, Figure 15 (a) is the support pressure influence coefficient N under the first soil density γ The law of change, Figure 15 (b) is the support pressure influence coefficient N under the second soil density γ The law of change, Figure 15 (c) is the support pressure influence coefficient N under the third soil density γ The law of change, Figure 15 (d) is the support pressure influence coefficient N under the fourth soil density γ Laws of change.

[0222] from Figure 15It can be seen that when other parameters are constant, the influence coefficient N of soil weight on ultimate support pressure is γ Friction angle The increase of shows a significant nonlinear attenuation trend. Typical example (C / D=1、B / L=0.4、β=3%、 ) γ The value drops to 0.1486 and tends to 0, which proves that the effect of soil weight on support pressure in high friction angle strata is significantly weakened. When B / L=0.4, the corresponding slope angles β are The relationship curve shows a significant non-equidistant distribution characteristic. When B / L=0.7, N γ Value The increasing gradient shows an approximately equidistant distribution pattern. This difference in parameter sensitivity reveals the regulatory mechanism of B / L on the spatial distribution characteristics of soil strength parameters. Figure 15 (a) and (b) and (c) and (d) show that C / D is related to N γ There is still a certain impact, when When C / D increases, N γ The increase corresponds to a higher ultimate support pressure, and N γ Almost the same; when Finally, the increase of C / D leads to the increase of the concavity of the curve.

[0223] Figure 16 The coefficient N of influence of soil cohesion on ultimate support pressure provided in the embodiment of this application is c Transformation law; among them, Figure 16 (a) is the first type of soil cohesion on the ultimate support pressure coefficient N c Transformation rules, Figure 16 (b) is the influence coefficient N of the second soil cohesion on the ultimate support pressure c Transformation rules, Figure 16 (c) is the influence coefficient N of the third type of soil cohesion on the ultimate support pressure c Transformation rules, Figure 16 (d) is the fourth soil cohesion on the ultimate support pressure coefficient N c The multi-parameter coupling analysis reveals the influence coefficient N of soil cohesion on the ultimate support pressure. c Friction angle with soil The correlation characteristics of the study show that: N c Follow Increased presentation and N γ Consistent nonlinear attenuation law, but compared with N γ The significant slope sensitivity of N under different β values cThe change curve shows a weak correlation feature. Its internal mechanism is that the change of slope angle mainly controls the buried depth parameters and soil pressure distribution of the overlying stratum of the jacking pipe, but has little effect on cohesion. c The impact of decreases with the increase of When , the change curves almost overlap. Figure 16 (a) and (b) show that under the same B / L conditions, the two curves are closer when C / D = 2 than when C / D = 1. Figure 16 (b) and (d) show that under the same C / D conditions, N c Always greater than N when B / L=0.7 c .

[0224] Figure 17 The variation law of soil friction angle to ultimate support pressure provided in the embodiment of this application; wherein, Figure 17 (a) is the first type of soil friction angle variation law of the ultimate support pressure, Figure 17 (b) is the second type of soil friction angle and the change law of the ultimate support pressure. Figure 17 (c) in the figure is the variation law of the third soil friction angle on the ultimate support pressure. Figure 17 (d) in the figure is the fourth type of soil friction angle and the change of the ultimate support pressure. From 17, we can see that when other parameters are fixed, the ultimate support pressure changes with the internal friction angle. The increase of shows nonlinear attenuation characteristics. Its mechanical mechanism can be explained as follows: The value of soil shear strength parameter (c=0, ) is significantly enhanced, and the self-bearing capacity of the soil is strengthened, resulting in a corresponding reduction in the external support pressure required to maintain the stability of the excavation face. Taking the longitudinal slope of 6% as an example, when When the value increases from 15° to 45°, the ultimate support pressure drops by 68.5%, which fully confirms the mechanical response law. Comparative analysis with the existing six-block model (β=0%) shows that the solution obtained in this study has higher engineering safety by coupling the effect of the slope angle β on the overlying soil layer and the mechanical contribution of the soil in the soil compartment to the excavation surface. Further research found that when the support pressure area ratio B / L=0.7 is small, the support pressure curves corresponding to different slope angles β show an approximately equidistant distribution feature, indicating that the correlation between the slope angle change and the support pressure under this specific geometric condition is close to a linear relationship. This law is in good consistency with existing research results; under the condition of B / L=0.4, the ultimate support pressure curve caused by the equidistant change of the slope angle is not equidistantly distributed, and the distance between the curves increases with The increase is increasing slowly. Figure 17(c) and (d) show that the tunnel depth ratio C / D still has a certain influence on the ultimate support pressure. The increase of C / D leads to an increase in the ultimate support pressure, but its change does not affect the ultimate support pressure with the increase of C / D. The law of change.

