Risk-Based Inspection and Strength Evaluation of Suspension Bridge Main Cable Systems (2023)

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99 C H A P T E R 7 Illustrative Example Detailed Application of the Proposed Methodology To better explain the proposed methodology to estimate the cable strength, here a detailed example is presented, highlighting each single step of the procedure. All calculations were performed using MATLAB. This example uses data collected during previous inspections by members of the RT. However, some other data have been generated with the purpose of providing a better explanation of the methodology. The main cable under investigation comprises 6,080 high-strength steel galvanized wires, arranged in 45 rings. The length of the panel is 25 ft. In the following calculations, we assume that the unit length of a wire segment, ls, is 18 in. Cable Inspection The inspected panel is wedged at eight locations along the circumference of the cable using wedges, following the procedures described in the NCHRP NCHRP Report 534. The locations are every 45o with one of them being at the very top of the cross-section of the cable (12:00 location). The panel is wedged along its entire length (with the exception of the areas in the vicinity of the cable bands), starting from the center and moving towards the two cable bands. After the cable has been wedged, the number of inspection locations is decided. In this example, it is assumed that the wedged panel is inspected at three locations, with each segment 7.5 ft. in length. This will allow us to consider that each inspected location will be representative of a portion of the cable of 5 × 𝑙𝑙𝑠𝑠 = 5 × 18 𝑖𝑖𝑖𝑖. = 90 𝑖𝑖𝑖𝑖. = 7.5 ft. A total length of 3 × 7.5 = 22.5 ft of the panel will be modeled as part of the methodology to estimate the cable strength and can be considered as the effective development length, 𝐿𝐿𝑒𝑒, of the panel. The remaining 25.0 - 22.5 = 2.5 ft correspond to non-inspectable areas close to the cable bands. At each inspection location, the corrosion stage of every wire on the 16 faces of the eight wedged opening is identified and recorded, following the same recommendations as specified in NCHRP NCHRP Report 534. The findings are presented in the Figures 32, 33 and 34 for Location 1, Location 2 and Location 3, respectively. Once the inspection data becomes available, it is possible to build a model of the corrosion stage variation along the entire 𝐿𝐿𝑒𝑒 for each exposed wire (and for the wires in the corresponding half-sector). Tables 7 through 22 present the variation along the effective length 𝐿𝐿𝑒𝑒 of the corrosion stage for all the wires exposed on the 16 faces of the eight wedged position at the three inspection locations within the panel. The number in each cell represents the corrosion stage of a wire (and of the wires in the corresponding subsector) at that specific location. To create these tables, the following process is suggested:

100 1) The number of columns of the table depends on the number of inspection locations and on the number of unit length wire segments, 𝑙𝑙𝑠𝑠, assumed representative of that given location. In this example, since we have assumed three inspection locations and 5 × 𝑙𝑙𝑠𝑠 wire segments inspected at each panel, the total number of cells in a row (e.g. the total number of columns in the table) will be 3 × 5 = 15. The sequence of the 15 numbers will indicate the variation of the corrosion stage of a given wire along the effective length 𝐿𝐿𝑒𝑒 of the panel. 2) To fill the cells for each single wire inspected, let us look for an example at wire 28 on the left face of the wedged opening in sector 1. At Location 1, it is assigned a corrosion stage of 3, at Location 2 a corrosion stage of 2 and at Location 3 a corrosion stage of 3. Hence, the sequence of 15 numbers representative of the corrosion stage variation of wire 28 on the left face of the wedged location in sector 1 (and of all the wires in this subsector) is: 3 – 3 – 3 – 3 – 3 – 2 – 2 – 2 – 2 – 2 – 3 – 3 – 3 – 3 – 3 This corresponds to row 28 in Table 7. In the final corrosion stage map, this specific wire (and all the wires in the corresponding subsector) will be considered as a Corrosion Stage 3 wire (based on the worst corrosion stage condition along the entire effective length). This is the same as the current NCHRP 534 procedure. This operation has to be done for each single wire exposed at the wedged openings and extended to every single wire in the corresponding subsectors. At the end of this operation, all 6080 wires will have a model of the corrosion stage variation along the effective length 𝐿𝐿𝑒𝑒 of the panel. For the example in question, the 6,080 wires will be classified as follows: Corrosion Stage 1: 206 wires Corrosion Stage 2: 2559 wires Corrosion Stage 3: 2827 wires Corrosion Stage 4: 488 wires

101 Figure 37. Wire Corrosion Stage Data. Location 1

102 Figure 38. Wire Corrosion Stage Data. Location 2

103 Figure 39. Wire Corrosion Stage Data. Location 3

104 Table 7. Simulated Profiles Along the Length of All Wires on the Left Side of the Wedge, Sector 1 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 5 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 6 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 7 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 10 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 13 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 14 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 16 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 17 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 18 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 20 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 21 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 22 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 23 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 24 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 25 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 26 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 27 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 28 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 29 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 30 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 31 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 36 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 37 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 38 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

105 Table 8. Simulated Profiles Along the Length of All Wires on the Right Side of the Wedge, Sector 1 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 10 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 13 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 14 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 15 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 16 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 17 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 18 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 19 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 20 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 21 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 22 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 23 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 24 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 25 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 26 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 27 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 28 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 29 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 30 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 31 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 34 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 35 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

