Geotechnical engineering multi-failure mode reliability analysis method and system

Abstract

The application discloses a geotechnical engineering multi-failure mode reliability analysis method and system, and the method comprises the following steps: acquiring statistical characteristics of characteristic parameters based on survey data to generate an initial sample set; constructing a function function for multiple failure modes; training multiple intelligent models by using the initial sample set and function response values; inputting the current sample set into the intelligent models to obtain predicted response values of each failure mode, and taking the maximum value as a system response value; comparing the system response value with an intermediate threshold value, screening failure samples, and updating probability weights; generating a next layer sample set based on the failure samples, updating the threshold value, and iterating until the threshold value converges to a failure boundary; and calculating the reliability by counting the number of failure samples and weights. The method replaces the traditional function function with the intelligent model to reduce the calculation time; the maximum response value is extracted to convert the multi-failure mode into a single joint event; the layered sampling and dynamic weight updating accurately approach the dangerous area, and efficient, unbiased and accurate reliability evaluation is realized.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering analysis technology, and in particular to a reliability analysis method and system for multiple failure modes in geotechnical engineering. Background Technology

[0002] Reliability analysis is a core component of geotechnical engineering design and risk control. Based on statistical mathematics, it treats factors such as engineering loads, geotechnical material properties, soil layer properties, and structural strength as random variables. By quantifying their randomness and calculating reliability using probabilistic statistical methods, it serves as a fundamental scientific criterion for assessing the safety of geotechnical engineering facilities and their ancillary structures. The magnitude of the reliability index quantitatively reflects the risk level of geotechnical structures, thus providing engineers with a scientific basis for optimizing design schemes and reducing construction costs.

[0003] However, natural soil and rock masses possess complex layered structures and multi-material properties. In practical engineering, the instability of soil and rock structures is often complex and typically faces multiple coexisting failure modes (such as sliding failure and settlement failure). To accurately represent these complex failure mechanisms, numerical simulation software such as finite element method (FEM) or finite difference method (FD) is usually required to construct various forms of structural function functions. Existing geotechnical engineering reliability analysis methods face the following technical bottlenecks when dealing with such complex scenarios: First, reliability analysis essentially requires large-scale sampling of random parameters and repeated calls to the function to obtain response values. For complex geotechnical structures, traditional numerical models are already very time-consuming in a single solution, and with large-scale sampling, the enormous computational load makes conventional analysis methods difficult to implement effectively.

[0004] Secondly, existing analytical methods (such as first-order reliability analysis) have low computational accuracy when dealing with highly nonlinear geotechnical problems, and require repeated derivative calculations for different failure modes, which is cumbersome. While traditional stochastic simulation methods such as Monte Carlo simulation (MCS) can handle nonlinear problems, they require millions of samples when dealing with the assessment of extremely small failure probabilities commonly seen in engineering practice, resulting in extremely low computational efficiency.

[0005] In summary, the industry needs a new reliability analysis solution for geotechnical engineering. Summary of the Invention

[0006] The purpose of this invention is to provide a reliability analysis method and system for multiple failure modes in geotechnical engineering that effectively reduces overall computation time and can unify multiple interrelated failure events under the same theoretical framework for systematic evaluation, thereby improving evaluation efficiency.

[0007] To achieve the above objectives, the present invention provides a reliability analysis method for multiple failure modes in geotechnical engineering, comprising: Statistical characteristics of several characteristic parameters of geotechnical engineering are obtained based on survey data, and an initial sample set is generated based on the statistical characteristics. Multiple functional functions are constructed to address various failure modes in geotechnical engineering. Using the initial sample set and the function response values ​​calculated based on the corresponding functional functions, multiple intelligent models corresponding to each failure mode are trained and generated. The reliability of multiple failure modes in geotechnical engineering is calculated based on an iterative calculation method, as follows: The sample set of the current iteration layer is input into multiple intelligent models to obtain multiple predicted response values ​​for each failure mode corresponding to each sample, and the maximum value among the multiple predicted response values ​​corresponding to each sample is extracted as the system response value. The system response value is compared with the intermediate threshold set in the current iteration layer. Samples whose system response value is less than or equal to the intermediate threshold are selected as failed samples. The probability weight of the sample set to be analyzed in the current iteration layer is updated according to the current selection ratio relative to the previous iteration layer. Based on the selected failure samples, the next iteration layer sample set is generated by sampling, and the intermediate threshold is updated to enter the next iteration layer until the intermediate threshold converges to the set failure boundary. The reliability is calculated by counting the number of failure samples that converge to the failure boundary and combining them with their corresponding probability weights.

