A green material slope protection scheme configuration method based on random field theory

Abstract

The application provides a green material slope protection scheme configuration method based on a random field theory, which quantifies the space-time variability of material parameters through layered modeling (ecological concrete, plant root system, graded broken stone and undisturbed soil). The parameters of the protection layer (shear strength, permeability coefficient and the like) are calibrated by adopting a logarithmic normal and Beta distribution, and the root system parameters of the reinforced layer are modeled by kernel density estimation and Bayesian updating, and the performance attenuation of the ecological concrete and the dynamic effects of the root system growth and decay are represented in combination with the space-time coupling random field. Based on Monte Carlo simulation and improved Bishop method, a double failure mode of shallow layer (root system reinforcement) and deep layer sliding is established, the joint failure probability is calculated by using a Copula function, and the dominant failure mechanism is identified. The material parameter threshold and space-time correlation length are optimized by using an NSGA-II algorithm, and a Pareto optimal scheme considering safety and ecological benefits is screened by combining TOPSIS decision.

Description

Technical Field

[0001] This invention relates to a green material slope protection scheme configuration method based on random field theory, belonging to the field of green slope engineering technology. Background Technology

[0002] In geotechnical engineering, the design of slope protection structures has long relied on deterministic analysis methods, the core of which is to assess slope stability through safety factors. However, these methods neglect two key scientific issues: the spatial variability and time dependence of material parameters. The physical parameters of slope protection materials (such as the shear strength of concrete and the mechanical properties of plant roots) are affected by geological conditions and environmental factors, exhibiting significant spatial non-uniformity. Traditional methods use fixed parameter mean values ​​or empirical reduction coefficients, leading to calculation results that deviate from actual working conditions. Furthermore, existing slope protection models often assume that material properties are time-invariant, but the carbonation decay of ecological concrete and the growth-decay cycle of plant roots can cause dynamic evolution of mechanical properties. These time-varying characteristics have not been fully quantified in existing design specifications. More seriously, traditional methods only consider a single failure mode (such as circular slip), while in actual engineering, multiple modes such as shallow slip and deep instability coexist and are strongly correlated. Ignoring the multi-mode coupling effect may lead to an underestimation of safety hazards. Therefore, there is an urgent need for a probabilistic analysis method for slope protection that integrates spatiotemporal variability and multi-mode coupling.

[0003] With the promotion of green building concepts, eco-friendly concrete and plant root reinforcement technology have been widely applied in slope protection projects, but their complexity poses new challenges to traditional design theories. Firstly, the shear strength of plant roots (…) ) and tensile strength ( The root system exhibits a highly non-Gaussian distribution, influenced by species, soil conditions, and growth stage. Existing studies often assume that root parameters follow a normal or Weibull distribution, but measured data show that their distribution often exhibits multimodality (due to differences in root strength at different depths) and truncation (limited by soil carrying capacity). Simple parameterization assumptions will lead to biases in reliability analysis.

[0004] Secondly, the permeability and porosity of eco-concrete exhibit strong spatial autocorrelation, and their statistical characteristics require modeling using random field theory. However, existing methods often employ stationary covariance functions, which struggle to characterize the layered non-stationary characteristics caused by variations in construction techniques in actual engineering projects. Furthermore, there is an inherent contradiction between the ecological benefits of green materials (such as vegetation coverage) and engineering costs (material usage), but existing optimization methods often employ single-objective weighting methods, lacking the ability to generate multi-objective equilibrium solution sets based on Pareto fronts. In summary, green slope protection design needs to overcome three major bottlenecks: non-Gaussian parameter modeling, non-stationary random field representation, and multi-objective collaborative optimization.

[0005] In recent years, probabilistic analysis methods have been gradually applied in geotechnical engineering, but limitations still exist. On the one hand, while Monte Carlo simulations combined with random fields can quantify the spatial variability of parameters, their computational efficiency is low, and they do not consider the time-varying characteristics of parameters. To address the coupling effect between plant roots and concrete performance degradation, a non-stationary spatiotemporal random field model needs to be constructed, but existing studies often handle time and spatial dimensions independently, leading to a disconnect between the model and the actual physical mechanism. On the other hand, dynamic reliability theory improves assessment accuracy through time-varying failure threshold updates, but its threshold weights (such as the contributions of displacement and pore water pressure) rely on empirical settings and lack an adaptive adjustment mechanism based on monitoring data. Furthermore, in multi-failure mode analysis, traditional methods assume that modes are independent, while in reality, shallow and deep slippage exhibit nonlinear correlations (such as the chain reaction triggered by soil strain softening).

[0006] In summary, proposing a green material slope protection scheme configuration method based on random field theory has significant engineering implications. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and provide a green material slope protection scheme configuration method based on random field theory, which can take into account both safety and ecological benefits.

[0008] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0009] In a first aspect, the present invention provides a method for configuring a green material slope protection scheme based on random field theory, comprising:

[0010] Step 1: Obtain the material parameters of the slope protection structure, and perform layered random field modeling based on the material parameters to quantify the spatiotemporal variability of the parameters in each layer;

[0011] Step 2: For the parameters of the guard layer in the random field, use log-normal and Beta distributions to calibrate and update the random field of the guard layer;

[0012] Step 3: Update the random field of the reinforcement layer by kernel density estimation and Bayesian method for the root system parameters of the reinforcement layer in the random field;

[0013] Step 4: Introduce a time-varying function into the random field and construct a non-stationary spatiotemporally coupled random field model based on the combined effect of concrete and plant roots;

[0014] Step 5: Establish a dual-index verification based on safety factor and failure probability, embed the non-stationary spatiotemporal coupled random field model into the Monte Carlo sampling process, perform spatiotemporal joint numerical simulation, and construct a time-varying reliability index.

[0015] Step 6: Based on the time-varying reliability index, establish a dual-mode criterion for deep and shallow potential sliding surfaces, and calculate the joint failure probability;

[0016] Step 7: Based on the joint failure probability, optimize the material parameter threshold and spatiotemporal correlation length using the NSGA-II algorithm, and combine TOPSIS decision screening to select the Pareto optimal solution that balances safety and ecological benefits, thus obtaining the optimal configuration of the slope protection scheme that balances safety and ecological benefits.

