Karst area shield tunnel face outburst prevention rock mass safety thickness prediction method

Abstract

The invention discloses a karst area shield tunnel face outburst prevention rock mass safety thickness prediction method, and belongs to the field of karst tunnel outburst prevention rock mass thickness predication.The method comprises the steps that environmental parameters in an area where tunnel engineering is located are collected, an orthogonal test table is established according to the environmental parameters, and according to the environmental parameters and the orthogonal test table, an outburst prevention rock mass safety thickness prediction method is established. Performing numerical simulation by using discrete element software 3DEC to obtain a plurality of working condition combined data; fitting a random forest model and a multiple linear regression equation which are used for predicting the safety thickness of the outburst prevention rock mass according to the combined data of each working condition; predicting a to-be-measured working condition by using the random forest model and the multiple linear regression equation to obtain a first prediction result and a second prediction result; and determining a final prediction result of the safety thickness of the outburst prevention rock mass according to the first prediction result and the second prediction result. The technical problems that an existing outburst prevention rock mass safety thickness prediction analysis result is low in accuracy and large in error are solved.

Description

Technical Field

[0001] This invention belongs to the field of rock mass thickness prediction for karst tunnels, and particularly relates to a method for predicting the safe thickness of rock mass at the face of a shield tunnel in a karst area. Background Technology

[0002] Karst areas are widely distributed with complex groundwater environments. With the increasing demand for tunnel construction, the presence of karst caves often leads to sudden water inrushes at the tunnel face, causing ground subsidence, mudslides, and other safety accidents. These sudden water inrushes not only threaten construction safety but can also damage surrounding surface buildings and underground pipelines. The stability of the anti-outrush layer is a key aspect of water inrush prevention. In existing research on the safe thickness of anti-outrush rock mass in karst tunnels, a multi-dimensional theoretical framework has been established. Methods such as the anti-outrush rock mass thickness theory based on fundamental theories like the double shear strength theory and the upper limit method model of limit analysis can quantify the mapping relationship between various factors and the minimum safe thickness of the tunnel face to a certain extent.

[0003] However, when existing theoretical models predict and analyze the safe thickness of rock mass for karst tunnel outburst prevention, the data in current numerical simulation studies are mainly two-dimensional data, lacking three-dimensional numerical simulation analysis of karst tunnels. This makes it impossible to restore the three-dimensional spatial effect of joint networks, and cannot fully consider the influence of the three-dimensional morphology of karst caves on principal stress deflection. Furthermore, the formula parameters mostly rely on empirical correction coefficients, resulting in significant differences between the prediction and analysis results and the actual state of karst tunnels, thus reducing safety during actual construction.

[0004] Furthermore, current prediction models are mainly trained using machine learning, but the scale and computational efficiency of the training models are insufficient to support full-factor orthogonal experiments. The model dimensions are not well adapted to the actual geological structure, resulting in difficulty in obtaining complete datasets, long prediction model establishment time, and large prediction errors for extreme working conditions, which affects the overall efficiency of shield tunnel engineering design. Summary of the Invention

[0005] In view of the above-mentioned shortcomings in the prior art, the present invention provides a method for predicting the safe thickness of rock mass at the face of a shield tunnel in karst areas to prevent rock bursts, which solves the technical problems of low accuracy and large error in the prediction and analysis results in the prior art.

[0006] To achieve the aforementioned objectives, the present invention employs the following technical solution: a method for predicting the safe thickness of rock mass at the face of a shield tunnel in karst areas, comprising the following steps: S1. Collect environmental parameters in the area where the tunnel project is located, establish an orthogonal test table based on the environmental parameters, and use the discrete element software 3DEC to perform numerical simulation based on the environmental parameters and the orthogonal test table to obtain several working condition combination data. S2. Fit random forest models and multiple linear regression equations to predict the safe thickness of rock mass for each working condition combination data. S3. For the test condition, use the random forest model and the multiple linear regression equation to make predictions respectively, and obtain the first prediction result and the second prediction result. S4. Based on the first and second prediction results, determine the final prediction result of the safe thickness of the rock mass to prevent rock bursts.

[0007] The beneficial effects of this invention are as follows: In this solution, the joint network is accurately restored through numerical simulation model, and the safe thickness of the anti-outburst rock mass at the face of the shield tunnel in karst area is predicted by combining random forest model algorithm and multiple linear regression equation. This breaks through the single variable analysis framework, achieves accurate analysis of nonlinear relationships, and improves both prediction accuracy and computational efficiency through optimization of random forest model algorithm. Furthermore, it can achieve high-precision and high-efficiency prediction through mutual verification of the triple mechanism of "numerical simulation-prediction formula-machine learning".

[0008] Furthermore, the establishment of the orthogonal experimental table based on environmental parameters in step S1 specifically involves: A1. Collect environmental parameters within the tunnel engineering area; the environmental parameters include surrounding rock parameters, groundwater depth, tunnel depth, relative position of karst caves to the tunnel face, karst cave morphology, and joint dip angle; A2. Determine the classification standards for surrounding rock parameters to obtain the surrounding rock grade; A3. Based on the surrounding rock grade, groundwater depth, tunnel depth, relative position of the karst cave to the working face, karst cave morphology and joint dip angle, establish a factor level table for the six-factor mixed level; A4. Establish an orthogonal experimental table based on the factor level table.

