Method for predicting critical safe distance between tunnel and karst cave under action of concealed karst cave

Abstract

The invention discloses a method for predicting the critical safe distance between a tunnel and a karst cave under the action of a concealed karst cave, and the method comprises the following steps: obtaining the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of surrounding rock and karst cave filler, and determining the influence factor range of the critical safe distance between the tunnel and the karst cave; the method comprises the following steps: constructing a tunnel-karst cave finite element model according to geometric dimension parameters of a tunnel and a karst cave and mechanical parameters of surrounding rock and karst cave filler, determining a mechanical criterion of surrounding rock instability, determining a single-factor test scheme based on a control variable method, calculating a critical safety distance under the influence of a single factor, carrying out unary regression, and designing an orthogonal test scheme. And performing multivariate nonlinear regression on the calculation result to obtain a prediction formula of the critical safe distance between the tunnel and the karst cave. By the adoption of the prediction method, the safe distance between the hidden karst cave existing at any position around the newly-built tunnel and the tunnel can be rapidly determined, so that whether the karst cave needs to be treated or not is judged, and a basis can be provided for on-site construction and operation of tunnel engineering.

Description

Technical Field

[0001] The present invention belongs to the technical field of tunnel engineering and relates to a method for predicting the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave. Background Art

[0002] Hidden karst caves are characterized by being difficult to explore, having uncertain positions, variable shapes, high fracture development, and strong permeability, which pose many challenges to the construction of hydraulic tunnels. When tunneling in karst areas, the existence of hidden karst caves easily causes stress concentration and excessive deformation of the surrounding rock between the karst cave and the tunnel, and even leads to the instability and failure of the tunnel, seriously threatening construction safety. To ensure the stability of the tunnel structure, it is necessary to judge whether the distance between the tunnel and the hidden karst cave meets the critical safety distance. The determination of the critical safety distance not only directly affects the route selection of the project, but also determines whether the karst cave needs to be treated and the difficulty of treatment. Therefore, reasonably determining the critical safety distance between a tunnel and an existing karst cave is a key issue to ensure the safety of tunnel construction and operation.

[0003] At present, regarding the determination of the safety distance between a hidden karst cave and a tunnel, most engineering designs rely on semi-empirical methods and lack systematic theoretical support. Since the determination of the critical safety distance between a hidden karst cave and a tunnel involves the instability criterion of the surrounding rock, the existing instability criteria include the non-convergence of iterative calculations and the penetration of the plastic zone, etc. The selection of the convergence criterion and the maximum number of iterations in iterative calculations has a certain degree of arbitrariness, resulting in too many invalid calculation steps. If the penetration of the plastic zone is used as the basis to predict the safety distance between a hidden karst cave and a tunnel, in actual situations, even if the plastic zone penetrates, the surrounding rock may remain stable through internal stress adjustment and does not necessarily mean that the structure will fail. Therefore, the safety distance judged based on the penetration of the plastic zone is too conservative and will overestimate the safety distance between the karst cave and the tunnel, resulting in uneconomical results. More and more studies have shown that the penetration of the plastic zone is a necessary condition for failure, but not a sufficient condition. In addition, existing numerical simulation studies mostly use uniform experimental designs, which are difficult to ensure the independence of the influence of various factors on the response variable, resulting in low reliability and efficiency of the simulation results. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave, which solves the problem of large errors in the prediction results of the existing methods for predicting the safety distance between a karst cave and a tunnel.

[0005] The technical solution adopted by the present invention is a method for predicting the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave, including the following steps: Step 1, obtain the geometric dimension parameters of the tunnel and the karst cave, the mechanical parameters of the surrounding rock and the filling material of the karst cave, and determine the range of influencing factors for the critical safety distance between the tunnel and the karst cave; Step 2: According to the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of the surrounding rock and the karst cave filling, a finite element model of the tunnel-karst cave is constructed by using Python parametric modeling; Step 3: Determine the mechanical criterion for the instability of the surrounding rock, determine the single-factor test scheme based on the control variable method, calculate the critical safety distance under the influence of a single factor and perform a univariate regression; Step 4: Design an orthogonal test scheme, perform a multivariate non-linear regression on the calculation results based on the form of the univariate regression formula, and obtain a prediction formula for the critical safety distance between the tunnel and the karst cave.

[0006] The geometric dimension parameters of the tunnel in Step 1 include the tunnel cross-section form, height, span and tunnel burial depth, and the geometric dimension parameters of the karst cave include the karst cave volume 、 The distance between the karst cave and the tunnel, and the relative azimuth angle between the karst cave and the tunnel, that is, the karst-tunnel azimuth angle.

[0007] The mechanical parameters of the surrounding rock and the karst cave filling include unit weight, elastic modulus, Poisson's ratio, internal friction angle and cohesion.

[0008] The influencing factors for the critical safety distance between the tunnel and the karst cave include the equivalent radius of the karst cave R , tunnel burial depth H , surrounding rock level V , karst-tunnel azimuth angle and karst cave filling degree T， The calculation formula for the equivalent radius of the karst cave R is as follows: (1) In the formula, Q represents the karst cave volume.

[0009] Surrounding rock level V is divided into five levels, namely level 1, level 2, level 3, level 4 and level 5. The surrounding rock level is determined according to the mechanical properties of the surrounding rock. The mechanical parameters of the surrounding rock are equally divided into five parts. The weaker the mechanical properties of the surrounding rock, the lower the corresponding surrounding rock level and the smaller the level number.

[0010] In Step 2, the constructed finite element model of the tunnel-karst cave is fully parameterized, including model boundaries, geometric dimension parameters of the karst cave and the tunnel, the distance between the karst cave and the tunnel, surrounding rock material parameters, karst cave spatial position parameters and mesh parameters, and a parametric modeling calculation script is written using the Python language.

