Deformation and Damage Evolution Characteristics in Laminated Rocks Using Discrete Element Method
Authors: Pothana Prasad , Ling Kegang , Garcia Fernando E. 
Published: August 2024

ABSTRACT:
Laminated rocks, prevalent in natural geological processes, exhibit pronounced mechanical anisotropy, a characteristic shared with unconventional hydrocarbon reservoirs. The arrangement of laminations significantly influences fluid flow and stress propagation, underscoring the imperative to comprehend the mechanical behavior of such materials. Traditional homogenization models and continuum-based numerical methods often struggle to accurately capture the intricate dynamics of granular materials, marked by variations and arching mechanisms crucial for system stability. In contrast, discrete element methods (DEM) offer a distinct advantage by considering heterogeneity and physical interactions at the level of individual grains. This study evaluates force and stress evolution in composite laminated rocks, employing digital representations of laminated materials with varying volume fractions of binary mixtures. Utilizing a particle flow code, we construct digital rock samples consisting of rigid grain assemblage and a flat joint contact model governing grain-to-grain contacts.
Three digital rocks were first constructed: matrix, stiff material, and soft material. The stiff and soft materials are embedded into the matrix material, similar to laminated rock types. We then investigate the effect of relative lamina thickness and the angle of laminations with respect to loading directions. We observed that the number of laminations has little impact on the elastic stiffness and strength of the laminated rocks. The material exhibits higher effective stiffness when loaded parallel to the laminations, while stiffness is lower perpendicular to the laminations. The evolution of cracks proves intricate, reflecting a delicate interplay between material elastic constants, strength properties, and loading direction. We observed that the initiation and propagation of cracks show strong dependence on the angle of laminations and inclusion type. These findings contribute valuable insights into the mechanical behavior of laminated composite granular rocks.

1 INTRODUCTION
The effects of sedimentary processes, mineralogical differences and mechanical deformation result in the generation of various laminae within the Earth's crustal rocks. Anisotropic properties typically result from mineral alignment in metamorphic rocks, layering in sedimentary rocks, and discontinuities in the igneous rock mass (Chenevert and Gatlin, 1965; Williams, 1990). In geoengineering applications, the consideration of anisotropy is paramount. The geoengineering applications that encounter anisotropic rocks include drilling and hydraulic fracturing operations in thin-bedded, laminated shall sand hydrocarbon reservoirs, fractured basement rocks, shale layers, excavations, and geotechnical design of anisotropic rocks (Winhausen et al., 2023; Yan et al.; Ni et al., 2023). Applications in engineering that overlook how rocks behave differently in various directions can lead to errors of varying degrees, depending on the extent of the rock's anisotropy Amadei (1996).