A Stochastic Interpolation-Based Fractal Model for Vulnerability Diagnosis of Water Supply Networks Against Seismic Hazards
Abstract
1. Introduction
2. Seismic Vulnerability of WSN and Its Modeling Method
2.1. The Basic Concept of Seismic Vulnerability of the WSN
2.2. Analysis of Indices: Searching for the Relationships between Indices and Vulnerability
2.3. Stochastic Interpolation-Based Fractal Model for Seismic Vulnerability Assessment of WSNs
3. Case Study
3.1. Feasibility Analysis of the Model
3.2. Application Example
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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District | Seismic Intensity (Degree) | Soil Type of the Site | Damage Rate (Places/km) |
---|---|---|---|
Tianjin City | 7–8 | Type 3 | 0.18 |
Tanggu district | 8 | Type 3 | 4.18 |
Hangu district | 9 | Type 3 | 10.00 |
Tangshan city | 10–11 | Type 2 | 4.00 |
San Fernando | 8 | Type 1 | 0.09 |
Los Angeles | 6 | Type 2 | 0.62 |
Sendai area | 9 | Type 1 | 0.03 |
Type 2 | 0.22 | ||
Type 3 | 0.87 |
Grade | x1 | x2 (mm) | x3 | x4 (Year) | x5 | x6 (m) |
---|---|---|---|---|---|---|
High (IV) | Wrapped FRP pipe Asbestos cement pipe Concrete pipe | x2 ≤ 200 | Adhesion connection Threaded connection Asbestos cement Self-stressing cement | 50 ≤ x4 | Type 4 | x6 ≤ 0.5 |
Medium (III) | Plain cast-iron pipe Prestressed reinforced concrete pipe | 200 < x2 ≤ 500 | Welding | 30 ≤x4 < 50 | Type 3 | 0.5 < x6 ≤ 1 |
Low (II) | Polyvinyl chloride pipe Steel pipe Ductile cast-iron pipe | 500 < x2 ≤ 800 | Hot-melt connection Flange connection | 10 ≤ x4 < 30 | Type 2 | 1 < x6 ≤ 2 |
Very low (I) | Polythene pipe Steel–plastic compound pipe | 800 < x2 | Rubber ring connection | x4 < 10 | Type 1 | 2 < x6 |
Grade | x1 | x2 (mm) | x3 | x4 (Year) | x5 | x6 (m) |
---|---|---|---|---|---|---|
High (IV) | 3.5–4.5 | 0–200 | 3.5–4.5 | 50–70 | 3.5–4.5 | 0.0–0.5 |
Medium (III) | 2.5–3.5 | 200–500 | 2.5–3.5 | 30–50 | 2.5–3.5 | 0.5–1.0 |
Low (II) | 1.5–2.5 | 500–800 | 1.5–2.5 | 10–30 | 1.5–2.5 | 1.0–2.0 |
Very low (I) | 0.5–1.5 | 800–1200 | 0.5–1.5 | 0–10 | 0.5–1.5 | 2.0–4.0 |
Grade | x1 | x2 | x3 | x4 | x5 | x6 |
---|---|---|---|---|---|---|
High (IV) | 0.750–1.000 | 0.833–1.00 | 0.750–1.000 | 0.714–1.000 | 0.750–1.000 | 0.875–1.000 |
Medium (III) | 0.500–0.750 | 0.583–0.833 | 0.500–0.750 | 0.429–0.714 | 0.500–0.750 | 0.750–0.875 |
Low (II) | 0.250–0.500 | 0.333–0.583 | 0.250–0.500 | 0.143–0.429 | 0.250–0.500 | 0.500–0.750 |
Very low (I) | 0.000–0.250 | 0.000–0.333 | 0.000–0.250 | 0.000–0.143 | 0.000–0.250 | 0.000–0.500 |
No | x1 | x2 | x3 | x4 | x5 | x6 | Y(j) | No | x1 | x2 | x3 | x4 | x5 | x6 | Y(j) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.011 | 0.018 | 0.012 | 0.001 | 0.004 | 0.008 | 1 | 21 | 0.523 | 0.602 | 0.519 | 0.432 | 0.514 | 0.752 | 3 |
