A slope system reliability analysis method based on improved Monte Carlo simulation

Abstract

The present invention discloses a slope system reliability analysis method based on improved Monte Carlo simulation, comprising the following steps: 1. determining the statistical characteristics of the shear strength parameters cohesion c and internal friction angle φ of the slope soil, and establishing a slope stability mechanical analysis model; 2. generating a large number of random samples consisting of soil shear strength parameters in a physical parameter space X-space to form an MCS sample library; 3. randomly selecting a sample from the MCS sample library, calculating a safety factor using a slope stability model, and obtaining a corresponding critical sample using the sample and the safety factor; 4. determining the number of partially failed and safe samples in the MCS library based on the critical sample according to the intrinsic relationship between the soil shear strength parameter and the slope safety factor, and removing these samples from the MCS library; and finally, repeating steps 3 and 4 until the MCS library is empty, calculating the slope failure probability, and identifying the key failure modes of the slope.

Description

Technical Field

[0001] The present invention belongs to the technical field of slope reliability analysis methods, and more specifically, relates to a slope system reliability analysis method based on improved Monte Carlo simulation. Background Art

[0002] Slope refers to an open surface with a certain slope that is formed naturally or when roads, buildings and other projects are constructed, under the action of natural gravity or human action. Slope stability is one of the key factors affecting project safety. The rock and soil in the construction site are affected by natural actions such as sedimentation, weathering, erosion and transportation, as well as historical loads. Their physical and mechanical parameters have significant randomness and differences, which makes the structural response of the slope (such as safety factor, deformation, etc.) full of uncertainty. Although the traditional "safety factor method" is simple and intuitive, it ignores the uncertainty of parameters, which often leads to inaccurate and inefficient slope safety assessment and design. Reliability analysis can quantitatively assess the failure probability of slopes under various adverse conditions, thereby identifying potential risks in advance and providing an effective tool for uncertainty quantification. Although the traditional Monte Carlo simulation (MCS) has high calculation accuracy, the target failure probability of most slope structures is low (10 -3 ), resulting in enormous computational costs, making slope reliability assessment extremely challenging, especially when complex working conditions are involved. Furthermore, slopes typically have a large number of potential failure sliding surfaces, each of which can lead to different failure modes. Understanding key failure modes is crucial for slope safety management. However, traditional MCS can only derive a slope's failure probability or reliability index, making it difficult to determine the most probable point (MPP) for slope failure. The corresponding failure mode is called a critical failure mode. Summary of the Invention

[0003] In response to the problems existing in the existing technology, the present invention provides a slope system reliability analysis method based on improved Monte Carlo simulation, starting from the physical and mechanical mechanism of slope stability. This method can significantly reduce the number of slope stability analyses in the MCS calculation process and effectively identify the key failure modes of the slope, providing a new and efficient analysis tool for slope system reliability assessment.

[0004] To achieve the above object, the present invention provides the following technical solution: a slope system reliability analysis method based on improved Monte Carlo simulation, comprising the following steps:

[0005] S1. Determine the statistical characteristics of slope soil shear strength parameters;

[0006] S2. Establish a slope stability model based on the slope geometry and the mean value of soil shear strength parameters to obtain the slope safety factor;

[0007] S3. Based on the statistical characteristics of the parameters, a large number of random samples of soil shear strength parameters are extracted in the physical parameter space and used as the MCS Monte Carlo simulation sample library S;

[0008] S4, randomly selecting a sample from the MCS sample library, calculating the safety factor using the slope stability model, and obtaining the corresponding critical sample using the sample and the safety factor;

[0009] S5. Based on the intrinsic relationship between soil shear strength parameters and slope safety factor, the number of partially failed and safe samples in the MCS library is determined using critical samples, and these samples are removed from the MCS library;

[0010] S6. Determine whether the MCS sample library S is an empty set. If S is an empty set, execute step S7; otherwise, return to step S4;

[0011] S7. Count the total number of slope failure samples and calculate the failure probability;

[0012] S8. Identify the key failure modes of the slope based on the slope failure samples.

