Near tip processes of fluid-driven fractures

The focus of the thesis is on constructing the solution of both semi-infinite and a finite fluid-driven cracks propagating in an impermeable linear elastic medium of arbitrary toughness. The tip region of a hydraulic fracture propagating in a permeable saturated medium is also considered under certain limiting conditions.;First, we consider a semi-infinite fluid-driven fracture and seek a solution which accounts for the presence of a lag of unknown length between the fluid front and the crack tip. It is shown that the solution is not only consistent with the square root singularity of linear elastic fracture mechanics, but that its asymptotic behavior at infinity is given by the singular solution of a semi-infinite hydraulic fracture. The asymptotic solution for large dimensionless toughness is derived, including the explicit dependance of the solution on the toughness. The intermediate part of the solution of the problem in the general case is obtained numerically and relevant results are discussed, including the universal relation between the fluid lag and the toughness.;Then we use this solution of the semi-infinite crack to build a consistent solution of a finite two-dimensional fluid-driven fracture propagating in an impermeable solid of non-zero toughness. The solution is constructed in the spirit of a singular perturbation technique based on the presence of three different lengthscales in the problem of finite fracture. The lengthscale L;Finally, we have analyzed the problem of the tip region of a hydraulic fracture propagating steadily in a permeable elastic region. We have shown that a consistent solution for the near-tip cavity can be constructed that simultaneously satisfies the diffusion equation in the permeable rock, the equations of linear elastic fracture mechanics, and the lubrication theory for the flow of pore fluid in the cavity. The solution indicates that circulation of pore fluid takes place between the rock and the tip cavity.(Abstract shortened by UMI.).