Method for rapidly judging stability of surrounding rock of shallow-buried large-span tunnel in upper-soft and lower-hard stratum

Abstract

The invention discloses a method for rapidly judging the surrounding rock stability of a shallow-buried large-span tunnel in an upper-soft and lower-hard stratum, and relates to the technical field of tunnel engineering design. Constructing a physical plane graph according to the engineering design drawing; mapping the physical plane graph to an image plane through a conformal mapping function; generating a stress field analytic equation corresponding to the physical plane according to each parameter in the image plane graph and the complex variable function analytic form; calculating a plurality of different principal stresses of the surrounding rock through the stress field analytic equation, calculating a shear failure stress according to the plurality of different principal stresses, and obtaining an expression between the normal stress and the shear stress of the surrounding rock; and defining the shear failure shear stress as tau c, the shear stress as tau and the shear safety coefficient as s = tau / tau c, judging whether s is greater than 1 or not, and if so, considering that the unit rock mass meets the failure condition. The method aims at quickly and accurately evaluating the surrounding rock stability of the large-span tunnel in the upper-soft and lower-hard stratum, and the safety risk and the cost pressure faced by tunnel construction are reduced.

Description

Technical Field

[0001] The invention relates to the technical field of tunnel engineering design, and in particular to a method for quickly judging the stability of surrounding rocks of a shallowly buried large-span tunnel in soft upper and hard lower strata. Background Art

[0002] In the current rapid urbanization, the demand for transportation infrastructure construction is increasing. Among them, large-span tunnels have gradually become an important part of urban underground projects due to their large transportation capacity and little impact on the surrounding environment. The construction of large-span tunnels can not only alleviate the pressure of urban ground traffic, but also effectively utilize underground space and improve the comprehensive carrying capacity of the city. However, the geological conditions faced by tunnel construction are complex and changeable, especially the "soft on top and hard on the bottom" strata commonly seen in urban geological environments, which brings many challenges to the design and construction of tunnels.

[0003] The "soft upper part and hard lower part" stratum is a typical geological condition. Usually, the upper part is a highly weathered layer with a high degree of weathering, weakness and fracture, and well-developed joints, while the lower rock layer conditions gradually improve. This stratum structure leads to the construction of shallow large-span tunnels. If the hard rock layer on the tunnel vault is too thin, the surrounding rock will be difficult to achieve a self-stabilizing state, the surface settlement will be difficult to control, and even a collapse accident may occur. To ensure the safety of tunnel construction, the thickness of the hard rock on the vault must meet the requirements of surrounding rock self-stabilization.

[0004] In this context, traditional construction methods rely more on empirical judgment and simple geological exploration methods, mainly including advanced geological prediction, geological radar detection, drilling sampling and other methods. Although these methods can provide certain geological information, they have problems such as information lag, insufficient detection accuracy, and difficulty in data interpretation. For example, advanced geological prediction technology is prone to misjudgment under complex geological conditions, the effective depth of geological radar detection is limited, and drilling sampling is costly and has a small coverage area. These technical means are difficult to meet the needs of quickly and accurately distinguishing and evaluating the stability of the surrounding rock for tunnel excavation in soft and hard strata, and cannot provide timely and effective guidance for construction.

[0005] In addition, most traditional tunnel support design methods are based on empirical formulas and semi-empirical and semi-theoretical models, lacking a comprehensive understanding of the mechanical behavior of surrounding rocks under complex geological conditions. These methods often show great uncertainty in soft upper and hard lower strata, leading to unreasonable support structure design, which may cause over-support, increase engineering costs, or under-support, leading to safety hazards.

[0006] Therefore, how to quickly and accurately evaluate the surrounding rock stability of large-span tunnels in soft upper and hard lower strata and reduce the safety risks and cost pressures faced by tunnel construction has become a technical problem that needs to be solved urgently. Summary of the invention

[0007] The main purpose of the present invention is to provide a method for quickly judging the stability of the surrounding rock of a shallowly buried large-span tunnel in a soft upper and hard lower stratum, aiming to quickly and accurately evaluate the stability of the hard surrounding rock of a large-span tunnel in a soft upper and hard lower stratum, thereby reducing the safety risks and cost pressures faced by tunnel construction.

[0008] In order to achieve the above object, the present invention proposes a method for quickly judging the stability of the surrounding rock of a shallowly buried large-span tunnel in a soft upper stratum and a hard lower stratum, comprising the following steps: According to the engineering design drawings, the upper soft soil layer and surface load of the engineering design drawings are combined into the external load of the bedrock boundary to construct the physical plane diagram; Mapping the physical plane image to an image plane by a conformal mapping function; Generate a stress field analytical equation corresponding to the physical plane according to various parameters in the image plane diagram and the analytical form of the complex variable function; Calculating multiple different principal stresses of the surrounding rock through the stress field analytical equation, calculating the shear failure stress according to the multiple different principal stresses, and obtaining an expression between the normal stress and the shear stress of the surrounding rock; The shear failure shear stress is defined as τc, the shear stress is τ, and the shear safety factor is s=τ / τc. When judging whether s is greater than 1, if so, it is considered that the unit rock mass reaches the failure condition.

