PSI - Issue 44

Iolanda Nuzzo et al. / Procedia Structural Integrity 44 (2023) 1832–1839 Iolanda Nuzzo et al./ Structural Integrity Procedia 00 (2022) 000–000

1836

7

Longitudinal

Transversal

Probability

Fig. 3. Fragility curves of piers in longitudinal and transversal directions.

2.4 Step 4: Monitoring System The monitoring sensors installed in the vicinity of Quarto station are triaxial accelerometers at the base of the piers, linear displacement transducers (LVDTs) at the bearings to measure relative movements, and temperature transducers. Particularly, one triaxial accelerometer is placed at the base of a pier located immediately after Quarto station in direction Torregaveta, while longitudinal and transversal transducers are placed in correspondence of bearings on the two sides of the deck to detect relative displacement with respect to the piers. 2.5 Step 5: Loss analysis The scope of this step is to determine the total cost resulting from any of the 16 scenarios obtained as a combination of mitigation strategy (from MS0 to MS4) and effective damage state, that can be null (DS0) or moderate to extreme (DS1 to DS3). To this purpose, the following 4 individual cost items are identified in Table 1: technical inspection (CT), technical repair (CR), interruption of the railway service and/or road service (CI) and cost of accident (CA). The Table 1 shows the main aspects considered in the estimations of the individual item costs, which have different loss implications according to the MSi and DSj.

Table 1. Main aspects considered in the estimation of the individual item costs. Cost Item CT CR

CI

CA

Medium urgency inspection High urgency inspection

Moderate reparation Medium reparation Severe reparation

Passenger – Tickets Road traffic – Pollutant emissions

Slightly or gravely injured Deceased

Main aspects

Table 2. Unitary cost matrix for CT. CT DS 0 DS 1 DS 2 DS 3 MS 0 c 00 c 01 c 02 c 03 MS 1 c 10 c 11 c 12 c 13 MS 2 c 20 c 21 c 22 c 23 MS 3 c 30 c 31 c 32 c 33

Thus, each individual cost has a loss matrix, cij. Particularly, Table 2 illustrates that matrix of the CT cost item. These coefficients were set as a column vector, which is defined as vCT = [c00 ,..., c03, c10 ,..., c13, c20 ,..., c23, c30 ,..., c33]T, where the super index [ ]T indicates the transpose operation. This array was applied to each individual cost item for creating a general cost matrix, Mpxq, as defined in Eq. (1). But each cost item can be expressed in function of different indicators (number of spans, number of piers, number of events). For example, the evaluation of the cost for the item CT was based on the number of spans of the section A of the viaduct. Whilst the item CR was stablished in proportion to the number of piers involved in this part of the structure. This was considered, due to the main contribution of the piers to the coupled vertical and horizontal resistance of the bridge. On the other hand, the other cost items consist of the interruption case (CI) and the accident case (CA). Therefore, their contributions to the loss function do not depend to a large extent on the structural configuration, but on the overall values of these items in a given seismic event. In this direction, it is introduced in the cost analysis a weight vector “a” that superimpose the contribution of each cost item for obtaining the general cost vector “C”, as described in the Eq. (2). In this equation, “a” is defined as [aCT, aCR, 1, 1]T and “C” as [C00 ,..., C03, C10 ,..., C13, C20 ,..., C23, C30 ,..., C33]T.