Slope anchor cable support optimization design method based on global sensitivity analysis

Abstract

The invention discloses a slope anchor cable support optimization design method based on global sensitivity analysis, and belongs to the technical field of engineering geology. The method comprises the following steps: screening parameters by using a local sensitivity analysis method to determine parameter subsets; secondly, in the anchor cable anchoring force loss calculation model, verifying and calibrating the parallel connection mode of the anchor cable body and the West original rock-soil body rheological model, designing a plurality of sensitivity analysis schemes, and constructing a joint probability density function of uncertainty parameters; and finally, establishing an anchor cable layout and parameter optimization model by taking maximum slope stability reliability as an optimization target and considering constraint conditions such as engineering cost and construction difficulty, and formulating corresponding anchor cable anchoring force compensation measures according to changes of key uncertainty parameters. According to the scheme, the stability risks of the side slope under different working conditions are evaluated more accurately, the engineering cost is effectively reduced and the construction difficulty is reduced on the premise of guaranteeing the stability of the side slope, and the stability of the side slope is jointly improved by designing all links from design to construction.

Description

Technical Field

[0001] The present invention belongs to the technical field of engineering geology, and particularly relates to an optimization design method for slope anchor cable support based on global sensitivity analysis. Background Art

[0002] As important means for slope stability and reinforcement, the design and construction of anchor cables and bolts are crucial for project safety. In slope engineering, parameters such as the layout, length, diameter, and prestress of anchor cables and bolts have a direct impact on slope stability. Therefore, performing sensitivity analysis on these parameters can help engineers optimize the design and improve slope stability and economy.

[0003] Sensitivity analysis is a method for evaluating the response degree of model output to changes in input parameters. In the design of anchor cables and bolts, sensitivity analysis can identify the parameters that have the greatest impact on slope stability, so as to pay special attention during the design and construction process. This method helps to reduce uncertainties in the design and improve the reliability of engineering design. In the sensitivity analysis of anchor cables and bolts, numerical simulation and experimental research are two main research means. Numerical simulation can simulate complex geological conditions and the behavior of the anchoring system, while experimental research provides physical data for verifying simulation results.

[0004] In the prior art, some scholars, in order to provide a basis for reference in the selection of prestressed anchorage parameters, used orthogonal experimental design to conduct sensitivity analysis on prestressed anchorage parameters (row and spacing of anchor cables, prestress, anchoring angle, anchoring section length, anchor cable length). The analysis results show that prestress and row and spacing of anchor cables are the main factors affecting the stability coefficient ("Sensitivity Analysis of Prestressed Anchorage Parameters for Slopes Based on Orthogonal Experimental Design", Yang Jing, etc.).

[0005] Some scholars used the software FLAC3D to conduct sensitivity analysis of parameters. The analysis results show that the setting of prestressed anchor cables makes the bending moment of the pile body locally "wavy", but as the pile diameter increases, this characteristic of the bending moment of the pile body showing a "wavy" shape gradually weakens; the effective bending length of the pile becomes longer as the pile diameter increases; the control bending moment of the pile body can be significantly reduced by increasing the prestress ("Sensitivity Analysis of the Parameters of the Anchor Cable Support Structure for Adjacent Foundation Pits", Wu Shuguang, etc.).

[0006] Some other scholars established a three-dimensional numerical model of the foundation pit by using the ABAQUS finite element software, studied the influence of the pile spacing to pile diameter ratio on the internal force and deformation of the support structure; conducted sensitivity analysis on each support parameter affecting the internal force and deformation of the support structure, and based on this, designed an orthogonal experiment and proposed an optimized design of sparse piles and strong anchors for the project in question ("Sensitivity Analysis of the Parameters of the Sparse Piles and Strong Anchors Support Structure for Deep Foundation Pits", Zhang Enxiang, etc.).

[0007] With the development of computing technology, intelligent algorithms such as genetic algorithms and neural networks have also begun to be applied to the sensitivity analysis of anchor cables and bolts. These algorithms can process a large amount of data and find optimal solutions in complex non-linear problems, providing new tools for the optimal design of the anchorage system.

[0008] However, there are still some problems in the existing technologies. For example, the existing slope stability assessment may only focus on a few conventional factors, such as the basic mechanical parameters of rock and soil masses. The influence of various complex factors such as strong unloading effect of high slopes, seismic effect, groundwater level change, and temperature change on slope stability is not considered. In addition, the existing anchor cable support design may focus on ensuring slope stability while ignoring engineering costs and construction difficulties. Moreover, the existing slope monitoring may only focus on individual indicators, such as the overall anchoring force of prestressed anchor cables. Summary of the Invention

[0009] The object of the present invention is to address the problems that the existing slope stability assessment only focuses on a few conventional factors and the existing anchor cable support design focuses on ensuring slope stability, thus ignoring engineering costs and construction difficulties. A method for optimizing the design of slope anchor cable support based on global sensitivity analysis is proposed. First, this method uses the local sensitivity analysis method to preliminarily screen each parameter to determine a subset of parameters that have a more significant impact on slope stability. Secondly, in the calculation model of anchor cable anchoring force loss, the parallel connection mode of the anchor cable body and the Nishihara rock and soil rheological model is verified and calibrated. In addition, multiple sensitivity analysis schemes are designed and the joint probability density function of uncertain parameters is constructed. Finally, with the maximum slope stability reliability as the optimization goal, considering constraints such as engineering costs and construction difficulties, an optimization model for the layout and parameters of anchor cables is established, and corresponding anchor cable anchoring force compensation measures are formulated for the changes of key uncertain parameters. This solution can more accurately evaluate the stability risks of slopes under different working conditions, effectively reduce engineering costs and construction difficulties on the premise of ensuring slope stability, and design from all aspects from design to construction, so as to jointly improve slope stability.

[0010] Specifically, the present invention provides a method for optimizing the design of slope anchor cable support based on global sensitivity analysis, including the following steps:

[0011] S1. Establish a sensitivity analysis model for slope anchor cable support and determine the model parameters;

[0012] S2. Use the Monte Carlo simulation method to obtain the slope failure probability and obtain the failure samples;

[0013] S3. Design multiple sensitivity analysis schemes and construct the joint probability density function of uncertain parameters;

[0014] S4. Obtain the slope failure probabilities under various sensitivity analysis scenarios and identify the key uncertainty parameters;

[0015] S5. Optimize the layout and parameters of the anchor cables according to the sensitivity analysis results and the prediction model of anchor cable anchoring force loss;

[0016] S6. Compare the calculation results of the optimized design scheme with the monitored values and conduct monitoring and early warning, and optimize through the anchor cable anchoring force compensation measures.

[0017] Preferably, the sensitivity analysis model for the slope anchor cable support includes a slope stability coefficient calculation model and a sensitivity analysis index calculation model; the slope stability coefficient calculation model calculates the slope stability coefficient through the simplified Bishop method in the limit equilibrium method, and at the same time considers the calculation formula of the anchor cable anti-sliding force under the action of the anchor cable support to obtain the calculation formula of the slope stability coefficient;

[0018] The sensitivity analysis index calculation model measures the sensitivity of parameters by using the relative sensitivity index. When calculating, only the value of one parameter is changed each time, and other parameters remain unchanged. By comparing the changes in the slope stability coefficient before and after the parameter change, the relative sensitivity index of this parameter is calculated, and then the parameter set affecting the slope stability is determined.

[0019] Preferably, the specific steps of S2 are as follows:

[0020] S21. Determine the value range and distribution type based on the parameter set affecting the slope stability and set them as random variables;

[0021] S22. Reasonably determine the number of simulation times of the Monte Carlo simulation technique according to relevant factors;

[0022] S23. Respectively construct the rheological model of the anchor cable body and the rheological model of the Nishihara geotechnical body. Under the same stress state, combine the rheological model of the anchor cable body and the rheological model of the Nishihara geotechnical body in parallel to obtain the calculation model of the anchor cable anchoring force loss; among them, the total anchoring force loss is the sum of the anchoring force losses generated by the two respectively;

[0023] S24. Use the same input parameters as the input, calculate the anchoring force loss and the corresponding geotechnical body and anchor cable deformation conditions through the rheological model in S23 and other mature rheological models respectively, and compare them with the actual engineering monitoring data. If the comparison difference is greater than the set threshold, adjust the parameters substituted into the rheological model;

[0024] S25. Generate random numbers according to their respective distribution types based on the set of parameters affecting slope stability, assign values, substitute the simulated parameter values into the slope stability coefficient calculation model and the anchor cable anchoring force loss calculation model respectively to obtain calculation results, and compare them with the user-defined critical stability value. If it is less than the user-defined critical stability value, it is determined that the slope is in a failure state at this time. If it is greater than or equal to the user-defined critical stability value, it is determined that the slope is in a stable state;

[0025] S26. Use a computer program to perform loop simulations based on the simulation method and the number of simulations in S25, record in detail all parameter combinations and the corresponding slope stability states for each simulation, and construct a failure sample library.

