Urban gate opening type tunnel three-dimensional excavation face stability upper limit analysis method

Abstract

The invention relates to the technical field of underground engineering stability analysis, and discloses a city gate opening type tunnel three-dimensional excavation face stability upper limit analysis method which comprises the steps that a city gate opening type tunnel three-dimensional geometric failure model is established, and a symmetric plane and a radial plane with a rotating shaft as the center are defined; discretizing an excavation surface into a plurality of unit nodes by adopting a spatial discretization technology, and iteratively calculating discrete point coordinates of a failure mechanism through a speed compatibility condition; based on an energy conservation principle, calculating external force acting power and an energy dissipation rate, and deducing a critical support pressure upper limit solution; and rotating parameters beta A and beta B are optimized through a genetic algorithm, and the most dangerous instability mode and the minimum support pressure are determined. According to the method, on the basis of the limit analysis upper limit theorem and the associated flow rule, the high-order difference scheme spatial discretization technology is adopted to capture and calculate control nodes, the three adjacent nodes and the projection points of the nodes on the symmetry plane form a calculation unit, and the problem of stability calculation of the urban gate opening type tunnel three-dimensional excavation face under the complex geometric boundary is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underground engineering stability analysis, in particular to a three-dimensional excavation face stability upper limit analysis method for a city gate type tunnel. BACKGROUND

[0002] Tunnel excavation face stability analysis refers to the evaluation and analysis of whether the exposed tunnel face (i.e., the excavation working face) will collapse, deform excessively, or other instability phenomena under the influence of factors such as geological conditions, construction methods, and support measures during tunnel construction through theoretical calculations, numerical simulations, and field monitoring. The core is to determine whether the excavation face can remain stable under the support of support measures or the strength of the rock-soil mass.

[0003] The existing city gate type tunnel excavation face stability analysis has the following problems:

[0004] 1. Geometric boundary restriction: traditional analytical methods are difficult to handle complex geometric boundary conditions (such as circular arch straight wall cross-sections);

[0005] 2. Limitation of failure mode: the existing rigid translational / rotational mechanism does not sufficiently match the actual instability form, resulting in large prediction errors;

[0006] 3. Calculation accuracy depends on experience: parameter optimization relies on manual trial and error, and lacks a systematic analysis method.

[0007] Therefore, a city gate type tunnel three-dimensional excavation face stability upper limit analysis method is needed to solve the above technical problems. SUMMARY

[0008] The purpose of the present application is to overcome the above technical problems by constructing a high-precision failure mechanism through spatial discretization technology and combining an optimization algorithm to achieve reliable prediction of the critical support pressure.

[0009] To achieve the above purpose, the present application is implemented according to the following technical solutions:

[0010] The city gate type tunnel three-dimensional excavation face stability upper limit analysis method comprises the following steps:

[0011] S1, a three-dimensional geometric failure model of a city gate type tunnel is established, and a symmetric plane and a radial plane centered on a rotation axis are defined;

[0012] In the three-dimensional geometric failure model of the city gate type tunnel, the tunnel region and the failure mechanism are included, and the contact surface between the tunnel region and the failure mechanism is the excavation face.

[0013] In the three-dimensional geometric failure model of the city gate type tunnel, C is the tunnel depth, L is the tunnel transverse width, H is the straight wall height, R is the circular arch radius, and a is the central angle of the circular arch.

[0014] S2, discretizing the excavation surface into a plurality of unit nodes by using a spatial discretization technique, and iteratively calculating the coordinates of the discrete points of the failure mechanism by using a velocity compatibility condition;

[0015] In the excavation surface constructed based on the spatial discretization technique, O is the rotation axis, C is the origin of the local coordinate system, Π is the radial plane, θ is the polar angle in the local coordinate system, β is the azimuth angle of the radial plane, x, y and z are the coordinates in the global coordinate system, and A is the spatial point on the working surface.

[0016] The spatial discretization technique adopts the following steps: defining a local coordinate system in the symmetry plane, and describing the position of the discrete point by using the polar coordinates (r, β); based on the coordinates of the discrete points in the adjacent planes and the normal vector of the velocity discontinuity surface, recursively calculating the coordinates of the discrete points in the subsequent planes.