106 Table 9. Simulated profiles along the length of all wires on the left side of the wedge. Sector 2 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 10 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 11 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 12 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 13 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 14 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 16 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 17 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 18 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 19 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 20 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 21 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 23 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 24 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 25 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 26 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 27 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 28 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 29 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 30 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 31 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 36 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

107 Table 10. Simulated profiles along the length of all wires on the right side of the wedge. Sector 2 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 10 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 11 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 12 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 13 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 14 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 15 3 3 3 3 3 1 1 1 1 1 3 3 3 3 3 16 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 17 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 18 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 19 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 20 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 21 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 23 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 24 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 25 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 26 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 27 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 28 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 29 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 30 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 31 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

108 Table 11. Simulated profiles along the length of all wires on the left side of the wedge. Sector 3 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 10 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 18 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 20 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 21 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 23 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 24 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 25 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 26 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 27 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 28 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 29 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 30 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 31 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

109 Table 12. Simulated profiles along the length of all wires on the right side of the wedge. Sector 3 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 10 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 16 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 17 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 18 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 20 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 21 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 22 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 23 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 24 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 25 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 26 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 27 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 28 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 29 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 30 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 31 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 34 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 35 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 37 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

110 Table 13. Simulated profiles along the length of all wires on the left side of the wedge. Sector 4 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 6 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 9 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 10 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 13 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 14 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 16 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 17 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 18 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 19 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 20 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 21 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 23 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 24 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 25 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 26 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 27 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 28 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 29 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 30 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 31 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 32 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 34 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 35 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

111 Table 14. Simulated profiles along the length of all wires on the right side of the wedge. Sector 4 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 6 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 9 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 10 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 11 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 12 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 13 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 14 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 15 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 16 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 17 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 18 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 19 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 20 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 21 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 23 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 24 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 25 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 26 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 27 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 28 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 29 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 30 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 31 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 32 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 33 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 34 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 35 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 36 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 37 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 38 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 39 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 40 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 41 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 42 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 43 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 44 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 45 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 46 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

112 Table 15. Simulated profiles along the length of all wires on the left side of the wedge. Sector 5 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 6 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 9 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 10 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 11 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 12 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 13 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 14 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 16 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 17 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 18 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 19 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 20 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 21 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 23 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 24 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 25 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 26 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 27 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 28 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 29 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 30 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 31 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 32 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 36 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 37 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 38 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 39 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 40 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 41 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 42 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 43 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 44 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 45 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 46 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2

113 Table 16. Simulated profiles along the length of all wires on the right side of the wedge. Sector 5 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 2 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 6 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 9 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 10 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 11 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 12 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 13 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 14 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 16 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 17 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 18 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 19 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 20 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 21 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 23 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 24 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 25 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 26 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 27 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 28 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 29 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 30 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 31 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 37 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

114 Table 17. Simulated profiles along the length of all wires on the left side of the wedge. Sector 6 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 5 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 6 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 9 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 10 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 13 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 14 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 16 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 17 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 18 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 19 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 20 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 21 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 22 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 23 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 24 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 25 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 26 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 27 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 28 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 29 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 30 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 31 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 36 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1

115 Table 18. Simulated profiles along the length of all wires on the right side of the wedge. Sector 6 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 4 4 4 4 4 2 2 2 2 2 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 5 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 10 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 13 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 14 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 16 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 17 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 18 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 19 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 20 3 3 3 3 3 1 1 1 1 1 3 3 3 3 3 21 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 23 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 24 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 25 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 26 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 27 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 28 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 29 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 30 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 31 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 36 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 37 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

116 Table 19. Simulated profiles along the length of all wires on the left side of the wedge. Sector 7 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 6 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 13 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 14 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 15 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 16 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 17 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 18 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 19 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 20 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 21 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 23 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 24 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 25 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 26 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 27 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 28 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 29 3 3 3 3 3 1 1 1 1 1 3 3 3 3 3 30 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 31 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

117 Table 20. Simulated profiles along the length of all wires on the right side of the wedge. Sector 7 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 13 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 14 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 15 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 16 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 17 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 18 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 19 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 20 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 21 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 23 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 24 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 25 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 26 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 27 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 28 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 29 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 30 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 31 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 40 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

118 Table 21. Simulated profiles along the length of all wires on the left side of the wedge. Sector 8 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 6 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 9 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 10 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 11 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 13 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 14 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 16 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 17 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 18 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 19 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 20 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 21 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 22 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 23 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 24 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 25 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 26 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 27 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 28 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 29 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 30 4 4 4 4 4 2 2 2 2 2 3 3 3 3 3 31 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 32 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 40 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

119 Table 22. Simulated profiles along the length of all wires on the right side of the wedge. Sector 8 Ring # Corrosion stage/grade variation along the length of long wire Location 1 Location 2 Location 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 6 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 9 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 10 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 11 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 12 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 13 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 14 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 16 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 17 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 18 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 19 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 20 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 21 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 22 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 23 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 24 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 25 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 26 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 27 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 28 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 29 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 30 3 3 3 3 3 2 2 2 2 2 3 3 3 3 3 31 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 32 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 33 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 34 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 35 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 37 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 38 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 39 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 40 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 41 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 43 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 44 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 46 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

