Solving Stress-Deformation Problems with Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 782

stress state variable approaches zero (Fig. 14.66b). Therefore,
the calculated elastic modulus with respect to changes in net
normal stress E becomes extremely small (and approaches
zero) at low net normal stresses (Fig. 14.66c). The elastic
modulus with respect to a change in matric suction H also
becomes extremely small at low matric suctions (or zero
suction) (Fig. 14.66c). These unrealistically small values of
elastic moduli at low net normal stress and matric suction can
result in an unstable solution in numerical modeling. As well,
the solutions may produce unreasonably large deformations.

The procedure for analysis purposes should adequately
describe void ratio changes at low net normal stresses
and matric suctions (Fig. 14.67). The equation should also
be continuous, smooth, physically reasonable, and differ-
entiable over the entire range of net normal stresses and
matric suctions. An appropriate constitutive equation needs
to include a value for void ratio at zero suction and zero net
normal stress, such as is illustrated in Fig. 14.67. Unrealis-
tic, large values of void ratio under low net normal stresses
and matric suctions need to be avoided.