Effect Of Initial Stress Field Research Articles

Transverse penny-shaped hydraulic fracture propagation in naturally-layered rocks under stress boundaries: A 3D phase field modeling

The ground (tectonic) stress and layered structures of rocks are the among the main factors that influences the hydraulic fracturing behavior. The purpose of this study is to examine the suitability of the phase field model (PFM) in simulating transverse penny-shaped hydraulic fracture propagation and to investigate the phase field feature for the transverse penny-shaped hydraulic fracture in layered rocks under stress boundaries. A phase field model for 3D transverse penny-shaped hydraulic fracture propagation in naturally-layered rocks considering the effect of initial stress field is established. The mathematical model is based on Biot poroelasticity theory and the phase field fracture theory, while the governing equations are solved by using the finite element method in a staggered manner. The established PFM is validated experimentally and analytically by 2D and 3D examples. At last, the influences of the initial stress field, stiffness contrast and inclination angle of the layer interface on the penny-shaped fracture evolution in naturally-layered rocks are investigated by using the PFM. The study indicates that the phase field model has excellent feasibility and practicability in predicting penny-shaped hydraulic fractures. The layer inclination has nearly no effect on the penny-shaped fracture evolution in naturally-layered rocks. The stress ratio Sv/Sh on the boundaries has a significant effect on propagation of the penny-shaped hydraulic fracture. With the increase in Sv/Sh, the hydraulic fracture deflects and propagates along the direction of the maximum in-situ stress. For a high Sv/Sh, branching scenarios can be observed. The stiffness contrast of the rock layers determines whether the penny-shaped hydraulic fracture can penetrate into the adjacent layer. The predictions on the effects of the initial stress field, stiffness contrast and inclination angle of the layer interface provide new understanding of penny-shaped hydraulic fracture propagation in underground geological environment.

Effects of Initial Stress Field and Critical Slip-Weakening Distance on Rupture Selectivity of 3D Buried Branched Faults

ABSTRACTUsing the boundary integral equation method with the slip-weakening friction law, we investigate the effects of the initial stress field and the critical slip-weakening distance on the rupture selectivity on the 3D buried branched faults. The numerical results show that after reaching the bifurcation line between the main fault and the branched faults, rupture continues to propagate on one or both bifurcation planes (BPs), with rupture on one plane more favorable than the other. The initial stress distribution plays a decisive role in the selection of the favorable BP (FBP), and there is a critical status of stress distribution, around which rupture propagates on both planes, whereas the FBP switches between the two. For a given fault geometry, the critical status of initial stress, which is described by a ratio Fp between normal stresses, is related to the critical slip-weakening distance Dc.

Phase field method for quasi-static hydro-fracture in porous media under stress boundary condition considering the effect of initial stress field

Phase field model (PFM) is an efficient fracture modeling method and has high potential for hydraulic fracturing (HF). However, the current PFMs in HF do not consider well the effect of in-situ stress field and the numerical examples of porous media with stress boundary conditions were rarely presented. The main reason is that if the remote stress is applied on the boundaries of the calculation domain, there will be relatively large deformation induced on these stress boundaries, which is not consistent with the engineering observations. To eliminate this limitation, this paper proposes a new phase field method to describe quasi-static hydraulic fracture propagation in porous media subjected to stress boundary conditions, and the new method is more in line with engineering practice. A new energy functional, which considers the effect of initial in-situ stress field, is established and then it is used to achieve the governing equations for the displacement and phase fields through the variational approach. Biot poroelasticity theory is used to couple the fluid pressure field and the displacement field while the phase field is used for determining the fluid properties from the intact domain to the fully broken domain. In addition, we present several 2D and 3D examples to show the effects of in-situ stress on hydraulic fracture propagation. The numerical examples indicate that under stress boundary condition our approach obtains correct displacement distribution and it is capable of capturing complex hydraulic fracture growth patterns.

The effect of gravity and hydrostatic initial stress with variable thermal conductivity on a magneto-fiber-reinforced

The present paper is concerned at investigating the effect of hydrostatic initial stress, gravity and magnetic field in fiber-reinforced thermoelastic solid, with variable thermal conductivity. The formulation of the problem applied in the context of the three-phase-lag model, Green-Naghdi theory with energy dissipation, as well as coupled theory. The exact expressions of the considered variables by using state-space approaches are obtained. Comparisons are performed in the absence and presence of the magnetic field as well as gravity. Also, a comparison was made in the three theories in the absence and presence of variable thermal conductivity as well as hydrostatic initial stress. The study finds applications in composite engineering, geology, seismology, control system and acoustics, exploration of valuable materials beneath the earth's surface.

Numerical Simulation for Thermal Shock Resistance of Ultra-High Temperature Ceramics Considering the Effects of Initial Stress Field

Taking the hafnium diboride ceramic as an example, the effects of heating rate, cooling rate, thermal shock initial temperature, and external constraint on the thermal shock resistance (TSR) of ultra-high temperature ceramics (UHTCs) were studied through numerical simulation in this paper. The results show that the external constraint has an approximately linear influence on the critical rupture temperature difference of UHTCs. The external constraint prepares a compressive stress field in the structure because of the predefined temperature field, and this compressive stress field relieves the tension stress in the structure when it is cooled down and then it improves the TSR of UHTCs. As the thermal shock initial temperature, a danger heating rate (or cooling rate) exists where the critical temperature difference is the lowest.