Slope system reliability analysis method based on improved Monte Carlo simulation

Abstract

The invention discloses an improved Monte Carlo simulation-based slope system reliability analysis method, which comprises the following steps of: 1, determining statistical characteristics of a shear strength parameter cohesive force c and an internal friction angle phi of a slope soil body, and establishing a slope stability mechanical analysis model; 2, random samples formed by a large number of soil shear strength parameters are generated in a physical parameter space X, and an MCS sample library is formed; 3, randomly selecting a sample from the MCS sample library, calculating a safety coefficient by using the slope stability model, and obtaining a corresponding critical sample by using the sample and the safety coefficient; 4, determining the number of partial failure and safety samples in the MCS library by using the critical samples according to the internal relationship between the soil shear strength parameter and the slope safety coefficient, and removing the samples from the MCS library; and finally, repeatedly executing the steps 3 and 4 until the MCS library is an empty set, calculating the slope failure probability and identifying the key failure mode of the slope.

Description

Technical Field

[0001] The invention belongs to the technical field of slope reliability analysis methods, and more specifically, particularly 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, due to 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 variability, 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 often leads to inaccurate and inefficient slope safety assessment and design because it ignores the uncertainty of parameters. Reliability analysis can quantitatively evaluate 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 huge computational costs, especially when it comes to complex working conditions, slope reliability assessment becomes extremely challenging. In addition, slopes usually have a large number of potential failure sliding surfaces. Different failure sliding surfaces may lead to different failure modes of the slope. Mastering the key failure mode plays an important guiding role in slope safety management. However, traditional MCS can only obtain the failure probability or reliability index of the slope, and it is difficult to obtain the most probable sample point (Most Probable Point, MPP) of the slope failure. The corresponding failure mode is called the key failure mode. Summary of the invention

[0003] In view of the problems existing in the prior art, the present invention provides a slope system reliability analysis method based on improved Monte Carlo simulation 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. According to the geometric dimensions of the slope and the mean values ​​of the soil shear strength parameters, a mechanical model for slope stability analysis is established to obtain the safety factor of the slope stability;

[0007] S3. Based on the statistical characteristics of the parameters, a large number of random samples consisting 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 select a sample in the MCS sample library, calculate the safety factor using the slope stability model, and use the sample and the safety factor to obtain the corresponding critical sample;

[0009] S5. According to 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, judging whether the MCS sample library S is an empty set, if S is an empty set, executing step S7; otherwise, returning 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, etc.;

[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 measured 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. According to the actual geometric dimensions of the slope, a geometric model of the slope is established in the numerical analysis software;

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

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

[0029] S31, generating a large number of random samples according to parameter probability distribution data;

[0030] S32, storing 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 ith 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, denoted as sample x. k ;

[0039] S42. For the selected sample x k , the slope stability model is used to calculate 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] The slope safety factor under the critical shear strength parameter is 1, that is,

[0047] Optionally, in step S5, the process of determining the failed sample and the safe sample is as follows:

[0048] The safety factor FS is defined based on 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:

[0049]

[0050] Where: τ and σ n are the shear stress and normal stress on the failure sliding surface of the slope, respectively;

[0051] L is the sliding surface of the slope;

[0052] A and B represent the entry and exit points of the slope sliding surface, respectively;

[0053] M is the number of vertical soil strips divided along the bottom of the sliding surface;

[0054] c iand φ i are the cohesion and internal friction angle of the bottom sliding surface of the i-th soil strip, respectively;

[0055] l i is the length of the bottom sliding surface of the i-th soil strip;

[0056] In the slope with the same geometry and soil gravity, when c m >c n And φ m >φ n ,but

[0057]

[0058] Get FS m >FS n , indicating that FS = f(c, φ) is a monotonically increasing function of cohesion c and internal friction angle φ;

[0059] According to step S5, critical samples are obtained, and the number of safe samples and failed samples in the MCS sample library S is determined by the critical samples, and these two parts of samples are removed from the MCS library;

[0060] The critical sample corresponds to FS=1;

[0061] The safety sample corresponds to FS i >1;

[0062] The failed sample corresponds to FS i <1.