[0013] Optionally, in step S1, the slope soil shear strength parameters include: cohesion c and internal friction angle φ;

[0014] The statistical characteristics include: probability distribution type, mean and standard deviation or coefficient of variation;

[0015] The probability distribution types of the cohesion c and the internal friction angle φ include: normal distribution, lognormal distribution and exponential distribution;

[0016] The distribution type is determined after a goodness of fit test is performed using statistical software;

[0017] The goodness of fit test is to compare the degree of fit between different distribution types and measured data;

[0018] The mean is used to describe the average level of soil shear strength parameters, and the formula is:

[0019]

[0020] Where: μ j is the mean value of the jth shear strength parameter, x i is the measurement value of each sample, n is the number of samples;

[0021] The standard deviation is used to reflect the degree of fluctuation of the parameter value around the mean, and its formula is:

[0022]

[0023] Where: j is the standard deviation of the j-th shear strength parameter,

[0024] The coefficient of variation is the ratio of the standard deviation to the mean, and is used to reflect the variability of parameter values under different conditions.

[0025] Optionally, in step S2, the specific steps of obtaining the safety factor are:

[0026] S21. Establish a geometric model of the slope in numerical analysis software based on the actual geometric dimensions of the slope;

[0027] S22. Investigate the soil's density and shear strength parameter data, and calculate the slope safety factor with the help of analysis software based on the soil's physical and mechanical properties.

[0028] Optionally, in step S3, the step of generating the random sample includes:

[0029] S31. Generate a large number of random samples based on parameter probability distribution data;

[0030] S32, saving the acquired sample data in the MCS sample library;

[0031] The MCS sample library is S=[x1,x2,x3,…,x N ] T ;

[0032] The i-th sample x i =[c 1i ,c 2i ,…,c pi ,φ 1i ,φ 2i ,…,φ qi ];

[0033] Where: c pi represents the p-th soil cohesion variable of the ith sample;

[0034] φ qi represents the internal friction angle variable of the qth soil of the i-th sample;

[0035] i=1,2,…,N;

[0036] p and q are the number of variables c and φ respectively.

[0037] Optionally, in step S4, the specific steps include:

[0038] S41. In the MCS sample library S, a sample is selected using random sampling technology and recorded as sample x. k ;

[0039] S42. For the selected sample x k , calculate with the help of slope stability model, and obtain the safety factor corresponding to the sample, which is recorded as FS k ;

[0040] S43. Based on the strength reduction theory, use the preset formula to calculate the sample x k The parameters are reduced or adjusted to obtain the corresponding critical samples

[0041] The formula is a mathematical expression that describes the strength reduction process and is related to the critical state. The specific formula is:

[0042]

[0043] in: and It is the critical shear strength parameter that puts the slope in a state of ultimate equilibrium;

[0044] in is the pth critical soil cohesion variable of the kth sample;

[0045] is the qth critical soil internal friction angle variable of the kth sample;

[0046] c pk represents the p-th soil cohesion variable of the k-th sample;

[0047] φ qk represents the qth soil internal friction angle variable of the kth sample;

[0048] The slope safety factor under the critical shear strength parameter is 1, that is,

[0049] Optionally, in step S5, the process of determining failed samples and safe samples is as follows:

[0050] The safety factor FS is defined as the ratio of the shear strength on the sliding surface of the slope soil to the sliding shear force. FS is expressed as a function of the cohesion c and the internal friction angle φ, that is:

[0051]

[0052] Where: τ and σ n are the shear stress and normal stress on the failure sliding surface of the slope, respectively;

[0053] L is the sliding surface of the slope;

[0054] A and B represent the entry and exit points of the slope sliding surface, respectively;

[0055] M is the number of vertical soil strips divided along the bottom of the sliding surface;

[0056] c i and φ i are the cohesion and internal friction angle of the bottom sliding surface of the i-th soil strip, respectively;

[0057] l i is the length of the bottom sliding surface of the i-th soil strip;

[0058] In slopes with the same geometry and soil gravity, when c m >c n And φ m >φ n ,but

[0059]

[0060] Get FS m >FS n , indicating that FS = f(c,φ) is a monotonically increasing function of cohesion c and internal friction angle φ;

[0061] According to step S5, a critical sample is obtained, and the number of safe samples and failed samples in the MCS sample library S is determined by the critical sample, and these two parts of samples are removed from the MCS library;

[0062] The critical sample corresponds to FS=1;

[0063] The safety sample corresponds to FS i >1;

[0064] The failed sample corresponds to FS i <1.

