Uncertainty Analysis and Risk Assessment for Variable Settlement Properties of Building Foundation Soils
Abstract
1. Introduction
2. Field Experiment and Data Characteristics
2.1. Test Procedure and Statistical Characteristics
2.2. Spatial Variability Characterization
2.3. Cross-Correlation Characterization
3. Uncertainty Analysis of Building Foundation Soils
3.1. Mathematical Equations and Elastoplastic Method
3.2. Uncertainty Analysis Method of Settlement
3.3. Workflow of Proposed Framework
- (1)
- Standard testing procedures to evaluate the soil properties through field and laboratory methods, including sampling, penetration tests, and triaxial compression tests. Statistical analysis processes the measured data to determine the central trends, variability ranges, and spatial correlation patterns.
- (2)
- Quantifying the soil variability using spatial random fields involves analyzing how the soil properties change across locations. This method treats the soil characteristics as continuous random variables, capturing their spatial patterns and correlations.
- (3)
- Copula methods quantify the statistical dependence in the soil properties by modeling their joint distributions without assuming linear relationships. They capture complex correlations between different soil parameters, such as the EM, PR, CF, and FA, using flexible multivariate frameworks.
- (4)
- The variable stiffness elastoplastic method for soil deformation considers how the soil stiffness changes under loading. It combines elastic and plastic behaviors, adjusting the stiffness based on stress levels to better simulate real-world soil responses. Through the incremental stress–strain relationship and considering the load step, the deformation characteristics are calculated by self-programming.
- (5)
- Stochastic finite element analysis for soils involves modeling the spatial variability through random field generation, discretizing it into finite elements, and performing Monte Carlo simulations to compute probabilistic structural responses. This method efficiently quantifies the uncertainty in geotechnical behavior under varying conditions.
4. Risk Assessment of Variable Settlement Properties
4.1. Distribution Fitting Test
4.2. Failure Probability
5. Results and Analyses
5.1. Validation of Uncertainty Stability Analysis Model
5.2. Stability Indicators at Different Locations
5.3. Impact of Spatial Variation on Building Settlement
5.4. Impact of Cross-Correlation on Building Settlement
6. Conclusions
- (1)
- The four different mechanical parameters can be regressed to linear equations. The linear fitting degrees are all greater than 0.99. The horizontal fluctuation scale is significantly larger than the vertical scale. This phenomenon primarily results from stratified deposition processes during soil formation, where sedimentation creates more continuous horizontal layers compared to vertical profiles. Different soil parameters have different correlation structures. The most significant difference lies in the rate at which the function graphs change.
- (2)
- Copula theory provides a powerful framework for modeling complex dependence structures among soil parameters, overcoming the limitations of traditional correlation coefficients. The EM has a negative correlation with the PR, while the CF has a positively correlation with the FA. The discrete characteristics of the simulated data have similar discrete characteristics to those of the original data. The statistics of the simulated data and test data are basically the same. The bootstrap approach circumvents parametric assumptions by harnessing empirical data to improve the reliability in variable land subsidence analyses.
- (3)
- The test results of the mean settlement are basically the same as the simulation results. The stability analysis method for uncertain geotechnical properties for variable land subsidence processes in this paper is scientific and reasonable. The variable land subsidence follows a normal distribution with a significance level of 0.1. The influence of the variability parameter on the variable land subsidence processes is greater than that of the correlation structure.
