Nonlinear Finite Element Analysis of Concrete Structures

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- the criterion proposed by the writer (1977) . This criterion
corresponds to a smooth and convex surface It will be considered
in more details later and it is implemented in the
finite element program.
- the classical Coulomb criterion with tension cut-offs. This
criterion is also implemented in the finite element program
and an evaluation will be postponed until the previously
mentioned criteria have been compared mutally and together
with some representative experimental results.
As mentioned above we will in the first place disregard the Coulomb
criterion with tension cut-offs. The coefficients involved
in the criteria considered are calibrated by some distinct strength
values, for instance, uniaxial compressive strength a (a > 0),
uniaxial tensile strength a. (a > o), etc. In some proposals
such a calibration was already partly carried out leaving only
a few strength values to be inserted by the user, while others
need more strength values. Noting that all coordinate systems
considered here are normalized by a , the applied strength values
are shown in the following table.
Table 2.1-1: Strength values used to calibrate coefficients in
the failure criteria.
V a c
a ,/a
eb' c
£/ø p /a-
' c c c
Vo c
p fc /a c
Reimann-Janda (1965, 1974)
Willam and Warnke (1974)
Chen and Chen (1975)
Cedolin et al. (1977)
Ottosen (1977)
0.08
0.08
0.08
1.15
1.15
-3.20 2.87
-3.20 1.80
a : uniaxial tensile strength (a > o) , a : uniaxial compressive
strength (a > o), a . : biaxial compressive strength (a . > o) .
The additional strength values applied in the Willam and Warnke
criterion are chosen to fit the experimental data of fig. 2.