[0011] The specific process of Step 3 is as follows: Step 3.1: Adopt the maximum tensile strain criterion as the judgment criterion for the range of the surrounding rock deformation failure area. The calculation formula for the maximum tensile strain ε is; (2) In the above formula,R t denotes the uniaxial tensile strength of surrounding rock E is the elastic modulus of surrounding rock; Step 3.2: Determine the single-factor test scheme based on the control variable method; Step 3.3: Use the parametric modeling calculation script in Step 2 to determine the critical safety distance under different values of each influencing factor; Step 3.4: Plot the influencing factors and the corresponding critical safety distances as scatter plots, and judge whether to use linear regression or non-linear regression based on the data trend.

[0012] The specific process of Step 3.3 is as follows: Step 3.3.1: Automatically complete the tunnel excavation construction simulation calculation under different single-factor change conditions through the parametric script established in Step 2, and extract the plastic strain nephogram of the tunnel-cave finite element model; Step 3.3.2: Mark the surrounding rock deformation failure area on the plastic strain nephogram according to the maximum tensile strain calculated in Step 3.1. The surrounding rock deformation failure area is divided into the tunnel deformation failure area and the cave deformation failure area; Step 3.3.3: Judge whether the tunnel deformation failure area and the cave deformation failure area are connected according to the spatial distribution positions of the tunnel deformation failure area and the cave deformation failure area in the plastic strain nephogram. If it is in a connected state, execute Step 3.3.4; if it is in a non-connected state, execute Step 3.4.5; Step 3.3.4: Distance increment optimization. Gradually increase the distance between the cave and the tunnel in increments of 0.05 m to 0.2 m, and loop to execute the modeling calculation process in Step 3.3.1 until the tunnel deformation failure area and the cave deformation failure area are in a non-connected state for the first time. At this time, the recorded distance between the cave and the tunnel is the critical safety distance; Step 3.3.5: Distance decrement optimization. Gradually decrease the distance between the cave and the tunnel in increments of 0.05 m to 0.2 m, and loop to execute the modeling calculation process in Step 3.3.1 until the tunnel deformation failure area and the cave deformation failure area are in a connected state for the first time. At this time, the recorded distance between the cave and the tunnel is the critical safety distance; Step 3.3.6: Repeat Steps 3.3.3 to 3.3.5 to obtain the critical safety distance between the tunnel and the cave under different values of each influencing factor.

[0013] The specific process of Step 4 is as follows: Step 4.1: Determine the number of factors and the number of levels according to the range of influencing factors of the critical safety distance between the tunnel and the cave. Design an orthogonal test according to the number of factors and the number of levels, and calculate the critical safety distance between the cave and the tunnel under each test according to Step 3.3; Step 4.2, construct the correlation function between multiple influencing factors and the critical safety distance between the karst cave and the tunnel based on the unary regression formula of different factors: (3) In the above formula, L is the critical safety distance between the karst cave and the tunnel, a and b are both trend term coefficients, c 、 d 、 e 、 f 、 g and h are all periodic term coefficients, a 、 b, c 、 d 、 e 、 f 、 g and h are used to describe the non-linear relationship between the karst-tunnel azimuth angle and the critical safety distance, i is the linear correlation coefficient between the equivalent radius of the karst cave and the critical safety distance between the tunnel and the karst cave, j is the linear correlation coefficient between the tunnel burial depth and the critical safety distance between the tunnel and the karst cave, k is the linear correlation coefficient between the surrounding rock level and the critical safety distance between the tunnel and the karst cave, m is the linear correlation coefficient between the filling degree of the karst cave and the critical safety distance between the tunnel and the karst cave, n is a constant to be determined; Step 4.3, extract the orthogonal test data of the critical safety distance between the karst cave and the tunnel in Step 4.1, and perform multiple regression fitting using the non-linear least squares method. The objective function is to minimize the sum of the squared residuals of the predicted value and the experimental value. Based on the empirical formula or the preliminary linear regression result, set the initial value of the coefficient to be determined, and use the Levenberg-Marquardt algorithm to iteratively optimize the parameters, and gradually adjust each coefficient until the objective function converges, that is, the residual change rate < 10 -6 ,and then calculate the goodness of fit R 2 . When R 2 > 0.95, substitute the fitted coefficient to be determined into formula (3) to obtain the correlation function between the critical safety distance between the karst cave and the tunnel and each influencing factor.

[0014] When the surrounding rock is Class IV surrounding rock, the range of the equivalent radius of the karst cave in the surrounding rock is 1m - 5m, the range of the tunnel burial depth is 74m - 234m, the range of the karst-tunnel azimuth angle is 0° - 180°, and the range of the filling degree of the karst cave is 0 - 100%. Perform multiple regression fitting using the non-linear least squares method to obtain the correlation function between the critical safety distance between the karst cave and the tunnel and each influencing factor as: (4) The beneficial effects of the present invention are as follows: taking the penetration of the deformation and failure area between the karst cave and the tunnel as the basis for judging the safety distance between the hidden karst cave and the tunnel, quickly constructing a three-dimensional refined finite element model of the karst cave - tunnel through Python script, designing an orthogonal test scheme including five sensitive parameters such as surrounding rock parameters, karst cave size, tunnel burial depth, karst - tunnel azimuth, and karst cave filling degree, and calculating the critical safety distance of the tunnel under the action of the hidden karst cave under the coupling of various influencing factors. Based on the finite element analysis results, a regression formula for the critical safety distance of various influencing factors is obtained through multiple nonlinear regression analysis. The present invention overcomes the deficiencies of the traditional method of simulating and calculating the safety distance value between the hidden karst cave and the tunnel based on the penetration of the plastic zone, which is troublesome in the process and the rationality of the results remains to be discussed. It quickly determines the safety distance between the hidden karst cave existing at any position within 360° around the newly built tunnel and the tunnel, so as to judge whether the karst cave needs to be disposed, and can provide a basis for the on - site construction and operation of the tunnel project. Description of the Drawings