[0017] The constructed failure mechanism is in a rigid rotation mode, and rotates around the rotation axis of point O at an angular velocity ω, and the projection of the velocity discontinuity surface of the failure mechanism on the symmetry plane is two logarithmic spiral lines:

[0018]

[0019] In formula (1), r A and r B are the polar radii of r1 and r2 when the azimuth angles are β A and β B , respectively, is the internal friction angle of the soil.

[0020] When the spatial discretization technique is used to construct the boundary surface of the failure mechanism, a local coordinate system (C j , x c,j , y c,j ) is defined in each radial plane Π j . In the spatial rectangular coordinate system, the spatial coordinates of the centroid C j in the plane Π j can be expressed as:

[0021]

[0022] In formula (2), β j is the azimuth angle of the plane Π m , and the polar radius r j is the distance from the midpoint of the connecting line of the upper and lower trace lines in the symmetry plane to point O when the azimuth angle is β j .

[0023] In the plane Π i,j , the vector C j P j composed of the discrete point P i,j and the centroid C j of the plane is defined as:

[0024] C j P i,j =(x i,j -x c,j ,y i,j -y c,j ,z i,j -z c,j ) (3);

[0025] The vector y j consisting of the center point C j of the plane and the point O is defined as:

[0026] y j =(0,-sinβ j ,cosβ j ) (4);

[0027] The angle between the vector C j P i,j and the vector y j is θ i,j , and the relative spatial position of the discrete point P i,j in the plane Π j can be determined according to the azimuth angle θ i,j . The azimuth angle θ i,j can be calculated as follows:

[0028]

[0029] In the discrete method, the spatial position of the discrete point P j+1 on the radial plane Π i,j+1 is determined by two discrete points P j and P i-1,j on the previous radial plane Π i,j according to the velocity compatibility condition. When solving the spatial coordinates of the point P i,j+1 , three conditions are commonly used, which are:

[0030] ① The angle between the normal vector of the plane where the three points P i-1,j , P i,j , P i,j+1 are located and the velocity vector at the midpoint M i,j of the line connecting P i-1,j and P i,j is

[0031] ② The discrete point P i,j+1 is on the plane Π j+1 ;

[0032] ③ The azimuth angle θ i,j+1 is θ i-1,j and θ i,jhalf of the sum of the two.

[0033] Based on the above three conditions, the specific spatial position of the discrete point P i-1,j and P i,j can be determined together. i,j+1 In solving the coordinates of the discrete point P i,j+1 , it is necessary to first calculate the unit normal vector N(x i-1,j , y i,j , z i,j+1 ) of the plane where P n , P n , P n are located. As described above, the unit normal vector N is defined to point outward from the plane, and the unit normal vector N needs to satisfy the following three conditions:

[0034] ① The normal vector N is a unit vector:

[0035]

[0036] ② The normal vector N is perpendicular to the vectors P i-1,j P i,j :

[0037]

[0038] x n (x i,j -x i-1,j ) + y n (y i,j -y i-1,j ) + z n (z i,j -z i-1,j ) = 0 (7);

[0039] ③ The angle between the normal vector N and the unit velocity vector v at the midpoint M i,j of the line connecting the points P i-1,j and P i,j is

[0040]

[0041] Based on the above three conditions, the unit normal vector N of the plane where P i-1,j , P i,j , P i,j+1 are located can be solved as:

[0042]

[0043] where,

[0044] A = -cotβ j (10);

[0045]

[0046] E = A 2 + C 2 + 1 (14);

[0047] F = 2(AB + CD) (15);

[0048] G = B 2 + D 2 - 1 (16);

[0049] Δ = F 2 - 4EG (17);

[0050] The unit normal vector N obtained has two directions, one of which is directed towards the inner side of the velocity discontinuity surface, and the other is directed towards the outer side. To ensure that the normal vector N obtained is directed towards the outer side of the velocity discontinuity surface, the normal vector N also needs to satisfy:

[0051] N · (P i-1,j P i,j x v) > 0 (18);

[0052] In addition, the discrete point P i,j+1 should also be located on the plane Π j+1 , then:

[0053] C j+1 P i,j+1 = r i,j+1 δ i,j+1 (19);