[0017] Further, step 1: Obtain the material parameters of the slope protection structure, and perform layered random field modeling based on the material parameters to quantify the spatiotemporal variability of the parameters in each layer, including:

[0018] Obtain slope protection structure parameters; based on the slope protection structure parameters, divide the slope protection structure into multiple layers according to the materials and identify the key parameters of each layer of materials; and define the key parameters of each layer of materials as random fields.

[0019] Key parameters of the material include concrete shear strength. Permeability coefficient Porosity Shear strength of plant roots Root tensile strength and the shear strength parameters of the soil; the shear strength parameters of the soil include cohesion. internal friction angle .

[0020] Furthermore, the slope protection structure is divided into multiple layers based on the materials used, and the key parameters of each layer are identified. The key parameters of each layer are defined as random fields, including:

[0021] Based on the main materials, the slope protection structure is divided into the following multiple layers:

[0022] Protective layer: eco-friendly concrete;

[0023] Reinforcing layer: plant roots;

[0024] Transition layer: graded crushed stone;

[0025] Base soil layer: undisturbed soil;

[0026] The key parameters of the following material layers are defined as spatial random fields:

[0027] Protective layer: concrete shear strength Permeability coefficient Porosity ;

[0028] Reinforcement layer: Root shear strength ,tensile strength Cohesion internal friction angle Permeability coefficient Porosity ;

[0029] Transition layer: Gradient size distribution of crushed stone;

[0030] Subgrade layer: Subgrade soil density.

[0031] The thickness of the protective layer of ecological concrete, the root distribution density of the reinforced layer, the particle size distribution of the graded crushed stone in the transition layer, and the compaction of the original soil in the subgrade layer are used as boundary conditions of the random field. The spatial interpolation and parameter assignment of the layered random field parameters are realized by the three-dimensional finite difference grid discretization method.

[0032] The Kriging interpolation algorithm is used to assign spatial parameters to the layer parameters to ensure a smooth transition of parameters between adjacent layers.

[0033] Further, step 2: For the shielding parameters in the random field, the shielding random field is updated using log-normal and Beta distribution calibration, including:

[0034] concrete shear strength Permeability coefficient Labeled as random variables with log-normal statistical characteristics, the maximum likelihood estimation method was used to determine the values ​​based on field borehole sampling and indoor triaxial test data. mean with standard deviation ;

[0035] porosity The variables are labeled as random variables with a Beta distribution, and the Beta distribution parameters are corrected using ground-penetrating radar inversion data. , To characterize porosity Spatial cutoff distribution characteristics;

[0036] Considering the spatial autocorrelation characteristics and spatial distribution features of the three parameters, an exponential covariance function is used to quantify the spatial variation range of these three parameters and determine the spatial correlation length of the key parameters of the protective layer. Range of values.

[0037] Further, step 3: For the root system parameters of the reinforcement layer in the random field, update the random field of the reinforcement layer using kernel density estimation and Bayesian methods, including:

[0038] Shear strength of plant roots in soil after reinforcement Root tensile strength Cohesion of soil internal friction angle Permeability coefficient Porosity Kernel density estimation and Bayesian update methods were used to define the spatial variation range of these parameters and determine the spatial correlation length of the soil after the plant roots were mixed with the slope soil. .

[0039] Further, step 4: Introduce a time-varying function into the random field, and construct a non-stationary spatiotemporally coupled random field model based on the combined effect of concrete and plant roots, including:

[0040] Based on the time-varying properties of ecological concrete materials and the growth-decay cycle of plant roots, a time-varying function is introduced and a non-stationary spatiotemporally coupled random field model is constructed.

[0041] Among them, the performance degradation of ecological concrete:

[0042]

[0043] Let t be the initial strength, e be the time parameter, and a, b, and c be the exponential function parameters. The strength is calibrated through accelerated aging tests. The calibration method is as follows: place the specimen in a high-temperature and high-humidity environment, measure the strength decay curve periodically, and fit the exponential function parameters.

[0044] Root growth-decay model:

[0045]

[0046] in, d represents the initial intensity, and d represents the growth amplitude. The growth angle frequency, Let m be the initial phase angle, m be the baseline value of root strength, and t be the time variable;

[0047] Combining the time evolution function with a spatial random field forms a non-stationary spatiotemporal sample:

[0048]

[0049] Where X(x,t) represents the material parameter values ​​at spatial location x and time t, X space (x) represents the spatial random field component, X time (t) represents the time-varying function component.

[0050] Further, step 5: Establish a dual-index verification based on the safety factor and failure probability, embed the non-stationary spatiotemporally coupled random field model into the Monte Carlo sampling process, perform spatiotemporal joint numerical simulation, and construct a time-varying reliability index, including:

[0051] Based on the constructed non-stationary spatiotemporally coupled random field model, spatiotemporal random field samples are generated using the Karhunen-Loève (KL) expansion. Material parameters are decomposed into deterministic time-varying functions and random field components:

[0052]

[0053] in, is the shear strength of concrete at spatial location x and time t, is the output value of the spatiotemporally coupled random field, and f(t) is the time-varying decay function. The eigenvalues ​​of the covariance function Let them be independent standard Gaussian random variables. Let M be the characteristic function of the covariance function, and M be the cutoff order of the KL expansion.

[0054] For each Monte Carlo sample, calculate the safety factor using the following steps:

[0055] Slope discretization: The potential sliding body is divided into n vertical strips, where the width of strip i is b. i Bottom slope angle α i ,

[0056] Parameter assignment: Extract material parameters for each block from the random field;

[0057] Iterative solution of FS: Solving the Bishop equation using the Newton-Raphson iterative method:

[0058]

[0059] Where FS is the safety factor, and c i W represents the cohesion of the i-th soil strip. i Let u be the weight of the i-th soil strip. i Let b be the pore water pressure at the bottom of the i-th soil strip. i Let φ be the width of the i-th soil strip. i Let T be the internal friction angle of the i-th soil strip. r,i α contributes to the tensile strength of the root system in the soil strip. i Let be the inclination angle of the sliding surface at the bottom of the i-th soil strip;

[0060] Define dynamic failure threshold :

[0061]

[0062] in, This is a dynamic failure threshold (a critical value for the safety factor that is adjusted in real time based on monitoring data). The initial threshold (such as the static threshold of 1.35 required by the specification). This is the sensitivity coefficient (range 0~1). To correct the steepness (default 3). For displacement rate, The maximum allowable displacement rate.

