Fragility of open-topped oil storage tanks under wind in Patagonia

Figures (8) Tables (6)

Figure 1.
Geometric characteristics of open-topped oil storage considered in this paper.
Figure 2.
Ring stiffener, (a) design according to API 650, (b) equivalent section^[22].
Figure 3.
Examples of fragility curves, (a) step-function, (b) 'S' shape function.
Figure 4.
Damage computed for a tank with D = 45 m and H = 12 m. (a) Deflected shape for damage DS1; (b) Equilibrium path for node A (DS1); (c) Deflected shape for damage DS2 (critical mode).
Figure 5.
Probability of reaching a damage level P[DSi/V], (a) DS0, (b) DS0, DS1, DS2 and DS3.
Figure 6.
Oil producing regions in Argentina. (Adapted from IAPG^[47]).
Figure 7.
Wind speed map of Argentina. (Adapted from CIRSOC 102^[45]).
Figure 8.
Probability P[DSi/V] to reach damage levels DS1, DS2 and DS3 in tanks located in the Patagonia region of Argentina.

H (m)	Courses	Thickness t (m)
H (m)	Courses	D = 35 m	D = 40 m	D = 45 m	D = 50 m	D = 55 m	D = 60 m
12	V1	0.014	0.016	0.018	0.018	0.020	0.022
	V2	0.012	0.012	0.014	0.016	0.016	0.018
	V3	0.008	0.010	0.010	0.010	0.012	0.012
	V4	0.006	0.008	0.008	0.008	0.008	0.008
14	V1	0.016	0.018	0.020	0.022	0.025	0.025
	V2	0.014	0.014	0.016	0.018	0.020	0.020
	V3	0.010	0.012	0.012	0.014	0.014	0.016
	V4	0.008	0.008	0.008	0.010	0.010	0.010
	V5	0.006	0.008	0.008	0.008	0.008	0.008
16	V1	0.018	0.020	0.022	0.025	0.028	0.028
	V2	0.016	0.018	0.018	0.020	0.022	0.025
	V3	0.012	0.014	0.016	0.016	0.018	0.020
	V4	0.010	0.010	0.012	0.012	0.014	0.014
	V5	0.006	0.008	0.008	0.008	0.008	0.010
	V6	0.006	0.008	0.008	0.008	0.008	0.010
18	V1	0.020	0.022	0.025	0.028	0.030	0.032
	V2	0.018	0.020	0.022	0.025	0.025	0.028
	V3	0.014	0.016	0.018	0.020	0.020	0.022
	V4	0.012	0.012	0.014	0.016	0.016	0.018
	V5	0.008	0.010	0.010	0.010	0.012	0.012
	V6	0.008	0.010	0.010	0.010	0.012	0.012
20	V1	0.022	0.025	0.028	0.030	0.032	0.035
	V2	0.020	0.022	0.025	0.028	0.028	0.032
	V3	0.016	0.018	0.020	0.022	0.025	0.028
	V4	0.014	0.014	0.016	0.018	0.020	0.020
	V5	0.010	0.012	0.012	0.014	0.014	0.016
	V6	0.010	0.012	0.012	0.014	0.014	0.016
	V7	0.010	0.012	0.012	0.014	0.014	0.016

Table 1.

Geometry and course thickness of 30 tanks considered in this work.

Damage states (DS) Description

DS0 No damage
DS1 Large deflections on the cylindrical shell
DS2 Buckling of the cylindrical shell
DS3 Large deflections on the stiffening ring

Table 2.
Damage states under wind for open-top tanks with a wind girder.