[0225] Figure 18 The variation law of the ratio B / L of the area with smaller support pressure (block II) to the ultimate support pressure provided in the embodiment of this application; wherein, Figure 18 (a) shows the variation of B / L to the ultimate support pressure when the slope angle is 3%. Figure 18 (b) shows the variation of B / L to the ultimate support pressure when the slope angle is 9%.

[0226] The uphill optimization model provided by this application and the existing six-block model (β = 0) reveal similar critical internal friction angle phenomena: when When , the ultimate support pressure is positively correlated with B / L; Within the interval, the support pressure corresponding to different B / L values ​​tends to converge; when When B / L increases, the support pressure decreases inversely and shows a significant nonlinear characteristic.

[0227] This application uses the large-scale finite element software ABAQUS to simulate the instability problem of the local excavation surface of a shallow-covered rectangular jacking tunnel under longitudinal slope conditions, draws the λ-s curve, obtains the ultimate support pressure for active instability of the excavation surface under longitudinal slope conditions, and reveals the active failure mode of the excavation surface under longitudinal slope conditions. The longitudinal slope optimization model is then compared with the numerical model to verify the rationality of the theoretical optimization model, and relevant parameter analysis of the finite element simulation is performed to provide a reference for determining the lower limit of the support pressure in the construction of rectangular jacking tunnels.

[0228] Specifically, the finite element software ABAQUS was used to simulate the active failure phenomenon of the rectangular tunnel excavation face under longitudinal slope conditions in sandy soil. The unified parameters of the numerical simulation were γ = 19.8 kN / m3, D = 6 m, c / γD = 0, C / D=1.0~2.0, L / D=1.5~2.0, B / L=0.4~0.7, β=3%~9%, σ s =0kPa.

[0229] This application simulates 2 models with 2 depth ratios (C / D=1.0, 2.0), 2 aspect ratios (L / D=1.5, 2.0), 4 proportions of the area with smaller support pressure (block II) (B / L=0.4, 0.5, 0.6, 0.7), 6 uphill and downhill slopes (slopes of 3%, 6%, and 9%), and 7 different soil internal friction angles of some models, for a total of 264 sets of schemes.

[0230] The soil properties are assumed to be isotropic, continuous, and uniformly distributed across all components. Therefore, solid elements (C3D8R) are used for simulation. The theoretical optimization model targets sandy soils, while the Mohr-Coulomb plasticity model is primarily used for granular materials under monotonic loading. Therefore, the Mohr-Coulomb plasticity model is used for the soil, with parameter values ​​shown in Table 4. Because the optimization model does not consider the influence of groundwater, the total stress method is used for soil modeling.

[0231] Table 4

[0232] <![CDATA[重度 / kN / m 3 > Elastic modulus / MPa Cohesion / kPa Friction angle / (°) Poisson's ratio 19.8 30 0 15～45 0.25

[0233] Taking advantage of the symmetry of the tunnel model, only half of the tunnel geometry model is established for analysis. For example, with a slope of 3%, C / D = 1, L / D = 1.5, and B / L = 0.4, the geometry model is as follows: Figure 19 As shown, the model size is 50m (length) × 25m (width) × 30m (height), and the numerical model grid is divided as follows Figure 20 As shown in the figure, in order to improve the accuracy of the data, the mesh of the excavation surface area was encrypted, and the unit attribute adopted the eight-node hexahedron unit, which was divided into 35420 nodes and 32130 units.

