Lateral earth stress and strain

Abstract

A popular method for estimating in‐situ horizontal stress assumes that the horizontal elastic strain is zero. This paper discusses whether and when this model might be useful. Clearly the model is not applicable in tectonically active areas where there is lateral extension, compression or wrenching. In young passively subsiding basins, sediments are mechanically compacted with little lateral strain, so the model might be expected to work there. However, existing experimental data on uniaxial mechanical compaction show clearly that even if total horizontal strain is zero, the elastic strain is far from zero because there is an equal but opposite inelastic strain that balances it. The horizontal elastic strain is thus determined by the inelastic rock properties, so the elastic strain will generally be nonzero and non‐uniform from one formation to another. There is one geological situation in which elastic strains may tend towards zero. Consider a passive basin that is neither subsiding nor eroding. Over geologically long time periods, rocks may creep and thereby approach an equilibrium stress state. To the extent that such rock masses in the earth are thermodynamically closed systems, equilibrium occurs at minimum energy. I show here that the condition of zero lateral elastic strain minimizes the elastic strain energy. This could be a quasi‐equilibrium condition in the earth if there is a relaxation mechanism that can reduce the elastic energy to a minimum without also relaxing shear stresses to zero. If such a mechanism exists, it might produce zero lateral elastic strain in strata that are tectonically quiescent.