Gravel soil liquefaction potential index calculation and disaster prediction method based on fuzzy mathematics

Abstract

This invention, based on fuzzy mathematics, proposes a method for calculating the liquefaction potential index (LPI) of gravelly soil and predicting hazard levels. Belonging to the fields of earthquake engineering and geotechnical engineering, it aims to address the technical problems of traditional LPI methods, such as underestimation of deep liquefaction in gravelly soil, difficulty in quantifying model uncertainty, and hard segmentation of hazard levels. The method first integrates 12 key influencing factors of gravelly soil liquefaction and predicts the liquefaction probability at each depth using the MCMC-BN model. Then, it calculates the depth weights using a hyperbolic depth weighting function and obtains the values ​​through integration. Finally, it constructs a trapezoidal membership function fuzzy evaluation model and determines the hazard levels of minor, moderate, and severe liquefaction based on the principle of maximum membership. This invention simultaneously quantifies parameters and model uncertainty, improves the deep liquefaction identification rate, achieves smooth hazard level classification, significantly improves prediction accuracy and classification accuracy, has clear physical meaning, is easy to operate, is applicable to gravelly soil sites, has high evaluation accuracy, effectively handles various uncertainties, and has strong engineering practicality.

Description

Technical Field

[0001] This invention relates to the fields of earthquake engineering and geotechnical engineering, and in particular to a method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics. Background Technology

[0002] The Liquefaction Potential Index (LPI) is a core indicator for comprehensively assessing the severity of surface hazards caused by soil liquefaction under seismic loading. Traditional LPI calculation methods, developed based on the liquefaction characteristics of sandy sites, have been widely applied in engineering assessments of liquefaction hazards in sandy sites. This method calculates the liquefaction safety factor and performs integral calculations using a linear depth-weighted function to obtain the LPI. Then, it classifies liquefaction hazard levels based on fixed thresholds, becoming a standard method for assessing liquefaction risk in sandy sites.

[0003] However, due to its coarse-grained skeleton, heterogeneous pore structure, and multi-scale seepage characteristics, gravelly soil exhibits a fundamentally different liquefaction mechanism compared to sandy soil. Therefore, the traditional Liquefaction Potential Index (LPI) method suffers from significant limitations in its applicability to gravelly soil sites. Firstly, the linear depth-weighted function used in traditional methods fails to accurately reflect the nonlinear decay of gravelly soil liquefaction effects with depth, easily leading to an underestimation or even complete neglect of the liquefaction contribution from deeper soil layers. This results in biased liquefaction risk assessments for gravelly soil sites, posing a safety hazard to seismic design. Secondly, traditional methods classify liquefaction hazard levels using fixed numerical thresholds, failing to consider the continuity and randomness of the seismic liquefaction process. Furthermore, they cannot quantify the model and parameter uncertainties introduced by geotechnical and seismic parameters. When the index value approaches the level boundary, it is prone to skipping hazard level classifications, making the assessment results insufficient in terms of rationality and precision to meet actual engineering needs.

[0004] Specifically, the existing technology has the following shortcomings: Traditional LPI (Liquefaction Per Intake) methods, based on the characteristics of sandy soil sites, calculate the LPI value by integrating the liquefaction safety factor and a linear depth weighting function, and then classify the hazard level according to a fixed threshold. However, in gravelly soil sites, the linear depth weighting function fails to accurately reflect the physical law of the nonlinear decay of liquefaction impact with depth, leading to an underestimation of the liquefaction contribution of deeper soil layers; and the fixed threshold classification of hazard levels does not consider the continuity and uncertainty of the liquefaction process, easily resulting in classification jumps.

[0005] For example, CN114154332A discloses a method for assessing seismic liquefaction of gravelly soils. This method includes five steps: establishing a comprehensive database of dynamic penetration tests, establishing a deterministic model, calculating the safety factor against liquefaction triggering, establishing a classification map of liquefiable and non-liquefiable zones, and evaluating the prediction effect. Although this method utilizes multiple global seismic databases, improving data diversity and model universality, it is still based on the research foundation of sand liquefaction and does not adequately consider the unique characteristics of gravelly soils, such as their coarse-grained skeleton and heterogeneous pore structure. It also has limitations, particularly in assessing the impact of deep liquefaction and quantifying uncertainties.

[0006] For example, CN121053740A discloses a disaster early warning method and system for wide-graded gravelly soil. This method acquires multi-source state data of the soil, performs data dimensionality reduction and analysis, and screens a set of key disaster-causing factors. Based on the set of key disaster-causing factors, it uses coupled simulation technology to simulate the disaster evolution process of the soil and extracts quantitative early warning indicators. It uses an adaptive weighted average algorithm to fuse data from multiple monitoring points and calculates the comprehensive risk assessment results through fuzzy comprehensive evaluation to determine the risk level. Although this method shows high accuracy and real-time performance in disaster early warning of wide-graded gravelly soil, it mainly focuses on the simulation and early warning of the disaster process and does not propose a systematic solution for calculating the liquefaction potential index and classifying disaster levels for gravelly soil sites. In particular, it is insufficient in dealing with the nonlinear depth decay law and uncertainty quantification unique to gravelly soil liquefaction.

[0007] For example, IN202531084474 discloses a system and method for assessing the liquefaction probability of gravelly soils using JDRV (Joint Distributed Random Variable) technology. This system and method utilize joint distributed random variable (JDRV) techniques, combined with dynamic penetration test (DPT) data, seismic parameters, and site condition data, to assess the liquefaction probability of gravelly soils. Although this method performs well in handling the randomness and uncertainty of input variables, and the accuracy of the results has been verified by comparison with Monte Carlo simulation (MCS), it still does not completely solve the problems of underestimation of deep impacts and unreasonable hazard level classification in gravelly soil liquefaction assessment.

