Stochastic Damage Model of the Concrete Structure of the High-speed Railway Tunnel Base

Based on thermodynamic and energy dissipation principles, and directed towards the repeated “tensile-compressive-tensile-compressive” stress of the concrete structure of the high-speed railway tunnel base, double scalar damage variables are defined, the hardening function is introduced, the elastoplastic Helmholtz free energy is amended, and the nonlinear stochastic damage constitutive model that describes strain-softening of the concrete under tensile and compressive conditions is derived. In the effective stress space, the evolution rule of the damage variables is derived based on the normality rule of the plastic mechanics. After solving the probability density evolution equation, the numerical analysis solving algorithm of “elastic prediction-plastic amendment-damage amendment” was established. Further, secondary development of the program is performed, which realizes the numerical computation of the stochastic damage constitutive model. By comparing with the indoor uniaxial tensile and uniaxial compressive test results obtained in previous studies, the accuracy and the adaptability of the derived stochastic damage constitutive model were verified. This model not only reflects the stress-strain relationship of the concrete when in tension or compression in terms of the mean value but also simulates the discrete range in terms of probability, which closely reflects the non-linearity and randomness of the loading behaviour of the concrete. Through algorithm analysis, this model can be adopted to calculate the damage evolution rules and fatigue damage life of the tunnel base concrete.