Dynamic Behavior of Concrete: Experimental Aspects - Dynamic Behavior of Concrete and Seismic Engineering - page 9

considered as the viscous element of the composite) is not always constant. In the
same way, the propagation of waves disrupted by the module differs between
cement pastes, and aggregates can also be different depending on the composition of
the studied material;
- even if we managed to identify the intrinsic properties of the material on big
enough samples, for many structures, the “representative material point” size is
important compared with the dimensions of the smallest pieces (building shells
about 20 cm, bridge webs from 30 to 45 cm). Furthermore, significant stress
variations on the scale of the structure can be discerned over short distances of the
same order of magnitude as the dimensions of the test sample. What is then involved
is the application of continuous medium theory, which is based on the assumption -
generally not well verified - that the material point is infinitely small compared to
the structure;
- a problem (which occurs in statics too) that becomes crucial as far as the
dynamic interpretation of tests is concerned is that the sample is not submitted to an
homogenous state of strain and stress owing to its size, and has to be considered as a
structure submitted to transient loading.
Because concrete is a brittle material (like most geomaterials, concrete can only
withstand very weak extension strains and its apparent “failure” takes place for a
compression strength about 10 to 20 times as strong as its traction strength), most of
the time, in practice, while interpreting the tests, we must consider:
- that we are dealing with an elastic homogenous material (which implies the
size precautions referred to above): the assumption is necessary for relatively low
velocities or low strain levels, in continuity with the quasi-static field. It is not good
enough to interpret the totality of a test when the speed increases, since the
maximum stress is reached when localized cracking has been reached significantly
on only a part of the structure;
- that beyond the stage corresponding to localized cracking, the test sample can
be modeled as a cracked structure where damage concentrates in the crack area,
which corresponds to fracture models;
- that beyond a stage corresponding to a distributed deterioration (which
corresponds to the bonding material crumbling away), the material can be described
by combining damage and plasticity models.
Hence, at the material failure of the sample, the interpretation of the tests
requires different analysis models, regardless of whether we are mainly in a
deviatoric behavior with a possible extension direction allowing localized cracking,
or in a mainly “spherical” behavior, and depending on the stress peak being
identifiable or not.