Method for calculating ultimate supporting force of excavation face of fault fracture zone based on local instability

Abstract

The invention belongs to the field of tunnel engineering and rock-soil mechanics, and discloses a fault fracture zone excavation face limit support force calculation method based on local instability, through a fault fracture zone tunnel excavation simulation test, an excavation face local instability form is obtained, an improved cone instability model is provided, and a fault fracture zone excavation face limit support force calculation method is provided. The problem that the lateral soil pressure coefficient is difficult to accurately estimate is solved, and calculation is simplified; carrying out mechanical analysis based on symmetry of the rotating body, and establishing a calculation method for the ultimate supporting force of the tunnel excavation face in the fault area; and the accuracy is verified by comparing with the existing test result, and the influence of key factors such as cohesive force, internal friction angle and soil weight is analyzed.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of tunnel engineering and geotechnical mechanics, and particularly relates to a calculation method of limit support force of an excavation face of a fault fracture zone based on local instability. BACKGROUND

[0002] When a tunnel passes through a fault fracture zone, karst, soft stratum and other adverse geology, disasters such as collapse of the excavation face and gushing water are likely to occur. For example, the advanced heading pit construction of the entrance main tunnel of the Yuanliangshan Tunnel of the Chongqing-Huaiyang Railway encountered a mud burst at the DK354+879 mileage, and the Yonglian Tunnel of the Jilian Expressway in Jiangxi Province encountered a large amount of water-rich soft and broken medium during the process of passing through the F1-F4 faults, resulting in a water and mud burst disaster. When a tunnel passes through a fault with high water pressure, loose and broken stratum and strong permeability, it is important to correctly determine the instability form of the excavation face and accurately calculate the limit support force of the excavation face in order to prevent instability of the tunnel excavation face.

[0003] Scale model tests and physical simulation tests are the main methods for studying the instability of a tunnel excavation face. Through the tests, the instability process, mode, form and range of the tunnel excavation face can be studied. Chambon P, Xiaoqing Zhang, Renpeng Chen and other scholars conducted model tests of the instability of the excavation face in sandy soil stratum and found that the collapse of the tunnel excavation face is divided into two forms, namely local collapse and overall collapse. H / D (the ratio of the tunnel burial depth to the diameter) has a great influence on the collapse form of the excavation face. When the tunnel burial depth ratio (H / D) is relatively small, the instability region extends to the ground surface; when the tunnel burial depth ratio is relatively large, the instability region is limited to the vicinity of the excavation face and does not extend to the ground surface. Other scholars have also found this form of local instability in tests and numerical simulations. Huayang Lei and other people used transparent soil material to conduct model tests of the instability of the tunnel excavation face and studied the failure form of the tunnel excavation face. The results showed that the failure region stopped changing after developing to a certain height, forming a bulb-shaped failure mode, and the formation region of the soil arch is approximately within the range of 1.5D-2.0D (D is the diameter of the tunnel) above the top of the tunnel. Niu H and other people studied the variation law of the support pressure and instability mode of the excavation face under different soil parameters based on centrifugal tests and found that with the increase of H / D, the height and width of the soil arch continuously increase. When H / D>1.5, the limit support force tends to be stable, and the influence of the soil arch effect gradually weakens. Mayang Chen and other people simulated the instability process of the excavation face based on the smooth particle hydrodynamics method. When the excavation face is in a local instability limit equilibrium state, two shear zones with a certain width appear at the top and bottom of the tunnel arch, and the shear zone near the top of the arch first extends to the ground surface. Xilin Lv and other people found that with the increase of the critical strength of the sand, the failure form contour line in front of the excavation face appears to shrink, the instability range of the excavation face significantly reduces, and the instability is concentrated in a local range in front of the excavation face. The simulation test results provide a basis for the construction of a model of the support force of the tunnel excavation face.

[0004] Accurate calculation of the tunnel face support force is essential to ensure its stability. In order to calculate the face support force, it is necessary to construct a mechanical model of the failure zone according to the failure mode of the excavation face. As mentioned above, existing model tests and engineering practices show that the tunnel face instability can be divided into global failure and local failure, and researchers have proposed a series of analytical solutions for face support force based on limit equilibrium method. M. Horn first established a three-dimensional wedge global instability model, considering that the failure mode of the excavation face is composed of a lower wedge and an upper silo body, and the minimum support force of the excavation face is determined by the mechanical equilibrium of the combined model. Jancsecz, Broere, Anagnostou, Chen and others further improved the silo model in terms of failure zone shape, lateral pressure calculation and soil arching effect. Some scholars have also conducted in-depth research on local instability. Zhang Mengxi and others studied the local failure mode of shield tunnel face in cohesive soil stratum, and proposed a three-dimensional horizontal spherical shell local instability model. This model takes into account the influence of the main stress axis deflection on the active limit support force of deep tunnel, and combines with the traditional soil pressure formula of the loose soil to derive a general solution for the limit support force of local instability of the excavation face. Jinfeng Zou and others proposed an improved three-dimensional rotating body local failure model based on the limit analysis method. This model assumes that the failure zone is composed of an ellipsoidal and a rotating body, and the lateral soil pressure coefficient is improved to fully reflect the soil arching effect, which improves the calculation accuracy of the model, but the disadvantage is that the model is complex and the calculation is large.