[0009] The beneficial effects of the above-mentioned further scheme are as follows: The efficient multi-factor experimental method based on orthogonal arrays, using orthogonal experimental design, can scientifically arrange multi-factor, multi-level experiments, reduce the number of experiments, and analyze the impact of each factor on the results. Furthermore, it enables the design of different working conditions through full-element orthogonal experimental design, maximizing the collection of data to construct a high-coverage dataset.

[0010] Furthermore, in step S1, numerical simulations are performed using the discrete element method software 3DEC based on the working conditions in the orthogonal experimental table to obtain the safe thickness of the rock mass for each working condition; in the numerical simulation, the working face pressure is applied using the water and soil combined calculation formula:

[0011] In the formula, For the calculation of water and soil pressure, K 0 represents the coefficient of earth pressure at rest; It is the acceleration due to gravity; The density of saturated soil H soil The depth of soil cover. The density of the water in the cave. Groundwater level.

[0012] Furthermore, the critical condition for water inrush when numerically simulating the safe thickness of the anti-outburst rock mass in step S1 is as follows:

[0013] In the formula, Critical pressure for water inrush. For the minimum principal stress, For fracture toughness, Pi This is the equivalent crack size.

[0014] Furthermore, it also includes: step S2 specifically comprises: S201. Preprocess the data of each working condition combination to obtain a sample set of safe thickness of rock mass for preventing rock bursts. S202. The random forest model is trained using the sample set of safe thickness of rock mass to obtain a random forest model for predicting the safe thickness of rock mass. S203. Divide the sample set of safe thickness of rock mass for rock burst prevention into sample subsets corresponding to each surrounding rock grade according to the surrounding rock grade. S204. Establish the relationship between the safe thickness of the rock mass at the tunnel face for preventing outbursts and the influencing factors; S205. Based on the sample subsets corresponding to each surrounding rock grade, the relationship between the safe thickness of the anti-outburst rock mass at the tunnel face and the influencing factors is fitted to obtain the multiple linear regression equations corresponding to each surrounding rock grade.

[0015] The beneficial effects of the above-mentioned further scheme are: by using the random forest machine learning model, the prediction results of the minimum rock mass for each combination of working conditions can be more accurate, thereby improving the overall accuracy of the prediction results.

[0016] Further, in step S201, the decision tree of the random forest model uses the CART type and utilizes the Gini index to select the splitting attribute; the random forest model obtains the final prediction result based on the Bagging ensemble strategy and the averaging method.

[0017] Furthermore, the relationship between the safe thickness of the anti-outburst rock mass at the shield tunnel face and the influencing factors in step S204 is as follows:

[0018] In the formula, Tmin M represents the safe thickness of the rock mass at the tunnel face for preventing outbursts; θ represents the tunnel excavation depth; H represents the joint dip angle; and H represents the groundwater depth. D c This represents the positional characteristic value of the cave relative to the working face; M c The morphological characteristic values ​​of the cave are α, β, γ, δ, ε, and These are undetermined constant coefficients.

[0019] The beneficial effects of the above-mentioned further scheme are as follows: the formula includes the remaining five influencing factors other than the surrounding rock grade, wherein the joint dip angle is calculated from the angle value to the numerical value using the sine trigonometric function, so as to perform sample fitting regression.

[0020] Furthermore, it also includes: step S205 specifically comprises: S2051. Based on the sample subsets corresponding to each surrounding rock grade, the relationship between the safe thickness of the anti-outburst rock mass at the tunnel face and the influencing factors is fitted to obtain the initial multiple linear regression equations corresponding to each surrounding rock grade. S2052. For the initial multiple linear regression equations corresponding to each surrounding rock grade, determine whether they meet the first condition. If yes, proceed to step S2053; otherwise, the true relationship between the independent and dependent variables is nonlinear. Perform nonlinear transformations on the independent variables, such as logarithmic or square root transformations, or check the data accuracy and increase the sample size. Refit the initial multiple linear regression equations. The first condition is the determination coefficient R. 2 Greater than R 2 The threshold is set, and the significance of each independent variable is less than the significance threshold. S2053. Perform independence diagnosis, multicollinearity diagnosis, and residual diagnosis on the initial multiple linear regression equations corresponding to each surrounding rock grade. If all three diagnoses meet the second condition, the multiple linear regression equations corresponding to each surrounding rock grade are obtained. Otherwise, check the accuracy of the sample data, or adjust the range of independent variable values ​​and re-perform the orthogonal experiment. The second condition is that the DW value of the independence diagnosis is within the DW threshold range, the VIF value of the multicollinearity diagnosis is less than the VIF threshold, and the regression standardized residual histogram of the residual diagnosis is normally distributed.

