A simple shear wall model taking into account stiffness degradation

Complex destructive phenomena take place in
reinforced concrete structures during earthquake excitations.
These include concrete cracking, interaction
effects between steel and concrete, steel yielding and
concrete crushing in compression. The damage generated
can be translated into a damage variable which takes
the local destructive effects into account in a global manner.
As damage increases within the reinforced concrete
structure, the alteration of the mechanical characteristics
yields modal characteristics changes. In this way, Chen
et al. [1] investigated the structural damage by means of
the identification method of modal changes. At a critical
damage level, they indicated that a decrease of the fundamental
frequency up to 10% can be expected for steel
beams. For reinforced concrete structures, the fundamen-
tal frequency reduction, related to the structural damage
can be significantly larger. Pseudodynamic tests carried
out at the European Laboratory for Structural Assessment
(JRC-Ispra) in fact showed fundamental frequency
reductions of more than 60% (Pegon et al. [2]). Such
fundamental frequency decrease strongly influences the
dynamic response of the structure subjected to a seismic
excitation.
In this paper, a simplified model for a particular lowrise
heavily reinforced shear wall is proposed. Its original
formulation is based explicitly on changes in fundamental
frequency according to a pertinent damage variable.
First of all, a detailed finite element analysis is
carried out with constitutive local models taking into
account the main destructive phenomena involved during
seismic excitation. The relevance of the modelling
is evaluated by comparing numerical results with experimental
available data. The following stage is devoted
to the identification of the decrease of the fundamental
frequency. This is realised by applying the finite element
modelling of the wall to a variety of ideal excitations
composed of sinusoidal cycles. The numerical results
allow to identify in a robust manner the decrease of the
fundamental frequency as a function of damage. Then,
this function is introduced in a simple dynamic uniaxial
model, expressed in terms of displacements at the top of
the wall. In the final stage, the validity of the proposed
simplified model is assessed by comparing numerical
results with experimental results in a first time, and, in
a second time, with the results issued from fine finite
element analyses for different types of seismic excitations.
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