Calculation Method of Ultimate Support Force for Excavation Face in Fault Fracture Zone Based on Local Instability

Abstract

This invention belongs to the fields of tunnel engineering and geotechnical mechanics. It discloses a method for calculating the ultimate support force of the excavation face in fault fracture zones based on local instability. Through simulation tests of tunnel excavation in fault fracture zones, the local instability morphology of the excavation face was obtained. An improved conical instability model was proposed, which solved the problem of the difficulty in accurately estimating the lateral earth pressure coefficient and simplified the calculation. Based on the symmetry of the rotating body, a mechanical analysis was conducted to establish a method for calculating the ultimate support force of the tunnel excavation face in fault areas. The accuracy was verified by comparing with existing test results, and the influence of key factors such as cohesion, internal friction angle, and soil weight was analyzed.

Description

Technical Field

[0001] This invention relates to the fields of tunnel engineering and geotechnical mechanics, and in particular to a method for calculating the ultimate support force of excavation faces in fault fracture zones based on local instability. Background Technology

[0002] When tunnels traverse fault fracture zones, karst formations, or weak strata, they are highly susceptible to excavation face collapses and sudden water inrushes. For example, the Yuanliangshan Tunnel on the Chongqing-Huaihua Railway encountered a blowout-type mudslide at kilometer marker DK354+879 during the construction of the pilot tunnel ahead of the main tunnel entrance. Similarly, the Yonglian Tunnel on the Jiangxi Jilian Expressway encountered a large amount of water-rich, weak, and fractured media during its passage through faults F1-F4, resulting in water and mudslide disasters. When tunnels traverse faults characterized by high water pressure, loose and fractured strata, and high permeability, accurately assessing the instability morphology of the excavation face and precisely calculating the ultimate support force of the excavation face are crucial for preventing tunnel instability.

[0003] Scaled-down model tests and physical simulation tests are the main methods for studying tunnel excavation face instability. These tests allow for the investigation of the instability process, modes, morphology, and extent of tunnel excavation face failure. Researchers such as Chambon P, Xiaoqing Zhang, and Renpeng Chen conducted excavation face instability model tests in sandy soil strata, finding that tunnel excavation face collapse can be categorized into two forms: partial collapse and overall collapse. The H / D ratio (tunnel depth to diameter) has a significant impact on the collapse mode. When the tunnel depth ratio (H / D) is relatively small, the instability area extends to the surface; when the tunnel depth ratio is relatively large, the instability area is confined to the vicinity of the excavation face and does not extend to the surface. Other researchers have also discovered local instability as a failure mode in experiments and numerical simulations. Huayang Lei et al. conducted tunnel excavation face instability model tests using transparent soil materials to study the failure modes of the tunnel excavation face. The results showed that the failure area stops changing after reaching a certain height, forming a bulb-shaped failure mode, and the soil arch formation area is roughly within 1.5D~2.0D (D is the tunnel diameter) above the tunnel top. Niu H et al. studied the variation of excavation face support pressure and instability modes under different soil parameters based on centrifuge 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 ultimate support force tends to stabilize, and the influence of the soil arch effect gradually weakens. Ma Yangchen et al. simulated the instability process of the excavation face based on the smooth particle fluid dynamics method. When the excavation face is in a local instability limit equilibrium state, two shear bands with a certain width appear at the tunnel arch crown and arch bottom, with the shear band near the arch crown extending to the ground surface first. Lü Xilin et al. found that as the critical strength of sand increases, the outline of the failure morphology in front of the excavation face shrinks, the instability range of the excavation face shrinks significantly, and the instability is concentrated in a local area in front of the excavation face. The above simulation test results provide a basis for the construction of tunnel excavation face support force models.

[0004] Accurate calculation of the support force at the tunnel excavation face is crucial for ensuring its stability. To calculate this support force, a mechanical model of the failure zone needs to be constructed based on the instability morphology of the excavation face. As mentioned above, existing model tests and engineering practices show that tunnel excavation face instability can be divided into overall failure and local failure. Researchers have proposed a series of analytical solutions for the support force at the excavation face based on methods such as the limit equilibrium method. M. Horn first established a three-dimensional wedge-shaped overall instability model, arguing that the failure morphology of the excavation face consists of a lower wedge and an upper silo, and determining the minimum support force at the excavation face through 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 et al. studied the local failure mode of the excavation face of a shield tunnel under cohesive soil strata and proposed a three-dimensional horizontal spherical cap local instability model. This model considers the influence of principal stress axis deflection on the active ultimate support force of deeply buried tunnels. Combining the traditional Terzaghi loose earth pressure formula, they derived a general solution for the ultimate support force of local instability at the excavation face. Jinfeng Zou et al. proposed an improved three-dimensional rotating body local failure model based on the limit analysis method. This model assumes that the failure area consists of an ellipsoid and a rotating body. To fully reflect the soil arching effect, the lateral earth pressure coefficient was improved, which improved the calculation accuracy of the model. However, the disadvantage is that the model is complex and the calculation is large.

