Experimental Study on the Mechanical Characteristics of Saturated Granite under Conventional Triaxial Loading and Unloading Tests
Abstract
:1. Introduction
Rock Type | Stress Path | σ3 (MPa) | Unloading Rate vu (MPa/s) | Reference |
---|---|---|---|---|
Sandstone | 1. Increase σ1, unload σ3 | 4–19 | 0.02–0.14 | [47] |
4–10 | 0.05 | [48] | ||
5–30 | 0.005 | [49] | ||
15–30 | 0.05, 0.1, 0.2 | [50] | ||
15–45 | 2 | [51] | ||
2. Keep σ1, unload σ3 | 15–30 | 0.0003–0.1667 | [52] | |
1. Increase σ1, unload σ3 2. Keep σ1, unload σ3 | 10–30 | 0.1, 0.5 | [53] | |
3. Unload σ1, σ3 | 10–30 | 0.0008 | [33] | |
Marble | 1. Increase σ1, unload σ3 | 40 | 0.05 | [37] |
2. Keep σ1, unload σ3 | 20 | 0.01–0.2 | [40,42] | |
10–60 | 0.01–1 | [54] | ||
3. Unload σ1, σ3 | 20–60 | 0.05 | [55] | |
20–40 | 0.1–10 | [11] | ||
1. Increase σ1, unload σ3 3. Unload σ1, σ3 | 20–40 | 0.26-1.28 | [26] | |
Granite | 1. Increase σ1, unload σ3 | 5–30 | 0.0017–0.0333 | [56] |
30–60 | 0.05 | [57] | ||
2. Keep σ1, unload σ3 | 10 | 0.005–0.0115 | [19] | |
10–30 | 0.1 | [17,58] | ||
1. Increase σ1, unload σ3 3. Unload σ1, σ3 | 10–60 | 0.2 | [45] | |
1. Increase σ1, unload σ3 2. Keep σ1, unload σ3 3. Unload σ1, σ3 | 10–30 | - | [43] | |
Mudstone | 1. Increase σ1, unload σ3 | 6-15 | 0.05, 0.1, 0.2 | [50] |
10–50 | 0.005–0.5 | [59] | ||
Limestones | 2. Keep σ1, unload σ3 | 15 | 0.0217 | [39] |
Shale | 1. Increase σ1, unload σ3 | 20–60 | 0.4–1.0 | [27] |
2. Keep σ1, unload σ3 | 20–60 | 0.4 | [27] | |
Basalt | 1. Increase σ1, unload σ3 | 3–12 | 0.008 | [60] |
3. Unload σ1, σ3 | 3–12 | 0.008 | [60] | |
Coal | 1. Increase σ1, unload σ3 | 30 | 0.001–0.005 | [34] |
4–8 | 0.012–0.024 | [35] | ||
4–10 | 0.02–0.14 | [47] | ||
Dacite | 2. Keep σ1, unload σ3 | 5–15 | 0.0083 | [44] |
Rock salt | 2. Keep σ1, unload σ3 | 15–25 | 0.005 | [10] |
23 | 0.001–0.5 | [31] | ||
Mudstone | 2. Keep σ1, unload σ3 | 8–20 | 0.05 | [61] |
3. Unload σ1, σ3 | 8–20 | 0.05 | [61] | |
Rock-Like | 2. Keep σ1, unload σ3 | 4–8 | 0.0083–0.0333 | [30] |
2. Materials and Methods
2.1. Specimen Preparation
2.2. Test Scheme
3. Results and Discussion
3.1. Mechanical Characteristics
3.1.1. Stress–Strain Curve
3.1.2. Strength Characteristics
3.1.3. Strain Characteristics
3.2. Energy Evolution Characteristics
3.2.1. Evolution of Strain Energy in the Triaxial Compression Test
3.2.2. Evolution of Strain Energy in a Triaxial Compression Unloading Confining Pressure Test
3.3. Rock Failure Characteristics and Destruction Mechanism
4. Conclusions
- (1)
- In the conventional triaxial unloading test, the circumferential deformation is the leading cause of failure, and its strain is greater than that of conventional triaxial loading. Under the same axial loading rate, the faster the unloading rate and axial loading rate, the smaller the σ3f and σ1f at the time of failure, and the failure point is outside the envelope of conventional triaxial compression tests. While under the same unloading rate, a faster axial loading corresponds to a larger σ3f and σ1f.
- (2)
- The variation of circumferential energy ΔUc decreases with the unloading rate, and ΔUd, ΔUa, ΔU and ΔUe showed inverted V-shaped and V-shaped va = 0.06 and 0.6 mm/min, respectively. When va = 6 mm/min, except for a slight increase in ΔUa, the rest of the variation of energy decreases with the increase of the unloading rate. The variation of dissipation energy changes from being determined by the unloading rate and the axial loading rate together to being determined by the axial loading rate with the axial loading rate increasing.
