Instability and Spacing of Cooling or Shrinkage Cracks

When a system of parallel equidistant cooling crack propagates into halfspace, it reaches at a certain depth a critical state at which the growth of every other crack is arrested. Later these cracks reach a second critical state at which they close. The intermediate cracks, at doubled spacing, open about twice as wide and advance further as cooling penetrates deeper. Determination of the critical states requires calculation of the derivatives of the stress intensity factors with regard to crack lengths, which is here accomplished by finite element method. It is found that the crack depth-to-spacing ratio at which the critical state is reached is extremely sensitive to the temperature profile. This ratio greatly increases as the cooling front becomes steeper. The effect of transverse isotropy of the material upon the location of critical states is found to be relatively mild. The results are of interest for one recently proposed geothermal energy scheme for hot dry rock, as well as for shrinkage cracks in concrete.