[0005] Wang Haifeng and Hu Ruiqing et al. established a tunnel excavation face failure model based on the collapse arch and limit analysis method, and proposed an analytical solution for the ultimate support force applicable to gravel tunnels. Zhong Junhao et al., addressing the stability problem of the excavation face of deeply buried tunnels under nonlinear conditions, established a multi-curve conical failure model of the excavation face based on the upper bound theorem of limit analysis. This model couples strength nonlinearity into the theoretical analysis and introduces the concept of tensile stress truncation into the nonlinear PL criterion for the first time.

[0006] Currently, most tunnel excavation face instability tests are conducted in clay and sandy soil strata, and the sliding surface morphology after excavation face instability in fault fracture zones remains unclear. Current methods for calculating excavation face support force are mostly based on overall instability mechanical models where the damaged area extends to the surface, and research on local instability modes near the excavation face is lacking.

[0007] In view of this need, this invention focuses on how to solve the problem of the difficulty in accurately estimating the lateral earth pressure coefficient, and proposes a model for judging the instability type of tunnel excavation face in fault fracture zones and a method for obtaining the ultimate support force. Summary of the Invention

[0008] This invention provides a method for calculating the ultimate support force of excavation faces in fault fracture zones based on local instability, overcoming the problem in existing technologies of accurately estimating the lateral earth pressure coefficient. To provide a basic understanding of some aspects of the disclosed embodiments, a brief summary is given below. This summary is not intended as a general commentary, nor is it intended to identify key / important components or describe the scope of protection of these embodiments. Its sole purpose is to present some concepts in a simple form as a prelude to the detailed description that follows.

[0009] According to a first aspect of the present invention, a method for calculating the ultimate support force of an excavation face in a fault fracture zone based on local instability is provided, comprising the following steps:

[0010] S1: Determine whether the damage to the tunnel excavation face in the fault fracture zone is a state of local instability;

[0011] S2: Once it is determined that the situation is in a state of local instability, the ultimate support pressure p is obtained using the following formula:

[0012] (twenty two)

[0013] In the formula, A1-A4 is the unit weight of the soil, r, and D1-D2 is the internal friction angle of the soil. φ E1-E6 represents the soil cohesion c, θ represents the angle between the sliding body cone and the XOY plane, and H represents the tunnel depth.

[0014] Based on the above scheme, the method for determining whether the damage to the tunnel excavation face in the fault fracture zone belongs to a state of local instability in step S1 specifically includes:

[0015] Combine formulas (1), (2), and (3) and substitute the active earth pressure coefficient K. a The following parameters are used: unit weight γ, initial reference height H0 for tunnel burial depth, tunnel radius r, and θ (the fracture angle when the soil undergoes active failure). By inputting different burial depths H (e.g., 0, 1, 2, 3...), the overburden thickness H2 can be calculated, and then the ultimate span B and arch height h of the underground chamber can be obtained. The specific formulas are as follows:

[0016] (1)

[0017] (2)

[0018] (3)

[0019] In the formula, H2+h is the distance from the arch foot of the soil arch to the ground, φ is the internal friction angle of the soil, c is the soil cohesion, and K a f is the active earth pressure coefficient of the soil. kγ is the soil firmness coefficient, γ is the soil unit weight, and B is the ultimate span of the underground chamber.

[0020] Based on the above scheme, the method for determining whether the damage to the tunnel excavation face in the fault fracture zone belongs to a state of local instability in step S1 also includes:

[0021] By establishing a quantitative relationship between the ultimate span B of the underground chamber and the overlying soil thickness H2, the range of burial depth H where local instability occurs can be determined, specifically including:

[0022] (1) When H2+h is greater than H, it means that a chamber that can support the upper soil cannot be formed under the burial depth conditions. At this time, the soil failure area at the excavation face extends to the ground surface, and the instability mode is judged to be overall instability.

[0023] (2) When H2+h=H, the burial depth H is the minimum burial depth at which local instability occurs;

[0024] (3) When H2+h is less than H, it indicates that the soil failure area at the excavation face has not extended to the ground surface, and the instability mode is judged to be local instability;

[0025] The above H2+h represents the distance from the arch foot of the earthen arch to the ground.

[0026] Based on the above scheme, in step S2, after determining that the situation is in a local instability state, the method for obtaining the ultimate support pressure p using the following formula specifically includes:

[0027] S21: Obtain the physical parameters of the soil at the tunnel shield excavation site through indoor tests;

[0028] S22: Substitute the obtained parameters into formula (22) and calculate the ultimate support pressure p through a series of different tunnel burial depths H.

[0029] Based on the above scheme, the physical parameters of the soil mentioned in step S21 include: the unit weight of the soil r, the internal friction angle of the soil φ, the cohesion of the soil c, the angle θ between the sliding body cone surface and the XOY plane, and the tunnel burial depth H.

[0030] Based on the above scheme, the angle θ between the sliding body cone surface and the XOY plane is the fracture angle when the soil undergoes active failure, which is related to the internal friction angle φ of the soil, θ = 45° + φ / 2

[0031] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects:

[0032] This invention, through simulated tunnel excavation tests in fault fracture zones, obtained the local instability morphology of the excavation face and proposed an improved conical instability model, solving the problem of accurately estimating the lateral earth pressure coefficient and simplifying the calculation. Furthermore, based on the symmetry of a rotating body, this invention establishes a method for calculating the ultimate support force of the tunnel excavation face in fault zones. The accuracy was verified by comparing with existing experimental results, and the influence of key factors such as cohesion, internal friction angle, and soil weight was analyzed.

