Wave Velocity by Dynamic Loading 



The stress conditions of a loaded elastic medium build up according to its 

 stiffness and mass: 



c = (^) , (1) 



where 



c = wave velocity 

 E = young modulus 

 y - mass density. 



For usual soil types, the mass densities are relatively stable. Therefore, the 

 variations of the soil properties affecting the soil modulus E would be expected to 

 influence wave velocities. It should be noted that the applicability of an elastic 

 theory to soil may be seriously questioned; yet, any system of particles may be 

 considered elastic within the following limitations: (1) the volume of the specimen 

 must be large in comparison to individual particle dimensions; (2) the stresses and 

 strains considered average and small in value; and (3) the sample must be essentially 

 isotropic. The wave velocity noted in Eq. (1) may be longitudinal or transverse. 

 The longitudinal may be either a dilatation wave caused by a fully constrained sample 

 or a rod wave for which deformation is allowed laterally. The transverse waves 

 are shear waves and are slower. A second theoretical equation relates the resonant 

 frequency of a mass to wave velocity and soil modulus: 



v¥ . 



c = 4 L fn - \ ^ , (2) 



where 



fn = resonant frequency 

 L - length of sample 



And finally we arrive at the correlation of the various moduli 



1 



2 (1 + v) 



E (3) 



M = ^^^^^ E (4) 



(1 + v) (1 - 2v) 



383 