H	D	ID	DS0	DS1	DS2	DS3
H12	D35	1	137.76	162.06	194.82	336.02
	D40	2	160.62	181.31	227.16	360.73
	D45	3	153.32	174.19	216.82	374.04
	D50	4	145.23	165.27	205.39	373.76
	D55	5	152.76	180.83	216.03	374.75
	D60	6	145.11	170.75	205.22	370.98
H14	D35	7	145.57	162.05	205.87	295.03
	D40	8	148.55	166.20	210.08	311.24
	D45	9	136.42	153.72	192.92	334.54
	D50	10	155.36	177.51	219.71	339.86
	D55	11	145.24	165.34	205.39	343,17
	D60	12	141.89	167.26	200.67	338.77
H16	D35	13	131.32	161.94	185.71	262.20
	D40	14	146.95	163.99	207.82	277.08
	D45	15	150.58	170.90	212.95	293.37
	D50	16	138.97	161.05	196.54	303.62
	D55	17	138.51	174.17	195.88	313.97
	D60	18	156.34	182.78	221.10	326.83
H18	D35	19	146.80	160.79	207.60	223.18
	D40	20	159.01	177.71	224.87	243.63
	D45	21	157.10	179.51	222.17	265.32
	D50	22	152.54	172.17	215.72	293.32
	D55	23	164.93	188.10	233.25	305.94
	D60	24	163.69	180.32	231.49	315.63
H20	D35	25	163.64	199.59	231.42	195.03
	D40	26	171.24	195.14	242.18	216.47
	D45	27	171.58	203.68	242.64	293.32
	D50	28	182.46	209.43	258.03	259.41
	D55	29	178.95	208.23	253.07	272.48
	D60	30	174.47	196.11	246.74	290.86

Table 3.

Wind speed for each tank considered reaching a damage level.

ID	DS0	DS1	DS2	DS3
11	145.2	165.3	205.4	343.2
6	145.1	170.7	205.2	371.0
3	153.3	174.2	216.8	374.0
9	136.4	153.7	192.9	334.5
28	182.5	209.4	258.0	259.4
22	152.5	172.2	215.7	293.3
13	131.3	161.9	185.7	262.2
19	146.8	160.8	207.6	223.2
3	153.3	174.2	216.8	374.0
12	141.9	167.3	200.7	338.8
30	174.5	196.1	246.7	290.9
23	164.9	188.1	233.2	305.9
2	160.6	181.3	227.2	360.7
17	138.5	174.2	195.9	314.0
11	145.2	165.3	205.4	343.2

Table 4.

Random tank selection for V = 165 km/h, assuming wind interval [162.5 km/h, 167.5 km/h].

DS0 DS1 DS2 DS3

1 1 0 0
1 0 0 0
1 0 0 0
1 1 0 0
0 0 0 0
1 0 0 0
1 1 0 0
1 1 0 0
1 0 0 0
1 1 0 0
0 0 0 0
1 0 0 0
1 0 0 0
1 0 0 0
1 1 0 0
Total 13 6 0 0
h_i 0.87 0.4 0 0

Table 5.
Damage matrix for random tank selection (V = 165 km/h), assuming wind interval [162.5 km/h, 167.5 km/h].

V inf (km/h)	V m (km/h)	V sup (km/h)	Ln (Vm)	f_i	F_i	h_i	H_i
127.5	130	132.5	4.87	0	0	0.000	0
132.5	135	137.5	4.91	2	2	0.133	0.133
137.5	140	142.5	4.94	1	3	0.067	0.200
142.5	145	147.5	4.98	3	6	0.200	0.400
147.5	150	152.5	5.01	1	7	0.067	0.467
152.5	155	157.5	5.04	4	11	0.267	0.733
157.5	160	162.5	5.08	0	11	0.000	0.733
162.5	165	167.5	5.11	2	13	0.133	0.867
167.5	170	172.5	5.14	0	13	0.000	0.867
172.5	175	177.5	5.16	0	13	0.000	0.867
177.5	180	182.5	5.19	2	15	0.133	1.000

Table 6.

Damage DS0: Wind speed intervals [km/h] shown on the left; logarithm of wind speed; and relative and absolute frequencies (shown on the right).