Efficient analysis and risk assessment method and system for slope reliability

Abstract

The invention discloses a slope reliability efficient analysis and risk assessment method and system, and the method comprises the steps: obtaining the basic parameters of a to-be-analyzed slope, and the basic parameters comprise a slope calculation model and soil layer parameters; on the basis of the basic parameters, a representative sliding surface of the slope is searched; analyzing the representative sliding surface to obtain an analysis result; based on the analysis result, the slope system failure probability is calculated; and based on the slope system failure probability and the representative sliding surface, completing evaluation of the slope failure risk. According to the slope reliability efficient analysis and risk assessment method provided by the invention, a representative sliding surface is efficiently identified by adopting a random search method, and the problem of dimension explosion of random variables when spatial variability of soil parameters is considered is further solved through a local average method, so that a secondary reliability analysis method is applied; and efficient analysis of the reliability of the slope system is realized.

Description

Technical Field

[0001] The invention relates to the technical field of slope engineering assessment, and in particular to a method and system for efficiently analyzing and risk assessing slope reliability. Background Art

[0002] Soil parameters in geotechnical engineering show strong spatial variability, which is the main source of soil uncertainty. It has become an industry consensus to consider this spatial variability in slope reliability analysis and design. However, when considering the spatial variability of soil parameters, the evaluation of the systematic failure probability of the slope becomes very complicated. In order to consider the spatial variability of soil parameters, a large number (easily hundreds or thousands) of random variables are often required to simulate the random field of soil parameters. The ensuing "dimensionality disaster" problem brings great challenges to the reliability analysis of the slope system.

[0003] At the same time, due to the "dimensionality disaster" problem caused by the discretization of random fields, the application of traditional reliability analysis methods based on semi-analytical theory (such as the first-order reliability method, the first-order second-order moment method, etc.) is relatively limited. Although local averaging can be performed on the sliding surface to reduce the number of random variables in reliability analysis, this method only considers a single failure mode and does not regard the slope as a system composed of countless potential sliding surfaces in series. The calculated failure probability is too small. The representative sliding surface method that considers multiple important failure modes reduces the complexity of slope system reliability analysis, but under the random field model of soil parameters, this method often requires the use of Monte Carlo simulation for correlation analysis and reliability analysis. At the same time, most of the existing studies have statistically analyzed the slope failure risk based on the Monte Carlo simulation results, and there is a lack of research on the evaluation of slope failure risk using the representative sliding surface method.

[0004] In general, the current analysis method takes a long time from slope modeling to identification of representative sliding surfaces, and then to system reliability analysis and failure risk assessment, and cannot meet the needs of slope reliability design. Summary of the invention

[0005] In order to solve the technical problems in the above background, the present invention aims to provide an efficient analysis and risk assessment method for slope reliability, and applies the traditional reliability analysis method based on semi-analytical theory to the slope reliability analysis considering the spatial variability of soil parameters, thereby significantly improving the efficiency of slope reliability analysis, meeting the needs of engineering applications, and providing a prerequisite for promoting reliability-based slope design optimization.

[0006] To achieve the above object, the present invention provides an efficient slope reliability analysis and risk assessment method, which is characterized by comprising the following steps:

[0007] Obtaining basic parameters of the slope to be analyzed, the basic parameters including the slope calculation model and soil layer parameters;

[0008] Based on the basic parameters, searching for a representative sliding surface of the slope;

[0009] Analyzing the representative sliding surface to obtain analysis results;

[0010] Based on the analysis results, calculating the failure probability of the slope system;

[0011] Based on the failure probability of the slope system and the representative sliding surface, the risk of slope failure is assessed.

[0012] Preferably, the method for searching the representative sliding surface includes: based on the slope calculation model, performing a deterministic analysis under mean conditions to obtain an initial representative sliding surface; taking the initial representative sliding surface as a starting point, performing a random search in combination with the soil layer parameters to obtain the representative sliding surface.

