Influence of Correlation Distance of Soil Parameters on Pile Foundation Failure Probability
Abstract
:1. Introduction
2. Materials and Methods
2.1. Random Field Model
- (1)
- The mean value of the soil parameter (random variable) at each point is the same;
- (2)
- The covariance of soil parameters (two random variables) at any two points is only a function of the distance between the two points.
2.2. Calculation Method of Correlation Distance
- (1)
- Select an average spatial range h = kh0, where k is a positive integer and h0 is the sampling spacing;
- (2)
- Take k = 1, 2, 3, …, in sequence and calculate the mean value of adjacent k + 1 points to form a spatial average random field xh(z);
- (3)
- Calculate the point variance σ2 and the spatial mean-variance Var[xh(z)];
- (4)
- Calculate the variance reduction function Γ2(h) = Var[xh(z)]/σ2 by Equation (3);
- (5)
- Calculate the value of hΓ2(h) and draw the hΓ2(h)~h curve;
- (6)
- Find the value of hΓ2(h) that tends to converge smoothly from the hΓ2(h)~h curve and take it as the desired correlation distance δ.
2.3. Failure Probability of Pile Foundation
2.4. Static Cone Penetration Test Data
3. Results
3.1. Distribution Characteristics of Each Layer of Soil Parameters without Considering the Influence of Correlation Distance
3.2. Average Spatial Characteristics of Each Layer of Soil Parameters Considering the Influence of the Correlation Distance
3.2.1. Calculation of the Correlation Distance
3.2.2. Average Spatial Distribution Characteristics of Each Layer of Soil Parameters
3.3. Failure Probability of Pile Foundation
4. Discussion
4.1. Influence of Correlation Distance on Parameter Distribution
4.2. Error Analysis
4.3. Action Mechanism of Correlation Distance
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Layer Name | Lateral Friction Resistance (kPa) | Cone Tip Resistance (kPa) | ||
---|---|---|---|---|
Mean | Standard Deviation | Mean | Standard Deviation | |
① Planting soil | 32.74 | 3.20 | 2.97 | 0.34 |
② Silt | 118.98 | 37.51 | 3.19 | 0.84 |
③ Silt | 199.87 | 91.60 | 8.55 | 2.94 |
④ Silt | 130.32 | 37.33 | 2.79 | 0.79 |
⑤ Silt | 227.57 | 72.71 | 6.89 | 3.77 |
⑥ Silty clay | 64.79 | 24.54 | 1.33 | 0.51 |
⑦ Silt | 334.35 | 161.57 | 7.11 | 3.43 |
⑧ Silt | 161.77 | 98.89 | 5.26 | 3.87 |
⑨ Silty clay | 37.87 | 14.81 | 1.80 | 0.36 |
⑩ Fine sand | 169.55 | 43.54 | 19.76 | 6.16 |
Layer Name | Lateral Friction Resistance | Cone Tip Resistance | ||
---|---|---|---|---|
λ | ζ | λ | ζ | |
① Planting soil | 3.48 | 0.10 | 1.08 | 0.11 |
② Silt | 4.73 | 0.31 | 1.13 | 0.26 |
③ Silt | 5.20 | 0.44 | 2.09 | 0.33 |
④ Silt | 4.83 | 0.28 | 0.99 | 0.28 |
⑤ Silt | 5.38 | 0.31 | 1.80 | 0.51 |
⑥ Silty clay | 4.10 | 0.37 | 0.21 | 0.37 |
⑦ Silt | 5.71 | 0.46 | 1.86 | 0.46 |
⑧ Silt | 4.93 | 0.56 | 1.44 | 0.66 |
⑨ Silty clay | 3.56 | 0.3772 | 0.57 | 0.20 |
⑩ Fine sand | 5.10 | 0.25 | 2.94 | 0.30 |
Layer Name | Layer Bottom Depth (m) | Layer Thickness (m) | Correlation Distance (m) | |
---|---|---|---|---|