[0005] Wang Haifeng and Hu Riqing and others established a tunnel face failure model based on the collapse arch and the limit analysis method, and proposed an analytical solution for the limit support force suitable for sand and gravel tunnels. Zhong Junhao and others established a multi-curve conical failure model of the excavation face based on the upper bound theorem of limit analysis for the stability of deep tunnel excavation face under nonlinear conditions. This model couples the strength nonlinearity into the theoretical analysis, and for the first time introduces the concept of tensile stress truncation into the nonlinear P-L criterion.

[0006] At present, most of the tunnel face instability tests are carried out in clay and sandy soil stratum, and the sliding surface shape of the tunnel face instability in fault fracture zone is not clear. The current calculation method of face support force is mostly based on the global instability mechanical model of the failure zone extending to the ground surface, and there is still a lack of research on the local instability mode near the excavation face.

[0007] In view of this need, the present invention focuses on how to solve the problem of difficult accurate estimation of lateral soil pressure coefficient, and proposes a model for judging the instability type of tunnel face in fault fracture zone and a method for obtaining the limit support force. SUMMARY

[0008] The embodiment of the present application provides a limit support force calculation method for an excavation surface of a fault fracture zone based on local instability, so as to overcome the problem of how to accurately estimate a lateral earth pressure coefficient in the prior art. In order to have a basic understanding of some aspects of the disclosed embodiments, a brief summary is given below. This part is not a general review, nor is it intended to determine the key / important elements or delineate the protection scope of these embodiments. Its only purpose is to present some concepts in a simple form as a prelude to the detailed description below.

[0009] According to a first aspect of the embodiment of the present application, a limit support force calculation method for an excavation surface of a fault fracture zone based on local instability is provided, comprising the following steps: S1: determining whether the failure of the excavation surface of the fault fracture zone tunnel is in a local instability state; S2: when it is determined that it is in the local instability state, obtaining a limit support pressure p through the following formula: (22) In the formula, A1-A4 are the specific gravity r of the soil, D1-D2 are the internal friction angle of the soil body φ , E1-E6 are the cohesion c of the soil body, θ is the included angle between the cone surface of the sliding body and the XOY plane, and H is the tunnel burial depth.

[0010] On the basis of the above scheme, the method for determining whether the failure of the excavation surface of the fault fracture zone tunnel is in a local instability state in step S1 specifically comprises: The formula (1), (2), (3) are simultaneously solved with the active earth pressure coefficient K a of the soil body, the specific gravity γ, the initial reference height H0 of the tunnel burial depth, the tunnel radius r, and θ is the rupture angle of the soil body when active failure occurs, and different burial depths H (such as 0, 1, 2, 3,...) are input to solve the overlying soil thickness H2, and then the limit span B and the arch height h of the underground chamber can be obtained, and the specific formula is as follows: (1) (2) (3) In the formula, H2+h is the distance from the soil arch springing to the ground, φ is the internal friction angle of the soil body, c is the cohesion of the soil body, K a is the active earth pressure coefficient of the soil body, f k is the firmness coefficient of the soil body, γ is the specific gravity of the soil, and B is the limit span of the underground chamber.

[0011] On the basis of the above scheme, the method for determining whether the failure of the excavation surface of the fault fracture zone tunnel is in a local instability state in step S1 further comprises: By establishing the quantitative relationship between the limit span B of the underground chamber and the overlying soil thickness H2, the range of the buried depth H of the local instability is determined, which specifically includes: (1) When H2+h is greater than H, it is indicated that the chamber cannot be formed to support the upper soil under the buried depth condition, at this time, the soil failure zone of the excavation surface extends to the ground surface, and the instability form is determined as the overall instability; (2) The buried depth H of H2+h=H is the minimum buried depth of the local instability; (3) When H2+h is less than H, it is indicated that the soil failure zone of the excavation surface does not extend to the ground surface, and the instability form is determined as the local instability; The H2+h above is the distance from the soil arch springing to the ground.

[0012] On the basis of the above scheme, when it is determined to belong to the local instability state in step S2, the method for obtaining the limit supporting pressure p is obtained by the following formula, which specifically includes: S21: obtaining the physical parameters of the soil at the tunnel shield excavation through indoor test; S22: bringing the obtained parameters into formula (22), and calculating the limit supporting pressure p through a series of different tunnel buried depths H.

[0013] On the basis of the above scheme, the physical parameters of the soil in step S21 include: the specific gravity r of the soil, the internal friction angle φ of the soil, the cohesion c of the soil, the angle θ between the sliding body cone surface and the XOY plane, and the tunnel buried depth H.

[0014] On the basis of the above scheme, the angle θ between the sliding body cone surface and the XOY plane is the rupture angle when the soil is actively damaged, which is related to the internal friction angle φ of the soil, and θ=45°+φ / 2 The technical scheme provided by the embodiment of the present application can include the following beneficial effects: The present application obtains the local instability form of the excavation surface through the fault fracture zone tunnel excavation simulation test, proposes an improved conical body instability model, solves the problem of difficult accurate estimation of the lateral earth pressure coefficient, and simplifies the calculation. In addition, the present application performs mechanical analysis based on the symmetry of the rotating body, and establishes a calculation method for the limit supporting force of the tunnel excavation surface in the fault area. The accuracy is verified by comparison with the existing test results, and the influence of key factors such as cohesion, internal friction angle and soil specific gravity is analyzed.

