Imagine clinging to a rock wall a thousand feet above the ground and looking up to see a sheet of granite tumbling directly toward you. Climbers in the Yosemite Valley hope never to be in this situation. But rock falls are all too common on the imposing face of Yosemite National Park's Half Dome in California.
Fractures called sheeting joints develop parallel to the rock surface when tectonic stresses and erosion weaken the granite. Ultimately, sheeting joints create and cause large slabs of rock to eventually fall away in a process known as exfoliation. But the mechanism by which sheeting joints occur presents a paradox.
Fractures require tensile stress or localized fluid pressure that exceeds ambient compressive stresses—those are the stresses created by parts of the material pressing against each other. According to a paper published in Geophysical Research Letters by University of Hawaii geophysicist Stephen Martel
The paradox is that sheeting joints require a tension perpendicular to the rock surface at shallow depths, yet the surface itself sustains no such tension, and gravity increases the vertical compressive stress with depth.
Martel presents a new model that treats the relationship between depth and tension perpendicular to ground surface as a function of surface shape, gravitational stresses, and compressive stresses parallel to the surface. In his model tension can indeed increase with depth. And if compressive stresses parallel to the surface are strong enough and the surface is convex enough, sheeting joints could open.
The model focuses on sources of compression parallel to the rock surface. Curvature and slope, rather than relief, are the key geometric parameters for formation of a sheeting joint, and rock type is important due to its unconfined compressive strength and density. The depth to which curvature-induced tension can penetrate will increase as surface curvature decreases.
Think of an outer traction-free layer or skin of a rock outcrop. If compressive (negative) stresses act parallel to the convex (negative curvature) surface and yield a net outward (positive) force that overcomes the inward net force due to gravity, the section will separate. That condition leads to the shingle-like slabs seen on domes and ridges with high compressive stresses.
If, however, surface curvatures are concave (positive curvature) and stresses parallel to the surface are compressive (negative), their negative product won't drive separation That condition is responsible for the lack of sheeting joints in bowls and valleys.
Even slopes that appear flat to the unaided eye can possess sufficient curvature to cause tensile stresses normal to the surface where lateral compressive stresses are high.
Broader applications of the model include explaining local fracture processes in terms of tectonic stresses, estimating stresses where topography is known but stresses can't be measured, and predicting delamination of engineering materials and coatings on curved surfaces.
The model also serves as good food for thought for the Yosemite rock climber clinging to the sheeting joints on the way to Half Dome's summit.