- (3)
- The failure modes of the specimens were mainly controlled by the axial stress and showed a single shear crack before va = 0.6 mm/min, while it is influenced by both axial and circumferential stress after the axial loading rate of not less than 6 mm/min, and the failure surface is a conjugate shear failure and tensile strain failure.
- (4)
- In the triaxial unloading test, the specimens were in the high expansion process most of the time, and the dilatancy angle of the specimens showed an overall upward trend except for vu = 10 MPa/s, va = 0.6 mm/min and 6 mm/min.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Test Scheme | Specimen Number | Initial Confining Pressure (MPa) | Axial Loading Rate | Unloading Rate of σ3 |
---|---|---|---|---|
Group-I | TC-0 | 0 | 0.12 mm/min | - |
TC-10 | 10 | - | ||
TC-30 | 30 | - | ||
TC-50 | 50 | - | ||
Group-II | G-0.06-X * | 50 | 0.06 mm/min | 0.1 MPa/s, 1 MPa/s, 5 MPa/s, 10 MPa/s |
G-0.6-X | 50 | 0.6 mm/min | ||
G-6-X | 50 | 6 mm/min |
Test Scheme | Specimen No. | Dry Density (kg/m3) | Saturated Density (kg/m3) | σ30 (MPa) | σ3f (MPa) | σ1f (MPa) | E (GPa) | ν |
---|---|---|---|---|---|---|---|---|
Group I | TC-0 | 2637.49 | 2644.55 | 0 | 0 | 104.93 | 43.04 | 0.10 |
TC-10 | 2631.32 | 2637.24 | 10 | 10 | 202.99 | 42.67 | 0.10 | |
TC-30 | 2635.72 | 2641.16 | 30 | 30 | 361.84 | 53.96 | 0.11 | |
TC-50 | 2635.67 | 2639.43 | 50 | 50 | 480.32 | 50.57 | 0.12 | |
Group II | G-0.06-0.1 | 2635.13 | 2638.36 | 50 | 34.42 | 390.08 | 51.4 | 0.10 |
G-0.06-1 | 2637.42 | 2641.45 | 50 | 25.53 | 358.82 | 58.04 | 0.28 | |
G-0.06-5 | 2635.50 | 2641.38 | 50 | 21.06 | 361.00 | 51.71 | 0.11 | |
G-0.06-10 | 2638.97 | 2643.01 | 50 | 18.77 | 354.14 | 62.64 | 0.18 | |
G-0.6-0.1 | 2632.97 | 2637.00 | 50 | 44.48 | 470.63 | 58.39 | 0.17 | |
G-0.6-1 | 2651.75 | 2655.78 | 50 | 28.83 | 398.89 | 59.08 | 0.23 | |
G-0.6-5 | 2638.89 | 2642.93 | 50 | 21.81 | 378.21 | 59.03 | 0.21 | |
G-0.6-10 | 2636.85 | 2640.88 | 50 | 23.47 | 384.67 | 56.05 | 0.20 | |
G-6-0.1 | 2632.28 | 2636.32 | 50 | 49.31 | 508.61 | 60.45 | 0.24 | |
G-6-1 | 2602.96 | 2606.98 | 50 | 43.97 | 465.05 | 56.32 | 0.18 | |
G-6-5 | 2620.01 | 2624.07 | 50 | 32.07 | 400.16 | 62.90 | 0.18 | |
G-6-10 | 2592.90 | 2596.95 | 50 | 27.74 | 412.31 | 53.09 | 0.26 |
Specimen No. | σ30 (MPa) | Unloading Point | Failure Point | Δεvf (×10−3) | ||||
---|---|---|---|---|---|---|---|---|
εa0 (×10−3) | εc0 (×10−3) | εv0 (×10−3) | εaf (×10−3) | εcf (×10−3) | εvf (×10−3) | |||
TC-0 | 0 | 2.19 | −0.14 | 1.91 | 2.92 | −2.43 | −1.94 | −3.85 |
TC-10 | 10 | 3.55 | −0.49 | 2.57 | 4.53 | −2.81 | −1.09 | −3.66 |
TC-30 | 30 | 5.17 | −0.97 | 3.23 | 7.38 | −3.70 | −0.02 | −3.25 |
TC-50 | 50 | 8.16 | −1.84 | 4.48 | 10.24 | −3.91 | 2.42 | −2.06 |
G-0.06-0.1 | 50 | 7.14 | −1.22 | 4.70 | 9.06 | −4.55 | −0.05 | −4.75 |
G-0.06-1 | 6.26 | −2.30 | 1.67 | 6.89 | −9.75 | −12.60 | −14.27 | |