[0063] Optionally, in step S7, the failure probability calculation formula is:

[0064] P f =M / N

[0065] Where, M is the total number of slope failure samples;

[0066] N is the total number of slope samples in the MCS database.

[0067] Optionally, in step S8, the specific steps include:

[0068] 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;

[0069] S82, calculating the correlation coefficient between the design point and all other samples, and eliminating the samples with correlation coefficients greater than a threshold value ρ0;

[0070] S83, repeating step S81 and step S82, performing the same operation on each remaining failed sample in the set, until there are no remaining failed samples in the set;

[0071] S84, according to the obtained design point, input the parameters into the slope stability analysis model, and obtain the key failure mode of the slope;

[0072] 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 ),

[0073] The Φ is the standard normal cumulative distribution function.

[0074] Optionally, in step S81,

[0075] The formula for the distance D between the failed sample and the coordinate origin is:

[0076]

[0077] Among them, the failure sample points are composed of k independent standard normal variables;

[0078] k=p+q;

[0079] The failure sample point of the U space is u=[u1,u2,…,u k ].

[0080] Optionally, the calculation formula in step S82 is:

[0081]

[0082] Where: u i and u j They are two samples in U space respectively;

[0083] ρ ij is the correlation coefficient between the two samples;

[0084] D i and D j are the distances calculated between the two samples and the coordinate origin respectively;

[0085] Set the threshold ρ0=0.5.

[0086] Technical effects and advantages of the present invention: The traditional MCS method mainly relies on the simulation of a large number of random samples to estimate the failure probability. On the basis of the traditional MCS method, the present invention integrates the physical relationship between the slope shear strength parameter and the safety factor FS into the probability statistical analysis, thereby reducing the number of slope stability analyses while still maintaining the accuracy of the analysis results;

[0087] 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, which significantly reduces the amount of calculation and can obtain the same failure probability as the traditional MCS method. In addition, further post-processing of the failed samples can also obtain 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.

[0088] 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 attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 It is a technical flow chart of the present invention;

[0090] Figure 2 is a schematic diagram of slope profile and geometric parameters in an embodiment of the present invention;

[0091] Figure 3 is a schematic diagram of safe samples and failed samples obtained by the first iterative calculation in an embodiment of the present invention;

[0092] Figure 4 is a schematic diagram of sample security status and position distribution at the end of iterative calculation in an embodiment of the present invention;

[0093] Figure 5 is a comparison diagram of calculation results of the method of the present invention and the MCS method in an embodiment of the present invention;

[0094] Figure 6 is a schematic diagram of the number of sample points whose safety status is unknown in an embodiment of the present invention;

[0095] Figure 7 Schematic diagram of two key failure modes of the slope in the embodiment of the present invention. DETAILED DESCRIPTION

[0096] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with 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.

[0097] like Figures 1 to 7 As shown, a slope system reliability analysis method based on improved Monte Carlo simulation provided by an embodiment of the present invention includes the following steps:

[0098] S1. Determine the statistical characteristics of slope soil shear strength parameters;

[0099] S2. According to the geometric dimensions of the slope and the mean values ​​of the soil shear strength parameters, a mechanical model for slope stability analysis is established to obtain the safety factor of the slope stability;

[0100] S3. Based on the statistical characteristics of the parameters, a large number of random samples consisting of soil shear strength parameters are extracted in the physical parameter space and used as the MCS Monte Carlo simulation sample library S;

[0101] S4, randomly select a sample in the MCS sample library, calculate the safety factor using the slope stability model, and use the sample and the safety factor to obtain the corresponding critical sample;

[0102] S5. According to 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;

[0103] S6, judging whether the MCS sample library S is an empty set, if S is an empty set, executing step S7; otherwise, returning to step S4;

[0104] S7. Count the total number of slope failure samples and calculate the failure probability;

[0105] S8. Identify the key failure modes of the slope based on the slope failure samples.

