Shear stress enhancement of void compaction

Abstract

Motivated by the success of the spherical model in predicting the volumetric compaction behavior of both porous rocks and metals to a hydrostatic pressure, we consider the applicability of the spherical model to nonhydrostatic loading conditions. Specifically, the spherical model is used to examine the influence of the presence of a shear stress on the volumetric compression of a porous solid. We first obtain the linear, elastic solution for a hollow sphere subject to homogeneous tractions on the outer boundary. Then, assuming that the matrix material is governed by the Drucker‐Prager yield criterion, we use the elastic solution to derive an analytic expression for the onset of yield in the hollow sphere. The expression for the initial yield surface shows that the presence of a shear stress hastens the onset of yield in the sphere in comparison to a hydrostatic loading condition. This result agrees well with experimental data which shows that, for porous solids, permanent crush‐up begins at a lower mean stress under a nonhydrostatic loading than when the applied loading is a hydrostatic pressure. At this point, due to difficulty in obtaining an analytic solution, we turn to a numerical scheme (finite element method) to extend the analysis of the hollow sphere problem into the elasto‐plastic range. The spherical model results clearly exhibit the experimental finding that the presence of a shear stress tends to enhance the volumetric compaction of porous solids in comparison to a hydrostatic loading condition. For both a porous rock and metal sample, agreement between the spherical model and experimental results is excellent.

Mechanical Compaction of Porous Sandstone

“…In the cataclastic flow regime, the triaxial curve for a given effective pressure coincided with the hydrostat up to a critical stress state (indicated by C* in Figure 4b), beyond which there was an accelerated decrease in porosity in comparison to the hydrostat. At stress levels beyond C* the deviatoric stress field provided significant contribution to the compactive strain, and this phenomenon is referred to as "shear-enhanced compaction" (Curran and Carroll, 1979;Wong et al, 1992). In contrast, the porosity change behavior at effective pressures of 5 and 20 MPa was such that the compaction decelerated in comparison to the hydrostat beyond critical stress states marked as C' (Fig.…”

Dilatancy, compaction, and failure mode in Solnhofen limestone

“…Extrapolation of our laboratory data to the temporal and spatial scales of geologic settings would require a fundamental understanding of the micromechanics of the brittle-ductile transition, which may involve the complex interplay of microcracking, crystal plasticity, and diffusive mass transfer processes in Solnhofen limestone. for the elastic moduli of calcite, but as noted by Curran and Carroll [1979], the yield envelope has a relatively weak dependence on the elastic moduli. Except for slight differences in the curvatures, our curves in Figure 10a are nearly the same as theirs calculated using different elastic moduli.…”

Mechanical Behavior of Cement Paste and Alterations of Hydrates under High-Pressure Triaxial Testing

“…13, the porosity decreased drastically in the 400 MPa case compared with the 100 MPa case. In porous rock, a sudden volume decrease due to the collapse of pores at certain very high pressures was reported (Curran and Carroll 1979;Wong and Baud 2012). In HCP, sudden pore collapse might take place between P c = 100 and 400 MPa and this collapse could be one of the reasons for the pulverization shown in Fig.…”