[0234] The starting surface of the jacking tunnel is set as the XOZ coordinate plane (coordinates see Figure 19 The model is in the lower left corner. The top surface of the model adopts free boundary conditions, the four lateral boundaries impose normal displacement constraints, and the bottom surface implements full constraints. After the soil is excavated, a displacement of σ is imposed on the excavation surface. t0 The support pressure of each boundary constraint is described mathematically as follows:

[0235]

[0236] Among them, u x | x＝0 is the x-direction displacement of the plane x=0m, u x | x＝25 is the x-direction displacement of the plane x=25m; u y | y＝0 is the y-direction displacement of the plane y=0m, u y | y＝50 is the y-direction displacement of the plane y=50m, u x | z＝0 is the x-direction displacement of the z=0m plane, u y | z＝0 is the y-direction displacement of the z=0m plane, u z | z＝0 is the z-direction displacement of the plane z=0m.

[0237] Pipe jacking construction is originally a cyclic operation process that proceeds sequentially. However, the research focus of this application is on the active failure mode of the excavation face and its ultimate support capacity. Therefore, in order to reduce calculation time, this application simplifies the simulation process and directly applies radial constraints around the tunnel after excavating to the middle position of the jacking direction. The pressure applied on both sides of the excavation face is the lateral static earth pressure at the corresponding depth in the soil layer, and the support pressure in the middle area of ​​the excavation face is continuously reduced. The specific simulation process is as follows: (1) The Mohr-Coulomb constitutive model is used to characterize the nonlinear mechanical properties of the sand layer. Due to the geometric regularity of the model, the automatic ground stress balance analysis step in the finite element software is used to accurately restore the initial stress field distribution of the stratum; (2) In the tunnel step-by-step excavation simulation, a normal displacement constraint is applied to the excavation contour line to simulate the initial support effect. At the same time, a trapezoidal distribution support force corresponding to the initial ground stress field is applied to the tunnel face. The dynamic balance of the excavation stage is achieved through finite element software calculation; (3) The load release coefficient method is used to reduce the tunnel face support force in stages. The surrounding rock stress redistribution characteristics and displacement field evolution law are recorded in each analysis step; (4) When the support force drops to the critical active earth pressure value, even if the pressure change amplitude is very small, the displacement in the central area of ​​the excavation face will still increase sharply, causing obvious deformation of the soil. At this time, it is determined that the excavation face has entered an unstable state and the calculation program automatically terminates.

[0238] The excavation face support pressure defined in this application is a simplified parameter that characterizes the non-uniform trapezoidal distribution of support pressure. Its physical meaning is the equivalent pressure value at the center point of the excavation face. In order to measure the magnitude of the excavation face support pressure, the concept of "support stress ratio" is introduced. Its calculation formula is as follows, which is used to more accurately reflect the relative size and change trend of the support pressure.

[0239]

[0240] Among them, σ t0 is the support pressure at the center of the excavation face, and σ0 is the lateral static earth pressure at the center of the excavation face.

[0241] Figure 21 The figure shows the support pressure ratio-displacement evolution curve of a typical uphill working condition (longitudinal slope 3%, burial depth ratio C / D=1, cross-section width-to-height ratio L / D=1.5, and the proportion of the area with smaller support pressure B / L=0.4). The data analysis results show that when the support pressure ratio reaches 0.28, the corresponding critical support stress value is 37.02kPa. At this time, the displacement curve has an obvious inflection point, indicating that the excavation face has entered a critical instability state. Figure 21It can be seen that the change in the support stress of the rectangular jacking tunnel excavation face presents a three-stage nonlinear response characteristic: 1) Elastic deformation stage: When λ>0.28, the displacement of the excavation face changes linearly with the decrease of λ; 2) Critical sensitivity stage: When 0.1<λ<0.28, a small decrease in support stress can trigger a sharp increase in displacement; 3) Progressive instability stage: When λ<0.1, the excavation face enters a plastic breakthrough state, and the displacement shows a self-sustaining growth. Even if a constant support pressure is maintained, it still continues to be unstable.

