Investigation of an Empirical Creep Constitutive Model of Changsha Red Loam
Abstract
:1. Introduction
2. Consolidation Creep Test of Changsha Red Loam
2.1. Test Sample
2.2. Test Instrument
2.3. Testing Program
2.4. Experimental Results and Analysis
3. Empirical Creep Model Theory
4. Establishment of Empirical Creep Constitutive Model
- (1)
- Strain–time relationship
- (2)
- Stress–strain relationship
- (3)
- Stress–strain–time relationship
5. Model Verification and Application
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Soil Layer | Modulus of Compression Es/MPa | Natural Gravity γ/(kN/m3) | Soil Thickness /m | Internal Friction Angle φ/° | Cohesion c/kPa | Poisson’s Ratio |
---|---|---|---|---|---|---|
No. Ⅲ Sandy soil | 10.93 | 21.1 | 5.90–11.20 | 35 | 30 | 0.32 |
No. Ⅳ Silty clay | 8.60 | 20.3 | 10.70–14.78 | 20 | 30 | 0.30 |
Soil Type | Number | Stress σ/kPa | Loading Method |
---|---|---|---|
Sandy soil (A) | A1 | 100 | Independent loading |
A2 | 200 | ||
A3 | 300 | ||
A4 | 400 | ||
A5 | 500 | ||
A6 | 600 | ||
A7 | 700 | ||
Silty clay (B) | B1 | 100 | |
B2 | 200 | ||
B3 | 300 | ||
B4 | 400 | ||
B5 | 500 | ||
B6 | 600 | ||
B7 | 700 |
Stress (kPa) | 100 | 200 | 300 | 400 | 500 | 600 | 700 | ||
---|---|---|---|---|---|---|---|---|---|
Deformation (mm) | |||||||||
Time (min) | |||||||||
10 | 0.172 | 0.296 | 0.378 | 0.570 | 0.708 | 0.830 | 0.982 | ||
30 | 0.250 | 0.460 | 0.610 | 0.822 | 1.020 | 1.292 | 1.494 | ||
60 | 0.302 | 0.538 | 0.730 | 0.916 | 1.116 | 1.440 | 1.628 | ||
120 | 0.314 | 0.548 | 0.742 | 0.928 | 1.128 | 1.454 | 1.646 | ||
180 | 0.326 | 0.556 | 0.754 | 0.942 | 1.140 | 1.466 | 1.664 | ||
240 | 0.334 | 0.564 | 0.764 | 0.952 | 1.148 | 1.474 | 1.680 | ||
300 | 0.344 | 0.574 | 0.776 | 0.964 | 1.174 | 1.484 | 1.694 | ||
420 | 0.358 | 0.582 | 0.786 | 0.974 | 1.182 | 1.492 | 1.708 | ||
540 | 0.364 | 0.590 | 0.796 | 0.982 | 1.190 | 1.504 | 1.720 | ||
720 | 0.372 | 0.596 | 0.804 | 0.988 | 1.196 | 1.512 | 1.728 | ||
900 | 0.378 | 0.604 | 0.810 | 0.994 | 1.200 | 1.518 | 1.734 | ||
1440 | 0.386 | 0.610 | 0.814 | 0.998 | 1.204 | 1.524 | 1.738 | ||
2160 | 0.394 | 0.616 | 0.820 | 1.004 | 1.204 | 1.528 | 1.740 | ||
2880 | 0.402 | 0.622 | 0.826 | 1.010 | 1.206 | 1.530 | 1.742 | ||
3600 | 0.406 | 0.626 | 0.834 | 1.016 | 1.210 | 1.534 | 1.742 | ||
4320 | 0.410 | 0.632 | 0.840 | 1.022 | 1.214 | 1.538 | 1.746 | ||
5040 | 0.414 | 0.636 | 0.844 | 1.026 | 1.220 | 1.548 | 1.750 | ||
5760 | 0.422 | 0.640 | 0.848 | 1.030 | 1.226 | 1.554 | 1.758 | ||
6480 | 0.426 | 0.642 | 0.850 | 1.034 | 1.232 | 1.558 | 1.764 | ||
7200 | 0.428 | 0.644 | 0.854 | 1.036 | 1.236 | 1.564 | 1.772 | ||
7920 | 0.432 | 0.644 | 0.856 | 1.038 | 1.244 | 1.568 | 1.780 | ||
