Experimental Quantification of the Evolution of the Static Mechanical Properties of Tight Sedimentary Rocks during Increasing-amplitude Load and Unload Cycling

Understanding the linearly and nonlinearly elastic behaviors of tight reservoir rocks is crucial for numerous geophysical and geomechanical applications in hydrocarbon exploration and production, geological repositories for greenhouse gases, and geothermal energy exploitation. We perform a suite of triaxial load and unload cycling tests with increasing stress amplitudes on three tight sedimentary rocks to explore the evolution of their static mechanical properties (Young’s modulus and Poisson’s ratio). We intend to depict the transition from linear to nonlinear elasticity by combining static measurements with dynamic measurements. The experimental results suggest that static mechanical properties increase upon load stress cycling but decrease upon unload stress cycling. Upon the increasing-amplitude unload cycling, static mechanical properties gradually decrease from values approaching dynamic properties to values closer to static properties upon load cycling. By quadratically fitting the static mechanical properties as functions of the strain amplitude in the process of unload cycling, we define a characteristic strain amplitude of about 5 × 10−5 to distinguish the linearly elasticity-dominated and nonlinearly elasticity-dominated behaviors for three tight rocks. Such transitional behavior in tight sedimentary rocks can be microscopically explained by the gradual activation of friction-controlled sliding from the beginning of the cyclic stress unload. These observations provide direct experimental evidence of the transition from linear to nonlinear elasticity for tight sedimentary rocks during the laboratory static measurements, which will facilitate understanding of the dynamic-static parameter correlation and the modeling of rock deformations in geoscience or geoengineering applications.

Nonlocal approximations to anisotropic Sobolev norms

We obtain some nonlocal characterizations for a class of variable exponent Sobolev spaces arising in nonlinear elasticity, in the theory of electrorheological fluids as well as in image processing for the regions where the variable exponent p ( x ) reaches the value 1.

Study of a mixed problem for a nonlinear elasticity system by topological degree

"In this paper, we consider a mixed problem for a nonlinear elasticity system with laws of general behavior. The coefficients of elasticity depends on x meanwhile the density of the volumetric forces depends on the displacement. The main aim of this paper is to apply the Schauder's fixed point theorem and the techniques of topological degree to prove a theorem of the existence and the uniqueness of the solution of the corresponding variational problem."