[0242] Furthermore, the geometric shape of the failure mode of the upslope finite element model was compared with that of the theoretical model to verify the rationality of the upslope finite element model. The unified calculation parameters were γ = 19.8 kN / m3, D = 6 m, c / γD = 0, C / D = 1.0, L / D = 2.0, B / L = 0.4-0.7, β = 6%. Comparison of the geometric shapes of the failure mode of the finite element model and the failure mode of the upslope theoretical model Figure 22 shown; among them, Figure 22 (a) is a comparison of the geometric shapes of the failure modes of the first finite element model and the uphill theoretical model. Figure 22 (b) is a comparison of the geometric shapes of the failure mode of the second finite element model and the failure mode of the uphill theoretical model. Figure 22 (c) is a comparison of the geometric shapes of the failure modes of the third finite element model and the uphill theoretical model. Figure 22 (d) is the geometric comparison of the failure mode of the fourth finite element model and the failure mode of the uphill theoretical model. Figure 22 (e) is the geometric comparison of the failure mode of the fifth finite element model and the failure mode of the uphill theoretical model. Figure 22 (f) is a comparison of the geometric shapes of the failure modes of the sixth finite element model and the upslope theoretical model. As can be seen from the figure, the bottom failure surface of the failure mode increases with the increase of B / L (the proportion of the area with smaller support pressure) and The shear slip surface of the tunnel base shows a significant inclination angle. When B / L is fixed, the upper affected area changes with The damage angle θ decreases with the increase of increases with the increase of When the soil friction angle is small, the top failure range will slightly expand with the increase of B / L, and the failure angle θ will decrease with the increase of B / L. The failure shapes calculated by the upslope optimization model of this application and the existing model and finite element model have slight deviations. In addition, the rules of the existing upslope model, the upslope optimized upslope model of this application and the finite element model are consistent, and the failure angle θ is However, the existing upslope model does not consider the uneven distribution of support pressure and the factor of B / L, so the predicted failure angle will not change when B / L changes.

[0243] The results of finite element simulation show that the failure mode of the uphill theoretical model and the failure mode of the finite element model are generally consistent with each other. The existing uphill model, the uphill optimized uphill model of this application and the uphill finite element model have proved the rationality of each other. Therefore, the uphill optimized uphill model and the uphill finite element model of this application can predict a reasonable instability failure mode.

[0244] In order to analyze the influence of B / L and slope angle β on the ultimate support pressure of rectangular tunnel excavation face under upslope conditions, the rationality of the upslope finite element model is verified by comparing with the existing theoretical solution. The unified calculation parameters are γ=19.8kN / m3,D=6m,c / γD=0, C / D=1.0~2.0, L / D=2.0, B / L=0.4, β=3%~9%. Figure 23 The uphill ultimate support pressure solution provided in the embodiment of the present application varies with the friction angle; wherein, Figure 23 (a) shows the variation of the upslope ultimate support pressure solution with the friction angle when C / D is 1. Figure 23 (b) shows the variation of the upslope ultimate support pressure solution with the friction angle when C / D is 2. Figure 23 It can be seen that the prediction trends of the uphill optimization model and the finite element model are basically the same, and both increase with the friction angle. This is because a larger friction angle can improve the stability of the soil, thereby reducing the support pressure to maintain the stability of the tunnel face. The change trends of different slopes β (3%, 6%, 9%) are similar, and both the upslope optimization model and the finite element model can well capture this change. When the slope β increases, the curve basically moves upward as a whole, that is, σ t0 / γD gradually increases, which indicates that the steeper the slope, the worse the stability, the larger the damage range of the tunnel, and the greater the required support pressure. The slope β has a significant impact on stability. When the friction angle is 15°, the solution of this application is σ when the slope is 9%. t0 The / γD value is 3.52% higher than that when the slope is 3%. When the friction angle is 45°, the solution of this paper is σ t0 The / γD value is 24.79% higher than that when the slope is 3%, which shows that at a larger friction angle When σ t0 / γD rises faster. This is because When the angle is less than 25°, the stability of the tunnel face is very sensitive to the change of the soil friction angle. The increase of the soil friction angle will greatly improve the soil stability. When the angle is greater than 25°, the sensitivity of the tunnel face stability to the change of the soil friction angle decreases, which reflects the sensitivity of the tunnel face stability to the slope β. Figure 23 From (a) and (b) in the figure, we can see that under different burial depth ratios (C / D), the support pressure solution changes with the friction angle. The trend of change is similar to that of the numerical solution, except that the value of the support pressure solution increases slightly with the increase of the burial depth ratio. The results of the upslope optimization model are generally higher than those of the numerical solution, but the trends of the two are consistent. The upslope optimization model can better predict the failure mode. When the uphill optimization model is close to the numerical solution, it shows that the uphill optimization model has higher prediction accuracy at smaller friction angles; The large discrepancy between the upslope optimization model and the numerical solution is likely due to the upslope optimization model assuming a more ideal failure mechanism, while the actual numerical simulation considers more influencing factors. The upslope optimization model well reflects the influence of slope and provides reasonable failure predictions, thus serving as an effective theoretical analysis tool.