[0008] Preferably, after calculating the reliability, the method further includes a sensitivity analysis of the characteristic parameters: Extract the global sample set consisting of all samples generated during the iterative calculation process, as well as the failure samples that converge to the failure boundary; For each of the aforementioned feature parameters, based on the weighted kernel density estimation method and combined with the probability weights corresponding to each sample, the global probability density distribution of each feature parameter in the global sample set and the local probability density distribution in the failure samples that converge to the failure boundary are respectively fitted. Calculate the distribution difference between the local probability density distribution and the global probability density distribution corresponding to each feature parameter; Sensitivity evaluation indices are generated based on the distribution difference, and these indices are used to quantify the degree of influence of the corresponding feature parameters on geotechnical engineering failures.

[0009] Preferably, the distributional dissimilarity is the KL divergence.

[0010] Preferably, the fitting method for the local probability density distribution includes: When the number of failed samples is less than a preset sample threshold, the interquartile range of the corresponding feature parameters is calculated using the Silverman criterion. The smoothing parameters of the weighted kernel density estimation method are determined based on the interquartile range to complete the fitting of the local probability density distribution.

[0011] Preferably, the characteristic parameters include the soil friction coefficient and the soil friction strength.

[0012] Preferably, the statistical characteristics include one or more of the following: mean, standard deviation, and probability distribution type; Based on the statistical characteristics, random sampling is performed using Monte Carlo simulation to generate a multidimensional vector set corresponding to the feature parameters, which serves as the initial sample set.

[0013] Preferably, the threshold corresponding to the failure boundary is 0; The method for comparing the system response value with the intermediate threshold set in the current iteration layer includes: Determine whether the system response value is less than or equal to 0; if so, determine that the sample has actually failed and stop generating the sample set for the next iteration layer.

[0014] The present invention also provides a reliability analysis system for multiple failure modes in geotechnical engineering, characterized in that the system performs reliability analysis based on the reliability analysis method for multiple failure modes in geotechnical engineering described above.

[0015] This invention also provides a reliability analysis system for multiple failure modes in geotechnical engineering, comprising: One or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including instructions for performing the geotechnical engineering multi-failure mode reliability analysis method as described above.

[0016] The present invention also provides a computer-readable storage medium, characterized in that it includes a computer program, which can be executed by a processor to perform the multi-failure mode reliability analysis method for geotechnical engineering as described above.

[0017] Compared with existing technologies, the multi-failure mode reliability analysis method for geotechnical engineering provided by the above-mentioned technical solution significantly reduces the computation time under large-scale sampling by training multiple intelligent models to replace the time-consuming traditional geotechnical physical function. Furthermore, it extracts the maximum value from the predicted response values ​​of each intelligent model as the unified individual system response value, transforming the originally isolated multiple failure modes into a single joint event. This completely breaks through the technical bottleneck of existing simulation methods that can only perform isolated and repeated calculations on single failure modes. Simultaneously, by setting progressively decreasing intermediate thresholds for comparison and screening, stratified directional sampling, and dynamic updates of probability weights, it can guide samples to quickly and accurately approximate the actual hazardous area. Therefore, through the synergistic combination of the above technologies, it not only multiplies the overall computational load in complex engineering scenarios with multiple coexisting failure modes but also achieves efficient, unbiased, and accurate reliability assessment for geotechnical engineering with extremely low failure probabilities. Attached Figure Description

[0018] Figure 1 This is a flowchart of the reliability analysis method in an embodiment of the present invention. Detailed Implementation

[0019] To illustrate the technical content, structural features, objectives, and effects of the present invention in detail, the following description is provided in conjunction with the embodiments and accompanying drawings.