[0021] The beneficial effects of the above-mentioned further scheme are as follows: Since the classification of surrounding rock grades is relatively complex and involves the calculation of multiple physical quantities, dividing the sample into multiple subsets according to the surrounding rock grade can simplify the sample set; the determination coefficient R of each sample subset can be used to determine the classification coefficient R. 2 Checking whether the significance of the independent variables meets the fitting requirements can initially guarantee the feasibility of the multiple linear regression fitting; testing the DW value, VIF value, and standardized residual histogram of the sample subset can further guarantee the accuracy of the results obtained from the fitting iteration.

[0022] Furthermore, the final predicted result of the safe thickness of the anti-outburst rock mass in step S4 is as follows: T 临界 =max{T min T ml} In the formula, T 临界 The final predicted thickness of the rock mass to prevent rock bursts; T min T represents the prediction result of the multiple linear regression equation. ml These are the prediction results from the random forest model.

[0023] The beneficial effects of the above-mentioned further scheme are as follows: In selecting the minimum value of the final anti-outburst rock mass, the maximum value of the calculation results of the random forest model and the multiple linear regression equation is selected to avoid the error between the prediction results and the actual geological conditions due to the difference between the uniform distribution of strata in numerical simulation and the actual strata conditions. Therefore, the maximum value of the prediction results of the two models is selected to improve the safety of the engineering construction process. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating the method for predicting the safe thickness of rock mass at the face of a shield tunnel in a karst region, as described in this embodiment of the invention.

[0025] Figure 2 This is a flowchart of the numerical simulation in an embodiment of the present invention.

[0026] Figure 3 This is a flowchart of the random forest model prediction process in an embodiment of the present invention.

[0027] Figure 4 This is a residual density curve of the random forest model in an embodiment of the present invention.

[0028] Figure 5 This is a residual plot of random forest prediction data in an embodiment of the present invention.

[0029] Figure 6 This is a learning curve diagram of the random forest model in an embodiment of the present invention.

[0030] Figure 7 This is a schematic diagram of the training results of the comparative example 1 of the present invention.

[0031] Figure 8 This is a schematic diagram of the training results of the comparative model 2 of this invention.

[0032] Figure 9 This is a schematic diagram of the training results of the comparative model 3 of this invention.

[0033] Figure 10 This is a schematic diagram of the training results of Comparative Example 4 of the present invention.

[0034] Figure 11 This is a schematic diagram of the training results of Comparative Example 5 of the present invention.

[0035] Figure 12 This is a schematic diagram of the model training results in an embodiment of the present invention. Detailed Implementation

[0036] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0037] In one embodiment of the present invention, such as Figure 1 As shown, a method for predicting the safe thickness of rock mass at the face of a shield tunnel in a karst area includes the following steps: S1. Collect environmental parameters in the area where the tunnel project is located, establish an orthogonal test table based on the environmental parameters, and use the discrete element software 3DEC to perform numerical simulation based on the environmental parameters and the orthogonal test table to obtain several working condition combination data. Specific environmental parameter information includes geological exploration information and hydrological exploration information. Geological exploration information can determine the range of physical and mechanical parameters of the surrounding rock in the area penetrated by the tunnel project, the size and distribution characteristics of karst caves, and hydrogeological conditions. Hydrological exploration information can determine the range of groundwater depth and tunnel depth based on hydrogeological surveys. In addition, when surveying environmental parameters, parameters such as joint dip angle, the position of karst caves relative to the tunnel face, and the morphology of karst caves are also detected.

[0038] S101. Based on the collected surrounding rock parameter information, the surrounding rock grade is divided into multiple grades. Specifically, when classifying the surrounding rock parameters, they can be divided into five grades: IV1, IV2, IV3, V1, and V2, according to the surrounding rock grade classification standard "Engineering Surrounding Rock Classification Standard GBT50218-2014". The formula for judging the rock strata grade includes:

[0039]

[0040] In the formula BQ These are basic quality indicators for rock masses, used for basic classification of rock masses; [BQ] For the quality indicators of rock mass in underground engineering; R c This represents the saturated uniaxial compressive strength of the rock. K v The rock mass integrity index; K 1、K 2 、K 3 are, in order, the correction coefficients for the influence of groundwater on underground engineering, the correction coefficients for the influence of the attitude of the main structural surfaces of underground engineering, and the correction coefficients for the influence of the initial stress state.

[0041] S102. Based on the collected hydrogeological information, establish a factor level table for the orthogonal experiment. Specifically, the establishment of the factor level table for the orthogonal experiment includes: A1. Collect environmental parameters within the tunnel engineering area; the environmental parameters include surrounding rock parameters, groundwater depth, tunnel depth, relative position of karst caves to the tunnel face, karst cave morphology, and joint dip angle; A2. Determine the classification standards for surrounding rock parameters to obtain the surrounding rock grade; A3. Based on the surrounding rock grade, groundwater depth, tunnel depth, relative position of the karst cave to the working face, karst cave morphology and joint dip angle, establish a factor level table for the six-factor mixed level; A4. Establish an orthogonal experimental table based on the factor level table.