[0245] Furthermore, in order to study the influence of the proportion of the area with smaller support force (block II) on the ultimate support pressure of the excavation face under uphill conditions, the parameters are determined as γ = 19.8 kN / m3, D = 6 m, c / γD = 0, C / D=1.0, L / D=2.0, B / L=0.4~0.7, β=0%~9%. Figure 24 The influence of B / L on the ultimate support pressure of the rectangular tunnel excavation face under different uphill slopes provided in the embodiment of the present application; wherein, Figure 24 (a) shows the influence of B / L on the ultimate support pressure of rectangular tunnel excavation face when the slope angle is 0%. Figure 24 (b) shows the influence of B / L on the ultimate support pressure of rectangular tunnel excavation face when the slope angle is 3%. Figure 24 (c) shows the influence of B / L on the ultimate support pressure of rectangular tunnel excavation face when the slope angle is 6%. Figure 24 (d) in the figure shows the influence of B / L on the ultimate support pressure of the rectangular tunnel excavation face when the slope angle is 9%. The study shows that: when horizontal excavation (β=0°), the uphill optimization model provided by this application degenerates into a six-block silo-wedge model. In the uphill situation (β>0°), whether it is the uphill optimization theoretical solution proposed in this application or the numerical simulation results, in any case where the B / L value ranges from 0.4 to 0.7, the ultimate support pressure shows a nonlinear decreasing trend with the increase of the internal friction angle. It is worth noting that the model of this application also reveals the critical internal friction angle phenomenon: when When , the ultimate support pressure is positively correlated with B / L; Within the interval, the support pressure corresponding to different B / L values ​​tends to converge; when When B / L increases, the support pressure decreases inversely, showing a significant nonlinear characteristic. When fixed, it increases with the increase of B / L.

[0246] when When B / L=0.4~0.7, β=3% increases to β=6%, and the support pressure solution increases by 2.01% on average; β=6% increases to β=9%, and the support pressure solution increases by 2.10% on average; When B / L=0.4~0.7, β=3% increases to β=6%, and the support pressure solution increases by an average of 6.48%. When β=6% increases to β=9%, the support pressure solution increases by an average of 6.29%. When B / L=0.4~0.7, β=3% increases to β=6%, and the support pressure solution increases by an average of 11.56%. β=6% increases to β=9%, and the support pressure solution increases by an average of 10.75%. It can be concluded that the size of the internal friction angle affects the sensitivity of the ultimate support pressure to the uphill slope angle. The larger the internal friction angle, the more sensitive the ultimate support pressure is to changes in the slope angle. Based on the comparative analysis of the theoretical model and the numerical simulation, it can be seen that the calculation results of the uphill optimization model are higher than the numerical solution, mainly due to its refined consideration of the friction between blocks: in the force balance process of block II, the friction provided by the adjacent blocks does not fully exert the shear potential of the soil (only partially utilized), and the support pressure needs to be increased to maintain stability. However, the numerical model is limited by the overall material assumption and cannot accurately simulate the mechanical transfer characteristics between blocks. Therefore, the uphill optimization model provided in this application has a higher safety redundancy and is more suitable for engineering support design.

[0247] In order to study the influence of slope β on the ultimate support pressure of the excavation face under uphill conditions, the unified calculation parameters are γ=19.8kN / m3,D=6m,c / γD=0, C / D=1.0, L / D=2.0, B / L=0.5, β=0% to 9%. Figure 25 The study revealed the influence of the slope angle β on the ultimate support pressure of the pipe jacking upslope. The study showed that when β = 0°, the model degenerates into a six-block silo-wedge model. In the upslope condition with β > 0°, except for the six-block silo-wedge model, the solutions of all other models show a linear increase with increasing β. The mechanism is that the slope change significantly alters the stress distribution in the overlying soil layer through geometric effects. Notably, the consistency of the slopes of the pressure-slope curves of each model indicates the universality of slope sensitivity, which verifies the reliability of the upslope optimization theoretical model proposed in this application for stability analysis under complex slope conditions.