[0015] Figure 1 is a schematic flow chart of the prediction method for the critical safety distance between the tunnel and the karst cave under the action of the hidden karst cave of the present invention; Figure 2 is a flow chart for calculating the critical safety distance between the karst cave - tunnel in the prediction method of the present invention; Figure 3 is an example of the finite element numerical model of the karst cave - tunnel in the prediction method of the present invention; Figure 4 is the finite element numerical model of the penetration state between the karst cave and the tunnel in Example 6 of the present invention; Figure 5 is the finite element numerical model of the non - penetration state between the karst cave and the tunnel in Example 6 of the present invention; Figure 6 is the linear fitting diagram of the karst cave radius and the critical safety distance between the karst cave - tunnel in Example 6 of the present invention Figure 7 is the linear fitting diagram of the tunnel burial depth and the critical safety distance between the karst cave - tunnel in Example 6 of the present invention; Figure 8 is the linear fitting diagram of the horizontal of the surrounding rock and the critical safety distance between the karst cave - tunnel in Example 6 of the present invention; Figure 9 is the linear fitting diagram of the karst cave filling degree and the critical safety distance between the karst cave - tunnel in Example 6 of the present invention; Figure 10 is the non - linear fitting diagram of the karst - tunnel azimuth angle and the critical safety distance between the karst cave - tunnel in Example 6 of the present invention; Figure 11 is the comparison diagram of the actual value and the predicted value of the critical safety distance between the karst cave - tunnel in Example 6 of the present invention; Figure 12It is a schematic diagram of the residual of the predicted data of the critical safety distance between a karst cave and a tunnel in Embodiment 6 of the present invention. Detailed implementation manners

[0016] The present invention will be described in detail below with reference to the accompanying drawings and specific implementation manners.

[0017] Embodiment 1 A method for predicting the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave, referring to Figure 1 , includes the following steps: Step 1, obtain the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of the surrounding rock and the karst cave filling, and determine the range of influencing factors for the critical safety distance between the tunnel and the karst cave; Step 2, according to the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of the surrounding rock and the karst cave filling, construct a tunnel-karst cave finite element model by using the Python parametric modeling method; Step 3, determine the mechanical criterion for the instability of the surrounding rock, determine the single-factor test scheme based on the control variable method, calculate the critical safety distance under the influence of a single factor and perform a unary regression; Step 4, design an orthogonal test scheme, perform a multi-variable non-linear regression on the calculation results based on the form of the unary regression formula, and obtain the prediction formula for the critical safety distance between the tunnel and the karst cave.

[0018] Embodiment 2 A method for predicting the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave, includes the following steps: Step 1, obtain the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of the surrounding rock and the karst cave filling, and determine the range of influencing factors for the critical safety distance between the tunnel and the karst cave; The geometric dimension parameters of the tunnel include the tunnel cross-section form, height, span and tunnel buried depth, and the geometric dimension parameters of the karst cave include the karst cave volume 、 The distance between the karst cave and the tunnel, and the relative azimuth angle between the karst cave and the tunnel, that is, the karst-tunnel azimuth angle. The mechanical parameters of the surrounding rock and the karst cave filling include unit weight, elastic modulus, Poisson's ratio, internal friction angle and cohesion.

[0019] The influencing factors for the critical safety distance between the tunnel and the karst cave include the equivalent radius of the karst cave R , tunnel buried depth H , horizontal of the surrounding rock V , karst-tunnel azimuth angle and the filling degree of the karst cave T， The calculation formula for the equivalent radius of the karst cave R is as follows: (1) In the formula, Q represents the karst cave volume.

[0020] Step 2: Construct a finite element model of the tunnel - karst cave according to the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of the surrounding rock and the karst cave filling material by using the Python parametric modeling method; Step 3: Determine the mechanical criterion for the instability of the surrounding rock, determine the single - factor test scheme based on the control variable method, calculate the critical safety distance under the influence of a single factor and perform a univariate regression; Step 4: Design an orthogonal test scheme, perform a multiple non - linear regression on the calculation results based on the form of the univariate regression formula, and obtain a prediction formula for the critical safety distance between the tunnel and the karst cave.

[0021] Example 3 A method for predicting the critical safety distance between a tunnel and a karst cave under the action of a concealed karst cave includes the following steps: Step 1: Obtain the geometric dimension parameters of the tunnel and the karst cave, the mechanical parameters of the surrounding rock and the karst cave filling material, and determine the range of influencing factors for the critical safety distance between the tunnel and the karst cave; The geometric dimension parameters of the tunnel include the tunnel cross - section form, height, span, and tunnel burial depth, and the geometric dimension parameters of the karst cave include the karst cave volume 、 The distance between the karst cave and the tunnel, and the relative azimuth angle between the karst cave and the tunnel, that is, the karst - tunnel azimuth angle. The mechanical parameters of the surrounding rock and the karst cave filling material include unit weight, elastic modulus, Poisson's ratio, internal friction angle, and cohesion.

[0022] The influencing factors for the critical safety distance between the tunnel and the karst cave include the equivalent radius of the karst cave R , the tunnel burial depth H , the surrounding rock level V , the karst - tunnel azimuth angle and the filling degree of the karst cave T， The calculation formula for the equivalent radius of the karst cave R is as follows: (1) In the formula, Q represents the karst cave volume.

[0023] The surrounding rock level V is divided into five levels, namely level 1, level 2, level 3, level 4, and level 5. The surrounding rock level is determined based on the mechanical properties of the surrounding rock. The mechanical parameters of the surrounding rock are equally divided into five parts. The weaker the mechanical properties of the surrounding rock, the lower the corresponding surrounding rock level and the smaller the level number.

