Analysis of faulting in three-dimensional strain field

Multiple faults, composed of three, four or more sets of faults, have been observed at a wide range of scales, from clay experiments to rift valleys. Multiple faults usually are explained by multiple phases of deformation. However, in several cases the multiple faults develop simultaneously; therefore, they cannot be explained by the common theories of faulting. Furthermore, these theories were derived for plane strain, whereas, multiple faults are associated with three-dimensional strain. An elementary analysis of faulting in three-dimensional strain field is presented here. The analysis considers the deformation of an idealized model due to slip along sets of faults; the model is subjected to strain boundary conditions. The analysis shows that (1) three or four sets of faults are necessary to accommodate three-dimensional strain, (2) there is a combination of four fault sets which minimize the dissipation of the deformation; the orientation of these faults depend on the strain state, and (3) if the resistance to slip along these four sets of faults is cohesive, then the stresses which cause slippage along them are equal or larger than the yielding stresses of a Tresca rigid-plastic with the same cohesion. The analysis presented here is too elementary to be directly applied to field observations; however, it indicates that multiple faults and rhomboid patterns of faults probably form when a body is strained three-dimensionally.