[0020] This embodiment discloses a reliability analysis method for multiple failure modes in geotechnical engineering. Geotechnical engineering projects (such as mine slopes, flood control embankments, tunnels, etc.) are located in complex geological environments, and their stability is affected by a combination of random factors such as soil and rock properties, hydrological conditions, and external loads. Furthermore, they typically face more than one structural instability mode. Figure 1 The method in this embodiment includes the following steps: S11: Obtain statistical characteristics of several characteristic parameters of geotechnical engineering based on survey data, and generate an initial sample set based on the statistical characteristics.

[0021] In the early stages of a project, various parameters related to geotechnical engineering are obtained through geological exploration, laboratory geotechnical tests, or in-situ testing. Due to the spatial variability of natural soil, these parameters should not be treated as fixed, deterministic values, but rather as random variables.

[0022] Based on the survey data, the statistical characteristics of each feature parameter are determined. In specific implementations, these feature parameters are not limited to single physical property indicators, but can encompass material parameters, geometric parameters, and external load parameters. Subsequently, a large set of data points is generated based on these statistical characteristics as an initial sample set to cover the possible range of parameter fluctuations.

[0023] Specifically, in many geotechnical engineering (such as stability analysis of earth-rock dam slopes in reservoirs) practical implementation scenarios, the characteristic parameters input into the system are usually including but not limited to the soil friction coefficient and soil friction strength (i.e., shear strength).

[0024] The friction coefficient and friction strength of soil are the core intrinsic factors controlling the magnitude of the anti-sliding force of the sliding surface, and they are highly susceptible to nonlinear decay due to factors such as groundwater level fluctuations, construction disturbances, and rainfall infiltration. Using these two core anti-sliding physical quantities as input characteristic parameters with statistical distribution characteristics for multi-failure mode analysis (such as the simultaneous existence of deep sliding and shallow collapse) can realistically recreate the failure evolution process of soil and rock under extreme working conditions, providing the most direct risk reference benchmark for the design dimensions and embedment depth of support anti-sliding piles.

[0025] In addition, the statistical features extracted from the acquired survey data include not only the mean and standard deviation, but also the probability distribution type of the feature data.

[0026] Different geological parameters often do not follow a single distribution (for example, soil weight usually follows a normal distribution, while permeability coefficient often follows a log-normal distribution).

[0027] Based on the confirmed mean, standard deviation, and specific probability distribution type, large-scale random sampling is performed in a multidimensional parameter space using Monte Carlo simulation. During this process, each generated set of data points forms a multidimensional vector containing all feature parameters.

[0028] Since the initial stage does not involve complex primitive function calls, the Monte Carlo mechanism can quickly and costlessly generate orders of magnitude from 10³ to 10⁻⁶. 4 Using a large set of multidimensional vectors as the initial sample set ensures that the computational basis fully covers the natural random properties of the soil and rock mass.

[0029] S12: Construct multiple functional functions for various failure modes in geotechnical engineering.

[0030] Soil and rock structures often exhibit complex failure mechanisms. For example, an anti-slide retaining wall may simultaneously face overall sliding failure, overturning failure, and foundation bearing capacity failure.

[0031] For each identified potential failure mode, a corresponding physical function is established. The output of the function (i.e., the response value) is used to characterize the safety margin of the structure under that set of characteristic parameters.

[0032] In practical engineering, functional functions can be expressed through analytical equations or implicitly through the backend calculation interfaces of numerical simulation software such as finite element and finite difference methods.

[0033] S13: Using the initial sample set and the function response values ​​calculated based on the corresponding functional functions, train and generate multiple intelligent models corresponding to each failure mode. These function response values, as well as the response values ​​in the following embodiments, include, but are not limited to, safety scores.

[0034] Since directly calling commercial numerical software to solve the functional problems of a large number of samples requires a huge amount of computing resources and time, this step introduces an intelligent model as a proxy for the physical model.

