Slope instability probability assessment method based on burial depth constraint spatial random field simulation

Abstract

The invention relates to a slope instability probability evaluation method based on burial depth constraint space random field simulation, and belongs to the technical field of slope engineering. The method comprises the following steps: acquiring shear strength parameters c and phi at different buried depths of a slope soil body in a research area; the obtained shear strength parameters are expanded according to Gaussian process regression in combination with a radial basis function, the reliability of the expanded parameters is determined through K-S inspection, and cross correlation between c and phi is obtained; determining statistical characteristics of the c and phi expansion data; under the burial depth constraint condition, slope model determinacy research is carried out, a safety coefficient is calculated, the model is compared with a traditional model, and the difference between the potential slip plane of the slope under the burial depth constraint and the potential slip plane of the traditional slope is obtained; the traditional Monte Carlo simulation MCS is optimized; according to deterministic analysis and a random field theory, carrying out uncertainty research on the side slope under the burial depth constraint, and calculating the instability probability of the depth evolution random field side slope model.

Description

Technical Field

[0001] This invention relates to a method for assessing the probability of slope instability based on depth-constrained spatial random field simulation, belonging to the field of slope engineering technology. Background Technology

[0002] Existing studies typically assume uniform geomechanical parameters for slope materials, a simplification that fails to accurately reflect the actual spatial variability of rock and soil masses. Using homogenized parameters in numerical simulations can lead to calculated safety factors (FS) greater than 1, while actual slopes may still experience instability and failure, demonstrating the significant limitations of traditional methods in risk assessment. In engineering practice, actual slope rock masses generally exhibit gradient distributions of strength parameters. On one hand, the self-weight stress field results in varying degrees of consolidation; on the other hand, different depths exhibit varying degrees of weathering, both exacerbating the spatial heterogeneity of rock mass strength. From the perspective of slope stability analysis, the spatial variability of rock mass shear strength parameters directly determines the location and scale of the most dangerous sliding surface. Using homogenized parameters will lead to significant deviations in numerical calculation results. Therefore, constructing a spatial variability model of rock mass shear strength parameters that considers depth effects is essential for analyzing slope stability and the location of the sliding surface.

[0003] Extensive and in-depth research has been conducted on the assessment of slope stability considering the spatial variability of soil and rock parameters. The core challenge in this field lies in how to accurately characterize the spatial heterogeneity of soil and rock materials through numerical simulation. Summary of the Invention

[0004] To address the issues of overestimation of variability and computational distortion in existing slope instability probability assessment technologies, this invention provides a slope instability probability assessment method based on depth-constrained spatial random field simulation. It constructs a dynamic convergence verification mechanism, significantly improving computational efficiency and ensuring the engineering reliability of the probability assessment. Through comparative analysis of the determinism and uncertainty of depth-constrained slopes and traditional slopes, the failure modes of slopes are reconstructed. The calculation process is simplified, computational efficiency is improved, and the propagation mechanism of uncertainty in Monte Carlo simulation is revealed. This has significant practical value for promoting the application of geotechnical engineering reliability and risk theory in engineering practice.

[0005] A method for assessing the probability of slope instability based on depth-constrained spatial random field simulation, the specific steps of which are as follows: S1. Obtain the shear strength parameters of the slope soil at different burial depths in the study area. The shear strength parameters include cohesion. c and internal friction angle f ; S2. The obtained shear strength parameters are extended based on Gaussian process regression combined with radial basis functions. The reliability of the extended parameters is determined using the KS test, and the cohesion is obtained. cand internal friction angle f There is cross-correlation between them; S3. Determine cohesion c and internal friction angle f Extend the statistical characteristics of the data; these statistical characteristics include distribution type, mean, standard deviation, and variability. S4. Conduct a deterministic study of the slope model under the burial depth constraint, calculate the safety factor, and compare the model with the traditional model to obtain the difference between the potential slip surface of the slope under the burial depth constraint and the traditional slope. S5. Optimize the traditional Monte Carlo simulation MCS; S6. Based on deterministic analysis and random field theory, conduct uncertainty research on slopes under depth constraints, calculate the instability probability of depth evolution random field slope models; at the same time, the instability probability of traditional random field slope models can be calculated. S7. Compare the instability modes of the two slope models, deep evolution random field and traditional random field, count the total number of slope instability samples, and identify the key instability modes of the slope based on the slope instability samples.

