The value of structural health monitoring in seismic emergency management of bridges

Abstract

The management of civil infrastructures in the aftermath of a seismic event is a concern for decision makers, which have to choose quickly among alternative actions with limited knowledge on the actual structural conditions. The availability of real time Structural Health Monitoring (SHM) data on the asset might be particularly useful. However, SHM data are not collected for free, and the cost of the SHM system should be compared with its associated benefit. A powerful tool to estimate such benefit is the Value of Information (VoI) from Bayesian decision theory. This paper provides a methodology to compute the VoI of SHM for seismic emergency management of roadway bridges. This methodology can be used by decision makers before the installation of a seismic SHM system to quantify the cost benefit of doing so and thus optimize the allocation of economic resources. Results show that the VoI is high when the expected costs of the decision alternatives (such as ‘keep the bridge open’ or ‘close the bridge’) evaluated without the SHM information are comparable. In this condition, which is highly dependent on the seismic hazard and on emergency management costs at stake, the SHM information provides the maximum support to decision making.

Keywords:

• Bridges
• decision making
• seismic hazard management
• structural health monitoring
• value of information

Acknowledgements

This study was partially funded by the Italian Civil Protection Department within the ReLUIS Project ‘Structural Health Monitoring and Satellite Data’ WP6-2019-21. The availability of data for the bridge on the SS114 road in Sicily provided by the Italian Seismic Observatory of Structures (OSS) is gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notations list

Variables related to the VoI and the Net Life-cycle VoI

Symbol: Meaning
$A_n$	=	Management actions
$D{S}_l$	=	Damage states of the structure
$D{P}_l$	=	Threshold for the damage parameter $DP$ related to the $l$-th damage state
$c_F\left(A_n\right)$	=	Costs related to structural failure
$c_{\overline{F}}\left(A_n\right)$	=	Costs related to structural survival
$\widehat{A}$	=	Optimal action in Prior analysis
$O_j$	=	SHM outcome
${IS}_j$	=	Inspection score
${\breve{A}}_{O_j}$	=	Optimal action in Pre-Posterior analysis (depends on $O_j$)
$c_1$	=	Expected cost of the optimal action in Prior analysis
$c_0$	=	Expected cost of decision making in Pre-Posterior analysis
$\mathrm{VoI}$	=	Value of Information
${\mathrm{VoI}}_{\mathrm{LC}}$	=	Life-cycle VoI
${\mathrm{NVoI}}_{\mathrm{LC}}$	=	Net Life-cycle VoI
$T_{LC}$	=	Reference period for the computation of the ${\mathrm{VoI}}_{\mathrm{LC}}$
$r$	=	Discount rate
$C_o$	=	Initial cost of the SHM system
$\Delta c_{SH{M}_i}$	=	Maintenance cost at year $i$
$C_{\mathit{SHM}}$	=	Life-cycle cost of the SHM system

Variables related to mainshocks
$T_m$	=	Generic mainshock
$M_m$	=	Magnitude of the mainshock
$R_m$	=	Mainshock epicentral distance from the bridge (km)
$I_m$	=	Intensity measure for the mainshock
${\mathbf{\Theta }}_{\mathbf{m}}$	=	Vector collecting the three parameters $M_m,$ $R_m,$ and $I_m$
${\lambda }_m$	=	Annual rate of earthquake occurrence
$\mathrm{a,}$$b$	=	Parameters of the Gutenberg-Richter law
$M_{m,l}$	=	Lower bound for mainshock magnitudes
$M_{m,u}$	=	Upper bound for mainshock magnitudes

Variables related to aftershocks
$M_a$	=	Magnitude of the aftershock
$M_{a,l}$	=	Lower bound for aftershock magnitudes
$M_{a,u}$	=	Upper bound for aftershock magnitudes
$a,$ $b,$ c, p	=	Parameters to model the occurrence of aftershock
$N_a$	=	Mean number of the aftershock
$R_a$	=	Aftershock epicentral distance from the bridge (km)
$S_a$	=	Area of occurrence of aftershocks
$I_a$	=	Intensity measure for the aftershock
$N_F$	=	Mean number of structural failure

Variables related to costs
$C_{RB}$	=	Rebuilding cost
$C_{RN}$	=	Cost of time lost
$C_{TL}$	=	Cost of detour
$C_{CC}$	=	Casualty cost
$C_1$	=	Unit rebuilding cost
$C_2$	=	Cost of running cars
$C_3$	=	Cost of running trucks
$C_4$	=	Value of time of car passengers
$C_5$	=	Value of time for truck drivers
$W$	=	Width of the bridge
$L$	=	Length in of the bridge
$D$	=	Detour length
$A$	=	Average daily traffic
$T$	=	Average daily truck traffic
$d$	=	Detour duration
$S$	=	Average detour speed
$O_{\mathit{car}}$	=	Average occupancy rate for cars
$O_{\mathit{trk}}$	=	Average occupancy rate for trucks
$C_L$	=	Average cost of human life loss
$D_S$	=	Stopping distance