[0024] Step 2: According to the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of the surrounding rock and the karst cave filling, a finite element model of the tunnel-karst cave is constructed by using Python parametric modeling. The constructed finite element model of the tunnel-karst cave is fully parameterized, including model boundaries, geometric dimension parameters of the karst cave and the tunnel, the distance between the karst cave and the tunnel, surrounding rock material parameters, karst cave spatial position parameters, and mesh parameters. A parametric modeling calculation script is written using the Python language. Step 3: Determine the mechanical criterion for the instability of the surrounding rock. Based on the control variable method, determine the single-factor test scheme, calculate the critical safety distance under the influence of a single factor, and perform a unary regression. Step 4: Design an orthogonal test scheme, and perform a multiple non-linear regression on the calculation results based on the form of the unary regression formula to obtain a prediction formula for the critical safety distance between the tunnel and the karst cave.

[0025] Example 4 A method for predicting the critical safety distance between a tunnel and a karst cave under the action of a concealed karst cave, comprising the following steps: Step 1: Obtain the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of the surrounding rock and the karst cave filling, and determine the range of influencing factors for the critical safety distance between the tunnel and the karst cave. The geometric dimension parameters of the tunnel include the tunnel cross-section form, height, span, and tunnel burial depth. The geometric dimension parameters of the karst cave include the karst cave volume 、 The distance between the karst cave and the tunnel, as well as the relative azimuth angle between the karst cave and the tunnel, i.e., the karst-tunnel azimuth angle. The mechanical parameters of the surrounding rock and the karst cave filling include unit weight, elastic modulus, Poisson's ratio, internal friction angle, and cohesion.

[0026] The influencing factors for the critical safety distance between the tunnel and the karst cave include the equivalent radius of the karst cave R , tunnel burial depth H , surrounding rock level V , karst-tunnel azimuth angle , and karst cave filling degree T， The calculation formula for the equivalent radius of the karst cave R is as follows: (1) In the formula, Q represents the karst cave volume.

[0027] Surrounding rock level V is divided into five levels, namely level 1, level 2, level 3, level 4, and level 5. The surrounding rock level is determined based on the mechanical properties of the surrounding rock. The mechanical parameters of the surrounding rock are divided into five equal parts. The weaker the mechanical properties of the surrounding rock, the lower the corresponding surrounding rock level, and the smaller the level number.

[0028] Step 2: According to the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of the surrounding rock and the karst cave filling, a finite element model of the tunnel-karst cave is constructed by using Python parametric modeling, and the Drucker-Prager yield criterion is used to simulate the rock failure process. The surrounding rock is simulated by four-node plane elements (PLANE42). The constructed finite element model of the tunnel-karst cave is fully parameterized, including the model boundary, the geometric dimension parameters of the karst cave and the tunnel, the distance between the karst cave and the tunnel, the surrounding rock material parameters, the spatial position parameters of the karst cave, and the mesh parameters. A parametric modeling calculation script is written using the Python language. Step 3: Determine the mechanical criterion for the instability of the surrounding rock, determine the single-factor test scheme based on the control variable method, calculate the critical safety distance under the influence of a single factor, and perform a unary regression. The specific process of Step 3 is as follows: Step 3.1: Adopt the maximum tensile strain criterion as the judgment criterion for the range of the surrounding rock deformation failure area. The calculation formula for the maximum tensile strain ε is; (2) In the above formula, R t represents the uniaxial tensile strength of the surrounding rock, E is the elastic modulus of the surrounding rock; The surrounding rock deformation failure area refers to the area closest to the tunnel section.

[0029] Step 3.2: Take the condition that the deformation failure areas of the tunnel and the karst cave just penetrate each other as the critical condition for the instability of the surrounding rock. (3) In the above formula, is the critical safety distance between the karst cave and the tunnel, is the range of the karst cave deformation failure area, is the range of the tunnel deformation failure area; Step 3.3: Determine the single-factor test scheme based on the control variable method; Step 3.4: Use the parametric modeling calculation script in Step 2 to determine the critical safety distance under different values of each influencing factor; Step 3.5: Plot the scatter diagram of each influencing factor and the corresponding critical safety distance, and judge whether to use unary linear regression or unary nonlinear regression according to the data trend.

[0030] Step 4: Design an orthogonal test scheme, perform a multiple nonlinear regression on the calculation results based on the form of the unary regression formula, and obtain the prediction formula for the critical safety distance between the tunnel and the karst cave.

[0031] Example 5 A method for predicting the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave, comprising the following steps: Step 1: Obtain the geometric dimension parameters of the tunnel and the karst cave, the mechanical parameters of the surrounding rock and the karst cave filling material, and determine the range of influencing factors for the critical safety distance between the tunnel and the karst cave; The geometric dimension parameters of the tunnel include the tunnel cross-section form, height, span, and tunnel burial depth. The geometric dimension parameters of the karst cave include the karst cave volume 、 The distance between the karst cave and the tunnel, and the relative azimuth angle between the karst cave and the tunnel, i.e., the karst-tunnel azimuth angle. The mechanical parameters of the surrounding rock and the karst cave filling material include unit weight, elastic modulus, Poisson's ratio, internal friction angle, and cohesion.

[0032] The influencing factors for the critical safety distance between the tunnel and the karst cave include the equivalent radius of the karst cave R , tunnel burial depth H , horizontal of the surrounding rock V , karst-tunnel azimuth angle , and karst cave filling degree T， The calculation formula for the equivalent radius of the karst cave R is as follows: (1) In the formula, Q represents the karst cave volume.

[0033] The horizontal of the surrounding rock V is divided into five levels, namely level 1, level 2, level 3, level 4, and level 5. The horizontal of the surrounding rock is determined based on the mechanical properties of the surrounding rock. The mechanical parameters of the surrounding rock are equally divided into five parts. The weaker the mechanical properties of the surrounding rock, the lower the corresponding horizontal of the surrounding rock, and the smaller the level number.

