Maybe be you should use one of those closed form solutions available in Bowles, for example, and use an E_r, or elastic modulus of rock mass instead of E_s, secant elastic modulus of cohesionless/cohesive soils.
Also, a rock mass elastic modulus may be derived by the velocity of shear waves and that's most useful when you don't have a rock outcrop where you can carry out structural surveys.
Whenever I've done that, even very fractured rocks yield high values of the spring constant, so much so that rock can be usually considered a rigid constraint, unless of course loadings are very substantial