8640 | 0.434 | 0.646 | 0.862 | 1.042 | 1.252 | 1.574 | 1.788 | ||
9360 | 0.436 | 0.646 | 0.866 | 1.046 | 1.260 | 1.580 | 1.798 | ||
10,080 | 0.440 | 0.650 | 0.868 | 1.052 | 1.266 | 1.590 | 1.818 | ||
10,800 | 0.436 | 0.648 | 0.872 | 1.058 | 1.276 | 1.604 | 1.842 | ||
11,520 | 0.444 | 0.650 | 0.878 | 1.068 | 1.296 | 1.622 | 1.892 |
Number | Stress σ/kPa | Total Strain ε/% | Primary Consolidation Strain εz/% | Creep Strain εc/% |
---|---|---|---|---|
A1 | 100 | 2.22 | 1.51 | 0.61 |
A2 | 200 | 3.25 | 2.69 | 0.56 |
A3 | 300 | 4.39 | 3.65 | 0.74 |
A4 | 400 | 5.34 | 4.58 | 0.76 |
A5 | 500 | 6.48 | 5.58 | 0.90 |
A6 | 600 | 8.11 | 6.93 | 1.18 |
A7 | 700 | 9.46 | 8.14 | 1.32 |
Stress (kPa) | 100 | 200 | 300 | 400 | 500 | 600 | 700 | ||
---|---|---|---|---|---|---|---|---|---|
Deformation (mm) | |||||||||
Time (min) | |||||||||
10 | 0.206 | 0.332 | 0.494 | 0.622 | 0.804 | 0.934 | 1.038 | ||
30 | 0.326 | 0.464 | 0.678 | 0.854 | 1.136 | 1.384 | 1.588 | ||
60 | 0.382 | 0.562 | 0.788 | 0.976 | 1.226 | 1.494 | 1.712 | ||
120 | 0.402 | 0.594 | 0.822 | 0.982 | 1.294 | 1.544 | 1.758 | ||
180 | 0.422 | 0.624 | 0.850 | 1.004 | 1.318 | 1.578 | 1.780 | ||
240 | 0.434 | 0.676 | 0.872 | 1.020 | 1.336 | 1.608 | 1.792 | ||
300 | 0.448 | 0.682 | 0.890 | 1.034 | 1.352 | 1.630 | 1.804 | ||
420 | 0.458 | 0.690 | 0.906 | 1.046 | 1.362 | 1.648 | 1.818 | ||
540 | 0.466 | 0.698 | 0.918 | 1.056 | 1.372 | 1.658 | 1.826 | ||
720 | 0.474 | 0.704 | 0.930 | 1.072 | 1.380 | 1.666 | 1.836 | ||
900 | 0.486 | 0.710 | 0.938 | 1.086 | 1.386 | 1.672 | 1.848 | ||
1440 | 0.492 | 0.716 | 0.944 | 1.102 | 1.390 | 1.676 | 1.856 | ||
2160 | 0.500 | 0.720 | 0.950 | 1.116 | 1.394 | 1.680 | 1.866 | ||
2880 | 0.508 | 0.722 | 0.954 | 1.128 | 1.402 | 1.686 | 1.872 | ||
3600 | 0.518 | 0.728 | 0.960 | 1.144 | 1.408 | 1.692 | 1.880 | ||
4320 | 0.522 | 0.736 | 0.966 | 1.150 | 1.414 | 1.698 | 1.890 | ||
5040 | 0.528 | 0.740 | 0.972 | 1.158 | 1.420 | 1.700 | 1.898 | ||
5760 | 0.532 | 0.746 | 0.976 | 1.168 | 1.422 | 1.704 | 1.906 | ||
6480 | 0.536 | 0.750 | 0.980 | 1.176 | 1.426 | 1.710 | 1.912 | ||
7200 | 0.544 | 0.752 | 0.986 | 1.184 | 1.430 | 1.714 | 1.918 | ||
7920 | 0.548 | 0.754 | 0.990 | 1.192 | 1.432 | 1.716 | 1.924 | ||
8640 | 0.544 | 0.754 | 0.994 | 1.200 | 1.432 | 1.722 | 1.930 | ||
9360 | 0.548 | 0.758 | 0.996 | 1.206 | 1.434 | 1.730 | 1.936 | ||
10,080 | 0.550 | 0.762 | 1.002 | 1.216 | 1.456 | 1.746 | 1.942 | ||
10,800 | 0.552 | 0.764 | 1.006 | 1.228 | 1.480 | 1.766 | 1.974 | ||
11,520 | 0.558 | 0.766 | 1.014 | 1.234 | 1.514 | 1.790 | 2.028 |
Number | Stress σ/kPa | Total Strain ε/% | Primary Consolidation Strain εz/% | Creep Strain εc/% |
---|---|---|---|---|
B1 | 100 | 2.79 | 1.91 | 0.88 |
B2 | 200 | 3.83 | 2.81 | 1.02 |
B3 | 300 | 5.07 | 3.94 | 1.13 |
