The Effect of Stress on Limestone Permeability and Effective Stress Behavior of Damaged Samples

Abstract

The evolution of permeability and its effective stress behavior is related to inelastic deformation and failure mode. This was systematically investigated in Indiana and Purbeck limestones with porosities of 16% and 14%, respectively. High-pressure compression tests were conducted at room temperature on water-saturated samples. At relatively high confinement shear-enhanced compaction was observed to initiate at a critical stress, accompanied by significant permeability reduction of up to a factor of~3. Overall, the permeability reduction due to inelastic compaction in our limestones is smaller than that observed in sandstones. At relatively low confinement, dilatant failure was observed, which was accompanied by a decrease and increase of permeability in Indiana and Purbeck limestones, respectively. There seems to be a trend for the correlation between porosity and permeability changes to switch from positive to negative with increasing porosity. The void space of both limestones has significant proportions of macropores and micropores. The effective stress behavior of such a limestone with dual porosity has been documented to be different from the prediction for a microscopically homogeneous assemblage, in that its effective stress coefficients for permeability and pore volume change may attain values significantly >1. In contrast, our investigation of damaged samples consistently showed effective stress coefficients for both permeability and pore volume change with values <1. This suggests that the behavior in the damaged samples is akin to that of a microscopically homogeneous assemblage, possibly due to pervasive collapse of macropores that would effectively homogenize the initially bimodal pore size distribution.

The Brittle‐Ductile Transition in Porous Limestone: Failure Mode, Constitutive Modeling of Inelastic Deformation and Strain Localization

“…This agreement with the normality condition motivates us to further test the postulate with two other limestones, which have recently been investigated in relation to the BDT and permeability evolution (Baud, Exner, et al., 2017; Brantut et al., 2018; Meng et al., 2019). The Purbeck limestone from England is made up of calcitic peloids (100–500 μm) in the form of micrites surrounded by sparry cement, as well as polycrystalline quartz dispersed in the aggregate.…”

“…The exterior appearance of the samples indicates shear band formation and brittle faulting. Previous studies of Indiana limestone (Meng et al., 2019; Vajdova et al., 2012) deformed to relatively large strains under similar pressures have reported band angle of ∼30°relatively to σ 1 . In contrast, at effective pressures of 30 MPa and beyond, shear‐enhanced compaction was observed to initiate at effective mean stresses lower than P* , ranging from 44 to 58 MPa (Figure 2b).…”

“…(2018) and Meng et al. (2019) for effective stress coefficients of several limestones over several loading and unloading cycles.…”

Effective Stress Law for the Permeability and Pore Volume Change of Clayey Sandstones

“…The clay shell model assumes that the permeability and pore volume change both depend solely on the radius a , and accordingly their effective stress coefficients are predicted to be identical, given by . Berryman (1992) has pointed out that this is speculative, and indeed recent experiments conducted by Wang et al (2018) and Meng et al (2019) on limestones showed that the predicted equality is consistently violated, such that the value of κ can be significantly greater than that of β.…”

“…A common feature of these models (with the exception of the clay particle model) is that their determination of κ is solely based on consideration of the pore volume change, with the premise that the coefficients κ and β for permeability and pore volume change are equivalent, which Berryman (1992) pointed out to be speculative. Indeed, his theoretical analysis suggested that the two coefficients can attain quite different values, and the data of Wang et al (2018) for limestones and Meng et al (2019) for deformed limestones show β values significantly lower than κ. Is this discrepancy between the two coefficients κ and β observed also in a clayey sandstone, and if so, how can existing models be modified to more realistically capture the laboratory data?…”