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Multiphase heterogeneity significantly affects mechanical and micro-cracking properties of geomaterials. Heterogeneity representations of geomaterials, however, can bring out fatal errors for cracking behavior investigations due to inaccurate characterizations of multiphase matrixes. This work aims to deeply characterize microscopic heterogeneity in rocks represented by digital multiphase matrixes, and to study their effects on cracking properties of geomaterials. X-ray μ-Computed Tomography (μCT) imaging under the same physical field of view is employed to obtain multiphase microstructures of sandstone with different resolutions. Digital colour difference segmentation (DCDS) and the coupling multiple point statistics-marching cube (MPS-MC) algorithms are applied to accurately characterize three-dimensional (3D) multiphase heterogeneity of rocks. Digital simulations coupled with uniaxial compression are conducted to study multiphase heterogeneity effects on micromechanics and cracking behaviors. Results show that with increasing resolution and voxel scale, heterogeneity index increases. Peak stress and crack ratio increase with increasing heterogeneity index, and the relative errors between experimental and numerical stresses are all less than 5% when the voxel is larger than 3003. Micro-pores extremely improve damage of multiphase microstructures, and the transgranular cracks initiate first, and then intergranular cracks initiate due to large heterogeneity of microscopic elements between micro-pores and microscopic interfacial transition zones (ITZs) and similar strength heterogeneity of microscopic elements in micro-grains. The proposed digital-analysis framework is effective to evaluate multiphase heterogeneity effects on mechanical and cracking responses in various engineering projects. [ABSTRACT FROM AUTHOR]

• A novel fractional viscoelastic-viscoplastic (FVEVP) constitutive law is proposed. • A numerical implementation strategy of the FVEVP model by an explicit time integration scheme is proposed. • A unified progressive damage-rupture criterion is proposed. • A non-linear creep-damage-fracture kinematic-constraint-inspired non-ordinary state-based peridynamics (KC NOSBPD) formulation is proposed. • The time-dependent deformation and fracturing behaviors of intact, macrofractured, and surrounding rock mass around underground openings are reproduced. An in-depth understanding of the time-dependent deformation and failure behavior of rocks is essential for the long-term stability of surrounding rock mass around underground engineering. In this paper, the kinematic-constraint-inspired non-ordinary state-based peridynamic (KC NOSBPD) formulation is proposed to incorporate time dependence by adopting a fractional viscoelastic-viscoplastic (FVEVP) constitutive law to describe the non-linear creep deformation behavior and conjugating it with a time-independent progressive damage-rupture criterion to reproduce creep damage and subsequent creep fracture process. The FVEVP constitutive model is established by coupling a Hooke body, an Abel dashpot and a fractional viscoplastic body. Through the Grünwald-Letnikov (GL) definition of the fractional-order derivatives, finite increment formulations for the FVEVP constitutive model are derived to facilitate numerical implementation by an explicit time integration scheme. The unified progressive damage-rupture criterion is obtained by combining the damage criterion with the rupture criterion via a strain-dependent isotropic scalar damage variable. The novel model is employed to reproduce the time-dependent deformation and fracturing behaviors of intact salt rock, macrofractured sandstone specimens, and surrounding rock mass around the salt cavern gas storage. The proposed model agrees well with experimental data and numerical results from other published literature. To the authors' knowledge, the FVEVP model is first developed to simulate fracture behaviors. [ABSTRACT FROM AUTHOR]

• A MPNN based graph network is proposed to learn the rules of the physical system behind the data. • The pre-trained model has the ability of forward prediction by considering the predicted value as input. • The crack propagation prediction under loading condition is realized by introducing edge updating module. In this paper, the message passage neural networks (MPNN) based graph networks is proposed for learning and prediction of boundary loading problem in solid mechanics. As a learnable physics engine, the proposed model is designed to learn from historical data to understand the rules of the physical system behind the data, and then to make predictions. By learning the historical displacement field sampling data of 2D intact plate, the proposed model successfully realizes its continuous displacement field prediction. On this basis, the trained model also achieves a good prediction in a plate containing holes under the same loading condition but without training, which verifies the generalization ability of the proposed model. Finally, the crack propagation can be realized by learning the historical data of the plate with prefabricated cracks subjected to tension, which shows the excellent predict ability and exciting prospect of the proposed model. [ABSTRACT FROM AUTHOR]

This paper discusses the relationship between statistical mechanics and nonlocal mechanical theories. Specifically, the relationship among statistical mechanics, nonlocal vector calculus, smoothed particle hydrodynamics (SPH), and peridynamics is established. Furthermore, a general particle dynamics method is proposed to solve the solid mechanics problem based on the nonlocal vector calculus and peridynamic bond constitutive model. The proposed method is a successful nonlocal mechanics theory; the convergence of the nonlocal property is verified by numerical experiments. [ABSTRACT FROM AUTHOR]

Water existing in micro-pores has tremendous influences on the mechanical and damage characteristics of rocks. This study aims to investigate the micro-pore water effects on the mechanical and damage characteristics of sandstone subjected to different loading configurations, in which four groups of sandstone specimens with different water contents were applied in the conventional uniaxial compression, cyclic loading and unloading experiments. X-ray CT imaging and 3D reconstruction techniques are applied to capture the cracking behaviors under uniaxial compression and cyclic loading–unloading. The digital microstructural variables are defined to describe the characteristics of microstructures and evolution of micro-pore water in rocks. Numerical simulation is applied to study the micro-pore effects on the mechanical properties of rocks. Results show that the specimens are mainly failed by the mixture modes of primary shear cracks and secondary tensile cracks. With increasing mass water content, the uniaxial compressive strength (UCS) decreases and the pore size first decreases, then increases, and finally decreases due to the infiltration of water phase in microstructures. The water content has a negative effect on the mechanical properties, in which the digital porosity and volumetric water content and the micro-pore water saturation have a negative effect on the UCS. In addition, the damage becomes easier near the pores with larger sizes. [ABSTRACT FROM AUTHOR]