[0006] Preferably, in step S2, the obtained shear strength parameters are predicted based on Gaussian process regression combined with radial basis functions, and the reliability is determined using the KS test to obtain the cohesion. c and internal friction angle f The cross-correlation exists between them, and the specific steps are as follows: S21. Normalize the depth, then normalize the depth. z Mapped to the interval [0,1]; S22. The obtained shear strength parameters are extended based on the Gaussian process regression model combined with radial basis functions; specifically, n points of the measured values ​​are randomly selected within the depth interval. A sample set is formed, and the mean is predicted using the Gaussian process regression model (GPR). m c ( z k ), m φ ( z k ) and covariance matrix Σ, based on joint distribution N ( m Sampling, Σ) yields Based on the Gaussian process regression model, m sets of cohesion are generated. c and internal friction angle f Extended data; The radial basis function is: (1); In the formula, l For relevant scales; s n For noise variance; S23. Regarding cohesion c and internal friction angle f The extended data and measured data were subjected to KS correlation test. Specifically, a depth stratification constraint strategy was adopted, dividing the depth interval into 1 m units. It was assumed that the parameters of each interval followed a normal distribution, and the null hypothesis that the predicted distribution was consistent with the measured distribution was established. H 0: F n (x) = F (x), when the correlation coefficient p When the value is greater than 0.05, it is considered that... H A correlation coefficient of 0 is true; when the correlation coefficient is 0. p When the value is ≤0.05, return to step S22 to increase the measured value of the randomly selected sample set by 5 points, until... H 0 is true; S24. Cohesion as a parameter against shear strength c and internal friction angle f Perform Pearson correlation coefficient analysis to calculate cohesion. c and internal friction angle f The correlation coefficient.

[0007] Preferably, the method for determining the distribution type in step S3 is as follows: using a goodness-of-fit test to examine the relationship between burial depth and cohesion. c and internal friction angle f The distribution type is determined, and the optimal distribution type is selected, wherein the distribution type is a linear distribution, a nonlinear distribution, or an exponential distribution. The formula for calculating the mean is: (2); Where: μ j x is the mean value of the shear strength parameter for the burial depth range j. i The measurement value for each sample, where n is the number of samples; The formula for calculating the standard deviation is: (3); Where: σ j Let be the standard deviation of the shear strength parameters within the burial depth range j; The coefficient of variation is the ratio of the standard deviation to the mean under the burial depth condition.

[0008] Preferably, step S4 involves conducting a deterministic study of the slope model under depth constraints, calculating the safety factor, and comparing the model with a traditional model to obtain the difference in potential slip surfaces between the slope under depth constraints and the traditional slope. The specific steps are as follows: S41. Based on the actual geometric dimensions of the slope, establish a geometric model of the slope in numerical analysis software; S42. Based on the soil shear strength parameter, cohesion. c (z) and internal friction angle f (z) Variables that vary with depth, establishing c (z) and f (z) Deterministic prediction analysis model with depth: (4); In the formula, z For the depth of soil burial, c (z) and f (z) is the depth trend component function, such as the soil strength parameter along the burial depth. z The mean function; S43. Investigate the unit weight and permeability coefficient of the soil. c (z) and f (z) The geometric model of the slope is given by the deterministic prediction analysis model with depth, the slope safety factor and the potential slip surface of the slope are calculated, and the difference between the potential slip surface of the slope under the burial depth constraint and the traditional slope is obtained by comparing the model with the traditional model.

[0009] Preferably, the method for optimizing the traditional Monte Carlo simulation MCS in step S5 is as follows: calculate the coefficient of variation every 100 iterations. d The d = s / m Calculated in 3 consecutive times d The simulation terminates when the slope instability probability (PF) is less than 0.5% and the PF fluctuation is less than 5%. The final output is the convergence MCS count, and the slope instability probability (PF) value is calculated. (5); In the formula, N f - The number of times the slope became unstable in the total number of simulations, N - the total number of simulations.

[0010] Preferably, in step S6, based on deterministic analysis and random field theory, an uncertainty study of the slope under depth constraints is conducted, and the instability probability of the depth evolution random field slope model is calculated; the specific steps are as follows: S61. Based on deterministic analysis and random field theory, establish an uncertainty prediction model for soil shear strength parameters under depth constraints; the specific steps are as follows: Soil shear strength parameters: effective cohesion c (z) and effective internal friction angle f (z) is defined as a random variable that varies with depth, and a system is established. c (z) and f(z) Uncertainty prediction analysis model with depth: (6); In the formula, z For the depth of soil burial, c (z) and f (z) is the depth trend component function, such as the soil strength parameter along the burial depth. z The mean function; w x (z) is the random fluctuation component function, mean m j Standard deviation s j A normally stationary random field that varies with burial depth; S62. The uncertainty prediction model of soil shear strength parameters is applied to the geometric model of the slope, and the instability probability of the depth evolution random field slope model is calculated based on the optimized Monte Carlo simulation.

