Softening/Hardening Damage Model and Numerical Implementation of Seabed Silt-Steel Interface in Yellow River Underwater Delta
Abstract
:1. Introduction
2. Softening/Hardening Damage Model
2.1. Assumption
- (1)
- Assuming the soil is isotropic and the structure is a fixed rigid body.
- (2)
- Divide the soil–structure interface into several microelements, assuming that there are only two states: undamaged (0) and damaged (1).
- (3)
- Assuming that all friction and contact on the soil–structure interface (between soil particles, between soil structure) are unevenly and randomly distributed, the shear strength and shear failure at the interface are also unevenly and randomly distributed.
- (4)
- Assuming that the damage process at the soil–structure interface is a continuous process that undergoes an evolution from undamaged to damage, the soil at the interface can be divided into two parts, damaged soil and undamaged soil (Figure 2), and the undamaged soil bears effective stress.
2.2. Model Derivation
2.3. Model Parameters
3. Interface Monotonic Shear Test
3.1. Test Equipment and Plan
3.2. Results and Analysis
3.2.1. Stress-Strain Rule
- (1)
- Normal stress
- (2)
- Roughness
- (3)
- Water content
3.2.2. Interface Shear Strength
- (1)
- Roughness
- (2)
- Water content
3.2.3. Volumetric Deformation Laws
- (1)
- Normal stress
- (2)
- Roughness
- (3)
- Water content
4. Model Validation and Numerical Implementation
4.1. Model Validation
4.2. Numerical Implementation
4.2.1. Subroutine Programming
4.2.2. Subroutine Validation
5. Conclusions
- (1)
- Compared to the strain hardening, shear shrinkage deformation and strain softening, the shear expansion deformation behavior of coarse-grained soil and cohesive soil silt exhibits two characteristics: softening/hardening and shear shrinkage/expansion under different conditions. The maximum shear stress increases with normal stress, roughness, and water content increase. Roughness has a significant impact on cohesion. As roughness increases, the cohesion and internal friction angle increase 1.56 times and by 17.67%, respectively; water content mainly affects the internal friction angle. As the water content increases, the internal friction angle decreases, with a decrease of 30.37%. The cohesion shows a trend of increasing and then decreasing, with an increase of 22.6% and −59.5%, respectively, and reaches its peak near optimal water content.
- (2)
- The proposed shear damage model has fewer parameters and a clear physical meaning. The strength parameters are τmax, G0, G1, γm, τr, and the model parameters are m and n. The softening model, based on the classic rock damage model, can better simulate the stress–strain relationship of the silt–steel interface under high normal stress and low water content. In contrast, the hardening model based on the classic hyperbola model can better simulate the stress–strain relationship under low normal stress and high water content. After using the model parameters obtained from the test results, the theoretical model curve is in good agreement with the shear test curve, which proves that the proposed contact surface damage model is reasonable. However, the model parameters m and n are simultaneously affected by normal stress, roughness and water content, so they cannot be simply corrected by fitting curves. Considering the complexity of factors affecting the soil–structure interface in real environments, the model still needs further optimization and improvement.