[0026] Preferably, the slope stability coefficient calculation model is specifically expressed as:

[0027]

[0028] Where: n is the number of soil strips; c i is the cohesion of the i-th soil strip; b i is the width of the i-th soil strip; W i is the gravity of the i-th soil strip; u i is the pore water pressure at the bottom of the i-th soil strip; is the internal friction angle of the i-th soil strip; φ i is the inclination angle of the bottom surface of the i-th soil strip.

[0029] Preferably, the S3 specifically includes the following steps:

[0030] S31. Determine the sensitivity analysis plan considering the high slope strong unloading action plan, seismic action plan, groundwater level change plan, groundwater level change plan and temperature change plan;

[0031] S32. For the parameters in each sensitivity analysis plan, determine their probability distribution types through on-site monitoring data, laboratory tests and similar engineering experience;

[0032] S33. According to the probability distribution type and statistical characteristics, establish a univariate probability distribution model for each parameter, select a suitable Copula function family and estimate the parameters in the Copula function to determine the specific Copula function model, so as to construct the joint probability density function of the uncertain parameters.

[0033] Preferably, based on the data in the failure sample library, statistical analysis is carried out on the Monte Carlo simulation results under each sensitivity analysis scheme, the sensitivity coefficients and variance contribution rates of each parameter are calculated, the order of the influence degree of each parameter on the slope failure probability is determined, and according to the sensitivity analysis results, the key uncertainty parameters affecting the slope stability reliability are clarified.

[0034] Preferably, the sensitivity coefficient includes the Sobol index based on variance, wherein the Sobol index based on variance is divided into the first-order index and the total-order index; the variance contribution rate refers to the proportion of the variance of each parameter in the total variance. For each parameter, the variance of the change in the slope failure probability caused by the change in the value of this parameter is calculated, and by analyzing the change in the failure probability corresponding to the change in this parameter in different samples, the variance calculation formula is used for statistics.

[0035] Preferably, the specific steps of S5 are as follows:

[0036] S51. Determine the decision variables, and with the maximum slope stability reliability as the main optimization goal, while considering the minimization of engineering cost and construction difficulty, use the linear weighted method to construct the objective function of the anchor cable anchoring force loss prediction model;

[0037] S52. Determine the constraint conditions, including slope stability constraints, anchor cable design parameter constraints, and other engineering constraints;

[0038] S53. Use the multi-objective genetic algorithm to solve the anchor cable anchoring force loss prediction model, obtain the optimization results, and select the optimization results as the final anchor cable layout and parameter optimization scheme according to the actual engineering requirements and the preferences of the decision maker;

[0039] S54. Select the anchor cable anchoring force time-dependent loss prediction model and determine the model parameters. According to the change curve of the anchoring force calculated by the anchor cable anchoring force time-dependent loss prediction model, set the anchoring force threshold and formulate the anchor cable anchoring force compensation measures.

[0040] Preferably, the objective function of the anchor cable anchoring force loss prediction model is specifically expressed as:

[0041] F(x 1 ,x 2 ,x 3 )=ω 1 β(x 1 ,x 2 ,x 3 )-ω 2 C(x 1 ,x 2 ,x 3 )-ω 3 D(x 1 ,x 2 ,x3 )

[0042] Among them, ω 1 , ω 2 , ω 3 are weight coefficients, which are determined according to the degree of emphasis on stability reliability, cost, and construction difficulty in the project, and ω 1 + ω 2 + ω 3 = 1.

[0043] Preferably, the S6 specifically includes: establishing a monitoring index system, collecting monitoring data in real time and using data mining and machine learning technologies to perform real-time analysis and processing on the monitoring data, comparing the curves of each monitoring index calculated by the optimized design scheme with the time-varying curve and the fitting curve of the actual monitoring value, setting clear abnormal phenomenon determination criteria and warning levels; when abnormal monitoring data appears, an alarm is issued in a timely manner according to the warning level, and the anchoring force compensation time and compensation amount are calculated based on the anchor cable anchoring force loss prediction model and compensation measures.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0045] 1. Advantages of multi-factor comprehensive sensitivity analysis

[0046] Traditional slope stability analysis often focuses on only a few main factors, while this solution comprehensively considers various factors such as high slope strong unloading effect, seismic effect, groundwater level change, temperature change, etc. for sensitivity analysis. By designing multiple sensitivity analysis schemes, various potential factors affecting slope stability and their interactions can be captured more comprehensively. Using the Copula function method to construct the joint probability density function of uncertain parameters breaks through the limitations of the traditional method's independent assumption or simple linear correlation processing of parameters, and accurately describes the complex joint distribution characteristics between parameters. This helps to more accurately evaluate the stability risk of slopes under different working conditions in the early design stage, provides a more reliable basis for subsequent targeted optimization design, and greatly reduces the risk of design defects caused by incomplete consideration of factors.

[0047] 2. Optimized model and algorithm improve design accuracy

[0048] With the maximum slope stability reliability as the core optimization goal, and taking into account engineering costs and construction difficulties, the optimization model for cable layout and parameters is constructed, achieving a balanced consideration of multiple objectives. The advanced multi-objective genetic algorithm is used to optimize and solve the key parameters such as the length, spacing, and prestress of the cables, and it can efficiently search for the Pareto optimal solution set in the complex parameter space. Compared with the traditional methods based on experience or single-objective optimization, this optimization model and algorithm can obtain a more scientific and reasonable cable design scheme, effectively reducing engineering costs and construction difficulties while ensuring slope stability. For example, by accurately calculating the optimal combination of cable spacing and length, it avoids the overuse of materials and unnecessary troubles during construction, improving the economy and operability of the project.

[0049] 3. Accurate prediction and compensation of cable anchor force loss

[0050] Based on the rheological properties of the rock and soil mass and the long-term stress and deformation law of the cable, a prediction model for the time-dependent loss of the cable anchor force is selected, which comprehensively considers the relaxation of the cable steel, the creep of the rock and soil mass, and the degradation of the bond performance of the anchorage section. The model parameters are determined through rigorous tests and analyses, enabling the model to accurately predict the change of the cable anchor force over time. The cable anchor force compensation measures formulated according to the prediction results, including clear compensation timing and calculation methods for the compensation amount, are completely different from the traditional methods that only rely on experience or rough estimation for compensation. This ensures that when there is a potential threat to slope stability, the anchor force can be compensated in a timely and appropriate manner, effectively extending the service life of the cable and maintaining the long-term stability of the slope, reducing the risk of slope instability caused by insufficient anchor force.

[0051] 4. A complete monitoring and early warning system to ensure safe operation

[0052] The established complete monitoring index system covers multiple key parameters such as the overall anchor force of the prestressed cable, cable stress, strain, rock and soil displacement, pore water pressure, etc., which is more comprehensive than the traditional monitoring of single or a few indicators. Using data mining and machine learning techniques to analyze and process the monitoring data in real time can quickly and accurately detect abnormal trends and changes in the monitoring data. By setting clear criteria for judging abnormal phenomena and warning levels, a hierarchical early warning management of the slope safety status is achieved. When abnormal monitoring data appears, an alarm can be quickly issued according to the warning level, and the reasonable anchor force compensation time and compensation amount can be automatically calculated with the help of the cable anchor force loss prediction model and compensation measures, guiding the on-site construction personnel to carry out the cable anchor force compensation operation in a timely manner. This fully automated and intelligent system from monitoring to early warning to compensation greatly improves the safety and reliability of the slope anchoring project, effectively avoiding safety accidents and ensuring the long-term safe and stable operation of the project.

