Is there a relation between concrete strength and wave speed? How can I determine the minimum acceptable wave speed?

Based on information reported in American Concrete Institute (ACI) 228.1 and some other codes and specifications, the concrete compressive strength is approximately proportional to the compression wave velocity to the 4th power. This means that, if σ is the concrete strength, W is the wave speed, and k₁ and k₂ are constants: σ = k₁ × W⁴ or W = k₂× σ^1/4 Those relationships can be used to compare the strength and wave speed of concretes with a similar mix. The following table might offer a rough guide:

fc	wave speed	fc	wave speed
psi	ft/sec	MPa	m/sec
2000	9,249	13.8	2,819
3000	10,235	20.7	3,120
4000	10,999	27.6	3,352
5000	11,630	34.5	3,545
6000	12,172	41.4	3,710
7000	12,650	48.3	3,856
8000	13,080	55.2	3,986
9000	13,470	62.1	4,106
10000	13,830	69.0	4,215

Suppose the minimum acceptable strength for the concrete of a drilled shaft project is σA. Also suppose that on a given shaft on that project you determine a wave speed W_M (by performing a Pile Integrity Test or by Cross Hole Sonic Logging) and measure a strength σ_M (by extracting a cylinder, for example). A relationship may be established for the minimum acceptable wave speed on other drilled shafts on the same project, WA, as follows: W_A = W_M (σ_A / σ_M)^1/4