A Unified Nonlinear Elastic Model for Rock Material
Abstract
:1. Introduction
2. Common Nonlinear Elastic Models
2.1. Nonlinear Elastic Models of Joints
2.2. Nonlinear Elastic Models of Joints
3. A New Unified Nonlinear Elastic Model
4. The Characteristics of the New Model
4.1. Sensitivity Analysis of the Parameters
4.2. Approximating to a Single Stress‒Strain Curve
5. Experimental Validation of the New Model
5.1. Experimental Methods
5.2. Experimental and Fitting Results
5.3. The m Value Range of the Rock Material
5.4. The Range of Eni Values for the Rock Material
6. Application of the New Model
7. Summary and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Type of Rock | UCS/MPa | Eni/MPa | m | Coefficients of Determination R2 |
---|---|---|---|---|
D01 | 62.15 | 5.82 | 0.9117 | 0.9951 |
D02 | 115.06 | 11.01 | 0.8911 | 0.9977 |
D03 | 124.10 | 12.79 | 0.9039 | 0.9792 |
D04 | 150.59 | 13.48 | 0.9626 | 0.9935 |
D05 | 136.74 | 14.38 | 0.8759 | 0.9917 |
D06 | 176.04 | 16.30 | 0.9216 | 0.9907 |
D07 | 168.37 | 17.41 | 0.9389 | 0.9922 |
D08 | 189.53 | 19.17 | 0.8630 | 0.9817 |
D09 | 192.21 | 19.94 | 0.9478 | 0.9976 |
D10 | 185.34 | 20.28 | 0.8880 | 0.9927 |
G01 | 36.24 | 3.14 | 0.6508 | 0.9939 |
G02 | 49.95 | 5.57 | 0.7621 | 0.9840 |
G03 | 69.71 | 6.74 | 0.8872 | 0.9859 |
G04 | 70.76 | 8.28 | 0.7335 | 0.9998 |
G05 | 84.64 | 9.97 | 0.7789 | 0.9934 |
G06 | 108.23 | 11.70 | 0.8899 | 0.9977 |
G07 | 140.88 | 13.81 | 0.9517 | 0.9861 |
G08 | 153.39 | 14.42 | 0.9488 | 0.9758 |
G09 | 171.11 | 17.03 | 0.9455 | 0.9846 |
G10 | 202.02 | 19.76 | 0.9919 | 0.9951 |
L01 | 23.72 | 1.91 | 0.8868 | 0.9907 |
L02 | 48.96 | 4.09 | 0.9927 | 0.9904 |
L03 | 48.28 | 5.12 | 0.9867 | 0.9850 |
L04 | 62.50 | 5.58 | 0.8569 | 0.9850 |
L05 | 75.60 | 6.81 | 1.0282 | 0.9733 |
L06 | 84.66 | 7.58 | 0.8631 | 0.9943 |
L07 | 99.42 | 8.90 | 0.8684 | 0.9897 |
L08 | 107.62 | 10.07 | 0.8406 | 0.9888 |
L09 | 116.59 | 10.23 | 0.8039 | 0.9948 |
L10 | 136.49 | 12.40 | 0.8981 | 0.9870 |
S01 | 32.69 | 2.88 | 1.0102 | 0.9954 |
S02 | 46.07 | 3.93 | 1.0529 | 0.9868 |
S03 | 70.80 | 5.37 | 0.9518 | 0.9947 |
S04 | 44.31 | 5.66 | 0.8245 | 0.9940 |
S05 | 89.10 | 8.69 | 0.9203 | 0.9853 |
S06 | 76.43 | 7.48 | 1.0095 | 0.9762 |
S07 | 104.29 | 9.61 | 1.0199 | 0.9775 |
S08 | 95.49 | 10.69 | 0.9901 | 0.9780 |
S09 | 155.85 | 14.17 | 1.0273 | 0.9916 |
S10 | 132.84 | 14.87 | 1.0529 | 0.9922 |
Type of Rock | Best-Fit Range | Range When R2 Values Exceed 0.95 | Range When R2 Values Exceed 0.80 |
---|---|---|---|
Dolomite | 0.86~0.96 | 0.58~1.20 | 0.08~1.46 |
Granite | 0.65~0.99 | 0.28~1.23 | 0.00~1.47 |
Limestone | 0.80~1.03 | 0.51~1.22 | 0.04~1.52 |
Sandstone | 0.82~1.05 | 0.49~1.26 | 0.00~1.32 |
Type of Rock | Range of Eni/MPa |
---|---|
Dolomite | 5.82~20.28 |
Granite | 3.14~19.76 |
Limestone | 1.91~12.40 |
Sandstone | 2.88~14.87 |
Type of Rock | Linear Fitting y = ax + b | Coefficients of Determination R2 | |
---|---|---|---|
a | b | ||
Dolomite | 8.92 | 15.74 | 0.950 |
Granite | 10.44 | −6.52 | 0.978 |
Limestone | 10.94 | 0.87 | 0.988 |
Sandstone | 9.29 | 7.38 | 0.915 |
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Chen, C.; Chen, S.; Zhang, Y.; Lin, H.; Wang, Y. A Unified Nonlinear Elastic Model for Rock Material. Appl. Sci. 2022, 12, 12725. https://doi.org/10.3390/app122412725
Chen C, Chen S, Zhang Y, Lin H, Wang Y. A Unified Nonlinear Elastic Model for Rock Material. Applied Sciences. 2022; 12(24):12725. https://doi.org/10.3390/app122412725
Chicago/Turabian StyleChen, Chong, Shenghong Chen, Yihu Zhang, Hang Lin, and Yixian Wang. 2022. "A Unified Nonlinear Elastic Model for Rock Material" Applied Sciences 12, no. 24: 12725. https://doi.org/10.3390/app122412725