Anisotropy and microcrack propagation induced by weathering, regional
stresses and topographic stresses
Abstract
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 gradient of damage follows that of the imposed
biotite weathering rate and does not extend beyond the weathering zone.
The direction of micro-cracks tends to align with that of the biotite
minerals. Relative to the stress field imparted by topographic and
regional stresses, 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.