[0106] Furthermore, the traditional MCS method mainly relies on the simulation of a large number of random samples to estimate the failure probability. On the basis of the traditional MCS method, the present invention integrates the physical relationship between the slope shear strength parameter and the safety factor FS into the probability statistical analysis, thereby reducing the number of slope stability analyses while still maintaining the accuracy of the analysis results.

[0107] 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, which significantly reduces the amount of calculation and can obtain the same failure probability as the traditional MCS method. In addition, further post-processing of the failed samples can also obtain 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.

[0108] Specifically, in step S1, the slope soil shear strength parameters include: cohesion c and internal friction angle φ;

[0109] The statistical characteristics include: probability distribution type, mean and standard deviation or coefficient of variation;

[0110] The probability distribution types of the cohesion c and the internal friction angle φ include: normal distribution, lognormal distribution and exponential distribution, etc.;

[0111] The distribution type is determined after a goodness of fit test is performed using statistical software;

[0112] The goodness of fit test is to compare the degree of fit between different distribution types and measured data;

[0113] The mean is used to describe the average level of soil shear strength parameters, and the formula is:

[0114]

[0115] Where: μ j is the mean value of the jth shear strength parameter, x i is the measured value of each sample, n is the number of samples;

[0116] The standard deviation is used to reflect the degree of fluctuation of the parameter value around the mean, and its formula is:

[0117]

[0118] Where: j is the standard deviation of the j-th shear strength parameter.

[0119] 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.

[0120] Furthermore, in the stability analysis of slope engineering, the accurate acquisition and reasonable application of soil shear strength parameters (cohesion c and internal friction angle φ) are crucial. These parameters not only reflect the physical and mechanical properties of the soil, but also directly affect the stability evaluation and design of the slope. At the same time, the consideration of statistical characteristics such as probability distribution type, mean and standard deviation or coefficient of variation provides a quantitative means for parameter uncertainty analysis.

[0121] Furthermore, the chi-square test was 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;

[0122] The specific inspection steps are as follows:

[0123] 1) Divide the measured data into several groups;

[0124] 2) Calculate the observation frequency of each group;

[0125] 3) Calculate the theoretical frequency of each group based on the assumed distribution type;

[0126] 4) Construct a test statistic (such as the chi-square statistic) and calculate its value;

[0127] 5) Based on the significance level α=0.05, determine whether the test statistic falls within the rejection region, thereby deciding whether to accept the assumed distribution type.

[0128] Specifically, in step S2, the specific steps of obtaining the safety factor are:

[0129] S21. According to the actual geometric dimensions of the slope, a geometric model of the slope is established in the numerical analysis software;

[0130] S22. Survey the soil weight and shear strength parameters and calculate the slope safety factor with the aid of analysis software based on the soil's physical and mechanical properties;

[0131] Specifically, in step S3, the step of generating the random sample includes:

[0132] S31, generating a large number of random samples according to parameter probability distribution data;

[0133] S32, storing the acquired sample data in the MCS sample library;

[0134] The MCS sample library is S = [x1, x2, x3, ..., x N ] T ;

[0135] The i-th sample x i =[c 1i ,c 2i ,…,c pi ,φ 1i ,φ 2i ,…,φ qi ];

[0136] Where: c pi represents the p-th soil cohesion variable of the ith sample;

[0137] φ qi represents the internal friction angle variable of the qth soil of the ith sample;

[0138] i=1,2,…,N;

[0139] p and q are the number of variables c and φ respectively.

