A Size-Dependent Bonded-Particle Model for Transversely Isotropic Rock and its Application in Studying the Size Effect of Shale

The bonded-particle model (BPM) method has been used to study the size effect and anisotropy of rock strength. This research proposes a new bonded-particle model which exhibits both size effect and anisotropy, for simulating transversely isotropic rocks. It assumes that transversely isotropic rocks consist of rock matrix, bedding planes, and randomly distributed cracks. Rock matrix is the base material which is isotropic and size independent, while bedding planes and cracks cause anisotropy and size effect respectively. The BPM of shale was developed in PFC2D. The BPM used bonded particles, smooth joints, and discrete fractures to model shale matrix, bedding planes, and cracks. The model introduced the three components and calibrated them progressively. At first, the matrix model was created, and its uniaxial compressive strength (UCS) was isotropic and size independent. Next, the bedding planes were introduced into the matrix model, and the UCS became anisotropic. In the meantime, the cracks were introduced into the matrix model, and the UCS became size dependent. At last, the shale model was created by combing the shale matrix, bedding planes, and cracks. The UCS of shale model exhibited “U-shaped” curve and followed the decreasing asymptotic trend. The failure pattern of these models show that bedding planes cause anisotropy as they control the macroscopic failure, and the influence of bedding planes is pronounced irrespective of model size. Cracks cause size effect as they induce the localized failure, and the influence of cracks increases with the increase in model size. When the model size is small, anisotropy and size effect coexist. When the model size reaches a certain size, size effect disappears. The numerical result matches with the findings of published literature. The proposed model and its calibration procedure are applicable to other transversely isotropic rocks for analyzing the size effect and anisotropy.