Analytical solutions for cavity contraction in strain-softening materials with linear or exponential strength decay

Abstract

Abstract This paper presents an analytical investigation into the contraction of spherical and cylindrical cavities excavated in strain-softening rock masses obeying the Mohr–Coulomb or Tresca yield criterion, with linear or exponential uniaxial compressive strength decay. The derivation of the ground response curves is based on the simplifying assumption that the strains inside the plastic zone are completely plastic. This significantly simplifies the mathematical formulation, enabling the derivation of closed-form solutions. An alternative simplifying approach which partially neglects the elastic strains inside the plastic zone and which is commonly adopted in the literature, is also examined. The accuracy of the simplified solutions is evaluated by comparing their predictions with rigorous solutions obtained by numerical finite-difference analyses. The investigation demonstrates that the proposed closed-form solutions represent a significant improvement on those based on the commonly-made simplifying assumption involving partial neglect of elastic strains.

Keywords

• Ground response curve
• Tunnelling
• Strain-softening
• Strength decay
• Tresca
• Mohr–Coulomb