[0009] In one embodiment of the present application, generating a stress field analytical equation corresponding to a physical plane according to various parameters in the image plane diagram and the analytical form of a complex variable function includes the following steps: Obtaining the hole edge stress condition of the image plane and the surface stress condition of the image plane, bringing the hole edge stress condition of the image plane and the surface stress condition of the image plane into the analytical form of the complex variable function, obtaining the stress field analytical function, expanding and simplifying it through the Fourier series, and obtaining the simplified expression of the hole edge stress condition and the simplified expression of the surface stress condition; After combining the simplified expressions of the hole side stress condition and the simplified expressions of the surface stress condition, the non-constant term coefficients of the stress field analytical function are obtained, and the corresponding relationship of the constant term of the stress field analytical function is obtained; The constant term coefficient of the stress field analytical function is obtained according to the corresponding relationship of the constant term of the stress field analytical function; and the stress field analytical equation corresponding to the physical plane diagram is generated according to the non-constant term coefficient, the constant term coefficient, and the stress field analytical function.

[0010] In one embodiment of the present application, the conformal mapping function is expressed as: ; in, Represents the plural form of physical coordinates; express and The mapping relationship between them; The complex form of the coordinates on the image plane; represents an imaginary unit; is a constant coefficient; represents a constant coefficient.

[0011] In one embodiment of the present application, the initial value of the inner diameter of the ring is set to α 0 , using the dichotomy method α The value of is approximated to map the perimeter of the hole L’ The original hole perimeter L The relationship is used as the convergence criterion. When the convergence condition is met, the approximation is stopped and the output is α Value and corresponding β k value.

[0012] In one embodiment of the present application, the hole edge stress condition of the physical plane is expressed as: ; in, Represents the analytical function of the stress at the first hole edge in the physical plane; Represents the plural form of physical coordinates; The analytical function of the stress at the second hole edge on the physical plane; represents the lateral pressure coefficient of rock mass; represents the rock mass density; A represents the starting point of integration; B represents the end point of integration; Indicates the depth of rock mass; Indicates soil bulk density; Indicates the soil burial depth; represents the surface load; represents the soil lateral pressure coefficient; represents a complex constant; The surface stress condition of the physical plane is expressed as: ; in, represents the analytical function of the first normal stress in the physical plane; Represents the plural form of physical coordinates; represents the analytical function of the second normal stress in the physical plane; represents the surface load; A represents the starting point of integration; B represents the end point of integration; Represents coordinates on the physical plane; It indicates the soil bulk density; Indicates the soil burial depth.

[0013] In one embodiment of the present application, the hole edge stress condition of the physical plane and the surface stress condition of the physical plane are brought into the conformal mapping function to obtain the hole edge stress condition of the corresponding image plane and the surface stress condition of the image plane; The hole edge stress condition of the image plane is expressed as: ; in, represents the analytical function of the stress at the first hole edge of the image plane; ; The analytical function of the stress at the second hole edge on the image plane; represents the lateral pressure coefficient of rock mass; represents the rock mass density; A represents the starting point of integration; B represents the end point of integration; Indicates the depth of rock mass; It indicates the soil bulk density; Indicates the soil burial depth; represents the surface load; represents the soil lateral pressure coefficient; represents a complex constant; represents the coordinates on the image plane; The surface stress condition of the image plane is expressed as: ; in, represents the analytical function of the first normal stress in the image plane; represents normal stress; represents the conformal mapping function; represents the analytical function of the second normal stress in the image plane; It indicates the soil bulk density; Indicates the soil burial depth; represents the surface load; A represents the starting point of integration; B represents the end point of integration; Represents the coordinates on the image plane.

[0014] In one embodiment of the present application, the simplified expression of the hole edge stress condition is expressed as: ; in, represents a constant term; , , , ; both represent constant coefficients; , All represent constants; represents a constant term; represents a complex constant term; represents the complex constant coefficient; represents the complex constant coefficient; The simplified expression of the surface stress condition is expressed as: ; in, represents a constant term; , , , ; both represent constant coefficients; represents a constant; represents a constant term; represents a complex constant term; represents the complex constant coefficient; represents a complex constant coefficient.

[0015] In one embodiment of the present application, the complex function is expressed in analytical form as follows:

[0016] in, a 0 、a j 、b j 、c 0 、c j 、d j is the complex constant to be determined.