[0035] The initial sample set is input into the original function to obtain a batch of real function response values ​​as training labels. Using this labeled data, a corresponding intelligent model is trained for each failure mode.

[0036] In some alternative implementations, the intelligent model can be a support vector machine (SVM), an artificial neural network (ANN), or a Kriging surrogate model, as long as it has the ability to fit nonlinear high-dimensional functional relationships. Once trained, the intelligent model can output predicted response values ​​in a very short time, thereby replacing the original functional function in subsequent massive iterative sampling calculations.

[0037] S14: Calculate the reliability of multiple failure modes in geotechnical engineering based on iterative calculation method.

[0038] This step uses a hierarchical, progressive logic to identify failure events within an extremely low probability range. The specific calculation process is as follows: First, the sample set of the current iteration layer (the initial sample set input for the first time) is input into multiple trained intelligent models. For each sample, multiple predicted response values ​​corresponding to various failure modes are obtained.

[0039] Subsequently, the maximum value among the multiple predicted response values ​​for each sample is extracted and used as the system response value for that sample. This extraction mechanism couples multiple parallel structural instability states into a single joint event. If the structure reaches its most dangerous state (i.e., the maximum response value that most closely approximates or exceeds the failure threshold) in any mode, the entire system is considered to be at that danger level. This process eliminates the need for separate, isolated iterations for each failure mode in subsequent calculations, significantly reducing the computational path length of the algorithm.

[0040] Next, a progressively decreasing intermediate threshold is set. The extracted system response values ​​are compared one by one with the intermediate threshold of the current layer, and samples with system response values ​​less than or equal to the intermediate threshold are selected as failure samples.

[0041] These failed samples represent "dangerous seeds" that have a high probability of leading to eventual failure at the current level. During this process, the probability weights of the sample set to be analyzed in the current iteration layer are updated based on the selection ratio of the current layer relative to the previous iteration layer (e.g., setting only the top 10% of dangerous samples to be retained, i.e., a selection ratio of 0.1). This weight update mechanism ensures that the true physical probability attribute of the sample occurrence frequency is not lost as the process of approaching the danger zone layer by layer.

[0042] Subsequently, based on the selected failure samples, sampling algorithms such as Markov Chain Monte Carlo (MCMC) are used to generate a new sample set for the next iteration layer, and the intermediate threshold is simultaneously reduced (updated) to enter the next iteration layer.

[0043] The above comparison and sampling steps are iterated until the set intermediate threshold converges to the set physical failure boundary.

[0044] Finally, the number of failure samples reaching the failure boundary is counted. This number is then multiplied by the probability weights obtained from the aforementioned multi-level iterative cumulative calculation and summed to obtain the joint reliability index of the geotechnical engineering project under multiple failure modes.

[0045] In this embodiment, by extracting the maximum value of multiple model responses and integrating it into the system response value, and by using an iterative optimization mechanism that updates the hierarchical probability weights, the calculation process can accurately locate the joint failure region with a very low probability while avoiding large-scale physical model calls. This solves the engineering and technical problems of long processing time in traditional direct sampling methods and the difficulty of conventional algorithms to be compatible with multiple failure modes concurrently.

[0046] In another embodiment, the threshold corresponding to the true failure boundary set by the system is defined as 0. During the step of comparing the system response value with the intermediate threshold set by the current iteration layer, it is determined whether the extracted maximum system response value is less than or equal to 0.

[0047] In the early iterations of the algorithm, the intermediate threshold is typically a large positive number. As the sampling approaches the target layer by layer, the intermediate threshold decreases. When the system response value at a certain level is less than or equal to 0, it is determined that the soil and rock mass combination represented by that sample has experienced actual physical failure. At this point, the system immediately cuts off further downward computational exploration, stops generating the next iteration layer sample set, and considers the current running state as convergence to the failure boundary.

[0048] The following specific application example illustrates the reliability calculation process described above: Test objective: To assess the overall probability of dam collapse under extremely adverse conditions.