G-0.06-5 | 7.07 | −1.28 | 4.51 | 9.88 | −5.49 | −1.09 | −5.60 | |
G-0.06-10 | 6.12 | −1.24 | 3.64 | 6.67 | −5.66 | −4.65 | −8.29 | |
G-0.6-0.1 | 50 | 6.55 | −2.24 | 2.07 | 9.90 | −8.39 | −6.88 | −8.95 |
G-0.6-1 | 6.56 | −2.07 | 2.42 | 8.43 | −9.84 | −11.25 | −13.67 | |
G-0.6-5 | 6.53 | −2.04 | 2.46 | 7.94 | −7.16 | −6.37 | −8.83 | |
G-0.6-10 | 6.78 | −3.86 | −0.94 | 7.34 | −6.44 | −5.53 | −4.59 | |
G-6-0.1 | 50 | 6.46 | −1.99 | 2.49 | 9.85 | −7.35 | −4.84 | −7.33 |
G-6-1 | 6.74 | −1.95 | 2.85 | 10.59 | −10.05 | −9.50 | −12.35 | |
G-6-5 | 6.19 | −2.25 | 1.68 | 7.20 | −11.92 | −16.63 | −18.31 | |
G-6-10 | 7.23 | −1.43 | 4.38 | 9.15 | −4.12 | 0.91 | −3.47 |
Specimen No. | σ30 (MPa) | Unloading Point | Failure Point | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Ua0 | Uc0 | U0 | Ue0 | Ud0 | Uaf | Ucf | Uf | Uef | Udf | ||
TC-0 | 0 | - | - | - | - | - | 0.16 | - | - | 0.13 | 0.03 |
TC-10 | 10 | - | - | - | - | - | 0.91 | 0.03 | 0.94 | 0.55 | 0.39 |
TC-30 | 30 | - | - | - | - | - | 2.55 | 0.14 | 2.70 | 1.74 | 0.95 |
TC-50 | 50 | - | - | - | - | - | 4.88 | 0.24 | 5.11 | 3.35 | 1.77 |
G-0.06-0.1 | 50 | 1.66 | −0.06 | 1.60 | 1.32 | 0.28 | 2.44 | −0.19 | 2.25 | 1.47 | 0.79 |
G-0.06-1 | 1.43 | −0.11 | 1.32 | 1.02 | 0.29 | 1.68 | −0.34 | 1.34 | 0.73 | 0.60 | |
G-0.06-5 | 1.63 | −0.06 | 1.56 | 1.30 | 0.26 | 2.69 | −0.17 | 2.51 | 1.56 | 0.96 | |
G-0.06-10 | 1.46 | −0.06 | 1.39 | 1.11 | 0.28 | 1.67 | −0.16 | 1.50 | 0.97 | 0.53 | |
G-0.6-0.1 | 50 | 1.53 | −0.11 | 1.42 | 1.08 | 0.34 | 3.02 | −0.40 | 2.62 | 1.59 | 1.53 |
G-0.6-1 | 1.51 | −0.10 | 1.40 | 1.11 | 0.30 | 2.27 | −0.37 | 1.90 | 1.11 | 1.51 | |
G-0.6-5 | 1.53 | −0.10 | 1.43 | 1.10 | 0.32 | 2.08 | −0.24 | 1.84 | 1.19 | 1.53 | |
G-0.6-10 | 1.57 | −0.19 | 1.37 | 0.96 | 0.41 | 1.79 | −0.26 | 1.52 | 1.11 | 1.57 | |
G-6-0.1 | 50 | 1.51 | −0.10 | 1.41 | −0.34 | 1.74 | 3.07 | −0.36 | 2.71 | −1.34 | 1.51 |
G-6-1 | 1.57 | −0.10 | 1.47 | 1.16 | 0.31 | 3.31 | −0.46 | 2.85 | 1.58 | 1.57 | |
G-6-5 | 1.44 | −0.11 | 1.33 | 1.01 | 0.32 | 1.90 | −0.45 | 1.45 | 0.67 | 1.44 | |
G-6-10 | 1.69 | −0.07 | 1.62 | 1.32 | 0.30 | 2.49 | −0.16 | 2.33 | 1.67 | 1.69 |
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Liu, Z.; Yi, W. Experimental Study on the Mechanical Characteristics of Saturated Granite under Conventional Triaxial Loading and Unloading Tests. Sustainability 2022, 14, 5445. https://doi.org/10.3390/su14095445
Liu Z, Yi W. Experimental Study on the Mechanical Characteristics of Saturated Granite under Conventional Triaxial Loading and Unloading Tests. Sustainability. 2022; 14(9):5445. https://doi.org/10.3390/su14095445
Chicago/Turabian StyleLiu, Zelin, and Wei Yi. 2022. "Experimental Study on the Mechanical Characteristics of Saturated Granite under Conventional Triaxial Loading and Unloading Tests" Sustainability 14, no. 9: 5445. https://doi.org/10.3390/su14095445