Advanced constitutive modelling of shotcrete: Model formulation and calibration

Shotcrete is one of the main support elements for tunnels constructed according to the principles of the New Austrian Tunnelling Method (NATM). In this paper, a sophisticated constitutive model for the complex mechanical and time-dependent behaviour of shotcrete is presented, which is formulated within the framework of elasto-plasticity. Two independent yield surfaces govern the material behaviour in compression and tension under multi-axial loading conditions, which is further controlled by non-linear plastic strain hardening and softening rules following uniaxial stress-strain curves. The main novelty of the model is the introduction of normalised hardening and softening parameters which enable a more realistic simulation of the shotcrete loading history. In addition, cracking of the shotcrete is treated within the smeared crack concept by applying a fracture energy approach as a regularisation technique, which eliminates the dependency of the results on the size of the elements in a finite element mesh. Furthermore, the model takes into account the gradual change of the main material properties of the shotcrete due to cement hydration during the first 28 days after spraying. Other important time effects such as creep, shrinkage and hydration temperature induced deformations at early ages are considered in the current model formulation. This paper aims to describe in detail the developed structure of the constitutive model and model calibration.