[0008] In recent years, Bayesian Networks (BNs) have been increasingly applied to liquefaction probability prediction research in geotechnical engineering due to their advantage in effectively quantifying parameter uncertainty. Markov Chain Monte Carlo (MCMC) sampling methods can achieve stable posterior inference with small sample data. The MCMC-BN (Markov Chain Monte Carlo-Metropolis-Hastings) model, combining these two methods, provides a new technical approach for the accurate calculation of soil liquefaction probability. Meanwhile, fuzzy mathematics has demonstrated good continuous classification characteristics in the field of disaster level assessment. It can characterize the fuzzy boundaries between disaster levels through membership functions, effectively alleviating the hard segmentation problem of traditional deterministic threshold division, and providing a new method for the reasonable determination of liquefaction disaster levels.

[0009] Although technologies such as Bayesian networks (BN) and Markov chain Monte Carlo (MCMC) have been initially applied in the field of soil liquefaction assessment, a unified technical framework integrating MCMC-BN models, nonlinear depth weighting functions, and fuzzy mathematical decision-making has not yet been formed. Key technical bottlenecks in liquefaction assessment for gravelly soil sites have not been systematically resolved. Existing technologies lack high-precision liquefaction hazard prediction methods specifically applicable to gravelly soil sites that can simultaneously assess deep liquefaction impacts and handle various uncertainties, thus failing to meet the practical engineering needs of seismic fortification and disaster risk management in gravelly soil sites in seismic zones.

[0010] Therefore, developing a new method for calculating the liquefaction potential index (LPI) and predicting disasters in gravelly soil has become an urgent technical problem. This invention proposes a fuzzy mathematics-based method for calculating the gravelly soil liquefaction potential index (GLPI) and predicting disasters, aiming to improve the prediction accuracy of deep liquefaction and disaster level classification, and provide a more scientific and accurate basis for seismic design and disaster prevention in earthquake engineering. This invention integrates a Markov chain Monte Carlo-Bayesian network (MCMC-BN) model, a hyperbolic depth weighting function, a gravelly soil liquefaction potential index (GLPI) calculation system, and a fuzzy mathematics evaluation model to construct an integrated method for predicting gravelly soil liquefaction disasters, effectively overcoming the shortcomings of existing technologies. Summary of the Invention

[0011] The technical problem this invention aims to solve is to provide a method for calculating the liquefaction potential index (LPI) of gravelly soil and predicting hazard levels based on fuzzy mathematics. This addresses the technical issues of underestimating deep liquefaction and inaccurate hazard classification in earthquake liquefaction hazard assessment of gravelly soil sites in the fields of earthquake engineering and geotechnical engineering. Specifically, the traditional LPI method, based on the characteristics of sandy soil sites, underestimates or ignores the impact of deep liquefaction when applied to gravelly soil sites due to the unique coarse-grained skeleton, heterogeneous pore structure, and multi-scale seepage characteristics of gravelly soil. Furthermore, the traditional method uses a fixed threshold for hazard level classification, failing to fully consider the continuity and uncertainty of the liquefaction process. This invention aims to overcome the limitations of traditional methods in deep liquefaction assessment and hazard level classification.

[0012] To achieve the above technical objectives, this invention adopts the following technical solution: It provides a method for calculating the liquefaction potential index (GLPI) of gravelly soil and predicting its hazard based on fuzzy mathematics, constructing a new framework for calculating the GLPI and predicting its hazard. High-precision assessment of gravelly soil liquefaction hazards is achieved through four key technologies. Specific technical means include the following aspects: A hybrid MCMC-BN model is proposed for predicting the liquefaction probability of gravelly soils at various depths, integrating magnitude data. Peak ground acceleration Epicenter distance Earthquake duration and geotechnical engineering parameters, groundwater level and depth Shear wave velocity Effective overlying pressure Gravel content Fine particle content Median particle size Non-drainage layer thickness Unsaturated layer thickness A total of 12 key influencing factors of gravelly soil liquefaction were identified, and a directed acyclic graph network structure was constructed to express the causal dependencies among these factors. Bayesian parameter learning was performed using the Markov chain Monte Carlo method, and the posterior probability distribution was obtained through random sampling. Parameter uncertainty and model uncertainty were simultaneously quantified, and the liquefaction probability distribution along the depth direction was output. And the corresponding confidence interval. The MCMC-BN model uses MCMC sampling to generate the posterior distribution, with 10,000 iterations.

[0013] Introducing a hyperbolic depth-weighted function to calculate the weight values ​​of soil layers at each depth. To overcome the shortcomings of traditional linear weighted functions, the function expression is as follows: (1); In the formula, These are surface weight control parameters; This is the weight decay rate control parameter. This represents the depth of the soil layer.

[0014] Parameters are determined by boundary conditions and constraints. , The function conforms to the physical law that the influence of liquefaction decreases nonlinearly with depth. The shallow soil has a larger weight to reflect its dominant role in surface disasters, while the deep soil has a smaller weight but is not zero, ensuring that the contribution of deep liquefaction to disaster assessment is not ignored.

[0015] Establish The computational framework outputs the liquefaction probability from the MCMC-BN model. Depth weights calculated with the hyperbolic depth weighting function Multiply, and calculate along the soil depth from 0 to the upper limit of the calculation. The formula for calculating definite integrals is as follows: (2); In the formula, Indicates depth The probability of liquefaction at the location; Indicates depth Depth weight at location ; To calculate the upper limit of depth.