[0049] The two intelligent models obtained from the training are K1 and K2. K1 is responsible for calculating the landslide safety score, and K2 is responsible for calculating the settlement safety score.

[0050] The initial sample set generated has 1000 samples.

[0051] The iterative calculation process is as follows: Iteration Layer 1: Based on two intelligent models, the initial sample set is scored, and the 1000 scores are sorted from low to high (from dangerous to safe): 1st place (most dangerous): 12 points; … 100th place (top 10%): 35 points; 1000th (safest): Score: 98 points.

[0052] The intermediate threshold for this layer is set at 35 points. No dam safety score was found to be less than 0, indicating that the dam is very safe.

[0053] These 1000 samples are purely random, representing 100% of the real-world situation, so the probability weight W for each dam is 0.001.

[0054] Iteration Layer 2: Using the top 100 samples from the above sorting as data seeds, the MCMC algorithm is used to mutate and reproduce, generating 1000 new samples that are slightly more dangerous and represent the safety status of the dam.

[0055] Next, the security scores of 1000 newly generated samples from the two intelligent models were evaluated, and then sorted again from low to high: 1st place (most dangerous): 2 points; … 100th place: Score of 15 points.

[0056] The intermediate threshold for this layer was lowered to 15 points, but the score still did not fall below 0 points, so the iteration continued.

[0057] It should be noted that these 1000 samples were derived from the "10% minimum circle" of the first iteration layer, so the probability weight of each sample became: W=0.1×0.001=0.0001.

[0058] Iteration Layer 3: Based on the top 100 seeds from Iteration Layer 2, continue to propagate 1000 new extremely dangerous samples, and re-score and rank them: 1st place: Score 0.5 points; … 100th place: Score of 4 points.

[0059] The intermediate threshold for this layer was lowered to 4 points, but the score still did not fall below 0 points, so the iteration continued.

[0060] It should be noted that these 1000 samples were derived from the "10% minimum circle" of the second iteration layer, so the probability weight of each sample became: W=0.1×0.1×0.001=0.00001.

[0061] Iteration Layer 4: Based on the top 100 seeds from Iteration Layer 3, continue to propagate 1000 new extremely dangerous samples, and re-score and rank them: 1st place: -5 points; 2nd place: -3 points; … 45th place: 0 points; 46th place: 0.2 points.

[0062] Because a sample with a score of 0 appeared in the fourth iteration layer, the iteration stop condition was triggered.

[0063] In the fourth iteration layer, the probability weight of each sample is W = 0.1 × 0.1 × 0.1 × 0.001 = 0.000001.

[0064] Furthermore, in iterative layer four, a total of 45 samples with scores less than or equal to zero were found, leading to the final conclusion: The calculated combined probability of multiple failure modes is f = 45 × 0.000001 = 0.000045 (i.e., 4.5 out of 100,000). In other words, the currently calculated probability of dam failure is 4.5 out of 100,000.

[0065] In another embodiment, in order to further identify and quantify the contribution of various characteristic parameters to the final failure of the geotechnical structure and provide data-level engineering reinforcement guidance, the sensitivity of the data flow is also analyzed after the reliability is calculated.

[0066] Specifically, when the iterative calculation ends, the system retains a large amount of full lifecycle data. The sensitivity analysis method in this embodiment first extracts a global sample set consisting of all samples generated during the entire iterative calculation process (including safe and dangerous states), and at the same time extracts those real failure samples that finally converge to the failure boundary.

[0067] For each feature parameter, based on the weighted kernel density estimation method, two probability density distributions are calculated and fitted: one is the global probability density distribution of the feature parameter in the global sample set, and the other is the local probability density distribution of the parameter in the final failure sample.

[0068] In this fitting process, the cumulative probability weights assigned to each sample during the iteration period are used as weighting factors for kernel density estimation. After stratified sampling, the absolute probability of failure samples occurring in the real physical world has been greatly compressed. Assigning weights can eliminate sampling bias and restore its true statistical distribution.

[0069] Subsequently, the distribution difference between the local probability density distribution and the global probability density distribution corresponding to each feature parameter is calculated.

