RESEARCH OF INTERACTIONS BETWEEN SHEAR FRACTURES ON THE BASIS OF APPROXIMATE ANALYTICAL ELASTIC SOLUTIONS
The article describes a method yielding approximate analytical solutions under the theory of elasticity for a set of interacting arbitrarily spaced shear fractures. Accurate analytical solutions of this problem are now available only for the simplest individual cases, such as a single fracture or two collinear fractures. A large amount of computation is required to yield a numerical solution for a case considering arbitrary numbers and locations of fractures, while this problem has important practical applications, such as assessment of the state of stress in seismically active regions, forecasts of secondary destruction impacts near systems of large faults, studies of reservoir properties of the territories comprising oil and gas provinces. In this study, an approximate estimation is obtained with the following simplification assumptions: (1) functions showing shear of fractures' borders are determined similar to the shear function for a single fracture, and (2) boundary conditions for the fractures are specified in the integrated form as mean values along each fracture. Upon simplification, the solution is obtained through the system of linear algebraic equations for unknown values of tangential stress drop. With this approach, the accuracy of approximate solutions is consistent with the accuracy of the available data on real fractures. The reviewed examples of estimations show that the resultant stress field is dependent on the number, size and location of fractures and the sequence of displacements of the fractures' borders.