Ranking first in the world, China is rich in the shale-gas reserves. The development of unconventional energy sources including shale gas is one of the national major projects. However, shale-gas reservoirs in China are of low porosity and permeability, making it much harder to exploit in China than in other countries. Effective hydraulic fracturing technology is required to improve the permeability of the shale gas in rocks. One of the basic problems in the development of shale-gas reservoirs is to form a large-scale crack network in shale by using the hydraulic fracturing technology. Hydraulic fracturing is a strongly non-linear solid-liquid-interface problem. In view of mechanics, Understanding the crack growth behaviors is essential to control the crack path and to reasonably design fracturing treatments. Even if the rock is modeled as an isotropic, homogeneous, impermeable and elastic full space, multi-scale problems are formed in light of the coupling between the fracture of rock and the flow of viscous fracturing fluid. Dominant-regime transitions, stress singularity alteration, the variation of the fluid-lag zone, moving contact line and high crustal stress increase the difficulty of solving this problem.

In this context, adopting theoretical analysis and numerical calculations, this dissertation focuses on two key academic issues: the crack growth behaviors of hydraulic fracturing with considering the full-stress coupling at the solid-liquid interfaces; the asymptotic properties of the solid-liquid interfaces, the stress singularities and fluid-lag zone near the crack tip.

A full-stress model is established to account for the combined effect of pressure and flow-induced shear stress at the solid-fluid interfaces. The fracturing fluid is modeled with a power-law rheology. Only pressure is considered at the solid-liquid interface in traditional hydraulic fracturing models. But it is proved the singularity of shear stress is stronger than that of the pressure, and the effect of shear stress is much underestimated when the laboratory-measured viscosity is used in the design of hydraulic fracturing. This model provides a more accurate scheme for the design and simulation of hydraulic fracturing.

It is clarified the dominant-regime transition and stress singularity alteration with a power-law fracturing fluid. From the perspective of time, dominant-regime transitions of the full-stress model and the corresponding dimensionless control parameters are obtained through the scale analysis. From the perspective of space, the stress singularity is obtained by using the asymptotic analysis, and the crack propagation criteria are further discussed and modified.

Shear-stress-dominant regime is discovered. The competition among shear stress, pressure, crustal stress, and surface tension near the crack tip is represented by the dimensionless parameters. The shear-stress-dominant regime appears in the initial stage of crack growth. In this regime, it is found, through the asymptotic analysis, that the assumption that the crack grows continuously and straightly is contrary to the crack propagation condition, and the growth of a hydraulic fracturing crack may be unstable. This phenomenon is validated and the instability criterion is obtained through the high-precision numerical scheme developed in this work.

The size of the fluid-lag zone at the crack tip is estimated and its effect on hydraulic fracturing is discussed. The ratio of the fluid-lag zone to the crack length decreases gradually in the fracturing process due to the in-situ stress, and a characteristic crack length is derived for the fluid-lag zone being negligible. The size is estimated under the condition for there being either a crustal stress or not. A numerical scheme for the full-stress model with a fluid-lag zone is developed, and the scheme does not rely on the initial conditions. With this numerical scheme, unstable crack growth is found indicating that the shear-stress-dominant regime is still applicable to the problem with a fluid-lag zone.

In this dissertation, the changes and mechanisms of the stress singularity and the solid-liquid interface near the crack tip are systematically explored during the hydraulic fracturing process. This study provides a theoretical basis for solving the basic problems in the shale-gas exploitation and controlling the crack propagation. Potential theoretical guidance is provided for the design of hydraulic fracturing treatments.