... and amount of shear-slip and the stress parallel to the NF wall are computed. Localized tensile stress occurs at the trailing edge of the shear-slip zone, with a logarithmic singularity which is similar to the elastic solution for a half-space subjected to a surface shear traction. The induced tensile stress...

... during propagation. The proposed method is based on the extended finite element methods with modifications to incorporate variable stress singularity at the crack tips for the transition between toughness-dominated and viscosity-dominated regimes. Moreover, a consistent enriched function is introduced...

... explanation of erratic changes in the orientation of hydraulic fracture growth. When hydraulic fractures intersect sealed natural fractures, a kink is formed in the fracture path. These kinks are the locations of stress singularity which makes them a secondary choice for fracture propagation. Results...

... rock behaviour in this region. This behaviour is necessarily non-linear because of the high stress concentration generated around the tip. ON THE SINGULAR BEHAVIOUR AT THE CRACK TIP Elasticity theory and lubrication theory are commonly used to predict the propagation of hydraulic fractures. The three...

... of the problem, analytical studies have only complemented the experimental work. Few attempts have been made to analyze the problem by the finite element method. The process being one of crack formation and progagation [3], any numerical investigation must be capable of modeling: the stress singularities...

... Reservoir Characterization displacement maximum tensile stress Upstream Oil & Gas Rock mechanics reservoir geomechanics criterion singularity geometry integration equation productivity stress field University crack tip fracture displacement field hydraulic fracturing...

... the follow- ing features: 1) the use of complex variable techniques avoids cal- culation in the region of the interface crack and 2) a more accurate description is given of singularities near corners. We feel that the present technique will accurately characterize conditions near the mouth of the initiating...

... byK or J or a related quantity) determines the magnitude of the crack tip stress singularity. When the toughness i low, as it cer tainly is in rocks, the.crack tip stresses are low on an absolute scale. However, in a rock or similar material containing fine microcracks, the "yield stress"; Y, {i.e...

... of singularities are imposed over the segments to produce traction-free conditions on the boundary elements representing the excavation surfaces. The method of analysis and the singularities used exploit the parall- elism and proximity of the boundaries 'of excavations in a tabular orebody, whiie the distributions...