[0033] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0034] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0035] Figure 1 This is a schematic diagram of the structure of a three-dimensional geophysical simulation test system according to an exemplary embodiment;

[0036] Figure 2 This is a structural schematic diagram of an excavation face support system according to an exemplary embodiment;

[0037] Figure 3 This is a schematic diagram of the monitoring section and sensor arrangement according to an exemplary embodiment, wherein (a) is a schematic diagram of the monitoring section arrangement (unit: cm), and (b) is a schematic diagram of the monitoring point arrangement (unit: cm).

[0038] Figure 4 The above is a schematic diagram of a curved surface obtained by drawing 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.

[0039] Figure 5 This is a schematic diagram of a cone model according to an exemplary embodiment, wherein (a) is a schematic diagram of the tunnel excavation face in the fault fracture zone, and (b) is a coordinate system 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 burial depth direction as the Z-axis;

[0040] Figure 6 This is a force analysis diagram of the unstable region below the tunnel arch, according to an exemplary embodiment.

[0041] Figure 7This is a schematic diagram showing the comparison and analysis results of the theoretical calculation results and experimental data of the calculated ultimate support force of the excavation face according to an exemplary embodiment.

[0042] Figure 8 This is a schematic diagram comparing different models according to an exemplary embodiment;

[0043] Figure 9 This is a schematic diagram illustrating the relationship between ultimate support force p, burial depth ratio H / D, and cohesion c according to an exemplary embodiment, wherein (a) shows the relationship between H / D and p under different cohesion c conditions, and (b) shows the relationship between cohesion c and the minimum burial depth ratio for local instability.

[0044] Figure 10 This is a schematic diagram illustrating the influence of the internal friction angle φ on the ultimate support force and the minimum burial depth ratio for local instability, according to an exemplary embodiment. In this diagram, (a) shows the relationship between H / D and p under different internal friction angles φ, and (b) shows the relationship between the internal friction angle φ and the minimum burial depth ratio for local instability.

[0045] Figure 11 The robustness factor f is shown according to an exemplary embodiment. k The influence of ultimate support force and minimum burial depth ratio for local instability, where (a) represents different robustness coefficients f k Under the given conditions, H / D is related to p, and (b) is the robustness coefficient f. k Relationship with the minimum burial depth for local instability;

[0046] Figure 12 The following is an exemplary embodiment illustrating the effect of specific gravity γ on ultimate support force and minimum burial depth ratio for local instability, wherein (a) is the relationship between H / D and p under different specific gravity γ conditions, and (b) is the relationship between specific gravity γ and minimum burial depth ratio for local instability. Detailed Implementation

[0047] The following description and accompanying drawings fully illustrate specific embodiments of this application to enable those skilled in the art to practice them. Some embodiments may include or replace parts and features of other embodiments. The scope of embodiments of this application includes the entire scope of the claims and all available equivalents thereof. In this application, the terms “first,” “second,” etc., are used only to distinguish one element from another, without requiring or implying any actual relationship or order between these elements. In fact, a first element can also be referred to as a second element, and vice versa. Furthermore, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a structure, apparatus, or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a structure, apparatus, or device. Without further limitation, an element defined by the phrase “comprising one…” does not exclude the presence of other identical elements in the structure, apparatus, or device that includes said element. The various embodiments in this application are described in a progressive manner, with each embodiment focusing on the differences from other embodiments; similar or identical parts between embodiments can be referred to interchangeably.

[0048] In this application, the character " / " indicates that the objects before and after it are in an "or" relationship. For example, A / B means: A or B.

[0049] In this application, the term "and / or" describes an association between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or A and B.

[0050] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0051] Example 1

[0052] This embodiment is based on a method for calculating the ultimate support force of the excavation face in a fault fracture zone with local instability, and includes the following steps:

[0053] S1: Determine whether the damage to the tunnel excavation face in the fault fracture zone is a state of local instability;

[0054] Specifically:

[0055] Combine formulas (1), (2), and (3) and substitute the active earth pressure coefficient K. a The following parameters are used: density γ, initial reference height H0 for tunnel burial depth, tunnel radius r, and θ is the fracture angle when the soil undergoes active failure. By inputting different burial depths H (such as 0, 1, 2, 3, etc.), the overburden thickness H2 can be solved, and then the ultimate span B and arch height h of the underground chamber can be obtained. Then, the range of burial depth H where local instability occurs can be determined.