[0011] The beneficial effects of this invention are: (1) This invention is based on the spatial random field simulation of burial depth constraint to calculate the probability of slope instability. The concept is clear and easy to understand. The Monte Carlo simulation (MCS) system is used to evaluate the probability of instability of the DE-RF slope model and compare it with the traditional random field model. The influence of depth effect on key safety indicators of slope can be quantitatively analyzed. It can effectively solve the problem of slope instability sensitivity analysis with single uncertainty parameter and multiple uncertainty parameters. It can also be well applied to the problem of stability instability sensitivity analysis of complex slopes. It has a wide range of applications. The method of this invention comprehensively considers the geological sedimentary history and provides a systematic evaluation framework for accurately measuring the probability analysis of slope stability under burial depth constraint. (2) In the probabilistic assessment of slope stability based on Monte Carlo simulation (MCS), traditional methods often lead to computational redundancy or insufficient reliability of results when calculating the distribution of safety factor (FS) and failure probability (PF, i.e., the proportion of FS < 1.0) due to the fixed number of simulations, especially for the stability reliability sensitivity analysis of complex slopes. This invention constructs a dynamic convergence verification mechanism, which significantly improves computational efficiency and ensures the engineering credibility of the probability assessment. The improved framework avoids the excessive or insufficient calculations performed by traditional MCS to meet convergence, and efficiently obtains statistically significant results through strict dual dynamic convergence criteria (stable coefficient of variation and stable failure probability), which has important engineering value, especially for the reliability analysis of slopes of major infrastructure. (3) This invention reconstructs the failure mode of slope by comparing the determinism and uncertainty of slope under burial depth constraints with traditional slope. The potential sliding surface of traditional random field slope model is mainly shallow sliding. The DE-RF slope model corrects the structure of random field through physical constraints, pushes the sliding surface from "shallow vulnerable area" to "deep robust area", and couples the "deep high strength + low variability" mechanism to suppress the instability mode dominated by shallow vulnerable zone, thus changing the failure mode from the root. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a schematic diagram of a slope mesh model; Figure 3 The following are experimental diagrams from a field direct shear test: a) is a cross-sectional view, and b) is a planar view. Figure 4 The following are data graphs from a field direct shear test: a) is the curve showing the relationship between shear stress and shear displacement, and b) is the curve showing the relationship between shear stress and normal stress. Figure 5 The predicted values ​​are based on the fitting of measured values. a) is a graph showing the change of cohesion with depth, and b) is a graph showing the change of internal friction angle with depth. Figure 6 To show the distribution trend of shear strength parameters under burial depth constraints, a) is a statistical diagram of the distribution of internal friction angle, and b) is a statistical diagram of the distribution of cohesion. Figure 7 c- f Correlation analysis plot; Figure 8 A schematic diagram of the deterministic analysis of a slope considering burial depth constraints; a) The average value in Table 1 is taken as the deterministic parameter; b) The potential slip surface of a traditional slope; c) c (z) and f (z) The prediction model with depth, where w x (z)=0, which is a deterministic parameter; d) is the potential slip surface of the slope under the burial depth constraint; Figure 9 This is a typical implementation of the DE-RF random field model; a) random field distribution of cohesion evolving with depth; b) random field distribution of internal friction angle evolving with depth. Figure 10 Probability distribution diagrams of safety factors calculated by the DE-RF slope model and the traditional random field model under rainfall conditions; a) DE-RF slope model; b) Traditional random field slope model; Figure 11The diagram illustrates the changes in instability probability calculated by the Deep Evolution Random Field (DE-RF) slope model and the traditional random field model under rainfall conditions; a) Instability probability of the DE-RF slope model; b) Instability probability of the traditional random field slope model. Detailed Implementation

[0013] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0014] Example 1: As Figure 1 As shown, a method for assessing the probability of slope instability based on depth-constrained spatial random field simulation is described, with the following specific steps: S1. Obtain the shear strength parameters of the slope soil at different burial depths in the study area. The shear strength parameters include cohesion. c and internal friction angle f ; In-situ immersion direct shear tests were conducted on slope soil at different burial depths in the study area (see...). Figure 3 To ensure uniform specimen (TW) thickness, the specimens were immersed in water for 72 hours before undergoing a water-immersion quick shear test. A pad was placed on top of the specimen, and vertical stress was applied in stages by accumulating heavy objects. The loading test was conducted in 3-4 stages, with each load stage held for 10 minutes. Shear stress (τ) and shear displacement (ε) were recorded every 30 seconds until the test was terminated. The trench test was a direct quick shear test, and shear tests were conducted on four soil blocks. The normal stress σ was used as the abscissa, and the shear stress τ was used as the ordinate. The test results were calculated using the least squares method. S2. The obtained shear strength parameters are extended based on Gaussian process regression combined with radial basis functions. The reliability of the extended parameters is determined using the KS test, and the cohesion is obtained. c and internal friction angle f There is a cross-correlation between them; the specific steps are as follows: S21. Normalize the depth, then normalize the depth. z Map to the interval [0,1] to eliminate the influence of dimensions; S22. The obtained shear strength parameters are extended based on the Gaussian process regression model combined with radial basis functions; considering cohesion... c and internal friction angle f This model conforms to the "hierarchical linear regression + random effects model" approach, utilizes machine learning-enhanced random field modeling, employs a Gaussian process regression model combined with non-stationary random fields for data expansion, and leverages the radial basis function (RBF) function within the Gaussian process regression (GPR) model to achieve input depth.z The cohesion at the corresponding location can then be obtained. c and internal friction angle f Specifically, n points of measured values ​​are randomly selected within the depth range. A sample set is formed, and the mean is predicted using the Gaussian process regression model (GPR). m c ( z k ), m φ ( z k ) and covariance matrix Σ, based on joint distribution N ( m Sampling, Σ) yields Based on the Gaussian process regression model, m sets of cohesion are generated. c and internal friction angle f Extended data; The radial basis function is: (1); In the formula, l For relevant scales; s n For noise variance; S23. Regarding cohesion c and internal friction angle f The extended data and measured data were subjected to KS correlation test. Specifically, a depth stratification constraint strategy was adopted, dividing the depth interval into 1 m units. It was assumed that the parameters of each interval followed a normal distribution, and the null hypothesis that the predicted distribution was consistent with the measured distribution was established. H 0: F n (x) = F (x), when the correlation coefficient p When the value is greater than 0.05, it is considered that... H A correlation coefficient of 0 is true; when the correlation coefficient is 0. p When the value is ≤0.05, return to step S22 to increase the measured value of the randomly selected sample set by 5 points, until... H 0 is true; S24. In actual slope stability analysis, cohesion... c and internal friction angle f Spatial variability exists, affecting the shear strength parameter cohesion. c and internal friction angle f Perform Pearson correlation coefficient analysis to calculate cohesion. c and internal friction angle f The correlation coefficient.

