be as low as 0.1 to 0.2 at small strains, or more than 0.5.

a. The modulus of subgrade reaction, ks, is

the ratio of load intensity to subgrade deformation, or:

ks =

q

(3-18)

∆

where

q = intensity of soil pressure, pounds or

kips per square foot

∆ = corresponding average settlement,

feet

b. Values of k. may be obtained from general

order of decreasing accuracy:

(1) Plate or pile load test (chaps 4 and 12).

(2) Empirical equations (additional discussion

in chap 10).

(3) Tabulated values (table 3-6).

U. S. Army Corps of Engineers

state of effective lateral stress in situ under at-rest

Figure 3-18. Empirical correlation between friction angle

conditions can be expressed through the coefficient of

and plasticity index from triaxial compression tests on

earth pressure at rest and the existing vertical

normally consolidated undisturbed clays.

overburden pressure. This ratio is termed Ko and given

by the following:

and Poisson's ratio are often used in connection with the

σh'

=

(3-19)

Ko

elasticity theory for estimating subsoil deformations.

σv'

Both of these elastic properties vary nonlinearly with

The coefficient of at-rest earth pressure applies for a

confining pressure and shear stress. Typical values

condition of no lateral strain. Estimate values of K0 as

given below refer to moderate confining pressures and

follows:

shear stresses corresponding to a factor of safety of 2 or

more.

Normally consolidated soil

a. In practical problems,

stresses before

Sand:

loading are generally anisotropic.

It is generally

K0 = 1 - sin φ`

(3-20)

considered that the modulus of elasticity is proportional

Clay:

to the square root of the average initial principal stress,

K0 = 0.95 - sin φ'

(3-21)

which may usually be taken as

Figure 3-21 may be used for estimates of K0 for both

normally consolidated and overconsolidated soils in

)

(

σv'

1/2

1 + 2K0

(3-16)

terms of PI. For overconsolidated soils, this figure

3

applies mainly for unloading conditions, and reloading

may cause a large drop in K0 values. For soils that

where K0 is the coefficient of at-rest earth pressure (para

display high overconsolidation ratios as a result of

3-10) and δv' is the effective vertical stress. This

desiccation, K0 will be overestimated by the relationship

proportionality holds for 0.5 < K0 < 2, when working

shown in figure 3-21.

stresses are less than one-half the peak strength.

b. The undrained modulus for normally

consolidated clays may be related to the undrained shear

and uniaxial compressive strength of various intact rocks

strength, su, by the expression

are shown in table 2 -7.

E

= 250 to 500

(3-17)

Behavioral

su

characteristics of shales are summarized in table 3-7;

where su is determined from Q tests or field vane shear

and physical properties of various shales, in table 3-8.

tests. The undrained modulus may also be estimated

Analyses of observed in situ behavior provide the most

from figure 3-20. Field moduli may be double these

reliable means for assessing and predicting the behavior

values.

of shales.

c. Poisson's ratio varies with strain and may

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