[0063] Failure probability calculation is optimized using importance sampling method:

[0064]

[0065] in, Let I be the time-varying failure probability, and let I(.) be the indicator function, which takes the value 1 when the condition is met and 0 otherwise. For the original distribution, For biased distribution, For the random variable samples in the i-th sampling, construct a time-varying reliability index:

[0066]

[0067] Where R(t) is the reliability index, σ is the inverse function of the standard normal distribution. FS and μ FS These are the standard deviation and mean of the safety factor, respectively.

[0068] Further, step 6: Based on time-varying reliability indices, establish a dual-mode criterion for deep and shallow potential sliding surfaces, and calculate the joint failure probability, including:

[0069] For the protective and reinforcing layers, the potential sliding surface depth is defined as 0.5~1.5m. In the Bishop method safety factor calculation, the root tensile strength is taken into account. Equivalent to an additional shear strength increment:

[0070]

[0071] in, For effective shear strength, c2 is the cohesion of the reinforced soil layer. For root tensile strength, Root distribution density, Angle A is the angle between the root system and the sliding surface. slip The area of ​​the sliding surface unit;

[0072] Shallow safety factor FS S Solve iteratively using the improved Bishop equation:

[0073]

[0074] Among them, FS S For shallow sliding safety factor, b iW is the width of the i-th soil strip. i Let u be the weight of the i-th soil strip. i φ is the pore water pressure at the bottom of the i-th soil strip, φ2 is the internal friction angle of the reinforced soil layer, and α is the pore water pressure at the bottom of the i-th soil strip. i Let be the inclination angle of the sliding surface at the bottom of the i-th soil strip;

[0075] The potential sliding surface penetrates the subgrade layer; the safety factor FS is calculated using the standard Bishop method. D Its shear strength parameters internal friction angle The permeability coefficient is affected by the spatial variability of the graded crushed stone in the transition layer. Parameters are assigned using non-stationary random fields.

[0076] Shallow and deep failure probabilities (FS) S and FS D Its marginal distribution function is:

[0077]

[0078]

[0079] Where, μ FS ,σ FS For the mean and standard deviation of the safety factor, FS cr S =1.25, FS cr D =1.35 is the dynamic failure threshold.

[0080] Constructing the joint failure probability based on the linear correlation coefficient ρ :

[0081]

[0082] in, , These represent the failure probabilities of the shallow sliding mode and the deep circular sliding mode, respectively. The cumulative distribution function of the standard normal distribution. The quantile function of the standard normal distribution. The linear correlation coefficient between the two failure modes is given. The function is a bivariate standard normal joint distribution function, and the correlation coefficient is... .

[0083] Furthermore, based on the joint failure probability and the dominant failure mechanism, the material parameter thresholds and spatiotemporal correlation length are optimized using the NSGA-II algorithm. Combined with TOPSIS decision screening, a Pareto optimal solution balancing safety and ecological benefits is obtained, resulting in the optimal configuration of the slope protection scheme that balances safety and ecological benefits, including:

[0084] The inverse of the failure probability is the optimization objective set.

[0085] The design variables are the threshold values ​​of material parameters for each layer, the spatial correlation length, and the time-varying function coefficients.

[0086] Constraints are constructed by combining time-varying reliability indices and joint failure probabilities.

[0087] Based on the NSGA-II multi-objective optimization algorithm, Latin hypercube sampling is used to generate the initial population, and an elite retention strategy and adaptive crossover mutation operator are introduced to improve the convergence of the Pareto front.

[0088] Based on the TOPSIS decision-making method, the target weight is determined by the entropy weight method. Combined with the equilibrium solution quantified by the fuzzy membership function, the optimal configuration of the slope protection scheme that meets the stability requirements of both shallow and deep modes is selected, thus obtaining the optimal configuration of the slope protection scheme that takes into account both safety and ecological benefits.

[0089] Furthermore, based on the joint failure probability and the dominant failure mechanism, the material parameter thresholds and spatiotemporal correlation length are optimized using the NSGA-II algorithm. Combined with TOPSIS decision screening, a Pareto optimal solution balancing safety and ecological benefits is obtained, resulting in the optimal configuration of the slope protection scheme that balances safety and ecological benefits, including:

[0090] Design variable set:

[0091] Material parameter thresholds: Lower limit of shear strength of protective layer ecological concrete Tensile strength threshold of plant roots Foundation soil density ,

[0092] Spatial related length: , ;

[0093] Time-varying function coefficients: decay parameters (a, b, c) and root growth parameters (d, ω). m);

[0094] Using the reciprocal of the failure probability as a safety metric, we construct a bi-objective optimization problem:

[0095] Objective 1: max( (reciprocal of shallow failure probability), Target 2: max( (reciprocal of the probability of deep failure)

[0096] Based on the time-varying reliability index R(t) in step 6, the minimum value must not be lower than the threshold throughout the entire lifecycle:

[0097] (R)min =3.0 (as required by the specification).

[0098] Latin hypercube sampling (LHS) is used to uniformly generate N variables within the design variable space. pop There are 1 individual, and each individual corresponds to a set of design variable combinations x. i (x( , ,a, )).

[0099] For each individual, perform the following process (accelerated by parallel computing): generate non-stationary spatiotemporal random field samples, update the spatiotemporal distribution of material parameters, and perform Monte Carlo simulation calculations. , And R(t), solve for the joint failure probability And the Sobol index.

[0100] Individuals are stratified according to their objective function values, with priority given to retaining solutions at higher dominance levels. The distribution density of solutions within the same level is calculated to avoid local convergence.

[0101]

[0102] in, Let be the crowding distance of the i-th individual, which measures the sparsity of the solution distribution in the target space. Let m be the value of the i-th individual for the m-th objective. Let be the maximum and minimum values ​​of the m-th target in the population.

[0103] The first N will be retained. elite From elite individuals to the next generation, simulated binary crossover (SBX) and polynomial mutation are used to adaptively adjust operator probabilities:

[0104]

[0105]

[0106] Where, p c p is the crossover probability. m Here, is the mutation probability, gen is the current generation, and maxGen is the maximum generation. The number of design variables.