[0042] One approach is to use SPSS software to establish a corresponding orthogonal experimental table based on the factor level table. Each experimental scheme in the orthogonal experimental table is a combination of different level values ​​of each influencing factor. The specific content of establishing the orthogonal experimental table is existing technology and will not be elaborated here.

[0043] In step S1, actual shield tunneling information is also collected. This information includes parameters of the shield machine used in the actual project, such as tunnel spacing, tunnel depth range, shield machine cutterhead diameter, segment length, segment thickness, segment inner diameter, segment material, lining material and thickness, and grouting layer material and thickness. The soil and rock mass adopts the Mohr-Column constitutive model. Specifically, in this embodiment, the actual shield tunneling information is as follows: the left and right line spacing of the double-line shield tunnel is 17.6m, the burial depth is 20.07~45.9m, the maximum slope is 23‰, the groundwater level burial depth is 0.10~17.20m, the annual variation of the water level with different precipitation is about 3.0~5.0m, and the groundwater elevation is 32.93~59.20m. The section was constructed using an earth pressure balance shield tunneling machine. The lining ring was constructed using C50 strength grade and P12 impermeability grade concrete segments with an elastic modulus of 34.5 GPa. The segments had an outer diameter of 8800 mm, an inner diameter of 7900 mm, and a ring width of 1800 mm.

[0044] As attached Figure 2The numerical simulation model shown includes the following steps: S111. When establishing the numerical simulation model, the parameter information collected in S1 is simulated using discrete element software. Specifically, during the engineering simulation, the initial ground stress and karst water pressure are first balanced in the discrete element software 3DEC. Then, the excavation of the newly excavated tunnel is simulated step by step using the discrete element software 3DEC, with each shield segment being excavated in 2m increments. Furthermore, the fluid-structure interaction switch is turned on in each excavation step during the simulation to simulate the dissipation of excess pore water pressure during the excavation of the new tunnel.

[0045] S112. For the karst cave, the double-line shield tunnel to be excavated, and the surrounding rock strata, a 3D model is created and meshed. Then, discrete element method (DEM) software is used to create the overlying soil layer of the surrounding rock and mesh it, grouping it into groups. The grouped meshes created from the 3D model are imported into the DEM software for numerical simulation. The imported 3D mesh models are named and grouped according to different structural locations and physical properties. In the model, 38-43m represents plain fill soil; 33m-38m represents clay soil; -30-38m represents coarse sand soil; and -20--30m represents surrounding rock strata. In this embodiment, Rhino software can be used for 3D model creation.

[0046] S113. Numerical simulation model parameter assignment: Specifically, after grouping the various parts in S202, the physical parameters, constitutive model and contact surface parameters, and densities of each stratum collected in S1 are assigned to the corresponding element parts. Subsequently, the porosity and permeability, fluid density and height, and global fluid physical parameters of each stratum element are set. The specific values ​​of the fluid-related porosity, permeability, fluid density, height, and global fluid physical parameters are existing technologies and will not be elaborated here.

[0047] S114. Constrain the displacement of the elements around the perimeter and bottom of the numerical simulation model; then perform geostress equilibrium calculations. The geostress equilibrium calculation of the numerical simulation model is existing technology and will not be described in detail here.

[0048] S115. Simulate the excavation of karst caves and tunnels using Discrete Element Method (DEM) software, and perform numerical simulations. Specifically, during the simulated excavation, first excavate the karst cave section in the DEM software and calculate until convergence, completing the initial ground stress balance and water pressure balance. Then, cyclically excavate the newly constructed double-track shield tunnel section, with an excavation step length of 2m. During the excavation process, apply the face pressure using the water and soil equilibrium formula in the numerical simulation.

[0049] In the formula: K 0 represents the coefficient of earth pressure at rest; specific values ​​can be found according to... Calculation, where It is the internal friction angle; This is the density of saturated soil, in units of ; H soil The depth of soil cover is expressed in meters (m). The density of the water in the cave. This refers to the groundwater head height.

[0050] Next, the shield tunnel segments and pre-grouting sections are established, and calculations are performed to convergence at each step. The critical condition for water inrush during the numerical simulation of the safe thickness of the anti-outburst rock mass is as follows:

[0051] In the formula Critical pressure for sudden water inrush For the minimum principal stress, For fracture toughness, Pi The equivalent crack size is used. Based on the surrounding rock grade and various environmental parameters defined in step S1, working conditions are combined, and the thickness of each anti-outburst rock mass is obtained during the simulation calculation. The specific minimum anti-outburst rock mass thickness obtained from the combined working conditions in this embodiment is shown in Table 1. Table 1 Combined operating conditions, simulation results, and prediction results

[0052] S2. Fit random forest models and multiple linear regression equations to predict the safe thickness of rock mass for each working condition combination data. As attached Figure 3 The specific predictions made by the random forest model shown are as follows: S201. Based on the working condition combination data formed in S1, preprocess the working condition combination data to obtain the rock mass safety thickness sample set for rock burst prevention; specifically, the data preprocessing includes data cleaning and data encoding of the acquired data.