[0054] where r i,j+1 is the distance between the discrete point P i,j+1 and the point C j+1 ; δ i,j+1 is a unit vector, which can be expressed in the space rectangular coordinate system as:

[0055]

[0056] Taking into account:

[0057] M i,j P i,j+1 = M i,j C j+1 + C j+1 P i,j+1 = M i,j C j+1 + r i,j+1 δ i,j+1 (21);

[0058] From the unit normal vector N and the vector M i,j Pi,j+1 Perpendicular to each other available:

[0059]

[0060] Simultaneous equations, the coordinates of the discrete point P i,j+1 :

[0061]

[0062] Based on the above calculation process for the spatial position of each discrete point on the velocity discontinuity, the velocity discontinuity of the entire failure mechanism can be obtained. When all the discrete points in the plane Π j above the ground surface, the calculation is terminated and the linear interpolation is used to adjust the discrete points above the ground surface to the ground surface. The calculation accuracy of the failure mechanism is controlled by the number of discrete points n on the initial plane and the angle increment Δβ between adjacent planes Π j and Π j+1 .

[0063] S3, based on the principle of energy conservation, the work done by external force and energy dissipation rate are calculated, and the upper limit solution of the critical support pressure is derived;

[0064] In the upper limit theorem, the work done by external force and energy dissipation rate are calculated by functional equation, and the upper limit value of the limit failure load is determined based on the principle of energy conservation. In the stability study of tunnel excavation surface, the work done by external force includes the work done by gravity, the work done by support pressure of excavation surface and the work done by surface overload.

[0065] In the failure mechanism, four adjacent discrete points P i,j , P i+1,j , P i,j+1 , P i+1,j+1 are taken as calculation units and grouped. The work done by external force and energy dissipation rate of the entire mechanism can be obtained by calculating and accumulating the sum of the functional equation of the calculation unit.

[0066] The work done by gravity is:

[0067]

[0068] In the formula, γ is the unit weight of soil, V i,j is the volume of the calculation unit, R i,j is the distance between the center of the calculation unit and the rotation center, and β i,j is the azimuth angle.

[0069] The work done by the support pressure of the tunnel excavation surface is:

[0070]

[0071] In the formula, σ Tσs j r j β j θ

[0072] The energy dissipation on the velocity discontinuity is:

[0073]

[0074] where c is the soil cohesion, S i,j R i β

[0075] The limit support pressure of the tunnel face at the critical state is obtained by equating the work done by external forces to the energy dissipation rate:

[0076]

[0077] where σ T γ is the soil unit weight, V i,j R i,j β i,j θ

[0078] S4, Optimizing the rotation parameters β A and β B to determine the most dangerous instability mode and the minimum support pressure.

[0079] The failure mechanism based on the spatial discretization technique contains two optimization parameters β A and β B . The objective function is constructed with β A and β B as optimization variables, and the genetic algorithm is used to optimize the values of β A and β B to obtain the optimal instability mode and the upper limit solution of the limit support pressure of the tunnel face. The optimization parameters β A and β B must satisfy the following constraints:

[0080]

[0081] The application is based on a three-dimensional excavation surface stability upper limit analysis method of a city gate type tunnel based on a spatial discretization technique, based on a limit analysis upper limit theorem and associated flow rules, using a high-order difference format spatial discretization technique to capture calculation control nodes, using adjacent three nodes and their projection points on the symmetry plane to form a calculation unit, solving the three-dimensional excavation surface stability calculation problem of the city gate type tunnel under complex geometric boundary conditions, then based on the principle of energy conservation, through functional equation calculation, deriving a strict upper limit solution of the critical support pressure of the excavation surface and the most dangerous instability zone, then comparing with the upper limit solution and instability failure mode given by the limit analysis finite element numerical model, verifying the reliability of the method of the application.