[0017] In one embodiment of the present application, the normal stress of the surrounding rock and shear stress The expression is expressed as:

[0018] Among them, 2 β =90°+ f , f is the internal friction angle, represents the first principal stress, .

[0019] In one embodiment of the present application, the shear failure shear stress is τc and is expressed as:

[0020] in, s is the normal stress of the oblique section inside the rock specimen unit; t c is the shear failure stress; C is the rock cohesion; f is the internal friction angle of rock.

[0021] By adopting the above technical solution, the upper soft soil layer and the surface load are combined and processed, which simplifies the actual engineering conditions and facilitates the subsequent mechanical analysis and calculation. At the same time, the construction of the physical plane map provides basic data for the subsequent conformal mapping and stress field analysis. The conformal mapping transformation converts the complex physical plane problem into a relatively simple image plane problem, making the subsequent stress field analysis calculation more convenient. Through conformal mapping, the stress distribution after tunnel excavation can be more intuitively understood and analyzed. The calculation of the principal stress helps to identify the stress concentration areas that may occur during the tunnel excavation process, thereby providing early warning and guidance for construction. By calculating the shear failure stress, it can be determined whether the surrounding rock will undergo shear failure at different locations. This process helps to identify the possible failure areas during the tunnel excavation process, thereby providing an important safety assessment basis for construction. The calculation results of the shear failure stress can be used to optimize the support design and reduce the construction risk. By determining the shear safety factor, the stability of the surrounding rock during tunnel excavation can be quickly evaluated, providing real-time safety monitoring data for construction, and improving construction efficiency and safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present invention is described in detail below with reference to specific embodiments and accompanying drawings, wherein: Figure 1 It is a schematic structural diagram of the first embodiment of the present invention. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention is described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the following specific embodiments are only used to explain the present invention and do not constitute a limitation to the present invention.

[0024] like Figure 1 As shown, in order to achieve the above purpose, the present invention proposes a method for quickly judging the stability of the surrounding rock of a shallowly buried large-span tunnel in a soft upper and hard lower stratum, comprising the following steps: According to the engineering design drawings, the upper soft soil layer and surface load of the engineering design drawings are combined into the external load of the bedrock boundary to construct the physical plane diagram; Mapping the physical plane image to an image plane by a conformal mapping function; Generate a stress field analytical equation corresponding to the physical plane according to various parameters in the image plane diagram and the analytical form of the complex variable function; Calculating multiple different principal stresses of the surrounding rock through the stress field analytical equation, calculating the shear failure stress according to the multiple different principal stresses, and obtaining an expression between the normal stress and the shear stress of the surrounding rock; The shear failure shear stress is defined as τc, the shear stress is τ, and the shear safety factor is s=τ / τc. When judging whether s is greater than 1, if so, it is considered that the unit rock mass reaches the failure condition.

[0025] Specifically, it is necessary to first obtain the design drawings and geological survey information of the project to determine the thickness, density and surface load of the upper soft soil layer. The upper soft soil layer and surface load are regarded as external loads at the bedrock boundary, and the linear variation of self-weight stress and horizontal tectonic stress with burial depth is considered. On this basis, a physical plane diagram of the analytical calculation model is constructed. The key parameters such as tunnel excavation boundary, surface load, and rock mass self-weight must be clearly marked in the physical plane diagram.

[0026] Using conformal mapping function , maps the physical plane image to the image plane. and is an undetermined constant that needs to be determined based on the actual engineering section form and hole control conditions. First, select the initial inner diameter of the ring α 0 ; Then approximate by trial calculation and bisection The value of to map the hole perimeter L’ The original hole perimeter L As the convergence criterion, when the convergence condition is met, stop the binary division and output Value and corresponding value.

[0027] According to the hole edge stress conditions and the surface stress conditions, the coefficients of the non-constant terms of the stress field analytical function are solved; according to the displacement boundary conditions, the remaining constant terms are solved to obtain all the coefficients of the stress field analytical function, and then the analytical calculation equation of the stress field around the tunnel is determined.

[0028] Calculate multiple principal stresses of surrounding rock through stress field analytical equations and The calculation formula is:

[0029] in, and represent the hoop stress and radial stress of the surrounding rock, respectively. Represents the square of shear stress.

[0030] According to the different principal stresses and , calculate the shear failure stress τc. The expressions of shear stress τ and shear failure stress τc are:

[0031]

[0032]

[0033] Among them, 2 β =90°+ f , f is the internal friction angle, represents the first principal stress, represents the second principal stress.

[0034] Define the shear failure shear stress as τc, the shear stress as τ, and the shear safety factor as s=τ / τc. Determine whether s is greater than 1. If so, it is considered that the unit rock mass has reached the failure condition. Specifically, when s>1, it indicates that the shear stress has exceeded the shear failure stress of the material, that is, the surrounding rock has reached the failure state; otherwise, the surrounding rock is still in a safe state.

