# Hydraulic Fracture Propagation near the Cavity in a Poroelastic Media
## 1 Introduction
Another model and solution results in the problem's planar formulation of the hydraulic fracture propagation in the coal seam in the vicinity of the mines were considered in [34]. It was shown that the stress field is important because it can have a significant effect on the path of the crack under certain conditions. [PERSON] et al. applied a phase field method (PFM) to simulate the propagation of a hydraulic fracture close to the cavity, and they verified the results by comparing them with previously published experimental data that were derived from cubic samples made of concrete [35]. [PERSON] et al. investigated the effect of the condition of the excavation stress on the behavior of cracks using a flow-coupled DEM while performing single-stage and multi-stage HF [36]. The results of the numerical simulation indicated that the in situ stresses and the location of the injection have major influences on the propagation of the HF. Some papers have investigated the situation in which the path of the crack was directed from the medium towards the cavity. The relevance of the problem is associated with two main areas of research:  
* existing possibility of natural and artificial cracks emerging into the working, which can disrupt its integrity and possibly stop the underground activity;
* carbonate oil and gas reservoirs, which contain abundant natural fractures and cavities and have great potential for development via hydraulic fracturing. The behavior of a hydraulic fracture near a mine in a plane-parallel formulation was investigated in [37]. It was shown that, when the hydrostatic pressure increases with respect to critical tensile stress, the fracture begins to deviate from the mine opening earlier and does not reach its surface. [PERSON] et al. developed an extended finite element model (XFEM) for the propagation of HF in fracture-cavity reservoirs that can be used to simulate the extension of cracks in cases of a single cave and a single natural fracture [38]. The results indicated severe stress concentrations near caves, resulting in deflections of the predominant propagation direction of the crack. Another factor that can affect the trajectory of the propagation of a crack is the poroelastic properties. It was shown that the lengths and openings of cracks in a poroelasticmedium, as well as the fracturing pressure, can differ significantly from the values obtained in the elastic model [39]. It was indicated that the trajectories of cracks near the free surface in elastic and poroelastic media differ from each other [40]. A fully coupled fluid flow and geomechanics model for the growth of hydraulic fractures in the near-wellbore region was validated against the experimental results presented in [41]. [PERSON] et al. developed a poroelastic-plastic HF model that allows the estimation of the growth of fractures by considering the effects of the cohesive zone and the plastic deformation in the bulk formation [42]. [PERSON] et al. studied the effects of poroelastic properties and permeability on hydraulic fracturing in an anisotropic medium [43]. The analysis and experimental results of the initiation and propagation of tensile fractures in different pore pressure fields were presented in [44]. It was noted that the magnitude of the local pore pressure contributed directly to the energy available for the fracture. Later, [PERSON] et al. applied the RFPA2D code to simulate the hydraulic fracturing mechanism in rock and compared the results with laboratory tests [45]. [PERSON] et al. used the XFEM code for these same purposes [46]. The process of the propagation of a hydraulic fracture was simulated using different geo-stress conditions, and the effects of rock heterogeneity, the pore-fluid pressure coefficient, and the pore-pressure gradient on the occurrence of hydraulic fracturing were investigated [47]. In this paper, we investigated the development of a hydraulic fracture in a poroelastic medium that contained a circular cavity and was uniformly compressed at infinity.