[0016] The value ranges from [0, 1]. The larger the value, the higher the potential for liquefaction disasters at the site. This indicator comprehensively reflects the liquefaction risk of the entire soil profile and is more global and representative than single-point liquefaction identification.

[0017] A fuzzy mathematical evaluation model based on the trapezoidal membership function, i.e., formula (3), is constructed, and three liquefaction hazard levels, namely minor, moderate, and severe, are defined: (3); In the formula, Indicates the minimum value of the category; This indicates complete subordination to the lower boundary; This indicates complete subordination to the upper boundary; Represents the maximum value of the category; where For a completely subordinate interval, and This is a transitional interval.

[0018] The four parameters of the trapezoidal membership function corresponding to each level are, in order, slight liquefaction, moderate liquefaction, and severe liquefaction. The trapezoidal function has a membership degree of 1 in the complete membership interval and changes linearly in the transition interval, achieving a smooth transition of disaster levels; the calculated... Substituting the values ​​into the membership functions for each level yields the corresponding membership degrees. The disaster level is determined based on the principle of maximum membership, and the membership vector is output to quantify the classification uncertainty.

[0019] The specific implementation steps of this invention are as follows: Step 1: Collect parameters of 12 factors affecting gravelly soil liquefaction at the site to be evaluated, and complete data quality checks and standardization. Step 2: Construct and train the MCMC-BN model. Input the measured site parameters and obtain the liquefaction probability distribution along the depth direction through Bayesian inference. ; Step 3, extract depths liquefaction probability value at the location ; Step 4: Calculate the weight value of each depth using the hyperbolic depth weighting function formula (1). ; Step 5, based on The calculation formula (2) is used to obtain the site to be evaluated by piecewise integration. value; Step 6: Construct a fuzzy mathematical evaluation model based on the trapezoidal membership function formula (3) and determine the function parameters for each disaster level; Step 7, Substitute the values ​​into the model to calculate the membership degree of each level, determine the liquefaction disaster level based on the principle of maximum membership degree, and output the membership degree vector.

[0020] The method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics provided by this invention has the following beneficial effects: 1. This invention effectively solves the technical problems of underestimation of deep liquefaction and inaccurate classification of disaster levels in the assessment of seismic liquefaction disasters in gravelly soil sites in the fields of earthquake engineering and geotechnical engineering, and successfully overcomes the limitations of traditional methods in deep liquefaction assessment and disaster level classification.

[0021] 2. By introducing a hyperbolic depth weighting function, this invention effectively solves the problem of underestimating the deep liquefaction of gravelly soils in traditional methods, retains the liquefaction contribution of deep soil layers, improves the identification rate of deep liquefaction sites by about 27%, and can more realistically reflect the impact of soil layers at different depths on surface disasters.

[0022] 3. This invention uses the MCMC-BN model to predict the liquefaction probability at various depths of gravelly soil, realizing the simultaneous quantification of parameter uncertainty and model uncertainty in the liquefaction assessment process. The model can still achieve stable posterior inference under small sample conditions, and the liquefaction probability prediction results are more reliable.

[0023] 4. This invention utilizes trapezoidal membership functions to construct fuzzy mathematical models, successfully overcoming the "hard segmentation" defect of traditional deterministic threshold methods and achieving a smooth transition of disaster levels. After 5-fold cross-validation, the model's classification accuracy reached 0.82, which is about 15.5% higher than traditional methods.

[0024] 5. The constructed GLPI calculation and disaster prediction framework has clear physical meaning, simple calculation method, close connection between each step and strong operability. After verification by actual earthquake sites, the prediction results are highly consistent with the actual earthquake damage. It has good engineering practicality and promotion value in the assessment and risk prediction of liquefaction disasters in gravelly soil sites in earthquake zones.

[0025] 6. This invention significantly improves the prediction accuracy of deep liquefaction and disaster level classification. This conclusion has been verified by case studies of gravelly soil liquefaction in the Wenchuan earthquake and other earthquake events at home and abroad, demonstrating the superiority and practicality of this invention in the assessment of earthquake liquefaction disasters in gravelly soil sites.

[0026] 7. By introducing a hyperbolic depth weighting function, this invention can more realistically reflect the nonlinear decay of liquefaction effects with depth. Compared with the traditional linear weighting function, it significantly improves the recognition rate of deep liquefaction sites.

[0027] 8. This invention utilizes a trapezoidal membership function to establish a fuzzy mathematical evaluation model, effectively solving the "hard segmentation" problem of traditional deterministic threshold methods, making disaster level classification smoother and more reasonable, and significantly improving classification accuracy.

[0028] 9. This invention achieves simultaneous quantification of parameter uncertainty and model uncertainty through the MCMC-BN model. The model output includes point estimates and confidence intervals of probability distributions, providing more comprehensive and reliable information for liquefaction probability calculation.

[0029] 10. This invention combines the Markov Chain Monte Carlo-Bayes Network (MCMC-BN) model to predict the liquefaction probability of gravelly soil at various depths, integrates 12 key influencing factors of gravelly soil liquefaction, and constructs a directed acyclic graph network structure to express the causal dependence between factors, thereby improving the accuracy of prediction.

[0030] 11. This invention introduces a hyperbolic depth-weighted function to calculate the weight of each depth. The form of this function conforms to the physical law that the influence of liquefaction decreases nonlinearly with depth, and can accurately reflect the differentiated contribution of soil layers at different depths to surface disasters.