[0070] Distribution variability is an objective quantitative indicator. When the local failure distribution pattern of a certain characteristic parameter deviates significantly from its global distribution pattern under natural conditions (for example, a certain type of soil parameter is uniformly distributed globally, but is concentrated in a certain extremely low value range in the failure sample), a large distribution variability occurs.

[0071] Finally, sensitivity evaluation indices for the corresponding characteristic parameters are generated based on the numerical values ​​of the aforementioned distributional differences. The larger the value of the indicator for a characteristic parameter, the deeper the impact of its fluctuations on the structure-induced multi-mode joint failure. This mechanism, which directly calculates sensitivity using the byproducts of the iterative process (failure samples and probability weights), avoids repeatedly performing derivative calculations on different characteristic parameters, reducing the additional computational overhead of parameter analysis.

[0072] Furthermore, KL divergence is used to quantify the distributional dissimilarity.

[0073] KL divergence is a mathematical tool used to measure the asymmetric difference between two probability distributions. In the data processing flow of this embodiment, the continuous range of feature parameter values ​​is divided into several discrete intervals, and the local probability density value and global probability density value of the feature parameter in each interval are extracted. By calculating the KL divergence value of the local probability density distribution relative to the global probability density distribution, a scalar greater than or equal to zero is obtained. This divergence value is directly mapped to a sensitivity evaluation index.

[0074] Specifically, when the divergence value is close to 0, it indicates that the variation of the characteristic parameter is not the dominant factor causing engineering failure; when the divergence value is significantly large, the characteristic parameter is determined to be a key sensitive parameter that causes multi-mode failure. Based on this, engineering designers can focus on developing improvement or support schemes for the characteristic parameter (such as the physical properties of a specific soil layer).

[0075] Furthermore, this embodiment incorporates robust optimizations for the fitting process of the local probability density distribution. First, the number of failed samples is calculated. A sample threshold is set to determine whether the samples are sparse. When the number of samples detected is less than this preset threshold, a small sample compensation mechanism is triggered: the interquartile range (IQR, the difference between the upper and lower quartiles) of the corresponding feature parameter distribution sequence is calculated using the Silverman criterion. The IQR, reflecting the inherent dispersion of the data, is used instead of the traditional single standard deviation to determine the smoothing parameter (bandwidth h) of the weighted kernel density estimation method.

[0076] This intervention logic, which adaptively adjusts the smoothing parameters, suppresses the interference of outliers on the kernel function fitting, ensuring the morphological continuity and numerical stability of the local probability density distribution in the extremely sparse sample space.

[0077] In summary, this invention discloses a reliability analysis method for multiple failure modes in geotechnical engineering. Taking a large coastal flood control embankment project as an example, the following section systematically elaborates on the full-process technical implementation mechanism covering multiple failure mode proxy calculation, hierarchical iteration, and parameter sensitivity quantification.

[0078] The flood control embankment has been subjected to long-term water erosion and geological variations, and has been identified as facing three coexisting potential failure modes: water-facing slope sliding failure (corresponding to function P1), embankment foundation anti-sliding failure (corresponding to function P2), and embankment body uneven settlement failure (corresponding to function P3). In the definition of function, when the response value is less than or equal to 0, it indicates that the embankment structure is in a state of complete failure.

[0079] During the engineering survey phase, three core characteristic parameters affecting the stability of the dam were obtained: parameter A is the soil friction coefficient, which follows a normal distribution with a mean of 0.35 and a standard deviation of 0.05; parameter B is the soil friction strength (shear strength), which follows a log-normal distribution with a mean of 45 kPa and a standard deviation of 5 kPa.

[0080] Based on the above statistical characteristics and probability distribution types, 10,000 three-dimensional data vectors were randomly generated using Monte Carlo simulation as the initial sample set for the first layer.

[0081] To avoid exhausting computational resources by directly performing large-scale finite element solutions on P1, P2, and P3, 300 training samples were extracted from the initial sample set and substituted into the original physical model to calculate the actual response values. Based on this, three intelligent models corresponding to the three failure modes were generated.