[0053] 5. Systematic Solutions Promote Engineering Sustainability

[0054] The overall solution forms a complete closed-loop system from slope stability analysis, cable anchor design optimization, anchoring force prediction and compensation to monitoring and early warning. Each link is interrelated and mutually supportive, and has stronger systematicness and coherence compared with traditional scattered technical means. This systematicness helps to comprehensively manage and maintain the slope anchoring project throughout the entire engineering life cycle, timely discover and solve various problems, and continuously optimize the engineering design and construction operation strategies. As a result, the durability and sustainability of the project are improved, the later maintenance costs and the environmental and social impacts caused by project failure are reduced, laying a solid foundation for the long-term stable operation and sustainable development of the slope project. Description of the Drawings

[0055] Figure 1 It is a schematic diagram of the overall process of an embodiment of the present invention. Detailed Implementation Modes

[0056] Example 1: As Figure 1 shown, the optimized design method for slope cable anchor support based on global sensitivity analysis includes the following steps:

[0057] S1. Establish a sensitivity analysis model for slope cable anchor support and determine the model parameters;

[0058] Through in-situ tests on site, laboratory tests and referring to similar engineering experiences, determine the length, diameter, prestress, spacing of the cable anchor and the instantaneous elastic modulus E B of the viscoelastic modulus E K and the viscosity coefficients η K and η B and other parameter value ranges and distribution types (such as normal distribution, uniform distribution, etc.).

[0059] Use the local sensitivity analysis method (such as the single factor analysis method) to preliminarily screen each parameter, and determine the parameter subset that has a more significant impact on slope stability, so as to focus on it in subsequent analysis.

[0060] S2. Use the Monte Carlo simulation method to obtain the slope failure probability and obtain the failure samples;

[0061] Adopt an improved Monte Carlo simulation technique, increase the number of simulations to more than [X] times to improve the accuracy and stability of the calculation of the slope failure probability.

[0062] In the calculation model of the loss of cable anchor force, the parallel connection method of the cable anchor body and the rheological model of the Xiyuan rock and soil mass is verified and calibrated. By comparing the calculation results of other mature rheological models and the actual engineering monitoring data, the model parameters are optimized to ensure that it can accurately reflect the rheological characteristics of the cable anchor and the rock and soil mass.

[0063] Detailedly record the parameter combinations of each simulation and the corresponding slope stability states to form a failure sample library for subsequent statistical analysis.

[0064] S3. Design multiple sensitivity analysis schemes and construct the joint probability density function of the uncertain parameters;

[0065] In addition to considering the influence of the strong unloading effect of the high slope, sensitivity analysis schemes for factors such as seismic action, groundwater level change, and temperature change can also be added. For each scheme, according to the physical relationship and statistical correlation between the parameters, use appropriate methods (such as the Copula function method) to construct the joint probability density function of the uncertain parameters to accurately describe the joint distribution characteristics of the parameters.

[0066] S4. Obtain the slope failure probabilities under each sensitivity analysis scheme and identify the key uncertain parameters;

[0067] Conduct in-depth statistical analysis on the Monte Carlo simulation results under each sensitivity analysis scheme, calculate the sensitivity coefficients of each parameter (such as the Sobol index based on variance) and the variance contribution rate, and determine the ranking of the influence degree of each parameter on the slope failure probability.

[0068] According to the sensitivity analysis results, clarify the key uncertain parameters affecting the slope stability and reliability, and provide the key attention objects for the subsequent optimization design.

[0069] S5. Optimize the layout and parameters of the cable anchor according to the sensitivity analysis results and the cable anchor force loss prediction model;

[0070] Taking the maximum slope stability and reliability as the optimization goal, and considering constraints such as engineering cost and construction difficulty, establish an optimization model for the layout and parameters of the cable anchor. Use advanced optimization algorithms (such as multi-objective genetic algorithms) to optimize and solve parameters such as the length, spacing, and prestress of the cable anchor to obtain the Pareto optimal solution set.

[0071] Based on the rheological characteristics of the rock and soil mass and the long-term stress and deformation law of the cable anchor, select a suitable prediction model for the aging loss of the cable anchor force (such as a comprehensive model considering the relaxation of the cable anchor steel, the creep of the rock and soil mass, and the degradation of the bond performance of the anchorage section), and determine the model parameters. According to the prediction model, formulate corresponding cable anchor force compensation measures for the changes in the key uncertain parameters, including the calculation methods of the compensation timing and compensation amount.

[0072] S6. Compare the calculated results of the optimized design scheme with the monitored values, and conduct monitoring and early warning and guide the time of anchor force compensation;

[0073] Establish a perfect monitoring index system. In addition to the overall anchor force of prestressed anchor cables, add monitoring items such as anchor cable stress, strain, displacement of rock and soil mass, pore water pressure, etc., and collect monitoring data in real time and transmit it to the data processing center.

[0074] Use data mining and machine learning technologies to conduct real-time analysis and processing of the monitoring data. Compare the curves of each monitoring index changing with time calculated by the optimized design scheme with the fitting curves of the actual monitored values, and set clear abnormal phenomenon determination criteria and early warning levels.

[0075] When the monitoring data shows abnormalities, issue an alarm in a timely manner according to the early warning level, and automatically calculate the reasonable anchor force compensation time and compensation amount based on the anchor force loss prediction model and compensation measures of the anchor cable, and guide the on-site construction personnel to carry out the anchor force compensation operation of the anchor cable to ensure the long-term safe and stable operation of the high slope anchoring project.

[0076] Example 2: A method for optimizing the design of slope anchor cable support based on global sensitivity analysis, including the following steps:

[0077] S1. Establish a sensitivity analysis model for slope anchor cable support and determine the model parameters;

[0078] 1. Slope stability coefficient calculation model

[0079] Use the simplified Bishop method in the limit equilibrium method to calculate the slope stability coefficient F s , and the calculation formula is as follows:

[0080]

[0081] Where: n is the number of soil strips; c i is the cohesion of the i-th soil strip; b i is the width of the i-th soil strip; W i is the gravity of the i-th soil strip; u i is the pore water pressure at the bottom of the i-th soil strip; is the internal friction angle of the i-th soil strip; φ i is the inclination angle of the bottom surface of the i-th soil strip.

[0082] Among them, m θi Through iterative calculation, at the beginning of the calculation, a value of F s can be assumed first (for example, F s = 1), and then this assumed value is substituted into the calculation formula of m θi , and a new F s is calculated. Then, the newly obtained Fs Substitute m again θi into the calculation formula of θi , and iterate repeatedly until the F values obtained from the previous and subsequent calculations s are very close (meeting a certain convergence criterion).

[0083] When considering the role of cable anchor support, add the anti-sliding force provided by the cable anchor to the numerator term. The calculation formula for the anti-sliding force of the cable anchor is:

[0084]

[0085] where: T i is the anti-sliding force provided by the i-th cable anchor; P i is the prestress of the i-th cable anchor; β i is the angle between the i-th cable anchor and the horizontal direction; is the bonding friction angle between the cable anchor and the rock and soil mass.

[0086] At this time, the calculation formula for the slope stability coefficient becomes:

[0087]

[0088] where m is the number of cable anchors.

[0089] 2. Calculation Model for Sensitivity Analysis Index

[0090] Use the relative sensitivity index S ij to measure the sensitivity of parameters. The calculation formula is:

[0091]

[0092] where: ΔF s is the change in the slope stability coefficient F s ; ΔX j is the change in the parameter X j ; X j represents the parameter to be analyzed, such as the length, diameter, prestress, spacing of the cable anchor, and the instantaneous elastic modulus E B , viscoelastic modulus E K , viscosity coefficient η K , η B etc.

[0093] Among them, η K In the context of the rheological model of rock and soil (such as the Nishihara model), η K is usually related to the viscoelastic part of the rock and soil mass. It reflects the viscous resistance characteristics in the viscoelastic deformation process when the rock and soil mass is subjected to stress. When the rock and soil mass is in the viscoelastic deformation stage, η KControls the rate of change of strain with time, that is, the degree of viscous resistance experienced by the recoverable deformation part related to time generated by the rock and soil mass under stress.

[0094] η B Similarly, it is a description of the properties of the rock and soil mass, but is related to other deformation mechanisms in the rheological model of the rock and soil mass. For example, it is related to the viscous characteristics in the viscoplastic deformation process of the rock and soil mass. When the rock and soil mass undergoes irreversible viscoplastic deformation, it reflects the magnitude of the viscous resistance in this deformation process. η B Characterizes the viscous property of the rock and soil mass to produce permanent deformation under long-term loading.

[0095] When calculating the viscoelastic strain of the rock and soil mass, η K Acts together with parameters such as the elastic modulus (such as the viscoelastic modulus). Its magnitude will affect the development trend of strain with time under short-term and medium-term loading of the rock and soil mass. For example, in the process of simulating the deformation recovery of the rock and soil mass after short-term dynamic loading such as an earthquake, different values of η will result in different speeds of strain recovery, thereby affecting the stability analysis results of the slope after dynamic action.

