Subsidence Induced by Fossil Fuel Extraction - Environmental Geomechanics - page 173

S

SI f

3

SI i

2

LC i

LC f

1

P

Figure 7.4. Coupling between SI and LC

One of the strong points of this model is the coupling between SI and LC. The
model supposes that an increase in SI leads to a movement of LC, but not
reciprocally (see Figure 7.4). This makes it possible to describe the effect of suction
on the increase in the mechanical strength of soils observed experimentally. For the
mathematical formulation, this coupling is introduced in the following two
hardening laws:

dp

*
0

v p

v

= d ε

[7.2]

*
0

p λ − ( 0 κ

dS v

0 p

vs

= d ε

[7.3]

( )

S + P λ− κ

0 atm s s

where p 0 * is the pressure of preconsolidation (yield stress in terms of stresses) in a
saturated state (null suction), S 0 is the maximum suction encountered by the soil
(yield stress in terms of suctions), d ε v p is the total plastic volumetric strain, d ε vs p is
the plastic volumetric strain due to suction, P atm is the atmospheric pressure, λ(0) is
the coefficient of compression at zero suction, λ s is the coefficient of compression
related to suction, κ is the elastic coefficient, and κ s is the elastic coefficient related
to suction. Considering that the plastic volumetric strain due to stress is dε vp p , the
total plastic volumetric strain can be written as:

[7.4]

p
v

p
vp

p
vs

d ε = d ε + d ε