[0034] Step 2: According to the geometric dimension parameters of the tunnel and the karst cave, the mechanical parameters of the surrounding rock and the karst cave filling material, use the method of parametric modeling in Python to construct a tunnel-karst cave finite element model. Parametrize the constructed tunnel-karst cave finite element model comprehensively, including model boundaries, geometric dimension parameters of the karst cave and the tunnel, distance between the karst cave and the tunnel, surrounding rock material parameters, karst cave spatial position parameters, and mesh parameters. Write a parametric modeling calculation script using the Python language; Step 3: Determine the mechanical criterion for the instability of the surrounding rock. Based on the control variable method, determine the single-factor test scheme, calculate the critical safety distance under the influence of a single factor, and perform a unary regression; The specific process of Step 3 is as follows: Step 3.1: Adopt the maximum tensile strain criterion as the criterion for judging the range of the surrounding rock deformation failure area. The calculation formula for the maximum tensile strain ε is; (2) In the above formula, R t represents the uniaxial tensile strength of the surrounding rock, E is the elastic modulus of the surrounding rock; The surrounding rock deformation and failure zone refers to the area closest to the tunnel section.

[0035] Step 3.2: Determine the single-factor test plan based on the control variable method; Step 3.3: Use the parametric modeling calculation script in Step 2 to determine the critical safety distance under different values of each influencing factor; See Figure 2 , and the specific process of Step 3.3 is as follows: Step 3.3.1: Automatically complete the tunnel excavation construction simulation calculation under different single-factor change conditions through the parametric script established in Step 2, and extract the plastic strain nephogram of the tunnel-cavern finite element model; Step 3.3.2: Mark the surrounding rock deformation and failure zone on the plastic strain nephogram based on the maximum tensile strain calculated in Step 3.1. The surrounding rock deformation and failure zone is divided into the tunnel deformation and failure zone and the cavern deformation and failure zone; Step 3.3.3: Judge whether the tunnel deformation and failure zone and the cavern deformation and failure zone are connected according to the spatial distribution positions of the tunnel deformation and failure zone and the cavern deformation and failure zone in the plastic strain nephogram, that is, take the condition that the tunnel deformation and failure zone and the cavern deformation and failure zone are just connected as the critical condition of surrounding rock instability: (3) In the above formula, is the critical safety distance between the cavern and the tunnel, is the range of the cavern deformation and failure zone, is the range of the tunnel deformation and failure zone; If it is in a connected state, then execute Step 3.3.4; if it is in a non-connected state, then execute Step 3.4.5; Step 3.3.4: Distance increment optimization. Gradually increase the distance between the cavern and the tunnel in increments of 0.05 m to 0.2 m, and loop to execute the modeling calculation process in Step 3.3.1 until the tunnel deformation and failure zone and the cavern deformation and failure zone are in a non-connected state for the first time. At this time, the recorded distance between the cavern and the tunnel is the critical safety distance; Step 3.3.5: Distance decrement optimization. Gradually decrease the distance between the cavern and the tunnel in increments of 0.05 m to 0.2 m, and loop to execute the modeling calculation process in Step 3.3.1 until the tunnel deformation and failure zone and the cavern deformation and failure zone are in a connected state for the first time. At this time, the recorded distance between the cavern and the tunnel is the critical safety distance; Step 3.3.6: Repeat Steps 3.3.3 to 3.3.5 to obtain the critical safety distance between the tunnel and the cavern under different values of each influencing factor.

[0036] Step 3.4: Plot the influencing factors and the corresponding critical safety distances as scatter plots, and determine whether to use linear regression or non-linear regression based on the data trend. The fitting functional expressions are as follows: (4) L 2= iR + n 2(5) L 3= jH + n 3(6) L 4= kV + n 4(7) L 5= mT + n 5(8) In the formulas, L1 represents the fitting function of the critical safety distance between the solution tunnel azimuth angle θ and the tunnel karst cave, L2 represents the fitting function of the critical safety distance between the equivalent radius of the karst cave R and the tunnel karst cave, L3 represents the fitting function of the critical safety distance between the tunnel buried depth H and the tunnel karst cave, L4 represents the fitting function of the critical safety distance between the surrounding rock horizontal V and the tunnel karst cave, L5 represents the fitting function of the critical safety distance between the karst cave filling degree T and the tunnel karst cave, a and b are both trend term coefficients, c 、 d 、 e 、 f 、 g and h are both periodic term coefficients, a 、 b, c 、 d 、 e 、 f 、 g and h are used to describe the non-linear relationship between the solution tunnel azimuth angle θ and the critical safety distance, i is the equivalent radius of the karst cave R and the linear correlation coefficient of the critical safety distance between the tunnel karst cave, j is the tunnel buried depth H and the linear correlation coefficient of the critical safety distance between the tunnel karst cave, k is the surrounding rock horizontal V and the linear correlation coefficient of the critical safety distance between the tunnel karst cave, m is the karst cave filling degree T and the linear correlation coefficient of the critical safety distance between the tunnel karst cave, n1. n 2. n 3. n 4 and n 5 are all undetermined constants; Step 4: Design an orthogonal test scheme, perform multiple non - linear regression on the calculation results based on the form of the unary regression formula, and obtain the prediction formula for the critical safety distance between the tunnel and the karst cave: (9) In the formula, L is the critical safety distance between the karst cave and the tunnel, n is an undetermined constant, n = n 1 + n 2 + n 3 + n 4 + n 5.

[0037] Example 6 A method for predicting the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave, comprising the following steps: Step 1: Obtain the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of the surrounding rock and the karst cave filling, and determine the range of influencing factors for the critical safety distance between the tunnel and the karst cave; The geometric dimension parameters of the tunnel include the tunnel cross - section form, height, span, and tunnel burial depth. In this example, the tunnel has a circular - arched straight - wall type cross - section, and the internal cross - section size of the tunnel is 5.5 m×7.3 m. The geometric dimension parameters of the karst cave include the karst cave volume 、 the distance between the karst cave and the tunnel, and the relative azimuth angle between the karst cave and the tunnel, i.e., the karst - tunnel azimuth angle. For the convenience of modeling, the irregular karst cave is approximately equivalent to a circle, and the calculation formula for the equivalent radius R of the karst cave is as follows: (1) In the formula, Q represents the karst cave volume.