[0015] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present application. BRIEF DESCRIPTION OF DRAWINGS

[0016] The drawings herein are incorporated into the specification and form part of the specification, show embodiments consistent with the present application, and together with the specification serve to explain the principles of the present application.

[0017] Figure 1 is a structural schematic diagram of a three-dimensional geophysical simulation test system according to an exemplary embodiment; Figure 2 is a structural schematic diagram of an excavation face support system according to an exemplary embodiment; Figure 3 is a schematic diagram of monitoring sections and sensor arrangement according to an exemplary embodiment, wherein (a) is a monitoring section arrangement schematic diagram (unit: cm), and (b) is a monitoring point arrangement schematic diagram (unit: cm); Figure 4 is a curved surface schematic diagram obtained by plotting the monitoring point with the largest vertical displacement in each monitoring section in the same coordinate system according to an exemplary embodiment, wherein (a) is the shape of the soil instability region of monitoring section I, (b) is the shape of the soil instability region of monitoring section II, (c) is the shape of the soil instability region of monitoring section III, and (d) is the shape of the soil instability region of monitoring section IV; Figure 5 is a schematic diagram of a conical model according to an exemplary embodiment, wherein (a) is a schematic diagram of a tunnel excavation face in a fault fracture zone, and (b) is a coordinate system established with the top point of the sliding body cone as the origin, the tunnel horizontal direction as the X axis, the tunnel excavation direction as the Y axis, and the tunnel burial depth direction as the Z axis; Figure 6 is a stress analysis diagram of the instability region below the tunnel vault according to an exemplary embodiment; Figure 7 is a schematic diagram of a comparison analysis result of the theoretically calculated limit support force of the excavation face and the test data according to an exemplary embodiment; Figure 8 is a comparison schematic diagram of different models according to an exemplary embodiment; Figure 9 is a schematic diagram of the relationship between the limit support force p and the burial depth ratio H / D and the cohesion c according to an exemplary embodiment, wherein (a) is the relationship between H / D and p under different cohesion c conditions, and (b) is the relationship between the cohesion c and the minimum burial depth ratio of local instability; Figure 10 is a schematic diagram of the influence of the internal friction angle φ on the limit support force and the minimum burial depth ratio of local instability according to an exemplary embodiment, wherein (a) is the relationship between H / D and p under different internal friction angle φ conditions, and (b) is the relationship between the internal friction angle φ and the minimum burial depth ratio of local instability; Figure 11 is a schematic diagram of the influence of the solidity coefficient f k on the limit support force and the minimum burial depth ratio of local instability, wherein (a) is the relationship between H / D and p under different solidity coefficient fk The relationship between H / D and p under different conditions, (a) is the relationship between f and the minimum buried depth ratio of local instability k The relationship between f and the minimum buried depth ratio of local instability Figure 12 The influence of γ on the limit support force and the minimum buried depth ratio of local instability is shown according to an exemplary embodiment, wherein (a) is the relationship between H / D and p under different γ, and (b) is the relationship between γ and the minimum buried depth ratio of local instability. DETAILED DESCRIPTION

[0018] The following description and drawings are illustrative of the specific embodiments of the present application and are not intended to limit the scope of the application. Parts and features of some embodiments can be included in, or alternative parts and features of other embodiments. The scope of the embodiments of the present application includes the entire scope of the claims and all available equivalents of the claims. In this application, the terms "first", "second", and the like are used to distinguish one element from another, but do not require or imply any actual relationship or order between such elements. In fact, the first element can also be referred to as the second element, and vice versa. Moreover, the terms "include", "contain" or any other variants thereof are intended to cover non-exclusive inclusion, so that the structure, device or equipment including a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such structure, device or equipment. Without more limitations, the element defined by the statement "including a" does not exclude the presence of additional identical elements in the structure, device or equipment including the element. In this application, each embodiment is described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same or similar parts between each embodiment can be referred to each other.

[0019] In this application, the character " / " represents an "or" relationship between the objects before and after it. For example, A / B means A or B.

[0020] In this application, the term "and / or" is a description of the relationship between the objects, which means that there can be three relationships. For example, A and / or B means that there are three relationships of A or B, or A and B.

[0021] In the case of no conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0022] Embodiment 1 This embodiment is based on the fault fracture zone excavation face limit support force calculation method of local instability, which includes the following steps: S1: Determine whether the failure of the fault fracture zone tunnel excavation face belongs to the state of local instability; Specifically: Combined formulas (1), (2), and (3) and the active earth pressure coefficient K of the soil is: a , severity γ, the initial reference height H0 of the tunnel burial depth, the tunnel radius r, and θ is the rupture angle when the soil undergoes active failure. Different burial depths H (such as 0, 1, 2, 3...) are input to solve the overburden thickness H2, and then the ultimate span B and arch height h of the underground chamber can be obtained, and then the range of the burial depth H where local instability occurs can be determined.