- (4)
- The failure probabilities of variable stratum settlement for different cross-correlations of geotechnical properties under copula conditions are different. When using the Clayton Copula to characterize the cross-correlation of the geotechnical properties, the failure probability is higher. When using the Gaussian Copula to characterize the cross-correlation of the geotechnical properties, the failure probability is smaller. It can be seen that different cross-correlation structures have different influences on the failure probability of variable stratum settlement.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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№ | Particle Sizes and Their Percentages (%) | ||||
---|---|---|---|---|---|
<0.002 mm | 0.002 mm~0.005 mm | 0.005 mm~0.05 mm | 0.05 mm~0.075 mm | >0.075 mm | |
1# | 7.26 | 39.80 | 32.05 | 13.24 | 4.40 |
2# | 8.16 | 41.96 | 32.13 | 14.64 | 3.83 |
3# | 7.16 | 39.79 | 31.90 | 13.32 | 4.71 |
4# | 7.39 | 39.99 | 32.17 | 15.69 | 3.91 |
5# | 8.41 | 40.06 | 33.05 | 13.66 | 4.18 |
6# | 9.38 | 41.28 | 32.13 | 12.55 | 4.50 |
7# | 8.15 | 40.04 | 31.79 | 11.85 | 4.98 |
8# | 9.23 | 39.89 | 32.31 | 13.89 | 4.79 |
9# | 8.23 | 42.33 | 33.09 | 14.20 | 3.93 |
10# | 8.27 | 40.17 | 31.62 | 13.01 | 4.34 |
№ | Density (g/cm3) | Dry Density (g/cm3) | Moisture Content (%) | Specific Gravity of Solids | Plastic Limits (%) | Liquid Limits (%) |
---|---|---|---|---|---|---|
1# | 1.77 | 1.37 | 29.16 | 2.67 | 20.48 | 41.07 |
2# | 1.83 | 1.43 | 27.80 | 2.74 | 19.53 | 41.89 |
3# | 1.91 | 1.47 | 29.81 | 2.78 | 19.24 | 38.67 |
4# | 1.78 | 1.42 | 25.67 | 2.65 | 20.40 | 39.97 |
5# | 1.99 | 1.51 | 31.84 | 2.58 | 19.16 | 38.67 |
6# | 1.91 | 1.52 | 26.03 | 2.70 | 19.22 | 40.90 |
7# | 1.94 | 1.52 | 28.02 | 2.75 | 19.64 | 40.60 |
8# | 1.89 | 1.46 | 29.56 | 2.71 | 19.11 | 39.38 |
9# | 1.54 | 1.18 | 30.74 | 2.83 | 20.34 | 39.33 |
10# | 1.93 | 1.49 | 29.77 | 2.67 | 19.83 | 39.10 |
№ | Vertical Direction of the Stratum (m) | Horizontal Direction of the Stratum (m) | ||||||
---|---|---|---|---|---|---|---|---|
EM | PR | CF | FA | EM | PR | CF | FA | |
1# | 1.05 | 1.20 | 0.90 | 0.95 | 1.45 | 1.91 | 1.92 | 1.61 |
2# | 1.06 | 1.16 | 0.97 | 1.01 | 1.58 | 1.96 | 1.87 | 1.77 |
3# | 1.13 | 1.15 | 0.88 | 1.04 | 1.51 | 2.03 | 1.99 | 1.66 |
4# | 1.03 | 1.15 | 0.90 | 1.00 | 1.47 | 2.10 | 2.02 | 1.72 |
5# | 1.16 | 1.10 | 0.92 | 1.01 | 1.61 | 2.10 | 1.97 | 1.70 |
6# | 1.15 | 1.11 | 0.95 | 1.02 | 1.59 | 1.95 | 2.18 | 1.77 |
7# | 1.06 | 1.15 | 1.03 | 1.04 | 1.54 | 2.15 | 1.90 | 1.87 |
8# | 1.14 | 1.21 | 0.95 | 1.10 | 1.52 | 2.12 | 1.96 | 1.92 |
9# | 1.17 | 1.12 | 0.92 | 1.12 | 1.48 | 2.23 | 1.73 | 1.82 |
10# | 1.12 | 1.24 | 0.97 | 1.05 | 1.41 | 2.03 | 1.87 | 1.73 |
Function Type | Detailed Mathematical Expression | Relationship Between Parameters |
---|---|---|
2-DSQX | ||
2-DSMK | ||
2-DCSX |
Copula | C(u1,u2; θ) | D(u1,u2; θ) | Range of θ |
---|---|---|---|
Gaussian | [−1, 1] | ||
Frank | |||
Gumbel | |||
Clayton |
