A simplified multiscale damage model is proposed for the transversely isotropic shale rocks under tensile loading. In this framework, the multiscale representations for the shale rocks are presented by introducing the microcrack-weakened equivalent solid with hierarchical microstructures, whose transversely isotropic properties are obtained by performing multilevel homogenization procedures. To simplify the calculation process for the damage-induced properties, the equivalent isotropic medium is attained by applying the Voigt–Reuss–Hill averaging process to the transversely isotropic solid. Subsequently, the microcrack-induced inelastic compliances are approximately derived in terms of microcrack opening displacements in the equivalent isotropic medium of the shale rock under tensile loading. The sizes and orientations of microcracks are taken as random variables. Both stationary and evolutionary damage models are considered. Microcrack kinetic equations are characterized through the use of a fracture mechanics-based stability criterion and microcrack geometry within a representative volume element. Numerical examples including experimental validations and comparisons with existing micromechanical models are presented to verify the proposed multiscale damage model. Finally, the influences of the silt inclusions and porosity on the material intrinsic and damage-induced properties are discussed.

In this paper, the mechanical performance of an ultra-high-performance concrete (UHPC) repaired cementitious composite system, including the old matrix and the new reinforcement (UHPC), under various high temperature levels (20 °C, 100 °C, 300 °C, and 500 °C) was studied. In this system, UHPC reinforced with different contents of steel fibers and polypropylene (PP) fibers was utilized. Moreover, the physical, compressive, bonding, and flexural behaviors of the UHPC repaired system after being exposed to different high temperatures were investigated. Meanwhile, X-ray diffraction (XRD), baseline evaluation test (BET), and scanning electron microscope (SEM) tests were conducted to analyze the effect of high temperature on the microstructural changes in a UHPC repaired cementitious composite system. Results indicate that the appearance of the bonded system changed, and its mass decreased slightly. The average percentage of residual mass of the system was 99.5%, 96%, and 94–95% at 100 °C, 300 °C, and 500 °C, respectively. The residual compressive strength, bonding strength, and flexural performance improved first and then deteriorated with the increase of temperature. When the temperature reached 500 °C, the compressive strength, bonding strength, and flexural strength decreased by about 20%, 30%, and 15% for the UHPC bonded system, respectively. Under high temperature, the original components of UHPC decreased and the pore structure deteriorated. The cumulative pore volume at 500 °C could reach more than three times that at room temperature (about 20 °C). The bonding showed obvious deterioration, and the interfacial structure became looser after exposure to high temperature.

A stochastic micromechanical framework is proposed to quantitatively characterize the probabilistic behavior of the mechanical performance of the saturated concrete healed by the electrochemical deposition method. Micromechanical model for the healed saturated concrete is presented based on the material microstructures, and new multilevel homogenization procedures are proposed to quantitatively predict the effective properties of the repaired concrete considering the inter-particle interactions. The evolutions of the deposition products are characterized by non-stationary random process, which is represented by Karhunen–Loeve approximations with limited random variables. The probabilistic behavior for the effective properties of the repaired concrete is reached by incorporating the maximum entropy principle and Monte Carlo simulations. The predictions obtained by the proposed stochastic micromechanical framework are then compared with the available experimental data, existing models, and commonly used probability density functions, which indicate that the presented stochastic micromechanical framework is capable of describing the electrochemical deposition method healing process, considering the inherent randomness of the material microstructures. Finally, the influences of the deposition products on the probabilistic behavior of the repaired concrete are discussed on the basis of the proposed models.