Machine Learning-Enhanced Analysis of Small-Strain Hardening Soil Model Parameters for Shallow Tunnels in Weak Soil
Abstract
1. Introduction
2. The Small-Strain Hardening-Soil-Model
- E50 (secant modulus for primary loading)—Governs soil stiffness under deviatoric loading.
- Eoed (oedometer modulus)—Defines soil stiffness under one-dimensional compression.
- Eur (unloading/reloading modulus)—Controls stiffness during unloading and reloading.
- Gref (reference shear modulus at small strains)—Represents soil stiffness at very small strains.
- γ0.7 (shear strain at 70% degradation of Gref)—Describes strain-dependent stiffness degradation.
- c (effective cohesion)—Governs shear strength.
- ϕ (effective friction angle)—A key parameter for soil shear strength.
- Ψ (dilatancy angle)—Defines volume expansion during shearing.
- m (power law parameter for stress-dependent stiffness)—Controls the nonlinear stiffness variation with confining pressure.
- K0 (lateral earth pressure coefficient for normally consolidated soil)—Governs the initial lateral stress state.
- OCR (overconsolidation ratio)—Represents pre-consolidation history.
- pref (reference pressure)—A scaling parameter for stiffness dependency.
3. Case Study Information
4. Finite-Element Modelling
5. Machine-Learning Analysis
5.1. Regression Models
5.2. Classification Models
6. Summary and Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Support Element | Input Parameter | Value |
---|---|---|
Tunnel liner | Thickness [cm] | 40 |
Young’s modulus [MPa] | 30,000 | |
Poisson ratio [-] | 0.2 | |
Temporary tunnel invert | Thickness [cm] | 35 |
Area (m2) | 30,000 | |
Poisson ratio [-] | 0.2 | |
Temporary side liner | Thickness [cm] | 10 |
Young’s modulus [MPa] | 30,000 | |
Poisson ratio [-] | 0.2 | |
Inclined pile | Young’s modulus [MPa] | 200,000 |
Area [m2] | 0.000484 | |
Spacing [m] | 0.6 | |
Poisson ratio [-] | 0.25 | |
Jet Grout | Young’s modulus [MPa] | 1400 |
Poisson ratio [-] | 0.3 | |
Friction angle (degrees) | 34 | |
Cohesion (MPa) | 0.93 |
Parameter | Unit | Min | Max | Relationship |
---|---|---|---|---|
[MPa] | 1 | 150 | ||
[MPa] | 0.5 | 225 | ||
[MPa] | 1 | 1575 | ||
[-] | 0.5 | 1 | ||
υ | [-] | 0.2 | 0.3 | |
[-] | 0.4 | 0.6 | ||
ϕ | [Deg] | 20 | 40 | |
Ψ | [Deg] | 0 | 10 | ϕ-30° |
cohesion | [MPa] | 0 | 0.01 | |
Rf | [-] | 0.6 | 0.9 | |
ψ | [Deg] | 0 | 10 | |
[MPa] | 1.1 | 2677.5 | ||
[-] | 0.0001 | 0.001 |
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Eilat, T.; McQuillan, A.; Mitelman, A. Machine Learning-Enhanced Analysis of Small-Strain Hardening Soil Model Parameters for Shallow Tunnels in Weak Soil. Geotechnics 2025, 5, 26. https://doi.org/10.3390/geotechnics5020026
Eilat T, McQuillan A, Mitelman A. Machine Learning-Enhanced Analysis of Small-Strain Hardening Soil Model Parameters for Shallow Tunnels in Weak Soil. Geotechnics. 2025; 5(2):26. https://doi.org/10.3390/geotechnics5020026
Chicago/Turabian StyleEilat, Tzuri, Alison McQuillan, and Amichai Mitelman. 2025. "Machine Learning-Enhanced Analysis of Small-Strain Hardening Soil Model Parameters for Shallow Tunnels in Weak Soil" Geotechnics 5, no. 2: 26. https://doi.org/10.3390/geotechnics5020026
APA StyleEilat, T., McQuillan, A., & Mitelman, A. (2025). Machine Learning-Enhanced Analysis of Small-Strain Hardening Soil Model Parameters for Shallow Tunnels in Weak Soil. Geotechnics, 5(2), 26. https://doi.org/10.3390/geotechnics5020026