Numerical modeling of the evolution of arcades and rock pillars

Arcades, i.e. lenticular and other specifically shaped hollows controlled by discontinuities, have recently been recognized as a weathering form typical for sandstones, weathered quartzites, granites, or tuffs. They are produced by accelerated weathering and erosion in stress shadows related to the redistribution of gravity-induced stress along planar discontinuities in the rock. These forms occur worldwide in various settings (inland humid, arid, and coastal). The origin of arcades has been demonstrated via physical experiments and supported by a relatively simplistic numerical modeling. However, details on their shaping and the evolution of related forms have not been explained. We performed an advanced numerical modeling to produce various shapes of arcades and rock pillars during the erosion of rock masses dissected by discontinuities. We demonstrate that the erosion model, in which erosion takes place when the maximum principal stress is below a certain critical value, can adequately describe the formation of arcades. In the modeling, we set higher critical values for stresses at discontinuities than in a homogeneous material (representing a rock mass) to represent the higher tendency for disintegration of the discontinuity material, which was weakened by the discontinuity formation processes. By applying various discontinuity geometries and values of critical stresses, we were able to reproduce the formation of various arcade shapes and complex-three-dimensional clusters of arcade cavities with rock pillars. Discontinuities and stress-controlled erosion/weathering are the only necessary conditions for arcade formation. (C) 2020 Elsevier B.V. All rights reserved.