[0096] For long-term slope stability analysis, especially when considering irreversible deformations such as creep of the rock and soil mass, η B Plays a key role. It is interrelated with parameters such as the long-term strength of the rock and soil mass. Different values of η B Will result in different degrees of viscoplastic deformation of the rock and soil mass under long-term loading, thus affecting the stability of the slope during long-term operation. For example, under the long-term action of groundwater or continuous mountain pressure, η B Will affect the deformation and possible failure modes of the rock and soil mass.

[0097] During the calculation, only change the value of one parameter each time, keep other parameters unchanged, and calculate the relative sensitivity index of this parameter by comparing the changes in the slope stability coefficient before and after the parameter change, so as to determine the sensitivity degree of each parameter to the slope stability.

[0098] For example, for the anchor cable length L, first calculate the initial slope stability coefficient F s0 (at this time the anchor cable length is L 0 ), then change the anchor cable length to L 1 , calculate the new slope stability coefficient F s1 , then the relative sensitivity index of the anchor cable length is:

[0099]

[0100] By performing similar calculations for each parameter, the relative sensitivity index of each parameter can be obtained, and then a subset of parameters that have a more significant impact on the slope stability can be determined.

[0101] S2. Obtain the slope failure probability using the Monte Carlo simulation method and obtain the failure samples;

[0102] 1. Determine the random variables and their distributions

[0103] First, based on the value ranges and distribution types (such as normal distribution, uniform distribution, etc.) of the parameters determined in step S1 (such as the length, diameter, prestress, spacing of the anchor cable, and the instantaneous elastic modulus E of the simulated rock and soil mass B , viscoelastic modulus E K , viscosity coefficient η K , η B , etc.), set these parameters as random variables. For example, if the value range of the anchor cable prestress P is [P min , P max and it follows a uniform distribution, then each time the value of this parameter is drawn during the simulation, it is randomly generated within this interval according to the rules of the uniform distribution.

[0104] 2. Set the number of simulations

[0105] Specify the number of simulations required for the improved Monte Carlo simulation technique and set it to more than [X] times (X is reasonably determined according to factors such as the actual engineering accuracy requirements and computing resources. Generally speaking, the more times, the more accurate the result, but the higher the computing cost).

[0106] 3. Construct the parallel connection mode of the anchor cable anchoring force loss calculation model

[0107] (1) Establish the rheological model of the anchor cable body. This model is usually constructed based on factors such as the mechanical properties and stress-strain relationship of the anchor cable material, reflecting the stress changes of the anchor cable under long-term stress and the influence of factors such as time. For example, considering the relaxation characteristics of the anchor cable steel, the stress change law of the anchor cable body with time can be described by a certain differential equation or empirical formula.

[0108] (2) Establish the Nishihara rock and soil body rheological model. The Nishihara model is a model that comprehensively considers the deformation characteristics of rock and soil bodies such as elasticity, viscoelasticity, and viscoplasticity, and describes the strain response of rock and soil bodies under different stress levels and time conditions through its constitutive equation.

[0109] (3) Combine the rheological model of the anchor cable body and the Nishihara rock and soil body rheological model in a parallel connection mode, that is, under the same stress state, both generate deformation and stress changes at the same time, and the total anchoring force loss is the sum of the anchoring force losses generated by each of them.

[0110] 4. Model verification and calibration

[0111] (1) Compare the calculation results of other mature rheological models (such as the Burgers model, Maxwell model, etc., which are commonly used to describe the rheological properties of rock and soil masses and materials). For the same input parameters (such as initial stress, time, etc.), use these different models to calculate the anchor force loss and the corresponding deformations of the rock and soil mass and the anchor cable respectively, and observe the differences in the calculation results.

[0112] (2) At the same time, combine the actual engineering monitoring data. The actual monitoring data may include information such as the change value of the anchor cable stress over time and the displacement of the rock and soil mass. Compare and analyze the results obtained from the simulation calculation with the actual monitoring data. If the deviation between the simulation results and the actual data is large, adjust the parameters in the model (such as the elastic modulus, viscosity coefficient, etc. in the rock and soil mass rheological model) so that the model calculation results can be as close as possible to the actual monitoring situation, realize the optimization of the model parameters, and ensure that the model can accurately reflect the rheological properties of the anchor cable and the rock and soil mass.

[0113] 5. Conduct Monte Carlo simulation and record data

[0114] (1) According to the set number of simulation times, use a computer program (a simulation program can be written using programming languages such as Python, leveraging its function libraries for random number generation, numerical calculation, etc.) to perform loop simulations. In each simulation:

[0115] Randomly generate the corresponding parameter values according to the distribution types of each random variable (parameter), and substitute these parameter values into the slope stability coefficient calculation formula (such as the calculation formula modified by combining the simplified Bishop method in the limit equilibrium method with the action of the anchor cable mentioned above) and the anchor cable anchor force loss calculation model.

[0116] Judge the slope stability state through the slope stability coefficient. If the calculated slope stability coefficient F s < 1 (or less than a certain set critical stability value, determined according to the actual engineering requirements), then it is determined that the slope is in a failure state at this time; if F s ≥ 1, then it is determined that the slope is in a stable state.

[0117] (2) Record in detail all the parameter combination situations and the corresponding slope stability states (failure or stability) of each simulation, and organize and store these data to form a failure sample library. For example, it can be recorded in the form of a table, with each row recording the parameter values of a simulation and the corresponding slope stability judgment result, which is convenient for subsequent statistical analysis.

[0118] The calculation process is as follows:

[0119] 1. Random number generation and parameter assignment

[0120] For each parameter set as a random variable (assuming there are n parameters in total, denoted as X 1 , X 2 , …, X n ), generate random numbers according to their respective distribution types and assign values. Taking the uniform distribution as an example, if the value range of parameter X i is [a i , b i , in the k-th simulation (k = 1, 2, …, [X]), use the uniform distribution random number generation formula:

[0121] X i,k = a i + (b i - a i ) × r i,k ;

[0122] where r i,k is a random number uniformly distributed in the interval [0, 1]. In this way, the value of parameter X i in the k-th simulation is obtained. All parameters are processed in this way to obtain a set of complete parameter values for the k-th simulation.

[0123] 2. Calculation of slope stability coefficient and determination of stability state

[0124] Substitute the parameter values obtained from the k-th simulation into the slope stability coefficient calculation formula, such as:

[0125]

[0126] where, T j,k represents the anti-sliding force provided by the j-th cable in the k-th simulation (its calculation also depends on the cable-related parameter values in this simulation). After calculating F s,k , according to the determination rule mentioned above, if F s,k < 1 (or other critical values), then set the slope stability state identification variable S k = 0 (indicating failure); if F s,k ≥ 1, then S k = 1 (indicating stability).

[0127] 3. Calculation and recording of cable anchoring force loss

[0128] Substitute the parameter values of the k-th simulation into the cable anchoring force loss calculation model (considering the parallel connection method of the cable body and the rheological model of Xiyuan rock and soil), and calculate the cable anchoring force loss value L k (the specific calculation is based on the corresponding rheological model calculation formula, and different models have different mathematical expressions). At the same time, record all the parameter values X 1,k , X 2,k,…,X n,k and the slope stability state S k , forming a record and storing it in the failure sample library.

[0129] 4. Repeat simulation and sample library construction

[0130] Repeat the above steps until the set [X] simulations are completed, and finally obtain a failure sample library containing multiple simulation data, which can be used for subsequent related analyses such as calculating the slope failure probability based on statistical analysis methods.

[0131] Slope failure probability P f is calculated by statistically counting the number of times N f that the slope is in the failure state in the failure sample library and the ratio of the total number of simulations [X], that is:

[0132]

[0133] Through the above detailed implementation methods and calculation processes, the task of obtaining the slope failure probability and failure samples in step S2 can be completed using the improved Monte Carlo simulation technology.

[0134] S3. Design multiple sensitivity analysis schemes and construct the joint probability density function of uncertainty parameters;

[0135] 1. Determine the sensitivity analysis scheme

[0136] (1) High slope strong unloading action scheme:

[0137] Analyze the influence of parameters related to unloading, such as unloading range and unloading degree, on slope stability under strong unloading action. Determine the key parameters characterizing unloading, such as the change rate of strength parameters of rock and soil masses in the unloading area (such as the reduction coefficients of cohesion and internal friction angle), the depth and range of the unloading area, etc. These parameters may be related to factors such as the original properties of rock and soil masses, the geometric shape of the slope, and the excavation method.

