Instability of Parallel Thermal Cracks and its Consequences for Hot-Dry Rock Geothermal Energy

Review of recent work on instabilities of crack systems and applications to the hot-dry rock geothermal energy scheme is presented. The basic variational formulation of the crack stability problem is outlined and the critical states of a system of parallel equidistant cooling cracks propagating into a halfspace are explained and analyzed. The solution, which shows that at a certain critical crack length-to-spacing ratio every other crack suddenly jumps ahead at constant temperature while the remaining cracks stop growing and subsequently close, determines the crack width and is of importance for heat withdrawal from hot rock by circulation of water in cooling cracks. Some typical numerical results obtained by finite elements are presented and the effect of the temperature drop profile on the critical crack length is discussed. Finally, some other applications, such as parallel cooling cracks or drying shrinkage cracks in reinforced solids, such as concrete, are pointed out.