[0013] Preferably, the method for obtaining the analysis result includes: performing reliability analysis and correlation analysis on the representative sliding surfaces obtained through the search, and sorting them according to their contribution to the system failure probability, to obtain a sorted system failure probability-representative sliding surface quantity curve, and the sorted system failure probability-representative sliding surface quantity curve is the analysis result.

[0014] Preferably, the method for obtaining the slope system failure probability comprises: fitting the sorted system failure probability-representative sliding surface number curve according to a hyperbola convergence mode, and obtaining the asymptote of the hyperbola as the final slope system failure probability, and the curve fitting formula is:

[0015]

[0016] Where a, b, c are the fitting parameters to be determined; N is the number of representative sliding surfaces; P f is the probability of system failure.

[0017] Preferably, the method for performing the risk assessment includes: calculating the contribution of each representative sliding surface to the system failure probability, using it as the weight of the sliding volume of each representative sliding surface, and calculating their average to obtain the slope failure risk; the calculation formula for the contribution of each representative sliding surface to the system failure probability is:

[0018]

[0019] Where P f,k is the failure probability of the subsystem composed of the first k representative sliding surfaces (after sorting); N is the number of representative sliding surfaces; ω i is the representative sliding surface Si The contribution degree to the system failure probability, the slope failure risk calculation formula is:

[0020]

[0021] In the formula, C i is the representative sliding surface S i The corresponding sliding volume, R * The final assessed slope failure risk.

[0022] The present invention also provides an efficient analysis and risk assessment system for slope reliability, the system is used to implement the above method, including: a collection module, a search module, an analysis module, a calculation module and an assessment module;

[0023] The acquisition module is used to obtain basic parameters of the slope to be analyzed, and the basic parameters include slope calculation model and soil layer parameters;

[0024] The search module is used to search for a representative sliding surface of the slope based on the basic parameters;

[0025] The analysis module is used to analyze the representative sliding surface to obtain analysis results;

[0026] The calculation module is used to calculate the failure probability of the slope system based on the analysis results;

[0027] The evaluation module is used to complete the evaluation of the slope failure risk based on the slope system failure probability and the representative sliding surface.

[0028] Preferably, the workflow of the search module includes: based on the slope calculation model, performing a deterministic analysis under mean conditions to obtain an initial representative sliding surface; taking the initial representative sliding surface as a starting point, performing a random search in combination with the soil layer parameters to obtain the representative sliding surface.

[0029] Preferably, the workflow of the analysis module includes: performing reliability analysis and correlation analysis on the representative sliding surfaces obtained through the search, and sorting them according to their contribution to the system failure probability, to obtain a sorted system failure probability-representative sliding surface quantity curve, and the sorted system failure probability-representative sliding surface quantity curve is the analysis result.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] The efficient slope reliability analysis and risk assessment method proposed in the present invention uses a random search method to efficiently identify representative sliding surfaces, and further solves the problem of "dimensional explosion" of random variables when considering the spatial variability of soil parameters through the local average method, so that the secondary reliability analysis method can be applied, and the efficient analysis of the reliability of the slope system is realized. At the same time, based on the identified representative sliding surfaces and their contribution to the reliability of the slope system, a rapid assessment of the risk of slope failure is achieved. The method provided by the present invention applies the traditional reliability analysis method based on semi-analytical theory to the slope reliability analysis considering the spatial variability of soil parameters, significantly improving the efficiency of slope reliability analysis, meeting the needs of engineering applications, and providing a prerequisite for promoting reliability-based slope design optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0033] Figure 1 A schematic diagram of a method flow of an embodiment of the present invention;

[0034] Figure 2 It is a schematic diagram of the slope dimensions of an embodiment of the present invention, wherein Su takes an average value of 23 kPa;

[0035] Figure 3 A schematic diagram of a representative sliding surface search method according to an embodiment of the present invention;

[0036] Figure 4 1 is a diagram showing representative sliding surface examples of an embodiment of the present invention, wherein (a), (b), and (c) are three model examples of representative sliding surfaces, respectively, and (d) represents 15 representative sliding surfaces finally obtained;