[0035] By adopting the above technical solution, the upper soft soil layer and the surface load are combined and processed, which simplifies the actual engineering conditions and facilitates the subsequent mechanical analysis and calculation. At the same time, the construction of the physical plane map provides basic data for the subsequent conformal mapping and stress field analysis. The conformal mapping transformation converts the complex physical plane problem into a relatively simple image plane problem, making the subsequent stress field analysis calculation more convenient. Through conformal mapping, the stress distribution after tunnel excavation can be more intuitively understood and analyzed. The calculation of the principal stress helps to identify the stress concentration areas that may occur during the tunnel excavation process, thereby providing early warning and guidance for construction. By calculating the shear failure stress, it can be determined whether the surrounding rock will undergo shear failure at different locations. This process helps to identify the possible failure areas during the tunnel excavation process, thereby providing an important safety assessment basis for construction. The calculation results of the shear failure stress can be used to optimize the support design and reduce the construction risk. By determining the shear safety factor, the stability of the surrounding rock during tunnel excavation can be quickly evaluated, providing real-time safety monitoring data for construction, and improving construction efficiency and safety.

[0036] In one embodiment of the present application, generating a stress field analytical equation corresponding to a physical plane according to various parameters in the image plane diagram and the analytical form of a complex variable function includes the following steps: Obtaining the hole edge stress condition of the image plane and the surface stress condition of the image plane, bringing the hole edge stress condition of the image plane and the surface stress condition of the image plane into the analytical form of the complex variable function, obtaining the stress field analytical function, expanding and simplifying it through the Fourier series, and obtaining the simplified expression of the hole edge stress condition and the simplified expression of the surface stress condition; After combining the simplified expressions of the hole side stress condition and the simplified expressions of the surface stress condition, the non-constant term coefficients of the stress field analytical function are obtained, and the corresponding relationship of the constant term of the stress field analytical function is obtained; The constant term coefficient of the stress field analytical function is obtained according to the corresponding relationship of the constant term of the stress field analytical function; and the stress field analytical equation corresponding to the physical plane diagram is generated according to the non-constant term coefficient, the constant term coefficient, and the stress field analytical function.

[0037] Specifically, in the image plane, the hole edge stress condition of the image plane and the surface stress condition of the image plane are obtained. The hole edge stress condition of the image plane includes the radial stress and tangential stress of the hole edge, and the surface stress condition of the image plane includes the vertical stress and horizontal stress of the surface. The values ​​and distribution of these stress conditions are obtained through measurement and calculation.

[0038] The hole side stress condition of the image plane and the surface stress condition of the image plane are brought into the analytical form of complex variable function to obtain the analytical function of stress field. The simplified expressions of the hole side stress condition of the image plane and the surface stress condition of the image plane are obtained by expanding and simplifying the same through Fourier series.

[0039] After combining the simplified expressions of the hole edge stress condition of the image plane and the simplified expressions of the surface stress condition of the image plane, the non-constant coefficients of the stress field analytical function are obtained. The unknown coefficients in the simplified expressions are extracted to construct a system of equations; by solving the system of equations, the specific values ​​of the non-constant coefficients are obtained.

[0040] According to the constant term corresponding relational expression of the stress field analytical function, the constant term coefficient of the stress field analytical function is obtained. The non-constant term coefficient is substituted into the stress field analytical function to construct the constant term corresponding relational expression; and the specific value of the constant term coefficient is obtained by solving the constant term corresponding relational expression.

[0041] According to the non-constant term coefficient, constant term coefficient, and stress field analytical function, a stress field analytical equation corresponding to the physical plane diagram is generated. The non-constant term coefficient and the constant term coefficient are substituted into the stress field analytical function to obtain a complete stress field analytical equation; the analytical equation is verified and checked to ensure its accuracy and applicability.

[0042] By adopting the above technical solution, the stress field around the tunnel can be accurately described by obtaining the hole side stress conditions and surface stress conditions of the image plane and bringing them into the analytical form of complex variable functions. The expansion and simplification process of the Fourier series ensures the accuracy of the stress field analytical function and makes the calculation results more reliable. The calculation process can be greatly simplified by simplifying the hole side stress conditions and surface stress conditions and solving the non-constant term coefficients and constant term coefficients simultaneously. In this way, the analytical equation of the stress field can be quickly obtained, saving computing time and resources. By generating the analytical equation of the stress field corresponding to the physical plane diagram, the stress distribution around the tunnel can be comprehensively analyzed to provide early warning and guidance for construction.

