Wavespeed for grouted Riser

[stanier]

Where a mine dewatering pump discharge is grouted in how does one determine the modulus from which one can determine the wavespeed (celerity). The application is a vertical mine dewatering pump discharge line running vertically through rock and grouted in position. it is presumed that the modulus will be much higher than that for the pipe material as it is basically reinforced by the rock. Is there a maximum that should be used for wavespeed?

 

[butelja]

Maximum speed will be assuming infinitely rigid pipe. The wave speed in this case is:

C = sqrt(Gamma*g_c/Rho)

Gamma = Bulk modulus of water, ~300,000 PSI
g_c = 386 lbm*in/(lbf*s^2)
Rho = Water Density 0.03611 lbm/in^3

This give C = 56,630 in/s = 4,720 ft/s

Wave speed in unreinforced schedule 40 steel pipe is slower, due to pipe elasticity. It is ~4,200 ft/s. Grouted in pipe backed by rock should be closer to the upper limit rather than the unreinforced pipe wave velocity.