Stochastic modeling of deterioration in buildings and civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 414

is the natural period of vibration based on the single-degree-of-freedom
(SDOF) idealization of the bent.
For this case study, we consider two modes of failure: deformation mode
of the bent column (d) and low-cycle fatigue of the longitudinal reinforcing
steel ( LC ) in the column. In the deformation mode of failure, the lateral
seismic loads generate excessive bending stresses in the RC column, causing
the concrete to fail in compression. This is a critical mode of failure for
seismically designed RC bridge columns owing to their dominant fl exural
behavior. The low-cycle fatigue mode of failure has also been reported as
an important mode of failure for RC bridge columns subject to multiple
earthquakes (e.g., El-Bahy et al. , 1999a,b; Kumar and Gardoni, 2012). In this
mode of failure, the longitudinal steel undergoes low-cycle fatigue due to
large strain reversals during cyclic loading. The low-cycle fatigue damage
index DI increases with each load cycle and the longitudinal steel reinforce-
ment bars rupture when DI > 1.0.
Along with the two modes of failure, we consider the following deteriora-
tion mechanisms that determine the time-dependence of the failure
probability:

• Reduction in lateral stiffness due to the cyclic earthquake loads.

• Reduction in deformation capacity due to reduction in reinforcement

area caused by corrosion.

• Reduction in lateral stiffness due to reduction in the reinforcement area

caused by corrosion.

16.4.2 Seismic deformation demand and capacity

The seismic demand of a structure for a given ground motion can be evalu-
ated by performing a time-history analysis. However, a time-history analysis
can be computationally demanding and because future ground motions are
not available, a large number of such analyses are required to compute the
probability distributions of the demand quantities. As a result, probabilistic
seismic demand models are better suited for computing such probability
distributions. Following the general formulation proposed by Gardoni et al.
(2002, 2003), probabilistic demand models can be developed akin to existing
deterministic demand models and procedures commonly used in practice,
but with additional correction terms that explicitly describe the inherent
systematic and random errors inherent in the common models and proce-
dures. Through the use of a set of 'explanatory' functions, terms that correct
the bias in the existing models can be identifi ed. A step-wise deletion
process can then be used to construct parsimonious models by identifying
which explanatory functions, from a set of potential ones, are more infor-
mative and which ones can be removed from the model with no signifi cant