Utility analysis for SHM durations and service life extension of welds on steel bridge deck

Figures & data

Figure 1. Road map of the proposed methodology.

Figure 2. Illustration of a decision tree.

Figure 3. Flow chart of monitoring data-based probabilistic model.

Table 1. Summary of the monitoring data from the monitoring system.

Monitoring system	Monitoring data
Temperature sensor	Pavement temperature
Toll system	Vehicle traffic counts
Strain gauges	Strain data

Figure 4. Illustration of Great Belt Bridge. (Temp. = Temperature, SG = Strain Gauge).

Figure 5. Illustration of strain monitoring system.

Figure 6. Strains gauges at welds (SG-TS = Strain Gauge Trough Splice, SG-TD: Strain Gauge Trough-to-deck).

Table 2. SHM strategies.

Figure 7. Prediction of probability of fatigue failure: (a) during service life of 120 years and with target probability (b) if doing nothing or rehabilitation given reference SHM data.

Table 3. Variables of the probabilistic model.

Parameter	Symbol	Distribution/Expression			Reference
		Function	Mean	Standard deviation
Trough-to-deck weld fatigue parameter	$\mathrm{A}$	Lognormal	7.30E11	4.23E11	(Eurocode, 2005), (Jcss, 2001)
Trough-splice weld fatigue parameter	$\mathrm{A}$	Lognormal	2.09E12	1.21E12	(Eurocode, 2005), (Jcss, 2001)
Miner’s damage at failure	$\mathrm{\Delta }$	Lognormal	1.0	0.3	(Wirsching, 1995)
Daily heavy traffic counts	$B_{\mathrm{\Delta }t}(t)$	Equations (6) – (8)
Daily averaged pavement temperatures	$T_{\mathrm{\Delta }t}(t)$	Equations (3) – (5)

Figure 8. Decision tree of posterior decision analysis.

Figure 9. Identification on the most valuable SHM strategies during the bridge service life.

Figure 10. utilities associated with different monitoring durations and choices of actions considering the variability of the model parameters: (a) target probability ${\mathrm{P}}_{\mathrm{Target}},$ (b) benefit $\mathrm{B},$ (c) failure cost ${\mathrm{C}}_{\mathrm{F}},$ (d) inspection and rehabilitation cost ${\mathrm{C}}_{\mathrm{R}},$ (e) monitoring cost ${\mathrm{C}}_{\mathrm{M}}$ and (f) discount rate $\mathrm{\gamma }.$

Table 4. Summary of the most valued decisions about the SHM strategy to adopt, regarding the critical parameters.

Critical parameter	Most valued decision
Target probability, $P_{\mathit{Target}}$	For $P_{\mathit{Target}}<{2·10}^{-5},$ monitoring for 4 consecutive weeks every 6 months, given the service lifetime is kept to 100 years ($e_3,a_0$)
	For ${2·10}^{-5}\le P_{\mathit{Target}}<{3·10}^{-5},$ monitoring for 6 consecutive weeks every 6 months, given the service lifetime is extended to 120 years ($e_4,a_1$)
	For ${3·10}^{-5}\le P_{\mathit{Target}}<{7·10}^{-5},$ monitoring for 4 consecutive weeks every 6 months, given the service lifetime is extended to 120 years ($e_3,a_1$)
	For $P_{\mathit{Target}}\ge {7·10}^{-5},$ monitoring for 1 week every 6 months, given the service lifetime is extended to 120 years ($e_1,a_1$)
Benefit, $B$	Monitoring for 1 week every 6 months, given the service lifetime is extended to 120 years ($e_1,a_1$)
Cost of failure, $C_F$
Cost of rehabilitation, $C_R$
Cost of monitoring, $C_M$
Discounting rate, $\gamma$

Jcss, J. (2001). Probabilistic model code. Joint Committee on Structural Safety. https://www.jcss-lc.org/jcss-probabilistic-model-code/

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Wirsching, P. (1995). Probabilistic fatigue analysis. In Probabilistic structural mechanics handbook (pp. 146–165). Springer, Boston, MA.

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