[0038] The mechanical parameters of the surrounding rock and the karst cave filling include unit weight, elastic modulus, Poisson's ratio, internal friction angle, and cohesion. In this example, the range of the mechanical parameters of the surrounding rock and the karst cave filling is shown in Table 1: Table 1 List of mechanical parameters of the surrounding rock and the karst cave filling

[0039] According to the summary of engineering experience, the influencing factors for the critical safety distance between the tunnel and the karst cave include the equivalent radius R of the karst cave, the tunnel burial depth H of the surrounding rock, the horizontal V of the surrounding rock, the karst - tunnel azimuth angle and the filling degree T, according to the geological exploration data statistics, the equivalent radius range of karst caves in Class IV surrounding rock is 1m - 5m, the buried depth range of the tunnel is 74m - 234m, and the filling degree range of karst caves is 0% - 100%. The azimuth angle range of the karst-tunnel is 0° - 360°. Considering the symmetry of modeling, only the concealed karst caves within the range of 0° - 180° of the included angle between the connecting line of the tunnel center and the karst cave center and the positive direction of the tunnel floor need to be studied. According to the exposure situation of the site heading face, the surrounding rock level V is divided into five levels, namely Level 1, Level 2, Level 3, Level 4 and Level 5. The surrounding rock level is determined according to the mechanical properties of the surrounding rock. The mechanical parameters of the surrounding rock are equally divided into five parts. The weaker the mechanical properties of the surrounding rock, the lower the corresponding surrounding rock level and the smaller the level number; The mechanical parameters of Class IV surrounding rock are divided into 5 kinds of surrounding rock levels, as shown in Table 2: Table 2 Surrounding rock level and corresponding surrounding rock mechanical parameters

[0040] Step 2, refer to Figure 3 , according to the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of the surrounding rock and the karst cave filling material, a finite element model of the tunnel-karst cave is constructed by using the method of Python parametric modeling; The specific process of Step 2 is as follows: Step 2.1, establish a geometric model of the tunnel-karst cave according to the geometric dimension parameters of the tunnel and the karst cave obtained in Step 1. The shortest distance between the model boundary and the analyzed concealed karst cave or tunnel is greater than 6 times the tunnel span. The karst cave is simulated according to the "open-stope mechanical model", that is, the karst cave is regarded as the original cavity, and the Drucker-Prager yield criterion is used to simulate the rock failure process. The surrounding rock is simulated by four-node plane elements (PLANE42). The geometric dimensions and mechanical parameters of the surrounding rock and the karst cave filling material are determined in Step 1. Normal constraints are applied to the left and right sides and the bottom boundary of the model, and the upper boundary of the model is free; Step 2.2, adopt the following method to simulate the tunnel construction sequence: balance the initial in-situ stress field by repeatedly importing the odb file, and excavate the chamber in one pass of the full section, which is simulated by killing elements; Step 2.3, fully parameterize the constructed finite element model of the tunnel-karst cave, including the model boundary, geometric dimension parameters of the karst cave and the tunnel, distance between the karst cave and the tunnel, surrounding rock material parameters, spatial position parameters of the karst cave, and mesh parameters, and write a parametric modeling calculation script using the Python language; Step 3, determine the mechanical criterion for the instability of the surrounding rock, determine the single-factor test scheme based on the control variable method, calculate the critical safety distance under the influence of a single factor and conduct a unary regression; The specific process of Step 3 is as follows: Step 3.1: According to the deformation and stress state of the surrounding rock after tunnel excavation, the surrounding rock is divided into three regions: the deformation and failure zone, the plastic zone, and the elastic zone. The deformation and failure zone is the area closest to the tunnel section. Due to the free face generated by tunnel excavation, the surrounding rock undergoes severe deformation and is prone to collapse failure. The plastic zone is located outside the deformation and failure zone. Although the surrounding rock enters the plastic state and produces inelastic deformation, the tangential stress is greater than the in-situ stress, and self-stabilization is achieved through stress redistribution.

[0041] The maximum tensile strain criterion is adopted as the criterion for judging the range of the deformation and failure zone of the surrounding rock. The calculation formula for the maximum tensile strain ε is: (2) In the above formula, R t represents the uniaxial tensile strength of the surrounding rock, E is the elastic modulus of the surrounding rock; Step 3.2: Based on the control variable method, determine the single-factor test scheme, a total of 25 kinds. The value ranges of each parameter are shown in Table 3; Table 3 Single-factor test scheme

[0042] Step 3.3: Use the parametric modeling calculation script in Step 2 to determine the critical safety distance under different values of each influencing factor; The specific process of Step 3.3 is as follows: Step 3.3.1: Automatically complete the tunnel excavation construction simulation calculation under different single-factor change conditions through the parametric script established in Step 2.3, and extract the plastic strain contour map of the tunnel-cavern finite element model; Step 3.3.2: Mark the deformation and failure zone of the surrounding rock on the plastic strain contour map according to the maximum tensile strain calculated in Step 3.1. The deformation and failure zone of the surrounding rock is divided into the deformation and failure zone of the tunnel and the deformation and failure zone of the cavern; Step 3.3.3: Judge whether the deformation and failure zone of the tunnel and the deformation and failure zone of the cavern form a continuous penetration zone according to the spatial distribution position of the deformation and failure zone of the tunnel and the deformation and failure zone of the cavern in the plastic strain contour map, that is, take the condition that the deformation and failure zone of the tunnel and the deformation and failure zone of the cavern just penetrate as the critical condition for the instability of the surrounding rock: (3) In the above formula, is the critical safety distance between the cavern and the tunnel, is the range of the deformation and failure zone of the cavern, is the range of the deformation and failure zone of the tunnel; If it is in a penetrated state, as Figure 4 shown, then execute Step 3.3.4. If it is in a non-penetrated state, as Figure 5 shown, then execute Step 3.4.5; Step 3.3.4, distance increment optimization: Gradually increase the distance between the karst cave and the tunnel by an increment of 0.1 m, and loop to execute the modeling and calculation process in Step 3.3.1 until it first appears that the deformation and failure areas of the tunnel and the karst cave are non - connected. At this time, the distance between the karst cave and the tunnel recorded is the critical safety distance; Step 3.3.5, distance decrement optimization: Gradually decrease the distance between the karst cave and the tunnel by an increment of 0.1 m, and loop to execute the modeling and calculation process in Step 3.3.1 until it first appears that the deformation and failure areas of the tunnel and the karst cave are connected. At this time, the distance between the karst cave and the tunnel recorded is the critical safety distance; Step 3.3.6, repeat Step 3.3.3 to Step 3.3.5 to obtain the critical safety distance between the tunnel and the karst cave under different values of each influencing factor.

