where 



G = modulus of elasticity in shear 



V = Poisson's ratio (0. 5 for fully saturated soils under dynamic loading) 

 M = constrained modulus of elasticity. 



Equipment 



The longitudinal wave vibration apparatus is used to determine the soil 

 modulus by utilizing a resonant frequency technique. The wave forms are displayed 

 on the oscilloscope. 



For the torsional wave vibration apparatus, Fig. 3, a loudspeaker is me- 

 chanically attached to rotate a pedestal in torsion. The sample is placed on the 

 pedestal and phonograph cartridge pickups are placed in contact with the top and 

 bottom of the sample and connected to the oscilloscope. The resonant frequency in 

 shear is obtained by varying the frequency to obtain the maximum torsional displace- 

 ment output in comparison to the input. 



Results and Discussion 



a. Dry Ottawa Sand 



From a test series on dry Ottawa sand, the variation of longitudinal 

 wave velocity with confining pressure, void ratio, length-diameter ratio and lateral 

 constraint was determined. 



In each test, the Ottawa sand was confined in a thin rubber membrane, 

 and sound velocities were determined as shown in Fig. 4. This series of tests also 

 revealed the reduction in velocity due to increased side friction of the longer samples. 

 (A separate short study of sound velocities in samples confined in steel tubes with 

 varying degrees of skin roughness also confirmed the fact that wave propagation is 

 reduced by side friction. ) 



Curve "C" represents an Ottawa sand sample confined in a rather stiff 

 rubber tube within the air chamber. This might be considered anisotropic consoli- 

 dation with resultant reduction in velocity. 



Some of the specimens were tested first at high pressure and later at 

 low pressures with little correlation to the virgin pressure-velocity line. This 

 undoubtedly reflects the over-consolidation effects found in consolidation and shear 

 tests. 



384 