120 Cumulative Distribution Functions for Different Corrosion Stage Wires To build the empirical CDF of the wire strength for the different corrosion stages, it is necessary to have the experimental results of ultimate tension tests on wire specimens of length 𝑙𝑙 𝑠𝑠 . As specified in this report, a sufficient number of wire specimens is recommended in order to have reliable CDF curves. In this example, the data obtained by the RT from a previous bridge inspection are used. In this example, the procedure to obtain empirical CDFs is described for corrosion stage 3 wires and it is understood that it has to be repeated for wires in all the other corrosion stages. As shown in Table 23, there are 211 wire specimens classified as Corrosion Stage 3. The corresponding ultimate stress 𝑢𝑢 is also listed, as obtained from laboratory tension tests. To obtain the corresponding empirical CDF, first rearrange the ultimate stress 𝑢𝑢 , ranking them from the smallest to the largest. Note that the value of the rank also indicates the number of wire specimens that have an ultimate stress 𝑢𝑢 equal or less that the value of the 𝑢𝑢 corresponding to the rank: for example, in Table 23, for the wire specimen having the rank value equal to 10, this means that there are 10 wires that have an ultimate stress 𝑢𝑢 that is less or equal than 220.0 ksi. This is important in computing the probability that a wire segment has the ultimate stress 𝑢𝑢 equal or less than a certain value. Once the ultimate stresses have been sorted and ranked, then the value of the corresponding CDF can be easily obtained by dividing, for each single wire, the corresponding rank by the total number of wires tested plus one (in this example 211+1=212). (Note: the additional 1 is added so that for the last specimen, the probability is slightly less than 1). As from Table 23, the first ranked wire has an ultimate stress 𝑢𝑢 = 196.8 ksi and the corresponding value of the CDF is: 1 211 + 1 = 0.00471698 For the second ranked wire, the ultimate stress 𝜎𝜎𝑢𝑢 = 197.5 ksi and the corresponding value of the CDF is: 2 211 + 1 = 0.00943396 and so on until, for the last ranked (211th) wire, the ultimate stress 𝜎𝜎𝑢𝑢 is equal to 255.5 ksi and the corresponding value of the CDF is: 211 211 + 1 = 0.99528302 At this point, there will be 211 pairs of 𝜎𝜎𝑢𝑢 and corresponding values of the CDF that can be plotted as (Figure 35 and Table 23):

121 Table 23. Generate CDF Corrosion Stage συ Sorted συ Rank Empirical CDF (ksi) (ksi) 3 232.8 196.8 1 0.00471698 3 232.0 197.5 2 0.00943396 3 243.5 209.2 3 0.01415094 3 240.7 214.5 4 0.01886792 3 240.9 216.5 5 0.02358491 3 223.2 218.0 6 0.02830189 3 225.9 218.0 7 0.03301887 3 244.6 218.0 8 0.03773585 3 245.6 219.4 9 0.04245283 3 244.9 220.0 10 0.04716981 3 242.3 222.1 11 0.05188679 3 241.1 222.7 12 0.05660377 3 233.7 223.2 13 0.06132075 3 238.4 223.5 14 0.06603774 3 237.1 223.7 15 0.07075472 3 238.5 224.0 16 0.0754717 3 245.6 224.7 17 0.08018868 3 244.2 224.8 18 0.08490566 3 243.0 224.9 19 0.08962264 3 240.6 224.9 20 0.09433962 3 249.8 225.1 21 0.0990566 3 245.6 225.1 22 0.10377358 3 245.1 225.3 23 0.10849057 3 232.7 225.4 24 0.11320755 3 231.6 225.8 25 0.11792453 3 251.1 225.9 26 0.12264151 3 250.7 226.0 27 0.12735849 3 250.3 226.2 28 0.13207547 3 249.9 226.2 29 0.13679245 3 231.8 226.6 30 0.14150943 3 228.2 226.6 31 0.14622642 3 230.2 226.6 32 0.1509434 3 231.9 226.9 33 0.15566038 3 238.8 226.9 34 0.16037736 3 239.7 227.0 35 0.16509434

122 Corrosion Stage συ Sorted συ Rank Empirical CDF (ksi) (ksi) 3 236.6 227.1 36 0.16981132 3 238.7 227.3 37 0.1745283 3 242.7 227.3 38 0.17924528 3 239.7 227.5 39 0.18396226 3 242.3 227.6 40 0.18867925 3 236.1 227.7 41 0.19339623 3 241.1 227.8 42 0.19811321 3 233.8 227.9 43 0.20283019 3 245.5 228.0 44 0.20754717 3 247.9 228.2 45 0.21226415 3 253.1 228.4 46 0.21698113 3 254.5 228.5 47 0.22169811 3 254.3 228.5 48 0.22641509 3 214.5 228.6 49 0.23113208 3 224.0 229.0 50 0.23584906 3 237.8 229.0 51 0.24056604 3 235.2 229.5 52 0.24528302 3 239.3 229.5 53 0.25 3 238.3 229.5 54 0.25471698 3 216.5 230.1 55 0.25943396 3 219.4 230.1 56 0.26415094 3 230.8 230.2 57 0.26886792 3 224.8 230.3 58 0.27358491 3 244.5 230.8 59 0.27830189 3 248.1 231.1 60 0.28301887 3 244.7 231.1 61 0.28773585 3 248.3 231.4 62 0.29245283 3 253.6 231.4 63 0.29716981 3 251.6 231.6 64 0.30188679 3 243.5 231.6 65 0.30660377 3 248.5 231.7 66 0.31132075 3 242.3 231.8 67 0.31603774 3 240.5 231.9 68 0.32075472 3 240.4 231.9 69 0.3254717 3 241.2 231.9 70 0.33018868 3 239.7 232.0 71 0.33490566

