Optimal probabilistic design of seismic dampers for the protection of isolated bridges against near-fault seismic excitations

Abstract A probabilistic, simulation-based framework is presented in this paper for risk assessment and optimal design of supplemental dampers for multi-span bridge systems supported on abutments and intermediate piers through isolation bearings. The adopted bridge model explicitly addresses nonlinear characteristics of the isolators and the dampers, the dynamic behavior of the abutments, and the effect of pounding between the neighboring spans against each other as well as against the abutments. Nonlinear dynamic analysis is used to evaluate the bridge performance, and a realistic stochastic ground motion model is presented for describing the time history of future near-fault ground motions and relating their characteristics to the seismic hazard for the structural site. A probabilistic foundation is used to address the various sources of structural and excitation uncertainties and ultimately characterize the seismic risk for the bridge. This risk is given by the expected value of the system response over the adopted probability models. Stochastic simulation is used for evaluating the multi-dimensional integral representing this expected value and for performing the associated optimization when searching for the most favorable damper characteristics. An efficient probabilistic sensitivity analysis is also established for identifying the importance of each of the uncertain model parameters in affecting the overall risk. An illustrative example is presented that considers the design of nonlinear viscous dampers for the protection of a two-span bridge.

[1]  Peter Kall,et al.  Stochastic Programming , 1995 .

[2]  James L. Beck,et al.  Probabilistically robust nonlinear design of control systems for base‐isolated structures , 2008 .

[3]  James L. Beck,et al.  Stochastic Subset Optimization for reliability optimization and sensitivity analysis in system design , 2009 .

[4]  James L. Beck,et al.  An efficient framework for optimal robust stochastic system design using stochastic simulation , 2008 .

[5]  James C. Spall,et al.  Introduction to stochastic search and optimization - estimation, simulation, and control , 2003, Wiley-Interscience series in discrete mathematics and optimization.

[6]  Nicos Makris,et al.  Dimensional analysis of the earthquake‐induced pounding between adjacent structures , 2009 .

[7]  Nicos Makris,et al.  STRUCTURAL CHARACTERIZATION OF MODERN HIGHWAY OVERCROSSINGS--CASE STUDY , 2004 .

[8]  Alexandros A. Taflanidis,et al.  Robust Stochastic Design of Viscous Dampers for Base Isolation Applications , 2011 .

[9]  Anat Ruangrassamee,et al.  Control of nonlinear bridge response with pounding effect by variable dampers , 2003 .

[10]  David M. Boore,et al.  Simulation of Ground Motion Using the Stochastic Method , 2003 .

[11]  Reginald DesRoches,et al.  A Hertz contact model with non‐linear damping for pounding simulation , 2006 .

[12]  Costas Papadimitriou,et al.  RELIABILITY ANALYSIS OF BRIDGE MODELS WITH ELASTOMERIC BEARINGS AND SEISMIC STOPPERS UNDER STOCHASTIC EARTHQUAKE EXCITATIONS , 2009 .

[13]  W. Goldsmith,et al.  Impact: the theory and physical behaviour of colliding solids. , 1960 .

[14]  J. Beck,et al.  A new adaptive importance sampling scheme for reliability calculations , 1999 .

[15]  Armen Der Kiureghian,et al.  A stochastic ground motion model with separable temporal and spectral nonstationarities , 2008 .

[16]  S. Kramer.  Geotechnical Earthquake Engineering , 1996 .

[17]  Jonathan P. Stewart,et al.  Evaluation of the seismic performance of a code‐conforming reinforced‐concrete frame building—from seismic hazard to collapse safety and economic losses , 2007 .

[18]  Nicos Makris,et al.  Seismic Response Analysis of a Highway Overcrossing Equipped with Elastomeric Bearings and Fluid Dampers , 2004 .

[19]  Helmut Krawinkler,et al.  CONSIDERATION OF NEAR-FAULT GROUND MOTION EFFECTS IN SEISMIC DESIGN , 2000 .

[20]  Abdelkader Mokkadem,et al.  Estimation of the entropy and information of absolutely continuous random variables , 1989, IEEE Trans. Inf. Theory.

[21]  R. O. Davis,et al.  Pounding of buildings modelled by an impact oscillator , 1992 .

[22]  M. Ala Saadeghvaziri,et al.  Seismic behavior and capacity/demand analyses of three multi-span simply supported bridges , 2008 .

[23]  E. Polak,et al.  Reliability-based optimal design using sample average approximations , 2004 .

[24]  Hongbing Fang,et al.  Application of Micro-GA for optimal cost base isolation design of bridges subject to transient earthquake loads , 2010 .

[25]  Bjarni Bessason,et al.  Earthquake response of a base-isolated bridge subjected to strong near-fault ground motion , 2010 .

[26]  Harold Klee,et al.  Simulation of Dynamic Systems with MATLAB and Simulink , 2007 .

[27]  Meng-Hao Tsai,et al.  Performance of a Seismically Isolated Bridge under Near-Fault Earthquake Ground Motions , 2004 .

[28]  W. Silva,et al.  Stochastic Modeling of California Ground Motions , 2000 .

[29]  L. Györfi,et al.  Nonparametric entropy estimation. An overview , 1997 .

[30]  R. S. Jangid.  Stochastic Response of Bridges Seismically Isolated by Friction Pendulum System , 2008 .

[31]  James L. Beck,et al.  Life-cycle cost optimal design of passive dissipative devices , 2009 .

[32]  George P. Mavroeidis,et al.  A Mathematical Representation of Near-Fault Ground Motions , 2003 .

[33]  E. Jaynes.  Probability theory : the logic of science , 2003 .

[34]  Murat Dicleli,et al.  Performance of Seismic-Isolated Bridges in Relation to Near-Fault Ground-Motion and Isolator Characteristics , 2006 .

[35]  James L. Beck,et al.  Reliability-Based Design Using Two-Stage Stochastic Optimization with a Treatment of Model Prediction Errors , 2010 .

[36]  Nicos Makris,et al.  Dimensional Analysis of the Earthquake Response of a Pounding Oscillator , 2010 .

[37]  Panos Tsopelas,et al.  Experimental study of bridge seismic sliding isolation systems , 1996 .

[38]  J. Bray,et al.  Characterization of forward-directivity ground motions in the near-fault region , 2004 .

[39]  J. S. Hwang,et al.  Design formulations for supplemental viscous dampers to highway bridges , 2005 .