[0037] Figure 5 It is a schematic diagram of a method for calculating the local average equivalent parameter on a sliding surface according to an embodiment of the present invention;

[0038] Figure 6 A schematic diagram of a system failure probability convergence curve according to an embodiment of the present invention;

[0039] Figure 7 A schematic diagram of a slope failure probability convergence curve of an example of the present invention according to an embodiment of the present invention;

[0040] Figure 8 Schematic diagram of slope risk assessment according to an embodiment of the present invention. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] Embodiment 1

[0044] like Figure 1 FIG. 1 is a schematic diagram of the method flow of this embodiment, and the steps include:

[0045] S1. Obtain the basic parameters of the slope to be analyzed.

[0046] First, the basic parameters of the slope analysis are obtained for subsequent reliability risk assessment. In this embodiment, the basic parameters include the slope calculation model and soil layer parameters. The soil parameters include point variability parameters and spatial variability parameters. Specifically, the point variability parameters are further divided into the mean value μ of the undrained shear strength of the soil x and σ x , the spatial variability parameters include correlation function and correlation distance.

[0047] like Figure 2 As shown in the figure, the slope calculation model is a single-layer viscous slope with a slope height of 5m, a slope gradient of 1:2, and a soil weight of γ u 20kN / m 3 Undrained shear strength of soil S u It obeys lognormal distribution, with mean and coefficient of variation of 23 kPa and 0.3 respectively. At the same time, exponential correlation function is used to describe S u The spatial correlation of the horizontal and vertical correlation distances are: θ1 = 40m and θ2 = 4m, that is:

[0048]

[0049] Where ρ represents the correlation function; (x1, y1) and (x2, y2) represent any two points in space; θ1 and θ2 are the horizontal and vertical correlation distances, respectively.

[0050] S2. Based on basic parameters, search for representative sliding surfaces of the slope.

[0051] Based on the slope calculation model, a deterministic analysis under mean conditions is performed to obtain the initial representative sliding surface; taking the initial representative sliding surface as the starting point, a random search is performed in combination with soil layer parameters to obtain the representative sliding surface. The specific steps include:

[0052] S201. Based on the slope calculation model, a deterministic analysis is performed under mean conditions to obtain the initial representative sliding surface.

[0053] The initial representative sliding surface obtained by the deterministic analysis under the mean condition is obtained and used as the first representative sliding surface. Based on the slope calculation model, a deterministic analysis under the mean condition is performed. This analysis usually assumes that the soil parameters have a fixed mean and does not consider their spatial variability, thereby simplifying the problem. Through the above deterministic analysis, a possible sliding surface can be obtained. This sliding surface is the possible sliding path that may occur when the soil is unstable under the mean condition. The obtained sliding surface is used as the first representative sliding surface and is numbered S k ; At this time, let k = 0, and the sliding surface number obtained is S0.

[0054] S202. Randomly select a rectangular area inside the slope with horizontal and vertical related distances as the size, reduce the internal parameters, search for the most dangerous sliding surface at this time, and obtain the representative sliding surface of the slope.

[0055] like Figure 3 As shown, after obtaining the initial representative sliding surface, this embodiment further considers soil parameters and searches for more representative sliding surfaces through a randomization method for subsequent reliability analysis and risk assessment.

[0056] Specifically, the areas where strength reduction is required are randomly selected multiple times, and deterministic analysis is performed on each area to obtain a new representative sliding surface. The steps include:

[0057] 1) Let k = k + 1, and in the soil layer area (single layer is Figure 3 A point P is randomly selected from the slope geometric model area shown in the figure, and the geometric model area of ​​each soil layer in the case of multiple layers, and a rectangular area with point P as the center and horizontal and vertical related distances as the size is determined. The soil parameters in this area are taken as μ x -σ x , the soil parameters outside the area are taken as μ x .

[0058] 2) Perform deterministic analysis to obtain the sliding surface, denoted as S.

[0059] 3) If the sliding surface S is the same as the previous sliding surface, that is, {S m |m=1,2,···,k}, the positions are close, then reject the sliding surface, that is, let k=k-1, otherwise accept the sliding surface, that is, let Sk =S.

