Strain Rate Effects on Characteristic Stresses and Dynamic Strength Criterion in Granite Under Triaxial Quasi-Static Compression
Abstract
:1. Introduction
2. Rock Specimens and Experiment Preparation
2.1. Rock Specimens and Testing System
2.2. Testing System
2.3. Procedures for Testing
3. Experimental Results and Analysis
3.1. Stress–Strain Curves
3.2. Strain Rate Effects on Characteristic Stresses
- The peak point of the axial stress–volumetric strain curve is the volumetric dilantancy point (point A in Figure 6), and the corresponding axial stress value is σcd;
- Assuring the point of σcd in the curve of the axial stress-–ateral strain and connecting it to the curve’s origin as the reference line, as shown in Figure 6;
- Drawing the curve based on the difference value between the curve of axial stress–lateral strain and the reference line, and the peak point of this curve corresponding to the axial stress is σci, as shown in Figure 6.
3.3. Macro-Fracture Patterns
3.4. Dynamic Strength Criterion
3.4.1. Mohr–Coulomb Strength Criterion
3.4.2. Dynamic Mohr–Coulomb Strength Criterion
4. Discussion
5. Conclusions
- (1)
- Under varying confining pressures, characteristic stresses of granite exhibit positive correlations with the logarithm of strain rate and confining pressure. Specifically, σcd and σp demonstrate significant linear positive correlations with the strain rate logarithm, while σci shows a relatively weaker correlation.
- (2)
- Under triaxial quasi-static loading conditions, the value of σci/σp ranges from 0.41 to 0.56, and the value of σcd/σp ranges from 0.75 to 0.84. Linear regression analysis demonstrates strong linear correlations between σci/σp and σcd/σp, expressed as σci = 0.58σp and σcd = 0.85σp.
- (3)
- Macroscopic fracture patterns of granite are controlled by the confining pressure and strain rate: Y-shaped shear fractures predominantly form under low confining pressures and strain rates. With increasing confining pressure and strain rate, fracture patterns progressively transition to X-shaped shear-dominated failures.
- (4)
- The strain rate-induced enhancement of dynamic compressive strength primarily originates from the rate-strengthening effect on cohesion, while the internal friction angle remains stable across varying strain rates.
- (5)
- The disparity in microcrack activity intensity during different deformation stages of rocks leads to the CSDIF of σci being lower than those of σcd and σp.
- (6)
- The CSDIF of σcd and σp decreases with elevated confining pressures. This differential behavior is explained by confinement-enhanced shear fracturing dominance during crack propagation stages combined with a lower strain rate sensitivity of shear versus tensile fracture toughness.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Specimen | Strain Rate (s−1) | CP (MPa) | D (mm) | H (mm) | M (g) | V (cm3) | D (g.cm−3) |
---|---|---|---|---|---|---|---|
GS-S-1 | 10−6 | 10 | 49.81 | 100.62 | 524.90 | 196.07 | 2.68 |
GS-S-2 | 20 | 49.92 | 100.26 | 524.90 | 196.23 | 2.67 | |
GS-S-3 | 30 | 49.91 | 100.67 | 523.90 | 196.95 | 2.66 | |
GS-S-4 | 40 | 49.95 | 100.72 | 526.00 | 197.37 | 2.67 | |
GS-S-5 | 10−5 | 10 | 49.94 | 100.71 | 526.00 | 197.27 | 2.67 |
GS-S-6 | 20 | 49.97 | 100.45 | 524.30 | 197.00 | 2.66 | |
GS-S-7 | 30 | 49.89 | 100.62 | 524.80 | 196.70 | 2.67 | |
GS-S-8 | 40 | 49.94 | 100.32 | 524.60 | 196.51 | 2.67 | |
GS-S-9 | 10−4 | 10 | 49.99 | 100.31 | 525.60 | 196.88 | 2.67 |
GS-S-10 | 20 | 49.92 | 100.33 | 525.40 | 196.37 | 2.68 | |
GS-S-11 | 30 | 49.99 | 100.51 | 525.30 | 197.27 | 2.66 | |
GS-S-12 | 40 | 49.91 | 100.19 | 524.10 | 196.02 | 2.67 | |
GS-S-13 | 10−3 | 10 | 49.99 | 100.44 | 526.50 | 197.13 | 2.67 |