[0056] Specifically, it includes:

[0057] A method for predicting the impact range of local instability and failure by establishing a quantitative relationship between the ultimate span B of the underground chamber and the overlying soil thickness H2:

[0058] (1)

[0059] In the formula, H2 is the height from the top of the pressure arch to the ground, and h is the height of the pressure arch. The calculation formula is as follows:

[0060] (2)

[0061] In the formula, H2+h is the distance from the arch foot of the soil arch to the ground, φ is the internal friction angle of the soil, c is the soil cohesion, and K a f is the active earth pressure coefficient of the soil. k γ is the soil firmness coefficient, γ is the soil unit weight, and B is the ultimate span of the underground chamber;

[0062] As can be seen from formula (1), the ultimate span B, the distance H2 from the top of the damaged area to the ground, and the arch height h are related, and H2+h is proportional to B. When the B~(H2+h) curve and the straight line L are plotted in the same plane coordinate system, B gradually increases as H2+h increases, and the B~(H2+h) curve eventually intersects the straight line L. The coordinates (B,H2+h) at the intersection point can represent the expansion range of local damage.

[0063] Substitute formulas (2) and (3) into formula (1) to obtain H2, and calculate B according to formula (3), where H0 = r(sinθtanθ + cosθ - 1);

[0064] (3)

[0065] From formula (1), we can see that H2 is directly proportional to B, which indicates that the greater the burial depth of the chamber, the larger the instability expansion radius.

[0066] The extent of the burial depth H where local instability occurs can be determined using the following method:

[0067] (1) When H2+h is greater than H, it means that a chamber that can support the upper soil cannot be formed under the burial depth conditions. At this time, the soil failure area at the excavation face extends to the ground surface, and the instability mode is judged to be overall instability.

[0068] (2) When H2+h=H, the burial depth H is the minimum burial depth at which local instability occurs;

[0069] (3) When H2+h is less than H, it indicates that the soil failure area at the excavation face has not extended to the ground surface, and the instability mode is judged to be local instability;

[0070] The above H2+h represents the distance from the arch foot of the earthen arch to the ground.

[0071] S2: Once it is determined that the situation is in a state of local instability, the ultimate support pressure p is obtained using the following formula:

[0072] (twenty two)

[0073] In the formula, A1~A4, D1~D2, and E1~E6 are parameters related to the unit weight 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 and the XOY plane, and the tunnel burial depth H.

[0074] Specifically, in step S2, after determining that the state is locally unstable, the method for obtaining the ultimate support pressure p using the following formula includes:

[0075] S21: Physical parameters of the soil at the tunnel shield excavation site were obtained through indoor tests. These physical parameters include: soil unit weight r, soil internal friction angle φ, soil cohesion c, the angle θ between the sliding body cone and the XOY plane, and the tunnel depth H. The angle θ between the sliding body cone and the XOY plane is the fracture angle when the soil undergoes active failure, and it is related to the soil internal friction angle φ, where θ = 45° + φ / 2.

[0076] S22: Substitute the obtained parameters into formula (22) and calculate the ultimate support pressure p through a series of different tunnel burial depths H.

[0077] Example 2

[0078] In order to obtain the morphology of the unstable area when the tunnel excavation face is locally unstable, a large-scale three-dimensional geophysical simulation test system was used to confirm the failure morphology of the excavation face and the displacement changes of the rock and soil mass at the fault location.

[0079] 1. Physical simulation test of tunnel crossing fault fracture zone

[0080] (1) Large-scale three-dimensional geophysical simulation test system

[0081] The test system consists of four parts: a model box, a stress loading system, an excavation face support system, and an information acquisition system. Figure 1 As shown, the internal dimensions of the model box are length × width × height = 8 m × 4.5 m × 5 m. The stress loading system provides the ground stress required for the test environment, supplied by hydraulic jacks; the information monitoring system consists of sensors, monitoring software, and a static resistance strain gauge.

[0082] The stress loading system applies pressure to the surface of the stratum, which is equivalent to the self-weight load of the overlying soil within a specific depth range of the stratum surface, thus simulating the surrounding rock pressure of tunnels at different burial depths. After the model box is filled, a steel pad is placed on the surface of the stratum, which evenly transmits the pressure generated by the jacks to the stratum.

[0083] A baffle is installed at the tunnel excavation face, and a force transmission rod is fixed at the center of the baffle. The other end of the force transmission rod is connected to a telescopic motor. Figure 2 As shown in the diagram. After the experiment began, a telescopic motor was driven to move the baffle at the excavation face away from the tunnel excavation face at a set speed. The soil at the excavation face was displaced due to the movement of the baffle, thus simulating the process of the excavation face gradually becoming unstable due to the reduction of support force. The soil pressure on the excavation face was recorded by soil pressure sensors installed on the baffle.

[0084] (2) Test plan

[0085] Uncirculated soil samples were taken from the F2 fault zone of Yonglian Tunnel as filling material for the model test. The physical and mechanical parameters of the uncirculated soil are shown in Table 1.

[0086] Table 1 Physical and mechanical parameters of undisturbed soil

[0087]

[0088] Before filling, the tunnel lining model and excavation face support system were installed. Material filling was carried out using a layered compaction method. Sensors were simultaneously installed during the filling process. Each fill height was 30 cm, with a total filling height of 4.5 m. At this point, the simulated tunnel depth was 2.7 m. After filling, the remaining ground pressure was compensated using a stress loading system. Different pressures were applied to the ground surface to simulate ground pressure under different tunnel depths. A total of four tests were conducted, and the test conditions are shown in Table 2.