[0060] 4) Randomly select point P again and repeat steps 1) to 3) until the number of representative sliding surfaces obtained reaches a preset value.

[0061] In the above process, to ensure that the searched sliding surface positions are not too close (for example Figure 3 In When considering whether to accept the sliding surface, it can be judged by calculating the Euclidean distance between the control parameters of the sliding surface and the control parameters of the previous sliding surface, that is:

[0062]

[0063] In the formula, x, y, and R are the horizontal and vertical coordinates and radius of the center point of the circular sliding surface respectively; d0 is a control parameter, which can be determined based on experience. When the above formula is fully satisfied, the sliding surface is accepted, otherwise it is not accepted. At the same time, when implementing this method, the maximum number of searches is 100, and the maximum number of representative sliding surfaces is 15, that is, when k ≥ 15 or m ≥ 100, the search for representative sliding surfaces is stopped.

[0064] like Figure 4 As shown, 3 pattern examples of searching for representative sliding surfaces (with different shear strength distributions) and the final 15 representative sliding surfaces are obtained.

[0065] S3. Analyze the representative sliding surface and obtain the analysis results.

[0066] Reliability analysis and correlation analysis are performed on the representative sliding surfaces obtained by the search, and they are sorted according to their contribution to the system failure probability to obtain the sorted system failure probability-number of representative sliding surfaces (P f ~N) curve. The specific steps include:

[0067] S301. Divide the sliding surface into several arcs (such as Figure 5 ), and calculate the local average equivalent parameters (including mean, variance, and correlation coefficient matrix) on each arc segment according to the following formula.

[0068]

[0069] Where R is the radius of the arc sliding surface; ρ represents the exponential correlation function; P(x,y) represents the random field; X i and X j represents the equivalent parameter on the sliding surface; r ij represents the local average parameter X i and X j The correlation coefficient of is; μ represents the mean of the random field; σ represents the standard deviation of the random field; θ i2 and θi1 are the center angles of the arc segments respectively; ξ1 and ξ2 are intermediate variables; γ i represents the variance reduction coefficient of Xi; γ j Represents X j The variance reduction coefficient; COV represents covariance; D represents variance; α1 and α2 both represent integral variables; E represents expectation.

[0070] For a specific sliding surface S i , the soil parameter random field is discretized into a series of related random variables X i , whose mean and standard deviation are μ Xi and σ Xi , the correlation coefficient matrix is ​​R i The reliability index β of the sliding surface is calculated according to the quadratic reliability method. i .

[0071] The correlation coefficient between the failure modes corresponding to each sliding surface is calculated as follows:

[0072]

[0073] In the formula, R ij is the equivalent parameter X on different sliding surfaces i and X j The correlation coefficient matrix of i * 、u j * S i and S j The corresponding limit state equation is the verification point in the standard normal space; β i and β j S i and S j Reliability index; L i and L j The correlation matrix R i and R j The Cholesky lower triangular decomposition matrix, that is, R = LL T Finally, the correlation coefficient matrix Λ, λ between the failure modes corresponding to each sliding surface is obtained ij are all the elements of the matrix Λ.

[0074] S302. Calculate the failure probability of the subsystem composed of M sliding surfaces.

[0075] Specifically, the calculation formula is as follows:

[0076] P fM，sys =1-Φ M (β, Λ)

[0077] In the formula, Φ M (·) is the cumulative probability distribution function of the M-variable standard normal distribution; β represents the reliability index matrix of the sliding surface.

[0078] According to the calculation results, the systems are ranked according to their contribution to the system failure probability, and the ranked system failure probability-sliding surface number convergence curve is obtained, that is, the analysis result, such as Figure 6 shown.

[0079] S4. Based on the analysis results, calculate the failure probability of the slope system.

[0080] After sorting, P f The ~N curve is fitted according to the hyperbola convergence mode, and the asymptote of the hyperbola is the final slope system failure probability. The curve fitting formula is:

[0081]

[0082] In the formula, a, b, c are the fitting parameters to be determined, N is the number of representative sliding surfaces, P f is the probability of system failure.