[0031] 12. This invention combines liquefaction probability and depth weighting to calculate the gravelly soil liquefaction potential index (GLPI). This index considers the liquefaction probability of each soil layer and reflects the contribution of soil layers at different depths to surface hazards, providing a more comprehensive basis for hazard assessment.

[0032] 13. This invention utilizes a trapezoidal membership function to establish a fuzzy mathematical evaluation model, defines three liquefaction hazard levels: minor, moderate, and severe, maps GLPI values ​​to the membership degree of each level, and determines the hazard level through the principle of maximum membership degree, making the evaluation results more intuitive and easier to understand.

[0033] 14. This invention uses the MCMC-BN model to replace the traditional statistical model, which accurately describes the complex nonlinear relationship between the influencing factors of gravelly soil liquefaction, and simultaneously quantifies the parameter uncertainty and model uncertainty, thereby improving the reliability of the assessment.

[0034] 15. This invention introduces a hyperbolic depth-weighted function to replace the traditional linear weighted function, which more realistically reflects the nonlinear decay law of liquefaction influence with depth, avoids the problem of underestimation or neglect of deep liquefaction influence in traditional methods, and improves the accuracy of deep liquefaction identification.

[0035] 16. This invention utilizes a trapezoidal membership function to establish a fuzzy mathematical evaluation model, which solves the "hard segmentation" problem of the traditional deterministic threshold method, making the disaster level classification more in line with the actual situation and improving the rationality of the evaluation.

[0036] 17. This invention effectively solves the problem that the impact of deep liquefaction in gravelly soil sites is underestimated or ignored by the traditional LPI method. By comprehensively considering the liquefaction contribution of soil layers at various depths, it improves the accuracy of deep liquefaction identification and provides a more reliable basis for disaster prevention.

[0037] 18. This invention effectively solves the problem that traditional methods use fixed thresholds in disaster level classification and do not fully consider the continuity and uncertainty of the liquefaction process. By introducing a fuzzy mathematical evaluation model, the disaster level classification becomes more reasonable and scientific.

[0038] 19. This invention effectively solves the problem of difficulty in quantifying parameter uncertainty and model uncertainty simultaneously in traditional methods. It achieves simultaneous quantification of both through the MCMC-BN model, providing more comprehensive and reliable information support for liquefaction probability calculation.

[0039] 20. This invention significantly improves the prediction accuracy of deep liquefaction and disaster level classification. Through practical case verification, the identification rate of deep liquefaction sites has been significantly improved compared with traditional methods, providing a more effective assessment tool for the fields of earthquake engineering and geotechnical engineering.

[0040] 21. This invention enhances the rationality of disaster level classification. By introducing a fuzzy mathematical evaluation model and a trapezoidal membership function, the disaster level classification becomes smoother and more reasonable, and the classification accuracy is significantly improved compared with traditional methods, thereby improving the accuracy and reliability of the assessment.

[0041] 22. This invention achieves simultaneous quantification of parameter uncertainty and model uncertainty through the MCMC-BN model. The model output includes point estimates and confidence intervals of probability distributions, providing more comprehensive and reliable information support for liquefaction probability calculation. It also has good engineering practicality and is easy to apply and promote in actual engineering. Attached Figure Description

[0042] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is Embodiment 3 of the present invention. Overall flowchart of the calculation; Figure 2 This is a structural diagram of the MCMC-BN model in Embodiment 3 of the present invention; Figure 3 This is a schematic diagram of the trapezoidal membership function in Embodiment 3 of the present invention. Detailed Implementation

[0043] The technical solutions of the present invention will be further described below with reference to the embodiments and accompanying drawings: Example 1 This embodiment provides a method for calculating the liquefaction potential index (GLPI) of gravelly soil and predicting disasters based on fuzzy mathematics. It addresses the general scenario of gravelly soil liquefaction disaster assessment, implementing GLPI calculation and disaster level determination based on the MCMC-BN model and fuzzy mathematics. The specific steps are as follows: Data Acquisition and Preprocessing: A training dataset of 65 samples was established, selected from gravelly soil liquefaction cases in the Wenchuan earthquake and other domestic and international earthquake events. Each sample included 12 key influencing factors of gravelly soil liquefaction and one liquefaction state label. Earthquake parameters included magnitude. (5.5~8.0) Peak ground acceleration (0.1g~0.8g), epicentral distance (10–200 km) and earthquake duration (15–120 s); Geotechnical parameters include: groundwater level depth (0.5~8.0m), shear wave velocity (120~300m / s), effective overburden pressure (20~400kPa), gravel content (30-70%) Fine particle content (2-15%), median particle size (5-25mm) Non-drainage layer thickness (0-5m) and unsaturated layer thickness (0~3m); All data are subjected to quality checks and standardization, and outliers are removed before being used for model training.

[0044] MCMC-BN model training: A 13-node Bayesian network with 12 influencing factor nodes and 1 liquefaction state node was constructed. The Metropolis-Hastings algorithm was used for parameter learning, with a total of 10,000 iterations. The first 2,000 iterations were the burn-in period, with a sampling interval of 10. With a uniform prior, the model convergence was validated by the Gelman-Rubin statistic. This achieves the requirement of stable convergence.

[0045] Liquefaction probability prediction: Twelve influencing factors of the site to be evaluated are input layer by layer into the trained MCMC-BN model at 1m depth intervals. The liquefaction probability distribution at each depth is obtained through Bayesian inference. The output includes the point estimate and the 95% confidence interval.