[0089] Table 2 Test Conditions

[0090]

[0091] The tunnel lining is a tempered glass cylinder with a diameter of 60 cm, and the excavation face is 200 cm from the tunnel entrance. The monitoring sections and sensor layout are as follows: Figure 3 As shown, four monitoring sections were set up within the fault, each spaced 60 cm apart, with the first monitoring section located at the excavation face. Displacement sensors were placed on each monitoring section to monitor the vertical displacement of the soil. After the test began, the excavation face support baffle was moved at a speed of 0.2 mm / min until the displacement monitoring data stabilized. During the test, the soil pressure at the excavation face and the vertical displacement of the strata were recorded in real time.

[0092] 2. Analysis of Experimental Results

[0093] Plotting the monitoring points with the largest vertical displacement in each monitoring section on the same coordinate system yields the following results: Figure 4 The surface shown reflects the shape of the unstable region. The bottom is spherical, and the portion above the sphere is conical. The surface is symmetrical along the X=0 plane. After the experiment, the unstable region did not extend to the ground surface, indicating that the instability was localized.

[0094] 3. Calculation of excavation face support force

[0095] I. Establishment of the Instability Model

[0096] Based on the failure results of the experimental excavation face, an improved cone model was adopted, 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 a straight line L in the YOZ plane around the Z-axis. The equation of line L is z = y tanθ, where θ is the angle between the cone surface and the XOY plane. The side surface of the model is a combination of the cone surface formed by rotating line L around the Z-axis and a partial spherical surface. The outer contour of the horizontal profile at any burial depth is a semi-circle. The following assumptions are made during the model analysis:

[0097] (1) After the excavation face becomes unstable, the entire damaged area is located within the fault fracture zone, and the soil is homogeneous and isotropic.

[0098] (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.

[0099] (3) The tunnel outline is circular, and is not considered. Figure 5 The force acting on the shaded area in (a) of the diagram;

[0100] (4) The angle θ between the sliding cone surface and the XOY plane is the fracture angle when the soil undergoes active failure, which is related to the internal friction angle φ of the soil. θ = 45° + φ / 2.

[0101] When local instability occurs at the excavation face, the failure area is confined within the conical model. Under the soil arching effect, the soil above the failure area does not collapse. This mechanical behavior is highly similar to the formation mechanism of natural caverns. By establishing a quantitative relationship between the ultimate span B of the underground cavern and the overlying soil thickness H2, the influence range of local instability can be predicted. The ultimate span B of the underground cavern considering the soil arching effect is calculated using the following formula:

[0102] (1)

[0103] In the formula, H2 is the height from the top of the pressure arch to the ground, and h is the height of the pressure arch. The calculation formula is as follows:

[0104] (2)

[0105] In the formula, H2+h is the distance from the arch foot of the soil arch to the ground, φ is the internal friction angle of the soil, c is the soil cohesion, and K a f is the active earth pressure coefficient of the soil. k γ is the soil firmness coefficient, γ is the soil unit weight, and B is the ultimate span of the underground chamber.

[0106] As shown in formula (1), the ultimate span B, the distance H2 from the crown of the damaged area to the ground, and the arch height h are related, and H2+h is directly proportional to B. Plotting the B~(H2+h) curve and the straight line L in the same plane coordinate system, B gradually increases with the increase of H2+h, and the B~(H2+h) curve eventually intersects the straight line L. The coordinates (B, H2+h) at the intersection point can represent the extent of local damage. Substituting formulas (2) and (3) into formula (1) to obtain H2, and calculating B according to formula (3), where H0=r(sinθtanθ+cosθ-1).

[0107] (3)

[0108] Formula (1) shows that H2 is directly proportional to B, indicating that the greater the burial depth of the chamber, the larger its instability propagation radius. When H2+h calculated by the above method is greater than H, it means that a chamber capable of supporting the upper soil cannot be formed under this burial depth condition. At this time, the collapse zone extends to the ground surface, and the failure mode of the excavation face soil is overall failure. The burial depth when H2+h=H is the minimum burial depth for local instability. The method for calculating the ultimate support force of the excavation face during local instability proposed in this application is applicable to the case where H2+h is less than H.

[0109] II. Stress Analysis of Sliding Soil and Determination of Excavation Face Support Pressure

[0110] The stress in the area below the arch of the excavation face is as follows Figure 6 As shown, this area is subjected to a vertical pressure p from the overlying soil. v The forces acting on the soil surface on the XOZ plane are: the excavation face support pressure p, the normal support force n1 and tangential force u1 on the conical surface, the normal support force n2 and tangential force u2 on the arc surface, and the soil weight G. The forces acting on the soil surface other than the excavation face are ignored. The tangential force u is composed of cohesion c and frictional force, u = ntanφ + c. The excavation face support pressure p is a value to be determined.

[0111] Gravity G, p, p v The resultant force is as shown in equations (4) to (6):

[0112] (4)

[0113] (5)

[0114] (6)

[0115] In the formula, K1 is the lateral earth pressure coefficient considering the soil arching effect. , The active earth pressure coefficient is B1 = (H0 + 2r) / tanθ.

