3D In Situ Stress Estimation by Inverse Analysis of Tectonic Strains
Abstract
:1. Introduction
2. Inverse Analysis for In Situ Stress Determination
2.1. Tectonic Stress-Based Approach
2.2. Tectonic Displacement-Based Approach
2.3. Proposed Tectonic-Strain-Based Approach
3. Application in the In Situ Stress Determination of Three Gorges Dam
3.1. Forward Numerical Model
3.2. Inverse Analysis
3.3. Results of Engineering-Scale In Situ Stress
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Rock Mass | Weight (104 N/m3) | Young Modulus (GPa) | Poisson’s Ratio | Cohesion (MPa) | Friction Angle (°) |
---|---|---|---|---|---|
Slightly weathered rock mass | 2.68 | 30 | 0.22 | 2.0 | 59 |
F20, F22, F32 | 2.6 | 15 | 0.25 | 0.20 | 35 |
F84 | 2.6 | 5 | 0.30 | 0.10 | 28 |
Test Points | (MPa) | (MPa) | (MPa) | (MPa) | (MPa) | (MPa) | |
---|---|---|---|---|---|---|---|
D2 | Measurement | −4.73 | −9.06 | −3.95 | 1.93 | 0.09 | −0.05 |
Stress based | −4.44 | −9.28 | −1.99 | 0.17 | 0.407 | −0.058 | |
Strain based | −4.55 | −8.98 | −3.79 | 1.19 | 0.30 | −0.65 | |
D3 | Measurement | −4.27 | −9.47 | −3.86 | 1.28 | 0.38 | −0.16 |
Stress based | −4.92 | −8.95 | −1.92 | 0.28 | 1.18 | −0.165 | |
Strain based | −4.88 | −9.52 | −3.67 | 1.35 | 0.29 | −0.34 | |
D4 | Measurement | −4.17 | −9.13 | −4.10 | 1.00 | −0.00 | −0.13 |
Stress based | −4.87 | −8.86 | −1.83 | 0.24 | 1.11 | −0.185 | |
Strain based | −4.59 | −7.82 | −2.69 | 1.12 | 0.24 | −0.12 | |
D5 | Measurement | −5.46 | −9.38 | −5.36 | 1.48 | 0.14 | −0.59 |
Stress based | −4.75 | −8.03 | −2.23 | 0.27 | 0.65 | −0.043 | |
Strain based | −4.86 | −8.92 | −3.14 | 1.24 | −0.21 | 0.46 | |
D6 | Measurement | −5.52 | −10.24 | −5.44 | 1.73 | −0.08 | −0.31 |
Stress based | −4.43 | −8.54 | −3.07 | 0.39 | 0.58 | 0.39 | |
Strain based | −4.71 | −9.24 | −2.52 | 1.46 | −0.62 | −0.10 | |
D7 | Measurement | −4.73 | −8.13 | −4.64 | −0.23 | 0.01 | −0.50 |
Stress based | −4.44 | −8.63 | −3.07 | 0.33 | 0.45 | 0.30 | |
Strain based | −4.63 | −8.26 | −3.40 | 1.29 | −0.20 | −0.14 | |
D8 | Measurement | −4.10 | −7.08 | −4.42 | 0.53 | 0.20 | −0.51 |
Stress based | −4.33 | −8.47 | −2.97 | 0.042 | 1.09 | 0.036 | |
Strain based | −4.81 | −9.51 | −4.34 | 0.94 | 0.45 | −0.55 |
Test Points | (MPa) | Azimuth (°) | Inclination (°) | (MPa) | Azimuth (°) | Inclination (°) | (MPa) | Azimuth (°) | Inclination (°) | |
---|---|---|---|---|---|---|---|---|---|---|
D2 | Measurement | 9.80 | 292.00 | 1.00 | 4.00 | 202.00 | 15.00 | 3.94 | 26.00 | 75.00 |
Stress based | 8.98 | 310.44 | 3.72 | 4.71 | 220.5 | 0.062 | 1.91 | 131.4 | 86.2 | |
Displacement based | 8.58 | 311.36 | 12.77 | 4.82 | 222.40 | 4.69 | 3.04 | 152.20 | 76.35 | |
Stain based | 9.32 | 298.33 | 4.73 | 4.60 | 205.29 | 32.69 | 3.39 | 35.62 | 56.88 | |
D3 | Measurement | 9.80 | 300.00 | 4.00 | 4.00 | 208.00 | 23.00 | 3.80 | 39.00 | 67.00 |
Stress based | 8.78 | 308.7 | 11.02 | 4.65 | 218.5 | 0.81 | 1.64 | 124.3 | 78.9 | |