[0023] Specifically include: By establishing a quantitative relationship between the ultimate span B of an underground chamber and the thickness H2 of the overburden, a method is used to predict the impact range of local instability and failure: (1) Where H2 is the height from the pressure arch to the ground, and h is the pressure arch height. The calculation formula is as follows: (2) Where H2+h is the distance from the arch foot to the ground, φ is the internal friction angle of the soil, c is the cohesion of the soil, and K a is the active earth pressure coefficient of soil, f k is the soil strength coefficient, γ is the soil density, and B is the ultimate span of the underground chamber; From formula (1), we can see that the ultimate span B, the distance H2 from the arch top to the ground in the failure area, and the arch height h are related, and H2+h is proportional to B. The B~(H2+h) curve and the straight line L are plotted in the same plane coordinate system. As H2+h increases, B gradually increases. The B~(H2+h) curve eventually intersects with the straight line L. The coordinates (B, H2+h) at the intersection can represent the extension range of the local failure. Substitute formulas (2) and (3) into formula (1) to solve and obtain H2. Calculate B according to formula (3), where H0 = r(sinθtanθ+cosθ-1); (3) From formula (1), it can be seen that H2 is proportional to B, indicating that the greater the depth of the chamber, the larger the instability expansion radius.

[0024] The range of the buried depth H where local instability occurs is determined by the following method: (1) When H2+h is greater than H, it means that no chamber that can support the upper soil can be formed under the buried depth condition. At this time, the damaged area of ​​the excavation surface soil extends to the surface, and the instability form is judged to be overall instability; (2) When H2+h=H, the burial depth H is the minimum burial depth for local instability to occur; (3) When H2+h is less than H, it means that the soil damage area of ​​the excavation surface has not extended to the surface, and the instability form is judged to be local instability; H2+h is the distance from the soil arch springing to the ground.

[0025] S2: When it is determined that it belongs to the local instability state, the limit supporting pressure p is obtained by the following formula: (22) In the formula, A1-A4, D1-D2, E1-E6 are parameters related to the specific gravity r of the soil, the internal friction angle φ of the soil, the cohesion c of the soil, the angle θ of the sliding body cone surface and the XOY plane, and the tunnel depth H.

[0026] Specifically, the method for obtaining the limit supporting pressure p when it is determined that it belongs to the local instability state in step S2 specifically comprises: S21: Obtain the physical parameters of the soil at the tunnel shield excavation site through indoor tests; the physical parameters of the soil include the specific gravity r of the soil, the internal friction angle φ of the soil, the cohesion c of the soil, the angle θ of the sliding body cone surface and the XOY plane, and the tunnel depth H. The angle θ of the sliding body cone surface and the XOY plane is the angle of rupture when the soil is actively damaged, which is related to the internal friction angle φ of the soil, θ = 45° + φ / 2.

[0027] S22: Bring the obtained parameters into formula (22) to calculate the limit supporting pressure p through a series of different tunnel depths H.

[0028] Example 2 In order to obtain the shape of the instability region when the tunnel excavation surface is locally unstable, a large three-dimensional geophysical simulation test system is used to confirm the excavation surface failure shape and the displacement change of the rock-soil mass at the fault position.

[0029] 1. Physical simulation test of tunnel passing through fault fracture zone (1) Large three-dimensional geophysical simulation test system The test system is composed of a model box, a stress loading system, an excavation surface supporting system, and an information acquisition system, as shown in Figure 1 The internal space size of the model box is length x width x height = 8 m x 4.5 m x 5 m. The stress loading system can provide the ground stress required by the test environment, which is provided by a hydraulic jack; the information monitoring system is composed of sensors, monitoring software, and static resistance strain gauges.

[0030] Among them, the stress loading system applies pressure on the surface of the stratum, which is equivalent to the self-weight load of the overlying soil in a certain depth range on the surface of the stratum, realizing the simulation of the surrounding rock pressure of tunnels with different depths. After the internal filling of the model box is completed, a steel base plate is placed on the surface of the stratum, and the pressure generated by the jack is uniformly transmitted to the stratum.

[0031] A baffle is arranged at the tunnel excavation face, a force transmission rod is fixed at the center of the baffle, and the other end of the force transmission rod is connected with the telescopic motor, as shown in Figure 2 After the test starts, the baffle at the excavation face is driven away from the tunnel excavation face at a set speed by driving the telescopic motor, the soil at the excavation face is displaced due to the movement of the baffle, thereby simulating the process of gradual instability of the excavation face caused by the reduction of the supporting force. The earth pressure on the excavation face is recorded by the earth pressure sensor arranged on the baffle.

[0032] (2) Test scheme The undisturbed soil at the F2 fault of Yonglian Tunnel is taken as the filling material for the model test, and the physical and mechanical parameters of the undisturbed soil are shown in Table 1.

[0033] Table 1 Physical and mechanical parameters of undisturbed soil Before filling, the tunnel lining model and the excavation face supporting system are installed, the materials are filled in a layered tamping manner, and the sensors are buried during the filling process. The filling height is 30 cm each time, and the total filling height is 4.5 m. At this time, the simulated tunnel burial depth is 2.7 m. After filling is completed, the remaining ground pressure is compensated by the stress loading system, different pressures are applied on the ground surface to simulate the ground pressure under different tunnel burial depths. A total of 4 tests are conducted, and the test conditions are shown in Table 2.

