G = ρVs

2

(1) A problem in using seismic methods to

(17-19)

obtain elastic properties is that any induced elastic pulse

where

ρ

(blast, impact, etc.) develops three wave types previously

=

y/32.2 = mass density of soil using

discussed, i.e., P-, S-, and R-waves. Because the

wet or total unit weight

velocity of all seismic waves is hundreds of feet per

Vs =

S-wave velocity (or R-wave), feet per

second and the pickup unit detects all three wave pulses

second

plus any random noise, considerable expertise is

This equation is independent of Poisson's ratio. The Vs

required to differentiate between the time of arrival of the

value is taken as representative to a depth of

wave of interest and the other waves. The R-wave is

approximately one-half wavelength. Alternatively, the

usually easier to identify (being slower, it arrives last;

shear modulus can be computed from the P-wave

traveling near the surface, it contains more relative

velocity and Poisson's ratio from:

energy). Because R- and S-wave velocities are relatively

p( 1 - 2)Vp

2

(17-20)

G=

close, the velocity of the R-wave is frequently used in

2(1- )

computations for elastic properties.

The use of this equation is somewhat limited because

(2) Because amplitudes in seismic survey

the velocity of a P-wave in water is approximately 5000

are very small, the computed shear and Young's moduli

feet per second (approximately the velocity in many

are considerably larger than those obtained from

soils) and Poisson's ratio must be estimated. For

conventional laboratory compression tests.

saturated or near saturated soils, - 0.5. The theoretical

(3) The shear modulus, G, may be

variation of the ratio Vs/Vp with is shown in figure 17-8.

calculated from the S- (approximately the R-wave) wave

velocity as follows:

U. S. Army Corps of Engineers

Figure 17-8. Theoretical relation between shear velocity ratio Vp/Vs and Poisson's ratio.

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