Nonlinear Finite Element Analysis of Concrete Structures

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a) p=19 MPo (9%) b) p=25.5 MPb (61%) c) p = t0.7 MPo m%)
Fig. 5.2-8: Development of contour lines for the
nonlinearity index in per cent.
below the ribs where inclined circumferential cracks are present,
cf. fig. 6. As supported also by fig. 7 the stress state in this
region is close to biaxial compression. The compressive crushing
of this region and the far below failure stresses in the central
part explain the observed failure mechanism with ejection of the
central part of the closure, cf. also fig. 5. Strain softening
of the concrete in this severest loaded region initiates when
the pressure = 38.7 MPa corresponding to 93% of the predicted
failure load.
Let us now consider the experimental and calculated centre deflection
of the upper surface as a function of pressure, cf. fig.
9. It appears that with the failure criterion of the writer
(1977) the calculations underestimate to some extent the deflections
at high pressures. This might be explained as a result of
the neglect of plastic strains in the flange. However, the
agreement is fair and the predicted failure load is 41.7 MPa
which is 13% above the experimental value. The consequence of
using the modified Coulomb criterion appears also from the figure
and the resulting failure load is 29.4 MPa which is 20%
below the experimental value. This underestimate is in eccordance
with the general conclusions from section 2.1.3. The difference
between the two predictions that amounts to about 30%
corresponds to initiation of failure in a region where almost
biaxial compression exists, cf. fig. 2.1-7.
The extreme assumption of no-softening in the post-failure region
has a remarkable effect, cf. fig. 9, where the writer's