Effect of topographic curvature on near-surface stresses and application to sheeting joints

Sheeting joints have attracted attention for more than two centuries, yet their cause has remained unclear. Sheeting joints are opening mode rock fractures that form subparallel to the topographic surface and develop to depths of at least 100 m. They are best developed beneath convex surfaces in massive rocks where the compressive stress parallel to the surface ( P) is high. A tensile stress normal to a convex traction-free surface will arise if the product of P and the surface curvature ( k) exceeds the product of the unit weight of rock ( rho g) and the cosine of the slope ( cos beta). The tensile stress contributes fundamentally to sheeting joints; erosion of overburden, by itself, does not. Rocks with high uniaxial compressive strengths host sheeting joints because they can sustain the high compressive stresses necessary to generate surface-normal tensile stresses given typical curvatures in landscapes.