[0138] (2) Earthquake action scheme:

[0139] Consider earthquake parameters such as peak ground acceleration, earthquake duration, and dominant earthquake period. The peak ground acceleration reflects the intensity of the earthquake and directly affects the inertial force on the slope; the earthquake duration affects the cumulative deformation and damage degree of rock and soil masses under earthquake action; the relationship between the dominant earthquake period and the natural vibration period of the slope affects the transmission and response of earthquake energy in the slope. At the same time, the change of dynamic characteristic parameters of rock and soil masses under earthquake action, such as dynamic elastic modulus and dynamic damping ratio, also needs to be considered. These parameters are related to factors such as rock and soil mass type, density, and saturation degree.

[0140] (3) Groundwater level change scheme:

[0141] Determine parameters such as the change range and rate of the groundwater level and the permeability coefficient of the groundwater. The change range of the water level affects the effective stress and pore water pressure distribution of the slope soil mass, and thus changes the shear strength of the rock and soil mass; the change rate may affect the dynamic change process of the seepage field and the fluid-solid coupling effect of the rock and soil mass; the permeability coefficient is related to the permeability of the rock and soil mass, and different types of rock and soil masses (such as sandy soil, clay, etc.) have different permeability characteristics.

[0142] (4) Temperature change scenario:

[0143] For temperature changes, consider parameters such as the thermal expansion coefficient, thermal conductivity, and the range and rate of temperature change of the rock and soil mass. The thermal expansion coefficient determines the degree of volume expansion or contraction of the rock and soil mass during temperature changes, which may lead to a redistribution of internal stresses in the rock and soil mass; the thermal conductivity affects the propagation speed of temperature in the rock and soil mass and the distribution of the temperature field; the range and rate of temperature change are related to factors such as environmental climate conditions, the geographical location of the slope, and the presence of heat sources.

[0144] 2. Determine the distribution type and statistical characteristics of the parameters

[0145] For the parameters in each sensitivity analysis scenario, determine their probability distribution types (such as normal distribution, lognormal distribution, uniform distribution, etc.) and statistical parameters (such as mean, standard deviation, etc.) through on-site monitoring data, laboratory tests, and similar engineering experiences. For example, the peak ground acceleration may follow a lognormal distribution in some seismically active areas, and its mean and standard deviation are statistically obtained based on historical earthquake data; while the change range of the groundwater level may approximately follow a uniform distribution in a specific season and area, and its upper and lower limits can be determined according to long-term water level observation data.

[0146] 3. Construct a Copula function model

[0147] The Copula function can connect multiple univariate marginal distributions to form a joint probability distribution, thereby describing the correlation between parameters. First, based on the determined marginal distribution types and statistical characteristics, establish a univariate probability distribution model for each parameter (such as the probability density function, distribution function, etc. of the normal distribution).

[0148] Then, select a suitable Copula function family (such as Gaussian Copula, t-Copula, etc.). The selection of the Copula function family is usually based on the prior understanding of the correlation structure between parameters and the data fitting effect. For example, if the correlation between parameters is relatively linear, Gaussian Copula may be a suitable choice; if there is thick-tailed correlation, t-Copula may be more suitable.

[0149] Estimate the parameters in the Copula function using sample data or prior information. Common estimation methods include the maximum likelihood estimation method, the moment estimation method, etc. By estimating the parameters in the Copula function, a specific Copula function model is determined, thus enabling the construction of the joint probability density function of the uncertainty parameters.

[0150] For example, the following high slope strong unloading action plan is taken as an example:

[0151] Let the cohesion reduction coefficient of the rock and soil mass in the unloading zone be C r , which follows a normal distribution The depth of the unloading zone is H d , which follows a uniform distribution U(aH d , bH d ).

[0152] First, establish the univariate probability distribution functions of C r and H d :

[0153] Normal distribution probability density function:

[0154]

[0155] Uniform distribution probability density function:

[0156]

[0157] Select the Gaussian Copula function, and its general form is: C(u 1 , u 2 ) = Φ ρ (Φ -1 (u 1 ), Φ -1 (u 2 ))), where Φ ρ is the joint distribution function of the two-dimensional standard normal distribution, the correlation coefficient is ρ, Φ -1 is the quantile function of the standard normal distribution, and u 1 and u 2 are the marginal distribution function values of C r and H d respectively.

[0158] Estimate the correlation coefficient in the Gaussian Copula function through sample data. For example, use the maximum likelihood estimation method to solve for the ρ value that maximizes the likelihood function. After obtaining ρ, the joint probability density function is determined:

[0159]

[0160] where The copula function is obtained based on the Gaussian Copula function, representing the correlation structure between parameters.

[0161] Through the above implementation methods and calculation processes, the joint probability density function of uncertainty parameters is constructed for different sensitivity analysis schemes, which can more comprehensively and accurately describe the joint distribution characteristics between parameters, providing a strong foundation for subsequent slope stability analysis.

[0162] S4. Obtain the slope failure probability under each sensitivity analysis scheme and identify key uncertainty parameters;

[0163] 1. Data preparation

[0164] Collect the data of the failure sample library obtained by Monte Carlo simulation under each sensitivity analysis scheme (this data has been generated in step S2). This data includes the value combinations of each uncertainty parameter and the corresponding slope stability state (judging whether the slope fails or is stable by whether the slope stability coefficient is less than the critical value, etc.) during each simulation. Organize the data of different sensitivity analysis schemes (such as high slope strong unloading action scheme, seismic action scheme, groundwater level change scheme, temperature change scheme, etc.) respectively to ensure the accuracy and integrity of the data for subsequent targeted statistical analysis.

[0165] 2. Calculation of Sobol index based on variance

[0166] Principle brief: The Sobol index is a method used to quantify the contribution degree of each input parameter to the variance of the model output (here is the slope failure probability). It can decompose the output variance into the sum of the contributions of each parameter and their interactions, so as to evaluate the importance of the parameters. The Sobol index based on variance is divided into the first-order index and the total-order index, etc. The first-order index measures the contribution of a single parameter itself to the output variance, and the total-order index measures the contribution of this parameter and all its interactions with other parameters to the output variance.

[0167] Specific calculation steps:

[0168] Step 1: Define the model and input parameters

[0169] Regard the slope failure probability calculation model (for example, the model modified based on the limit equilibrium method combined with the influence of various uncertainty factors, and this model has been applied in the previous steps for Monte Carlo simulation) as a function Y = f(X 1 ,X 2 ,...,X n ), where Y represents the slope failure probability, and X 1 ,X 2 ,...,X nThey are various uncertainty parameters (such as strong unloading related parameters, earthquake related parameters, water level change related parameters, temperature change related parameters, etc. corresponding to different scenarios).

[0170] Step 2: Sampling and matrix generation

[0171] For each input parameter, sampling is carried out within its value range according to a suitable sampling method (such as Latin hypercube sampling, etc., to ensure the uniformity and representativeness of sampling), generating N groups of samples (N is a relatively large number, generally determined according to the calculation accuracy requirements and calculation resources, usually less than the number of Monte Carlo simulations, but also need to be large enough to ensure the accuracy of the results), forming an input matrix X with a dimension of N×n. Each row represents a set of parameter value combinations. At the same time, according to the model f, the corresponding output vector Y with a dimension of N×1 is calculated.

[0172] Step 3: Calculate Sobol indices

[0173] To calculate the first-order Sobol index, each column of the input matrix X (corresponding to each parameter) is rearranged to generate a new matrix X', keeping other columns unchanged and only shuffling the value order of the parameters in this column, so that the data distributions of X and X' are the same in other columns except the column of the parameter to be analyzed. Then, for each parameter X i (i = 1, 2,..., n), calculate the estimated value of its first-order Sobol index S i :

[0174]

[0175] where Var(Y) is the variance of the output vector Y, which can be obtained through the conventional variance calculation formula.

[0176] When calculating the total-order Sobol index, the process is relatively more complex. Usually, an efficient algorithm based on Monte Carlo simulation is adopted, such as the algorithm based on the "pick-freeze" principle, etc. The general idea is to gradually approximate the estimated value of the total-order index by calculating relevant statistics through multiple rearrangements and grouped samplings. The specific calculation process can be implemented with the help of professional statistical analysis software or by writing code by oneself. For the total-order Sobol index of the parameter X i is denoted as S Ti .

