Constricting effect of bridges in hydraulic fracturing

Bridges which are unbroken materials connecting the opposite fracture faces usually exist in the hydraulic fractures as well as other cracks in geomaterials. The distribution of bridges is often over the entire fracture and the capability of bridges is restriction of fracture opening. Our laboratory experiments show that the bridges can even hold the sample in one piece after the hydraulic fractures traversed the sample. This kind of fracture can be modelled as a crack with Winkler layer. The stiffness of the Winkler layer is dictated by the geometry and distribution of bridges. It is shown by our model that only large fractures whose size are of the order of the characteristic scale of the bridge constriction are affected while the short-constricted fractures are similar to the conventional cracks. The characteristic scale of constriction is inversely proportional to the equivalent stiffness of bridges. The fracture opening and the Mode I stress intensity factor of constricted fracture are bounded as the fracture dimensions proportionally increase. This is fundamentally different from the conventional cracks in which both the fracture opening and the stress intensity factors tend to infinity with increasing crack size.