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mathematical modeling of real structures has great significance.
Concrete is a structural material sensitive to the rate of loading. Numerous tests have been carried
out to investigate its response to rapid loading. Experimental results reveal that the material strength,
stiffness and ductility (or brittleness) are rate-dependent. Hence, when a dam is subjected to the
earthquake excitation, the stress-strain relationship in different parts of it at different instant will be
different due to different strain rate it experiences. However, the conventional design practice
accounts for rate sensitivity by means of drastic simplifying assumptions. That is, in all cases, the
allowable stresses of an arch dam under earthquake load is increased by, say, 30% of the value
specified for static case. Similarly, the dynamic modulus of elasticity is assigned 30% higher than
its static value. The effect of dynamic behaviour of the dam and the effect of the waveform of the
earthquake excitation have been disregarded. As a result, the true response of the dam may be
altered to some extent. This paper aims to investigate the effect of strain-dependency on the seismic
response of arch darn. In the literature several researchers (Lee et al 1998, Cervera et al 1996)
studied the seismic response of a two dimensional concrete gravity dam by employing
rate-dependent damage model. In the plastic-damage model of Lee et al (1998), the rate-dependent
regularization is used to guarantee a unique converged solution for softening regions. No effect for
rate-dependency on the stress distribution is involved. In the rate-dependent isotropic damage
model, Cervera et al (1996) used a stress-strain curve that does not agree with the experimental
results of majority of investigators (Bischoff et al 1991, Bazant et al 1982). In this paper,
experiments on dynamic behaviour of concrete at high stain rates have been carried out and a
consistency viscoplastic three-parameter William-Wamke model is developed to study the strain
rate effects on the seismic response of arch dams.
STRESS-STRAIN RELATIONSHIP AT HIGH STRAIN RATE
Dynamic tensile and compressive tests of concrete at high strain rates have been carried out in our
laboratory. The stress-strain curves obtained are shown in Fig.l and Fig.2.
Strain (1Cf 8 )
Fig.l Typical stress-strain response of concrete
in tension
Strain (t(T 6 )
Fig.2 Typical stress-strain response of concrete
in compression
The strain rate enhancement in tension and in compression are given by