[0116] Based on the fact that the resultant force of the soil in the sliding zone is zero in the Y and Z directions, the force equilibrium equations are as follows:

[0117] (7)

[0118] n1 is the normal stress acting on the cone surface, and u1 is the tangential stress acting on the cone surface, as shown in formula (8):

[0119] (8)

[0120] In the formula, the lateral pressure coefficient K is the ratio of the vertical stress of the soil at any depth to the normal stress on the cone surface, and is an unknown quantity.

[0121] n1 and u1 are decomposed into XOY and Z directions as shown in formulas (9) and (10):

[0122] (9)

[0123] (10)

[0124] n 1z u 1z The resultant force N 1z U 1z As shown in formula (11), the direction is the same as that of the Z-axis:

[0125] (11)

[0126] In formula (11), A1, A2, and D1 are parameters, which are known quantities and are related to H, r, γ, φ, and θ.

[0127] (12)

[0128] In formula (12), C1 and C2 are parameters, which are known quantities and are related to r and θ.

[0129] (13)

[0130] The sliding cone is semi-circular in any horizontal section, and the horizontal components of n1 and u1 are n 1xy u 1xyActing on the surface of the cone, perpendicular to the tangent of the arc on the horizontal section, pointing towards or away from the center of the circle. The resultant force of n1 and u1 in the X direction is zero due to the symmetry of the sliding region. A 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 formula (14):

[0131] (14)

[0132] In formula (14), A3, A4, and D2 are parameters, which are known quantities and are related to H, r, γ, φ, and θ.

[0133] (15)

[0134] n2 and u2 are the normal and tangential stresses acting on the spherical surface of the sliding region, respectively. The outer contour of the cross-section of the spherical surface of the sliding region, parallel to the XOY plane, is semi-circular, and n2 and u2 are acting on it in the XY direction. 2xy u 2xy At the excavation face, there is a support pressure p.

[0135] Assuming the support pressure p is constant, on any semicircular cross-section perpendicular to the Z-axis, the force n acting on the arc... 2xy u 2xy The magnitude depends on Z, but not on X or Y. Therefore, p has the following relationship with n² and u²:

[0136] (16)

[0137] In the formula, θ i The angle between the tangent line on the bottom arc of the model and the XOY plane.

[0138] (17)

[0139] In the formula, z0 is the Z-coordinate of the circle's center:

[0140] (18)

[0141] The resultant forces of n2 and u2 in the Z and Y directions are shown in formula (19):

[0142] (19)

[0143] In formula (19), E1, E2, E3, E4, E5, and E6 are parameters, which are known quantities and are related to r, φ, and θ. p is the support pressure at the excavation face, which is an unknown quantity.

[0144] (20)

[0145] In formula (20), D3 is a parameter, which is a known quantity and is related to φ and θ.

[0146] (twenty one)

[0147] Solving formula (7) and eliminating the lateral pressure coefficient K, we can obtain the support pressure p.

[0148] (twenty two)

[0149] In formula (22), A1~A4, D1~D2, and E1~E6 are all parameters related to r, φ, c, θ, and H.

[0150] In summary, the results of this application and the experimental results are as follows:

[0151] Based on the parameters listed in Tables 1 and 2, the ultimate support force of the excavation face was calculated using the method of this application. The comparison and analysis results between the theoretical calculation results and the experimental data are as follows: Figure 7 As shown, the ultimate support force *p* at the point of excavation face instability is directly proportional to the burial depth ratio *H / D*, and its increase gradually slows down as *H / D* increases. When *H / D* ≤ 15, the theoretical calculated value is higher than the experimentally measured value; when *H / D* > 15, the theoretical value is lower than the experimental value. Figure 7 It can be seen that within the H / D range of 15-20, the relationship between theoretical and experimental values ​​changes, and the difference between the two continues to widen as H / D increases. Under deep-buried tunnel conditions, the experimentally measured ultimate support force at the excavation face is slightly higher than the theoretically calculated value as H / D increases. The error may be due to the fact that the experiment uses a stress loading system to simulate the self-weight stress of the strata. Compared with the actual burial depth conditions formed by the actual backfill, it is difficult to fully utilize the soil arching effect when the excavation face becomes unstable, resulting in a higher measured support pressure.

[0152] The errors between the theoretical calculations and the experimental results are shown in Table 3. The minimum error occurs at a burial depth ratio H / D=20, and the maximum error occurs at H / D=10. When H / D is in the range of 15~25, the error between the theoretical method and the experimental results is small, indicating that the method can effectively predict the ultimate support force when local instability occurs at the tunnel excavation face in the fault fracture zone.