[0034] Table 2 Test conditions The tunnel lining is a steel glass cylinder with a diameter of 60 cm, and the excavation face is 200 cm away from the tunnel entrance. The monitoring section and sensor arrangement are shown in Figure 3 Four monitoring sections are arranged in the fault, each monitoring section is spaced 60 cm apart, and the first monitoring section is located at the excavation face. Displacement sensors are arranged on each monitoring section to monitor the vertical displacement of the soil. After the test starts, the excavation face supporting baffle is moved at a speed of 0.2 mm / min, and the displacement monitoring data tends to be stable. The vertical displacement of the soil and the earth pressure on the excavation face are recorded in real time during the test.

[0035] 2. Analysis of test results The monitoring points with the maximum vertical displacement in each monitoring section are plotted in the same coordinate system to obtain the curved surface as shown in Figure 4 The curved surface can reflect the shape of the instability region, wherein the bottom is a spherical surface, the upper part of the spherical surface is a conical surface, and the curved surface is symmetrical along the X=0 plane. After the test is completed, the instability region does not expand to the ground surface, and it can be judged that the instability form is local instability.

[0036] 3. Calculation of excavation face supporting force I. Establishment of instability model According to the experimental excavation surface failure results, an improved cone model was used, such as Figure 5 As shown. A coordinate system is established with the vertex of the sliding cone as the origin, the horizontal direction of the tunnel as the X-axis, the tunnel excavation direction as the Y-axis, and the tunnel depth direction as the Z-axis. The sliding cone surface is generated by rotating the straight line L on the YOZ plane around the Z-axis. The equation of the straight line L is z = ytanθ, where θ is the angle between the cone surface and the XOY plane. The side of the model is a combination of the conical surface formed by rotating the straight line L around the Z-axis and a partial spherical surface. The outer contour of the horizontal section at any depth is a semicircle. The following assumptions are made during the model analysis: (1) After the excavation face becomes unstable, the damaged area is entirely located within the fault fracture zone, and the soil is homogeneous and isotropic; (2) The soil at the sliding surface obeys the Mohr-Coulomb criterion. The sliding soil is a rigid body, and the deformation caused by stress changes inside the soil is not considered. (3) The tunnel profile is circular and is not considered Figure 5 The forces acting in the shaded area in (a); (4) The angle θ between the sliding cone and the XOY plane is the rupture angle when the soil undergoes active failure, which is related to the internal friction angle φ of the soil, θ=45°+φ / 2.

[0037] When localized instability failure occurs on the excavation face, the failure zone is confined to the conical model. Due to the soil arching effect, the soil above the failure zone does not collapse. This mechanical behavior is highly similar to the formation mechanism of natural chambers. By establishing a quantitative relationship between the ultimate span B of an underground chamber and the overburden thickness H2, the impact range of localized instability failure can be predicted. The ultimate span B of an underground chamber considering the soil arching effect is calculated as follows: (1) Where H2 is the height from the pressure arch to the ground, and h is the pressure arch height. The calculation formula is as follows: (2) Where H2+h is the distance from the arch foot to the ground, φ is the internal friction angle of the soil, c is the cohesion of the soil, and K a is the active earth pressure coefficient of soil, f k is the soil strength coefficient, γ is the soil density, and B is the ultimate span of the underground chamber.

[0038] From formula (1), it can be seen that the limit span B, the distance from the arch top to the ground H2 and the arch height h are related, and H2+h is proportional to B. The B~(H2+h) curve and the straight line L are plotted in the same plane coordinate system, B gradually increases with the increase of H2+h, the B~(H2+h) curve eventually intersects with the straight line L, and the coordinates (B, H2+h) at the intersection point can represent the extension range of local damage. H2 is obtained by substituting formula (2) and (3) into formula (1), and B is obtained according to formula (3), wherein H0=r(sinθtanθ+cosθ-1).

[0039] (3) From formula (1), it can be seen that H2 is proportional to B, indicating that the greater the depth of the chamber, the greater the instability expansion radius. When H2+h calculated by the above method is greater than H, it is indicated that under the condition of the depth, the chamber cannot be formed to support the upper soil, at this time the collapse zone extends to the ground, and the failure form of the excavation surface soil is overall failure. The depth when H2+h=H is the minimum depth of local instability. The calculation method of the limit support force of the excavation surface in local instability proposed in the application is applicable to the case where H2+h is less than H.

[0040] II, stress analysis of sliding soil and determination of support pressure of excavation surface The stress of the region below the arch top of the excavation surface is shown in Figure 6 , which is subjected to the vertical pressure p v of the upper soil, the support pressure p of the excavation surface, the normal support force n1 and the tangential force u1 on the conical surface, the normal support force n2 and the tangential force u2 on the arc surface, the gravity G of the soil, and the stress on the soil surface in XOZ plane except the excavation surface is ignored. Among them, the tangential force u is composed of cohesive force c and friction force u=ntanφ+c, and the support pressure p of the excavation surface is the value to be solved.