2 | 0.028 | 0.049 | 0.029 | 0.014 | 0.035 | 0.083 | 1 | 22 | 0.528 | 0.608 | 0.531 | 0.484 | 0.530 | 0.763 | 3 |
3 | 0.075 | 0.096 | 0.070 | 0.035 | 0.054 | 0.145 | 1 | 23 | 0.569 | 0.634 | 0.568 | 0.491 | 0.555 | 0.779 | 3 |
4 | 0.083 | 0.127 | 0.078 | 0.052 | 0.094 | 0.176 | 1 | 24 | 0.593 | 0.675 | 0.599 | 0.522 | 0.577 | 0.791 | 3 |
5 | 0.107 | 0.158 | 0.107 | 0.068 | 0.122 | 0.235 | 1 | 25 | 0.614 | 0.698 | 0.622 | 0.566 | 0.623 | 0.808 | 3 |
6 | 0.127 | 0.168 | 0.131 | 0.079 | 0.134 | 0.258 | 1 | 26 | 0.630 | 0.721 | 0.627 | 0.585 | 0.643 | 0.824 | 3 |
7 | 0.157 | 0.202 | 0.163 | 0.087 | 0.167 | 0.348 | 1 | 27 | 0.665 | 0.751 | 0.659 | 0.622 | 0.664 | 0.837 | 3 |
8 | 0.176 | 0.236 | 0.177 | 0.109 | 0.182 | 0.377 | 1 | 28 | 0.682 | 0.776 | 0.684 | 0.640 | 0.683 | 0.843 | 3 |
9 | 0.213 | 0.293 | 0.210 | 0.116 | 0.213 | 0.434 | 1 | 29 | 0.703 | 0.803 | 0.717 | 0.665 | 0.704 | 0.853 | 3 |
10 | 0.244 | 0.331 | 0.228 | 0.131 | 0.246 | 0.452 | 1 | 30 | 0.730 | 0.815 | 0.740 | 0.687 | 0.741 | 0.872 | 3 |
11 | 0.272 | 0.350 | 0.270 | 0.162 | 0.275 | 0.519 | 2 | 31 | 0.754 | 0.844 | 0.767 | 0.717 | 0.752 | 0.882 | 4 |
12 | 0.277 | 0.372 | 0.284 | 0.184 | 0.279 | 0.544 | 2 | 32 | 0.784 | 0.851 | 0.778 | 0.765 | 0.779 | 0.892 | 4 |
13 | 0.306 | 0.393 | 0.305 | 0.213 | 0.306 | 0.569 | 2 | 33 | 0.801 | 0.868 | 0.818 | 0.780 | 0.804 | 0.904 | 4 |
14 | 0.326 | 0.410 | 0.327 | 0.246 | 0.335 | 0.578 | 2 | 34 | 0.838 | 0.896 | 0.828 | 0.817 | 0.830 | 0.918 | 4 |
15 | 0.361 | 0.453 | 0.369 | 0.259 | 0.352 | 0.617 | 2 | 35 | 0.858 | 0.915 | 0.853 | 0.856 | 0.858 | 0.930 | 4 |
16 | 0.375 | 0.466 | 0.380 | 0.295 | 0.392 | 0.637 | 2 | 36 | 0.879 | 0.925 | 0.891 | 0.869 | 0.883 | 0.942 | 4 |
17 | 0.422 | 0.498 | 0.410 | 0.337 | 0.410 | 0.655 | 2 | 37 | 0.905 | 0.935 | 0.908 | 0.905 | 0.905 | 0.957 | 4 |
18 | 0.430 | 0.527 | 0.439 | 0.363 | 0.450 | 0.677 | 2 | 38 | 0.948 | 0.964 | 0.941 | 0.936 | 0.931 | 0.972 | 4 |
19 | 0.452 | 0.536 | 0.456 | 0.375 | 0.460 | 0.721 | 2 | 39 | 0.967 | 0.972 | 0.969 | 0.955 | 0.972 | 0.980 | 4 |
20 | 0.483 | 0.561 | 0.491 | 0.404 | 0.491 | 0.729 | 2 | 40 | 0.987 | 0.988 | 0.990 | 0.990 | 0.993 | 0.993 | 4 |
No. | The Proposed Method in This Paper | AHP-Based Assessment Method [27] | Catastrophe Progression Method [26,52] | ||||
---|---|---|---|---|---|---|---|
Evaluation Value | Grade Value | Grade | Evaluation value | Grade | Evaluation value | Grade | |
1 | 2.697 | 2 | II | 0.468 | II | 0.895 | II |
2 | 2.913 | 2.2 | [II,III] | 0.568 | III | 0.915 | III |
3 | 2.853 | 2 | II | 0.551 | III | 0.915 | III |
4 | 2.853 | 2 | II | 0.491 | II | 0.900 | II |
5 | 2.882 | 2.0 | II | 0.486 | II | 0.900 | II |
6 | 2.229 | 2 | II | 0.472 | II | 0.842 | II |
7 | 2.562 | 2 | II | 0.440 | II | 0.883 | II |
