Serviceability Assessment for Cascading Failures in Water Distribution Network under Seismic Scenario

Table 1

The cascading failure processes ( and ).

Node	Failure process ()	Failure process ()
1	All nodes failed	All nodes failed
2	2 (3–10, 13, 14, 17) (12, 16)	2 (3–10, 13, 14, 17) ()
3	3 (4, 5, 6, 9, 10, 13, 14, 17) (8, 12, 16)	3 (4, 5, 6, 9, 10, 13, 14, 17) ()
4	4 (3, 5, 6, 9, 10, 13, 14, 17) (8, 12, 16)	4 (3, 5, 6, 9, 10, 13, 14, 17) ()
5	5 (4, 6, 8, 9, 10, 13, 14, 17) (12, 16)	5 (4, 6, 9, 10, 13, 14, 17) (3, 16)
6	6 (5, 9, 10, 14, 17) (4, 8, 13, 16) ()	6 no more failure nodes
7	7 (8, 14) (5, 6, 9, 10, 13, 16, 17) (4, 12)	7 (8, 14) (6, 10, 17)
8	8 (7, 14) (5, 6, 9, 10, 13, 16, 17) (4, 12)	8 (7, 14) (6, 10, 17)
9	9 (5, 6, 10, 13, 14, 16, 17) (4, 8, 12)	9 (6, 14) (5, 10, 17) () (3)
10	10 (5, 6, 9, 14) (4, 8, 13, 16, 17) ()	10 (6, 14) ()
11	11 (6, 10, 12–17) (4, 5, 9) (3, 8)	11 (6, 10, 12–17)
12	12 (13, 14) (5, 6, 9, 10, 16, 17) (4, 8)	12 (13, 14) (6, 10, 17) ()
13	13 (12, 14, 16, 17) (5, 6, 9, 10) (4, 8)	13 ()
14	14 (5, 6, 9, 10, 13, 16, 17) (4, 8, 12)	14 (6, 10, 17)
15	15 (14, 16, 17) (5, 6, 9, 10, 13) (4, 8, 12)	15 (14, 16, 17) (6, 10)
16	16 (14, 15, 17) (5, 6, 9, 10, 13) (4, 8, 12)	16 (14, 15, 17) (6, 10)
17	17 (13, 16) (6, 10, 12, 14) (4, 5, 9) (3, 8)	17 no more failure nodes