0 = 1/3 (1 + 2 + s) = mean normal effective stress, pounds per

square inch

(1) For sands and gravels, calculate the low-strain shear modulus as follows:

G = 1000(Ks)(0)0.5 (pounds per square foot)

(12-24)

where

K2 = empirical constant (table 12-5)

= 90 to 190 for dense sand, gravel, and cobbles with little clay

0 = mean normal effective stress as in equation (12-23) (but in units of

pounds per square foot)

(2) For cohesive soils as clays and peat, the shear modulus is related to Su as

follows:

G = K2su

(12-25)

For clays, K2 ranges from 1500 to 3000. For peats, K2 ranges from 150 to 160

(limited data base).

(3) In the laboratory, the shear modulus of soil increases with time even when all

other variables are held constant. The rate of increase in the shear modulus is

approximately linear as a function of the log of time after an initial period of about

1000 minutes. The change in shear modulus, ∆G, divided by the shear modulus

at 1000 minutes, G1000, is called the normalized secondary increase. The

normalized secondary increases ranges from nearly zero percent per log for

sensitive clays. For good correlation between laboratory and field measurements

of shear modulus, the age of the in situ deposit must be considered, and a

secondary time correction applies to the laboratory data.

12-1.5.5

cc = 2√km

(12-26)

Where k is the spring of vibrating mass and m represents mass undergoing vibration

(W/g). Viscous damping of all soils at low strain-level excitation is generally less than

about 0.01 percent of critical damping for most soils or:

D = c/cc ≤ 0.05

(12-27)

It is important to note that this equation refers only to material damping, and not to

energy loss by radiation away from a vibrating foundation, which may also be

conveniently expressed in terms of equivalent viscous damping. Radiation damping in

12-20

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