Minimum void ratio is an important soil property in the practice of geotechnical engineering. It correlates with the volume change tendency, the pore fluid conductivity, and the shear strength of the soil. Minimum void ratio for granular soil is highly dependent on its particle size distribution. However, very few analytical models are available for predicting minimum void ratios as a function of particle size distribution. This paper develops a mathematical model that can predict the minimum void ratio for granular soil with arbitrary particle size distribution based on a more fundamental approach using the concept of dominant particle network. The developed model is evaluated by the simulation results using a discrete element method (DEM) and by the experimental results on granular soil with four different gradations to illustrate the applicability of model. The results predicted by the model show very good agreement with the data from DEM simulations and experiments.

Summary: Mitigation and prevention of shale-formation damage caused by hydraulic-fracturing fluid/rock interactions play an important role in well-production stability and subsequent refracturing design. In this paper, the effect of converting typically hydrophilic fractured surfaces to hydrophobic ones on fluid-induced softening of shales was investigated. Specifically, nanoindentation was used to characterize changes in the mechanical properties of shale samples after different surface treatments. A thin layer of octadecyltrimethoxysilane (OTMS) coating was deposited on the initially hydrophilic surface of shale, followed by inundation in water for certain periods of time to allow for fluid/rock interactions. Nanoindentation testing was then conducted on the treated shales to characterize their hardness, Young's modulus, and fracture toughness to examine the alteration of shale's mechanical properties caused by fluid/rock interactions and to check whether hydrophobic coating can mitigate shale-softening. Results from nanoindentation testing were analyzed by a newly proposed clay-matrix criterion for data screening. Different rock-surface treatments lead to changes in rock properties. Both the hardness and Young's modulus of the treated samples converge and stabilize at relatively large depths. Samples with hydrophobic surfaces exhibit a much lower degree of softening, as reflected by their better mechanical properties (e.g., 40% increase in hardness, 25% increase in Young's modulus, and 35% increase in fracture toughness), compared with untreated shale samples. The results of this study also demonstrate that the continuous-stiffness-measurement (CSM) method and the repeated loading method for nanoindentation loading yield similar ranges of micromechanical properties of the bulk shale. However, the CSM method, if combined with the newly proposed clay-matrix-based criterion for data screening can better define and characterize fluid/shale interactions or softening of shales.

Preventation of shale formation damage by fracturing fluid-rock interactions plays an important role in well production performance and subsequent refracturing design. In this paper, the effect of converting typically hydrophilic fracture surface to hydrophobic ones on fluid-induced damage and softening is investigated. In particular, nanoindentation experiments were employed to characterize changes in the mechanical properties of shale samples with different surface treatments. Shale samples were treated by octadecyltrimethoxysilane (OTMS) to convert the initially hydrophilic surfaces to hydrophobic ones, followed by inundation in water to allow for fluid-rock interactions. Nanoindentation testing was then conducted on the samples to characterize hardness, Young's modulus, and fracture toughness to examine the effect of fluid-rock interactions on shale mechanical properties and whether surface treatment can mitigate shale-softening. Its unique advantage is that the near-surface properties (but not the entire bulk sample) can be characterized, thus elucidating how water-rock interactions migrate from the surface to the interior of the rock. Results obtained from nanoindentation testing were analyzed by statistical analysis and by a proposed clay matrix criterion. Different treatments lead to variable alterations to rock properties. The hardness and Young's modulus exhibit a reciprocal steady state trend at certain depths. Samples with hydrophobic surfaces exhibit a higher resistance to fluid-shale interactions, as reflected by a 40% higher hardness, a 25% higher Young's modulus, and a 35% higher fracture toughness, when compared with untreated shale samples. The untreated rock actually shows a 48% reduction in hardness, a 27% reduction in Young's modulus, and a 43% reduction in fracture toughness in the rock interior. This study also demonstrates that nanoindentation testing provides multiple advantages in characterizing the fracturing fluid-rock interactions at the micro/nano scale, since these interactions start from the rock surface and propagate to the interior without significantly involving the bulk rock. Nanoindentation testing is competent in characterizing micromechanically fluid-shale interactions and how surface treatment can mitigate the softening of shales.