Anisotropy and Microcrack Propagation Induced by Weathering, Regional Stresses and Topographic Stresses

This paper presents a new model for anisotropic damage in bedrock under the combined influences of biotite weathering, regional stresses, and topographic stresses. We used the homogenization theory to calculate the mechanical properties of a rock representative elementary volume made of a homogeneous matrix, biotite inclusions that expand as they weather, and ellipsoidal cracks of various orientations. With this model, we conducted a series of finite element simulations in bedrock under gently rolling topography with two contrasting spatial patterns in biotite weathering rate and a range of biotite orientations. In all simulations, damage is far more sensitive to biotite weathering than to topographic or regional stresses. The spatial gradient of damage follows that of the imposed biotite weathering rate at all times. The direction of micro-cracks tends to align with that of the biotite minerals. Relative to the topographic and regional stresses imparted by the boundary conditions of the model, the stress field after 1,000 years of biotite weathering exhibits higher magnitudes, wider shear stress zones at the feet of hills, more tensile vertical stress below the hilltops, and more compressive horizontal stress concentrated in the valleys. These behaviors are similar in simulations of slowing eroding topography and static topography. Over longer periods of time (500 kyr), the combined effects or weathering and erosion result in horizontal tensile stress under the hills and vertical tensile stress under and in the hills. These simulations illustrate how this model can help elucidate the influence of mineral weathering on Critical Zone evolution.