[0065] Optionally, in step S7, the failure probability calculation formula is:

[0066] P f =M / N

[0067] Where M is the total number of slope failure samples;

[0068] N is the total number of slope samples in the MCS database.

[0069] Optionally, in step S8, the specific steps include:

[0070] S81. In the independent standard normal space U space, calculate the distance between all failed samples and the coordinate origin, and select the sample with the smallest distance as the design point;

[0071] S82, calculating the correlation coefficient between the design point and all other samples, and eliminating samples with correlation coefficients greater than a threshold ρ0;

[0072] S83, repeating steps S81 and S82, performing the same operation on each remaining failed sample in the set, until no failed samples remain in the set;

[0073] S84. Based on the obtained design points, the parameters are input into the slope stability analysis model to obtain the key failure modes of the slope;

[0074] The distance between the design point corresponding to the critical failure mode and the coordinate origin is the key reliability index β of the slope j , and its corresponding failure probability P fj =1-Φ(β j ),

[0075] The Φ is the standard normal cumulative distribution function.

[0076] Optionally, in step S81,

[0077] The formula for the distance D between the failure sample and the coordinate origin is:

[0078]

[0079] Among them, the failure sample points are composed of k independent standard normal variables;

[0080] k=p+q;

[0081] Where: p and q are the number of variables c and φ respectively;

[0082] The failure sample point of the U space is u=[u1,u2,…,u k ].

[0083] Optionally, the calculation formula in step S82 is:

[0084]

[0085] Where: u i and u j are two samples in U space respectively;

[0086] ρ ij is the correlation coefficient between the two samples;

[0087] D i and D j are the distances calculated between the two samples and the coordinate origin;

[0088] Set the threshold ρ0=0.5.

[0089] The technical effects and advantages of the present invention are as follows: The traditional MCS method mainly relies on the simulation of a large number of random samples to estimate the failure probability. The present invention integrates the physical relationship between the slope shear strength parameter and the safety factor FS into the probabilistic statistical analysis based on the traditional MCS method, thereby reducing the number of slope stability analyses while still maintaining the accuracy of the analysis results.

[0090] By identifying the sensitivity between key parameters (such as shear strength parameters) and the safety factor FS, the new method can achieve efficient screening of samples in the MCS sample library, so that only a small number of representative samples need to be analyzed in detail to infer the safety status of the entire sample library, significantly reducing the amount of calculation and achieving the same failure probability as the traditional MCS method. In addition, further post-processing of the failed samples can also determine the design point or most likely point of slope failure. This in-depth analysis provides engineers with more intuitive slope failure modes and protective measures.

[0091] Further features and advantages of the present invention will become apparent from the following detailed description of exemplary embodiments of the present invention with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 It is a technical flow chart of the present invention;

[0093] Figure 2 is a schematic diagram of the slope profile and geometric parameters in an embodiment of the present invention;

[0094] Figure 3 Schematic diagram of safe samples and failed samples obtained by the first iterative calculation in an embodiment of the present invention;

[0095] Figure 4 Schematic diagram of the sample security status and position distribution at the end of iterative calculation in an embodiment of the present invention;

[0096] Figure 5 1 is a comparison chart of the calculation results of the method of the present invention and the MCS method in an embodiment of the present invention;

[0097] Figure 6 is a schematic diagram of the number of sample points with unknown security status in an embodiment of the present invention;

[0098] Figure 7 Schematic diagram of two key failure modes of the slope in an embodiment of the present invention. DETAILED DESCRIPTION

[0099] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0100] like Figures 1 to 7 As shown, an embodiment of the present invention provides a slope system reliability analysis method based on improved Monte Carlo simulation, comprising the following steps:

[0101] S1. Determine the statistical characteristics of slope soil shear strength parameters;

[0102] S2. Establish a slope stability model based on the slope geometry and the mean value of soil shear strength parameters to obtain the slope safety factor;

[0103] S3. Based on the statistical characteristics of the parameters, a large number of random samples of soil shear strength parameters are extracted in the physical parameter space and used as the MCS Monte Carlo simulation sample library S;

