Page 182 - Buried Pipe Design

156 Chapter Three

Enhanced soil model. The Duncan soil model, as described in previous
section, was developed to model deformation characteristics of soil as
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the confining pressure of the soil increases. Duncan et al. gave a brief
account of the behavior of soil on unloading and reloading. The Duncan
soil model could accommodate unloading and reloading by identifying
the elastic modulus constant K (defined previously) as the unloading
and reloading modulus. A typical stress-strain curve of soil which has
undergone primary loading, unloading, and reloading is shown in
Fig. 3.43. It can be seen that the soil does not unload to a zero strain as
the stress decreases and that the unloading tangent modulus of elastic-
ity (slope of the unloading stress-strain curve) is much higher than
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the slope of the primary loading curve. Duncan et al. indicated that the
unloading modulus is independent of stress level. Thus, the slope of the
unloading stress-strain curve will not change if unloading is performed
at any point on the primary stress-strain curve. They also indicate that
the unloading modulus is dependent only on confining pressure and the
bulk modulus is not a function of the stress history of the soil.
The equation that relates the unloading-reloading modulus to other
soil properties is

E = K P a ⎜ ⎛ 3 ⎞ n
ur ur ⎝ P ⎠ ⎟ (3.43)
a

where K is the unloading-reloading constant and E is the unloading
ur
ur
reloading modulus.

s 3 n
– E = K ur P a s 3
ur
s 1 P a

Figure 3.43 Unloading-reloading modulus. (After
Duncan et al. 6 )