8 | 3.002 | 2.7 | [II,III] | 0.572 | III | 0.919 | III |
9 | 2.630 | 2 | II | 0.524 | III | 0.906 | II |
10 | 2.386 | 2 | II | 0.480 | II | 0.850 | II |
11 | 2.852 | 2 | II | 0.550 | III | 0.915 | III |
12 | 2.318 | 2 | II | 0.476 | II | 0.845 | II |
13 | 2.698 | 2 | II | 0.528 | III | 0.909 | II |
14 | 2.453 | 2 | II | 0.484 | II | 0.854 | II |
15 | 2.696 | 2 | II | 0.527 | III | 0.909 | II |
16 | 3.381 | 3 | III | 0.665 | III | 0.930 | III |
17 | 2.562 | 2 | II | 0.440 | II | 0.883 | II |
18 | 3.701 | 3 | III | 0.711 | III | 0.945 | III |
19 | 2.882 | 2.0 | II | 0.486 | II | 0.900 | II |
No | x1 | x2 /mm | x3 | x4 /Years | x5 | x6 /m |
---|---|---|---|---|---|---|
1 | Concrete pipe | 800 | Rubber ring | 20 | 3 | 1.1 |
2 | Steel pipe | 400 | Welding | 13 | 3 | 1.1 |
3 | Steel pipe | 600 | Welding | 20 | 3 | 1.1 |
4 | Concrete pipe | 600 | Rubber ring | 20 | 3 | 1.1 |
5 | Grey cast-iron pipe | 300 | Rubber ring | 15 | 3 | 0.7 |
6 | Steel pipe | 1200 | Welding | 10 | 3 | 1.2 |
7 | Nodular cast iron pipe | 300 | Rubber ring | 8 | 3 | 0.7 |
8 | Steel pipe | 400 | Welding | 13 | 3 | 0.7 |
9 | Steel pipe | 800 | Welding | 15 | 3 | 1.1 |
10 | Steel pipe | 1200 | Welding | 15 | 3 | 0.8 |
11 | Steel pipe | 600 | Welding | 15 | 3 | 0.8 |
12 | Steel pipe | 1200 | Welding | 10 | 3 | 0.8 |
13 | Steel pipe | 800 | Welding | 20 | 3 | 1.1 |
14 | Steel pipe | 1200 | Welding | 20 | 3 | 0.8 |
15 | Steel pipe | 800 | Welding | 15 | 3 | 0.8 |
16 | Nodular cast-iron pipe | 200 | Asbestos cement | 8 | 3 | 0.4 |
17 | Nodular cast-iron pipe | 300 | Rubber ring | 8 | 3 | 0.7 |
18 | Gray cast-iron pipe | 200 | Asbestos cement | 15 | 3 | 0.4 |
19 | Gray cast-iron pipe | 300 | Rubber ring | 15 | 3 | 0.7 |
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Liu, C.; Li, Y.; Yin, H.; Zhang, J.; Wang, W. A Stochastic Interpolation-Based Fractal Model for Vulnerability Diagnosis of Water Supply Networks Against Seismic Hazards. Sustainability 2020, 12, 2693. https://doi.org/10.3390/su12072693
Liu C, Li Y, Yin H, Zhang J, Wang W. A Stochastic Interpolation-Based Fractal Model for Vulnerability Diagnosis of Water Supply Networks Against Seismic Hazards. Sustainability. 2020; 12(7):2693. https://doi.org/10.3390/su12072693
Chicago/Turabian StyleLiu, Chaofeng, Yawei Li, He Yin, Jiaxin Zhang, and Wei Wang. 2020. "A Stochastic Interpolation-Based Fractal Model for Vulnerability Diagnosis of Water Supply Networks Against Seismic Hazards" Sustainability 12, no. 7: 2693. https://doi.org/10.3390/su12072693
APA StyleLiu, C., Li, Y., Yin, H., Zhang, J., & Wang, W. (2020). A Stochastic Interpolation-Based Fractal Model for Vulnerability Diagnosis of Water Supply Networks Against Seismic Hazards. Sustainability, 12(7), 2693. https://doi.org/10.3390/su12072693