The use of the Smoothed Particle Hydrodynamics (SPH) method is relatively recent for geomechanics problems. The meshless nature of the SPH method has the potential to overcome the difficulties of mesh-based methods. In this paper, an attempt has been made to develop a numerical procedure for the SPH method which enables integrated simulation of pressure driven hydraulic fracture (HF) propagation, including consideration of natural fracture (NF) interaction. In this procedure, a NF plane or joint plane is approximated by straight line segments connected by a discrete set of joint particles. The jump in the velocity field and the surface traction, due to the discontinuity, are determined using joint stiffness properties on these joint particles. Joint points follow a Mohr–Coulomb friction law with a zero tension cutoff for modelling joint opening or shear behavior of the NF plane. For HF initiation and propagation in the continuous part of the domain, the model relies on the Drucker-Prager plasticity surface to predict the dilatancy aspect of the material response, and the Grady-Kipp damage model for tensile strain. This paper presents three numerical examples to show the capabilities of the proposed procedure for simulating HF-NF interaction. The first example deals with an internally pressurized circular hole under in-situ stress conditions, the second considers failure of a jointed circular rock sample, and last shows internally pressurized circular hole in the presence of a NF.


Hydraulic fracturing in rock material is a highly complex process, where this complexity is further compounded by the interaction between pre-existing discontinuities such as a natural fracture networks, faults, and bedding planes. The propagation of a hydraulic fracture (HF) can be either arrested or redirected by a natural fracture (NF), where either case will lead to reactivation of the natural fracture. There are two big challenges in predicting the resultant HF network. First, the natural discontinuity planes have to be identified in terms of geometric and mechanical properties. Second, an understanding of the mechanical deformation of rocks due to pressure driven fracture initiation, and propagation, in the presence of an in-situ stress state is required. Moreover, the interaction between the HF and NF could cause dilation of the NF either in shear or tension. Numerical simulation of hydraulic fracturing is an economical and efficient technique for understanding these complex phenomena. Mesh-based continuum methods have the advantage of using classical nonlinear material models, however they do not always work well in a complex medium involving large deformation, multiple intersecting fractures and their interactions with pre-existing discontinuities. In particular, special treatments and assumptions have to be made for modelling fracture propagation, closing of an opened fracture and shear, which introduce numerical and geometric complexities in the implementation and lead to degradation of accuracy.

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