[0046] Depth weight calculation: The weight value corresponding to each depth is calculated using the hyperbolic depth weighting function formula (1), and the parameters are determined by boundary conditions and constraints. , The function conforms to the physical law that the influence of liquefaction decreases nonlinearly with depth. The shallow soil layer has a larger weight to reflect its dominant role in surface disasters, while the deep soil layer has a smaller but non-zero weight to ensure that the contribution of deep liquefaction to disaster assessment is not ignored.

[0047] In the formula, The soil depth is represented by the function, which has a larger weight in shallow layers (0-5m) and a non-zero weight in deeper layers (>20m), thus retaining the contribution of deep liquefaction.

[0048] Value calculation: With 20m as the upper limit of the calculation depth and 1m as the integration step size, the value of the site to be evaluated is obtained by piecewise integration according to formula (2). Values, with a range normalized to [0, 1]:

[0049] Fuzzy evaluation model construction: Based on the GLPI statistical distribution of 65 historical cases, the trapezoidal membership function parameters were determined as follows: slight liquefaction [0.10, 0.20, 0.40, 0.50], moderate liquefaction [0.40, 0.50, 0.60, 0.70], and severe liquefaction [0.60, 0.80, 0.90, 1.00]. The parameters were optimized through 5-fold cross-validation.

[0050] Disaster level assessment: Substituting the values ​​into the trapezoidal membership function formula (3) for each level, the membership degree is calculated. : (3); In the formula, Indicates the minimum value of the category; This indicates complete subordination to the lower boundary; This indicates complete subordination to the upper boundary; Represents the maximum value of the category; where For a completely subordinate interval, and This is a transitional period; Based on the principle of maximum membership Determine the disaster level and output the membership vector. In this embodiment, the model achieves a classification accuracy of 0.82, which is 15.5% higher than the traditional deterministic thresholding method.

[0051] Example 2 In another preferred embodiment, based on Embodiment 1, this embodiment provides a method for calculating the liquefaction potential index of gravelly soil and predicting disasters using fuzzy mathematics. The gravelly soil site of Banqiao School in Mianzhu City, Sichuan Province, which was affected by the 2008 Wenchuan earthquake, is used as the verification object. This site is a typical area of ​​severe gravelly soil liquefaction, with a post-earthquake surface sandblasting thickness of 3-5 cm, differential settlement of buildings reaching 20 cm, and an inclination of approximately 1.2%. The method of this invention is used to predict liquefaction disasters and is verified with actual earthquake damage results. The specific steps are as follows: Site parameter acquisition: Obtain the seismic parameters of the site, including magnitude. Peak ground acceleration Epicenter distance Earthquake duration The depth of the groundwater level was obtained through ZK1 borehole testing. The remaining geotechnical engineering parameters were standardized according to the measured values ​​at the site and then input into the model.

[0052] Depth weight calculation: The weight value corresponding to each depth is calculated using the hyperbolic depth weighting function formula (1), and the parameters are determined by boundary conditions and constraints. , The function conforms to the physical law that the liquefaction effect decays nonlinearly with depth:

[0053] In the formula, The soil depth is represented by the function, which has a larger weight in shallow layers (0-5m) and a non-zero weight in deeper layers (>20m), thus retaining the contribution of deep liquefaction.

[0054] Liquefaction probability calculation: Substitute the above parameters into the trained MCMC-BN model to calculate the liquefaction probability at each key depth: Place , Place , Place , Place The probability of liquefaction in shallow soil is significantly higher than that in deep soil, which is consistent with the liquefaction pattern of gravelly soil.

[0055] Value Calculation: According to formula (2), the integral value is calculated in segments with a step length of 1m. The integral values ​​are 1.490 for the 0~2.5m segment, 0.525 for the 2.5~5.0m segment, 0.277 for the 5.0~7.5m segment, and 0.135 for the 7.5~10.0m segment. The total integral value is 2.427, which is obtained after normalization. .

[0056] Disaster level assessment: Substituting into the trapezoidal membership function formula (3), the membership degree of slight liquefaction is calculated. Medium liquefaction membership Severe liquefaction membership Based on the principle of maximum membership, the site was determined to be at the level of severe liquefaction.

[0057] Results Verification: The prediction results of the method of this invention are completely consistent with the actual earthquake damage at the site; while the traditional LPI method calculates... The value is 0.412, which is classified as a medium liquefaction level. This significantly underestimates the liquefaction hazard level of the site, verifying the accuracy of the method of the present invention in predicting liquefaction hazards in gravelly soil sites, and in particular, effectively identifying the contribution of deep liquefaction.

[0058] Example 3 In another preferred embodiment, based on embodiments 1 and 2, this embodiment provides a method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics. A typical gravelly soil site in a high-risk earthquake zone in western Sichuan is used as the assessment object. The soil layer of this site is mainly gravelly soil, with a coarse particle content of 55% to 68%, classifying it as a high-risk site for earthquake liquefaction. This method is used to assess the liquefaction hazard level of this site, following the procedures outlined below. Figure 1 shown The overall calculation flowchart completes all operations, ultimately achieving an accurate determination of the liquefaction hazard level of the site. The specific implementation process is as follows: Step 1: Data Acquisition and Preprocessing Twelve key influencing factor parameters required for the liquefaction assessment of gravelly soil at the site were collected on-site, with the seismic parameter set to magnitude according to the site's seismic design requirements. Peak ground acceleration Epicenter distance Earthquake duration Geotechnical engineering parameters were obtained through borehole exploration and laboratory testing: groundwater level depth Shear wave velocity Effective overlying pressure Gravel content Fine particle content Median particle size Non-drainage layer thickness Unsaturated layer thickness Meanwhile, 72 cases of gravelly soil liquefaction from both domestic and international sources were selected to establish a training dataset. Each sample included the aforementioned 12 influencing factors and one liquefaction state label. Data quality checks and standardization were performed on both the field-measured parameters and the training dataset, and outliers were removed before being used for subsequent calculations.