[0177] 3. Calculation of variance contribution rate

[0178] The variance contribution rate refers to the proportion of the variance of each parameter in the total variance, which is calculated as follows:

[0179] For each parameter X i, first calculate the variance of the change in the slope failure probability caused by the change in the parameter value (which can be statistically analyzed by analyzing the change in the corresponding failure probability when the parameter changes in different samples and using the variance calculation formula), denoted as Var(Y i ). Then, the variance of the total slope failure probability is denoted as Var(Y) (the total variance used in the Sobol index calculation), and the variance contribution rate C i of the parameter X i is calculated by the following formula:

[0180]

[0181] 4. Influence degree ranking

[0182] According to the calculated first-order Sobol index, total-order Sobol index, and variance contribution rate of each parameter, sort the parameters according to the numerical size respectively. Generally speaking, the larger the Sobol index or variance contribution rate of a parameter, the higher its influence degree on the slope failure probability. Considering the sorting results of the first-order and total-order Sobol indices and the variance contribution rate comprehensively, more comprehensively determine the sequence of the influence degrees of each parameter on the slope failure probability.

[0183] 5. Identify key uncertainty parameters

[0184] Based on the above influence degree ranking results, select several parameters ranked in the front (the specific number of selections can be determined according to the actual engineering situation and the required analysis accuracy, such as selecting the top 5 or the top 10, etc.) as the key uncertainty parameters affecting the slope stability and reliability. These parameters are the objects that need to be focused on and treated specifically in the subsequent optimization design process because they have a relatively significant impact on whether the slope fails.

[0185] S5. Optimize the layout and parameters of the anchor cable according to the sensitivity analysis results and the prediction model of the anchor cable anchoring force loss;

[0186] I. Establish an optimization model for the layout and parameters of the anchor cable

[0187] 1. Determine the decision variables

[0188] Set the decision variables as follows:

[0189] x 1 : The length of the anchor cable (L), and the value range is determined according to engineering experience and previous analysis, such as [L min , L max .

[0190] x 2 : The spacing of the anchor cables (S), and the value range is [S min , S max .

[0191] x 3 : The prestress of the cable anchor (P), and its value range is [P min , P max .

[0192] 2. Determine the optimization objective function

[0193] Take the maximum slope stability reliability as the main optimization objective, and at the same time consider the minimization of project cost and construction difficulty (transformed into a multi-objective optimization problem).

[0194] Slope stability reliability objective function:

[0195] Use the reliability index β to measure the slope stability reliability, and calculate it by the first-order second-moment method or other reliability calculation methods. Generally speaking, the larger the reliability index β, the higher the slope stability reliability. The objective function can be expressed as maxβ(x 1 , x 2 , x 3 );.

[0196] Project cost objective function:

[0197] The project cost is related to factors such as the length, spacing, prestress of the cable anchor, and material price. Assume that the cost per unit length of the cable anchor is C 1 , and the cost per unit prestress application is, then the project cost (here, considering that the smaller the spacing, the more cable anchors required per unit area and the higher the cost), and the objective is minC(x 1 , x 2 , x 3 ).

[0198] Construction difficulty objective function:

[0199] The construction difficulty can be measured by a comprehensive index, such as a function related to the length and spacing of the cable anchor. Let the construction difficulty index (k 1 , k 2 is the weight coefficient determined according to experience), and the objective is minD(x 1 , x 2 , x 3 ).

[0200] To transform the above multi-objective optimization problem into a single-objective optimization problem, methods such as the linear weighted method can be used. For example, construct a comprehensive objective function:

[0201] F(x 1 , x 2 , x 3 ) = ω 1 β(x 1 , x 2,x 3 ) - ω 2 C(x 1 ,x 2 ,x 3 ) - ω 3 D(x 1 ,x 2 ,x 3 );

[0202] where ω 1 , ω 2 , ω 3 are weight coefficients, determined according to the degree of emphasis of the project on stability reliability, cost, and construction difficulty, and ω 1 + ω 2 + ω 3 = 1.

[0203] 3. Determine the constraint conditions

[0204] Slope stability constraint:

[0205] The slope stability coefficient F s (x 1 ,x 2 ,x 3 ) ≥ F s,min , where F s,min is the specified minimum slope stability coefficient.

[0206] Anchor cable design parameter constraint:

[0207] L min ≤ x 1 ≤ L max , S min ≤ x 2 ≤ S max , P min ≤ x 3 ≤ P max ;

[0208] Other project constraints:

[0209] For example, the minimum distance limit between adjacent anchor cables, the length limit of the anchor cable anchorage section, etc., and determine the corresponding constraint condition expressions according to the specific project requirements.

[0210] II. Solve the optimization model using the multi - objective genetic algorithm

[0211] 1. Encoding

[0212] For the decision variables x 1 , x 2 , x 3Encoding is performed, and common encoding methods include binary encoding, real number encoding, etc. Taking real number encoding as an example, each decision variable is represented by a real number. For example, x 1 (the length of the anchor cable) is directly represented by its actual length value to form chromosome encoding.

[0213] 2. Initialize the population

[0214] Randomly generate a certain number (set as N) of initial individuals (chromosomes). Each individual represents a combination of a group of anchor cable layouts and parameters, that is, {x 1i , x 2i , x 3i} (i = 1, 2,..., N), and these individuals constitute the initial population.

[0215] 3. Fitness evaluation

[0216] Calculate the fitness value of each individual, that is, calculate the function value corresponding to each individual according to the optimization objective function F(x 1 , x 2 , x 3 ). The larger the fitness value, the better the individual.

[0217] 4. Selection operation

[0218] Adopt a suitable selection operator (such as roulette wheel selection, tournament selection, etc.) to select a part of the individuals from the current population as parent individuals for generating the next generation of individuals. The basis for selection is the fitness value of the individuals, and the individuals with higher fitness values have a greater probability of being selected.

[0219] 5. Crossover operation

[0220] Perform crossover operation on the selected parent individuals to generate new individuals. For example, for two parent individuals {x 1a , x 2a , x 3a} and {x 1b , x 2b , x 3b}, single-point crossover, multi-point crossover or uniform crossover can be used. Taking single-point crossover as an example, at a randomly determined crossover point, exchange part of the genes of the two parent individuals to obtain two offspring individuals.

[0221] 6. Mutation operation

[0222] Perform mutation operation on the offspring individuals after crossover to increase the diversity of the population. The mutation operation randomly changes a certain gene (decision variable) in the individual according to a certain mutation probability. For example, for the individual {x 1i , x 2i , x 3i} in x 1i, with a mutation probability p m Change it to x 1 ' i = x 1i + Δx 1 , where Δx 1 is a random increment determined according to the mutation range.

[0223] 7. Termination condition judgment

[0224] Repeat steps 3 - 6 until the termination condition is met. The termination condition can be reaching a predetermined number of iterations G max , or the fitness value of the optimal individual in the population has not changed significantly for several consecutive generations, etc.

[0225] 8. Obtain the Pareto optimal solution set

[0226] When the termination condition is met, the individuals in the population are the optimization results, and the cable anchor layouts and parameter combinations corresponding to these individuals constitute the Pareto optimal solution set. From the Pareto optimal solution set, select a suitable solution according to the actual engineering requirements and the decision - maker's preferences as the final cable anchor layout and parameter optimization scheme.

[0227] III. Select the prediction model for the time - dependent loss of cable anchor anchoring force and determine the model parameters

[0228] 1. Select the prediction model

[0229] Select a comprehensive model considering cable anchor steel relaxation, creep of rock and soil mass, and degradation of bond performance in the anchorage section. For example, the change of cable anchor anchoring force T(t) with time t can be represented by a model in the following form:

[0230] T(t) = T 0 ×(1 - R(t))×(1 - C(t))×(1 - B(t));

[0231] where, T 0 is the initial cable anchor anchoring force; R(t) is the cable anchor steel relaxation function, which can be obtained by fitting the cable anchor steel relaxation test data. For example, use the exponential decay function R(t) = αe -βt (α, β are fitting parameters); C(t) is the creep function of rock and soil mass, which can be determined based on the creep constitutive model of rock and soil mass. For example, use the power function C(t) = γt δ (γ, δ are parameters related to the properties of rock and soil mass); B(t) is the degradation function of bond performance in the anchorage section, which can be determined according to the force analysis and test data of the anchorage section. For example, use the linear decay function B(t) = εt (ε is a parameter related to the bond performance between the anchoring material and rock and soil mass).