[0015] S3. Determine cohesion c and internal friction angle fExtend the statistical characteristics of the data; these statistical characteristics include distribution type, mean, standard deviation, and variability. The method for determining the distribution type is as follows: goodness-of-fit test is used to examine the relationship between burial depth and cohesion. c and internal friction angle f The distribution type is determined, and the optimal distribution type is selected. The distribution type is either linear, nonlinear, or exponential. The goodness-of-fit test compares the degree of fit between different distribution types (linear, nonlinear, and exponential) and the measured data. The formula for calculating the mean (used to describe the average level of soil shear strength parameters under certain burial depth conditions) is as follows: (2); Where: μ j x is the mean value of the shear strength parameter for the burial depth range j. i The measurement value for each sample, where n is the number of samples; The formula for calculating the standard deviation (which reflects the degree of fluctuation of the parameter value around the mean) is as follows: (3); Where: σ j Let be the standard deviation of the shear strength parameters within the burial depth range j; The coefficient of variation is the ratio of the standard deviation to the mean under the burial depth condition, and is used to reflect the magnitude of the variability of the parameter value under different conditions.

[0016] S4. Conduct a deterministic study of the slope model under depth constraints, calculate the safety factor, and compare the model with the traditional model to obtain the difference in the potential slip surface between the slope under depth constraints and the traditional slope; the specific steps are as follows: S41. Based on the actual geometric dimensions of the slope, establish a geometric model of the slope in numerical analysis software; S42. Based on the soil shear strength parameter, cohesion. c (z) and internal friction angle f (z) Variables that vary with depth, establishing c (z) and f (z) Deterministic prediction analysis model with depth: (4); In the formula, z For the depth of soil burial, c (z) and f (z) is the depth trend component function, such as the soil strength parameter along the burial depth. z The mean function; S43. Investigate the unit weight and permeability coefficient of the soil. c (z) and f(z) The geometric model of the slope is given by the deterministic prediction analysis model with depth, the slope safety factor and the potential slip surface of the slope are calculated, and the difference between the potential slip surface of the slope under the burial depth constraint and the traditional slope is obtained by comparing the model with the traditional model.

[0017] S5. Optimize the traditional Monte Carlo simulation MCS; specifically, calculate the coefficient of variation every 100 iterations. d The d = s / m Calculated in 3 consecutive times d The simulation terminates when the slope instability probability (PF) is less than 0.5% and the PF fluctuation is less than 5%. The final output is the convergence MCS count, and the slope instability probability (PF) value is calculated. (5); In the formula, N f - The number of times the slope became unstable in the total number of simulations, N - the total number of simulations.

[0018] S6. Based on deterministic analysis and random field theory, conduct uncertainty research on slopes under depth constraints, and calculate the instability probability of the depth evolution random field slope model; simultaneously, the instability probability of the traditional random field slope model can be calculated; the specific steps are as follows: Soil shear strength parameters: effective cohesion c (z) and effective internal friction angle f (z) is defined as a random variable that varies with depth, and a system is established. c (z) and f (z) Uncertainty prediction analysis model with depth: (6); In the formula, z For the depth of soil burial, c (z) and f (z) is the depth trend component function, such as the soil strength parameter along the burial depth. z The mean function; w x (z) is the random fluctuation component function, mean m j Standard deviation s j A normally stationary random field that varies with burial depth; S62. The uncertainty prediction model of soil shear strength parameters is applied to the geometric model of the slope, and the instability probability of the depth evolution random field slope model is calculated based on the optimized Monte Carlo simulation.