[0140] Furthermore, since the shear strength parameters of soil often show large variability in actual engineering, and this variability is affected by many factors, such as soil type, moisture content, density, stress history, etc., the randomness of soil parameters is reflected by randomly generating samples, so that the simulation results are closer to the actual situation, and the generation of random samples can cover different areas in the parameter space, thus avoiding the limitation of only analyzing based on a limited number of fixed parameter values. In this way, the analysis results can be more comprehensive, and the influence of various possible parameter combinations on the shear strength of soil can be considered;

[0141] Specifically, in step S4, the specific steps include:

[0142] S41. In the MCS sample library S, a sample is selected using random sampling technology, denoted as sample x. k ;

[0143] S42. For the selected sample x k , the slope stability model is used to calculate the safety factor corresponding to the sample, which is recorded as FS k ;

[0144] 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

[0145] The formula is a mathematical expression that describes the strength reduction process and is related to the critical state. The specific formula is:

[0146]

[0147] in: and It is the critical shear strength parameter that puts the slope in a state of ultimate equilibrium;

[0148] in is the pth critical soil cohesion variable of the kth sample;

[0149] is the qth critical soil internal friction angle variable of the kth sample;

[0150] The slope safety factor under the critical shear strength parameter is 1, that is,

[0151] Specifically, in step S5, the process of determining the failed sample and the safe sample is as follows:

[0152] The safety factor FS is defined based on 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:

[0153]

[0154] Where: τ and σ n are the shear stress and normal stress on the failure sliding surface of the slope, respectively;

[0155] L is the sliding surface of the slope;

[0156] A and B represent the entry and exit points of the slope sliding surface, respectively;

[0157] M is the number of vertical soil strips divided along the bottom of the sliding surface;

[0158] c i and φ i are the cohesion and internal friction angle of the bottom sliding surface of the i-th soil strip, respectively;

[0159] l i is the length of the bottom sliding surface of the i-th soil strip;

[0160] In the slope with the same geometry and soil gravity, when c m >c n And φ m >φ n ,but

[0161]

[0162] Get FS m >FS n , indicating that FS = f(c, φ) is a monotonically increasing function of cohesion c and internal friction angle φ;

[0163] According to step S5, critical samples are obtained, and the number of safe samples and failed samples in the MCS sample library S is determined by the critical samples, and these two parts of samples are removed from the MCS library;

[0164] The critical sample corresponds to FS=1;

[0165] The safety sample corresponds to FS i >1;

[0166] The failed sample corresponds to FS i <1.

[0167] 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.

[0168] Specifically, in step S7, the failure probability calculation formula is:

[0169] P f =M / N

[0170] Where, M is the total number of slope failure samples;

[0171] N is the total number of slope samples in the MCS database.

[0172] Specifically, in step S8, the specific steps include:

[0173] 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;

[0174] S82, calculating the correlation coefficient between the design point and all other samples, and eliminating the samples with correlation coefficients greater than a threshold value ρ0;

[0175] S83, repeating step S81 and step S82, performing the same operation on each remaining failed sample in the set, until there are no remaining failed samples in the set;

[0176] S84, according to the obtained design point, input the parameters into the slope stability analysis model, and obtain the key failure mode of the slope;

[0177] 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 ),

[0178] The Φ is the standard normal cumulative distribution function.

[0179] Specifically, in step S81,

[0180] The formula for the distance D between the failed sample and the coordinate origin is:

[0181]

[0182] Among them, the failure sample points are composed of k independent standard normal variables;

[0183] k = p + q;

[0184] The failure sample point of the U space is u=[u1,u2,…,u k ].

[0185] Specifically, the calculation formula in step S82 is:

[0186]

[0187] Where: u i and u j They are two samples in U space respectively;

[0188] ρ ij is the correlation coefficient between the two samples;

[0189] D i and D j are the distances calculated between the two samples and the coordinate origin respectively;

[0190] Set the threshold ρ0=0.5.

[0191] Implementation examples:

[0192] 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°, and 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 They are independent random variables and obey log-normal distribution. The statistical characteristics of soil parameters are listed in Table 1.

[0193] Table 1 Summary of slope soil parameters

[0194]

[0195] 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 most dangerous sliding surface position is as follows Figure 2 shown.

[0196] Table 2 Comparison of design points obtained by different methods

[0197]

[0198] 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;

[0199] 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.