[0041] The resultant force of gravity G, p, p v is as formula (4)-(6): (4) (5) (6) In the formula, K1 is the lateral earth pressure coefficient considering the soil arching effect , B1=(H0+2r) / tanθ.

[0042] According to the balance equation of forces of the sliding zone soil in Y direction and Z direction, the balance equation of forces is: (7) n1 is the normal stress on the conical surface, u1 is the tangential stress on the conical surface, as shown in equation (8): (8) In the formula, the lateral pressure coefficient K is the ratio of the vertical stress of the soil body at any depth to the normal stress on the conical surface, and is an unknown quantity.

[0043] n1 and u1 are decomposed into XOY direction and Z direction as shown in equations (9) and (10): (9) (10) n 1z 、u 1z The resultant force N 1z 、U 1z is in the same direction as the Z axis as shown in equation (11): (11) In equation (11), A1, A2, and D1 are parameters and are known quantities related to H, r, γ, φ, and θ.

[0044] (12) In equation (12), C1 and C2 are parameters and are known quantities related to r and θ.

[0045] (13) The conical surface in the sliding zone is semicircular in any horizontal cross section, and the components n 1xy 、u 1xy of n1 and u1 acting on the conical surface are perpendicular to the tangent of the circular arc in the horizontal cross section and point towards or away from the center. The resultant force of n1 and u1 in the X direction is zero due to the symmetry of the sliding zone. An polar coordinate system (R, α) is established in the XOY plane, and the resultant force in the Y direction is obtained by integrating in the α and Z directions as shown in equation (14): (14) In equation (14), A3, A4, and D2 are parameters and are known quantities related to H, r, γ, φ, and θ.

[0046] (15) n2 and u2 are the normal and tangential stresses acting on the sliding zone spherical surface. The outer profile of the spherical surface parallel to the XOY plane is semicircular, and the components n 2xy 、u 2xy of n2 and u2 in the XY direction act on the sliding zone spherical surface, and the support pressure p acts on the excavation surface.

[0047] Let the support pressure p be constant, on any semicircular cross section perpendicular to the Z axis, the n 2xy 、u 2xy size is related to Z, and is independent of X and Y. Then p and n2, u2 have the following relationship: (16) In the formula, θ i is the angle between the tangent on the bottom arc of the model and the XOY plane (17) In the formula, z0 is the Z coordinate of the center of the circle: (18) The resultant force of n2, u2 in the Z direction and the Y direction is shown in formula (19): (19) In formula (19), E1, E2, E3, E4, E5, E6 are parameters, which are known quantities related to r, φ, θ. p is the support pressure of the excavation surface, which is an unknown quantity.

[0048] (20) In formula (20), D3 is a parameter, which is a known quantity related to φ and θ.

[0049] (21) Solving formula (7) and eliminating the lateral pressure coefficient K, the support pressure p is obtained (22) In formula (22), A1-A4, D1-D2, E1-E6 are all parameters related to r, φ, c, θ, H.

[0050] Based on the above, the application is compared with the test results, and the results are as follows: Based on the parameters listed in Tables 1 and 2, the limit support force of the excavation surface is calculated by the method of the application, and the comparison analysis results of the theoretical calculation results and the test data are shown in Figure 7 The limit support force p of the excavation surface when it loses stability is proportional to the buried depth ratio H / D, and its increase gradually slows down with the increase of H / D. When H / D≤15, the theoretical calculation value is higher than the test measured value; when H / D>15, the theoretical value is lower than the test value. From Figure 7It can be seen that the size relationship between the theoretical value and the test value changes in the interval of 15~20, and the difference between them shows a continuous expansion trend with the increase of H / D. Under the condition of deep-buried tunnel, the limit support force of the excavation face measured by the test is slightly higher than the theoretical calculation value with the increase of H / D. The reason for the error may be that the stress loading system used in the test simulates the stress of the stratum self weight, which is difficult to fully play the soil arching effect when the excavation face loses stability compared with the actual buried depth condition formed by the actual filling, resulting in the measured support pressure being too high.

[0051] The error between the theoretical calculation results and the test results is shown in Table 3, the minimum error occurs at the buried depth ratio H / D=20, and the maximum error occurs at H / D=10. When H / D is in the interval of 15~25, the error between the theoretical method and the test results is smaller, indicating that this method can effectively predict the limit support force of the tunnel excavation face in the fault fracture zone when local instability occurs.

[0052] Table 3 Model calculation results The results of the comparison with the existing local instability model are as follows: Zhang Xiaqing et al. (Zhang Xiaqing. Research on the instability mechanism and soil pressure distribution pattern of deep-buried shield tunnel excavation face[D]. Shanghai University, 2018) carried out an excavation face instability model test in Fujian sandy stratum under different buried depths, and the research showed that the soil failure zone shape changes significantly with the buried depth. Under the condition of shallow burial, with the increase of the displacement of the excavation face retreat, the front soil failure zone gradually presents a “wedge + prism” shape and extends to the ground surface; under the condition of deep burial, the tunnel excavation face failure zone is spherical and does not extend to the ground surface. Based on this, Zhang Mengxi et al. (Zhang Mengxi, Dai Zhiheng, Zhang Xiaqing, et al. Calculation method of active limit support pressure of deep-buried shield tunnel excavation face considering principal stress axis deflection[J]. Rock and Soil Mechanics, 2021, 40(11): 2366-2376.) proposed a spherical local damage model for calculating the limit support force of the excavation face.

