Theoretical size of hydraulically induced horizontal fractures and corresponding surface uplift in an idealized medium

For the disposal of radioactive wastes by hydraulic fracturing and grout injection, it is considered essential that the induced fractures be nearly horizontal. Bottom-hole injection pressure in excess of overburden pressure has been recognized as one indication that fracturing is horizontal. The amount of uplift of the ground surface caused by the injection can be used as another indicator. For an impervious, homogeneous, isotropic medium, a mathematical model for calculating the amount of uplift of the ground surface, the maximum separation of the horizontally induced fracture at the injection well site, and the radius of extension of the fracture was developed from the basic formulas derived by I.N. Sneddon (1946) and A.E. Green (1949). If the bottom-hole injection pressure is greater than the overburden pressure, and the observed uplift is nearly the same as the calculated uplift, the fracture orientation probably is nearly horizontal. Uplifts from 9 injections made at the Oak Ridge National Laboratory, Tennessee, from 1960 through 1965, have been used to test the validity of the mathematical model. The calculations agree reasonably well with the observed data. (31 refs.)