[0104] S4, randomly selecting a sample from the MCS sample library, calculating the safety factor using the slope stability model, and obtaining the corresponding critical sample using the sample and the safety factor;

[0105] S5. Based on the intrinsic relationship between soil shear strength parameters and slope safety factor, the number of partially failed and safe samples in the MCS library is determined using critical samples, and these samples are removed from the MCS library;

[0106] S6. Determine whether the MCS sample library S is an empty set. If S is an empty set, execute step S7; otherwise, return to step S4;

[0107] S7. Count the total number of slope failure samples and calculate the failure probability;

[0108] S8. Identify the key failure modes of the slope based on the slope failure samples.

[0109] Furthermore, the traditional MCS method mainly relies on the simulation of a large number of random samples to estimate the failure probability. Based on the traditional MCS method, the present invention integrates the physical relationship between the slope shear strength parameter and the safety factor FS into the probabilistic statistical analysis, reducing the number of slope stability analyses while still maintaining the accuracy of the analysis results.

[0110] By identifying the sensitivity between key parameters (such as shear strength parameters) and the safety factor FS, the new method can achieve efficient screening of samples in the MCS sample library, so that only a small number of representative samples need to be analyzed in detail to infer the safety status of the entire sample library, significantly reducing the amount of calculation and achieving the same failure probability as the traditional MCS method. In addition, further post-processing of the failed samples can also determine the design point or most likely point of slope failure. This in-depth analysis provides engineers with more intuitive slope failure modes and protective measures.

[0111] Specifically, in step S1, the slope soil shear strength parameters include: cohesion c and internal friction angle φ;

[0112] The statistical characteristics include: probability distribution type, mean and standard deviation or coefficient of variation;

[0113] The probability distribution types of the cohesion c and the internal friction angle φ include normal distribution, lognormal distribution and exponential distribution;

[0114] The distribution type is determined after a goodness of fit test is performed using statistical software;

[0115] The goodness of fit test is to compare the degree of fit between different distribution types and measured data;

[0116] The mean is used to describe the average level of soil shear strength parameters, and the formula is:

[0117]

[0118] Where: μ j is the mean value of the jth shear strength parameter, x i is the measurement value of each sample, n is the number of samples;

[0119] The standard deviation is used to reflect the degree of fluctuation of the parameter value around the mean, and its formula is:

[0120]

[0121] Where: j is the standard deviation of the j-th shear strength parameter,

[0122] The coefficient of variation is the ratio of the standard deviation to the mean, and is used to reflect the variability of parameter values under different conditions.

[0123] Furthermore, the accurate acquisition and proper application of soil shear strength parameters (cohesion c and internal friction angle φ) are crucial in slope stability analysis. These parameters not only reflect the physical and mechanical properties of the soil but also directly impact slope stability assessment and design. Furthermore, consideration of statistical characteristics, such as the probability distribution type, mean, and standard deviation or coefficient of variation, provides a quantitative approach for parameter uncertainty analysis.

[0124] Furthermore, the chi-square test is used in the goodness of fit test, by calculating the difference between the observed frequency and the theoretical frequency and constructing the chi-square statistic to judge the goodness of fit;

[0125] The specific inspection steps are as follows:

[0126] 1) Divide the measured data into several groups;

[0127] 2) Calculate the observation frequency of each group;

[0128] 3) Calculate the theoretical frequency of each group based on the assumed distribution type;

[0129] 4) Construct a test statistic (such as the chi-square statistic) and calculate its value;

[0130] 5) Based on the significance level α = 0.05, determine whether the test statistic falls within the rejection region, and thus decide whether to accept the hypothesized distribution type.

[0131] Specifically, in step S2, the specific steps of obtaining the safety factor are:

[0132] S21. Establish a geometric model of the slope in numerical analysis software based on the actual geometric dimensions of the slope;

[0133] S22. Survey the soil's gravity and shear strength parameters, and calculate the slope safety factor using analysis software based on the soil's physical and mechanical properties;

[0134] Specifically, in step S3, the random sample generation step includes:

[0135] S31. Generate a large number of random samples based on parameter probability distribution data;

[0136] S32, saving the acquired sample data in the MCS sample library;

[0137] The MCS sample library is S=[x1,x2,x3,…,x N ] T ;

[0138] The i-th sample x i =[c 1i ,c 2i ,…,cpi ,φ 1i ,φ 2i ,…,φ qi ];

[0139] Where: c pi represents the p-th soil cohesion variable of the ith sample;

[0140] φ qi represents the internal friction angle variable of the qth soil of the i-th sample;

[0141] i=1,2,…,N;

[0142] p and q are the number of variables c and φ respectively.