[0043] In one embodiment of the present application, the conformal mapping function is expressed as: ; in, Represents the plural form of physical coordinates; express and The mapping relationship between them; The complex form of the coordinates on the image plane; represents an imaginary unit; is a constant coefficient; represents a constant coefficient.

[0044] Specifically, the points on the physical plane hole boundary are mapped to the inner boundary of the unit circle in the image plane through the conformal mapping transformation. This mapping is conformal, that is, the angle remains unchanged. By adjusting the constant coefficient and , the properties of the mapping can be flexibly changed. This can meet the needs of different application scenarios, such as different geometric shapes and boundary conditions. Since the mapping formula contains the Fourier series part, it can handle complex geometric shapes and periodic boundary conditions.

[0045] In one embodiment of the present application, the initial value of the inner diameter of the ring is set to α 0 , using the dichotomy method α The value of is approximated to map the perimeter of the hole L’ The original hole perimeter L The relationship is used as the convergence criterion. When the convergence condition is met, the approximation is stopped and the output is α Value and corresponding β k value.

[0046] Specifically, the inner diameter of the ring is approximated by the bisection method α , so that the map hole perimeter L’ and the original hole perimeter L The relationship between satisfies the convergence criteria, thus determining the optimal α Value and corresponding β k Since the dichotomy method is an existing technology, it will not be described in detail here.

[0047] Using the above technical solution, the binary method is a numerical method that gradually reduces the interval range and can achieve a high-precision approximation result in a short time. By setting a reasonable error range, the accuracy of the final result can be ensured. The binary method reduces the interval by half at each step and has good stability and convergence. Even if the initial interval is large, it can gradually approach the target value, avoiding the problem of numerical instability.

[0048] In one embodiment of the present application, the hole edge stress condition of the physical plane is expressed as: ; in, Represents the analytical function of the stress at the first hole edge in the physical plane; Represents the plural form of physical coordinates; The analytical function of the stress at the second hole edge on the physical plane; represents the lateral pressure coefficient of rock mass; represents the rock mass density; A represents the starting point of integration; B represents the end point of integration; Indicates the depth of rock mass; It indicates the soil bulk density; Indicates the soil burial depth; represents the surface load; represents the soil lateral pressure coefficient; represents a complex constant; The surface stress condition of the physical plane is expressed as: ; in, represents the analytical function of the first normal stress in the physical plane; Represents the plural form of physical coordinates; represents the analytical function of the second normal stress in the physical plane; represents the surface load; A represents the starting point of integration; B represents the end point of integration; Represents coordinates on the physical plane; It indicates the soil bulk density; Indicates the soil burial depth.

[0049] Specifically, the hole edge stress condition of the physical plane is expressed as: ; in, Represents the analytical function of the stress at the first hole edge in the physical plane; Represents the plural form of physical coordinates; The analytical function of the stress at the second hole edge on the physical plane; represents the lateral pressure coefficient of rock mass; represents the rock mass density; A represents the starting point of integration; B represents the end point of integration; Indicates the depth of rock mass; It indicates the soil bulk density; Indicates the soil burial depth; represents the surface load; represents the soil lateral pressure coefficient; represents a complex constant.

[0050] The hole edge stress condition equation expresses the stress distribution of the hole edge on the physical plane. As physical coordinates, the description and calculation of stress distribution can be simplified. Complex form of analytical function and It provides a convenient mathematical tool to deal with complex stress distribution problems. The integral part of the equation represents the stress accumulation along the hole edge. These integral terms take into account factors such as the bulk density, burial depth, and lateral pressure coefficient of the rock and soil mass, thereby accurately describing the stress distribution at the hole edge. Complex constant As part of the equation, it is used to adjust and correct the overall level of stress distribution to ensure the accuracy and applicability of the equation.

[0051] The surface stress condition of the physical plane is expressed as: ; in, represents the analytical function of the first normal stress in the physical plane; Represents the plural form of physical coordinates; represents the analytical function of the second normal stress in the physical plane; represents the surface load; A represents the starting point of integration; B represents the end point of integration; Represents coordinates on the physical plane; It indicates the soil bulk density; Indicates the soil burial depth.

[0052] The integral part of the equation represents the accumulation of stress along the surface. These integral terms take into account the bulk density of the soil, the depth of burial, and the surface load, thus accurately describing the stress distribution on the surface.

[0053] By adopting the above technical solution, the stress distribution at the edge of the hole can be accurately described through analytical functions and complex forms. Various physical parameters of rock mass and soil mass are taken into account, making the model closer to the actual situation. Since the analytical function in complex form is used, this method can adapt to complex geometric shapes and boundary conditions and has strong applicability. By using the mathematical properties of complex numbers and analytical functions, the calculation process of surface stress distribution can be simplified and the calculation efficiency can be improved.