[0053] The limit support force results of the calculation method of this application and Zhang Mengxi et al. (Zhang Mengxi, Dai Zhiheng, Zhang Xiaqing, et al. Calculation method of active limit support pressure of deep-buried shield tunnel excavation face considering principal stress axis deflection[J]. Rock and Soil Mechanics, 2021, 40(11): 2366-2376.) are compared and analyzed with the model test data of Zhang Xiaqing et al. (Zhang Xiaqing. Research on the instability mechanism and soil pressure distribution pattern of deep-buried shield tunnel excavation face[D]. Shanghai University, 2018). The parameters used in the calculation are as follows: internal friction angle φ=36.6°, cohesion c=0, soil firmness coefficient f k =0.5, soil bulk density γ=15.34kN / m 3, tunnel radius r = 0.032m. Substitute the above parameters into formula (22) to calculate the excavation face support pressure p, as follows Figure 8 shown.

[0054] The excavation face instability test conducted by Zhang Xiaoqing et al. (Zhang Xiaoqing. Research on the instability mechanism and soil pressure distribution pattern of deep shield tunnel excavation face [D]. Shanghai University, 2018) shows that: as the tunnel depth ratio (H / D) increases, the expansion range of the instability zone gradually decreases; when H / D=4, the instability form is local instability. The minimum critical depth ratio for local instability calculated by the proposed method is H / D=3 ( Figure 8 The dashed line is consistent with the above test value, which confirms the accuracy of this method in calculating the minimum depth of local instability. This method is suitable for calculating the ultimate support force of the excavation face when H / D>3. Figure 8 It can be seen that when H / D=4~6, the calculation results of the method of this application and Zhang Mengxi et al. (Zhang Mengxi, Dai Zhiheng, Zhang Xiaoqing, et al. Calculation method of active limit support pressure of deep shield tunnel excavation face considering principal stress axis deflection [J]. Chinese Journal of Rock Mechanics and Engineering, 2021, 40(11): 2366-2376.) are relatively close to the experimental values, and the theoretical calculation results of this application are closer to the experimental values; while in the range of H / D=2~3, both models have large errors, and the calculation results of this application are closer to the experimental values. When H / D=2~3, there is a large error between the calculation results of this application and the experimental value. The main reason is that within the tunnel depth ratio range, the excavation face instability mode is overall instability. The method of this application and Zhang Mengxi et al. (Zhang Mengxi, Dai Zhiheng, Zhang Xiaoqing, et al. Calculation method of active limit support pressure of deep buried shield tunnel excavation face considering principal stress axis deflection [J]. Chinese Journal of Rock Mechanics and Engineering, 2021, 40(11): 2366-2376.) are applicable to local instability mode, so there is some deviation in predicting the excavation face support force within the low tunnel depth ratio range.

[0055] From the above derivation process, we can know that the ultimate support force p of the excavation face is related to the cohesion c, the internal friction angle φ, and the Pugh firmness coefficient f. k , soil density γ, and tunnel depth H. Therefore, these parameters were selected for analysis to further explore the influence of each factor on the ultimate support capacity of the excavation face. The minimum depth ratio for local instability was also calculated for different values ​​of these factors. In the influencing factor analysis, the tunnel radius r = 6m and the H / D ratio ranged from 0 to 6. The remaining parameters were selected based on references to the literature. Detailed parameter values ​​are shown in Table 4.

[0056] Table 4 Parameter values Based on the given parameters, the ultimate support force p of the excavation surface corresponding to different burial depth ratios H / D is calculated using formula (22). The results are as follows:Figure 9 (a) Figure 10 (a) Figure 11 (a) Figure 12 As shown in (a), the horizontal axis corresponding to the vertical dotted line in the figure represents the critical burial depth ratio of local instability. The relationship between the formation parameters and the critical burial depth ratio of local instability is shown in Figure 9 (b) Figure 10 (b) Figure 11 (b) Figure 12 As shown in (b) in .

[0057] (1) Cohesion c Figure 9 Figure (a) shows that the ultimate support force, p, increases with the depth ratio, H / D, and is negatively correlated with the cohesion, c. The minimum critical depth for local instability decreases with increasing cohesion, c. This is because greater cohesion strengthens the bonding between rock and soil particles, making it easier to form a stable self-supporting arch structure, thereby reducing the required cover thickness for stability.

[0058] (2) Internal friction angle φ The ultimate support force, p, shows a significant negative correlation with the internal friction angle, φ. This phenomenon stems from the multiple mechanisms by which increasing the φ value improves soil mechanical properties: directly enhancing soil shear strength while optimizing the stress distribution in the surrounding rock and promoting the formation and development of the soil arching effect. This synergistic effect not only significantly reduces the support force required to maintain excavation face stability, but also flattens the pH / D curve, a pattern consistent with the experimental results of Chen et al. Furthermore, studies have shown that the critical depth ratio for local instability decreases with increasing φ. The mechanism is that a high φ value not only enhances the self-bearing capacity of the surrounding rock, reducing the risk of collapse; it also optimizes the stress arch morphology, increasing the efficiency of load transfer to the sides; and it also inhibits the expansion of the plastic zone, reducing the extent of loosened surrounding rock.