[0019] S7. Compare the instability modes of two slope models: Deep Evolutionary Random Field (DERF) and Traditional Random Field (TRF). Count the total number of slope instability samples and identify the key instability modes based on these samples. Traditional TRF models often suffer from cognitive biases, assuming a vertically uniform distribution of soil parameters and underestimating the instability risk dominated by shallow weak zones. Therefore, instability may be caused only by local weak zones, failing to consider the "safety redundancy" provided by deep, high-strength zones, leading to a systematic underestimation of the instability probability. Count the total number of slope failure samples and identify the instability modes of depth-constrained slopes based on these samples.

[0020] Example 2: Taking a typical profile slope of an open-pit mine in Yunnan as an example, the slope instability probability assessment method based on depth-constrained spatial random field simulation is verified. The slope has a height of 25 m, a length of 40 m, a slope ratio of 0.75, and a step width of 15 m. It is divided into 2599 grid cells. The spatial variation of the intensity parameters is simulated based on a deep evolutionary random field model. Figure 2 Assuming no water accumulation on the slope, rainfall infiltration is applied to the slope using unit flow rate as the boundary condition. The underlying material is bedrock, and the groundwater is located 25 m below the surface. The steps for slope stability analysis under rainfall infiltration conditions are as follows: 1) Based on the average rainfall during the rainy season, perform steady-state seepage analysis on the established slope model to determine the initial hydraulic conditions with a constant infiltration rate (average monthly rainfall during the rainy season is 383.28 mm), and a permeability of 4.32 × 10⁻⁶ m / s; 2) Perform transient seepage analysis under selected rainfall events to simulate the slope hydraulic response during rainfall; 3) Perform slope stability analysis and calculate the slope safety factor (FS) at different times under specific rainfall events. like Figure 1 As shown, a method for assessing the probability of slope instability based on depth-constrained spatial random field simulation is described, with the following specific steps: S1. Obtain the shear strength parameters of the slope soil at different burial depths in the study area. The shear strength parameters include cohesion. c and internal friction angle f ; Direct shear tests were conducted on slope soil samples at different burial depths within the study area. Square specimens were prepared using a cutting machine or manually, ensuring uniform specimen (TW) thickness. In-situ immersion direct shear tests were then performed (see...). Figure 3 Specifically, after immersing the specimen in water for 72 hours, a quick-shear test was performed. A pad was placed on top of the specimen, and vertical stress was applied in stages by stacking heavy objects. The loading test was carried out in 3 to 4 stages, with each load held for 10 minutes. The vertical displacement (Δ) was recorded. hThe rate of change was reduced to <0.05 mm / min. The test was terminated when the shear force decreased by ≥20% after reaching its peak or when the horizontal displacement reached 10% (55 mm) of the specimen length and the shear force stabilized. Shear stress (τ), shear displacement (ε), shear stress (τ) and shear displacement (ε) curves, and the relationship curve between shear stress (τ) and normal stress (σ) were recorded every 30 seconds (see...). Figure 4 This test was a direct quick shear test, and the shear test was conducted on four soil blocks. The normal stress σ was used as the abscissa and the shear stress τ was used as the ordinate. The test results were calculated using the least squares method. The strength parameters of 16 groups of slope soils at different depths are shown in Table 1. Table 1 Dataset of rock mass strength parameters at different burial depths ; S2. The obtained shear strength parameters are extended based on Gaussian process regression combined with radial basis functions. The reliability of the extended parameters is determined using the KS test, and the cohesion is obtained. c and internal friction angle f There is a cross-correlation between them; the specific steps are as follows: S21. Normalize the depth, then normalize the depth. z Map to the interval [0,1] to eliminate the influence of dimensions; S22. The obtained shear strength parameters are extended based on the Gaussian process regression model combined with radial basis functions; considering cohesion... c and internal friction angle f This model conforms to the "hierarchical linear regression + random effects model" approach, utilizes machine learning-enhanced random field modeling, employs a Gaussian process regression model combined with non-stationary random fields for data expansion, and leverages the radial basis function (RBF) function within the Gaussian process regression (GPR) model to achieve input depth. z The cohesion at the corresponding location can then be obtained. c and internal friction angle f ; The radial basis function is: (1); In the formula, l For relevant scales; s n For noise variance; Specifically, 16 points of measured values ​​were randomly selected within the depth range. A sample set is formed, and the mean is predicted using the Gaussian process regression model (GPR). m c ( z k ), m φ ( z k) and covariance matrix Σ, based on joint distribution N ( m Sampling, Σ) yields 1000 sets of cohesion were generated based on the Gaussian process regression model. c and internal friction angle f Extended data, such as Figure 5 As shown; S23. Regarding cohesion c and internal friction angle f The extended data and measured data were subjected to KS correlation test. Specifically, a depth stratification constraint strategy was adopted, dividing the depth interval into 1 m units. It was assumed that the parameters of each interval followed a normal distribution, and the null hypothesis that the predicted distribution was consistent with the measured distribution was established. H 0: F n (x) = F (x), when the correlation coefficient p When the value is greater than 0.05, it is considered that... H A correlation coefficient of 0 is true; when the correlation coefficient is 0. p When the value is ≤0.05, return to step S22 to increase the measured value of the randomly selected sample set by 5 points, until... H 0 is true; the test results are shown in Table 2. Table 2 KS Test Analysis As shown in Table 2, extended data can replace measured data in constructing random field models; S24. In actual slope stability analysis, cohesion... c and internal friction angle f Spatial variability exists, affecting the shear strength parameter cohesion. c and internal friction angle f Perform Pearson correlation coefficient analysis to calculate cohesion. c and internal friction angle f The correlation coefficient.