Statistics | Field Experiment Results | Numerical Simulation Results | Comparative Values | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
EM | PR | CF | FA | EM | PR | CF | FA | EM | PR | CF | FA | |
Sample size | 100 | 100 | 100 | 100 | 1000 | 1000 | 1000 | 1000 | ||||
Mean (10A MPa) | 10.013 | 0.300 | 65.585 | 25.051 | 9.895 | 0.297 | 64.787 | 25.216 | 0.118 | 0.003 | 0.798 | −0.165 |
SD (10A MPa) | 0.502 | 0.014 | 2.989 | 1.424 | 0.491 | 0.014 | 2.987 | 1.408 | 0.011 | 0.000 | 0.002 | 0.016 |
COV | 0.050 | 0.047 | 0.046 | 0.057 | 0.051 | 0.046 | 0.045 | 0.057 | −0.001 | 0.001 | 0.001 | 0.000 |
Max (10A MPa) | 11.366 | 0.337 | 71.815 | 28.687 | 11.307 | 0.333 | 70.846 | 28.612 | 0.059 | 0.004 | 0.969 | 0.075 |
Min (10A MPa) | 8.678 | 0.266 | 58.617 | 21.214 | 8.707 | 0.263 | 58.464 | 20.957 | −0.029 | 0.003 | 0.153 | 0.257 |
Skewness | −0.113 | −0.292 | −0.074 | −0.055 | −0.113 | −0.296 | −0.074 | −0.055 | 0.000 | 0.004 | 0.000 | 0.000 |
Peakedness | 0.106 | −0.074 | −0.649 | −0.300 | 0.106 | −0.074 | −0.650 | −0.303 | 0.000 | 0.000 | 0.001 | 0.003 |
№ | Group (ti−1, ti] | Absolute Frequency, fi | Frequency, fi/n | Cumulative Frequency |
---|---|---|---|---|
1 | [11.776, 12.930] | 15 | 0.0015 | 0.0650 |
2 | (12.930, 14.084] | 121 | 0.0121 | |
3 | (14.084, 15.238] | 619 | 0.0619 | |
4 | (15.238, 16.392] | 1902 | 0.1902 | 0.2141 |
5 | (16.392, 17.546] | 3011 | 0.3011 | 0.489 |
6 | (17.546, 18.701] | 2649 | 0.2649 | 0.7693 |
7 | (18.701, 19.855] | 1314 | 0.1314 | 0.9313 |
8 | (19.855, 21.009] | 316 | 0.0316 | 0.9313 + 0.0687 = 1 |
9 | (21.009, 22.163] | 47 | 0.0047 | |
10 | (22.163, 23.317] | 6 | 0.0006 |
№ | Group (ti−1, ti] | Absolute Frequency, fi | Frequency, pi | npi | (fi−npi)2/npi |
---|---|---|---|---|---|
1 | (−∞, 15.238] | 755 | 0.0769 | 769.00 | 0.2549 |
2 | (15.238, 16.392] | 1902 | 0.1898 | 1898.00 | 0.0084 |
3 | (16.392, 17.546] | 3011 | 0.3050 | 3050.00 | 0.4987 |
4 | (17.546, 18.701] | 2649 | 0.2658 | 2658.00 | 0.0305 |
5 | (18.701, 19.855] | 1314 | 0.1256 | 1256.00 | 2.6783 |
6 | (19.855, +∞] | 369 | 0.0376 | 376.00 | 0.1303 |
Total | 10,000 | 1.0000 | 10,000 | 3.6011 |
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Zhou, X.; Wang, T. Uncertainty Analysis and Risk Assessment for Variable Settlement Properties of Building Foundation Soils. Buildings 2025, 15, 2369. https://doi.org/10.3390/buildings15132369
Zhou X, Wang T. Uncertainty Analysis and Risk Assessment for Variable Settlement Properties of Building Foundation Soils. Buildings. 2025; 15(13):2369. https://doi.org/10.3390/buildings15132369
Chicago/Turabian StyleZhou, Xudong, and Tao Wang. 2025. "Uncertainty Analysis and Risk Assessment for Variable Settlement Properties of Building Foundation Soils" Buildings 15, no. 13: 2369. https://doi.org/10.3390/buildings15132369
APA StyleZhou, X., & Wang, T. (2025). Uncertainty Analysis and Risk Assessment for Variable Settlement Properties of Building Foundation Soils. Buildings, 15(13), 2369. https://doi.org/10.3390/buildings15132369