[0082] Subsequently, the iterative calculation phase begins. The 10,000 samples from the first layer are input into the three intelligent models mentioned above, and each sample obtains three predicted response values ​​for slope sliding, embankment slippage, and dam settlement.

[0083] For a single sample, the maximum of the three predicted response values ​​is extracted as the system response value for that sample. The system response values ​​of all samples in the first layer are arranged in ascending order, and a selection ratio of 0.1 (i.e., 10%) is set. The value ranked 1000th (e.g., 4.5) is taken as the intermediate threshold for the current iteration layer. The system selects 1000 samples with system response values ​​less than or equal to 4.5 as first-layer failure samples, and updates the probability weights of these samples based on the selection ratio of 0.1.

[0084] Based on the aforementioned 1000 failure samples, the system uses a Markov chain Monte Carlo sampling algorithm to generate 10,000 new second-layer sample sets. These new sample sets are then input into the intelligent model to repeat the aforementioned operations of extracting maximum values ​​and comparisons. In the second layer, the intermediate threshold decreases to 1.2. When the system continues sampling into the third-layer iteration, the monitoring node detects that 45 samples have system response values ​​less than or equal to 0. At this point, the system determines that the parameter combination formed by these 45 samples caused the actual physical failure of the dam and forcibly stops generating the next iteration layer sample set.

[0085] The number of these 45 real failure samples was counted, and combined with the probability weights accumulated through three layers of sampling, the joint failure probability of the flood control embankment under the coupling effect of multiple failure modes was calculated to be 0.00045 (i.e., 45 out of 100,000), and this was converted into the corresponding reliability index.

[0086] After completing the reliability calculation, the parameter sensitivity analysis process begins. A total of 30,000 samples generated during the three-layer iteration process are extracted as the global sample set, along with the 45 failure samples that ultimately bottomed out. Since the number of failure samples (45) is less than the set sample threshold (e.g., set to 50), direct fitting could easily lead to curve divergence. Using the Silverman criterion, the interquartile range (IQR) of the sequences of parameters A and B in these 45 samples is calculated. Based on this, the smoothing parameter bandwidth of the weighted kernel density estimation is adjusted, thereby robustly fitting the local probability density distribution of each parameter.

[0087] The distribution difference (KL divergence) between the local and global probability density distributions of parameters A and B was calculated. The results showed that the KL divergence for parameter A (soil friction coefficient) was 0.12, while the KL divergence for parameter B (soil friction strength) was as high as 4.85. This quantitative data indicates that the distribution pattern of soil friction strength deviated most drastically from the natural state in the failure samples. This sensitivity evaluation index clearly indicates that even a slight decrease in soil friction strength is the core cause of the multi-mode combined collapse of flood control dikes. Based on this conclusion, the engineering design department prioritized subsequent flood control reinforcement budgets for deep soil grouting consolidation (improving shear strength) of the dike foundation, avoiding the inefficient design of blindly increasing the thickness of the retaining wall on the water-facing side.

[0088] In another preferred embodiment of the present invention, a reliability analysis system for multiple failure modes in geotechnical engineering is also disclosed. This system performs reliability analysis based on the reliability analysis method for multiple failure modes in geotechnical engineering described in the above embodiments.

[0089] This invention also discloses another reliability analysis system, which includes one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors. The programs include instructions for performing the reliability analysis method as described above. The processor may be a general-purpose central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, used to execute the relevant programs to implement the functions required by the modules in the reliability analysis system of this application embodiment, or to execute the reliability analysis method of the method embodiment of this application.

[0090] This invention also discloses a computer-readable storage medium comprising a computer program executable by a processor to perform the reliability analysis method described above. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be read-only memory (ROM), random access memory (RAM), or magnetic media, such as floppy disks, hard disks, magnetic tapes, magnetic disks, or optical media, such as digital versatile discs (DVDs), or semiconductor media, such as solid-state disks (SSDs).