[0107] frontier solution set Normalize the target value:

[0108]

[0109] in, Let m be the normalized target value, ranging from [0,1]. This is the original target value;

[0110] Calculate the information entropy of target m and assign weights accordingly:

[0111]

[0112] Among them, E m Let the information entropy of the m-th target be [0,1]. The number of Pareto front solutions.

[0113] Weighting:

[0114]

[0115] Among them, w m E represents the weight of the m-th objective. m Information entropy of the m-th target

[0116] Finally, calculate the positive ideal solution f. + and negative ideal solution f - :

[0117] ,

[0118] Calculate proximity:

[0119] ,

[0120] in, Let i be the proximity of the i-th solution. To find the Euclidean distance to the positive ideal solution, To find the Euclidean distance to the negative ideal solution, The target weight is determined by the entropy weight method.

[0121] Select The largest solution is taken as the optimal configuration, thus obtaining the optimal configuration of the slope protection scheme that takes into account both safety and ecological benefits.

[0122] Secondly, the present invention provides a green slope protection probability analysis device based on random field theory, including a processor and a storage medium;

[0123] The storage medium is used to store instructions;

[0124] The processor is configured to operate according to the instructions to perform the steps of the method according to the first aspect.

[0125] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0126] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0127] (1) By constructing a hierarchical random field model, the spatial autocorrelation characteristics of each layer of materials (ecological concrete, root system, foundation soil, etc.) are quantified, and a time-varying function is introduced to describe the aging of materials and the growth-decay cycle of the root system. This achieves non-stationary spatiotemporal coupling modeling, significantly improves the accuracy of long-term stability analysis, and is more in line with the dynamic evolution law of material properties in actual engineering.

[0128] (2) Establish shallow-deep dual-mode criteria, combine the joint failure probability model (Copula function) to quantify the correlation between modes, clarify the key control parameters through sensitivity analysis (Sobol index), fully cover the complex instability scenarios of multi-mode coupling in actual engineering, and enhance the robustness of the design scheme.

[0129] (3) By jointly optimizing the material parameter threshold and spatial distribution, the performance of ecological materials can be precisely controlled, breaking through the contradiction between ecology and safety in traditional design, and providing a sustainable slope protection engineering solution. Attached Figure Description

[0130] Figure 1 This is a flowchart of the method;

[0131] Figure 2 This is a schematic diagram showing the division of the slope protection structure;

[0132] Figure 3 This is a schematic diagram of a shallow-deep dual-sliding mode. Detailed Implementation

[0133] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0134] Example 1:

[0135] like Figure 1 The flowchart illustrates a method for configuring a green material slope protection scheme based on random field theory. The steps are as follows:

[0136] Step (1): First, based on the main materials, the slope protection structure is divided into a protective layer (ecological concrete), a reinforcement layer (plant root system), a transition layer (graded crushed stone), and a base soil layer (undisturbed soil), such as... Figure 2 As shown, the key performance parameters of each layer of material are defined as spatial random fields:

[0137] Protective layer: concrete shear strength Permeability coefficient Porosity ;

[0138] Reinforcement layer: Root shear strength ,tensile strength Cohesion internal friction angle Permeability coefficient Porosity ;

[0139] Transition layer and subgrade soil layer: Gradient size distribution of crushed stone and compaction of subgrade soil are used as random field boundary conditions;

[0140] A three-dimensional finite difference mesh discretization method is used to map the geometric boundaries of each layer to the computational domain. The Kriging interpolation algorithm is employed to spatially assign parameters to the layers, ensuring a smooth transition of parameters between adjacent layers.

[0141] Step (2): Based on field drilling sampling and indoor triaxial test data, calibrate the statistical characteristics of the protective layer parameters: shear strength. With permeability coefficient mean and standard deviation Its probability density function is determined through maximum likelihood estimation:

[0142]

[0143] in, , , where n is the number of samples.

[0144] coefficient of variation The range of values ​​is determined statistically using the Bootstrap method.

[0145] Porosity obtained by ground-penetrating radar inversion data The spatial distribution of the shape parameters is estimated using the moment matching method. , The probability density function is:

[0146]

[0147] in, , , Determined based on the extreme values ​​of the inversion data.

[0148] The autocorrelation of parameter space is quantified using an exponential covariance function:

[0149]

[0150] Where h is the spatial point spacing. For the relevant length, through the semi-mutation function The fitting experimental data were used to determine the results.

[0151] Random field samples that satisfy the covariance structure are generated using the Cholesky decomposition method or the Fourier transform method.

[0152] Step (3): Shear strength of plant roots in soil after reinforcement Root tensile strength and soil shear strength parameters (cohesion) internal friction angle ), permeability coefficient Porosity Considering the spatial distribution characteristics of these parameters, kernel density estimation and Bayesian update methods are used to define the spatial variation range of these random variables (parameters) and determine the coefficient of variation of the soil after mixing plant roots with slope soil. Spatial related length Its specific implementation is as follows:

[0153] Sampling points were laid out in the slope protection reinforcement layer (plant root system layer) using a grid method, and samples were taken in layers along the depth direction (0-0.5m shallow layer, 0.5-1.5m middle layer, 1.5-3m deep layer), and the spatial coordinates (x, y, z) of each sample point were recorded.

[0154] The shear strength of plant roots was determined by in-situ pull-out test. Determination of tensile strength by single-strand tensile test Cohesion was obtained through triaxial shear tests. internal friction angle Variable head permeability test to determine permeability coefficient Determination of porosity by drying method Outliers (such as root fracture failure data) are removed, and missing values ​​are filled using Kriging interpolation.

[0155] For each parameter Sample dataset The probability density function is estimated using a Gaussian kernel function:

[0156]

[0157]

[0158] Where n is the number of samples, h is the bandwidth, and h is optimized using the Silverman criterion. ( (sample standard deviation) Let u be the Gaussian kernel function, and u be the normalized distance.

[0159] The Kolmogorov-Smirnov test was used to compare the goodness of fit between the kernel density estimation (KDE) distribution and traditional parametric distributions (such as normal and log-normal) to select the optimal model.

[0160] Then, a Bayesian update was used to calibrate the spatial variability model, with the KDE results used as the likelihood function of the parameters. and use Perform posterior distribution calculation.