[0053] S2011. Data cleaning mainly includes checking for missing values ​​and outliers in the acquired data. The specific details of checking for missing values ​​and outliers are existing technologies and will not be elaborated here.

[0054] When encoding the data, the discrete values ​​of soil parameters in the combined working condition data are converted into digital identifiers that the model can recognize; specifically, in this embodiment, the three parameters of surrounding rock grade, relative position of karst cave to the working face, and karst cave morphology are converted into digital identifiers that the model can recognize.

[0055] S2012. After cleaning and encoding the data, the dataset for each combination of working conditions is split into training and testing sets. Specifically, during data splitting, the data is resampled to randomly generate training and testing sets containing a preset percentage of all sample data. In this embodiment, the cleaned and encoded data is resampled using the Bootstrap method to randomly generate a training set containing 80% of all samples, with the remaining 20% ​​used as the testing set. The specific details of the data resampling are existing technology and will not be elaborated here.

[0056] In step S202, the dataset's attributes are further divided, and the dataset's purity is measured. Preferably, in this embodiment, the Gini index is used to divide the dataset's attributes and to measure its purity. The specific calculation of the Gini index for dataset purity is as follows:

[0057] In the formula, D For a dataset, p k The proportion of samples of class k in the current dataset, k = (1, 2, 3, ..., ...). ); This represents the total number of categories in the current dataset.

[0058] Then, calculate the Gini index for each attribute based on the calculated Gini index of dataset purity:

[0059] In the formula, V For discrete properties a For dataset D The number of branch nodes generated after partitioning D v For the first v Each branch node contains D All in the attributes a The upper value is a v The sample, a v Discrete properties a The possible values ​​of .

[0060] Based on the calculated Gini index of the dataset, calculate the optimal splitting attribute for the dataset: ; In the above formula, A For the set of candidate attributes, a It is an attribute.

[0061] S202. Train the random forest model using the training set of rock mass safety thickness for rock burst prevention to obtain a random forest model for predicting the safety thickness of rock mass for rock burst prevention; the specific combination strategy for the random forest model construction is the averaging method (Bagging ensemble strategy), and its algorithm model is as follows:

[0062] in T For the number of decision trees, For the first i The predicted value for each tree.

[0063] In step S202, the decision tree in the random forest model adopts the CART type.

[0064] S203. The sample set of safe thickness of the rock mass for preventing rock bursts is divided into training subsets corresponding to each rock mass grade based on the surrounding rock grade. Specifically, the random forest model is first tuned, using a grid search method to find the optimal hyperparameters in the hyperparameter space. The core hyperparameters for tuning the random forest model include the number of decision trees (n_estimators), the maximum depth of a single tree (max_depth), the minimum number of samples for node splits (min_samples_split), the minimum number of samples for leaf nodes (min_samples_leaf), and the maximum number of features considered in each split (max_features). Systematic parameter testing is performed using grid search to optimize model complexity and generalization balance. The selected hyperparameter range in this embodiment is shown in Table 2. Table 2 Model Hyperparameter Range

[0065] When tuning model hyperparameters using grid search, each candidate parameter is iterated through and every possibility is tried; the parameter that performs best is the final result. Specifically, in the model tuning process, the mean squared error (MSE), root mean squared error (RMSE), and coefficient of determination R are used to predict the model's hyperparameters. 2 This refers to the deviation between the predicted and actual values ​​of the indicator and the termination condition for parameter tuning.

[0066] The formula for the mean square error of the prediction model is:

[0067] The formula for calculating the root mean square error is:

[0068] The formula for calculating the coefficient of determination is:

[0069] In the formula n Represents the total number of samples, and represents the true value. Indicates the predicted value. This represents the mean of the true values.

[0070] In step S203, after each parameter tuning of the random forest model, the random forest model is trained. In this embodiment, K-fold cross-validation is used to train the random forest model. The specific details of K-fold cross-validation are existing technology and will not be described further here. The performance of the random forest model in this embodiment is shown in the attached figure. Figures 4-7 As shown, the prediction model has an MSE of 0.1216 ± 0.0281, an RMSE of 0.3460 ± 0.0428, and an R² value of 0.1216 ± 0.0281. 2 The _score is generally above 90%, and the random forest model in this embodiment performs well and the prediction results are accurate.

[0071] S204. Based on the working condition combination data obtained in step S1, establish the relationship between the safe thickness of the anti-outburst rock mass at the tunnel face and the influencing factors:

[0072] In the formula, T min M represents the safe thickness of the rock mass at the tunnel face for preventing outbursts; θ represents the tunnel excavation depth; H represents the joint dip angle; and H represents the groundwater depth. D c These are the positional characteristics of the cave relative to the working face (1~3 correspond to upper, middle, and lower, respectively). M c The morphological characteristics of the cave (1-4 correspond to horizontal cylinder, vertical cylinder, rectangle, and sphere respectively); α, β, γ, δ, ε and These are undetermined constant coefficients. When analyzing various influencing factors, the surrounding rock grade is taken as the primary prerequisite, and the distribution of the plastic failure zone and the maximum stress on the tunnel face are the main criteria for judgment, supplemented by the tunnel arch displacement value, surface settlement value and stratum stress distribution for comprehensive judgment.

