Nonlinear Finite Element Analysis of Concrete Structures

tensile and compressive meridians was shown previously in fig. 4.
However, to facilitate caparison cf Lhe tailure criteria considered
there, not all available experiaental results were giv ^r.
when tensile stresses are present. A sore detailed comparison
with the failure criterion considered now is therefore illustrated
in fig. 7.
a. ;v
i
(12
'-
I
Modified Coulomb
--02
-0.4
j - - -06
•-- Kupfer et al. I 969. 19731
.-0.8
r tt2
Ottosen (1977)
--1.0
•-12
Fig. 2.1-7: Biaxial tests of Kupfer et al. (1969, 1973), - =
58.3 MPa. - = 0.08 a used in both criteria,
t
c
The agreement is considered satisfactory, the largest difference
occurring in compression when • /?-
- 0-5. In this case Kupfer
et al. obtained a, = -1.27 -, as the mean value of tests
2 c
with a
ranging from 18.7 - 58.3 MPa; on the other hand the failure
criterion with the parameters of table 2 gives - 1.35 ' ,
- 1.38 -. and - 1.41 a for a/o = 0.08, 0.10, and 0.12, rec
e t c
spectively. It is interesting to note that the classical biaxial
tests of Wastlund (1937) with a
ranging from 24.5 - 35.0 MPa
give o. = - 1.37 a with almost the same biaxial strength
(1.14 ' ) as the results of Kupfer et al (1.16 n ).
c
c
Suranarizing, the failure criterion given by eqs. (5) and (8) contains
the three stress invariants explicitly and it corresponds
to a smooth convex surface with curved meridians which open in
the negative direction of the hydrostatic axis. The trace in the
deviatoric plane changes from an almost triangular to a more