[0232] 2. Determine the model parameters

[0233] Relaxation parameters α, β of the anchor cable steel:

[0234] By conducting relaxation tests on the anchor cable steel, measuring the stress relaxation values at different times, and then using fitting methods such as the least squares method to determine the values of α and β, so that the error between the fitting curve and the test data is minimized.

[0235] Creep parameters γ, δ of the rock and soil mass:

[0236] Conduct creep tests on the rock and soil mass to obtain the curves of creep strain of the rock and soil mass varying with time at different stress levels. According to the selected form of the creep function of the rock and soil mass, use the test data to fit and determine the γ and δ parameters.

[0237] Degradation parameter ε of the bonding performance of the anchorage section:

[0238] By conducting pull-out tests or long-term monitoring on the anchorage section, analyzing the attenuation of the anchoring force over time, and combining with the selected form of the degradation function of the bonding performance of the anchorage section, determine the value of ε.

[0239] IV. Formulate measures for compensating the anchor cable anchoring force

[0240] 1. Determine the compensation timing

[0241] According to the curve of the anchoring force varying with time calculated by the prediction model of the time-dependent loss of the anchor cable anchoring force, set an anchoring force threshold T th . When the predicted anchor cable anchoring force T(t) drops below T th , the timing t for compensating the anchoring force is reached c .

[0242] t c = min{t|T(t) < T th};

[0243] 2. Calculate the compensation amount

[0244] Calculating the compensation amount ΔT needs to consider making the slope reach or approach the stable reliability required by the design again. First, according to the current slope state (including changes in rock and soil mass parameters, existing anchor cable anchoring forces, etc.), use the slope stability analysis method to calculate the minimum increase in the anchoring force ΔT required to meet the requirements of the slope stable reliability min . Then, consider a certain safety reserve coefficient k s (generally k s > 1), and the compensation amount ΔT = k s ΔT min .

[0245] Through the above implementation methods and calculation processes, it is possible to optimize the layout and parameters of the anchor cables according to the sensitivity analysis results and the prediction model of the anchor cable anchoring force loss, and formulate corresponding anchoring force compensation measures to improve the long-term stability and reliability of the slope, while taking into account factors such as project cost and construction difficulty. In actual projects, it is necessary to further adjust and improve the model and parameters according to specific engineering geological conditions, engineering requirements, and monitoring data, etc.

[0246] S6. Compare the calculation results of the optimized design scheme with the monitored values, and conduct monitoring early warning and guide the time of anchoring force compensation;

[0247] I. Establish a monitoring index system and data collection

[0248] 1. Determine the monitoring indexes

[0249] The overall anchoring force of the prestressed anchor cable: Directly measure the tension borne by the anchor cable through equipment such as an anchor cable load cell, which reflects the effect of the anchor cable on the slope anchoring.

[0250] The stress of the anchor cable: Install stress sensors at different parts of the anchor cable to measure the stress distribution of the anchor cable during the stress process, which helps to understand the change of the internal stress state of the anchor cable.

[0251] The strain of the anchor cable: Measure the strain of the anchor cable using strain gauges or fiber Bragg grating sensors, etc. Combining with stress monitoring, it can further analyze the change of the mechanical properties of the anchor cable and the interaction relationship with the rock and soil mass.

[0252] The displacement of the rock and soil mass: Use instruments such as total station, GPS or displacement meter to monitor the displacement changes of the slope rock and soil mass at different positions, including horizontal displacement and vertical displacement, to judge the overall deformation trend of the slope.

[0253] The pore water pressure: Install a pore water pressure gauge in the slope rock and soil mass to measure the magnitude and change of the pore water pressure, because the pore water pressure has an important impact on the strength and stability of the rock and soil mass.

[0254] 2. Install monitoring equipment and data collection system

[0255] Install the above-mentioned monitoring equipment at the key parts of the slope (such as the slope top, slope surface, slope toe, and anchor cable installation positions, etc.) according to the corresponding specifications and technical requirements. Connect these monitoring equipment to the data processing center through wired or wireless transmission methods, establish an automated data collection system, set an appropriate data collection frequency (for example, collect once per hour or adjust according to the stability status of the slope and engineering requirements), and collect the data of each monitoring index in real time and store it in the database.

[0256] II. Use data mining and machine learning technologies for data analysis

[0257] 1. Data preprocessing

[0258] Data cleaning: Clean the collected original monitoring data, removing outliers (such as obvious incorrect data caused by equipment failures, electromagnetic interference, etc.) and missing values. Statistical analysis-based methods (such as setting a reasonable range for the data, and considering data outside the range as outliers) and data interpolation methods (such as linear interpolation, spline interpolation, etc.) can be used to handle missing values.

[0259] Data standardization: To facilitate comparison between data of different monitoring indicators and subsequent data analysis and processing, standardize the cleaned data. Common standardization methods include normalization (mapping the data to the [0,1] interval) and standardization (making the data have zero mean and unit variance), etc. For example, for a certain monitoring indicator x, the normalization formula is where x min and x max are the minimum and maximum values of the data for this indicator respectively.

[0260] 2. Construct a data analysis model

[0261] Select a suitable machine learning algorithm: For example, time series analysis algorithms (such as ARIMA model, LSTM neural network, etc.) can be used to model and predict the time-varying sequence data of each monitoring indicator. Taking the LSTM neural network as an example, it can effectively learn the long-term dependence relationship of the data and is suitable for processing time-series monitoring data.

[0262] Model training: Divide the historical monitoring data (after preprocessing) into a training set and a validation set, and use the training set to train the selected machine learning model, adjusting the model parameters (such as the number of layers, number of neurons, learning rate, etc. of the LSTM network) to optimize the performance of the model. During the training process, evaluate the accuracy and generalization ability of the model through the validation set. For example, metrics such as mean squared error (MSE), mean absolute error (MAE), etc. are used to measure the error between the predicted value and the true value of the model.

[0263] 3. Comparative analysis and setting of abnormal judgment criteria

[0264] Use the trained model to predict each monitoring indicator, obtaining the curves of each monitoring indicator changing with time (prediction curves) calculated by the optimized design scheme. At the same time, draw the fitting curve of the actual monitoring values based on the real-time collected monitoring data.

[0265] Set abnormal phenomenon judgment criteria: By analyzing historical data and engineering experience, determine the normal change range and change trend of each monitoring index. For example, for the displacement of rock and soil mass, if the displacement suddenly increases within a certain period and exceeds the set threshold (such as the daily displacement exceeds 5 mm and shows an accelerating growth trend for several consecutive days), it is determined as abnormal; for the anchoring force of the cable anchor, if its decline rate exceeds the expected normal decay rate (determined according to the prediction model of cable anchor force loss) and is lower than the set safe anchoring force value, it is also determined as abnormal. Set different warning levels according to the severity of the abnormality, such as general warning, severe warning, etc.

[0266] III. Monitoring Warning and Anchoring Force Compensation Operation Guide

[0267] 1. Monitoring Warning

[0268] Real-time monitoring and judgment: The data processing center receives the newly collected monitoring data in real time, inputs it into the trained data analysis model for prediction, and conducts comparative analysis with the fitting curve of the actual monitoring value. Once it is found that the monitoring data meets the conditions of a certain warning level in the abnormal judgment criteria, the warning mechanism is immediately triggered.

[0269] Warning information release: According to the warning level, timely release warning information to relevant personnel (including project management personnel, technical personnel, on-site construction personnel, etc.) through various methods (such as SMS notification, system pop-up alarm, on-site sound and light alarm, etc.). The warning information should include abnormal monitoring indicators, location of abnormality, warning level, and possible risk tips, etc.

[0270] 2. Calculation and Operation Guide for Anchoring Force Compensation Time and Compensation Quantity

[0271] When the monitoring data shows abnormality and triggers a warning, calculate according to the cable anchor force loss prediction model and the pre-developed compensation measures. First, according to the current monitoring data (such as displacement of rock and soil mass, pore water pressure, cable anchor force, etc.) and the actual situation of the slope, use the cable anchor force loss prediction model to calculate the actual loss of the current cable anchor force and the required compensation quantity ΔT according to the slope stability requirements. The calculation method is as described in step S5.

[0272] Determine the compensation time: According to the change curve of the cable anchor force over time and the set anchoring force threshold T th , calculate the reasonable anchoring force compensation time t c , that is, the time point when the predicted cable anchor force T(t) drops below T th . The calculation method is the same as step S5.

