Large earthquakes impose substantial demands on bridge structures that
can result in widespread interruption to service, and in extreme cases,
collapse. This response is typically inelastic and results in structural damage
that is intended to be sustainable with proper structural detailing. Design of
common bridges using the AASHTO LRFD and Guide Specification methodologies rely
on elastic analysis from which inelastic demands are estimated. Accordingly, it
is paramount that the estimates be reliable. Inaccurate estimates of demand
could result in substantial service interruption and potentially bridge
collapse if the actual inelastic response is significantly larger than the
estimated design response.
Since the mid-1980’s AASHTO has been using an empirically derived,
simple coefficient method to estimate inelastic demands from elastic analyses.
This method, and its more recent variant that was introduced with the Guide
Specification, was based on earlier studies that used a computational damping methodology
that has been shown to be unconservative as described in many of the references
listed below. With this newer information, it is clear that the current AASHTO
methodologies could put new bridges at greater risk of unacceptable damage, and
this situation should be corrected.
Recently in an effort to better equip the bridge engineering community
to achieve robust designs whose performance can be predicted in future
earthquakes, extensive research effort had been directed towards
‘Performance-Based Seismic Design (PBSD)’. In this design process, bridges are
designed to achieve prescribed levels of damage under prescribed levels of
earthquake intensity. Ultimately PBSD will augment the basic AASHTO design
methods and may someday replace these methods. However, accurate estimation of actual
inelastic response of bridges will still be as important as they are in the
current AASHTO methods.
There are three main components to PBSD: (1) Accurate means to define
displacement capacities at key performance limit states; (2) Accurate means to
define displacement demands; and (3) A design methodology that allows the
engineer to connect the above two aspects. In 2011, AASHTO released the first
edition of the Guide Specification for LRFD Seismic Bridge Design which aimed
to provide initial guidance that achieved these three aspects of PBSD.
Currently, through NCHRP 12-106, Proposed Guidelines for Performance-Based
Seismic Bridge Design, a methodology has been proposed that outlines the steps
required to achieve PBSD, thus advancing the community beyond the current Guide
During the conduct of the work in NCHRP 12-106, inconsistencies were
discovered regarding the estimation of inelastic displacement demands. The
inconsistency was traced to the manner in which viscous damping is modelled in
analysis, which subsequently impacts the simplified methods used by engineers
to calculate displacement demands. It was shown that calculation of displacements
using currently established procedures may severely underestimate the actual
displacements that the bridge may be subjected to in future earthquakes. Regardless
of whether the engineering community continues to use its conventional methods
or transitions towards implementation of PBSD, such inaccuracies are
unacceptable and must be addressed. This is a critical need in the bridge
A snapshot of references related
to the impact of damping models in structural response is shown below.
Chai, Y.H., and Kowalsky, M.J.
(2014). “An Examination of Non-Viscous Damping on Seismic Inelastic
Displacements” Journal of Structural Stability and Dynamics, Vol. 15#5.
Charney, F. (2008).
“Unintended consequences of modeling damping in structures”. ASCE Journal of
Structural Engineering. Vol. 134#4, pp581-592.
Hall, J. F. (2006). ‘‘Problems
encountered from the use (or misuse) of Rayleigh damping,’’ Earthquake
Engineering and Structural Dynamics, Vol. 35, pp525–545.
Hall, J. F. (2018). ‘‘Performance
of viscous damping in inelastic seismic analysis of moment-frame buildings,’’
Earthquake Engineering and Structural Dynamics, Vol. 47, pp2756–2776.
Hardyniec, A. and Charney, F.
(2015). ‘‘An investigation into the effects of damping and nonlinear geometry
models in earthquake engineering analysis,’’ Earthquake Engineering and
Structural Dynamics, Vol. 44#15, pp2695-2715.
Hasgul, U. and Kowalsky M.J.
(2014). “Impact of Viscous Damping Models on Nonlinear Response of SDOF
Systems”. Proceedings of the 10th National Conference in Earthquake
Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.
Lanzi and Luco (2018). ‘‘Elastic
velocity damping model for inelastic structures,’’ ASCE Journal of Structural
Engineering, Vol. 144#6.
Luco and Lanzi (2017). ‘‘A new
inherent damping model for inelastic time history analysis,’’ Earthquake
Engineering and Structural Dynamics, Vol. 46, pp1919–1939
Otani, S. (1981). ‘‘Hysteresis
models of reinforced concrete for earthquake response analysis,’’ Journal of
the Faculty of Engineering, The University Tokyo, Vol. 36#2, pp. 407-441.
Petrini, L., Maggi, C.,
Priestley, M.J.N. and Calvi, G.M. (2008). “Experimental Verification of Viscous
Damping Modeling for Inelastic Time History Analyzes”, Journal of Earthquake
Engineering, Vol 12#1, pp125-145.
Priestley, M. J. N. and Grant,
D. N. (2005). ‘‘Viscous Damping in Seismic Design and Analysis’’ Journal of
Earthquake Engineering Vol. 9 #SP2, pp229–255.
Priestley, M.J.N., Calvi,
G.M., and Kowalsky, M.J. (2007) “Direct Displacement-Based Seismic Design of
Structures” IUSS Press, Pavia Italy, ISBN 978-88-6198-000-6. 740 pp.