B4 | 400 | 6.17 | 4.88 | 1.29 |
B5 | 500 | 7.57 | 6.13 | 1.44 |
B6 | 600 | 8.95 | 7.47 | 1.48 |
B7 | 700 | 10.14 | 8.56 | 1.58 |
Press σ/kPa | Fitting Parameters | Correlation Index |
---|---|---|
100 | 0.0709 | 0.9951 |
200 | 0.0367 | 0.9951 |
400 | 0.0258 | 0.9895 |
500 | 0.0226 | 0.9557 |
700 | 0.0193 | 0.9158 |
Time t/min | Fitting Parameters | Correlation Index | Time t/min | Fitting Parameters | Correlation Index |
---|---|---|---|---|---|
60 | 0.8430 | 0.9980 | 3600 | 0.7286 | 0.9949 |
120 | 0.8288 | 0.9977 | 4320 | 0.7244 | 0.9950 |
180 | 0.8162 | 0.9974 | 5040 | 0.7209 | 0.9949 |
240 | 0.8082 | 0.9971 | 5760 | 0.7139 | 0.9943 |
300 | 0.7999 | 0.9972 | 6480 | 0.7114 | 0.9941 |
420 | 0.7842 | 0.9965 | 7200 | 0.7111 | 0.9939 |
540 | 0.7786 | 0.9963 | 7920 | 0.7098 | 0.9935 |
720 | 0.7699 | 0.9960 | 8640 | 0.7103 | 0.9935 |
900 | 0.7626 | 0.9959 | 9360 | 0.7117 | 0.9933 |
1440 | 0.7530 | 0.9955 | 10,080 | 0.7117 | 0.9928 |
2160 | 0.7427 | 0.9951 | 10,800 | 0.7230 | 0.9929 |
2880 | 0.7330 | 0.9948 | 11,520 | 0.7272 | 0.9912 |
Soil Layer | k | m | n |
---|---|---|---|
No. Ⅲ Sandy soil | 1.5100 | 0.0351 | 0.7510 |
Press σ/kPa | Fitting Parameters | Correlation Index |
---|---|---|
100 | 0.0971 | 0.9641 |
300 | 0.0666 | 0.9386 |
500 | 0.0493 | 0.9083 |
700 | 0.0480 | 0.8825 |
Time t/min | Fitting Parameters | Correlation Index | Time t/min | Fitting Parameters | Correlation Index |
---|---|---|---|---|---|
60 | 0.7820 | 0.9829 | 3600 | 0.6719 | 0.9808 |
120 | 0.7692 | 0.9806 | 4320 | 0.6693 | 0.9811 |
180 | 0.7491 | 0.9805 | 5040 | 0.6654 | 0.9809 |
240 | 0.7294 | 0.9826 | 5760 | 0.6627 | 0.9813 |
300 | 0.7201 | 0.9816 | 6480 | 0.6606 | 0.9813 |
420 | 0.7136 | 0.9811 | 7200 | 0.6555 | 0.9801 |
540 | 0.7073 | 0.9811 | 7920 | 0.6533 | 0.9799 |
720 | 0.7019 | 0.9819 | 8640 | 0.6583 | 0.9816 |
900 | 0.6930 | 0.9811 | 9360 | 0.6563 | 0.9810 |
1440 | 0.6887 | 0.9822 | 10,080 | 0.6587 | 0.9819 |
2160 | 0.6834 | 0.9820 | 10,800 | 0.6659 | 0.9811 |
2880 | 0.6789 | 0.9813 | 11,520 | 0.6736 | 0.9780 |
Soil Layer | k | m | n |
---|---|---|---|
No. Ⅳ Silty clay | 1.9100 | 0.0653 | 0.6903 |
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Long, L.; Li, Z.; Li, Y. Investigation of an Empirical Creep Constitutive Model of Changsha Red Loam. Buildings 2023, 13, 1064. https://doi.org/10.3390/buildings13041064
Long L, Li Z, Li Y. Investigation of an Empirical Creep Constitutive Model of Changsha Red Loam. Buildings. 2023; 13(4):1064. https://doi.org/10.3390/buildings13041064
Chicago/Turabian StyleLong, Lin, Zhida Li, and Yunyu Li. 2023. "Investigation of an Empirical Creep Constitutive Model of Changsha Red Loam" Buildings 13, no. 4: 1064. https://doi.org/10.3390/buildings13041064