[0082] Beneficial effects:

[0083] Limited by complex geometric boundary conditions, there is currently a lack of upper limit analysis model for the three-dimensional excavation surface stability of tunnels with a city gate type cross-section shape. The application is based on a limit analysis upper limit theorem and associated flow rules, using a high-order difference format spatial discretization technique to capture calculation control nodes, using adjacent three nodes and their projection points on the symmetry plane to form a calculation unit, solving the three-dimensional excavation surface stability calculation problem of the city gate type tunnel under complex geometric boundary conditions. The upper limit solution and instability failure mode given by the method of the application can provide theoretical guidance for the stability evaluation of similar engineering tunnel face and reinforcement of the most dangerous instability zone. BRIEF DESCRIPTION OF DRAWINGS

[0084] Figure 1 is a three-dimensional geometric failure model of a city gate type tunnel and a coordinate definition diagram of the application (describing the relationship between tunnel cross-section size parameters L / H / R / α and the coordinate system);

[0085] Figure 2 is a failure mechanism configuration schematic diagram based on spatial discretization technology of the application (showing logarithmic spiral projection, discrete node distribution and velocity interval surface);

[0086] Figure 3 is a limit analysis finite element numerical model established for comparison and verification of the failure surface of the failure mechanism in the application; Figure 4 is a tunnel excavation surface failure mode comparison diagram of the application. DETAILED DESCRIPTION

[0087] The application will be further described in detail below with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the application and do not limit the application.

[0088] Example 1

[0089] The three-dimensional excavation surface stability upper limit analysis method of a city gate type tunnel comprises the following steps:

[0090] S1. Establish a three-dimensional geometric failure model of a city gate tunnel and define the symmetry plane and radial plane centered on the rotation axis;

[0091] like Figure 1 Figure 2 shows the three-dimensional geometric failure model of a gate-type tunnel and its coordinate definition diagram (describing the relationship between the tunnel cross-sectional dimension parameters L / H / R / α and the coordinate system) of the present invention. The three-dimensional geometric failure model of the gate-type tunnel includes a tunnel region and a failure mechanism, and the contact surface between the tunnel region and the failure mechanism is the excavation surface.

[0092] In the three-dimensional geometric failure model of the city gate tunnel, C is the tunnel depth, L is the tunnel lateral width, H is the vertical wall height, R is the arch radius, and α is the arch center angle.

[0093] S2. Use spatial discretization technology to discretize the excavation surface into several unit nodes, and iteratively calculate the coordinates of the discrete points of the destruction mechanism through velocity compatibility conditions;

[0094] like Figure 2 , which is a schematic diagram of the destruction mechanism structure based on the spatial discretization technology of the present invention (showing the logarithmic spiral projection, discrete node distribution and velocity interval surface);

[0095] In the excavation face constructed based on spatial discretization technology, point O is the rotation axis, C is the origin of the local coordinate system, π is the radial plane, θ is the polar angle in the local coordinate system, β is the azimuth angle of the radial plane, x, y, and z are the coordinates of the global coordinate system, and A is the spatial point on the tunnel face.

[0096] The spatial discretization technique adopts the following steps: defining a local coordinate system in the symmetric plane and describing the position of the discrete point by polar coordinates (r, β); recursively calculating the coordinates of the subsequent plane discrete points based on the coordinates of the adjacent plane discrete points and the velocity discontinuity surface normal vector constraints.

[0097] The constructed destruction mechanism is a rigid rotation mode, and the rotation axis around point O rotates rigidly at an angular velocity ω. The projection of the velocity discontinuity surface of the destruction mechanism on the symmetry plane is two logarithmic spirals:

[0098]

[0099] In formula (1), r A and r B The azimuth angles are β A and β B When r1 and r2 are polar diameters, is the internal friction angle of soil.

[0100] When constructing the boundary surface of the destruction mechanism using the space discretization technology, in each radial plane Π j The local coordinate system (C j ,xc,j ,y c,j ). In the space rectangular coordinate system, the plane Π j Center centroid C j The spatial coordinates of can be expressed as:

[0101]

[0102] In formula (2), β j is the plane π j Azimuth, polar diameter r m The azimuth angle is β j The distance from the midpoint of the line connecting the upper and lower traces in the symmetry plane to point O.

