Nonlinear Finite Element Analysis of Concrete Structures

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concrete in the post-failure region according to fig. 2a).
The predicted crack development is shown in fig. 6 for increasing
pressure. Also given on th^ figure is the ratio of a given
loading to the predicted failure load as well as regions where
plastic strains exist in the liner. Obviously, when visualizing
calculated circumferential cracking as discrete cracks some
arbitrariness is necessarily involved. However, in the present
report this arbitrariness is minimized by ensuring rhat for each
cracked nodal point one discrete crack will in general be shown.
In accordance with experimental evidence, cracking initiates at
the centre when the pressure p = 2.7 MPa and radial cracks develop
quickly towards the flange, fig. 6a). At this small presj
i _.., /
a) p=3.9 MPa 19%) b) p = 9.8 MPa (24%) c) p = 13.7 MPa (33%)
i I i d '
a) p = 16.1 MPa IU%) e) p= 21.1 MPa (51%) *> P= 40.7 MPa (98%)
Pig. 5.2-6: Calculated crack development. Regions where plastic
strains exist in the liner are also shown,
sure plastic strains in the concrete have already developed at
the liner in the central part and at the liner below the flange.
Circumferential cracks near the flange initiate at p = 6.9 MPa,
cf. fig. 6b) and the radial cracks are already fully developed.
Fig. 6b) also shows that the liner becomes plastically deformed
in the central region at p = 9.8 MPa and at p = 12.6 MPa the liner
yields below the flange, cf. fig. 6c). This latter figure
indicates that circumferential cracks half-way between the centre
and the flange develop at p = 13.7 MPa. At p = 18.1 MPa in-