[0054] In one embodiment of the present application, the hole edge stress condition of the physical plane and the surface stress condition of the physical plane are brought into the conformal mapping function to obtain the hole edge stress condition of the corresponding image plane and the surface stress condition of the image plane; The hole edge stress condition of the image plane is expressed as: ; in, represents the analytical function of the stress at the first hole edge of the image plane; ; The analytical function of the stress at the second hole edge on the image plane; represents the lateral pressure coefficient of rock mass; represents the rock mass density; A represents the starting point of integration; B represents the end point of integration; Indicates the depth of rock mass; It indicates the soil bulk density; Indicates the soil burial depth; represents the surface load; represents the soil lateral pressure coefficient; represents a complex constant; represents the coordinates on the image plane; The surface stress condition of the image plane is expressed as: ; in, represents the analytical function of the first normal stress in the image plane; represents normal stress; represents the conformal mapping function; represents the analytical function of the second normal stress in the image plane; It indicates the soil bulk density; Indicates the soil burial depth; represents the surface load; A represents the starting point of integration; B represents the end point of integration; Represents the coordinates on the image plane.

[0055] Using the above technical solution, the conformal mapping function can map a complex geometric shape to a simpler geometric shape, making complex stress distribution problems easier to handle and analyze. Through conformal mapping, many complex integrals and solution processes can be performed on simpler geometric shapes, thereby improving computational efficiency. Conformal mapping maintains the angular relationship of the original geometric shape, which means that no additional errors are introduced during the mapping process, ensuring the accuracy and stability of stress calculations. After mapping to the image plane, the complexity of the boundary conditions is greatly reduced, making the processing of boundary conditions easier and more intuitive.

[0056] In one embodiment of the present application, the simplified expression of the hole edge stress condition is expressed as: ; in, represents a constant term; , , , ; both represent constant coefficients; , All represent constants; represents a constant term; represents a complex constant term; represents the complex constant coefficient; represents the complex constant coefficient; The simplified expression of the surface stress condition is expressed as: ; in, represents a constant term; , , , ; both represent constant coefficients; represents a constant; represents a constant term; represents a complex constant term; represents the complex constant coefficient; represents a complex constant coefficient.

[0057] Specifically, after the conformal mapping transformation, the complex variable function analytical form of the analytical calculation model obtained is:

[0058] z c = yes , F x For along the cave x The direction resultant force is 0. F y For along the cave y Direction force, k is a coefficient related to Poisson's ratio. In plane strain problems, k =3-4 m .

[0059] By deduction, F y The expression is:

[0060] f 0 ( z )and ψ 0 ( z ) is the analytical form of a complex variable function that can be expanded into a Laurent series form:

[0061] The hole edge stress condition of the image plane ; and surface stress conditions on the image plane ; Substitute into the analytical form of complex variable function, the tunnel hole side corresponds to the inner boundary of the mapping ring, simplify the left and right sides of the stress analytical function after the hole side stress conformal mapping transformation, and use Fourier series expansion to obtain the simplified expression of the hole side stress condition:

[0062] in, represents a constant term; , , , ; both represent constant coefficients; , All represent constants; represents a constant term; represents a complex constant term; represents the complex constant coefficient; represents the complex constant coefficient; The surface boundary corresponds to the outer boundary of the ring. Using a simplified analysis method similar to the hole edge stress, the final simplified expression of the surface stress condition is obtained:

[0063]

[0064]

[0065] Among them, among them, represents a constant term; , , , ; both represent constant coefficients; represents a constant; represents a constant term; represents a complex constant term; represents the complex constant coefficient; represents a complex constant coefficient.

[0066] Combine the simplified expressions of the hole edge stress condition and the surface stress condition, merge the similar terms on both sides of the equation to establish an equation with the same power coefficient, and solve the equation. f 0 ( g ), ψ 0 ( g ) is a convergent Laurent series, and its expansion is assumed to be n 2 Item truncation, then s 1 ~ s n2 and s-1 ~ s -n2 The power term is 4 n 2 equations, and obtain non-constant coefficients a j , b j , c j , d j ( j =1~ n 2 ) value.

[0067] According to the displacement boundary conditions, the remaining constant terms are solved to obtain the analytical function f ( g ), ψ ( g ) expression. The displacement boundary condition is expressed as:

[0068] In the formula, u is the horizontal displacement component, v is the vertical displacement component.

[0069] The relationship of the constant term can be obtained from the stress boundary conditions: ; Taking the horizontal displacement of the origin as 0 and the vertical displacement of the point approaching infinity below the surface as 0, we can get the expression of the constant term:

[0070] Where: a 0 = a 01 + yes 02 , T 1 = oh ( g ), T 2 = oh ( g ), T 3 = f ( g )- a 0 , T 4 = f' ( g ), T5 = ψ ( g )- c 0 .