[0103] In plane π j In the definition of discrete points P i,j and the plane centroid C j The vector C j P i,j for:

[0104] C j P i,j =(x i,j -x c,j ,y i,j -y c,j ,z i,j -z c,j ) (3);

[0105] Defined by the plane centroid point C j The vector y formed by the point O j for:

[0106] y j =(0,-sinβ j ,cosβ j ) (4);

[0107] Vector C j P i,j With vector y j The angle between them is θ i,j , according to the azimuth angle θ i,j The discrete point P can be determined i,j In plane π j The relative spatial position in . Azimuth angle θ i,j It can be calculated as follows:

[0108]

[0109] In the discrete method, the radial plane π j+1 Discrete point P on i,j+1 The spatial position of the previous radial plane Π jTwo discrete points P on i-1,j and P i,j Determined according to the velocity compatibility condition. Solve for point P i,j+1 There are three conditions used in the spatial coordinates of:

[0110] ①P i-1,j , P i,j , P i,j+1 The normal vector of the plane where the three points are located is P i-1,j and P i,j Connect the midpoint M i,j The angle between the velocity vectors at

[0111] ② Discrete point P i,j+1 In plane π j+1 superior;

[0112] ③Azimuth angle θ i,j+1 is θ i-1,j and θ i,j Half of the sum.

[0113] Based on the above three conditions, the discrete point P i-1,j and P i,j Together we determine the discrete point P i,j+1 The specific spatial position of the discrete point P i,j+1 When calculating the coordinates, you need to first calculate P i-1,j , P i,j , P i,j+1 The unit normal vector N(x n ,y n ,z n As mentioned above, the unit normal vector N is specified to point to the outside of the plane. The unit normal vector N must satisfy the following three conditions:

[0114] ①Normal vector N is a unit vector:

[0115]

[0116] ②Normal vector N and vector P i-1,j P i,j Perpendicular to each other:

[0117]

[0118] x n (x i,j -x i-1,j )+y n (y i,j -y i-1,j )+z n (z i,j -z i-1,j) = 0 (7);

[0119] The unit normal vector N and the point P i-1,j and the point P i,j The unit speed vector v at the midpoint M i,j of the connecting line is

[0120]

[0121] From the above three conditions, P i-1,j , P i,j , P i,j+1 can be solved. The unit normal vector N of the plane on which the three points P i-1,j , P i,j , P i,j+1 are located is:

[0122]

[0123] In the formula,

[0124] A = -cot β j (10);

[0125]

[0126] E = A 2 + C 2 + 1 (14);

[0127] F = 2 (AB + CD) (15);

[0128] G = B 2 + D 2 - 1 (16);

[0129] Δ = F 2 - 4EG (17);

[0130] The unit normal vector N obtained has two directions, one of which is towards the inner side of the velocity discontinuity surface, and the other is towards the outer side. To ensure that the normal vector N obtained is towards the outer side of the velocity discontinuity surface, the normal vector N also needs to satisfy:

[0131] N · (P i-1,j P i,j × v) > 0 (18);

[0132] In addition, the discrete point P i,j+1 should also be located on the plane Π j+1 , so:

[0133] C j+1 P i,j+1 = r i,j+1 δ i,j+1 (19);

[0134] Where r i,j+1The distance between the discrete point P i,j+1 and point C j+1 ; δ i,j+1 is a unit vector, which can be expressed in a space rectangular coordinate system as:

[0135]

[0136] It is considered that:

[0137] M i,j P i,j+1 =M i,j C j+1 +C j+1 P i,j+1 =M i,j C j+1 +r i,j+1 δ i,j+1 (21);

[0138] The unit normal vector N and the vector M i,j P i,j+1 are perpendicular to each other, and the following can be obtained:

[0139]

[0140] By solving the above equations, the coordinates of the discrete point P i,j+1 are obtained as:

[0141]

[0142] Based on the above calculation process, the spatial positions of each discrete point on the velocity discontinuity surface are calculated, and the velocity discontinuity surface of the entire failure mechanism is obtained. When all the discrete points in the plane Π j reach or are higher than the ground surface, the calculation is terminated, and linear interpolation is used to adjust each discrete point higher than the ground surface to the ground surface. The calculation accuracy of the failure mechanism is controlled by the number n of discrete points on the initial plane and the angle increment Δβ between adjacent two planes Π j and Π j+1 .

