Intelligent Model for Dynamic Shear Modulus and Damping Ratio of Undisturbed Marine Clay Based on Back-Propagation Neural Network
Abstract
:1. Introduction
2. Experimental Measurements
2.1. Materials
2.2. Test Apparatus and Procedure
2.3. Experimental Results
3. Intelligent Model
3.1. Model Framework
3.2. Model Settings and Procedures
3.3. Model Performance
4. Evaluation and Discussion
4.1. Evaluation of Prediction Results
4.2. Comparison with Function Models
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
References
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Function Forms | Data from | Soil Type |
---|---|---|
, where Gmax is the maximum shear modulus; γr is the reference strain; τmax is the maximum shear stress. | Hardin and Drnevich [19] | Cohesive soil and sand |
, where Dmax is the maximum damping ratio. | ||
, | Ishibashi and Zh-ang [20] | Sandy soil |
. | ||
, where n(PI) is the function related to the plasticity index of soil. | Plastic soil (Silt and Clay) | |
. | ||
, where a, b, and c are the curvature coefficient. | Borden et al. [21] | Piedmont residual soil (MH, ML, SM-ML, SM) |
. | ||
, where α is the curvature coefficient. | Stokoe et al. [22] Darendeli [23] | Undisturbed soil (CH, CL, CL-ML, MH, ML, SC, SM, SC-SM, SP, SP-SM, SW-SC, SW-SM) |
, where d is the scaling coefficient, Dmin is the small-strain damping ratio, and DMasing is the modeled masing damping. | Darendeli [23] | |
, where γr is the reference strain corresponding to the γ value when G/Gmax = 0.5, α is the curvature parameter, γr1 is the reference strain at a mean effective confining stress σm of 100 kPa, Pa is the reference stress at 100 kPa, and k is a stress-correction exponent. | Zhang et al. [24] | Quaternary soil Tertiary and older soil Residual/saprolite soil |
Torsional shear test, , where Dmin1 is the small-strain damping at σm of 100 kPa. |
Sample | Soil Depth H/m | Mean Effective Confining Pressure σm/kPa | Specific Gravity Gs | Water Content w/% | Density ρ/g·cm−3 | Plasticity Index PI |
---|---|---|---|---|---|---|
BH 1 | 6.3–6.5 | 43 | 2.67 | 40.72 | 1.9 | 15.99 |
BH 2 | 8.3–8.5 | 56 | 2.69 | 36.45 | 1.9 | 17.15 |
BH 3 | 10.8–11.0 | 73 | 2.70 | 38.95 | 1.95 | 16.88 |
BH 4 | 15.8–16.0 | 106 | 2.68 | 37.99 | 1.92 | 16.23 |
BH 5 | 23.5–23.7 | 157 | 2.67 | 37.87 | 1.97 | 16.98 |
BH 6 | 25.5–25.7 | 171 | 2.67 | 35.53 | 1.96 | 16.95 |
BH 7 | 29.8–30.0 | 199 | 2.67 | 38.96 | 1.91 | 15.00 |
BH 8 | 30.0–30.2 | 201 | 2.71 | 36.17 | 1.97 | 15.06 |
BH 9 | 31.8–32.0 | 213 | 2.67 | 39.04 | 1.92 | 17.12 |
BH 10 | 33.8–34.0 | 226 | 2.68 | 36.67 | 1.93 | 12.64 |
BH 11 | 35.2–35.4 | 235 | 2.69 | 36.82 | 1.93 | 17.23 |
BH 12 | 40.3–40.5 | 269 | 2.68 | 30.93 | 1.9 | 15.27 |
BH 13 | 43.3–43.5 | 289 | 2.70 | 38.17 | 1.94 | 15.95 |
BH 14 | 46.3–46.5 | 309 | 2.68 | 36.08 | 1.93 | 15.34 |
BH 15 | 61.8–62.0 | 413 | 2.68 | 33.74 | 2.04 | 13.55 |
BH 16 | 67.8–68.0 | 453 | 2.68 | 31.10 | 1.99 | 15.57 |
BH 17 | 69.8–70.0 | 466 | 2.67 | 30.84 | 2.01 | 13.14 |
HZ 1 | 18.3–18.5 | 123 | 2.68 | 15.52 | 1.81 | 15.52 |
HZ 2 | 23.3–25.5 | 156 | 2.67 | 15.64 | 1.94 | 15.64 |
HZ 3 | 28.3–28.5 | 190 | 2.70 | 14.37 | 1.97 | 14.37 |
HZ 4 | 33.3–33.5 | 233 | 2.67 | 15.07 | 2.06 | 15.07 |
HZ 5 | 40.8–41.0 | 273 | 2.71 | 16.57 | 2.07 | 16.57 |
HZ 6 | 48.3–48.5 | 323 | 2.70 | 14.76 | 2.07 | 14.76 |
HZ 7 | 53.3–53.5 | 356 | 2.69 | 13.35 | 2.04 | 13.35 |
HZ 8 | 58.3–58.5 | 390 | 2.70 | 14.76 | 2.06 | 14.76 |
HZ 9 | 63.3–63.5 | 423 | 2.70 | 15.97 | 2.06 | 15.97 |
HZ 10 | 68.3–68.5 | 456 | 2.69 | 14.08 | 2.03 | 14.08 |
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Wu, Q.; Wang, Z.; Qin, Y.; Yang, W. Intelligent Model for Dynamic Shear Modulus and Damping Ratio of Undisturbed Marine Clay Based on Back-Propagation Neural Network. J. Mar. Sci. Eng. 2023, 11, 249. https://doi.org/10.3390/jmse11020249
Wu Q, Wang Z, Qin Y, Yang W. Intelligent Model for Dynamic Shear Modulus and Damping Ratio of Undisturbed Marine Clay Based on Back-Propagation Neural Network. Journal of Marine Science and Engineering. 2023; 11(2):249. https://doi.org/10.3390/jmse11020249
Chicago/Turabian StyleWu, Qi, Zifan Wang, You Qin, and Wenbao Yang. 2023. "Intelligent Model for Dynamic Shear Modulus and Damping Ratio of Undisturbed Marine Clay Based on Back-Propagation Neural Network" Journal of Marine Science and Engineering 11, no. 2: 249. https://doi.org/10.3390/jmse11020249
APA StyleWu, Q., Wang, Z., Qin, Y., & Yang, W. (2023). Intelligent Model for Dynamic Shear Modulus and Damping Ratio of Undisturbed Marine Clay Based on Back-Propagation Neural Network. Journal of Marine Science and Engineering, 11(2), 249. https://doi.org/10.3390/jmse11020249