[0071] Stress components caused by excavation in an orthogonal curvilinear coordinate system: ; Initial geostress components: ; Final stress components: ; The above technical solution improves the simplicity, flexibility and accuracy of the expression through simplified expression and parameterized representation. It has the advantages of wide applicability and ease of calculation, and can provide a reliable basis for engineering design and stress analysis.

[0072] In one embodiment of the present application, the complex function is expressed in analytical form as follows:

[0073] in, a 0 、a j 、b j 、c 0 、c j 、d j is the complex constant to be determined.

[0074] Specifically, the stress problem on the physical plane is transformed to the complex plane using conformal mapping, thereby simplifying the processing of complex geometric shapes and boundary conditions. After the conformal mapping transformation, the complex variable function analytical form of the analytical calculation model obtained is:

[0075] z c = yes , F x For along the cave x The direction resultant force is 0. F y For along the cave y Direction force, k is a coefficient related to Poisson's ratio. In plane strain problems, k =3-4 m .

[0076] Solving for the resultant force by integration Fy The expression is:

[0077] f 0 ( z )and ψ 0 ( z ) is the analytical form of a complex variable function that can be expanded into a Laurent series form:

[0078] By adopting the above technical solution, complex geometric shapes are converted into more regular complex plane geometric shapes through conformal mapping, which simplifies the processing of stress distribution problems. The use of complex variable functions and conformal mapping can simplify the calculation process and improve the calculation efficiency. Conformal mapping maintains the angular relationship of the original geometric shape and ensures the accuracy and stability of stress calculation.

[0079] In one embodiment of the present application, the normal stress of the surrounding rock and shear stress The expression is expressed as:

[0080] Among them, 2 β =90°+ f , f is the internal friction angle, represents the first principal stress, .

[0081] The above technical solution directly reflects the relationship between the stress state of the surrounding rock and the principal stress, which can help understand the stress distribution and deformation characteristics.

[0082] In one embodiment of the present application, the shear failure shear stress is τc and is expressed as:

[0083] in, s is the normal stress of the oblique section inside the rock specimen unit; t c is the shear failure stress; C is the rock cohesion; f is the internal friction angle of rock.

[0084] The rapid identification method provided by the present invention adopts theoretical analysis for research and judgment, which can reflect the stability state of the surrounding rock of the actual project more quickly than numerical simulation and model test, and provide theoretical reference and support suggestions for construction; The rapid identification method provided by the present invention uses mathematical equations to perform analytical calculations of the stress field, and the overall evaluation process is simple and the identification accuracy is high; The rapid identification method provided by the present invention can perform identification and evaluation only by relying on on-site geological survey data and design and construction drawings, without the need for other operations, without consuming engineering resources, and with good economic benefits.

[0085] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A method for quickly judging the surrounding rock stability of a shallowly buried large-span tunnel in soft upper and hard lower strata, characterized in that: The following steps are involved: According to the engineering design drawings, the upper soft soil layer and surface load of the engineering design drawings are combined into the external load of the bedrock boundary to construct the physical plane diagram; Mapping the physical plane image to an image plane by a conformal mapping function; Generate a stress field analytical equation corresponding to the physical plane according to various parameters in the image plane diagram and the analytical form of the complex variable function; Calculating multiple different principal stresses of the surrounding rock through the stress field analytical equation, calculating the shear failure stress according to the multiple different principal stresses, and obtaining an expression between the normal stress and the shear stress of the surrounding rock; The shear failure shear stress is defined as τc, the shear stress is τ, and the shear safety factor is s=τ / τc. When judging whether s is greater than 1, if so, it is considered that the unit rock mass reaches the failure condition.

2. The method for rapidly determining the surrounding rock stability of a shallowly buried large-span tunnel in soft upper and hard lower strata as claimed in claim 1, characterized in that: According to the various parameters in the image plane diagram and the analytical form of the complex variable function, generating the stress field analytical equation corresponding to the physical plane includes the following steps: Obtaining the hole edge stress condition of the image plane and the surface stress condition of the image plane, bringing the hole edge stress condition of the image plane and the surface stress condition of the image plane into the analytical form of the complex variable function, obtaining the stress field analytical function, expanding and simplifying it through the Fourier series, and obtaining the simplified expression of the hole edge stress condition and the simplified expression of the surface stress condition; After combining the simplified expressions of the hole side stress condition and the simplified expressions of the surface stress condition, the non-constant term coefficients of the stress field analytical function are obtained, and the corresponding relationship of the constant term of the stress field analytical function is obtained; The constant term coefficient of the stress field analytical function is obtained according to the corresponding relationship of the constant term of the stress field analytical function; and the stress field analytical equation corresponding to the physical plane diagram is generated according to the non-constant term coefficient, the constant term coefficient, and the stress field analytical function.