[0153] Table 3 Model Calculation Results

[0154]

[0155] This application is compared with existing local instability models, and the results are as follows:

[0156] Zhang Xiaoqing et al. (Zhang Xiaoqing. Study on instability mechanism and earth pressure distribution pattern of deep-buried shield tunnel excavation face [D]. Shanghai University, 2018) conducted instability model tests of excavation face at different burial depths in sandy strata in Fujian. The study showed that the morphology of the soil failure zone changed significantly with the burial depth. Under shallow burial conditions, as the excavation face retreated and the displacement increased, the soil failure zone in front gradually showed a "wedge + prism" shape and extended to the ground surface; under deep burial conditions, the tunnel excavation face failure zone was spherical and did not extend to the ground surface. Based on this, Zhang Mengxi et al. (Zhang Mengxi, Dai Zhiheng, Zhang Xiaoqing, et al. Calculation method of active ultimate 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.) proposed a spherical cannula local failure model for calculating the ultimate support force of the excavation face.

[0157] The results of the ultimate support force of the excavation face obtained by the method of this application and the calculation method of Zhang Mengxi et al. (Zhang Mengxi, Dai Zhiheng, Zhang Xiaoqing, et al. Calculation method of active ultimate 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 compared and analyzed with the model test data of Zhang Xiaoqing et al. (Zhang Xiaoqing. Study on instability mechanism and earth 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 weight γ=15.34kN / m 3 The tunnel radius r = 0.032m. Substituting the above parameters into formula (22), the excavation face support pressure p is calculated, as follows: Figure 8 As shown.

[0158] The instability test of the excavation face by Zhang Xiaoqing et al. (Zhang Xiaoqing. Research on instability mechanism and earth pressure distribution pattern of deep-buried shield tunnel [D]. Shanghai University, 2018) shows that: as the tunnel burial depth ratio (H / D) increases, the expansion range of the instability zone gradually decreases; when H / D=4, the instability mode is local instability. The minimum critical burial depth ratio for local instability calculated by the method of this application is H / D=3 ( Figure 8 (Dashed line) The values ​​are basically consistent with the above experimental values, confirming the accuracy of this method in calculating the minimum burial depth for local instability. The method in this application is applicable to calculating the ultimate support force of the excavation face when H / D>3, and is derived from... Figure 8It can be seen that when H / D=4~6, the calculation results of the method in this application and those of Zhang Mengxi et al. (Zhang Mengxi, Dai Zhiheng, Zhang Xiaoqing, et al. Calculation method of active ultimate 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 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, the calculation results of this application have a large error compared with the experimental values. The main reason is that within this tunnel burial depth ratio range, the instability mode of the excavation face is overall instability. The method of this application and the method of Zhang Mengxi et al. (Zhang Mengxi, Dai Zhiheng, Zhang Xiaoqing, et al. Calculation method of active ultimate 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 the local instability mode. Therefore, there is a deviation when predicting the support force of the excavation face in the low tunnel burial depth ratio range.

[0159] From the above derivation process, it can be seen that the ultimate support force p at the excavation face is related to the cohesion c, the internal friction angle φ, and the Protodyakonov stability coefficient f. k The soil weight γ and tunnel burial depth H are related. Therefore, the above parameters were selected for analysis to further explore the influence of each factor on the ultimate support force of the excavation face. At the same time, the minimum burial depth ratio for local instability under different factor values ​​was calculated. In the influencing factor analysis, the tunnel radius r = 6m, the value of H / D ranged from 0 to 6, and the selection of other parameters referred to the literature. The detailed parameter values ​​are shown in Table 4.

[0160] Table 4 Parameter Values

[0161]

[0162] Based on the given parameters, the ultimate support force p of the excavation face corresponding to different burial depth ratios H / D was calculated using formula (22), and the results are as follows: Figure 9 (a) Figure 10 (a) Figure 11 (a) Figure 12 As shown in (a) of the figure, the horizontal axis corresponding to the vertical dashed line represents the critical depth ratio for local instability. The relationship between the formation parameters and the critical depth ratio for local instability is as follows: Figure 9 (b) Figure 10 (b) Figure 11 (b) Figure 12 As shown in (b) of the diagram.

[0163] (1) Cohesion c

[0164] Figure 9(a) shows that the ultimate support force p increases with the increase of the burial depth ratio H / D, while it is negatively correlated with the cohesion c. The minimum critical burial depth for local instability decreases with the increase of cohesion c. This is because the greater the cohesion, the stronger the bonding between soil particles, and the easier it is to form a stable self-supporting arch structure, thereby reducing the thickness of the overburden layer required to maintain stability.

[0165] (2) Angle of internal friction φ

[0166] 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 the soil's mechanical properties: directly enhancing the soil's shear strength, optimizing the stress distribution of the surrounding rock, and promoting the formation and development of the soil arching effect. These synergistic effects not only significantly reduce the support force required to maintain the stability of the excavation face, causing the pH / D curve to flatten, a trend consistent with the experimental results of Chen et al., but also indicate that the critical burial depth for local instability decreases with increasing *φ*. The mechanism is that a high *φ* value, on the one hand, enhances the self-supporting capacity of the surrounding rock, reducing the risk of collapse; on the other hand, it optimizes the stress arch shape, improving the efficiency of load transfer to both sides; furthermore, it inhibits the expansion of the plastic zone, reducing the extent of loosened surrounding rock.

