| Description |
Elastic deformation of strata is investigated using theory. Transverse shear, horizontal stress, strata clustering, and dynamic loading are considered using elementary theory. Body force loading and material anisotropy are considered using elastic theory. These analyses are used to estimate critical span and critical strain energy in strata under three different support conditions. Larger strata heights, tensile strengths, and densities increase critical span and critical strain energy. Lower Young's moduli and Poisson's ratios increase strain energy. In general, because increasing Young's modulus is correlated to increasing tensile strength, increasing Young's modulus is indirectly related to increasing critical strain energy. High compressive horizontal stress and strata clustering, where strata interfaces are bonded, have dramatic impacts on increasing both critical span and critical strain energy. Horizontal tensile stress decreases critical span and increases critical strain energy. Dynamically loaded strata have lower critical spans and critical strain energies compared to strata that are statically loaded. The results of the body force analysis differ from the distributed load analysis only with respect to the normal stress in the 3-direction. Elasticity analysis using a transversely anisotropic material model indicated that for weak anisotropy solutions are negligibly different. Mechanics modeling using FLAC is conducted. This analysis is used to validate critical span and critical strain energy estimates provided by theory. Tensile failure by three-point loading in a sandstone is investigated. Petrographic analysis indicates the sandstone is quartz arenite, which is texturally mature. Ultrasonic testing is conducted to estimate wave velocities. These tests indicate that the texturally mature sandstone has isotropic material properties. Cross correlation of fracture wave records is used to locate fractures in specimens. Estimates of critical strain energy, fracture energy, and seismic energy in sandstone specimens are made. Lower bound estimates for seismic energy are made from signal processing of fracture wave records. Upper bound estimates for seismic energy are made indirectly from fracture testing. The range of estimated seismic energies does not discount the possibility frictional energy is negligible in tensile failure in strata. |
