The implications of joint deformation in analyzing the properties and behavior of fractured rock masses, underground excavations, and faults

Abstract

Abstract For a given stress state, joint deformation depends on the joint’s geometry, including surface roughness, spatial geometry of the contact area, and large-scale topographical features such as dips. Under normal stress, contacting asperities compress, and the half spaces bounding the joint are deformed. A very significant consequence of half-space deformation is that it allows mechanical interaction among all contact points between the joint surfaces. As a result, the contact area’s overall spatial geometry plays an important role in determining the distribution of stress across joint surfaces and the change in geometry of the void space between surfaces that occurs with changes in stress. Mechanical interaction among contact points is important in determining normal joint stiffness: two joints with the same total contact area can have substantially different stiffnesses depending on the spatial geometry of their contact areas. Modeling results indicate that joints with small contact areas uniformly distributed across the surfaces can be nearly as stiff as a perfectly mated interface. These results have significant implications for almost any endeavor in fractured rock, including designing underground excavations, predicting the hydraulic response of a rock mass to changes in stress, understanding the deformation and failure of joints under shear stress, and analyzing the stability of faults. In underground excavations, for example, deformation of the roof and floor means that the load acting on any supporting pillar and the distribution of stress throughout the pillar depend on: the pillar’s size and shape; the size, shape, and proximity of neighboring pillars; and the spatial geometry of the pillar array. Purely elastic deformation can lead to either catastrophic or progressive failure. Similarly, to accurately predict fluid flow through jointed rock, changes in void space geometry that result from changes in stress must be considered; these changes in geometry are not predicted by methods that assume that aperture changes uniformly across the joint. For joints and faults, the nonuniform distribution of normal and shear stresses resulting from surface roughness and mechanical interaction between contact points suggests a progressive form of shear failure. Failure is initiated at points of low normal stress and propagates as stress from failed asperities is redistributed to neighboring asperities. Consistent with observations on many faults, modeling and analytical results predict that earthquakes on a fault would be clustered in time and space because of mechanical interaction between persistent asperities.