[0073] S205. Based on the training subsets corresponding to each surrounding rock grade, the relationship between the safe thickness of the anti-outburst rock mass at the shield tunnel face and influencing factors is fitted to obtain the multiple linear regression equations corresponding to each surrounding rock grade. In step S205, since the surrounding rock grade is a discrete value and a fixed value, it is used as a prerequisite for segmentation. The segmented experimental parameters and calculation results are imported into SPSS software, using T... min As dependent variables, M, θ, H, D c and Mc As independent variables, multiple linear regression analysis is performed to observe the extent, R, of how well the independent variables explain the dependent variable in the analysis results. 2 The analysis includes the significance of each independent variable, the Durbin-Watson (DW) value (used to test for autocorrelation in the residuals of a regression analysis), the VIF (variance inflation factor, a measure of the severity of multicollinearity in a multiple linear regression model, representing the ratio of the variance of the regression coefficient estimates to the variance assumed to be nonlinearly correlated among the independent variables), and the residual distribution plot. When analyzing the regression equation, it is crucial to determine whether the independent variables can explain the dependent variable T. min The degree of R 2 Is the value greater than R? 2 The threshold, preferably R in this embodiment 2 The threshold is 0.3. The significance of each independent variable is checked against the significance threshold; preferably, the significance threshold in this embodiment is 0.05. When both conditions are met, the regression equation is diagnosed for independence, multicollinearity, and residuals. Otherwise, if the true relationship between the independent and dependent variables is nonlinear, the independent variables are subjected to nonlinear transformations such as logarithmic or square root transformations, or the accuracy of the sample data is checked and the sample size is increased. If all three diagnoses meet the second condition, where the DW value for independence is within the DW threshold range, the VIF value for multicollinearity is less than the VIF threshold, and the regression standardized residual histogram for residuals is normally distributed, then the multiple linear regression equations corresponding to each rock grade are obtained. Otherwise, the accuracy of the sample data is checked, or the range of independent variable values ​​is adjusted, and the orthogonal experiment is repeated. The specific content of the diagnosis and the judgment content of the second condition are as follows: For independence assessment, a DW threshold of 2.0 indicates that the data groups are independent and have low autocorrelation. The formula for calculating DW is:

[0074] In the formula, n For sample size, e t Indicates the first t The residuals of each observation (the difference between the actual and predicted values). e t-1 Indicates the first t-1 The residuals of each observation.

[0075] Multicollinearity diagnosis VIF The value should be less than 5, at which point there is no multicollinearity among the independent variables. VIF The calculation formula is: In the formula The multiple correlation coefficient is the coefficient of the independent variable in a regression analysis with respect to the other independent variables.

[0076] For residual diagnosis, observe whether the histogram of standardized regression residuals is normally distributed. If it is normally distributed, it indicates that the residuals are random and the regression equation matches the data well.

[0077] In S205, when performing regression equation analysis, α, β, γ, δ, ε, and γ can be obtained once the analysis and diagnosis of the regression equation meet the requirements. The values ​​of undetermined coefficients are determined, and the final regression equation is obtained. In this embodiment, the independent variables and T under different surrounding rock grades are obtained through multiple linear regression analysis. min The relational expressions are shown in Table 3: Table 3 Individual variables and T for different surrounding rock grades min Relationship table

[0078] The accuracy of the prediction results of the random forest model and the multiple linear regression equation is verified by the simulation results of the numerical simulation model. In this embodiment, the results of the mathematical analysis of the multiple linear regression equation, the machine learning model using random forest prediction, and the simulation results of the numerical simulation model are compared in Table 4. Table 4 Comparison of Prediction Data for Each Model

[0079] The table above shows that the average prediction accuracy for rock grades IV1 to V2 is 96.43%, 96.65%, 96.67%, 94.10%, and 90.56%, respectively, with errors not exceeding 10%. The average prediction accuracy of the random forest prediction model is 95.01%.

[0080] S3. Based on the random forest model and multiple linear regression equation established in step S2, predict the safe thickness of the rock mass to prevent rock bursts. The first prediction result is obtained through the random forest prediction model, and the second prediction result is obtained through the multiple linear regression equation.

[0081] S4. Based on the first and second prediction results obtained from the prediction analysis of the safe thickness of the rock mass for preventing rock bursts obtained in S3, select the safe thickness value of the rock mass for preventing rock bursts in the area where the tunnel project is located.

