Study on the Empirical Probability Distribution Model of Soil Factors Influencing Seismic Liquefaction
Abstract
1. Introduction
2. Analysis of Liquefaction Influencing Factors and the Collection and Processing of Field Liquefaction Investigation Cases
2.1. Analysis of Soil Properties via Liquefaction Influencing Factors
2.2. Collection and Processing of Field Liquefaction Investigation Cases Based on SPT
3. Study on the Soil Property Variables’ Probability Distribution
3.1. Interval Discretization and Probability Distribution Fitting
3.2. Probability Distribution Hypothesis Test
3.3. Further Analysis of Factors Whose Probability Distribution Failed the Hypothesis Test
4. Probability Distribution Determination Results
4.1. Probability Distribution Fitting
4.2. Probability Distribution Hypothesis Testing Results
4.3. Further Analysis of the Factors That Failed the Hypothesis Test
5. Liquefaction Probability Calculation Given the Distribution of Influencing Factors
5.1. Method for Determining Liquefaction Probability Based on Variable Distributions
5.2. The Principle and Process of Liquefaction Probability Calculations Using Monte Carlo Method
- Step 1: Determination of correlations among the variables in the joint distribution
- Step 2: Sample generation with a certain correlation using the Monte Carlo method
- Step 3: Liquefaction probability calculation with the generated samples
5.3. Case Verification Clculation
5.4. Sensitivity Analysis
6. Discussion
7. Conclusions
- (1)
- The probability distributions of the same variable under different soil types were not identical. (N1)60, SM, S, and GM followed a Gaussian distribution, while CL and ML followed a lognormal distribution. FC, SM, and GM followed a lognormal distribution, while d50, ML, and S followed the Gaussian and lognormal distributions, respectively. The distribution curves of FC under CL, ML, S, and d50 under SM, CL, and GM can be calculated by the kernel density estimation;
- (2)
- The method of calculating liquefaction probability by using Monte Carlo simulations was feasible. The liquefaction probability calculation result of the case was similar to the existing probability model and consisted with the actual situation, indicating that the proposed methods are reliable;
- (3)
- Regional differences can be considered by introducing the normal distribution error term. The liquefaction probability accuracy can be improved to a certain extent. The method proposed in this paper can either regard amax and M as fixed values to calculate the liquefaction probability at a specific seismic level, or substitute the joint distribution P(amax, M) to determine the total probability within a certain period in the future.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Factors | Influencing Factors | |||
---|---|---|---|---|
Method | Dynamic Loading | Environmental Factors | Soil Factors | |
Deterministic method | NCEER | M, amax | ds, dw, σ, σ’ | (N1)60, FC, DR |
Chinese code | M, amax, R | ds, dw | N, ρc | |
Probabilistic method | Idriss | M, amax | ds, dw, σ, σ’ | (N1)60, FC, DR |
Liao | amax | σ, σ’ | N | |
Cetin | M, amax | σ, σ’ | (N1)60, FC | |
Chen | M, amax | σ, σ’ | (N1)60, FC, DR | |
Machine learning method | Support vector machine | M, ED, R | ds, dw | N |
Neural network | M, amax | ds, dw, σ, σ’ | (N1)60, FC, d50 | |
Bayesian network | M, amax, R | ds, dw, σ, σ’ | (N1)60, FC, d50, ST |
Soil Type | Factors | Minimum Value | Maximum Value | Mean Value | Variance | Variation Coefficient |
---|---|---|---|---|---|---|
SM | (N1)60 | 1.5 | 86 | 14.74 | 86.85 | 0.63 |
FC | 0 | 99 | 32.75 | 674.33 | 0.79 | |
d50 | 0.0028 | 96 | 0.55 | 20.59 | 8.18 | |
CL | (N1)60 | 0.98 | 56.68 | 9.92 | 39.43 | 0.63 |
FC | 8 | 100 | 83.07 | 398.91 | 0.24 | |
d50 | 0.002 | 5 | 0.043 | 0.06 | 5.74 | |
ML | (N1)60 | 2.16 | 29.28 | 9.30 | 25.63 | 0.54 |
FC | 5.73 | 99 | 72.50 | 477.35 | 0.30 | |
d50 | 0 | 0.22 | 0.045 | 0.001 | 0.80 | |
S | (N1)60 | 1.1 | 68.87 | 15.78 | 111.92 | 0.67 |
FC | 7 | 96 | 49.22 | 832.64 | 0.59 | |
d50 | 0.0065 | 15 | 0.57 | 4.08 | 3.54 | |
GM | (N1)60 | 7.46 | 77.20 | 39.94 | 357.83 | 0.47 |
FC | 7 | 95 | 24.72 | 344.59 | 0.75 | |
d50 | 0.0055 | 12 | 2.97 | 12.64 | 1.20 |
Distribution Name | Gaussian | Lognormal | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
SM | CL | ML | S | GM | SM | CL | ML | S | GM | |
(N1)60 | 0.31 | 0.02 | 0.51 | 0.25 | 0.80 | 0.00 | 0.69 | 0.76 | 0.18 | 0.13 |
FC | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.28 | 0.00 | 0.00 | 0.00 | 0.88 |
d50 | 0.00 | 0.00 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.53 | 0.00 |
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Yang, Z.; Fan, M.; Li, J.; Liu, X.; Zhao, J.; Yang, H. Study on the Empirical Probability Distribution Model of Soil Factors Influencing Seismic Liquefaction. Buildings 2025, 15, 2861. https://doi.org/10.3390/buildings15162861
Yang Z, Fan M, Li J, Liu X, Zhao J, Yang H. Study on the Empirical Probability Distribution Model of Soil Factors Influencing Seismic Liquefaction. Buildings. 2025; 15(16):2861. https://doi.org/10.3390/buildings15162861
Chicago/Turabian StyleYang, Zhengquan, Meng Fan, Jingjun Li, Xiaosheng Liu, Jianming Zhao, and Hui Yang. 2025. "Study on the Empirical Probability Distribution Model of Soil Factors Influencing Seismic Liquefaction" Buildings 15, no. 16: 2861. https://doi.org/10.3390/buildings15162861
APA StyleYang, Z., Fan, M., Li, J., Liu, X., Zhao, J., & Yang, H. (2025). Study on the Empirical Probability Distribution Model of Soil Factors Influencing Seismic Liquefaction. Buildings, 15(16), 2861. https://doi.org/10.3390/buildings15162861