123 Corrosion Stage συ Sorted συ Rank Empirical CDF (ksi) (ksi) 3 237.8 232.0 72 0.33962264 3 242.4 232.1 73 0.34433962 3 229.5 232.3 74 0.3490566 3 228.5 232.5 75 0.35377358 3 231.1 232.7 76 0.35849057 3 231.9 232.7 77 0.36320755 3 235.2 232.8 78 0.36792453 3 231.4 232.8 79 0.37264151 3 233.0 233.0 80 0.37735849 3 235.5 233.4 81 0.38207547 3 225.1 233.6 82 0.38679245 3 227.9 233.7 83 0.39150943 3 245.8 233.7 84 0.39622642 3 245.9 233.7 85 0.4009434 3 250.1 233.8 86 0.40566038 3 245.2 233.8 87 0.41037736 3 218.0 233.9 88 0.41509434 3 220.0 234.0 89 0.41981132 3 218.0 234.1 90 0.4245283 3 236.7 234.9 91 0.42924528 3 235.7 235.0 92 0.43396226 3 238.3 235.0 93 0.43867925 3 233.9 235.2 94 0.44339623 3 235.3 235.2 95 0.44811321 3 236.2 235.2 96 0.45283019 3 239.9 235.3 97 0.45754717 3 237.5 235.5 98 0.46226415 3 243.3 235.6 99 0.46698113 3 239.7 235.7 100 0.47169811 3 222.1 235.8 101 0.47641509 3 227.3 235.9 102 0.48113208 3 246.6 236.1 103 0.48584906 3 251.3 236.1 104 0.49056604 3 242.2 236.2 105 0.49528302 3 247.6 236.3 106 0.5 3 225.3 236.4 107 0.50471698

124 Corrosion Stage συ Sorted συ Rank Empirical CDF (ksi) (ksi) 3 222.7 236.4 108 0.50943396 3 236.4 236.6 109 0.51415094 3 238.5 236.7 110 0.51886792 3 237.8 237.0 111 0.52358491 3 238.5 237.1 112 0.52830189 3 225.8 237.2 113 0.53301887 3 223.7 237.3 114 0.53773585 3 226.6 237.4 115 0.54245283 3 226.6 237.5 116 0.54716981 3 226.9 237.8 117 0.55188679 3 225.4 237.8 118 0.55660377 3 231.9 237.8 119 0.56132075 3 224.9 238.3 120 0.56603774 3 241.8 238.3 121 0.57075472 3 240.6 238.3 122 0.5754717 3 227.1 238.4 123 0.58018868 3 225.1 238.5 124 0.58490566 3 239.1 238.5 125 0.58962264 3 237.2 238.5 126 0.59433962 3 242.0 238.7 127 0.5990566 3 234.9 238.8 128 0.60377358 3 245.4 239.0 129 0.60849057 3 243.0 239.1 130 0.61320755 3 245.7 239.1 131 0.61792453 3 242.4 239.3 132 0.62264151 3 218.0 239.7 133 0.62735849 3 226.0 239.7 134 0.63207547 3 223.5 239.7 135 0.63679245 3 227.0 239.7 136 0.64150943 3 227.3 239.9 137 0.64622642 3 234.0 240.0 138 0.6509434 3 235.9 240.1 139 0.65566038 3 229.5 240.3 140 0.66037736 3 235.0 240.4 141 0.66509434 3 240.1 240.5 142 0.66981132 3 235.2 240.5 143 0.6745283

125 Corrosion Stage συ Sorted συ Rank Empirical CDF (ksi) (ksi) 3 236.1 240.6 144 0.67924528 3 232.0 240.6 145 0.68396226 3 232.7 240.6 146 0.68867925 3 235.6 240.7 147 0.69339623 3 209.2 240.9 148 0.69811321 3 255.5 240.9 149 0.70283019 3 250.2 241.1 150 0.70754717 3 253.5 241.1 151 0.71226415 3 243.1 241.2 152 0.71698113 3 244.4 241.5 153 0.72169811 3 232.3 241.6 154 0.72641509 3 233.7 241.7 155 0.73113208 3 235.8 241.8 156 0.73584906 3 232.8 242.0 157 0.74056604 3 232.5 242.2 158 0.74528302 3 231.1 242.2 159 0.75 3 230.1 242.3 160 0.75471698 3 236.3 242.3 161 0.75943396 3 237.0 242.3 162 0.76415094 3 224.9 242.4 163 0.76886792 3 232.1 242.4 164 0.77358491 3 226.6 242.7 165 0.77830189 3 228.6 242.9 166 0.78301887 3 227.8 243.0 167 0.78773585 3 229.0 243.0 168 0.79245283 3 231.4 243.1 169 0.79716981 3 233.8 243.3 170 0.80188679 3 231.7 243.5 171 0.80660377 3 228.5 243.5 172 0.81132075 3 229.0 244.2 173 0.81603774 3 228.4 244.4 174 0.82075472 3 239.0 244.5 175 0.8254717 3 240.6 244.6 176 0.83018868 3 231.6 244.7 177 0.83490566 3 234.1 244.9 178 0.83962264 3 233.4 245.1 179 0.84433962