[0059] Step 2: Liquefaction Probability Prediction Build as Figure 2 The MCMC-BN model shown contains 12 nodes representing influencing factors of gravelly soil liquefaction and 1 node representing the liquefaction state (Liq). Causal dependencies are established between each influencing factor node and the liquefaction state node through directed edges. The Metropolis-Hastings algorithm is used to learn the model's parameters, with a total of 10,000 iterations, the first 2,000 iterations serving as the burn-in period, and a sampling interval of 10. With a uniform prior, the model convergence was validated by the Gelman-Rubin statistic. The system achieves stable convergence. Standardized measured parameters of the site are then input layer by layer into the trained MCMC-BN model, and the liquefaction probability distribution along the depth direction is obtained through Bayesian inference. The critical depth liquefaction probability is: Place , Place , Place , Place The model outputs include point estimates and 95% confidence intervals.

[0060] Step 3: Depth Weight Calculation The depths of the site were calculated using a hyperbolic depth weighting function. Depth weight at location The function expression is: (1); In the formula, These are surface weight control parameters; This is the weight decay rate control parameter. This represents the depth of the soil layer.

[0061] Among them, surface weight control parameters Weight decay rate control parameters The weight values ​​for each critical depth are calculated using this formula: Place , Place , Place , Place This achieves a depth-weighted effect with a higher weighting of shallow soil and a non-zero weighting of deep soil.

[0062] Step 4 Value Calculation Calculate the liquefaction potential index of the gravelly soil at this site using formula (2): (2); In the formula, Indicates depth The probability of liquefaction at the location; Indicates depth Depth weight at location ; To calculate the upper limit of depth.

[0063] Set the upper limit of the calculation depth Integral step size The liquefaction probability at each depth is integrated using a piecewise integration method, multiplying the product of the liquefaction probability and the depth weight. After calculation and normalization, the site's liquefaction probability is obtained. The value is 0.586.

[0064] Step 4: Construction of Fuzzy Mathematical Evaluation Model Adopting such Figure 3 The trapezoidal membership function shown is used to construct a fuzzy mathematical evaluation model. The model defines three liquefaction hazard levels: slight liquefaction, moderate liquefaction, and severe liquefaction. The four parameters of the trapezoidal membership function corresponding to each level are: slight liquefaction [0.10, 0.20, 0.40, 0.50], moderate liquefaction [0.40, 0.50, 0.60, 0.70], and severe liquefaction [0.60, 0.80, 0.90, 1.00]. The membership curves of each level follow the trend... The values ​​exhibit linear transition and complete membership characteristics, and Figure 3 The variation pattern of the membership function of the trapezoid is consistent.

[0065] Step 5: Disaster Level Determination The calculation of the site Substituting the value 0.586 into the trapezoidal membership functions for the three levels mentioned above, we can calculate the membership degree for each disaster level: (3); In the formula, Indicates the minimum value of the category; This indicates complete subordination to the lower boundary; This indicates complete subordination to the upper boundary; Represents the maximum value of the category; where For a completely subordinate interval, and This is a transitional interval.

[0066] Slight liquefaction membership Medium liquefaction membership Severe liquefaction membership Based on the principle of maximum membership The level corresponding to the largest membership degree is selected as the liquefaction hazard level of the site, and the site is ultimately determined to be at the severe liquefaction level. The membership degree vector is also output. This serves as a confidence level reference indicator for the disaster level.

[0067] This embodiment fully verifies the operability and accuracy of the proposed method by predicting liquefaction hazards in a typical gravelly soil site in western Sichuan. The method can accurately quantify the liquefaction probability of gravelly soil at different depths, and achieves smooth discrimination of hazard level through trapezoidal membership function. Compared with traditional assessment methods, the determination of liquefaction hazard level of this site is more in line with the actual engineering geological conditions of the site, providing a reliable technical basis for the subsequent seismic fortification engineering design of the site.

[0068] In the preferred embodiment, the relevant parameters mentioned in step 1 are 12 key influencing factors of gravelly soil liquefaction, including earthquake parameters such as magnitude. Peak ground acceleration Epicenter distance Earthquake duration and geotechnical engineering parameters, groundwater level and depth Shear wave velocity Effective overlying pressure Gravel content Fine particle content Median particle size Non-drainage layer thickness Unsaturated layer thickness The preprocessing involves data quality checks and standardization of 12 influencing factors. The above settings, by comprehensively covering key parameters of seismic characteristics and soil physical state, provide multidimensional data support for accurately characterizing the liquefaction triggering conditions of gravelly soil, which helps to reveal the dynamic change law of the dominant liquefaction factors under different scenarios and improve the adaptability of the evaluation model to complex geological conditions.

[0069] In the preferred embodiment, the construction and calculation process of the MCMC-BN model in step 2 is as follows: First, a directed acyclic graph network structure containing 12 influencing factor nodes and 1 liquefaction state node is constructed. Then, the MCMC method is used for parameter learning and iterative generation of posterior distribution samples. The conditional probability table of each node is calculated. Finally, the measured site parameters are input into the network, and the liquefaction probability distribution is obtained through Bayesian inference. , The soil depth is represented by the MCMC method, which uses either the Metropolis-Hastings algorithm or Gibbs sampling. The model output is... It includes confidence intervals for point estimates and probability distributions; the above settings, by constructing a causal dependency network structure, explicitly express the interaction of multiple factors, and combine the MCMC method to realize the quantitative propagation of parameter uncertainty. The output confidence intervals for probability distributions provide dynamic early warning thresholds for risk decision-making, significantly improving the scientific nature and engineering applicability of the assessment results.

