Identification of stresses acting in a plane (homogeneous and isotropic) elastic domain is performed based on the analysis of principal stress trajectories. This problem, originated in photoelasticity, is now of great importance in geodynamics. Given stress trajectories, in photoelasticity stresses are found by solving a certain boundary value problem. We propose the solution of the problem without appealing to boundary conditions, which is advantageous to geodynamics where boundary stresses are poorly constrained. The analysis of the given stress trajectory pattern is equivalently reduced to the investigation of the argument, α, of the complex-valued bi-holomorphic function, D, which represents the stress deviator of the 2D stress tensor. Necessary and sufficient conditions for the stress trajectory pattern to be admissible in elasticity are established. A procedure to obtain a particular solution, D1, is presented. The general solution for D derived from D1 depends on four (if α is a harmonic function) or one (otherwise) arbitrary real constants. The procedure is illustrated by model examples for West European and Australian platforms.
Formation of thin macrofractures and high porosity bands parallel to the compression axis in the unconsolidated sedimentary rocks is treated on the basis of unified approach by considering migration of microdefects (pores) with respect to particles of the medium. The migration of pores is driven by a common cause, namely, a trend of a system to lower its total energy. The mechanism of how discontinuities develop along the maximum compressive stress Tmax is discussed and quantitatively investigated. A single pore splits into two separate holes which move away along the Tmax axis. The trace left by moving hole is interpreted as a macro-discontinuity. Multiple pores migrate so that they form a system of chains extending along the Tmax axis. We associate these chains with observed high porosity bands.
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