- (3)
- The numerical simulation application of the damage model was achieved through the FRIC subroutine, providing a mathematical model basis for subsequent research on the stability analysis of offshore structures considering interface weakening effects.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Group | Roughness R (mm) | Water Content ω (%) | Normal Stress σ (kPa) |
---|---|---|---|
1 | 0.05 | 16 | 100 |
2 | 200 | ||
3 | 300 | ||
4 | 20 | 100 | |
5 | 200 | ||
6 | 300 | ||
7 | 24 | 100 | |
8 | 200 | ||
9 | 300 | ||
10 | 0 | 20 | 100 |
11 | 200 | ||
12 | 300 | ||
13 | 0.025 | 100 | |
14 | 200 | ||
15 | 300 |
Test Conditions | τmax (kPa) | τr (kPa) | γm (mm) | m | n | |||
---|---|---|---|---|---|---|---|---|
Test Value | Theoretical Value | Test Value | Theoretical Value | Test Value | Theoretical Value | |||
Hardening type | ||||||||
σ = 100 kPa R = 0.05 mm ω = 20% | 18.47 | 18.61 | 0.4271 | 4.4132 × 10−3 | ||||
σ = 200 kPa R = 0.05 mm ω = 20% | 33.43 | 33.53 | 0.3175 | 2.2541 × 10−3 | ||||
σ = 100 kPa R = 0.025 mm ω = 20% | 15.92 | 16.53 | 0.5137 | 4.6871 × 10−3 | ||||
σ = 100 kPa R = 0.05 mm ω = 24% | 14.21 | 13.71 | 0.5546 | 5.1247 × 10−3 | ||||
Softening type | ||||||||
σ = 200 kPa R = 0.05 mm ω = 16% | 35.53 | 35.01 | 33.28 | 33.01 | 12.4 | 13.6 | 0.2985 | 2.1187 × 10−3 |
σ = 300 kPa R = 0.05 mm ω = 16% | 50.12 | 50.93 | 46.78 | 47.42 | 15.1 | 15.7 | 0.1782 | 1.7895 × 10−3 |
σ = 300 kPa R = 0.05 mm ω = 20% | 45.08 | 46.61 | 41.14 | 42.33 | 12.6 | 14.3 | 0.2297 | 2.0891 × 10−3 |
σ = 300 kPa R = 0.025 mm ω = 20% | 42.33 | 43.84 | 40.17 | 39.83 | 10.1 | 11.3 | 0.2457 | 2.1879 × 10−3 |
Category | Elastic Modulus E (MPa) | Poisson’s Ratio v | Unit Weight γ (kN/m3) | Cohesion c (kPa) | Internal Friction Angle φ (°) |
---|---|---|---|---|---|
Rigid body | 2.1 × 105 | 0.3 | 78 | / | / |
Soil mass | 3 | 0 | 8 | 12 | 20 |
Category | G (MPa) | τr (kPa) | α (kPa) | m | n |
Hardening | 23.13 | / | 15.45 | 0.4271 | 4.4132 × 10−3 |
Softening | 74.89 | 40.13 | / | 0.2297 | 2.0891 × 10−3 |
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Yu, P.; Liu, H.; Geng, L.; Wang, S.; Yu, Y.; Zhu, C.; Yang, Q.; Liu, H.; Guan, Y. Softening/Hardening Damage Model and Numerical Implementation of Seabed Silt-Steel Interface in Yellow River Underwater Delta. J. Mar. Sci. Eng. 2023, 11, 1415. https://doi.org/10.3390/jmse11071415
Yu P, Liu H, Geng L, Wang S, Yu Y, Zhu C, Yang Q, Liu H, Guan Y. Softening/Hardening Damage Model and Numerical Implementation of Seabed Silt-Steel Interface in Yellow River Underwater Delta. Journal of Marine Science and Engineering. 2023; 11(7):1415. https://doi.org/10.3390/jmse11071415
Chicago/Turabian StyleYu, Peng, Honghua Liu, Lin Geng, Shuai Wang, Yang Yu, Chenghao Zhu, Qi Yang, Hongjun Liu, and Yong Guan. 2023. "Softening/Hardening Damage Model and Numerical Implementation of Seabed Silt-Steel Interface in Yellow River Underwater Delta" Journal of Marine Science and Engineering 11, no. 7: 1415. https://doi.org/10.3390/jmse11071415
APA StyleYu, P., Liu, H., Geng, L., Wang, S., Yu, Y., Zhu, C., Yang, Q., Liu, H., & Guan, Y. (2023). Softening/Hardening Damage Model and Numerical Implementation of Seabed Silt-Steel Interface in Yellow River Underwater Delta. Journal of Marine Science and Engineering, 11(7), 1415. https://doi.org/10.3390/jmse11071415