[0248] Based on the method for calculating the support pressure of a rectangular tunnel surface with non-uniform longitudinal slope provided in the above embodiment, the embodiment of the present application further provides a device for calculating the support pressure of a rectangular tunnel surface with non-uniform longitudinal slope, which specifically includes:

[0249] A model optimization module is used to adjust the angle between the wedge and the working surface in the six-block silo-wedge model used to simulate the tunnel soil failure zone based on the slope of the tunnel to be excavated, thereby obtaining an optimized upslope model of the tunnel to be excavated;

[0250] The wedge mechanics equation construction module is used to construct the mechanics equations of the quadrangular pyramid wedge and the triangular prism wedge during the excavation process based on the force systems of the quadrangular pyramid wedge and the triangular prism wedge in the upslope optimization model during the excavation process;

[0251] A wedge support pressure equation construction module is used to derive the critical support pressure control equation that characterizes the stability of the working face during tunneling based on the mechanical equations of a quadrangular pyramid wedge and a triangular prism wedge during tunneling.

[0252] The soil compartment diaphragm support pressure equation construction module is used to construct the soil compartment diaphragm support pressure equation based on the soil deadweight and critical support pressure control equation, using the force balance principle of the soil compartment along the excavation slope during excavation.

[0253] The excavation parameter adjustment module is used to use the support pressure equation of the soil compartment diaphragm based on the excavation slope, burial depth, working face width, height and inclination angle of the wedge sliding surface during the excavation process to calculate the soil compartment diaphragm support pressure in real time to determine whether the working face is stable during the excavation of the tunnel to be excavated, thereby adjusting the excavation parameters.

[0254] An embodiment of the present application also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the above-mentioned method for calculating the support pressure of a rectangular tunnel face with non-uniform longitudinal slope are implemented.

[0255] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for calculating support pressure on a rectangular tunnel face with non-uniform longitudinal slope, characterized in that: include: Based on the slope of the tunnel to be excavated, the angle between the wedge and the working surface in the six-block silo-wedge model used to simulate the tunnel soil failure area is adjusted to obtain the upslope optimization model of the tunnel to be excavated. Based on the force system of the quadrangular pyramid wedge and triangular prism wedge in the upslope optimization model during the excavation process, the mechanical equations of the quadrangular pyramid wedge and the triangular prism wedge during the excavation process are constructed; Based on the mechanical equations of a quadrangular pyramid wedge and a triangular prism wedge during tunneling, the critical support pressure control equation that characterizes the stability of the working face during tunneling is obtained. The support pressure equation of the soil compartment diaphragm is constructed based on the force balance principle of the soil in the soil compartment along the excavation slope during excavation, the self-weight of the soil in the soil compartment and the critical support pressure control equation. The support pressure equation of the soil compartment diaphragm is used to calculate the support pressure of the soil compartment diaphragm in real time based on the excavation slope, burial depth, working face width, height and inclination angle of the wedge sliding surface during the excavation process. This is used to determine whether the working face is stable during the excavation of the tunnel to be excavated, and thus adjust the excavation parameters.

2. The method for calculating support pressure of a rectangular tunnel face with non-uniform longitudinal slope according to claim 1 is characterized in that: The process of constructing the mechanical equations of the quadrangular pyramid wedge during tunneling includes: The stress analysis of the pyramid wedge was conducted. Based on the principle of force balance of the pyramid wedge during excavation, the vertical load equation of the overlying soil column, the relationship equation between the normal force and friction resistance of the base sliding surface, the relationship equation between the normal force and friction resistance of the outer contact surface, the support pressure equation of the working face, and the deadweight load equation of the pyramid wedge were constructed. Based on the bidirectional static equilibrium conditions, a bidirectional static equilibrium equation group is constructed for the mechanical equations of the tetrahedral wedge during the excavation process; the bidirectional static equilibrium equation group is solved to obtain the normal force equation and friction force equation of the inner contact surface of the tetrahedral wedge during the excavation process.