126 Corrosion Stage συ Sorted συ Rank Empirical CDF (ksi) (ksi) 3 228.0 245.2 180 0.8490566 3 226.2 245.4 181 0.85377358 3 227.5 245.5 182 0.85849057 3 226.2 245.6 183 0.86320755 3 224.7 245.6 184 0.86792453 3 230.3 245.6 185 0.87264151 3 233.6 245.6 186 0.87735849 3 235.0 245.7 187 0.88207547 3 241.6 245.8 188 0.88679245 3 227.6 245.9 189 0.89150943 3 230.1 246.6 190 0.89622642 3 229.5 247.6 191 0.9009434 3 245.6 247.9 192 0.90566038 3 196.8 248.1 193 0.91037736 3 236.4 248.3 194 0.91509434 3 241.7 248.5 195 0.91981132 3 242.2 249.8 196 0.9245283 3 239.1 249.9 197 0.92924528 3 241.5 250.1 198 0.93396226 3 240.5 250.2 199 0.93867925 3 240.9 250.3 200 0.94339623 3 238.3 250.6 201 0.94811321 3 237.4 250.7 202 0.95283019 3 237.3 251.1 203 0.95754717 3 240.3 251.3 204 0.96226415 3 250.6 251.6 205 0.96698113 3 242.9 253.1 206 0.97169811 3 240.0 253.5 207 0.97641509 3 226.9 253.6 208 0.98113208 3 227.7 254.3 209 0.98584906 3 197.5 254.5 210 0.99056604 3 233.7 255.5 211 0.99528302

127 Figure 40. Empirical CDF for Group 3 Wire Specimens An identical process has to be followed using the other corrosion stage wire specimens to obtain the CDFs corresponding to Corrosion Stage 1 (Group 1), Corrosion Stage 2 (Group 2) and Corrosion Stage 4 (Group 3) wires. Once the CDFs are available, they can be used to obtain different random realizations of the spatial variation of the wire strength along the entire effective length of the panel. Simulating the Variation of the Wire Strength Along the Effective Panel Length This process has to be repeated for each single wire in the exposed 16 faces at the wedged openings, as obtained at the end of the section on Cable Inspection of this Chapter and as presented in Tables 7 through 22. The value of the ultimate stress of each wire will be also representative of the ultimate stress of the wires in the corresponding subsector. As an example, refer again to wire 28 on the left face of the wedged opening in sector 1. It was classified as a wire of Corrosion Stage 3 and was modeled as: 3 – 3 – 3 – 3 – 3 – 2 – 2 – 2 – 2 – 2 – 3 – 3 – 3 – 3 – 3 a combination of 10 wire segments of corrosion stage 3 and 5 segments of corrosion stage 2. Then, generate 10 random numbers uniformly distributed in the interval [0,1] for corrosion stage 3 and 5 uniformly distributed random numbers in the interval [0,1] for corrosion stage 2. These generated

128 random numbers represent the values of the CDF for the wire segments in the model of the wire. To generate random numbers between 0 and 1, the function Rand can be used in Excel. For the case in question, the following random numbers were generated: For corrosion stage 3: 1 2 3 4 5 6 7 8 9 10 0.1576 0.9706 0.9572 0.4854 0.8003 0.1419 0.4218 0.9157 0.7922 0.9595 For corrosion stage 2: 1 2 3 4 5 0.6557 0.0357 0.8491 0.9340 0.6787 For each generated random number, representing the value of the CDF for a given wire segment, it is possible to obtain the value of the corresponding 𝜎𝜎𝑢𝑢 using the plots from Section 3. For example, for the first segment, the value of the CDF is 0.1576 and the corresponding 𝜎𝜎𝑢𝑢 is 226.9 ksi. For the second segment, the value of the CDF is 0.9706 and the corresponding 𝜎𝜎𝑢𝑢 is 252.7, etc. These values of 𝜎𝜎𝑢𝑢 can be obtained from the table of the values of the CDF: • if the random value of the CDF is one of the values of the CDF in the table, then just use the corresponding value of the 𝜎𝜎𝑢𝑢 (Figure 36). • if instead the random value of the CDF is not one of the values in the table but it is in between two values in the table of the CDF, use linear interpolation between these two values (Figure 36). Figure 41. Empirical CDF for Group 3 Wire Specimens

129 Repeating the same procedure for each single wire segment, we obtain the following values of the 𝜎𝜎𝑢𝑢 For Corrosion Stage 3: 1 2 3 4 5 6 7 8 9 10 0.1576 0.9706 0.9572 0.4854 0.8003 0.1419 0.4218 0.9157 0.7922 0.9595 226.9 252.7 251.1 236.1 243.2 226.6 234.0 248.3 243.0 251.2 For Corrosion Stage 2: 1 2 3 4 5 0.6557 0.0357 0.8491 0.9340 0.6787 238.7 215.0 246.1 251.1 238.9 At this point, the “estimated” variation of the wire strength for wire 28 on the left face of the wedged opening in sector 1 (and all the wires in the corresponding subsector), with an “overall” classification as a Corrosion Stage 3 wire and modeled as: 3 – 3 – 3 – 3 – 3 – 2 – 2 – 2 – 2 – 2 – 3 – 3 – 3 – 3 – 3 will be represented as: Table 24. Ultimate Stresses determined from CDF Segment Corrosion Stage 𝝈𝝈𝒖𝒖 ksi 3 226.9 3 252.7 3 251.1 3 236.1 3 243.2 2 238.7 2 215.0 2 246.1 2 251.1 2 238.9 3 226.6 3 234.0 3 248.3 3 243.0 3 251.2 At this point, using the weakest link assumption, the ultimate stress of this representation of the wire 28 on the left face of the wedged opening in sector 1 (and all the wires in the corresponding subsector) will be 𝜎𝜎𝑢𝑢,𝑙𝑙 = 215.0 ksi.