GS-S-14 | 20 | 49.98 | 100.28 | 525.70 | 196.74 | 2.67 | |
GS-S-15 | 30 | 50.03 | 100.34 | 525.80 | 197.25 | 2.67 | |
GS-S-16 | 40 | 49.92 | 100.47 | 524.40 | 196.64 | 2.67 | |
GS-S-17 | 10−2 | 10 | 50.01 | 100.59 | 526.00 | 197.59 | 2.66 |
GS-S-18 | 20 | 49.87 | 100.44 | 525.10 | 196.19 | 2.68 | |
GS-S-19 | 30 | 50.03 | 100.18 | 524.70 | 196.94 | 2.66 | |
GS-S-20 | 40 | 49.88 | 100.43 | 525.60 | 196.25 | 2.68 |
Scheme 1. | Strain Rate (s−1) | CP (MPa) | σci (MPa) | σcd (MPa) | σp (MPa) | σci/σp | σcd/σp | σci/σcd |
---|---|---|---|---|---|---|---|---|
GS-S-1 | 10−6 | 10 | 101.43 | 172.30 | 228.10 | 0.44 | 0.76 | 0.59 |
GS-S-2 | 20 | 161.63 | 220.12 | 289.38 | 0.56 | 0.76 | 0.73 | |
GS-S-3 | 30 | 179.28 | 282.83 | 356.78 | 0.50 | 0.79 | 0.63 | |
GS-S-4 | 40 | 207.14 | 313.10 | 399.84 | 0.52 | 0.78 | 0.66 | |
GS-S-5 | 10−5 | 10 | 111.66 | 174.73 | 211.90 | 0.53 | 0.82 | 0.64 |
GS-S-6 | 20 | 151.43 | 225.78 | 301.60 | 0.50 | 0.75 | 0.67 | |
GS-S-7 | 30 | 201.57 | 302.40 | 372.48 | 0.54 | 0.81 | 0.67 | |
GS-S-8 | 40 | 235.18 | 328.94 | 411.37 | 0.57 | 0.80 | 0.71 | |
GS-S-9 | 10−4 | 10 | 125.83 | 188.48 | 237.52 | 0.53 | 0.79 | 0.67 |
GS-S-10 | 20 | 157.54 | 251.04 | 318.16 | 0.50 | 0.79 | 0.63 | |
GS-S-11 | 30 | 188.19 | 295.80 | 371.28 | 0.51 | 0.80 | 0.64 | |
GS-S-12 | 40 | 229.33 | 349.96 | 433.78 | 0.53 | 0.81 | 0.66 | |
GS-S-13 | 10−3 | 10 | 138.72 | 210.61 | 269.64 | 0.51 | 0.78 | 0.66 |
GS-S-14 | 20 | 164.19 | 254.99 | 328.23 | 0.50 | 0.78 | 0.64 | |
GS-S-15 | 30 | 200.82 | 315.18 | 379.26 | 0.53 | 0.83 | 0.64 | |
GS-S-16 | 40 | 248.45 | 371.26 | 454.48 | 0.55 | 0.82 | 0.67 | |
GS-S-17 | 10−2 | 10 | 115.59 | 195.80 | 257.07 | 0.45 | 0.76 | 0.59 |
GS-S-18 | 20 | 196.51 | 282.44 | 354.03 | 0.56 | 0.80 | 0.70 | |
GS-S-19 | 30 | 213.29 | 332.89 | 412.68 | 0.52 | 0.81 | 0.64 | |
GS-S-20 | 40 | 247.12 | 382.10 | 468.68 | 0.53 | 0.82 | 0.65 |
CP (MPa) | σci | σcd | σp | |||
---|---|---|---|---|---|---|
Fitting Equation | R2 | Fitting Equation | R2 | Fitting Equation | R2 | |
10 | 0.38 | 0.69 | 0.64 | |||
20 | 0.55 | 0.94 | 0.99 | |||
30 | 0.65 | 0.87 | 0.81 | |||
40 | 0.77 | 0.99 | 0.99 |
Confining Pressure (MPa) | CSDIF (σci) | CSDIF (σcd) | CSDIF (σp) |
---|---|---|---|
0 | 1.15 | 1.30 | 1.41 |
10 | 1.14 | 1.14 | 1.13 |
20 | 1.22 | 1.28 | 1.22 |
30 | 1.19 | 1.18 | 1.16 |
40 | 1.19 | 1.22 | 1.17 |
Strain Rate (s−1) | Parameters of Fitting Equation | Internal Friction Angle (°) | Cohesion (MPa) | |
---|---|---|---|---|
A | B | |||
10−6 | 152.24 | 7.52 | 49.93 | 27.76 |
10−5 | 146.52 | 8.04 | 51.15 | 25.84 |
10−4 | 169.23 | 7.77 | 50.53 | 30.36 |
10−3 | 187.15 | 7.70 | 50.36 | 33.72 |
10−2 | 193.28 | 8.15 | 51.39 | 33.85 |
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Liu, L.; Ouyang, J.; Yang, W.; Wang, S. Strain Rate Effects on Characteristic Stresses and Dynamic Strength Criterion in Granite Under Triaxial Quasi-Static Compression. Appl. Sci. 2025, 15, 6214. https://doi.org/10.3390/app15116214
Liu L, Ouyang J, Yang W, Wang S. Strain Rate Effects on Characteristic Stresses and Dynamic Strength Criterion in Granite Under Triaxial Quasi-Static Compression. Applied Sciences. 2025; 15(11):6214. https://doi.org/10.3390/app15116214
Chicago/Turabian StyleLiu, Lu, Jinhui Ouyang, Wencheng Yang, and Sijing Wang. 2025. "Strain Rate Effects on Characteristic Stresses and Dynamic Strength Criterion in Granite Under Triaxial Quasi-Static Compression" Applied Sciences 15, no. 11: 6214. https://doi.org/10.3390/app15116214
APA StyleLiu, L., Ouyang, J., Yang, W., & Wang, S. (2025). Strain Rate Effects on Characteristic Stresses and Dynamic Strength Criterion in Granite Under Triaxial Quasi-Static Compression. Applied Sciences, 15(11), 6214. https://doi.org/10.3390/app15116214