Environmental Engineering Reference
In-Depth Information
12.6.4
Numerical methods
Numerical modelling techniques such as the finite element method were first applied to
the dynamic analysis of embankment dams by Clough and Chopra (1966). This was fol-
lowed by major improvements by Ghaboussi (1967), Schnabel et al. (1972), Ghaboussi
and Wilson (1973), Idriss et al. (1973), Martin et al. (1975), Finn et al. (1977), Lee and
Finn (1978), White et al. (1979), Zienkiewicz and Shiomi (1984), Finn et al. (1986),
Medina et al. (1990) and Li et al. (1992). Today, numerical methods are routinely used
as both investigative and design tools in many geotechnical earthquake engineering
problems.
The dynamic numerical codes used in practice may be divided into two main categories:
total stress codes, and effective stress codes (Zienkiewicz et al., 1986; Finn, 1993). A brief
discussion of some of the more frequently used codes within each category is provided in
the following sub-sections.
12.6.4.1
Total stress codes
The total stress codes, as can be inferred from the classification, are based on the total
stress concept and do not take account of pore pressures in the analysis. Therefore they
are used in situations where the seismically induced pore pressures are negligible. The
total stress codes may be divided into two main categories: (1) codes based on the equiv-
alent linear (EQL) method of analysis, and (2) fully non-linear codes.
12.6.4.1.1 Equivalent linear analysis (EQL)
The earlier total stress codes were based on the EQL method of analysis developed by
Seed and his colleagues in 1972. EQL is essentially an elastic analysis and was developed
for approximating non-linear behaviour of soils under cyclic loading. Typical of the EQL
codes used in practice are: SHAKE (Schnabel et al., 1972), QUAD-4 (Idriss et al., 1973)
and FLUSH (Lysmer et al., 1975). SHAKE is a one dimensional wave propagation pro-
gram and is used primarily for site response analysis. QUAD-4 and FLUSH are two-
dimensional versions of SHAKE and are used for seismic response analysis of dams and
embankments. Given the elastic nature of the EQL analysis, however, these codes cannot
take account of material yielding and material degradation under cyclic loading.
Therefore, they tend to predict a stronger response than actually occurs. Also, they can-
not predict the permanent deformations directly. Indirect estimates of permanent defor-
mations can however be obtained using the acceleration or stress data obtained from an
EQL analysis and the semi-empirical methods proposed by Newmark (1965) and/or Seed
et al. (1973).
12.6.4.1.2 Fully non linear analysis
More accurate and reliable predictions of permanent deformations can be obtained using
the elasto-plastic nonlinear codes. Typical of the elasto-plastic non-linear codes used in
the analysis of embankments are DIANA (Kawai, 1985), ANSYS (Swanson, 1992), FLAC
(Cundull, 1993), etc. The constitutive models used in these codes vary from simple hys-
teretic non-linear models to more complex elasto-kinematic hardening plasticity models.
Compared to the EQL codes, the elasto-plastic non-linear codes are more complex and
put heavy demand on computing time. However, they provide more realistic analyses of
embankments under earthquake loading, especially under strong shakings. Critical assess-
ments of non-linear elasto-plastic codes can be found in Marcuson et al. (1992) and Finn
(1993).
12.6.4.2
Effective stress codes
A major stimulus for the development of the effective stress codes has been the need for
modeling pore pressure generation and dissipation in materials susceptible to liquefaction