[0167] (3) Strength coefficient f k

[0168] Ultimate support force p and soil stability coefficient f k They are inversely proportional. The reason for this is that f k When the soil mass increases, its compressive and shear strength and self-stability are enhanced, allowing it to bear greater loads through internal stress redistribution, thus reducing the demand for support forces. Equation (2) shows that when the maximum expansion range B of the local instability zone increases, the resulting arch height h also increases, leading to a decrease in the distance from the top of the collapsed body to the ground surface. Therefore, f k It is positively correlated with the ratio of the minimum critical burial depth for local instability.

[0169] (4) Severe γ

[0170] The soil weight γ is directly proportional to the ultimate support force at the excavation face, but inversely proportional to the minimum burial depth ratio at which local instability occurs. Notably, a significant nonlinear relationship exists between γ and the minimum burial depth ratio. As γ increases, the soil's self-weight stress increases rapidly, causing the pressure arching effect to appear at shallower burial depths, thus reducing the minimum burial depth ratio. With continued increases in γ, the influence of soil strength on stability gradually becomes apparent, leading to a more gradual decrease in the minimum burial depth ratio. Ultimately, when γ exceeds a certain critical value, the plastic zone of the surrounding rock is fully developed, and its expansion tends to stabilize, further weakening the rate of change of the minimum burial depth ratio with increasing γ.

[0171] Finally, it should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0172] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them; although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications can still be made to the specific implementation of the present invention or equivalent substitutions can be made to some technical features without departing from the spirit of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the scope of the technical solutions claimed in the present invention.

Claims

1. A method for calculating the ultimate support force of excavation faces in fault fracture zones based on local instability, characterized in that, Includes the following steps: S1: Determine whether the damage to the tunnel excavation face in the fault fracture zone is a state of local instability; S2: Once it is determined that the condition is locally unstable, the ultimate support pressure is obtained using the following formula. p : (22) In the formula, G is the weight of the soil. p v This refers to the vertical pressure on the upper soil mass. r The internal friction angle of the soil around the tunnel radius. φ , A 1. A 2. D The formula is as follows; (12) In the formula, θ The fracture angle when soil undergoes active failure. H For tunnel burial depth, H 0 represents the initial reference height for tunnel burial depth. γ The weight of soil. φ The internal friction angle of the soil; c For soil cohesion, C 1. C Formula 2 is as follows: (13) In the formula, A 3. A 4. D Formula 2 is as follows: (15) In the formula, E 1. E 2. E 3. E 4. E 5. E The formula is as follows: (20) In the formula, D The formula is as follows; (21)。 2. The method for calculating the ultimate support force of the excavation face in a fault fracture zone based on local instability, as described in claim 1, is characterized in that... The method for determining whether the failure of the tunnel excavation face in the fault fracture zone belongs to a state of local instability in step S1 specifically includes: Combine formulas (1), (2), and (3) and substitute the active earth pressure coefficient of the soil. K a Severe γ Initial reference height for tunnel burial depth H 0. Tunnel radius r The angle of failure when soil undergoes active failure θ Input different burial depths H Solve for the thickness of the overburden. H 2. This allows us to obtain the ultimate span of the underground chamber. B Arch height h The specific formula is as follows: (1) (2) (3) In the formula, H 2 +h This is the distance from the arch foot of the earthen arch to the ground. φ The internal friction angle of the soil. c For soil cohesion, K a This is the active earth pressure coefficient of the soil. f k The soil's firmness coefficient. γ The weight of soil. B This is the maximum span of the underground chamber.

3. The method for calculating the ultimate support force of the excavation face in a fault fracture zone based on local instability, as described in claim 2, is characterized in that... The method for determining whether the failure of the tunnel excavation face in the fault fracture zone belongs to a state of local instability in step S1 also includes: By establishing the ultimate span of the underground chamber B With the thickness of the overlying soil H The quantitative relationship of 2 is used to determine the burial depth at which local instability occurs. H The scope specifically includes: (1) When H 2 +h Greater than H When this occurs, it indicates that a chamber capable of supporting the upper soil cannot be formed under the conditions of this burial depth. At this time, the soil failure area at the excavation face extends to the ground surface, and the instability mode is judged to be overall instability. (2) When H 2 +h = H Burial depth at time H The minimum burial depth at which local instability occurs; (3) When H 2 +h Less than H hour ， This indicates that the area of ​​soil failure at the excavation face did not extend to the ground surface, and the instability is judged to be a local instability. The above H 2 +h This refers to the distance from the arch foot of the earthen arch to the ground.

4. The method for calculating the ultimate support force of the excavation face in a fault fracture zone based on local instability, as described in claim 1, is characterized in that... In step S2, after determining that the situation is in a state of local instability, the ultimate support pressure is obtained using the following formula. p The methods specifically include: 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) to obtain a series of different tunnel depths. H The ultimate support pressure was calculated. p .

5. The method for calculating the ultimate support force of the excavation face in a fault fracture zone based on local instability, as described in claim 4, is characterized in that... The physical parameters of the soil mentioned in step S21 include: the unit weight 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 burial depth H.

6. The method for calculating the ultimate support force of the excavation face in a fault fracture zone based on local instability, as described in claim 5, is characterized in that... The angle θ between the sliding body cone surface 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, and θ = 45° + φ / 2.

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