[0083] The undetermined parameter a obtained is the systematic failure probability of the slope.

[0084] According to the reliability analysis and correlation analysis methods of S3 and S4, the 15 representative sliding surfaces are analyzed and re-ranked according to their contribution to the system failure probability. The ranked Pf~N convergence curve is as follows: Figure 7 As shown in the figure, the systematic failure probability of the slope is 0.075, which is close to the result (0.076) obtained after 100,000 Monte Carlo simulations in the experiment.

[0085] S5. Complete the assessment of slope failure risk based on the failure probability of the slope system and representative sliding surfaces.

[0086] Calculate the contribution of each representative sliding surface to the probability of system failure, and use it as the weight of the sliding volume of each representative sliding surface. The average of them is the slope failure risk (defined as the sliding volume after the slope fails). The calculation formula for the contribution of each representative sliding surface to the probability of system failure is:

[0087]

[0088] Where P f,k is the failure probability of the subsystem composed of the first k representative sliding surfaces (after sorting); N is the number of representative sliding surfaces; ω i is the representative sliding surface S i The contribution to the probability of system failure. The slope failure risk calculation formula is:

[0089]

[0090] In the formula, C i is the representative sliding surface S i The corresponding sliding volume, R * The final assessed slope failure risk.

[0091] The calculated slope failure risk is plotted as Figure 8 As shown in the figure, the horizontal axis is the sliding body volume corresponding to each representative sliding surface, the upper vertical axis is its contribution to the system failure probability, and the lower vertical axis is the product of the corresponding sliding body volume and the representative sliding surface's contribution to the system failure probability (that is, the contribution of the corresponding representative sliding surface to the slope failure risk). Calculate the sum of the lower vertical axes corresponding to all representative sliding surfaces, and the failure risk of the slope is 106.1m 3 / m, which is consistent with the result of 100,000 Monte Carlo simulations (103.3m3 / m).

[0092] Embodiment 2

[0093] The present embodiment also provides an efficient analysis and risk assessment system for slope reliability, comprising: an acquisition module, a search module, an analysis module, a calculation module and an evaluation module; the acquisition module is used to obtain basic parameters of the slope to be analyzed, the basic parameters including the slope calculation model and soil layer parameters; the search module is used to search for representative sliding surfaces of the slope based on the basic parameters; the analysis module is used to analyze the representative sliding surfaces to obtain analysis results; the calculation module is used to calculate the failure probability of the slope system based on the analysis results; the evaluation module is used to complete the assessment of the failure risk of the slope based on the failure probability of the slope system and the representative sliding surfaces.

[0094] Among them, the workflow of the search module includes: based on the slope calculation model, a deterministic analysis is carried out under the mean condition to obtain the initial representative sliding surface; taking the initial representative sliding surface as the starting point, a random search is carried out in combination with the soil layer parameters to obtain the representative sliding surface.

[0095] The workflow of the analysis module includes: performing reliability analysis and correlation analysis on the representative sliding surfaces obtained through the search, and sorting them according to their contribution to the system failure probability to obtain a sorted system failure probability-representative sliding surface quantity curve. The sorted system failure probability-representative sliding surface quantity curve is the analysis result.

[0096] The workflow of the calculation module includes: fitting the sorted system failure probability-representative sliding surface number curve according to the hyperbola convergence mode, and the asymptote of the hyperbola is the final slope system failure probability. The curve fitting formula is:

[0097]

[0098] In the formula, a, b, c are the fitting parameters to be determined, N is the number of representative sliding surfaces, P f is the probability of system failure.

[0099] The workflow of the assessment module includes: calculating the contribution of each representative sliding surface to the probability of system failure, taking it as the weight of the sliding volume of each representative sliding surface, and calculating their average to obtain the slope failure risk; the calculation formula for the contribution of each representative sliding surface to the probability of system failure is:

[0100]

[0101] Where P f,k is the failure probability of the subsystem composed of the first k representative sliding surfaces (after sorting); N is the number of representative sliding surfaces; ω i is the representative sliding surface S i The contribution degree to the system failure probability, the slope failure risk calculation formula is:

[0102]

[0103] In the formula, C i is the representative sliding surface S i The corresponding sliding volume, R * The final assessed slope failure risk.