[0082] Specifically, through comparison of multiple regression and random forest analysis, two mathematical models were derived to predict the safe thickness of the rock mass at the tunnel face under the disturbance of shield tunnel construction in karst strata. Since the strata in the numerical simulation are uniformly distributed, which still differs from actual strata conditions, to improve engineering safety, the critical safe thickness of the rock mass for preventing outbursts is taken from the multiple linear regression prediction result (T...). min ) and random forest prediction results (T ml The maximum value of ), i.e., T 临界 =max{T min T ml}

[0083] Compared to existing technologies, this solution predicts the safe thickness of the anti-outburst rock mass at the tunnel face in karst areas by detecting the joint dip angle in the actual construction area and constructing a karst stratum model with multi-scale joint grids based on 3DEC discrete element software. Parametric modeling and the introduction of a multi-field coupling mechanism simulate the dynamic tunneling process, enabling multiple linear regression prediction of the minimum safe thickness of the anti-outburst rock mass at the tunnel face based on the surrounding rock grade, groundwater depth, tunnel depth, joint dip angle, relative position of karst caves to the tunnel face, and karst cave morphology.

[0084] Furthermore, in this scheme, when making predictions using the random forest model, multiple working conditions are designed based on engineering geological survey data and combined with empirical parameter analysis. The working conditions are simulated using 3DEC discrete element software to establish a basic dataset. After comprehensively comparing various models, the random forest model is selected for training. The optimal hyperparameters are selected and K-fold cross-validation is performed to improve the model accuracy, forming a triple verification mechanism of "numerical simulation-regression analysis-machine learning". Through specific engineering cases, it is verified that the error between the prediction model and the theoretical model can be controlled within 5%, which has high prediction accuracy.

[0085] Comparative Example 1 Unlike the embodiments, in Comparative Example 1, the machine learning model in step S2 is replaced by a Naive Bayes model to predict the thickness of the rock mass for each working condition. The prediction training results of this model are attached. Figure 7 As shown.

[0086] Comparative Example 2 Unlike the embodiments, in Comparative Example 1, the machine learning model in step S2 is replaced by a decision tree model to predict the thickness of the rock mass for each working condition. The prediction training results of this model are attached. Figure 8 As shown.

[0087] Comparative Example 3 Unlike the embodiments, in Comparative Example 3, the machine learning model in step S2 is replaced by a KNN model to predict the thickness of the rock mass for each working condition. The prediction training results of this model are attached. Figure 9 As shown.

[0088] Comparative Example 4 Unlike the embodiments, in Comparative Example 4, the machine learning model in step S2 is replaced by a linear model to predict the thickness of the rock mass for each working condition. The prediction training results of this model are attached. Figure 10 As shown.

[0089] Comparative Example 5 Unlike the embodiments, in Comparative Example 5, the machine learning model in step S2 is replaced by an SVM model to predict the thickness of the rock mass for each working condition. The prediction training results of this model are attached. Figure 11 As shown.

[0090] The training results of the random forest model used in this embodiment are shown in the appendix. Figure 12 As shown in Table 5, the training results of the machine learning models in each pair of examples and embodiments are as follows: Table 5 Comparison of Training Results for Various Machine Learning Models Machine learning model types Training results (how well the model fits the data) Example (Random Forest Model) <![CDATA[R 2 :0.8053 ~ 0.936]]> Comparative Example 1 (Naive Bayes Model) <![CDATA[R 2 :0.6336 ~ 0.6576]]> Comparative Example 2 (Decision Tree Model) <![CDATA[R 2 :0.7154 ~ 0.8928]]> Comparative Example 3 (KNN Model) <![CDATA[R 2 :0.1204 ~ 1.0000]]> Comparative Example 4 (Linear Model) <![CDATA[R 2 :0.6375~ 0.6637]]> Comparative Example 5 (SVM Model) <![CDATA[R 2 :-0.0609 ~ 0.8206]]> As shown in Table 5, the prediction results of the random forest model selected in this application embodiment are significantly better than those of the other models selected in Comparative Examples 1 to 5, which can guarantee the accuracy requirements of the anti-blowout rock mass thickness prediction by the machine learning model in this solution.

Claims

1. A method for predicting the safe thickness of rock mass at the face of a shield tunnel in a karst area to prevent rock bursts, characterized in that, Includes the following steps: S1. Collect environmental parameters in the area where the tunnel project is located, establish an orthogonal test table based on the environmental parameters, and use the discrete element software 3DEC to perform numerical simulation based on the environmental parameters and the orthogonal test table to obtain several working condition combination data. S2. Based on the data of each working condition combination, a random forest model and a multiple linear regression equation are obtained, which are used to predict the safe thickness of the rock mass to prevent rock bursts. S3. For the test condition, use the random forest model and the multiple linear regression equation to make predictions respectively, and obtain the first prediction result and the second prediction result. S4. Based on the first and second prediction results, determine the final prediction result of the safe thickness of the rock mass to prevent rock bursts.

2. The method for predicting the safe thickness of rock mass at the face of a shield tunnel in karst areas according to claim 1, characterized in that, The establishment of the orthogonal experimental table based on environmental parameters in step S1 is specifically as follows: A1. Collect environmental parameters within the tunnel engineering area; the environmental parameters include surrounding rock parameters, groundwater depth, tunnel depth, relative position of karst caves to the tunnel face, karst cave morphology, and joint dip angle; A2. Determine the classification standards for surrounding rock parameters to obtain the surrounding rock grade; A3. Based on the surrounding rock grade, groundwater depth, tunnel depth, relative position of the karst cave to the working face, karst cave morphology and joint dip angle, establish a factor level table for the six-factor mixed level; A4. Establish an orthogonal experimental table based on the factor level table.