[0021] Cohesion c and internal friction angle f The spatial coefficient of variation (CV) is affected by factors such as soil and rock type, water content, density, and geological conditions, generating 1000 sets of cohesion. c and internal friction angle f The extended data was divided into 5 groups according to depth, and variability analysis was performed, as shown in Table 3. The data was then visualized, and the results are as follows: Figure 6 As shown; Table 3. Descriptive Statistics of Shear Strength Parameters ; As shown in Table 3 and Figure 6, the coefficient of variation of the random field of internal friction angle does not differ significantly at different burial depths, fluctuating between 12.41 and 14.01; while the coefficient of variation of the random field of cohesion changes significantly, and gradually decreases with increasing burial depth, ranging from 16.34 to 26.30.

[0022] To generate 1000 sets of cohesion c and internal friction angle f Visualize the correlation of the extended data and plot the graphs. c - f Scatter plot (see) Figure 7 ), thus cohesion can be obtained c and internal friction angle f The correlation coefficient is 0.132.

[0023] S3. Determine cohesion c and internal friction angle f Extend the statistical characteristics of the data; these statistical characteristics include distribution type, mean, standard deviation, and variability. The method for determining the distribution type is as follows: goodness-of-fit test is used to examine the relationship between burial depth and cohesion. c and internal friction angle f The distribution type is determined, and the optimal distribution type is selected. The distribution type is either linear, nonlinear, or exponential. The goodness-of-fit test compares the degree of fit between different distribution types (linear, nonlinear, and exponential) and the measured data. The formula for calculating the mean (used to describe the average level of soil shear strength parameters under certain burial depth conditions) is as follows: (2); Where: μ j x is the mean value of the shear strength parameter for the burial depth range j. i The measurement value for each sample, where n is the number of samples; The formula for calculating the standard deviation (which reflects the degree of fluctuation of the parameter value around the mean) is as follows: (3); Where: σ j Let be the standard deviation of the shear strength parameters within the burial depth range j; The coefficient of variation is the ratio of the standard deviation to the mean under the burial depth condition, and is used to reflect the magnitude of the variability of the parameter value under different conditions.

[0024] S4. Conduct a deterministic study of the slope model under depth constraints, calculate the safety factor, and compare the model with the traditional model to obtain the difference in the potential slip surface between the slope under depth constraints and the traditional slope; the specific steps are as follows: S41. Based on the actual geometric dimensions of the slope, establish a geometric model of the slope in numerical analysis software; S42. Based on the soil shear strength parameter, cohesion. c (z) and internal friction angle f (z) Variables that vary with depth, establishing c (z) and f (z) Deterministic prediction analysis model with depth: (4); In the formula, z For the depth of soil burial, c (z) and f (z) is the depth trend component function, such as the soil strength parameter along the burial depth. z The mean function, where a1 and b1 in the data are as follows: Figure 5 As shown in (a), a2 and b2 are as follows: Figure 5 As shown in (b); S43. Investigate the unit weight and permeability coefficient of the soil. c (z) and f (z) The geometric model of the slope is given by the deterministic prediction analysis model with depth, the slope safety factor and the potential slip surface of the slope are calculated, and the difference between the potential slip surface of the slope under the burial depth constraint and the traditional slope is obtained by comparing the model with the traditional model.

[0025] The evolution of the potential slip surface and safety factor of a deterministic slope with embedded constraints during rainfall is shown in the figure. Figure 8 It was found that current slope stability analysis generally ignores the effect of burial depth constraint, which leads to the positioning deviation of the slip surface and the underestimation of the safety factor. It is necessary to incorporate the burial constraint into the random field modeling framework.