[0143] Furthermore, since soil shear strength parameters often exhibit large variability in actual engineering, and this variability is affected by a variety of factors, such as soil type, moisture content, density, and stress history, randomly generating samples to reflect the randomness of soil parameters makes the simulation results closer to the actual situation. In addition, the generation of random samples can cover different regions in the parameter space, thus avoiding the limitation of analyzing based on only a limited number of fixed parameter values. This can make the analysis results more comprehensive and take into account the influence of various possible parameter combinations on the shear strength of the soil.

[0144] Specifically, in step S4, the specific steps include:

[0145] S41. In the MCS sample library S, a sample is selected using random sampling technology and recorded as sample x. k ;

[0146] S42. For the selected sample x k , calculate with the help of slope stability model, and obtain the safety factor corresponding to the sample, which is recorded as FS k ;

[0147] S43. Based on the strength reduction theory, use the preset formula to calculate the sample x k The parameters are reduced or adjusted to obtain the corresponding critical samples

[0148] The formula is a mathematical expression that describes the strength reduction process and is related to the critical state. The specific formula is:

[0149]

[0150] in: and It is the critical shear strength parameter that puts the slope in a state of ultimate equilibrium;

[0151] in is the pth critical soil cohesion variable of the kth sample;

[0152] is the qth critical soil internal friction angle variable of the kth sample;

[0153] c pk represents the p-th soil cohesion variable of the k-th sample;

[0154] φ qk represents the qth soil internal friction angle variable of the kth sample;

[0155] The slope safety factor under the critical shear strength parameter is 1, that is,

[0156] Specifically, in step S5, the process of determining whether a failed sample is a safe sample is as follows:

[0157] The safety factor FS is defined as the ratio of the shear strength on the sliding surface of the slope soil to the sliding shear force. FS is expressed as a function of the cohesion c and the internal friction angle φ, that is:

[0158]

[0159] Where: τ and σ n are the shear stress and normal stress on the failure sliding surface of the slope, respectively;

[0160] L is the sliding surface of the slope;

[0161] A and B represent the entry and exit points of the slope sliding surface, respectively;

[0162] M is the number of vertical soil strips divided along the bottom of the sliding surface;

[0163] c i and φ i are the cohesion and internal friction angle of the bottom sliding surface of the i-th soil strip, respectively;

[0164] l i is the length of the bottom sliding surface of the i-th soil strip;

[0165] In slopes with the same geometry and soil gravity, when c m >c n And φ m >φ n ,but

[0166]

[0167] Get FS m >FS n , indicating that FS = f(c,φ) is a monotonically increasing function of cohesion c and internal friction angle φ;

[0168] According to step S5, a critical sample is obtained, and the number of safe samples and failed samples in the MCS sample library S is determined by the critical sample, and these two parts of samples are removed from the MCS library;

[0169] The critical sample corresponds to FS=1;

[0170] The safety sample corresponds to FS i >1;

[0171] The failed sample corresponds to FS i <1.

[0172] Furthermore, the safety factor provides a quantitative indicator to evaluate the stability of the slope. By calculating the safety factor, the stability of the slope in its current state can be clarified, providing a scientific basis for subsequent design, construction and maintenance. By calculating and analyzing the safety factor, potential safety hazards can be discovered in a timely manner and appropriate measures can be taken to deal with them.

[0173] Specifically, in step S7, the failure probability calculation formula is:

[0174] P f =M / N

[0175] Where M is the total number of slope failure samples;

[0176] N is the total number of slope samples in the MCS database.

