ORIGINAL PAPER A Constitutive Model for Strain-Controlled Strength Degradation of Rockmasses (SDR) A. Kalos 1 • M. Kavvadas 1 Received: 25 October 2016 / Accepted: 23 July 2017 Ó Springer-Verlag GmbH Austria 2017 Abstract The paper describes a continuum, rate-indepen- dent, incremental plasticity constitutive model applicable in weak rocks and heavily fractured rockmasses, where mechanical behaviour is controlled by rockmass strength rather than structural features (discontinuities). The model describes rockmass structure by a generalised Hoek–Brown Structure Envelope (SE) in the stress space. Stress paths inside the SE are nonlinear and irreversible to better sim- ulate behaviour at strains up to peak strength and under stress reversals. Stress paths on the SE have user-controlled volume dilatancy (gradually reducing to zero at large shear strains) and can model post-peak strain softening of brittle rockmasses via a structure degradation (damage) mecha- nism triggered by accumulated plastic shear strains. As the SE may strain harden with plastic strains, ductile behaviour can also be modelled. The model was implemented in the Finite Element Code Simulia ABAQUS and was applied in plane strain (2D) excavation of a cylindrical cavity (tunnel) to predict convergence-confinement curves. It is shown that small-strain nonlinearity, variable volume dilatancy and post-peak hardening/softening strongly affect the predicted curves, resulting in corresponding differences of lining pressures in real tunnel excavations. Keywords Rockmass  Constitutive model  Plasticity  Nonlinear stiffness  Volume dilatancy  Structure degradation List of symbols SDR Constitutive model for Strength Degradation of Rockmasses SE Structure Envelope SPR Stress Path Reversal SSR Stress Sign Reversal a, r c , m b , s Genearlised Hoek–Brown parameters b Rotation of the SE axis o with respect to the isotropic (r) axis C e Tangent non-plastic stiffness matrix c Primary strength anisotropy parameter varied along each of the five shearing directions (values c 1 ,c 2 , … c 5 along deviatoric axes S 1 ,S 2 , … S 5 ) d State variable controlling the tensile strength of the rockmass, d = (s/m b ) r c d in , d fin Initial and final values of structure variable d H Plastic hardening modulus I Unit isotopic tensor K, G Nonlinear bulk and shear moduli m b,in , m b,fin Initial and final values of structure variable m b n Material constant controlling the non-plastic stiffness mean stress dependency P Plastic potential tensor P, P 0 Volumetric plastic potential and plastic potential deviator p atm Atmospheric pressure (p atm % 101.3 kPa) Q Gradient of the SE Q, Q 0 Isotropic and deviatoric components of gradient Q q Scalar stress deviator (shear stress) r Radial distance along the springline measuring from the tunnel centre (r C R, where R is the tunnel diameter) & A. Kalos alkalos83@gmail.com 1 Geotechnical Department, School of Civil Engineering, National Technical University of Athens (NTUA), 9, Iroon Polytechniou Street, 157 80 Zografou, Greece 123 Rock Mech Rock Eng DOI 10.1007/s00603-017-1288-x