Displacement based | 8.95 | 316.89 | 9.89 | 5.48 | 227.06 | 0.977 | 2.31 | 142.65 | 80.06 | |
Stain based | 9.91 | 297.73 | 3.36 | 4.58 | 206.82 | 15.24 | 3.58 | 39.85 | 74.38 | |
D4 | Measurement | 9.30 | 302.00 | 4.00 | 4.20 | 218.00 | 60.00 | 3.90 | 30.00 | 30.00 |
Stress based | 8.72 | 308.7 | 10.5 | 4.59 | 218.5 | 1.52 | 1.59 | 120.4 | 79.3 | |
Displacement based | 10.50 | 313.75 | 6.35 | 3.27 | 223.91 | 1.49 | 4.02 | 147.13 | 83.48 | |
Stain based | 8.19 | 295.62 | 2.79 | 4.24 | 205.53 | 1.72 | 2.68 | 83.90 | 86.72 | |
D5 | Measurement | 9.90 | 294.00 | 4.00 | 5.70 | 198.00 | 55.00 | 4.60 | 27.00 | 35.00 |
Stress based | 8.16 | 307.6 | 6.68 | 4.67 | 217.9 | 2.81 | 2.17 | 150.6 | 82.7 | |
Displacement based | 7.32 | 323.60 | 4.42 | 5.10 | 235.90 | 27.62 | 4.04 | 45.26 | 61.90 | |
Stain based | 9.28 | 297.09 | 3.07 | 4.61 | 206.30 | 14.34 | 3.02 | 38.89 | 75.32 | |
D6 | Measurement | 10.80 | 295.00 | 2.00 | 5.60 | 208.00 | 64.00 | 4.80 | 24.00 | 26.00 |
Stress based | 8.95 | 308.2 | 5.26 | 4.80 | 319.5 | 18.5 | 2.72 | 203.2 | 70.7 | |
Displacement based | 7.46 | 313.13 | 18.12 | 5.46 | 239.13 | 40.09 | 2.97 | 24.40 | 44.30 | |
Stain based | 9.71 | 296.87 | 4.53 | 4.32 | 207.54 | 8.39 | 2.43 | 178.81 | 80.45 | |
D7 | Measurement | 8.10 | 316.00 | 6.00 | 5.20 | 234.00 | 43.00 | 4.20 | 41.00 | 45.00 |
Stress based | 8.97 | 308.3 | 4.13 | 4.76 | 320.5 | 15.8 | 2.79 | 204.06 | 73.65 | |
Displacement based | 6.51 | 308.80 | 21.20 | 5.14 | 205.80 | 30.00 | 2.61 | 68.50 | 51.80 | |
Stain based | 8.68 | 295.35 | 1.60 | 4.27 | 205.70 | 12.61 | 3.35 | 18.24 | 77.29 | |
D8 | Measurement | 7.20 | 303.00 | 7.00 | 4.70 | 204.00 | 56.00 | 3.70 | 35.00 | 34.00 |
Stress based | 8.89 | 312.5 | 10.82 | 4.40 | 316.13 | 7.17 | 2.65 | 166.7 | 76.97 | |
Displacement based | 7.95 | 304.5 | 16.19 | 4.15 | 209.30 | 17.19 | 3.52 | 75.30 | 66.01 | |
Stain based | 9.75 | 301.56 | 5.85 | 4.94 | 207.55 | 34.27 | 3.98 | 40.00 | 55.09 |
Method | (%) | Azimuth (%) | Inclination (%) | (%) | Azimuth (%) | Inclination (%) | (%) | Azimuth (%) | Inclination (%) |
---|---|---|---|---|---|---|---|---|---|
Stress based | 3.64 | 3.03 | 123.34 | 0.56 | 24.29 | 87.14 | 46.53 | 414.84 | 99.33 |
Displacement based | 10.6 | 4.37 | 369.16 | 1.35 | 6.66 | 64.10 | 21.71 | 199.01 | 65.15 |
Strain based | 1.50 | 0.86 | 48.61 | 3.47 | 1.58 | 40.46 | 21.06 | 123.81 | 90.62 |
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Guo, M.; Yin, S.; Li, C.; Wang, S. 3D In Situ Stress Estimation by Inverse Analysis of Tectonic Strains. Appl. Sci. 2021, 11, 5284. https://doi.org/10.3390/app11115284
Guo M, Yin S, Li C, Wang S. 3D In Situ Stress Estimation by Inverse Analysis of Tectonic Strains. Applied Sciences. 2021; 11(11):5284. https://doi.org/10.3390/app11115284
Chicago/Turabian StyleGuo, Mingwei, Shunde Yin, Chunguang Li, and Shuilin Wang. 2021. "3D In Situ Stress Estimation by Inverse Analysis of Tectonic Strains" Applied Sciences 11, no. 11: 5284. https://doi.org/10.3390/app11115284