[0177] Specifically, in step S8, the specific steps include:

[0178] S81. In the independent standard normal space U space, calculate the distance between all failed samples and the coordinate origin, and select the sample with the smallest distance as the design point;

[0179] S82, calculating the correlation coefficient between the design point and all other samples, and eliminating samples with correlation coefficients greater than a threshold ρ0;

[0180] S83, repeating steps S81 and S82, performing the same operation on each remaining failed sample in the set, until no failed samples remain in the set;

[0181] S84. Based on the obtained design points, the parameters are input into the slope stability analysis model to obtain the key failure modes of the slope;

[0182] The distance between the design point corresponding to the critical failure mode and the coordinate origin is the key reliability index β of the slope j , and its corresponding failure probability P fj =1-Φ(β j ),

[0183] The Φ is the standard normal cumulative distribution function.

[0184] Specifically, in step S81,

[0185] The formula for the distance D between the failure sample and the coordinate origin is:

[0186]

[0187] Among them, the failure sample points are composed of k independent standard normal variables;

[0188] k=p+q;

[0189] Where: p and q are the number of variables c and φ respectively;

[0190] The failure sample point of the U space is u=[u1,u2,…,u k ].

[0191] Specifically, the calculation formula in step S82 is:

[0192]

[0193] Where: u i and u j are two samples in U space respectively;

[0194] ρ ij is the correlation coefficient between the two samples;

[0195] D i and D j are the distances calculated between the two samples and the coordinate origin;

[0196] Set the threshold ρ0=0.5.

[0197] Implementation examples:

[0198] The method of the present invention is verified by taking a double-layer clay slope as an example. Figure 2 As shown, the slope height is 24m, the slope angle is 36.9°, the thickness of the upper and lower soil layers are 18m and 10m respectively. The soil weight is 19kN / m 3 , undrained shear strength of double-layer clay c u1 and c u2 are independent random variables and obey the lognormal distribution. The statistical characteristics of soil parameters are listed in Table 1.

[0199] Table 1 Summary of slope soil parameters

[0200]

[0201]

[0202] When the uncertain parameters are averaged, the FS calculated by the simplified Bishop method is 1.991, which is consistent with the results in the literature (such as 1.992, 1.997, 1.993, and 1.990), verifying the accuracy of the slope determination analysis model. The position of the most dangerous sliding surface is as follows: Figure 2 shown.

[0203] Table 2 Comparison of design points obtained by different methods

[0204]

[0205] According to the calculation process proposed by the present invention, the result after the first iterative calculation can be obtained, such as Figure 3 As shown;

[0206] As can be seen from the figure, only one slope stability analysis is required to identify the safety status of a large number of samples in the MCS sample library, without repeatedly calling the slope stability model to solve the accurate FS.

[0207] When the iterative calculation is completed, the security status of all samples in the MCS library and the location distribution of different samples can be obtained, such as Figure 4 As shown;

[0208] Safety Sample FS i >1 and failed sample FS i The interface with a value of <1 represents the limit state boundary, which is composed of two intersecting straight lines, indicating that the performance function of the slope is highly nonlinear.

[0209] Slope reliability analysis usually takes the result of direct MCS calculation as the exact solution. On a computer with Intel Core i5, 2.4GHz, 16GB memory and quad-core CPU, the P obtained by performing 1 million traditional MCS analyses on the slope in this example is f =3.874×10 -3 , which took about 19.4 hours.

[0210] The present invention only needs to perform 160 slope stability analyses to obtain the slope P f =3.874×10 -3 , which is completely consistent with the traditional MCS analysis results, but takes only 55.2s, saving 99.92% of the calculation cost and greatly improving the analysis efficiency.

[0211] The comparison of the calculation results of the method of the present invention and the MCS method is as follows: Figure 5As shown in the figure, the failure probability of the proposed method begins to converge after only 20 slope stability analyses, while the MCS method requires 480 slope stability analyses to identify one failure sample and 200,000 slope stability analyses before the failure probability tends to be stable.

[0212] like Figure 6 As shown in Figure 2, a comparison of the convergence rates of the two methods is further presented. Given the same number of slope stability analyses, the present invention significantly reduces the number of sample points with unknown safety states compared to the MCS. After post-processing the failed samples, the design point for the slope can also be obtained. Table 2 compares the design points obtained by different methods.