[0104] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. An efficient slope reliability analysis and risk assessment method, characterized in that the steps include: Obtaining basic parameters of the slope to be analyzed, the basic parameters including the slope calculation model and soil layer parameters; Based on the basic parameters, searching for a representative sliding surface of the slope; Analyzing the representative sliding surface to obtain analysis results; Based on the analysis results, calculating the failure probability of the slope system; Based on the failure probability of the slope system and the representative sliding surface, an assessment of the slope failure risk is completed.

2. The efficient slope reliability analysis and risk assessment method according to claim 1 is characterized in that: The method for searching the representative sliding surface includes: based on the slope calculation model, performing a deterministic analysis under mean conditions to obtain an initial representative sliding surface; taking the initial representative sliding surface as a starting point, performing a random search in combination with the soil layer parameters to obtain the representative sliding surface.

3. The efficient slope reliability analysis and risk assessment method according to claim 1 is characterized in that: The method for obtaining the analysis result includes: performing reliability analysis and correlation analysis on the representative sliding surfaces obtained by the search, and sorting them according to their contribution to the system failure probability, to obtain a sorted system failure probability-representative sliding surface quantity curve, and the sorted system failure probability-representative sliding surface quantity curve is the analysis result.

4. The efficient slope reliability analysis and risk assessment method according to claim 1 is characterized in that: The method for obtaining the slope system failure probability includes: fitting the sorted system failure probability-representative sliding surface number curve according to a hyperbola convergence mode, and obtaining the asymptote of the hyperbola is the final slope system failure probability. The curve fitting formula is: Where a, b, c are the fitting parameters to be determined; N is the number of representative sliding surfaces; P f is the probability of system failure.

5. The efficient slope reliability analysis and risk assessment method according to claim 1 is characterized in that: The method for performing the risk assessment includes: calculating the contribution of each representative sliding surface to the system failure probability, taking it as the weight of the sliding volume of each representative sliding surface, and calculating their average to obtain the slope failure risk; the calculation formula for the contribution of each representative sliding surface to the system failure probability is: Where P f,k is the failure probability of the subsystem composed of the first k representative sliding surfaces (after sorting); N is the number of representative sliding surfaces; ω i is the representative sliding surface S i The contribution degree to the system failure probability, the slope failure risk calculation formula is: In the formula, C i is the representative sliding surface S i The corresponding sliding volume, R * The final assessed slope failure risk.

6. An efficient slope reliability analysis and risk assessment system, the system is used to implement the method according to any one of claims 1 to 5, characterized in that: include: Acquisition module, search module, analysis module, calculation module and evaluation module; The acquisition module is used to obtain basic parameters of the slope to be analyzed, and the basic parameters include slope calculation model and soil layer parameters; The search module is used to search for a representative sliding surface of the slope based on the basic parameters; The analysis module is used to analyze the representative sliding surface to obtain analysis results; The calculation module is used to calculate the failure probability of the slope system based on the analysis results; The evaluation module is used to complete the evaluation of the slope failure risk based on the slope system failure probability and the representative sliding surface.

7. The efficient slope reliability analysis and risk assessment system according to claim 6, characterized in that: The workflow of the search module includes: based on the slope calculation model, performing a deterministic analysis under mean conditions to obtain an initial representative sliding surface; taking the initial representative sliding surface as a starting point, performing a random search in combination with the soil layer parameters to obtain the representative sliding surface.

8. The efficient slope reliability analysis and risk assessment system according to claim 6, characterized in that: The workflow of the analysis module includes: performing reliability analysis and correlation analysis on the representative sliding surfaces obtained by the search, and sorting them according to their contribution to the system failure probability, to obtain a sorted system failure probability-representative sliding surface quantity curve, and the sorted system failure probability-representative sliding surface quantity curve is the analysis result.

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