130 Hence, in the final corrosion map of the cross-section, the wire 28 on the left face of the wedged opening in sector one and all the wires in the corresponding subsector will be categorized as Corrosion Stage 3 wires and their ultimate stress 𝜎𝜎𝑢𝑢,𝑙𝑙 = 215.0 ksi. This operation has to be done for each single wire exposed at the wedged openings and extended to every single wire in the corresponding subsectors. At the end of this operation, the final corrosion map of the cross-section will be obtained; each of the 6080 wires will be categorized in one of the four corrosion stages (the worst along the inspected length) and will have a value of the ultimate stress 𝜎𝜎𝑢𝑢,𝑙𝑙 that accounts for the spatial variation of the wire strength along the effective length 𝐿𝐿𝑒𝑒 of the panel. At the end of this operation, the final corrosion map used to calculate the ultimate strength will comprise: • 206 Corrosion Stage 1 wires with associated 206 values of 𝜎𝜎𝑢𝑢,𝑙𝑙 • 2559 Corrosion Stage 2 wires with associated 2559 values of 𝜎𝜎𝑢𝑢,𝑙𝑙 • 2827 Corrosion Stage 3 wires with associated 2827 values of 𝜎𝜎𝑢𝑢,𝑙𝑙 • 488 Corrosion Stage 4 wires with associated 488 values of 𝜎𝜎𝑢𝑢,𝑙𝑙 Accounting for Broken Wires in the Inspected Panel and in the Panels in the Redevelopment Length In this example, the redevelopment length is obtained following the same procedure contained in NCHRP NCHRP Report 534. The redevelopment length is equivalent to seven panels. Figure 42. Redevelopment Length for the Inspected Panel (Panel 1) 𝑁𝑁𝑏𝑏𝑑𝑑 represents the estimated number of broken wires in the 𝑖𝑖-th panel. During the panel inspection, 18 broken wires were found and were classified as follows (based on the final corrosion map, i.e. the highest stage of corrosion within the panel): • Corrosion Stage 1: 2 broken wires (11.1%) • Corrosion Stage 2: 2 broken wires (11.1%) • Corrosion Stage 3: 8 broken wires (44.5%) • Corrosion Stage 4: 6 broken wires (33.3%) Following the same procedure in NCHRP NCHRP Report 534, 139 wires were estimated broken in the inspected panel and they were classified based on the same percentages of the found broken wires. Hence, the 139 estimated broken wires were classified as:

131 • Corrosion Stage 1: 15 estimated broken wires • Corrosion Stage 2: 15 estimated broken wires • Corrosion Stage 3: 63 estimated broken wires • Corrosion Stage 4: 46 estimated broken wires. At this point, these broken wires have to be removed from the corrosion map obtained in the previous step. They can be removed according to the following procedure: • For the Corrosion Stage 1 wires, generate 15 random numbers in the range [1-206] and remove the corresponding 15 wires from the 206 wires in the Corrosion Stage 1 group. • For the Corrosion Stage 2 wires, generate 15 random numbers in the range [1-2559] and remove the corresponding 15 wires from the 2559 wires in the Corrosion Stage 2 group. • For the Corrosion Stage 3 wires, generate 63 random numbers in the range [1-2827] and remove the corresponding 63 wires from the 2827 wires in the Corrosion Stage 3 group. • For the Corrosion Stage 4 wires, generate 46 random numbers in the range [1-488] and remove the corresponding 46 wires from the 488 wires in the Corrosion Stage 4 group. At this point, the number of effective wires in the inspected cable panel is: • Corrosion Stage 1: 206 – 15 = 191 • Corrosion Stage 2: 2559 – 15 = 2544 • Corrosion Stage 3: 2827 – 63 = 2764 • Corrosion Stage 4: 488 – 46 = 442 for a total number of effective wires equal to 5941 wires. METHOD 1 To account for the broken wires in the neighboring panels following Method 1, first, the estimates of the number of broken wires in the six neighboring panels should be obtained (𝑁𝑁𝑏𝑏𝑑𝑑 , 𝑖𝑖 =2, 3, 4, 5, 6). In this example, it is assumed that the number of estimated broken wires in the neighboring panels is the same as the number of estimated broken wires in the inspected panel and with the same distribution among the corrosion stages (see Table 3.5-2). In this example, the redevelopment length Le (Le=7) and redevelopment factors Cdi can be estimated by Eq. 4.5.2-1 to Eq. 4.5.2-4 in NCHRP 534 and shown in Table 25. Table 25. Redevelopment factors, Cdi Panel i 1 2 & 3 4 & 5 6 & 7 Cdi 0 0.25 0.50 0.75

