Numerical Methods in Geotechnical Tunneling & Underground Excavation: Convergence-Confinement Theory, Elasto-Plastic Constitutive Modeling, and Ground Response Kinetics
Numerical methods in geotechnical tunneling and deep underground excavation evaluate stress redistribution and deformation kinetics within rock and soil masses during excavation sequence execution. Mechanical excavation disrupts initial in-situ geostatic stress fields ($\sigma_{v0}, \sigma_{h0}$), creating localized shear stress concentrations and plastic deformation zones around the tunnel perimeter. Simulating these dynamic soil-structure interactions requires coupled non-linear numerical modeling to optimize support installation timing and ensure structural stability. According to Convergence-Confinement Theory , the internal radial support pressure ($P_i$) required to balance ground radial convergence displacement ($u_r$) along the wall of a circular tunnel of radius $R$ in an elastic domain is modeled as: $$u_r = \frac{1 + \nu}{E} \cdot R \cdot (p_0 - P_i)$$ Where $p_0$ is mean hydrostatic far-field stress, $E$ is elastic modulus of the rock mass, and $\nu$ is Poisson's...