[0213] As can be seen from Table 2, the design point (or MPP) values calculated by the method of the present invention and the first order reliability analysis method (FORM) are basically consistent, and the P values of the two failure modes corresponding to the design points are fj Basically consistent. Figure 7 Two key failure modes of the slope are identified: failure along the interface between the upper and lower soil layers, and failure at the slope base, which is a circular sliding surface. These results demonstrate the efficiency and accuracy of the patented method, overcoming the shortcomings of traditional MCS methods.

[0214] In summary, based on the traditional MCS method, the present invention integrates the physical relationship between slope shear strength parameters and safety factor FS into the probabilistic statistical analysis, which reduces the number of slope stability analyses while still maintaining the accuracy of the analysis results.

[0215] First, based on the strength reduction theory, samples with a slope safety factor FS of 1.0 were determined. Second, the intrinsic relationship between the slope soil shear strength parameters and the safety factor was used to directly determine whether the slope was in a safe or failed state, avoiding the tedious FS precise solution and significantly improving the computational efficiency of the traditional MCS method. Finally, the failed samples were used to obtain the key failure modes of the slope.

[0216] Therefore, the present invention provides a new and efficient calculation method for slope system reliability analysis, and the identification of key failure modes provides guidance for slope safety reinforcement and landslide disaster management.

[0217] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A slope system reliability analysis method based on improved Monte Carlo simulation, characterized by: The steps include: S1. Determine the statistical characteristics of slope soil shear strength parameters; S2. Establish a slope stability model based on the slope geometry and the mean value of soil shear strength parameters to obtain the slope safety factor; S3. Based on the statistical characteristics of the parameters, a large number of random samples of soil shear strength parameters are extracted in the physical parameter space and used as the MCS Monte Carlo simulation sample library S; S4, randomly selecting a sample from the MCS sample library, calculating the safety factor using the slope stability model, and obtaining the corresponding critical sample using the sample and the safety factor; S5. Based on the intrinsic relationship between soil shear strength parameters and slope safety factor, the number of partially failed and safe samples in the MCS library is determined using critical samples, and these samples are removed from the MCS library; S6. Determine whether the MCS sample library S is an empty set. If S is an empty set, execute step S7; otherwise, return to step S4; S7. Count the total number of slope failure samples and calculate the failure probability; S8. Identify the key failure modes of the slope based on the slope failure samples.

2. The slope system reliability analysis method based on improved Monte Carlo simulation according to claim 1 is characterized by: In step S1, the slope soil shear strength parameters include: cohesion c and internal friction angle φ; The statistical characteristics include: probability distribution type, mean and standard deviation or coefficient of variation; The probability distribution types of the cohesion c and the internal friction angle φ include: normal distribution, lognormal distribution and exponential distribution; The distribution type is determined after a goodness of fit test is performed using statistical software; The goodness of fit test is to compare the degree of fit between different distribution types and measured data; The mean is used to describe the average level of soil shear strength parameters, and the formula is: Where: μ j is the mean value of the jth shear strength parameter, x i is the measurement value of each sample, n is the number of samples; The standard deviation is used to reflect the degree of fluctuation of the parameter value around the mean, and its formula is: Where: j is the standard deviation of the j-th shear strength parameter, The coefficient of variation is the ratio of the standard deviation to the mean, and is used to reflect the variability of parameter values under different conditions.

3. The slope system reliability analysis method based on improved Monte Carlo simulation according to claim 1 is characterized by: In step S2, the specific steps of obtaining the safety factor are: S21. Establish a geometric model of the slope in numerical analysis software based on the actual geometric dimensions of the slope; S22. Investigate the soil's density and shear strength parameter data, and calculate the slope safety factor with the help of analysis software based on the soil's physical and mechanical properties.

4. The slope system reliability analysis method based on improved Monte Carlo simulation according to claim 1 is characterized by: In step S3, the random sample generation step includes: S31. Generate a large number of random samples based on parameter probability distribution data; S32, saving the acquired sample data in the MCS sample library; The MCS sample library is S=[x1,x2,x3,…,x N ] T ; The i-th sample x i =[c 1i ,c 2i ,…,c pi ,φ 1i ,φ 2i ,…,φ qi ]; Where: c pi represents the p-th soil cohesion variable of the ith sample; φ qi represents the internal friction angle variable of the qth soil of the i-th sample; i=1,2,…,N; p and q are the number of variables c and φ respectively.

