Nonlinear Finite Element Analysis of Concrete Structures

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Table 2.1-3: A.-values and their dependence on the o /a -ratio,
a./a A. A A /A^
t c t c c' t
0.08
: 0.10
14.4725
11.7109
7.7834
6.5315
0.5378
0.5577 .
; 0.12
9.8720
5.6979
0.5772
1
Although the parameters A, B, K 1 and K„ show considerable dependence
on the a t /a c -ratio, the failure stresses, when only compressive
stresses occur, are influenced only to a minor extent.
Using o t /a c = 0.10 as reference, the difference amounts to less
than 2.5%.
Comparison of predictions of the failure criterion with some experimental
results has already been given in figs. 2 and 4. Fig.
5 shows a further comparison with some of the earlier applied
experimental results, but now for a larger loading range. Fig. 6
contains additional experimental results of Chinn and Zimmerman
(1965), Mills and Zimmerman (1970) and the mean of the test results
of Launay et al. (1970, 1971, 1972). Comparisons of the
last two figures indicate considerable scatter of the test results
on the compressive meridian for £,/o < - 5.0, the tendencies
being opposite in the two last figures. Along the tensile meridian
the failure criterion underestimates the results of Launay
et al. (1970, 1971, 1972) and Chinn and Zimmerman (1965) for
C/a c > - 6, in accordance with the higher biaxial compressive
strength determined in these tests (1.8 o and 1.9 a , respectively)
compared with that used to determine the parameters of
the failure criterion. Mills and Zimmerman (1970) determined the
biaxial compressive strength to 1.3 a .
c
If the compressive and tensile meridians are accurately represented,
the trace of the failure surface in the deviatoric plane
is confined to within rather narrow limits provided that the
trace is a smooth, convex curve. This is especially pronounced
when the P t /P c ratio is close to the minimum value 0.5. The a-
bility of the considered failure surface to represent the experimental
biaxial results of Kupfer et al. (1969, 1973) outside the