SHALE SYMPOSIUM
A combined constitutive modeling approach with Continuum Damage and
Cohesive Zone methods for Mode I Fractures
H. Xu1, C. Arson1, S. Busetti2
haoxu@gatech.edu, chloe.arson@ce.gatech.edu, seth.busetti@conocophillips.com
1. School of Civil and Environmental Engineering, Georgia Institute of Technology, GA, USA
2. ConocoPhillips, Houston, TX, USA
Abstract
Hydraulic fracturing of rocks occurs when pressurized fluid enters into discontinuities and causes failure
local to the fracture tip, which in turns creates new surface area into which the pressurized fluid can
progress. Ahead of the fracture tip, cracks may propagate in the rock mass under shear or opening modes,
though Mode I tension is typically emphasized. Approaches for modeling Mode I fractures numerically
can mainly be differentiated as into continuous or discontinuous models. In continuum descriptions, such
as Continuum Damage Mechanics (CDM), an equivalent fracture is represented as a homogenized
damage zone within a volume of material (the Representative Elementary Volume, REV). The second
method is to introduce explicitly represented discontinuous surfaces into the materials, e.g., the Cohesive
Zone Method (CZM), Extended Finite Element Method (X-FEM).
The objective of this work is to use a CDM approach to predict the extent of the damage zone ahead of
CZM-based discontinuities representing mode I fractures, such as those created by fluid injection in shale.
The focus is on the mechanical problem, in which the effect of fluid pressure is accounted for by a stress
boundary condition at the surface of the fracture. Damage is modeled using the Differential Stress
Induced Damage (DSID) model (Xu & Arson, 2014), which is based on CDM and can capture the
anisotropy of rock stiffness and deformation induced by deviatoric stress variations. The DSID
parameters are calibrated for subsurface core data for North Dakota Bakken shale, based on matching
stress-strain curves from triaxial compression tests using a least square method. Finite Element
simulations performed with the calibrated DSID model are used to model the extent of the damage zone
and the degree of anisotropy ahead of a mode I fracture in a continuum with and without initial damage.
Results agree with previous studies that the width and length of the fracture relate to the extent of the
damage zone. Additionally, numerical simulations in which fractures propagate at multiple scales
simultaneously show both the mode I fracture and the damage zone evolve upon fluid injection.
Keywords: shale, mode I fracture, damage process zone, Continuum Damage Mechanics, Finite Element
Method, Cohesive Zone Method, hydraulic fracturing
References
H. Xu, C. Arson, 2014. Anisotropic Damage Models for Geomaterials: Theoretical and Numerical
Challenges, International Journal of Computational Methods, Special Issue on Computational
Geomechanics, vol.11, n.2, DOI: 10.1142/S0219876213420073