[0026] S5. Optimize the traditional Monte Carlo simulation MCS; specifically, calculate the coefficient of variation every 100 iterations. d The d = s / m Calculated in 3 consecutive times d The simulation terminates when the slope instability probability (PF) is less than 0.5% and the PF fluctuation is less than 5%. The final output is the convergence MCS count, and the slope instability probability (PF) value is calculated. (5); In the formula, N f - The number of times the slope became unstable in the total number of simulations, N - the total number of simulations.

[0027] S6. Based on deterministic analysis and random field theory, conduct uncertainty research on slopes under depth constraints, and calculate the instability probability of depth evolution random field slope models and traditional random field slope models; the specific steps are as follows: Based on large-scale in-situ direct shear tests, the cohesion and internal friction angle of soil and rock masses at different depths were obtained. The predicted values ​​of cohesion and internal friction angle at different depths were obtained by using the constructed GPR model. Through KS test, it was found that the predicted values ​​and the measured values ​​meet the consistency requirements. Furthermore, based on the predicted values, the cohesion can be constructed into a linear discrete random model, and the internal friction angle can be constructed into an exponential discrete random model. Soil shear strength parameters: effective cohesion c (z) and effective internal friction angle f (z) is defined as a random variable that varies with depth, and a system is established. c (z) and f (z) Uncertainty prediction analysis model with depth: (6); In the formula, z For the depth of soil burial, c (z) and f (z) is the depth trend component function, such as the soil strength parameter along the burial depth. z The mean function; w x (z) is the random fluctuation component function, mean m j Standard deviation s j A normally stationary random field that varies with burial depth, where a1 and b1 in the data are as follows: Figure 5 As shown in (a), a2 and b2 are as follows: Figure 5 As shown in (b); S62. The uncertainty prediction model of soil shear strength parameters is applied to the geometric model of the slope to construct a deep evolutionary random field (DE-RF) slope model (see...). Figure 9 Based on the optimized Monte Carlo simulation, the slope safety factor FS is analyzed, and the instability probability of the depth evolution random field slope model is calculated. S7. Compare the instability modes of the two slope models, deep evolution random field and traditional random field, count the total number of slope instability samples, and identify the key instability modes of the slope based on the slope instability samples; Eight hundred sets of model data were generated using both the traditional random field slope model and the deep evolution random field (DE-RF) slope model for calculation. The probability distribution of the safety factor calculated by the DE-RF and traditional random field models under rainfall conditions is shown in the figure. Figure 10Traditional random field models may generate spurious local weakening zones due to "statistical noise," resulting in slip surfaces that are not the actual slip surfaces. This leads to the random generation of discontinuous weak regions in deeper layers, incorrectly predicting deep composite slip surfaces. Furthermore, the excessively dispersed safety factor arises because some samples in the MCS exhibit abnormally low FS values ​​due to statistical anomalies, lowering the overall stability assessment. The adopted DE-RF model, through intensity gradient constraints, limits shallow-layer damage, resulting in more concentrated stability analysis results and an FS distribution that more closely approximates actual operating conditions.

[0028] A schematic diagram illustrating the changes in instability probability calculated by the Deep Evolution Random Field (DE-RF) slope model and the conventional random field model under rainfall conditions is shown below. Figure 11 As the number of simulations increased, the calculated instability probability tended to stabilize. The DE-RF model calculated an instability probability of approximately 4% (after 300 simulations), while the traditional random field model calculated an instability probability as high as 33% (after 200 simulations). During rainfall, both random field models showed a continuous upward trend in slope instability probability. The DE-RF model calculated an increase of only 3%, while the traditional model calculated an increase of 9%, indicating that the traditional random field model is overly sensitive to rainfall. Therefore, random field models that ignore burial depth constraints underestimate slope reliability, leading to over-support or slope reduction.

[0029] The specific embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for evaluating the probability of slope instability based on a depth-constrained space random field simulation, characterized in that, The specific steps are as follows: S1. obtaining shear strength parameters of a slope soil body at different depths in a study area, the shear strength parameters including cohesion c and internal friction angle φ ; S2. The shear strength parameters obtained are extended by Gaussian process regression combined with radial basis functions, and the reliability of the extended parameters is determined by K-S test to obtain the correlation between the cohesion c and the internal friction angle φ ; S3. Determine Cohesive Force c and internal friction angle φ Statistical features of the expanded data; the statistical features include distribution type, mean, standard deviation, and variability; S4. Under the constraint condition of burial depth, the certainty of the slope model is researched, the safety factor is calculated, and the difference between the potential slip surface of the slope under the constraint of burial depth and the traditional slope is obtained by comparing the model with the traditional model; S5. The traditional Monte Carlo simulation (MCS) is optimized; S6. According to the certainty analysis and the random field theory, the uncertainty of the slope under the constraint of burial depth is researched, and the instability probability of the depth evolution random field slope model is calculated.