3. The method for calculating support pressure of a rectangular tunnel face with non-uniform longitudinal slope according to claim 2 is characterized in that: The vertical load equation of the overlying soil column on the quadrangular pyramid wedge during the excavation process is expressed as: Where P1 represents the vertical load of the overlying soil column on the pyramid wedge during the excavation process; γ represents the soil bulk density; C represents the depth of the tunnel to be excavated; σ s represents the surface load; L represents the width of the working face of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge; The relationship between the normal force and friction resistance of the base sliding surface is expressed as: Wherein, T1 represents the friction resistance of the base sliding surface; c represents the cohesion of the soil of the tunnel to be excavated; N1 represents the normal force of the base sliding surface; It represents the soil friction angle of the tunnel to be excavated; The relationship equation between the normal force and friction resistance of the outer contact surface is expressed as: Where, N3 represents the normal force of the outer contact surface; K0 represents the static earth pressure coefficient, σ z represents the vertical stress on the lateral sliding surface, σ z =γC+γz, where z represents the integral variable; The support pressure equation of the working face is expressed as: Among them, S1 represents the support pressure of the working face; s1 represents the support pressure acting on the excavation surface of the quadrangular wedge during excavation. K a represents the active earth pressure coefficient, The self-weight load equation of the quadrangular pyramid wedge is expressed as: Where G1 represents the deadweight load of the tetrahedral wedge; V1 represents the volume of the tetrahedral wedge; The two-way static equilibrium equations are expressed as: Among them, T 21 represents the friction resistance of the inner contact surface of the quadrangular pyramid wedge during the excavation process; α represents the base angle of the mid-waist trapezoidal surface of the overlying soil part of the upslope optimization model; The normal force equation of the inner contact surface of the quadrangular pyramid wedge during the excavation process is expressed as: N 21 =(P1+G1)cosθ+S1sinθcosβ-S1sinβcosθ-N3cosαsinθ, Among them, N 21 It represents the normal force on the inner contact surface of the quadrangular pyramid wedge during the excavation process; The friction equation of the inner contact surface of the quadrangular pyramid wedge during the excavation process is expressed as: T 21 =-P1sinθ-G1sinθ-N3cosαcosθ+T3sinα+T1+S1cosθcosβ+S1sinθsinβ。 4. The method for calculating support pressure of a rectangular tunnel face with non-uniform longitudinal slope according to claim 1, characterized in that: The process of constructing the mechanical equations of the triangular prism wedge during tunneling includes: The force analysis of the triangular prism wedge was conducted. Based on the force balance principle of the triangular prism wedge during the excavation process, the vertical stress equation of the overlying soil column, the relationship equation between the normal force and friction resistance of the base contact surface, the support reaction force equation of the working face, the normal force equation and friction resistance equation of the symmetrically distributed lateral contact surface, and the deadweight load equation of the triangular prism wedge were constructed. A set of spatial equilibrium equations is constructed based on the normal force equation and friction force equation of the symmetrically distributed lateral contact surface; the normal force equation and friction force equation of the lateral contact surface of the triangular prism wedge during the excavation process are obtained by solving the spatial equilibrium equation.

5. The method for calculating support pressure of a rectangular tunnel face with non-uniform longitudinal slope according to claim 4 is characterized in that: The vertical stress equation of the overlying soil column subjected to the triangular pyramid wedge during the excavation process is expressed as: P2=σ v BDcosβ(cotθ+tanβ), Where P2 represents the vertical stress of the overlying soil column on the triangular pyramid wedge during the excavation process; σ v represents the Terzaghi loosening earth pressure, R represents the ratio of the overlying soil volume to the lateral area, γ represents the soil bulk density, K0 represents the static earth pressure coefficient, c represents the soil cohesion of the tunnel to be excavated, represents the soil friction angle of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge; The relationship equation between the normal force and friction resistance of the substrate contact surface is expressed as: Wherein, T2 represents the friction resistance of the substrate contact surface; N2 represents the normal force of the substrate contact surface; The support reaction equation of the working face is expressed as: S2=σ s2 BD, Among them, S2 represents the support reaction force of the working face; σ s2 represents the critical support pressure; The normal force equation and friction resistance equation for the symmetrically distributed lateral contact surface are expressed as: Among them, T 12 represents the friction resistance of the first lateral contact surface of the triangular prism wedge; T 32 Indicates the friction resistance of the second lateral contact surface of the triangular prism wedge; N 12 Represents the normal force on the first lateral contact surface of the triangular prism wedge; N 32 represents the normal force on the second lateral contact surface of the triangular prism wedge; The self-weight load equation of the triangular prism wedge is expressed as: Where G2 represents the deadweight load of the triangular prism wedge; V2 represents the volume of the triangular prism wedge; The spatial equilibrium equations are expressed as: The normal force equation of the lateral contact surface of the triangular prism wedge during the excavation process is expressed as: The friction equation of the lateral contact surface of the triangular prism wedge during the excavation process is expressed as: N 12 =(P2+G2)cosθ+S2sinθcosβ-S2sinβcosθ。 6. The method for calculating support pressure of a rectangular tunnel face with non-uniform longitudinal slope according to claim 1 is characterized in that: The critical support pressure control equation is expressed as: Among them, σ s2 represents the critical support pressure; γ represents the soil bulk density; C represents the depth of the tunnel to be excavated; σ s represents the surface load; L represents the width of the working face of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge; K0 represents the static earth pressure coefficient, c represents the soil cohesion of the tunnel to be excavated, represents the soil friction angle of the tunnel to be excavated; K a represents the active earth pressure coefficient, R represents the ratio of the overlying soil volume to the lateral area, α represents the base angle of the mid-waist trapezoidal surface in the overlying soil part of the upslope optimization model.