[0161] in For the parameters to be calibrated, such as mean, variance, or spatial covariance parameters, Based on prior probability distributions, and assumptions from literature or experience, Let be the likelihood function, representing the likelihood of the parameter. The probability of observing actual data (constructed from KDE results). The posterior probability distribution is the parameter distribution updated using Bayes' theorem, reflecting the data's correction of the prior.

[0162] For the spatial sample data of each parameter, calculate the experimental half-variogram:

[0163]

[0164] Where N(h) is the number of point pairs with a spacing h, h is the Euclidean distance between two points in space, and z(x) is the number of point pairs with a spacing h. i ) represents the parameter value;

[0165] Using an exponential model Fit experimental values, where C0 represents the nugget effect and C is the sill value. For spatially related length,

[0166] The coefficient of variation is calculated based on the mean and standard deviation of the posterior distribution. :

[0167]

[0168] Where σ is the standard deviation of the posterior distribution and μ is the mean of the posterior distribution;

[0169] Step (4): Shear strength of plant roots Enhance soil shear resistance and root tensile strength through combined effects Reinforcement and anchoring can directly improve the slope's anti-sliding capacity. Uneven root growth increases the coefficient of variation of shear strength, decay cavities reduce the spatial correlation length, leading to an increased probability of shallow instability. Vertical extension of the taproot increases the correlation length of the permeability coefficient, but local root holes increase the coefficient of variation of permeability, exacerbating the risk of deep seepage.

[0170] Step (5): Based on the time-varying properties of ecological concrete materials and the growth-decay cycle of plant roots, a time-varying function is introduced and a non-stationary spatiotemporally coupled random field model is constructed.

[0171] Among them, the performance degradation of ecological concrete:

[0172]

[0173] Let t be the initial strength, t be the time parameter, and a, b, and c be the exponential function parameters. The strength is calibrated through accelerated aging tests. The calibration method is as follows: place the specimen in a high temperature and high humidity environment, measure the strength decay curve periodically, and fit the exponential function parameters.

[0174] Root growth-decay model:

[0175]

[0176] in, d represents the initial intensity, and d represents the growth amplitude. The growth angle frequency, The initial phase angle is given, m is the baseline value of root strength (m>0), and t is the time variable;

[0177] Combining the time evolution function with a spatial random field forms a non-stationary spatiotemporal sample:

[0178]

[0179] Where X(x,t) represents the material parameter values ​​at spatial location x and time t, X space (x) represents the spatial random field component, X time (t) represents the time-varying function component.

[0180] Step (6): Establish a system based on the safety factor (FS) and the probability of failure ( The dual-index verification of the non-stationary random field model is achieved by embedding the Monte Carlo sampling process into the model, realizing spatiotemporal joint numerical simulation, calculating the Bishop method safety factor through Monte Carlo parallelization, and introducing a time-varying reliability index to adjust the failure threshold in real time according to the monitoring data.

[0181] Based on the constructed non-stationary spatiotemporally coupled random field model, spatiotemporal random field samples are generated using the Karhunen-Loève (KL) expansion. Material parameters are decomposed into deterministic time-varying functions and random field components:

[0182]

[0183] in, is the shear strength of concrete at spatial location x and time t, is the output value of the spatiotemporally coupled random field, and f(t) is the time-varying decay function. The eigenvalues ​​of the covariance function Let them be independent standard Gaussian random variables. Let M be the characteristic function of the covariance function, and M be the cutoff order of the KL expansion.

[0184] For each Monte Carlo sample, calculate the safety factor using the following steps:

[0185] Slope discretization: The potential sliding body is divided into n vertical strips, where the width of strip i is b. i Bottom slope angle α i ,

[0186] Parameter assignment: Extracting material parameters for each block from the random field:

[0187] Iterative solution of FS: Solving the Bishop equation using the Newton-Raphson iterative method:

[0188]

[0189] Where FS is the safety factor, and c i W represents the cohesion of the i-th soil strip. i Let u be the weight of the i-th soil strip. i Let b be the pore water pressure at the bottom of the i-th soil strip. i Let φ be the width of the i-th soil strip. i Let T be the internal friction angle of the i-th soil strip. r,i α contributes to the tensile strength of the root system in the soil strip. i Let be the inclination angle of the sliding surface at the bottom of the i-th soil strip;

[0190] Define dynamic failure threshold :

[0191]

[0192] in, This is a dynamic failure threshold (a critical value for the safety factor that is adjusted in real time based on monitoring data). The initial threshold (such as the static threshold of 1.35 required by the specification). This is the sensitivity coefficient (range 0~1). To correct the steepness (default 3). For displacement rate, The maximum allowable displacement rate.

[0193] Failure probability calculation is optimized using importance sampling method:

[0194]

[0195] in, Let I be the time-varying failure probability, and let I(.) be the indicator function, which takes the value 1 when the condition is met and 0 otherwise. For the original distribution, For biased distribution, For the random variable samples in the i-th sampling, construct a joint index of safety factor and failure probability (time-varying reliability index):

[0196]

[0197] Where R(t) is the reliability index, σ is the inverse function of the standard normal distribution. FS and μ FS These are the standard deviation and mean of the safety factor, respectively.

[0198] Step (6) yields the mean and standard deviation of the time-varying failure probability Pf(t), the time-varying reliability index R(t), and the safety factor FS. Steps (7) (dual-mode criterion, joint failure probability) and (8) (multi-objective optimization) directly rely on the output of step (6) as input data or constraints.