132 Table 26. Estimated broken wires in the panels within the redevelopment length Corrosion Stage Group, k Proportion % Estimated broken wires in inspected panel Develop 25% strength Develop 50% strength Develop 75% strength 1 11.1% 15 (2 observed) 30 30 30 2 11.1% 15 (2 observed) 30 30 30 3 44.5% 63 (8 observed) 126 126 126 4 33.3% 46 (6 observed) 92 92 92 Total 100% 139 (18 observed) 139*2=278 139*2=278 139*2=278 To account for the effect of broken wires in adjacent panels, the following procedure should be followed: For Corrosion Stage 1, generate 30 random numbers in the range [1-191] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.25. Now, for the remaining 191 – 30 = 161 wires, again generate 30 random numbers in the range [1-161] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.5. Finally, for the remaining 191 – 30 – 30 = 131 wires, generate 30 random numbers in the range [1-131] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.75. For the remaining 101 wires in Corrosion Stage 1, their 𝜎𝜎𝑢𝑢,𝑙𝑙 will remain unchanged. For Corrosion Stage 2, generate 30 random numbers in the range [1-2544] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.25. Now, for the remaining 2544 – 30 = 2514 wires, again generate 30 random numbers in the range [1-2514] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.5. Finally, for the remaining 2544 – 30 – 30 = 2484 wires, generate 30 random numbers in the range [1-2484] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.75. For the remaining 2454 wires in Corrosion Stage 2, their 𝜎𝜎𝑢𝑢,𝑙𝑙 will remain unchanged. For Corrosion Stage 3, generate 126 random numbers in the range [1-2764] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.25. Now, for the remaining 2764 – 126 = 2638 wires, again generate 126 random numbers in the range [1-2638] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.5. Finally, for the remaining 2764 – 126 – 126 = 2512 wires, generate 126 random numbers in the range [1-2512] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.75. For the remaining 2386 wires in Corrosion Stage 3, their 𝜎𝜎𝑢𝑢,𝑙𝑙 will remain unchanged. For Corrosion Stage 4, generate 92 random numbers in the range [1-442] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.25. Now, for the remaining 442 – 92 = 350 wires, again generate 92 random numbers in the range [1-350] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.5. Finally, for the remaining 442 – 92 – 92 = 258 wires, generate 30 random numbers in the range [1-258] and multiply the corresponding 𝜎𝜎𝑢𝑢,𝑙𝑙 (as obtained in Section 4) times 0.75. For the remaining 166 wires in Corrosion Stage 4, their 𝜎𝜎𝑢𝑢,𝑙𝑙 will remain unchanged.

133 At the end of this process, the final corrosion map of the cable cross-section will still be comprised of 5941 wires but, for some of them, the ultimate stress 𝜎𝜎𝑢𝑢,𝑙𝑙 has been properly reduced to account for broken wires in the neighboring panels. At this point, the iterative procedure to estimate the ultimate strength of the entire cable can start. METHOD 2 To account for the broken wires in the neighboring panels following Method 2, first, the estimates of the number of broken wires in the six neighboring panels should be obtained (𝑁𝑁𝑏𝑏𝑑𝑑 , 𝑖𝑖 =2, 3, 4, 5, 6). In this example, it is assumed that the number of estimated broken wires in the neighboring panels is the same as the number of estimated broken wires in the inspected panel and with the same distribution among the corrosion stages (see Table 26). This approach is similar to the one proposed in the NCHRP NCHRP Report 534. The redevelopment length Le and redevelopment factor Cd can be estimated by Eq. 4.5.2-1 to Eq. 4.5.2-4 in NCHRP 534 as shown in Table 25. Then, the equivalent number of broken wires within the panel under consideration, 𝑁𝑁𝑒𝑒𝑏𝑏, accounting for the redevelopment length in broken wires in neighboring panels, can be estimated by: 𝑁𝑁𝑒𝑒𝑏𝑏 = 𝑁𝑁𝑏𝑏1 + ∑ 𝑁𝑁𝑏𝑏𝑑𝑑 ∗ (1 − 𝐶𝐶𝑑𝑑𝑑𝑑) 𝐿𝐿𝑒𝑒 𝑑𝑑=2 (15) where 𝑁𝑁𝑏𝑏𝑑𝑑 is the number of broken wires in the 𝑖𝑖 −th panel, 𝑁𝑁𝑏𝑏1 is the number of broken wires in the evaluated panel; and 𝐶𝐶𝑑𝑑𝑑𝑑 is the redevelopment factor in the 𝑖𝑖 −th panel. The additional estimated number of broken wires, accounting for the effects of broken wires in neighboring panels, can be obtained as follows: For Corrosion Stage 1, the estimated number of broken wires is obtained as: 0.25 * 30 + 0.5 * 30 + 0.75 * 30 = 45 wires Considering the population of Corrosion Stage 1 wires (191), generate 45 random numbers in the range [1-191] and remove the corresponding wires from the Corrosion Stage 1 group. Hence, the final total number of wires in Corrosion Stage 1 is 191 – 45 = 146 For Corrosion Stage 2, the estimated number of broken wires is obtained as: 0.25 * 30 + 0.5 * 30 + 0.75 * 30 = 45 wires Considering the population of Corrosion Stage 2 wires (2544), generate 45 random numbers in the range [1-2544] and remove the corresponding wires from the Corrosion Stage 2 group. The final total number of wires in Corrosion Stage 2 is 2544 – 45= 2499. For Corrosion Stage 3, the estimated number of broken wires is obtained as: 0.25 * 126 + 0.5 * 126 + 0.75 * 126 = 189 wires Considering the population of Corrosion Stage 3 wires (2764), generate 189 random numbers in the range [1-2764] and remove the corresponding wires from the Corrosion Stage 3 group. The final total number of wires in Corrosion Stage 3 is 2764 – 189= 2575. For Corrosion Stage 4, the estimated number of broken wires is obtained as: 0.25 * 92 + 0.5 * 92 + 0.75 * 92 = 138 wires Considering the population of Corrosion Stage 4 wires (442), generate 138 random numbers in the range [1-442] and remove the corresponding wires from the Corrosion Stage 4 group. The final total number of wires in Corrosion Stage 4 is 442 – 138 = 304.