[0070] In the preferred embodiment, the relevant parameter collection in step 1 involves selecting gravelly soil liquefaction cases from earthquake events to establish a training dataset. The training dataset contains no fewer than 65 samples, with each sample including 12 influencing factors and 1 liquefaction state label. This setup ensures the stability of model parameter learning through large-sample data training. The 65 cases cover different magnitudes, geological conditions, and liquefaction degrees, effectively avoiding the risk of overfitting and enabling the model to have stronger generalization ability, making it applicable to liquefaction prediction needs in different regions and engineering scenarios.

[0071] In the preferred embodiment, the MCMC-BN model described in step 2 is sampled using MCMC to generate the posterior distribution, with 10,000 iterations and a convergence threshold of [value missing]. The above settings ensure sufficient convergence of the posterior distribution through a high number of iterations, and the convergence threshold of 4110 strictly controls the accuracy of parameter estimation, avoiding deviations caused by insufficient sampling. This makes the liquefaction probability distribution output by the model closer to the real physical process, providing a reliable basis for engineering disaster prevention design.

[0072] In the preferred embodiment, step 3 involves calculating the depth using a hyperbolic depth weighting function. Depth weight at location The above settings accurately characterize the decay of liquefaction effects with depth through a nonlinear weighting function, overcoming the underestimation of the contribution of traditional linear weighting to deep soil. It is particularly suitable for deep soft soil layers or engineering sites with large burial depths, and significantly improves the accuracy of deep liquefaction assessment.

[0073] In the preferred scheme, step 4 calculates the liquefaction potential index of gravelly soil. Formula (2) is used to calculate the upper limit of depth H = 20m. The GLPI value is calculated using a piecewise integration method with an integration step size of Δz = 1m. The range of the GLPI value is [0, 1], and the larger the value, the higher the liquefaction hazard potential of the site to be evaluated. The above settings cover most engineering concerns with a depth limit of 20m, and the integration step size of 1m balances calculation efficiency and accuracy. The piecewise integration method effectively integrates the contributions of soil layers at different depths. The normalized output of GLPI makes the hazard potential intuitively comparable, which facilitates engineers to quickly identify high-risk areas.

[0074] In the preferred embodiment, the trapezoidal membership function in step 5 is defined using formula (3), and the liquefaction disaster levels defined in the fuzzy mathematical evaluation model include three categories: slight liquefaction, moderate liquefaction, and severe liquefaction; the above settings, In the preferred scheme, the membership degrees corresponding to the minor, moderate, and severe liquefaction hazard levels calculated in step 6 are used to select the level corresponding to the maximum membership degree as the liquefaction hazard level of the site to be evaluated. At the same time, the membership degree vector is output as a reference index for the confidence level of the hazard level. The above settings achieve a smooth transition of hazard levels through the trapezoidal membership degree function, avoiding the evaluation jump problem caused by traditional hard division. The three-level division takes into account the continuity between the engineering risk classification requirements and the actual liquefaction characteristics, making the evaluation results more consistent with the field observation patterns.

[0075] In the preferred scheme, the trapezoidal membership function parameters corresponding to various liquefaction hazard levels are as follows: minor liquefaction [0.10, 0.20, 0.40, 0.50], moderate liquefaction [0.40, 0.50, 0.60, 0.70], and severe liquefaction [0.60, 0.80, 0.90, 1.00]. These settings provide confidence information on hazard levels by outputting membership vectors, assisting decision-makers in comprehensively assessing risks. The trapezoidal parameter design ensures reasonable overlap between different levels, enhancing the model's tolerance to boundary cases and improving the robustness of the assessment results.

[0076] In the preferred embodiment, when learning the parameters of the MCMC-BN model, the total number of iterations is 10,000, with the first 2,000 iterations serving as the burn-in period and a sampling interval of 10; the model prior distribution is selected as follows. With a uniform prior, the convergence of the model is judged by the Gelman-Rubin statistic. The above settings are considered as the model being stable and convergent. The initial sampling bias is eliminated through the burn-in period, the sampling interval is optimized to reduce autocorrelation, the uniform prior avoids prior bias on parameters, and the Gelman-Rubin statistic strictly controls convergence, ensuring the stability and reliability of parameter estimation and providing a solid statistical foundation for liquefaction probability prediction.

[0077] In summary, this invention proposes a method for calculating the liquefaction potential index (LPI) of gravelly soil and predicting hazard outcomes based on fuzzy mathematics. This method effectively addresses the problems of underestimation of deep liquefaction and inaccurate hazard classification in the assessment of seismic liquefaction hazards on gravelly soil sites in the fields of earthquake engineering and geotechnical engineering. Traditional LPI methods, based on the characteristics of sandy soil sites, tend to underestimate or ignore the impact of deep liquefaction when applied to gravelly soil sites due to the unique coarse-grained skeleton, heterogeneous pore structure, and multi-scale seepage characteristics of gravelly soil. Furthermore, traditional methods use fixed thresholds to classify hazard levels, failing to fully consider the continuity and uncertainty of the liquefaction process, thus making it difficult to meet practical engineering needs.