5. The slope system reliability analysis method based on improved Monte Carlo simulation according to claim 1 is characterized in that: Step S4 The specific steps include: S41. In the MCS sample library S, a sample is selected using random sampling technology and recorded as sample x. k ; S42. For the selected sample x k , calculate with the help of slope stability model, and obtain the safety factor corresponding to the sample, which is recorded as FS k ; S43. Based on the strength reduction theory, use the preset formula to calculate the sample x k The parameters are reduced or adjusted to obtain the corresponding critical samples The formula is a mathematical expression that describes the strength reduction process and is related to the critical state. The specific formula is: in: and It is the critical shear strength parameter that puts the slope in a state of ultimate equilibrium; in is the pth critical soil cohesion variable of the kth sample; is the qth critical soil internal friction angle variable of the kth sample; c pk represents the p-th soil cohesion variable of the k-th sample; φ qk represents the qth soil internal friction angle variable of the kth sample; The slope safety factor under the critical shear strength parameter is 1, that is, 6. The slope system reliability analysis method based on improved Monte Carlo simulation according to claim 1 is characterized by: In step S5, the process of determining failed samples and safe samples is as follows: The safety factor FS is defined as the ratio of the shear strength on the sliding surface of the slope soil to the sliding shear force. FS is expressed as a function of the cohesion c and the internal friction angle φ, that is: Where: τ and σ n are the shear stress and normal stress on the failure sliding surface of the slope, respectively; L is the sliding surface of the slope; A and B represent the entry and exit points of the slope sliding surface, respectively; M is the number of vertical soil strips divided along the bottom of the sliding surface; c i and φ i are the cohesion and internal friction angle of the bottom sliding surface of the i-th soil strip, respectively; l i is the length of the bottom sliding surface of the i-th soil strip; In slopes with the same geometry and soil gravity, when c m >c n And φ m >φ n ,but Get FS m >FS n , indicating that FS = f(c,φ) is a monotonically increasing function of cohesion c and internal friction angle φ; According to step S5, a critical sample is obtained, and the number of safe samples and failed samples in the MCS sample library S is determined by the critical sample, and these two parts of samples are removed from the MCS library; The critical sample corresponds to FS=1; The safety sample corresponds to FS i >1; The failed sample corresponds to FS i <1.

7. The slope system reliability analysis method based on improved Monte Carlo simulation according to claim 1 is characterized by: In step S7, the failure probability calculation formula is: P f =M / N Where M is the total number of slope failure samples; N is the total number of slope samples in the MCS database.

8. The slope system reliability analysis method based on improved Monte Carlo simulation according to claim 1 is characterized by: In step S8, the specific steps include: S81. In the independent standard normal space U space, calculate the distance between all failed samples and the coordinate origin, and select the sample with the smallest distance as the design point; S82, calculating the correlation coefficient between the design point and all other samples, and eliminating samples with correlation coefficients greater than a threshold ρ0; S83, repeating steps S81 and S82, performing the same operation on each remaining failed sample in the set, until no failed samples remain in the set; S84. Based on the obtained design points, the parameters are input into the slope stability analysis model to obtain the key failure modes of the slope; The distance between the design point corresponding to the critical failure mode and the coordinate origin is the key reliability index β of the slope j , and its corresponding failure probability P fj =1-Φ(β j ), The Φ is the standard normal cumulative distribution function.

9. The slope system reliability analysis method based on improved Monte Carlo simulation according to claim 8 is characterized by: In step S81, The formula for the distance D between the failure sample and the coordinate origin is: Among them, the failure sample points are composed of k independent standard normal variables; k=p+q; Where: p and q are the number of variables c and φ respectively; The failure sample point of the U space is u=[u1,u2,…,u k ].

10. The slope system reliability analysis method based on improved Monte Carlo simulation according to claim 8, characterized in that: The calculation formula in step S82 is: Where: u i and u j are two samples in U space respectively; ρ ij is the correlation coefficient between the two samples; D i and D j are the distances calculated between the two samples and the coordinate origin; Set the threshold ρ0=0.5.

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