[0199] Step (7): This step establishes a shallow-deep dual-slip mode criterion by integrating the Bishop method with the root reinforcement mechanical model, such as... Figure 3 As shown, the joint failure probability is quantified using the Gaussian Copula function, and the dominant failure mechanism is identified based on the Sobol exponent. The specific implementation is as follows:

[0200] For the surface layer of the slope protection structure (protective layer and reinforcement layer), the potential sliding surface depth is defined as 0.5~1.5m, taking into account the reinforcement effect of plant roots. In the Bishop method safety factor calculation, the root tensile strength is considered. Equivalent to an additional shear strength increment:

[0201]

[0202] in, For effective shear strength, c2 is the cohesion of the reinforced soil layer. For root tensile strength, Root distribution density, Angle A is the angle between the root system and the sliding surface. slip The area of ​​the sliding surface unit;

[0203] Shallow safety factor FS S Solve iteratively using the improved Bishop equation:

[0204]

[0205] Among them, FS S For shallow sliding safety factor, b i W is the width of the i-th soil strip. i Let u be the weight of the i-th soil strip. i φ is the pore water pressure at the bottom of the i-th soil strip, φ2 is the internal friction angle of the reinforced soil layer, and α is the pore water pressure at the bottom of the i-th soil strip. i Let be the inclination angle of the sliding surface at the bottom of the i-th soil strip;

[0206] The potential sliding surface penetrates the subgrade layer; the safety factor FS is calculated using the standard Bishop method. D Its shear strength parameters internal friction angle The permeability coefficient is affected by the spatial variability of the graded crushed stone in the transition layer. Parameters are assigned using non-stationary random fields.

[0207] The shallow and deep failure probabilities FS are obtained through Monte Carlo simulation (step 6). S and FS D Its marginal distribution function is:

[0208]

[0209]

[0210] Where, μ FS ,σ FS For the mean and standard deviation of the safety factor, FS cr S =1.25, FS cr D =1.35 is the dynamic failure threshold.

[0211] Constructing the joint failure probability based on the linear correlation coefficient ρ :

[0212]

[0213] in, , These represent the failure probabilities of the shallow sliding mode and the deep circular sliding mode, respectively. The cumulative distribution function of the standard normal distribution. The quantile function of the standard normal distribution. , where is the linear correlation coefficient between the two failure modes (dimensionless, range [-1,1]). The function is a bivariate standard normal joint distribution function, and the correlation coefficient is... ;

[0214] Next, a global sensitivity analysis was performed, taking into account material parameters (plant root shear strength). Root tensile strength Root distribution density Spatial related length ( , Using ) as input variables, analyze the safety factors of shallow and deep layers ( , and combined failure probability The contribution of each parameter to the failure probability is quantified using the Sobol exponent:

[0215] (First-order exponent) ;

[0216]

[0217] Where Y is the output response and X is the input variable. To remove All other input variables besides To be in a fixed At that time, other variables Conditional expectation of Y To variance The total variance of the output response Y; With other variables fixed hour Conditional expectation of Y For other variables The variance;

[0218] The purpose of quantifying the contribution of each parameter to the failure probability using the Sobol exponent is to identify the dominant failure mechanism (shallow or deep slip) and its key parameters. For example, after inputting parameters, the output is the failure probability, but some parameter samples are generated in the middle according to Monte Carlo. By calculating the contribution of each parameter to the failure probability, we can identify whether it is a key parameter (key parameters will determine the optimization direction).

[0219] like ,illustrate The interaction effect is significant when a certain parameter is If the value is greater than 0.1, it is determined to be a critical parameter. The critical parameter is included in the design variable set of the NSGA-II multi-objective optimization below. During the optimization process, the critical parameter is given higher priority to improve efficiency and reliability.

[0220] The correlation of this pattern is: if the shear strength of plant roots... right of Significantly higher than the shear strength of plant roots right of If the sliding pattern is positive, then shallow sliding is the dominant mode; otherwise, deep sliding is the dominant mode.

[0221] The meaning of "significantly higher" is generally "difference of 2-10 times", but this threshold is determined based on engineering experience and is used to quickly determine the dominant mode.

[0222] The core function of identifying whether shallow or deep slip is dominant is to guide the direction of optimization design. It can determine the optimization priority of key parameters. For example, when shallow slip is dominant, the focus is on optimizing the root tensile strength threshold, while when deep slip is dominant, the priority is to adjust the compaction of the subgrade layer.

[0223] The dominant mode is not directly used for real-time monitoring feedback. The identification of the dominant failure mechanism (through the Sobol index) is mainly used in the optimization process (NSGA-II algorithm to optimize material parameters), rather than in the real-time monitoring cycle. Real-time monitoring feedback is only reflected in the adjustment of the dynamic failure threshold (based on general monitoring data such as displacement rate), and does not form a complete cyclical interaction with the dominant mode.

[0224] Step (8): The implementation process based on the NSGA-II multi-objective optimization algorithm is as follows:

[0225] Design variable set:

[0226] Based on the key parameters determined in step (7);

[0227] Material parameter thresholds: Lower limit of shear strength of protective layer ecological concrete Tensile strength threshold of plant roots Foundation soil density ,

[0228] Spatial related length: , ;

[0229] Time-varying function coefficients: decay parameters (a, b, c) and root growth parameters (d, ω). (m);

[0230] Using the reciprocal of the failure probability as a safety metric, we construct a bi-objective optimization problem:

[0231] Objective 1: max( (reciprocal of shallow failure probability), Target 2: max( (The inverse of the probability of deep failure);

[0232] Based on the time-varying reliability index R(t) in step 6, the minimum value must not be lower than the threshold throughout the entire lifecycle:

[0233] (R)min =3.0 (as required by the specification).

[0234] Latin hypercube sampling (LHS) is used to uniformly generate N variables within the design variable space. pop There are 1 individual, and each individual corresponds to a set of design variable combinations x. i (x( ,a, )).

[0235] For each individual, perform the following process (accelerated by parallel computing): generate non-stationary spatiotemporal random field samples, update the spatiotemporal distribution of material parameters, and perform Monte Carlo simulation calculations. , And R(t), solve for the joint failure probability And the Sobol index.

[0236] Individuals are stratified according to their objective function values, with priority given to retaining solutions at higher dominance levels. The distribution density of solutions within the same level is calculated to avoid local convergence.

[0237]

[0238] in, Let be the crowding distance of the i-th individual, which measures the sparsity of the solution distribution in the target space. Let m be the value of the i-th individual for the m-th objective. Let be the maximum and minimum values ​​of the m-th target in the population.

[0239] The first N will be retained. elite From elite individuals to the next generation, simulated binary crossover (SBX) and polynomial mutation are used to adaptively adjust operator probabilities:

[0240]

[0241]

[0242] Where, p c p is the crossover probability. m Here, is the mutation probability, gen is the current generation, and maxGen is the maximum generation. The number of design variables.

