An Empirical Dilatancy Model for Coarse-Grained Soil under the Influence of Freeze–Thaw Cycles
Abstract
:1. Introduction
2. Development of an Empirical Model for CGS under Different FTCs
3. Results and Discussion
3.1. Static Freeze–Thaw Triaxial Test
3.2. An Empirical Dilatancy Model for CGS Considering FTCs
3.3. Validation of the Proposed Equation with the Literature
4. Conclusions
- (1)
- An empirical dilatancy model of CGS considering FTCs was proposed to represent the dilatancy of CGS. The relationship between the stress ratio and the dilatancy ratio can be well-captured by a second-order polynomial fitting. The values of the empirical constants a, b and c introduced in this model depend on the FTCs and σ3.
- (2)
- The best fit a and c values increase in the form of an exponential function with increasing σ3, while b values exhibit the opposite trend. On the other hand, the changing law of the a and b values increase with increasing FTCs following a form of an exponential function. Meanwhile, c values exhibit the opposite trend. It is interesting to note that the a, b, and c values vary between −0.37 and −4.53, 1.82 and 11.03, −4.32 and 1.41, respectively.
- (3)
- The prediction performance of the proposed model was verified using experimental data, and the validity and applicability of the proposed model was validated. The minimum value of the biggest determination coefficient R2 is 0.816 except for sandy soil under frozen state, which show that the proposed non-linear stress-dilatancy equation capture the test data well for the FTC conditions.
- (4)
- Further research is needed to address the limitations in the present study; for instance, certain aspects related to stress-induced anisotropy, the effects of creep, long-term cyclic loading and the influence of particle breakage will need to be investigated in the future as an extension of the proposed model.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Confining Pressure, σ3 (kPa) | FTC, NFT (−) | a | b | c | R2 |
---|---|---|---|---|---|
30 | 1 | −0.5822 | 1.8480 | 1.1303 | 0.825 |
3 | −1.3870 | 3.9102 | −0.2301 | 0.808 | |
6 | −2.4030 | 6.1883 | −1.5292 | 0.869 | |
10 | −4.5342 | 11.0304 | −4.3194 | 0.909 | |
60 | 1 | −0.3523 | 1.3240 | 1.2973 | 0.856 |
3 | −0.6427 | 1.8171 | 1.0671 | 0.543 | |
6 | −2.0180 | 4.8403 | −0.6425 | 0.823 | |
10 | −3.3690 | 7.6584 | −2.1612 | 0.845 | |
90 | 1 | −0.2907 | 1.1040 | 1.4135 | 0.539 |
3 | −0.3732 | 1.2260 | 1.3086 | 0.875 | |
6 | −1.0870 | 2.6253 | 0.5784 | 0.786 | |
10 | −2.4421 | 5.3794 | −0.8606 | 0.899 |
Fitting Equations | Regression Coefficients | Values |
---|---|---|
−3.2310 | ||
−0.0122 | ||
8.5480 | ||
−0.0132 | ||
8.0590 | ||
0.0031 | ||
0.2898 | ||
0.2024 | ||
0.3517 | ||
0.1745 | ||
1.2390 | ||
−0.0451 |
Source of Experimental Data | Material | FTC | Confining Pressure, σ3 (kPa) | R2 | |||
---|---|---|---|---|---|---|---|
Liu et al. [16] | Tailing soil | NFT = 1 | 100 | −2.892 | 4.440 | 0.324 | 0.816 |
Ishikawa and Miura [17] | Volcanic coarse-grained soil | NFT = 1 | 49 | −4.017 | 6.409 | −0.998 | 0.889 |
He et al. [18] | Sandy soil | Frozen | 1000 | −5.514 | 11.710 | −4.246 | 0.633 |
Ling et al. [14] | Coarse-grained soil | NFT = 1 | 60 | −3.408 | 7.797 | −2.339 | 0.845 |
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Ye, Y.; Cai, D.; Tian, S.; Yan, H.; Ling, X.; Tang, L.; Wu, Y. An Empirical Dilatancy Model for Coarse-Grained Soil under the Influence of Freeze–Thaw Cycles. Materials 2022, 15, 3167. https://doi.org/10.3390/ma15093167
Ye Y, Cai D, Tian S, Yan H, Ling X, Tang L, Wu Y. An Empirical Dilatancy Model for Coarse-Grained Soil under the Influence of Freeze–Thaw Cycles. Materials. 2022; 15(9):3167. https://doi.org/10.3390/ma15093167
Chicago/Turabian StyleYe, Yangsheng, Degou Cai, Shuang Tian, Hongye Yan, Xianzhang Ling, Liang Tang, and Yike Wu. 2022. "An Empirical Dilatancy Model for Coarse-Grained Soil under the Influence of Freeze–Thaw Cycles" Materials 15, no. 9: 3167. https://doi.org/10.3390/ma15093167