[0143] S3, based on the principle of energy conservation, the work rate of external force and energy dissipation rate are calculated, and the upper limit solution of critical support pressure is derived;

[0144] In the upper limit theorem, the work rate of external force and energy dissipation rate are calculated through the functional equation, and the upper limit value of the limit failure load is determined based on the principle of energy conservation. In the stability study of tunnel excavation surface, the work rate of external force includes the work rate of soil gravity, the work rate of excavation surface support pressure and the work rate of surface overload.

[0145] In the failure mechanism, four adjacent discrete points P i,j , P i+1,j , P i,j+1, P i+1,j+1 The work done by external force and energy dissipation rate of the whole mechanism can be calculated by the function equation of the calculation unit and the summation.

[0146] The work done by gravity of the soil mass is:

[0147]

[0148] where γ is the unit weight of the soil mass, V i,j is the volume of the calculation unit, R i,j is the distance between the centroid of the calculation unit and the rotation center, β i,j is the azimuth angle.

[0149] The work done by the support pressure of the tunnel excavation face is:

[0150]

[0151] where σ T is the support pressure of the tunnel excavation face, s j is the area of the calculation unit, r j is the distance between the centroid of the calculation unit and the rotation center, β j is the azimuth angle between the centroid of the calculation unit and the rotation axis.

[0152] The energy dissipation on the velocity discontinuity surface is:

[0153]

[0154] where c is the cohesion of the soil mass, S i,j is the area of the calculation unit on the failure surface, R i ′,j is the distance between the centroid of the calculation unit and the rotation center.

[0155] According to the equality of the work done by external force and the energy dissipation rate, the limit support pressure of the tunnel excavation face under the critical state (i.e., the critical support pressure) is:

[0156]

[0157] where σ T is the support pressure of the tunnel excavation face, γ is the unit weight of the soil mass, V i,j is the volume of the calculation unit, R i,j is the distance between the centroid of the calculation unit and the rotation center, β i,j is the azimuth angle.

[0158] S4. Optimizing the rotation parameter β A and β B to determine the most dangerous instability mode and the minimum support pressure.

[0159] The total number of failure mechanisms based on spatial discretization technology is β A and β B Two optimization parameters. Construct A and β B To optimize the objective function of variables, a genetic algorithm is used to A and β B The optimal value of β is optimized to obtain the optimal instability mode and the corresponding upper limit solution of the ultimate support pressure of the tunnel excavation face. A and β B The following constraints must be met:

[0160]

[0161] Example 2

[0162] The tunnel depth is 5m, the tunnel width is 10m, the vertical wall height is 5m, the arch radius is 5m, and the arch center angle is 180°. The soil weight is 20kN / m 3 , the internal friction angle is 15°, and the cohesion is 20kPa.

[0163] According to the above parameters, the method described in Example 1 is used to adjust the geometric parameter β A and β B An optimization search was performed, and the ultimate support pressure of the tunnel excavation face obtained by the method described in Example 1 was 9.98 kPa.

[0164] The calculated results are used as the external force boundary conditions in the numerical model and applied to the tunnel excavation surface. The friction angle in the soil is continuously reduced by combining the strength reduction technology. and cohesion c, and calculate the safety factor of the tunnel excavation face in the numerical model.

[0165] Considering that the external boundary condition is the ultimate support pressure of the tunnel under the critical state given by the discretization method, that is, at this point the tunnel is about to fail, corresponding to a critical safety factor of 1, the closer the safety factor calculated by the numerical model is to 1, the better the agreement between the two methods. After three iterative calculations and the introduction of mesh adaptation technology, the safety factor calculated in the limit analysis finite element method with a grid size of 15,861 was 0.975, which is very close to that of the proposed method with an error of only 2.5%, thus verifying the reliability and effectiveness of the spatial discretization method proposed in this paper.

[0166] The reliability of the method of the embodiment was verified using the three-dimensional limit analysis finite element software Optum G3. The established limit analysis finite element numerical model is shown in the attached figure. Figure 3 shown.