[0243] frontier solution set Normalize the target value:

[0244]

[0245] in, Let m be the normalized target value, ranging from [0,1]. This is the original target value;

[0246] Calculate the information entropy of target m and assign weights accordingly:

[0247]

[0248] Among them, E m Let the information entropy of the m-th target be [0,1]. The number of Pareto front solutions.

[0249] Weighting:

[0250]

[0251] Among them, w m E represents the weight of the m-th objective. m The information entropy of the m-th target;

[0252] By adjusting the weights, the optimization is made more biased towards the critical failure mode (the critical failure mode is the dominant mode), while the dual-objective framework remains unchanged to ensure a global balance between ecology and security.

[0253] Finally, calculate the positive ideal solution f. + and negative ideal solution f - :

[0254] ,

[0255] Calculate proximity:

[0256] ,

[0257] in, Let i be the proximity of the i-th solution. To find the Euclidean distance to the positive ideal solution, To find the Euclidean distance to the negative ideal solution, The target weight is determined by the entropy weight method.

[0258] The solution with the highest approximation is selected as the optimal configuration, thus obtaining the optimal configuration of the slope protection scheme that balances safety and ecological benefits.

[0259] The above describes the NSGA-II multi-objective optimization process. First, the design variables are determined. Then, an initial population is generated. The objective function is evaluated for each individual. Next, the evolutionary algorithm iterates. Then, Pareto front screening is performed. Finally, TOPSIS decision is performed, the proximity is calculated, and the maximum value solution is selected. The results (optimization vector) are returned to the random field model for adjustment of optimization variables.

[0260] Example 2:

[0261] This embodiment provides a green slope protection probability analysis device based on random field theory, including a processor and a storage medium;

[0262] The storage medium is used to store instructions;

[0263] The processor is configured to operate according to the instructions to perform the steps of the method according to Embodiment 1.

[0264] Example 3:

[0265] This embodiment provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0266] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0267] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0268] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0269] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0270] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A green material slope protection scheme configuration method based on the random field theory, characterized in that, Comprising: Step 1: Obtain the material parameters of the slope protection structure, and model the layered random field according to the material parameters to quantify the spatio-temporal variability of each layer parameter; Step 2: For the protection layer parameters in the random field, adopt lognormal and Beta distribution calibration to update the random field of the protection layer; Step 3: For the root system parameters of the reinforcement layer in the random field, update the random field of the reinforcement layer through kernel density estimation and Bayesian update; Step 4: Introduce a time-varying function in the random field, and construct a non-stationary spatio-temporal coupled random field model based on the combined action of concrete and plant roots; Step 5: Establish a double-index verification based on safety factor and failure probability, embed the non-stationary spatio-temporal coupled random field model into the Monte Carlo sampling process, perform spatio-temporal joint numerical simulation, and construct time-varying reliability indicators; Step 6: According to the time-varying reliability indicators, establish a double-mode criterion for deep and shallow potential sliding surfaces, and calculate the joint failure probability, including: Step 1: Obtain the material parameters of the slope protection structure, and model the layered random field according to the material parameters to quantify the spatio-temporal variability of each layer parameter, including: Obtain the material parameters of the slope protection structure, and divide the slope protection structure into multiple layers according to the material and confirm the key parameters of each layer material, and define each layer material key parameter as a random field based on the slope protection structure parameters; For the protective and reinforcing layers, the potential sliding surface depth is defined as 0.5~1.5m. In the Bishop method safety factor calculation, the root tensile strength is taken into account. Equivalent to an additional shear strength increment: ； wherein, c2 is the soil cohesion of the reinforcement layer, c3 is the tensile strength of the roots, c4 is the root distribution density, c5 is the angle between the roots and the sliding surface, A slip A is the unit area of the sliding surface; Shallow safety factor FS S Solved iteratively by the improved Bishop equation: ； wherein FS S is the safety factor of shallow sliding, b i is the width of the ith soil strip, W i is the weight of the ith soil strip, u i is the pore water pressure at the bottom of the ith soil strip, φ2 is the internal friction angle of the reinforced layer soil, φ i is the internal friction angle of the ith soil strip, α i is the inclination angle of the sliding surface at the bottom of the ith soil strip; The potential sliding surface goes through the foundation soil layer, and the standard Bishop method is used to calculate the safety factor FS D The shear strength parameters The internal friction angle The permeability coefficient The permeability coefficient is affected by the spatial variability of the transition layer graded gravel; Shallow and deep failure probabilities FS S and FS D whose marginal distribution functions and are: ； ； wherein, is the standard normal cumulative distribution function, μ FS ,σ FS is the mean and standard deviation of the safety factor, FS cr S = 1.25, FS cr D = 1.35 is the dynamic failure threshold; Constructing joint failure probability based on linear correlation coefficient p : ； where, , are the marginal distribution functions of the failure probabilities of the shallow and deep circular slip modes, respectively, is the cumulative distribution function of the standard normal distribution, is the quantile function of the standard normal distribution, is the linear correlation coefficient of the two failure modes, is the bivariate standard normal joint distribution function with the correlation coefficient . 2.The green material revetment scheme configuration method based on the random field theory of claim 1, wherein, Divide the slope protection structure into multiple layers according to the material and confirm the key parameters of each layer material, and define each layer material key parameter as a random field, including: Divide the slope protection structure into the following multiple layers according to the main material: Key parameters of the material include the concrete shear strength , the permeability coefficient , the porosity , the shear strength of the plant root system , the tensile strength of the root system and the shear strength parameters of the soil mass; the shear strength parameters of the soil mass include the cohesion , the internal friction angle . 3.The green material revetment scheme configuration method based on the random field theory of claim 2, wherein, Protection layer: ecological concrete; Reinforcement layer: plant root system; Transition layer: graded gravel; Base soil layer: undisturbed soil; Define the key parameters of each layer material as a spatial random field: Transition layer: graded gravel particle size distribution; Base soil layer: base soil density; Protective layer: concrete shear strength , permeability coefficient , porosity ; Reinforcing layer: root shear strength , tensile strength , cohesion , internal friction angle , permeability coefficient , porosity ; Take the thickness of the protection layer ecological concrete, the distribution density of the reinforcement layer plant root system, the particle size distribution of the transition layer graded gravel, and the undisturbed soil density of the base soil layer as the boundary conditions of the random field, and realize the spatial interpolation and parameter assignment of the layered random field parameter through the three-dimensional finite difference grid discretization method; Use Kriging interpolation algorithm to realize the spatial assignment of layered parameters to ensure smooth transition of parameters between adjacent layers. Step 2: For the protection layer parameters in the random field, adopt lognormal and Beta distribution calibration to update the random field of the protection layer, including: Step 3: For the root system parameters of the reinforcement layer in the random field, update the random field of the reinforcement layer through kernel density estimation and Bayesian update, including: 4.The green material revetment scheme configuration method based on the random field theory of claim 2, wherein, Step 4: Introduce a time-varying function in the random field, and construct a non-stationary spatio-temporal coupled random field model based on the combined action of concrete and plant roots, including: Shear strength of concrete Permeability coefficient The random variable with logarithmic normal distribution statistical characteristics is calibrated, the mean value and the standard deviation are determined based on the field drilling sampling and indoor triaxial test data by using the maximum likelihood estimation method ;​​ porosity The porosity is calibrated as a random variable with a Beta distribution, the Beta distribution parameters being corrected using the geological radar inversion data , The porosity is calibrated as a random variable with a Beta distribution, the Beta distribution parameters being corrected using the geological radar inversion data The porosity is calibrated as a random variable with a Beta distribution, the Beta distribution parameters being corrected using the geological radar inversion data Considering the spatial autocorrelation and spatial distribution characteristics of the three parameters, the exponential covariance function was used to quantify the spatial variation range of the three parameters, and the spatial correlation length of the key parameters of the protective layer was determined value range. 5.The green material revetment scheme configuration method based on the theory of random field according to claim 2, characterized in that, ​ Shear strength of soil with plant roots Tensile strength of roots Cohesion of soil Internal friction angle Permeability Porosity The spatial variability of these parameters is calibrated using the kernel density estimation and Bayesian updating method, and the spatial correlation length of the soil mixed with plant roots is determined . 6.The green material revetment scheme configuration method based on the random field theory of claim 2, wherein, ​ Based on the time-varying law of the ecological concrete material performance and the plant root growth-rot cycle, a time-varying function is introduced and a non-stationary space-time coupled random field model is constructed, wherein the ecological concrete performance attenuation model is: ； wherein, is the decay model value, is the initial intensity, t is the time parameter, a, b, c are the parameters of the exponential function, calibrated by accelerated aging test; the root growth-rot model is: ； wherein, is a root growth-rot model value, is an initial strength, d is a growth amplitude value, is a growth angular frequency, is an initial phase angle, m is a root strength baseline value, t is a time variable; The time evolution function is combined with the spatial random field to form a non-stationary space-time sample: ； where X(x, t) is the value of the material parameter at spatial location x and time t, X space (x) is the spatial random field component, X time (t) is the time varying function component. 7.The green material revetment scheme configuration method based on the random field theory of claim 6, wherein, Step 5: Establish a double-index verification based on the safety factor and failure probability, embed the non-stationary space-time coupled random field model into the Monte Carlo sampling process, perform space-time joint numerical simulation, and construct time-varying reliability indexes, including: Based on the constructed non-stationary space-time coupled random field model, the Karhunen-Loève expansion is used to generate space-time random field samples; the material parameters are decomposed into deterministic time-varying functions and random field components: ； wherein, is the concrete shear strength at spatial position x and time t, is the output value of the spatio-temporal coupled random field, f(t) is a time-varying decay function, is the eigenvalue of the covariance function, is an independent standard Gaussian random variable, is the eigenfunction of the covariance function, M is the truncation order of the KL expansion, For each Monte Carlo sample, the safety factor is calculated according to the following steps: Slope discretization: divide potential sliding body into n vertical strips, width of strip i is b i , bottom inclination angle is a i , Parameter assignment: extract the material parameters of each block from the random field; Iterative solution of FS: solve the Bishop equation by Newton-Raphson iteration: ； where FS is the safety factor, c i is the cohesion of the ith slice, W i is the weight of the ith slice, u i is the pore water pressure at the bottom of the ith slice, b i is the width of the ith slice, φ i is the internal friction angle of the ith slice, T r,i is the contribution of the tensile strength of the root system in the slice, a i is the inclination of the slip surface at the bottom of the ith slice; Defining dynamic failure thresholds : ； wherein, is a dynamic failure threshold, is an initial threshold, is a sensitivity coefficient, is a correction steepness, is a displacement rate, is an allowed maximum displacement rate; The failure probability calculation is optimized by the importance sampling method: ； where, is the time-varying failure probability, I(.) is the indicator function, which takes 1 when the condition is satisfied and 0 otherwise, is the original distribution, is the biased distribution, is the random variable sample in the i-th sampling, N is the total number of samplings, and the time-varying reliability index is constructed: ； where R(t) is a reliability index, is the inverse function of the standard normal distribution, σ FS and μ FS are the standard deviation and mean of the safety factor, respectively. 8.The green material revetment scheme configuration method based on the random field theory of claim 7, wherein, According to the joint failure probability, the material parameter threshold and the space-time correlation length are optimized by the NSGA-II algorithm, and the Pareto optimal scheme considering safety and ecological efficiency is screened by the TOPSIS decision-making method, to obtain the optimal configuration of the slope protection scheme considering safety and ecological efficiency, including: Take the reciprocal of the failure probability as the optimization objective set; Take the material parameter threshold of each layer, the spatial correlation length and the time-varying function coefficient as the design variables; Combine the time-varying reliability indexes and the joint failure probability to construct the constraint condition; Based on the NSGA-II multi-objective optimization algorithm, the Latin hypercube sampling is used to generate the initial population, and the elite reservation strategy and adaptive crossover and mutation operators are introduced to improve the convergence of the Pareto frontier; Based on the TOPSIS decision-making method, the target weight is determined by the entropy weight method, and the balanced solution is quantified by the fuzzy membership function to screen the optimal configuration of the slope protection scheme that meets the shallow-deep dual mode stability requirement, and the optimal configuration of the slope protection scheme considering safety and ecological efficiency is obtained.

9. A green slope protection probability analysis device based on the random field theory, characterized by, including a processor and a storage medium; The storage medium is used to store instructions; The processor is used to operate according to the instructions to perform the steps of the method according to any one of claims 1-8.

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