[0200] When the iterative calculation is finished, 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;

[0201] Safety Sample FS i >1 and failed sample FS i The interface of <1 represents the limit state boundary, which is composed of two straight lines intersecting each other, indicating that the functional function of the slope is highly nonlinear.

[0202] Slope reliability analysis usually takes the result of direct MCS calculation as the exact solution. On a computer with Intel Corei5, 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.

[0203] 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, saves 99.92% of the calculation cost, and greatly improves the analysis efficiency.

[0204] The comparison of the calculation results of the method of the present invention and the MCS method is as follows: Figure 5 As shown in the figure, it can be seen that the failure probability of the method of the present invention begins to converge after only 20 slope stability analyses; while the MCS method needs to perform 480 slope stability analyses to identify one failure sample, and perform 200,000 slope stability analyses before the failure probability tends to be stable.

[0205] like Figure 6 As shown in Figure 2, a comparison of the convergence speed of the two methods is further given. When the number of slope stability analyses is the same, the number of sample points with unknown safety status in the present invention is significantly less than that in MCS. After post-processing the failed samples, the design point of the slope can also be obtained. Table 2 gives a comparison of the design points obtained by different methods.

[0206] It can be seen from Table 2 that 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 point are fj Basically consistent. Figure 7 Two key failure modes of the slope are given, which are the arc sliding surface along the interface between the upper and lower soil layers and the slope base failure. Therefore, the above results verify the efficiency and accuracy of the patent of this invention and overcome the defects of the traditional MCS method.

[0207] In summary, 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 probability statistical analysis, which reduces the number of slope stability analyses while still maintaining the accuracy of the analysis results;

[0208] Firstly, the samples with slope safety factor FS of 1.0 are determined according to the strength reduction theory. Secondly, the intrinsic relationship between the shear strength parameters of the slope soil and the safety factor is used to directly judge whether the slope is in a safe state or a failed state, thus avoiding the tedious FS precise solution and significantly improving the calculation efficiency of the traditional MCS method. Finally, the key failure modes of the slope are obtained using the failed samples.

[0209] 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.

[0210] 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, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to 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 protection scope 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. According to the geometric dimensions of the slope and the mean values ​​of the soil shear strength parameters, a mechanical model for slope stability analysis is established to obtain the safety factor of the slope stability; 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 select a sample in the MCS sample library, calculate the safety factor using the slope stability model, and use the sample and the safety factor to obtain the corresponding critical sample; S5. According to 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, judging whether the MCS sample library S is an empty set, if S is an empty set, executing step S7; otherwise, returning 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, etc.; 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 measured 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. According to the actual geometric dimensions of the slope, a geometric model of the slope is established in the numerical analysis software; S22. Investigate the soil density and shear strength parameters and other data, and calculate the slope safety factor with the help of analysis software based on the physical and mechanical properties of the soil.

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, generating a large number of random samples according to parameter probability distribution data; S32, storing 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 ith 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 by: Step S4 The specific steps include: S41. In the MCS sample library S, a sample is selected using random sampling technology, denoted as sample x. k ; S42. For the selected sample x k , the slope stability model is used to calculate 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; 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 the failed samples and the safe samples is as follows: The safety factor FS is defined based on 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 the slope 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, critical samples are obtained, and the number of safe samples and failed samples in the MCS sample library S is determined by the critical samples, 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 the samples with correlation coefficients greater than a threshold value ρ0; S83, repeating step S81 and step S82, performing the same operation on each remaining failed sample in the set, until there are no remaining failed samples in the set; S84, according to the obtained design point, input the parameters into the slope stability analysis model, and obtain the key failure mode 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 1 is characterized by: In step S81, The formula for the distance D between the failed sample and the coordinate origin is: Among them, the failure sample points are composed of k independent standard normal variables; k = p + q; 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 1 is characterized by: The calculation formula in step S82 is: Where: u i and u j They 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 respectively; Set the threshold ρ0=0.5.

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