[0043] Step 3.4, plot the influencing factors and the corresponding critical safety distances as scatter plots, and judge whether to use linear regression or non - linear regression based on the data trend, as Figures 6 - 10 shown.

[0044] Step 4, design an orthogonal test scheme, perform multiple non - linear regression on the calculation results based on the form of the unary regression formula to obtain the prediction formula for the critical safety distance between the tunnel and the karst cave.

[0045] The specific process of Step 4 is as follows: Step 4.1, determine the number of factors and the number of levels according to the range of influencing factors of the critical safety distance between the tunnel and the karst cave. In this embodiment, the number of factors is 5 and the number of levels is also 5. According to the number of factors and the number of levels, design an orthogonal test and select L 25 (5 5 ) orthogonal array, as shown in Table 4. Calculate the critical safety distance between the karst cave and the tunnel under each test according to Step 3.3; Table 4 List of critical safety distances between the karst cave and the tunnel under each working condition

[0046] Step 4.2, construct the correlation function between multiple influencing factors and the critical safety distance between the karst cave and the tunnel based on the unary regression formula of different factors: (4) In the above formula, L is the critical safety distance between the karst cave and the tunnel, a and b are both trend - term coefficients, c 、 d 、 e 、 f 、 g and hAll are periodic term coefficients, a , b, c , d , e , f , g and h are used to describe the non - linear relationship between the solution tunnel azimuth angle and the critical safety distance, i is the linear correlation coefficient between the equivalent radius of the karst cave and the critical safety distance between the tunnel and the karst cave, j is the linear correlation coefficient between the buried depth of the tunnel and the critical safety distance between the tunnel and the karst cave, k is the linear correlation coefficient between the horizontal of the surrounding rock and the critical safety distance between the tunnel and the karst cave, m is the linear correlation coefficient between the filling degree of the karst cave and the critical safety distance between the tunnel and the karst cave, n is a constant to be determined; Step 4.3: Extract the orthogonal test data of the critical safety distance between the karst cave and the tunnel in Step 4.1, and perform multiple regression fitting using the non - linear least - squares method. The objective function is to minimize the sum of the squared residuals between the predicted value and the experimental value. Based on the empirical formula or the preliminary linear regression result, set the initial value of the coefficient to be determined, and use the Levenberg - Marquardt algorithm to iteratively optimize the parameters, and gradually adjust each coefficient until the objective function converges, that is, the residual change rate < 10 -6 , and then calculate the goodness of fit R 2 . Wait until R 2 > 0.95. As shown in Figures 11 - 12 , substitute the fitted coefficient to be determined into formula (4) to obtain the correlation function between the critical safety distance between the tunnel and the karst cave and each influencing factor, that is, the prediction formula for the critical safety distance between the tunnel and the karst cave: (5).

Claims

1. Prediction method for critical safety distance between tunnel and karst cave under the action of hidden karst cave, characterized in that, It includes the following steps: Step 1: Obtain the geometric dimension parameters of the tunnel and the karst cave, the mechanical parameters of the surrounding rock and the karst cave filling, and determine the range of influencing factors for the critical safety distance between the tunnel and the karst cave; Step 2: According to the geometric dimension parameters of the tunnel and the karst cave, and the mechanical parameters of the surrounding rock and the karst cave filling, construct a tunnel-karst cave finite element model by using the parameterized modeling method in Python; Step 3: Determine the mechanical criterion for the instability of the surrounding rock, determine the single-factor test scheme based on the control variable method, calculate the critical safety distance under the influence of a single factor and conduct a unary regression; Step 4: Design an orthogonal test scheme, conduct a multi-variable non-linear regression on the calculation results based on the form of the unary regression formula, and obtain a prediction formula for the critical safety distance between the tunnel and the karst cave.

2. The prediction method for the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave according to claim 1, characterized in that The geometric dimension parameters of the tunnel in step 1 include the tunnel cross-section form, height, span, and tunnel burial depth, and the geometric dimension parameters of the karst cave include the karst cave volume. 、 The distance between the karst cave and the tunnel, and the relative azimuth angle between the karst cave and the tunnel, that is, the karst-tunnel azimuth angle.

3. The prediction method for the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave according to claim 1, wherein The mechanical parameters of the surrounding rock and the karst cave filling include unit weight, elastic modulus, Poisson's ratio, internal friction angle and cohesion.

4. The prediction method for the critical safety distance between a tunnel and a karst cave under the action of a concealed karst cave according to claim 3, characterized in that The influencing factors of the critical safety distance between the tunnel and the karst cave include the equivalent radius of the karst cave R , the buried depth of the tunnel H , the horizontal of the surrounding rock V , the azimuth angle of the tunnel and the karst cave and the filling degree of the karst cave T， The calculation formula of the equivalent radius of the karst cave R is as follows: (1) In the formula, Q represents the volume of the karst cave.