2. The method of claim 1, wherein the method is characterized by: Step S2. Predict the obtained shear strength parameters based on Gaussian process regression combined with radial basis functions, and determine their reliability using the KS test to obtain the cohesion. c and internal friction angle φ The cross-correlation exists between them, and the specific steps are as follows: S21. Normalize the depth, mapping the depth z to the interval [0, 1]; S22. According to the Gaussian process regression model combined with the radial basis function, the obtained shear strength parameters are expanded; specifically, n points of the measured values are randomly selected in the depth interval The sample set is formed, and the Gaussian process regression model GPR is used to predict the mean value μ c ( z k )、 μ φ ( z k ) and the covariance matrix Σ, based on the joint distribution N ( μ , Σ) sampling, obtaining On the basis of the Gaussian process regression model, m groups of cohesion c and internal friction angle φ expansion data are generated; The radial basis function is: （1） wherein l is the relevant scale; σ n is the noise variance; S23. The extension data and the measured data of the cohesion c and internal friction angle φ are subjected to K-S correlation test, specifically, a deep hierarchical constraint strategy is adopted, the depth interval is divided into units of 1 m, it is assumed that the parameters of each interval are subject to normal distribution, and the original hypothesis that the prediction distribution is consistent with the measured distribution is established H 0: F n (x) = F (x), when the correlation coefficient p > 0.05, it is considered that H 0 is established; when the correlation coefficient p ≤ 0.05, the measured value of the randomly selected sample set is increased by 5 points until H 0 is established; S24. The parameter of the shear strength, cohesion c and the internal friction angle φ The Pearson correlation coefficient analysis was performed to calculate the correlation coefficient of cohesion c and the internal friction angle φ .

3. The method of claim 1, wherein the method further comprises: The step S3 is a distribution type determination method, which is to use a goodness-of-fit test to determine the distribution type of the buried depth and cohesion c and internal friction angle φ , select the optimal distribution type, and the distribution type is linear distribution, nonlinear distribution or exponential distribution. The calculation formula of the mean value is: （2） Where: μ j is the average value of the shear strength parameter in the buried depth range j, x i is the measured value of each sample, and n is the number of samples. The calculation formula of the standard deviation is: （3） where: σ j is the standard deviation of the shear strength parameter for the range of embedment depths j; The coefficient of variation is the ratio of the standard deviation to the mean value under the constraint of burial depth.

4. The slope instability probability evaluation method based on the burial depth constraint space random field simulation according to claim 1, characterized in that: Step S4. Under the constraint condition of burial depth, the certainty of the slope model is researched, the safety factor is calculated, and the difference between the potential slip surface of the slope under the constraint of burial depth and the traditional slope is obtained by comparing the model with the traditional model; the specific steps are as follows: S41. According to the actual geometric size of the slope, a geometric model of the slope is established in a numerical analysis software; S42. The soil body shear strength parameter cohesion c (z) and internal friction angle φ (z) as a function of depth, establishing c (z) and φ (z) deterministic predictive analytical model as a function of depth: （4） wherein z is the depth of the soil, c (z) and φ (z) is a depth trend component function, such as a mean function of the soil strength parameter along the depth z of the soil. S43. Survey the soil body's specific weight and permeability coefficient, will c (z) and φ (z) The deterministic prediction analysis model with depth gives the geometric model of the slope, calculates the slope safety factor and the potential slip surface of the slope, and compares the model with the traditional model to obtain the difference between the potential slip surface of the slope and the traditional slope under the constraint of burial depth.

5. The method of claim 1, wherein the method further comprises: The S5 method for optimizing the traditional Monte Carlo simulation (MCS) is: calculating the coefficient of variation every 100 iterations δ , the δ = σ / μ , the δ < 5% and the PF fluctuation is less than 0.5%, the simulation is terminated, the number of converged MCS is finally output, the slope instability probability PF value is calculated, and the slope instability probability PF value is: （5） where N is the number of slope failures f - the number of slope failures in the total number of simulations, N - total number of simulations.

6. The method of claim 1, wherein the method further comprises: S6. According to the certainty analysis and the random field theory, the uncertainty of the slope under the constraint of burial depth is researched, and the instability probability of the depth evolution random field slope model is calculated; the specific steps are as follows: S61. According to the certainty analysis and the random field theory, an uncertainty prediction model of the soil shear strength parameter under the constraint of burial depth is established; the specific steps are as follows: Soil shear strength parameters effective cohesion c (z) and effective internal friction angle φ (z) are defined as random variables varying with depth, establishing c (z) and φ (z) uncertainty prediction analysis model with depth: （6） wherein z is the depth of the soil, c (z) and φ (z) is a depth trend component function, such as a mean function of the soil strength parameter along the depth z of the soil. w x (z) is a random fluctuation component function, mean m j , standard deviation s j normal stationary random field as a function of the depth S62. The uncertainty prediction model of the soil shear strength parameter is assigned to the geometric model of the slope, and the analysis is carried out according to the optimized Monte Carlo simulation, so as to calculate the instability probability of the depth evolution random field slope model.

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