Stress and strain evolution during single-layer folding under pure and simple shear

Folds in rocks are commonly used in geology for strain analysis. They contain information about rock rheology, and the kinematics and mechanics of deformation. The systematic analysis of the evolution of stress and strain during rock folding can provide key information on the mechanical behaviour of rocks and the efficiency of the folding process. In order to investigate the evolution of rock rheology during fold development, a series of two-dimensional simulations of single-layer folding are presented here. They are run using the finite element method BASIL, integrated within the software platform ELLE, to simulate linear and non-linear viscous deformation. The kinematics of deformation, the competence ratio between the folding layer and surrounding matrix as well as the stress exponent of the power-law viscous material are systematically varied. The results allow comparing the stages of folding under different deformation kinematic conditions. For all simulations the folding amplification process starts when the second invariant of the strain rate tensor in the competent layer deviates from the theoretical strain rate curve for a homogeneous material, which corresponds to a viscosity ratio between layer and matrix of m = 1. The relative time when the fold amplification starts is determined by the viscosity ratio between the competent layer and its surrounding matrix, the initial layer orientation with respect to the shear plane, the kinematics of deformation and the stress exponent. The folding process is more effective in cases with high viscosity ratio, non-linear rheology and layers initially oriented at a low angle with respect to the shear plane, because the second invariant of the strain rate tensor at the layer deviates earlier from the theoretical curve. The results also show differences depending on the boundary conditions, where (1) folding a competent layer requires less work in simple shear than in pure shear, and (2) the geometrical softening experienced by the competent layer due to fold development is followed by a hardening stage in pure shear and by a major softening phase in simple shear. The simulation results suggest that the decrease of stress of a competent layer without decreasing the mechanical strength has a direct influence on the behaviour of a lithospheric layer around the crust-mantle boundary, which may experience geometrical softening depending on the tectonic settings rather than material softening due metamorphic reactions or grain size reduction.