Geoscience Reference
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in Eq. (13.18), fourth order fabric tensors in the incremental constitutive equations in
Eqs. (13.19) and (13.20) (Iai, 1993). Evolution of these fabric tensors is governed by
the collective effects of the multiple mechanisms specified by Eqs. (13.21) and (13.22).
An example of evolution of fabric tensors during rotation of principal stress axes can be
found in Iai et al. (1994).
3. Some findings on seismic analysis
Someofthefindingsusefulinpracticeofseismicanalysisarereviewedwithrespecttothe
seismic analyses of soil under initial deviator stress, embankments, embedded structures
and retaining walls as follows. These findings can be recognized as the priority areas for
further study inseismicanalysis.
3.1. CYCLIC DEFORMATION OFSOIL UNDER INITIALDEVIATOR STRESS
The effect of dilatancy, especially induced by the stress path in the vicinity of failure
line, governs the gradual or rapid increase in strain amplitude during cyclic loading.
For undrained cyclic loading tests of soil with lateral normal strain constrained, usually
calledliquefactiontests,primaryfocusofthestraincomponentsisdirectedonshearstrain
amplitude. Typical results of measured (Matsuo et al., 2000) and computed stress-strain
and stress path are shown in Figure 13.3 (Ozutsumi, 2003). In this figure, conventional
modelisbasedonthealgorithmthatdilatancyisdefinedasafunctionofcumulativeshear
strainenergyasmentionedearlier.Themodifiedmodelisbasedonthealgorithmthatdila-
tancy is defined as a function of partial components of cumulative shear strain energy, in
which the contributions from the shear strain energy from the stress path beyond the
phase transformation line (i.e. dilatative regime) is intentionally not taken into account.
This minor modification in the algorithm for computing dilatancy does not affect the
computed stress-strain and stress path for conventional liquefaction tests as shown in
Figure 13.3.
For stress-strain and stress path for lateral normal strain unconstrained but with keeping
the axial stress difference constant, that is often the case with two or three dimensional
deformation of soil-structure systems, the effect of dilatancy on the strains becomes sig-
nificant as shown in Figure 13.4. In fact, the difference in the computed normal strain
component from the conventional and modified algorithms are almost in two order in
magnitude. Further parameter study suggests that the algorithm best describes the exist-
inglaboratorydatawhenthealgorithmdoesnottakeintoaccounttheshearstrainenergy
forstresspathbeyondthelinebetweenthephasetransformationlineandthefailureline.
Althoughthesefindingsaretieddowntothespecificformofconstitutiveequations,these
findings can be generalized into a statement that dilatancy in the vicinity of failure line
should be carefully studied inthe development of soil model.