134 The total number of effective wires in the cross-section, accounting for the broken wires in the neighboring panels, is: 5941 – 45 – 45 – 189 – 138 = 5524. At the end of this process, the final corrosion map of the cable cross-section will be comprised of 5524 wires but, contrary to Method 1, the ultimate stress 𝜎𝜎𝑢𝑢,𝑙𝑙 of these wires has remained unchanged. At this point, the iterative procedure to estimate the ultimate strength of the entire cable can start (for this example, all calculations were performed using MATLAB). Iterative Procedure to Estimate the Cable Strength Once the final map of the ultimate strength of the “effective” wires is finalized using either Method 1 or Method 2 described in the previous section, the process of estimating the overall strength of the cable can start. 1) Select an initial estimate of the force, 𝐹𝐹0, carried by the cable under service load conditions. In this example, we use 𝐹𝐹0 = 10260 kips which represents the maximum cable force. 2) Divide this force by the number of effective wires in the cross-section to find the force carried by a single wire, 𝐹𝐹0,𝑑𝑑: 𝐹𝐹0,𝑑𝑑 = 𝐹𝐹0 𝑁𝑁𝑒𝑒𝑒𝑒𝑒𝑒 where 𝑁𝑁𝑒𝑒𝑒𝑒𝑒𝑒 = 5941 (if using Method 1) or 𝑁𝑁𝑒𝑒𝑒𝑒𝑒𝑒 = 5524 (if using Method 2). 3) Divide 𝐹𝐹0,𝑑𝑑 by the area 𝐴𝐴𝑤𝑤 of a single wire (0.02895 in2) to obtain an average stress 𝜎𝜎𝑎𝑎𝑎𝑎 : 𝜎𝜎𝑎𝑎𝑎𝑎 = 𝐹𝐹0,𝑑𝑑 𝐴𝐴𝑤𝑤 4) Compare the value of 𝜎𝜎𝑎𝑎𝑎𝑎 with all the values in the map of long wire ultimate strengths 𝜎𝜎𝑢𝑢,𝑙𝑙 as obtained in Section 5. If there are values of the wire ultimate strengths 𝜎𝜎𝑢𝑢,𝑙𝑙 that are less than the value of 𝜎𝜎𝑎𝑎𝑎𝑎, then the corresponding wires are eliminated and a new number of effective wires, 𝑁𝑁𝑒𝑒𝑒𝑒𝑒𝑒′ is obtained. 5) Repeat Step 2 to Step 4 until the newly computed 𝜎𝜎𝑎𝑎𝑎𝑎 is smaller than any ultimate strength 𝜎𝜎𝑢𝑢,𝑙𝑙 of the remaining effective wires. 6) At this point, increase the cable force by an arbitrary small increment (Δ𝐹𝐹) and consider the new cable force: 𝐹𝐹1 = 𝐹𝐹0 + Δ𝐹𝐹 In this example, we have used a Δ𝐹𝐹 = 100 kips. 7) Repeat Steps 2 through 6 until, at the i-th iteration, the corresponding 𝜎𝜎𝑎𝑎𝑎𝑎 will be greater than the ultimate strength of all the remaining long wires. This would mean that all the wires will be considered broken.

135 8) The largest value of the cable force sustained by the long wires (the one corresponding to the (i-1)-th iteration, 𝐹𝐹(𝑑𝑑−1)) will represent an estimate of the overall cable strength for that given realization: 𝑅𝑅𝑢𝑢 = 𝐹𝐹(𝑑𝑑−1) The value of 𝑅𝑅𝑢𝑢 represents the estimate of the overall cable strength for the realization obtained following the steps described from Section 2 to Section 6 (all calculations were performed using MATLAB). Monte Carlo Simulations for the Estimation of the Overall Cable Strength The procedure described in the previous sections provides one value of the ultimate strength of the cable 𝑅𝑅𝑢𝑢 based on the specific realization of the spatial variation of the wire strength obtained in Section 3. To obtain reliable statistics of the overall cable strength, this procedure has to be repeated a large number of times. In this example, this procedure has been repeated 10000 times. Hence, the distribution of the overall cable strength, with its mean and standard deviation, could be obtained on a population of 10000 values. For a new repetition, the CDF’s determined in Articles 3.2 and Article 3.3 remain unchanged. Starting from Article 3.4, a new map of the ultimate stress 𝜎𝜎𝑢𝑢,𝑙𝑙 is obtained, following the same process described in Articles 3.4 and 3.5 and a new value of 𝑅𝑅𝑢𝑢 is derived through the process described in Article 3.6. Here are the results for the specific example.

136 Method 1 𝑅𝑅𝑢𝑢,𝑟𝑟𝑒𝑒𝑎𝑎𝑚𝑚 = 28,100 𝑘𝑘𝑖𝑖𝑘𝑘𝑘𝑘 Method 2 𝑅𝑅𝑢𝑢,𝑟𝑟𝑒𝑒𝑎𝑎𝑚𝑚 = 29,991 𝑘𝑘𝑖𝑖𝑘𝑘𝑘𝑘