Measurement of Properties - Geotechnical Engineering Investigation - page 175

level ground are illustrated in Figure 3.19; sloping ground results in more complex condi-
tions. (Changes in geostatic stresses are invoked by surface foundation loads, surface and
subsurface excavations, lowering of the groundwater level, and natural phenomena such
as erosion and deposition). Vertical earth pressures from overburden weight alone are
found by summing the weights from the various strata as follows:

z
0 γ n Z n

σ v

(3.13)

Coefficient of lateral earth pressure “at-rest” K 0 is the ratio of the lateral to vertical stress in a
natural deposit that has not been subject to lateral strain, the values for which vary sub-
stantially with material types and properties (see Section 3.4.2) . It is expressed as

K 0 σ h / σ v (3.14)

or

σ h K 0 σ v (3.15)

For an elastic solid

K 0 ν /1 ν (3.16)

In the above expressions, γ is the material unit weight ( γ n above groundwater level, γ b

below groundwater level) and ν is the Poisson's ratio (see Section 3.5.1) .

Total and Effective Stresses
The total stress on the soil element in Figure 3.19 at depth z is

σ v γ t Z (3.17)

If the static water table is at the surface, however, and the soil to depth z is saturated, there
is pressure on the water in the pores because of a piezoelectric head h w and the unit weight
of water

γ w . This is termed the neutral stress (acting equally in all directions), or the pore-
water pressure u w or u and is given as

u σ w h w (3.18)

The effective stress σ v , or actual intergranular stresses between soil particles, results from

a reduction caused by the neutral stress and is equal to the total stress minus the pore-
water pressure, or

σ v σ v u (3.19)

∞

z 1

1

z

z 2

2

z 3 σ v

3

K 0 z

σ h σ h

FIGURE 3.19
The geostatic stress condition and “at-rest” earth
pressures.

σ v