Solution of a plane hydrofracture problem with stress contrast

A plane hydrofracture problem for the Khristianovich–Geertsma–de Klerk model is extended and solved in the case where a confining stress closing a fracture is not constant in the direction of its propagation. A method is developed for solving the problem with an arbitrary stress contrast. It is stated that the transition through a contact with positive (negative) contrast occurs with fracture arresting (acceleration), whose intensity is controlled by a dimensionless parameter derived from theoretical considerations and numerical results