[0091] This application also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. The processor of an electronic device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the electronic device to perform the aforementioned reliability analysis method. The above-disclosed embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. Therefore, any equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

Claims

1. A reliability analysis method for multiple failure modes in geotechnical engineering, characterized in that, include: Statistical characteristics of several characteristic parameters of geotechnical engineering are obtained based on survey data, and an initial sample set is generated based on the statistical characteristics. Multiple functional functions are constructed to address various failure modes in geotechnical engineering. Using the initial sample set and the function response values ​​calculated based on the corresponding functional functions, multiple intelligent models corresponding to each failure mode are trained and generated. The reliability of multiple failure modes in geotechnical engineering is calculated based on an iterative calculation method, as follows: The sample set of the current iteration layer is input into multiple intelligent models to obtain multiple predicted response values ​​for each failure mode corresponding to each sample, and the maximum value among the multiple predicted response values ​​corresponding to each sample is extracted as the system response value. The system response value is compared with the intermediate threshold set in the current iteration layer. Samples whose system response value is less than or equal to the intermediate threshold are selected as failed samples. The probability weight of the sample set to be analyzed in the current iteration layer is updated according to the current selection ratio relative to the previous iteration layer. Based on the selected failure samples, the next iteration layer sample set is generated by sampling, and the intermediate threshold is updated to enter the next iteration layer until the intermediate threshold converges to the set failure boundary. The reliability is calculated by counting the number of failure samples that converge to the failure boundary and combining them with their corresponding probability weights. After calculating the reliability, the method further includes a sensitivity analysis of the characteristic parameters: Extract the global sample set consisting of all samples generated during the iterative calculation process, as well as the failure samples that converge to the failure boundary; For each of the aforementioned feature parameters, based on the weighted kernel density estimation method and combined with the probability weights corresponding to each sample, the global probability density distribution of each feature parameter in the global sample set and the local probability density distribution in the failure samples that converge to the failure boundary are respectively fitted. Calculate the distribution difference between the local probability density distribution and the global probability density distribution corresponding to each feature parameter; Based on the distribution difference, a sensitivity evaluation index is generated for the corresponding characteristic parameter. The sensitivity evaluation index is used to quantify the degree of influence of the corresponding characteristic parameter on geotechnical engineering failure. The fitting method for the local probability density distribution includes: When the number of failed samples is less than a preset sample threshold, the interquartile range of the corresponding feature parameters is calculated using the Silverman criterion. The smoothing parameters of the weighted kernel density estimation method are determined based on the interquartile range to complete the fitting of the local probability density distribution.

2. The reliability analysis method for multiple failure modes in geotechnical engineering according to claim 1, characterized in that, The degree of distributional dissimilarity is the KL divergence.

3. The reliability analysis method for multiple failure modes in geotechnical engineering according to claim 1, characterized in that, The characteristic parameters include the soil friction coefficient and the soil friction intensity.

4. The reliability analysis method for multiple failure modes in geotechnical engineering according to claim 1, characterized in that, The statistical characteristics include one or more of the mean, standard deviation, and probability distribution type; Based on the statistical characteristics, random sampling is performed using Monte Carlo simulation to generate a multidimensional vector set corresponding to the feature parameters, which serves as the initial sample set.

5. The reliability analysis method for multiple failure modes in geotechnical engineering according to claim 1, characterized in that, The threshold corresponding to the failure boundary is 0; The method for comparing the system response value with the intermediate threshold set in the current iteration layer includes: Determine whether the system response value is less than or equal to 0; if so, determine that the sample has actually failed and stop generating the sample set for the next iteration layer.

6. A reliability analysis system for multiple failure modes in geotechnical engineering, characterized in that, The system performs reliability analysis based on the multi-failure mode reliability analysis method for geotechnical engineering as described in any one of claims 1 to 5.

7. A reliability analysis system for multiple failure modes in geotechnical engineering, characterized in that, include: One or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including instructions for performing the geotechnical engineering multi-failure mode reliability analysis method as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, Includes a computer program that can be executed by a processor to perform the geotechnical engineering multi-failure mode reliability analysis method as described in any one of claims 1 to 5.

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