[0059] (3) Robustness coefficient f k Ultimate support force p and soil strength coefficient f k The reason is that f k When f increases, the soil's compressive and shear resistance and self-stability are enhanced, and it can bear greater loads through internal stress redistribution, reducing the demand for support force. Formula (2) shows that when the maximum expansion range B of the local instability zone increases, the arch height h formed will increase accordingly, resulting in a decrease in the distance from the top of the collapse body to the ground surface. Therefore, f k It is positively correlated with the minimum critical burial depth ratio for local instability.

[0060] (4) Severe γ The soil bulk density γ is proportional to the limit support force of the excavation face, but inversely proportional to the minimum buried depth ratio when local instability occurs. It is worth noting that there is a significant nonlinear relationship between γ and the minimum buried depth ratio. When γ increases, the self-weight stress of the soil increases rapidly, so that the pressure arch effect can be exhibited at a shallow buried depth, thereby reducing the minimum buried depth ratio. With the continuous increase of γ, the influence of soil strength on stability gradually appears, leading to the decrease of the minimum buried depth ratio to tend to be gentle. Finally, when γ exceeds a certain critical value, the plastic zone of the surrounding rock has been fully developed, and its expansion tends to be stable, which further reduces the change rate of the minimum buried depth ratio with the increase of γ.

[0061] Finally, it should be noted that: the various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts of each embodiment can be referred to.

[0062] The above embodiments are only used to illustrate the technical solutions of the present application but not limit it; although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the specific embodiments of the present application can be modified or some technical features can be replaced by equivalent ones without departing from the spirit of the technical solutions of the present application, which should be covered in the technical solution range of the present application.

Claims

1. A method for calculating the ultimate support capacity of the excavation surface of a fault fracture zone based on local instability, characterized by: The steps include: S1: Determine whether the failure of the tunnel excavation face in the fault fracture zone is a state of local instability; S2: When it is determined that the state is in local instability, the ultimate support pressure p is obtained by the following formula: (22) Where A1-A4 is the soil specific gravity r, D1-D2 is the soil internal friction angle φ , E1-E6 is the soil cohesion c, θ is the angle between the sliding body cone and the XOY plane, and H is the tunnel depth.

2. The method for calculating the ultimate support force of the excavation surface of a fault fracture zone based on local instability according to claim 1 is characterized in that: The method for determining whether the damage to the tunnel excavation surface in the fault fracture zone is a state of local instability in step S1 specifically includes: Combined formulas (1), (2), and (3) and the active earth pressure coefficient K of the soil is: a , gravity γ, initial reference height H0 of tunnel burial depth, tunnel radius r, rupture angle θ when soil is actively damaged, input different burial depths H, solve the overburden thickness H2, and then obtain the ultimate span B and arch height h of the underground chamber. The specific formula is as follows: (1) (2) (3) Where H2+h is the distance from the arch foot to the ground, φ is the internal friction angle of the soil, c is the cohesion of the soil, and K a is the active earth pressure coefficient of soil, f k is the soil strength coefficient, γ is the soil density, and B is the ultimate span of the underground chamber.

3. The method for calculating the ultimate support force of the excavation surface of a fault fracture zone based on local instability according to claim 2 is characterized in that: The method for determining whether the damage to the tunnel excavation surface in the fault fracture zone in step S1 is in a state of local instability further includes: By establishing a quantitative relationship between the ultimate span B of the underground chamber and the thickness of the overburden H2, the range of the burial depth H where local instability occurs can be determined, specifically including: (1) When H2+h is greater than H, it means that no chamber that can support the upper soil can be formed under the buried depth condition. At this time, the damaged area of ​​the excavation surface soil extends to the surface, and the instability form is judged to be overall instability; (2) When H2+h=H, the burial depth H is the minimum burial depth for local instability to occur; (3) When H2+h is less than H, it means that the soil damage area of ​​the excavation surface has not extended to the surface, and the instability form is judged to be local instability; The above H2+h is the distance from the arch foot to the ground.

4. The method for calculating the ultimate support force of the excavation surface of a fault fracture zone based on local instability according to claim 1 is characterized in that: In step S2, when it is determined that the local instability state exists, the method for obtaining the ultimate support pressure p by the following formula specifically includes: S21: Obtain the physical parameters of the soil at the tunnel shield excavation site through indoor tests; S22: Substitute the obtained parameters into formula (22) and calculate the ultimate support pressure p through a series of different tunnel burial depths H.

5. The method for calculating the ultimate support force of the excavation surface of a fault fracture zone based on local instability according to claim 4 is characterized in that: The physical parameters of the soil in step S21 include: soil density r, soil internal friction angle φ, soil cohesion c, angle θ between the sliding body cone and the XOY plane, and tunnel burial depth H.

6. The method for calculating the ultimate support force of the excavation surface of a fault fracture zone based on local instability according to claim 5 is characterized in that: The angle θ between the sliding body conical surface and the XOY plane is the rupture angle when the soil is actively damaged, which is related to the internal friction angle φ of the soil, θ=45°+φ / 2.

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