3. The method for predicting the safe thickness of rock mass at the face of a shield tunnel in karst areas according to claim 1, characterized in that, In step S1, numerical simulations are performed using the discrete element method software 3DEC based on the working conditions in the orthogonal test table to obtain the safe thickness of the rock mass for each working condition; in the numerical simulation, the working face pressure is applied using the water and soil combined calculation formula: In the formula, For the calculation of water and soil pressure, K 0 represents the coefficient of earth pressure at rest; It is the acceleration due to gravity; The density of saturated soil H soil The depth of soil cover. The density of the water in the cave. This refers to the groundwater head height.

4. The method for predicting the safe thickness of rock mass at the face of a shield tunnel in karst areas according to claim 3, characterized in that, The critical condition for water inrush when numerically simulating the safe thickness of the rock mass in step S1 is: In the formula, Critical pressure for water inrush. For the minimum principal stress, For fracture toughness, Pi This is the equivalent crack size.

5. The method for predicting the safe thickness of rock mass at the face of a shield tunnel in karst areas according to claim 1, characterized in that, Step S2 specifically involves: S201. Preprocess the data of each working condition combination to obtain a sample set of safe thickness of rock mass for preventing rock bursts. S202. The random forest model is trained using the sample set of safe thickness of rock mass to obtain a random forest model for predicting the safe thickness of rock mass. S203. Divide the sample set of safe thickness of rock mass for rock burst prevention into sample subsets corresponding to each surrounding rock grade according to the surrounding rock grade. S204. Establish the relationship between the safe thickness of the rock mass at the tunnel face for preventing outbursts and the influencing factors; S205. Based on the training subsets corresponding to each surrounding rock grade, the relationship between the safe thickness of the anti-outburst rock mass at the tunnel face and the influencing factors is fitted to obtain the multiple linear regression equations corresponding to each surrounding rock grade.

6. The method for predicting the safe thickness of rock mass at the face of a shield tunnel in karst areas according to claim 5, characterized in that, The decision tree of the random forest model uses the CART type and utilizes the Gini index to select the splitting attribute; the random forest model obtains the final prediction result based on the Bagging ensemble strategy and the averaging method.

7. The method for predicting the safe thickness of rock mass at the face of a shield tunnel in karst areas according to claim 5, characterized in that, The relationship between the safe thickness of the anti-outburst rock mass at the shield tunnel face and the influencing factors in step S204 is as follows: In the formula, T min M represents the safe thickness of the rock mass at the tunnel face for preventing outbursts, θ represents the tunnel excavation depth, θ represents the joint dip angle, and H represents the groundwater depth. This represents the positional characteristic value of the cave relative to the working face. The morphological characteristic values ​​of the cave are α, β, γ, δ, ε, and All of them are undetermined constant coefficients.

8. The method for predicting the safe thickness of rock mass at the face of a shield tunnel in karst areas according to claim 7, characterized in that, Step S205 specifically involves: S2051. Based on the sample subsets corresponding to each surrounding rock grade, the relationship between the safe thickness of the anti-outburst rock mass at the tunnel face and the influencing factors is fitted to obtain the initial multiple linear regression equations corresponding to each surrounding rock grade. S2052. For the initial multiple linear regression equations corresponding to each surrounding rock grade, determine whether they meet the first condition. If yes, proceed to step S2053; otherwise, perform a nonlinear transformation on the independent variables or check the accuracy of the sample data and increase the sample size, then refit the initial multiple linear regression equations. The first condition is the determination coefficient R. 2 Greater than R 2 The threshold is set, and the significance of each independent variable is less than the significance threshold. S2053. Perform independence diagnosis, multicollinearity diagnosis and residual diagnosis on the initial multiple linear regression equations corresponding to each surrounding rock grade. If all three diagnoses meet the second condition, the multiple linear regression equations corresponding to each surrounding rock grade are obtained. Otherwise, check the accuracy of the sample data or adjust the range of independent variable values, and re-perform the orthogonal experiment. The second condition is that the Durbin-Watson DW value for independence diagnosis is within the DW threshold range, the variance inflation coefficient (VIF) value for multicollinearity diagnosis is less than the VIF threshold, and the regression-standardized residual histogram for residual diagnosis is normally distributed.

9. The method for predicting the safe thickness of rock mass at the face of a shield tunnel in karst areas according to claim 1, characterized in that, The final predicted result of the safe thickness of the anti-outburst rock mass in step S4 is: T 临界 =max{T min ,T ml } In the formula, T 临界 To determine the final predicted thickness of the rock mass to prevent rock bursts, T min T represents the prediction result of the multiple linear regression equation. ml These are the prediction results from the random forest model.

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