5. The prediction method for the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave according to claim 4, characterized in that, The surrounding rock level V is divided into five levels, namely Level 1, Level 2, Level 3, Level 4 and Level 5. The surrounding rock level is determined according to the mechanical properties of the surrounding rock. The mechanical parameters of the surrounding rock are divided into five equal parts. The weaker the mechanical properties of the surrounding rock, the lower the corresponding surrounding rock level and the smaller the level number.

6. The prediction method for the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave according to claim 1, characterized in that, In Step 2, fully parameterize the constructed tunnel-karst cave finite element model, including model boundaries, geometric dimension parameters of the karst cave and the tunnel, the distance between the karst cave and the tunnel, surrounding rock material parameters, karst cave spatial position parameters and mesh parameters, and write a parameterized modeling calculation script using the Python language.

7. The prediction method for the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave according to claim 6, characterized in that The specific process of Step 3 is as follows: Step 3.1: Adopt the maximum tensile strain criterion as the judgment criterion for the range of the surrounding rock deformation failure area. The calculation formula for the maximum tensile strain ε is; (2) In the above formula, R t represents the uniaxial tensile strength of surrounding rock, E is the elastic modulus of surrounding rock; Step 3.2: Determine the single-factor test scheme based on the control variable method; Step 3.3: Use the parameterized modeling calculation script in Step 2 to determine the critical safety distance under different values of each influencing factor; Step 3.4: Plot the scatter diagram of each influencing factor and the corresponding critical safety distance, and judge whether to use unary linear regression or unary non-linear regression according to the data trend.

8. The prediction method for the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave according to claim 7, characterized in that, The specific process of Step 3.3 is as follows: Step 3.3.1: Automatically complete the tunnel excavation construction simulation calculation under different single-factor change conditions through the parameterized script established in Step 2, and extract the plastic strain nephogram of the tunnel-karst cave finite element model; Step 3.3.2: Mark the surrounding rock deformation failure area on the plastic strain nephogram through the maximum tensile strain calculated in Step 3.

1. The surrounding rock deformation failure area is divided into the tunnel deformation failure area and the karst cave deformation failure area; Step 3.3.3: Judge whether the tunnel deformation failure area and the karst cave deformation failure area are connected according to the spatial distribution position of the tunnel deformation failure area and the karst cave deformation failure area in the plastic strain nephogram. If it is in a connected state, execute Step 3.3.

4. If it is in a non-connected state, execute Step 3.4.5; Step 3.3.4: Distance increment optimization, gradually increase the distance between the karst cave and the tunnel in increments of 0.05m to 0.2m, and loop to execute the modeling calculation process in Step 3.3.1 until it first appears that the tunnel deformation failure area and the karst cave deformation failure area are in a non-connected state. At this time, the recorded distance between the karst cave and the tunnel is the critical safety distance; Step 3.3.5, distance reduction optimization, gradually reduce the distance between the cave and the tunnel in increments of 0.05m to 0.2m, and repeat the modeling and calculation process of step 3.3.1 until the tunnel deformation and damage zone and the cave deformation and damage zone are connected for the first time. At this time, the recorded distance between the cave and the tunnel is the critical safety distance; Step 3.3.6: Repeat steps 3.3.3 to 3.3.5 to obtain the critical safety distance between the tunnel and the cave under different values of each influencing factor.

9. The prediction method for the critical safety distance between a tunnel and a karst cave under the action of a hidden karst cave according to claim 8, wherein The specific process of step 4 is as follows: Step 4.1, according to the range of factors affecting the critical safety distance between the tunnel and the cave, determine the number of factors and levels, design an orthogonal experiment based on the number of factors and levels, and calculate the critical safety distance between the cave and the tunnel under each experiment according to step 3.3; Step 4.2, based on the univariate regression formula of different factors, the correlation function between multiple influencing factors and the critical safety distance between karst caves and tunnels is constructed: （3） where \(L\) is the critical safety distance between the karst cave and the tunnel, a and b are both trend term coefficients, c , d , e , f , g and h are all periodic term coefficients, a , b.c , d , e , f , g and h are used to describe the non - linear relationship between the azimuth angle of the karst - tunnel and the critical safety distance, i is the linear correlation coefficient between the equivalent radius of the karst cave and the critical safety distance between the karst cave and the tunnel, j is the linear correlation coefficient between the buried depth of the tunnel and the critical safety distance between the karst cave and the tunnel, k is the linear correlation coefficient between the horizontal of the surrounding rock and the critical safety distance between the karst cave and the tunnel, m is the linear correlation coefficient between the filling degree of the karst cave and the critical safety distance between the karst cave and the tunnel, n is a constant to be determined; Step 4.3: Extract the orthogonal test data of the critical safety distance between the karst cave and the tunnel in Step 4.1, and perform multiple regression fitting using the nonlinear least squares method. The objective function is to minimize the sum of the squared residuals between the predicted values and the experimental values. Based on the empirical formula or the preliminary linear regression results, set the initial values of the undetermined coefficients, and use the Levenberg-Marquardt algorithm to iteratively optimize the parameters, gradually adjusting each coefficient until the objective function converges, that is, the residual change rate < 10 -6 , and then calculate the goodness of fit R 2 . Wait until R 2 > 0.

95. Substitute the fitted undetermined coefficients into Equation (3) to obtain the correlation function between the critical safety distance between the karst cave and the tunnel and each influencing factor.

10. The prediction method for the critical safety distance between a tunnel and a karst cave under the action of a concealed karst cave according to claim 9, characterized in that, When the surrounding rock is Class IV, the equivalent radius of the karst cave in the surrounding rock ranges from 1m to 5m, the tunnel burial depth ranges from 74m to 234m, the karst tunnel azimuth ranges from 0° to 180°, and the karst cave filling degree ranges from 0% to 100%. The nonlinear least squares method is used for multivariate regression fitting, and the correlation function between the critical safety distance between karst caves and tunnels and the influencing factors is obtained as follows: (4)。

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