Constitutive Law for Salt Tectonics Modeling

Maurice B. Dusseault, Dennis Z. Mraz

Conventionally, a power-law relationship has been used to describe the rate-law connecting shear stress and strain rate (creep rate) for time-dependent processes such as halite deformation associated with diapirism. Studies in laboratories at strain rates several orders of magnitude greater than geologic rates have been extrapolated to the stress levels of interest as a constitutive law to permit modeling of processes. This approach is fundamentally flawed because a change in the dominant deformation mechanism from diffusion and dislocation to steady-state cracking takes place at a strain rate of approximately 2 - 20 × 10^-11s^-1, which is at or below the limit that laboratories are capable of reproducing. This approach thus leads to large overest mates of the value of the exponent in a typical power law relationship: strain rate = A (s₁ - s₂)ⁿ, where s₁ - s₂ is the differential stress and A accounts for other factors, including temperature. We propose a multimechanism law with a turning point (in a log-log plot) at a shear stress and strain rate that are basic material parameters, and we show how these can be estimated by lab tests and measurements in mines. These parameters are functions of temperature, and a log plot of the transition shear stress vs. temperature yields a straight line, implying a power-law rate dependency of temperature effects. There remains uncertainty as to the value of the exponent below the limit, but theory limits it to a value of 1 to 3, lower value dominating at low shear stresses. This formulation has permitted us to model salt and potash mines, and has application to geological processes.

AAPG Search and Discovery Article #91030©1988 AAPG Annual Convention, Houston, Texas, 20-23 March 1988.