3. The method for rapidly determining the stability of surrounding rock of a shallow-buried large-span tunnel in soft upper and hard lower strata as claimed in claim 2 is characterized in that: The conformal mapping function is expressed as: ； in, Represents the plural form of physical coordinates; express and The mapping relationship between them; The complex form of the coordinates on the image plane; represents an imaginary unit; is a constant coefficient; represents a constant coefficient.

4. The method for rapidly determining the stability of surrounding rock of a shallowly buried large-span tunnel in soft upper and hard lower strata as claimed in claim 3 is characterized in that: Set the initial value of the inner diameter of the ring to α 0, using dichotomy α The value of is approximated to map the perimeter of the hole L’ The original hole perimeter L The relationship is used as the convergence criterion. When the convergence condition is met, the approximation is stopped and the output is α Value and corresponding β k value.

5. The method for rapidly determining the stability of surrounding rock of a shallow-buried large-span tunnel in soft upper and hard lower strata as claimed in claim 2, characterized in that: The hole edge stress condition of the physical plane is expressed as: ； in, Represents the analytical function of the stress at the first hole edge in the physical plane; Represents the plural form of physical coordinates; The analytical function of the stress at the second hole edge on the physical plane; represents the lateral pressure coefficient of rock mass; represents the rock mass density; A represents the starting point of integration; B represents the end point of integration; Indicates the depth of rock mass; Indicates soil bulk density; Indicates the soil burial depth; represents the surface load; represents the soil lateral pressure coefficient; represents a complex constant; The surface stress condition of the physical plane is expressed as: ； in, represents the analytical function of the first normal stress in the physical plane; Represents the plural form of physical coordinates; represents the analytical function of the second normal stress in the physical plane; represents the surface load; A represents the starting point of integration; B represents the end point of integration; Represents coordinates on the physical plane; Indicates soil bulk density; Indicates the soil burial depth.

6. The method for rapidly determining the surrounding rock stability of a shallowly buried large-span tunnel in an upper soft and lower hard stratum as claimed in claim 5 is characterized in that: Substituting the hole edge stress condition of the physical plane and the surface stress condition of the physical plane into the conformal mapping function to obtain the hole edge stress condition of the corresponding image plane and the surface stress condition of the image plane; The hole edge stress condition of the image plane is expressed as: ； in, represents the analytical function of the stress at the first hole edge of the image plane; ; The analytical function of the stress at the second hole edge on the image plane; represents the lateral pressure coefficient of rock mass; represents the rock mass density; A represents the starting point of integration; B represents the end point of integration; Indicates the depth of rock mass; Indicates soil bulk density; Indicates the soil burial depth; represents the surface load; represents the soil lateral pressure coefficient; represents a complex constant; represents the coordinates on the image plane; The surface stress condition of the image plane is expressed as: ； in, represents the analytical function of the first normal stress in the image plane; represents normal stress; represents the conformal mapping function; represents the analytical function of the second normal stress in the image plane; Indicates soil bulk density; Indicates the soil burial depth; represents the surface load; A represents the starting point of integration; B represents the end point of integration; Represents the coordinates on the image plane.

7. The method for rapidly determining the surrounding rock stability of a shallowly buried large-span tunnel in an upper soft and lower hard stratum as claimed in claim 6, characterized in that: The simplified expression of the hole edge stress condition is expressed as: ； in, represents a constant term; , , , ; all represent constant coefficients; , All represent constants; represents a constant term; represents a complex constant term; represents the complex constant coefficient; represents the complex constant coefficient; The simplified expression of the surface stress condition is expressed as: ； in, represents a constant term; , , , ; all represent constant coefficients; represents a constant; represents a constant term; represents a complex constant term; represents the complex constant coefficient; represents a complex constant coefficient.

8. The method for rapidly determining the surrounding rock stability of a shallowly buried large-span tunnel in an upper soft and lower hard stratum as claimed in claim 7, characterized in that: The complex function analytical form is expressed as: in, a 0 、a j 、b j 、c 0 、c j 、d j is the complex constant to be determined.

9. The method for rapidly determining the stability of surrounding rock of a shallowly buried large-span tunnel in soft upper and hard lower strata as claimed in claim 1, characterized in that: Normal stress of surrounding rock and shear stress The expression is expressed as: Among them, 2 β =90°+ φ , φ is the internal friction angle, represents the first principal stress, .

10. The method for rapidly determining the surrounding rock stability of a shallowly buried large-span tunnel in soft upper and hard lower strata as claimed in claim 1, characterized in that: The shear failure shear stress τc is expressed as: in, σ is the normal stress of the oblique section inside the rock specimen unit; τ c is the shear failure stress; C is the rock cohesion; φ is the internal friction angle of rock.

Images