[0167] In the verification example, the specific data of example 2 is adopted, that is, the tunnel depth is 5m, the tunnel width is 10m, the straight wall height is 5m, the radius of the circular arch is 5m, the central angle of the circular arch is 180°, the soil bulk density is 20kN / m 3 , the internal friction angle is 15°, and the cohesion is 20kPa. Considering the symmetry of the model, only 1 / 2 of the geometric model is established to reduce the calculation amount. The bottom of the model is fully constrained, and the vertical boundary is constrained in the normal direction. In the analysis, it is assumed that the tunnel lining does not fail, so the displacement of the lining in all directions is constrained.

[0168] The method proposed in the application and the tunnel excavation face failure instability diagram given in the limit analysis finite element numerical model are as shown in Figure 4 From Figure 4 it can be seen that the method of the application is in good agreement with the failure surface predicted by the numerical simulation result. The instability zone of the soil extends from the tunnel face to the ground surface, and the displacement value of the soil at the bottom of the tunnel face is greater than that at the top, which further verifies the rationality of the tunnel excavation face instability failure mechanism constructed in the present application.

[0169] Limited by the complex geometric boundary conditions, there is still a lack of upper limit analysis model for the stability of the tunnel three-dimensional excavation face with the shape of the city gate type section. Based on the limit analysis upper limit theory and the associated flow rule, the high-order difference format spatial discrete technology is adopted to capture the calculation control node, and the adjacent three nodes and their projection points on the symmetry surface are used to form a calculation unit, so that the calculation difficulty of the stability of the city gate type tunnel three-dimensional excavation face under the complex geometric boundary is solved. The upper limit solution and the instability failure mode given by the method of the application can provide theoretical guidance for the stability evaluation of the tunnel face and the reinforcement of the most dangerous instability zone of similar projects.

[0170] The technical solution of the application is not limited to the limitation of the above specific embodiments, and any technical deformation made according to the technical solution of the application falls within the protection scope of the application.

Claims

1. An upper limit analysis method for the stability of a three-dimensional excavation surface of a city gate tunnel is characterized by: The following steps are involved: S1. Establish a three-dimensional geometric failure model of a city gate tunnel and define the symmetry plane and radial plane centered on the rotation axis; S2. Use spatial discretization technology to discretize the excavation surface into several unit nodes, and iteratively calculate the coordinates of the discrete points of the destruction mechanism through velocity compatibility conditions; S3. Based on the principle of energy conservation, calculate the external force power and energy dissipation rate, and derive the upper limit solution of critical support pressure; S4. Optimize the rotation parameter β by genetic algorithm A and β B , determine the most dangerous instability mode and the minimum support pressure.

2. The upper limit analysis method for the stability of a three-dimensional excavation surface of a city gate tunnel according to claim 1 is characterized by: In step S1, the three-dimensional geometric destruction model of the city gate tunnel includes a tunnel area and a destruction mechanism, and the contact surface between the tunnel area and the destruction mechanism is the excavation surface.

3. The upper limit analysis method for the stability of a three-dimensional excavation surface of a city gate tunnel according to claim 1 is characterized by: In step S2, the spatial discretization technology adopts the following steps: defining a local coordinate system in the symmetric plane, describing the position of the discrete point by polar coordinates (r, β); recursively calculating the coordinates of subsequent plane discrete points based on the coordinates of adjacent plane discrete points and the velocity discontinuity surface normal vector constraints.

4. The upper limit analysis method for the stability of the three-dimensional excavation surface of a city gate tunnel according to claim 2 is characterized in that: The breaking mechanism is a rigid rotation mode, and its velocity discontinuity surface is projected as a logarithmic spiral on the symmetry plane, satisfying: Where r A and r B The azimuth angles are β A and β B When r1 and r2 are polar diameters, is the internal friction angle of soil.

5. The method for analyzing the upper limit of stability of a three-dimensional excavation surface of a city gate tunnel according to claim 1 is characterized by: The critical support pressure calculation formula is: Where σ T is the support pressure of the tunnel excavation surface, γ is the soil density, V i,j To calculate the unit volume, R i,j To calculate the distance between the centroid and the rotation center of the unit, β i,j is the azimuth.

6. The method for analyzing the upper limit of stability of a three-dimensional excavation surface of a city gate tunnel according to claim 1 is characterized by: The most dangerous instability mode is determined by the following steps: constructing a A and β B To optimize the objective function of variables; genetic algorithm is used under the constraints Search for the optimal solution internally.

Images