7. The method for calculating support pressure of a rectangular tunnel surface with non-uniform longitudinal slope according to claim 1 is characterized in that: The supporting pressure equation of the soil compartment diaphragm is expressed as: Among them, σ t0 represents the supporting pressure of the soil compartment partition; γ represents the soil bulk density; C represents the burial depth of the tunnel to be excavated; σ s represents the surface load; L represents the width of the working face of the tunnel to be excavated; D represents the height of the working face of the tunnel to be excavated; B represents the width of the triangular prism wedge; β represents the excavation slope; θ represents the inclination angle of the sliding surface of the wedge; K0 represents the static earth pressure coefficient, c represents the soil cohesion of the tunnel to be excavated, represents the soil friction angle of the tunnel to be excavated; K a represents the active earth pressure coefficient, R represents the ratio of the overlying soil volume to the lateral area, α represents the bottom angle of the medium waist trapezoidal surface of the overlying soil part of the upslope optimization model; η represents the inverse of the loose coefficient of the soil in the soil compartment, K represents the looseness coefficient of the soil in the soil compartment; w represents the thickness of the soil in the soil compartment.

8. The method for calculating support pressure of a rectangular tunnel face with non-uniform longitudinal slope according to claim 1 is characterized in that: Obtaining the support pressure equation of the soil compartment partition also includes solving the support pressure equation of the soil compartment partition based on extreme value theory to obtain the maximum support pressure of the soil compartment partition, and using the maximum support pressure of the soil compartment partition as the critical support pressure to ensure the stability of the working face during excavation.

9. A device for calculating support pressure on a rectangular tunnel face with non-uniform longitudinal slope, characterized in that: include: A model optimization module is used to adjust the angle between the wedge and the working surface in the six-block silo-wedge model used to simulate the tunnel soil failure zone based on the slope of the tunnel to be excavated, thereby obtaining an optimized upslope model of the tunnel to be excavated; The wedge mechanics equation construction module is used to construct the mechanics equations of the quadrangular pyramid wedge and the triangular prism wedge during the excavation process based on the force systems of the quadrangular pyramid wedge and the triangular prism wedge in the upslope optimization model during the excavation process; A wedge support pressure equation construction module is used to derive the critical support pressure control equation that characterizes the stability of the working face during tunneling based on the mechanical equations of a quadrangular pyramid wedge and a triangular prism wedge during tunneling. The soil compartment diaphragm support pressure equation construction module is used to construct the soil compartment diaphragm support pressure equation based on the soil deadweight and critical support pressure control equation, using the force balance principle of the soil compartment along the excavation slope during excavation. The excavation parameter adjustment module is used to use the support pressure equation of the soil compartment diaphragm based on the excavation slope, burial depth, working face width, height and inclination angle of the wedge sliding surface during the excavation process to calculate the soil compartment diaphragm support pressure in real time to determine whether the working face is stable during the excavation of the tunnel to be excavated, thereby adjusting the excavation parameters.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the method for calculating the support pressure of a rectangular tunnel face with non-uniform longitudinal slope according to any one of claims 1 to 8.

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