[0078] This invention provides a method for calculating the liquefaction potential index and predicting disasters in gravelly soil based on fuzzy mathematics, successfully overcoming the limitations of traditional methods. Specifically, it is the first time that fuzzy mathematics has been applied to the calculation of the liquefaction potential index and disaster prediction in gravelly soil. By introducing a hyperbolic depth-weighted function to replace the traditional linear weighted function, it more realistically reflects the nonlinear decay of liquefaction impact with depth. This improvement preserves the liquefaction contribution of deep soil layers, improves the identification rate of deep liquefaction sites, and provides a new assessment approach for earthquake engineering and geotechnical engineering.

[0079] Meanwhile, this invention utilizes a trapezoidal membership function to construct a fuzzy mathematical evaluation model, solving the "hard segmentation" problem of traditional deterministic threshold methods and achieving a smooth transition of disaster levels. This improvement makes the evaluation results more consistent with reality, enhancing the accuracy and reliability of the evaluation. Furthermore, this invention employs the MCMC-BN model to predict the liquefaction probability at various depths in gravelly soil, integrating 12 key influencing factors and constructing a directed acyclic graph network structure to express the causal dependencies between these factors, achieving a precise characterization of the complex nonlinear relationships among the influencing factors of gravelly soil liquefaction.

[0080] Furthermore, this model simultaneously quantifies parameter and model uncertainties during liquefaction assessment, providing more comprehensive and reliable information for liquefaction probability calculation. This approach not only proposes new assessment methods and models but also demonstrates its excellent engineering applicability and promotional value through actual seismic site verification, providing strong technical support for seismic liquefaction hazard assessment of gravelly soil sites.

Claims

1. A method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics, characterized by: Includes the following steps: Step 1: Collect relevant parameters of the site to be evaluated and perform preprocessing; Step 2: The liquefaction probability distribution along the depth direction of the site to be evaluated is calculated using the Markov Chain Monte Carlo-Bayes Network (MCMC-BN) model. Step 3: Calculate the depth weights using the hyperbolic depth weighting function; Step 4: Calculate the liquefaction potential index of gravelly soil ; Step 5: Construct a fuzzy mathematical assessment model containing different liquefaction hazard levels using a trapezoidal membership function; Step 6: [The sentence is incomplete and requires more context to be translated accurately.] The values ​​are substituted into the fuzzy mathematical evaluation model to calculate the membership degree of each disaster level, and the liquefaction disaster level of the site to be evaluated is determined according to the principle of maximum membership degree.

2. The method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics according to claim 1, characterized in that: The relevant parameters mentioned in step 1 are 12 key influencing factors of gravelly soil liquefaction, including earthquake parameters such as magnitude. Peak ground acceleration Epicenter distance Earthquake duration and geotechnical engineering parameters, groundwater level and depth Shear wave velocity Effective overlying pressure Gravel content Fine particle content Median particle size Non-drainage layer thickness Unsaturated layer thickness The preprocessing involves data quality checks and standardization of the 12 influencing factors.

3. The method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics according to claim 2, characterized in that: The construction and calculation process of the MCMC-BN model described in step 2 is as follows: First, a directed acyclic graph network structure containing 12 influencing factor nodes and 1 liquefaction state node is constructed. Then, the MCMC method is used for parameter learning and iterative generation of posterior distribution samples. The conditional probability table of each node is calculated. Finally, the measured site parameters are input into the network, and the liquefaction probability distribution is obtained through Bayesian inference. , The soil depth is represented by the MCMC method, which uses either the Metropolis-Hastings algorithm or Gibbs sampling. The model output is... It includes the confidence intervals of the point estimate and the probability distribution.

4. The method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics according to claim 3, characterized in that: The relevant parameter collection mentioned in step 1 involves selecting gravelly soil liquefaction cases from earthquake events to establish a training dataset. The training dataset contains no fewer than 65 samples, with each sample containing 12 influencing factors and 1 liquefaction status label.

5. The method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics as described in claim 2, characterized in that: The posterior distribution of the MCMC-BN model described in step 2 is generated by MCMC sampling, with 10,000 iterations.

6. The method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics as described in claim 1, characterized in that, Step 3 involves calculating the depth using a hyperbolic depth weighting function. Depth weight at location The expression for the hyperbolic depth weighting function is: （1）； In the formula, These are surface weight control parameters; This is the weight decay rate control parameter. This represents the depth of the soil layer.

7. The method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics according to claim 1, characterized in that, Step 4: Calculate the liquefaction potential index of gravelly soil. Formula (2) is used: （2）； In the formula, Indicates depth The probability of liquefaction at the location; Indicates depth Depth weight at location ; To calculate the upper limit of depth.

8. The method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics according to claim 1, characterized in that: Step 4 The value is calculated using piecewise integration. The value ranges from [0, 1], and the larger the value, the higher the liquefaction hazard potential of the site to be evaluated.

9. The method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics according to claim 1, characterized in that: In step 5, the trapezoidal membership function is defined using formula (3). The liquefaction hazard levels defined in the fuzzy mathematical evaluation model include three categories: slight liquefaction, moderate liquefaction, and severe liquefaction. （3）； In the formula, Indicates the minimum value of the category; This indicates complete subordination to the lower boundary; This indicates complete subordination to the upper boundary; Represents the maximum value of the category; where For a completely subordinate interval, and This is a transitional interval.

10. The method for calculating the liquefaction potential index of gravelly soil and predicting disasters based on fuzzy mathematics according to claim 1, characterized in that: The membership degrees corresponding to the minor, moderate, and severe liquefaction hazard levels calculated in step 6 are used to select the level corresponding to the maximum membership degree as the liquefaction hazard level of the site to be evaluated. At the same time, the membership degree vector is output as a reference index for the confidence level of the hazard level.

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