Calculated by Lateral Friction Resistance | Calculated by Cone Tip Resistance | |||
① Planting soil | 0.5 | 0.5 | 0.14 | 0.1 |
② Silt | 2.5 | 2 | 0.21 | 0.29 |
③ Silt | 5.9 | 3.4 | 0.57 | 0.50 |
④ Silt | 9.2 | 3.3 | 0.59 | 0.40 |
⑤ Silt | 11.8 | 2.6 | 0.30 | 0.17 |
⑥ Silty clay | 12.8 | 1 | 0.18 | 0.13 |
⑦ Silt | 17 | 4.2 | 0.58 | 0.52 |
⑧ Silt | 22.5 | 5.5 | 0.25 | 0.25 |
⑨ Silty clay | 26.5 | 4 | 0.91 | 0.93 |
⑩ Fine sand | 29.5 | 3 | 0.23 | 0.36 |
Layer Name | Lateral Friction Resistance (kPa) | Cone Tip Resistance (kPa) | ||
---|---|---|---|---|
Mean | Standard Deviation | Mean | Standard Deviation | |
① Planting soil | 32.74 | 1.69 | 2.97 | 0.15 |
② Silt | 118.98 | 12.20 | 3.19 | 0.32 |
③ Silt | 199.87 | 37.51 | 8.55 | 1.12 |
④ Silt | 130.32 | 15.73 | 2.79 | 0.27 |
⑤ Silt | 227.57 | 24.57 | 6.90 | 0.96 |
⑥ Silty clay | 64.79 | 10.49 | 1.33 | 0.18 |
⑦ Silt | 334.35 | 59.82 | 7.11 | 1.21 |
⑧ Silt | 161.77 | 21.19 | 5.26 | 0.82 |
⑨ Silty clay | 37.87 | 7.07 | 1.80 | 0.17 |
⑩ Fine sand | 169.55 | 11.93 | 19.76 | 2.12 |
Layer Name | Lateral Friction Resistance | Cone Tip Resistance | ||
---|---|---|---|---|
λ | ζ | λ | ζ | |
① Planting soil | 3.49 | 0.05 | 1.09 | 0.05 |
② Silt | 4.77 | 0.10 | 1.16 | 0.10 |
③ Silt | 5.28 | 0.19 | 2.14 | 0.13 |
④ Silt | 4.86 | 0.12 | 1.02 | 0.10 |
⑤ Silt | 5.42 | 0.11 | 1.92 | 0.14 |
⑥ Silty clay | 4.16 | 0.16 | 0.27 | 0.14 |
⑦ Silt | 5.80 | 0.18 | 1.95 | 0.17 |
⑧ Silt | 5.08 | 0.13 | 1.65 | 0.16 |
⑨ Silty clay | 3.62 | 0.18 | 0.58 | 0.10 |
⑩ Fine sand | 5.13 | 0.07 | 2.98 | 0.11 |
Pile Diameter (m) | Pile Length (m) | Failure Probability (%) | |
---|---|---|---|
Not Considering Correlation Distance | Considering Correlation Distance | ||
0.6 | 21 | 24.57 | 1.196 |
23 | 16.662 | 0.058 | |
25 | 13.944 | 0.028 |
Pile Diameter (m) | Pile Length (m) | Confidence Interval | |
---|---|---|---|
Not Considering Correlation Distance | Considering Correlation Distance | ||
0.6 | 21 | (0.24193, 0.24947) | (0.01101, 0.01291) |
23 | (0.16335, 0.16989) | (0.00037, 0.00079) | |
25 | (0.13640, 0.14248) | (0.00013, 0.00043) |
Pile Diameter (m) | Pile Length (m) | Confidence Interval Length | |
---|---|---|---|
Not Considering Correlation Distance | Considering Correlation Distance | ||
0.6 | 21 | 0.00755 | 0.00191 |
23 | 0.00653 | 0.00042 | |
25 | 0.00607 | 0.00029 |
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Liu, C.; Zhang, H.; Yuan, Y.; Zhou, A.; Liu, W.; Guo, W. Influence of Correlation Distance of Soil Parameters on Pile Foundation Failure Probability. Sustainability 2023, 15, 4298. https://doi.org/10.3390/su15054298
Liu C, Zhang H, Yuan Y, Zhou A, Liu W, Guo W. Influence of Correlation Distance of Soil Parameters on Pile Foundation Failure Probability. Sustainability. 2023; 15(5):4298. https://doi.org/10.3390/su15054298
Chicago/Turabian StyleLiu, Chao, Hongrui Zhang, Ying Yuan, Aihong Zhou, Weiwen Liu, and Wanying Guo. 2023. "Influence of Correlation Distance of Soil Parameters on Pile Foundation Failure Probability" Sustainability 15, no. 5: 4298. https://doi.org/10.3390/su15054298