2022/11/08 by Walsh, Joseph B., Brown, Stephen R.
#FOS: Physical sciences #Geophysics (physics.geo-ph)
paper · doi:10.48550/arxiv.2211.04221
We consider a variation of Griffith's analysis of rupture, one which simulates the process of hydrofracturing, where fluid forced into a crack raises the fluid pressure until the crack begins to grow. Unlike that of Griffith, in this analysis fluid pressure drops as a hydrofracture grows. We find that growth of the fracture depends on the ratio of the compliances of the fluid and the fracture, a non-dimensional parameter called α0 here. The pressure needed to initiate a hydrofracture is found to be the same as that derived by Griffith. Once a fracture initiates, for relatively low values of the model parameter α0 (α0 ≤ 0.2) the fracture advances spontaneously to a new radius which depends on the value of α0. For α0 ≤ 0.2 further fluid injection is required to increase the fracture radius after spontaneous growth stops. For the case where α0 > 0.2 each increment of fracture growth requires injection of more fluid. For the extreme case where α0 = 0 our results are the same as Griffith's, i.e., a fracture once initiated grows without limit.