[0273] Operation guide: The calculated anchoring force compensation time t cThe information of the sum of compensation and ΔT is promptly conveyed to the on-site construction personnel, who, according to the requirements, at the time of the arrival of the compensation time t c carry out the anchoring force compensation operation on the anchor cable by using a suitable anchor cable prestress application device, with the compensation amount being ΔT, to ensure the long-term safe and stable operation of the high slope anchoring project. After the compensation operation is completed, continue to monitor the slope, observe the changes in each monitoring index, evaluate the effect of the compensation operation, and adjust the subsequent monitoring and maintenance strategies as needed.

[0274] Through the above complete implementation methods and calculation processes, the monitoring and early warning of the high slope anchoring project and the guidance of the anchoring force compensation operation can be effectively achieved, timely discovering and handling the potential safety hazards of the slope, and ensuring the long-term stability and safety of the project. In practical applications, it is necessary to continuously optimize and improve the monitoring index system, data analysis model, warning judgment criteria, etc. according to the actual situation of the project and the feedback of the monitoring data.

Claims

1. The optimization design method of slope anchor support based on global sensitivity analysis is characterized by: The steps include: S1. Establish a sensitivity analysis model for slope anchor support and determine model parameters; S2. Using Monte Carlo simulation method to obtain slope failure probability and failure samples; S3. Design multiple sensitivity analysis schemes and construct the joint probability density function of uncertainty parameters; S4, obtain the slope failure probability under each sensitivity analysis scheme and identify the key uncertainty parameters; S5. Optimize the layout and parameters of anchor cables based on the sensitivity analysis results and the anchor force loss prediction model; S6. Compare the calculation results of the optimized design scheme with the monitoring values ​​and conduct monitoring and early warning, and optimize through anchor cable anchoring force compensation measures.

2. The slope anchor cable support optimization design method based on global sensitivity analysis according to claim 1 is characterized in that: The sensitivity analysis model of the slope anchor cable support includes a slope stability coefficient calculation model and a sensitivity analysis index calculation model; the slope stability coefficient calculation model is to calculate the slope stability coefficient by using the simplified Bishop method in the limit equilibrium method, and at the same time consider the calculation formula of the anchor cable anti-sliding force under the action of the anchor cable support to obtain the slope stability coefficient calculation formula; The sensitivity analysis index calculation model measures the sensitivity of parameters by using relative sensitivity index. During the calculation, only one parameter value is changed each time, and other parameters remain unchanged. By comparing the change of slope stability coefficient before and after the parameter change, the relative sensitivity index of the parameter is calculated, and then the parameter set affecting slope stability is determined.

3. The slope anchor cable support optimization design method based on global sensitivity analysis according to claim 1 is characterized in that: The S2 specifically includes the following steps: S21, determining a value range and a distribution type based on the parameter set affecting slope stability and setting them as random variables; S22. Reasonably determine the number of simulations of the Monte Carlo simulation technology based on relevant factors; S23, constructing the anchor body rheological model and the Xiyuan rock and soil rheological model respectively, and combining the anchor body rheological model and the Xiyuan rock and soil rheological model in parallel under the same stress state to obtain the anchor force loss calculation model of the anchor cable; wherein the total anchor force loss is the sum of the anchor force losses generated by the two respectively; S24, using the same input parameters as input, respectively calculating the anchoring force loss and the corresponding deformation of the rock and soil mass and anchor cable through the rheological model of S23 and other mature rheological models, and comparing them with the actual engineering monitoring data; if the comparison difference is greater than the set threshold, adjusting the parameters of the rheological model; S25, based on the parameter set affecting slope stability, random numbers are generated and assigned according to their respective distribution types, and the parameter values ​​obtained by simulation are respectively substituted into the slope stability coefficient calculation model and the anchor cable anchoring force loss calculation model to obtain calculation results, and the calculation results are compared with the user-defined critical stability value. If the result is less than the user-defined critical stability value, it is determined that the slope is in a failed state at this time; if the result is greater than or equal to the user-defined critical stability value, it is determined that the slope is in a stable state; S26. Based on the simulation method of S25 and the number of simulations, a computer program is used to perform cyclic simulations, and all parameter combinations of each simulation and the corresponding slope stability state are recorded in detail to build a failure sample library.

4. The slope anchor cable support optimization design method based on global sensitivity analysis according to claim 3 is characterized in that: The slope stability coefficient calculation model is specifically expressed as: Where: n is the number of soil strips; c i is the cohesion of the i-th soil strip; b i is the width of the i-th soil strip; W i is the gravity of the i-th soil strip; u i is the pore water pressure at the bottom of the i-th soil strip; is the internal friction angle of the i-th soil strip; φ i is the inclination angle of the bottom surface of the i-th soil strip.

5. The slope anchor cable support optimization design method based on global sensitivity analysis according to claim 1 is characterized in that: The S3 specifically includes the following steps: S31. Determine the sensitivity analysis scheme by considering the high slope strong unloading scheme, earthquake action scheme, groundwater level change scheme, groundwater level change scheme and temperature change scheme; S32. For each parameter in the sensitivity analysis scheme, determine its probability distribution type through field monitoring data, laboratory tests and similar engineering experience; S33. According to the probability distribution type and statistical characteristics, a univariate probability distribution model for each parameter is established, an appropriate Copula function family is selected, and the parameters in the Copula function are obtained by estimation, and a specific Copula function model is determined, thereby constructing a joint probability density function of the uncertainty parameters.

6. The slope anchor cable support optimization design method based on global sensitivity analysis according to claim 1 is characterized in that: Based on the failure sample library data, the Monte Carlo simulation results under each sensitivity analysis scheme were statistically analyzed, the sensitivity coefficient and variance contribution rate of each parameter were calculated, and the ranking of the influence of each parameter on the slope failure probability was determined. According to the sensitivity analysis results, the key uncertainty parameters affecting the reliability of slope stability were clarified.

7. The slope anchor cable support optimization design method based on global sensitivity analysis according to claim 6 is characterized in that: The sensitivity coefficient includes a Sobol index based on variance, wherein the Sobol index based on variance is divided into a first-order index and a total-order index; the variance contribution rate refers to the proportion of the variance of each parameter to the total variance, wherein, for each parameter, the variance of the change in slope failure probability caused by the change in the parameter value is calculated, and the corresponding change in failure probability when the parameter changes in different samples is analyzed, and the variance calculation formula is used for statistics.

8. The slope anchor cable support optimization design method based on global sensitivity analysis according to claim 1 is characterized in that: The S5 specifically includes the following steps: S51. Determine the decision variables, and take the maximum slope stability reliability as the main optimization goal, while considering the minimization of engineering cost and construction difficulty, and use the linear weighted method to construct the objective function of the anchor cable anchoring force loss prediction model; S52. Determine constraints, including slope stability constraints, anchor cable design parameter constraints, and other engineering constraints; S53, using a multi-objective genetic algorithm to solve the anchor cable anchorage force loss prediction model, obtain the optimization result and select the optimization result as the final anchor cable layout and parameter optimization solution according to the actual needs of the project and the decision maker's preferences; S54. Select a prediction model for the time-dependent loss of anchoring force of anchor cables and determine the model parameters. According to the curve of anchoring force variation over time obtained by the prediction model for the time-dependent loss of anchoring force of anchor cables, set the anchoring force threshold and formulate compensation measures for the anchoring force of anchor cables.

9. The slope anchor cable support optimization design method based on global sensitivity analysis according to claim 8 is characterized in that: The objective function of the anchor cable anchoring force loss prediction model is specifically expressed as: F(x1,x2,x3)=ω1β(x1,x2,x3)-ω2C(x1,x2,x3)-ω3D(x1,x2,x3); Among them, ω1, ω2, ω3 are weight coefficients, which are determined according to the project's emphasis on stability and reliability, cost and construction difficulty, and ω1+ω2+ω3=1.

10. The slope anchor cable support optimization design method based on global sensitivity analysis according to claim 1, characterized in that: The S6 specifically includes: establishing a monitoring indicator system, collecting monitoring data in real time and applying data mining and machine learning techniques to perform real-time analysis and processing of the monitoring data, comparing the curves of each monitoring indicator changing with time obtained by the optimization design scheme with the fitting curve of the actual monitoring value, and setting clear abnormal phenomenon judgment standards and warning levels; when the monitoring data is abnormal, an alarm is issued in time according to the warning level, and the anchoring force compensation time and compensation amount are calculated based on the anchor cable anchoring force loss prediction model and compensation measures.

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