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The sloshing law of liquid surface for ground rested circular RC tank under unidirectional horizontal seismic action

Lin Gao
Lin Gao
 y 
Mingzhen Wang
Mingzhen Wang
   | 25 may 2021
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Publicado en línea: 25 may 2021
Páginas: 293 - 306
Recibido: 27 nov 2020
Aceptado: 26 feb 2021
DOI: https://doi.org/10.2478/amns.2021.2.00013
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© 2021 Lin Gao et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

The stress-strain curve of the materials in the numerical simulation. (a) The concrete and (b) The reinforcement.
The stress-strain curve of the materials in the numerical simulation. (a) The concrete and (b) The reinforcement.

Fig. 2

Time-history curves of the seismic ground motions. (a) HSDB-EW seismic ground motion and (b) HX-NS seismic ground motion.
Time-history curves of the seismic ground motions. (a) HSDB-EW seismic ground motion and (b) HX-NS seismic ground motion.

Fig. 3

The maximum and minimum sloshing wave heights for the A-70% condition.
The maximum and minimum sloshing wave heights for the A-70% condition.

Fig. 4

Time-history curves of the maximum sloshing wave heights for tank A. (a) HSDB-EW seismic ground motion and (b) HX-NS seismic ground motion.
Time-history curves of the maximum sloshing wave heights for tank A. (a) HSDB-EW seismic ground motion and (b) HX-NS seismic ground motion.

Fig. 5

Theoretical and ADINA calculation results of the maximum sloshing wave height. (a) A-10% condition, (b) A-30% condition, (c) A-50% condition, (d) A-70% condition, (e) B-70% condition and (f) C-70% condition.
Theoretical and ADINA calculation results of the maximum sloshing wave height. (a) A-10% condition, (b) A-30% condition, (c) A-50% condition, (d) A-70% condition, (e) B-70% condition and (f) C-70% condition.

Fig. 6

Two-dimensional distribution of h and Rβ1k values.
Two-dimensional distribution of h and Rβ1k values.

Fig. 7

Long-period seismic design β spectrum with 5% damping ratio.
Long-period seismic design β spectrum with 5% damping ratio.

Seismic zone factor Z.

Seismic map zone 1 2A 2B 3 4
Factor Z 0.075 0.15 0.2 0.3 0.4

Modal periods of part conditions (s).

Condition Sloshing mode Structural vibration mode
First-order Second-order Third-order First-order Second-order Third-order
A-0% / / / 0.026 0.026 0.023
A-10% 12.195 (12.500) 4.255 2.695 0.026 0.026 0.023
A-30% 7.143 (7.299) 2.688 1.873 0.027 0.026 0.023
A-50% 5.650 (5.770) 2.364 1.770 0.028 0.027 0.024
A-70% 4.926 (5.025) 2.268 1.754 0.030 0.029 0.027
B-70% 3.333 (3.472) 1.754 1.370 0.025 0.024 0.020
C-70% 9.091 (9.615) 3.704 2.632 0.040 0.039 0.039

Calculation results of h and dmax when k = Z = 0.075.

Condition A-10% A-30% A-50% A-70% B-70% C-70%
h 0.034 0.088 0.134 0.171 0.211 0.114
dmax 0.013 0.037 0.059 0.078 0.109 0.046
h/dmax 2.626 2.360 2.252 2.191 1.941 2.476

Importance factor I.

Tank use Factor I
Tanks containing hazardous materials 1.5
Tanks that are intended to remain usable for emergency purposes after an earthquake or tanks that are part of lifeline systems 1.25
All other tanks 1.0

The result of β1, hT, and hA under seismic actions with 100 gal peak acceleration.

Condition Parameter Seismic motion input
HSDB-EW JZGYF-NS PJW-NS BJ-EW CC-NS YL-NS HX-NS
A-10% β1 0.043 0.092 0.056 0.057 0.054 0.165 0.164
hT 0.024 0.052 0.032 0.032 0.030 0.093 0.093
hA 0.074 0.112 0.162 0.154 0.249 0.345 0.339
A-30% β1 0.055 0.137 0.143 0.088 0.268 0.977 0.394
hT 0.031 0.077 0.081 0.049 0.151 0.552 0.223
hA 0.101 0.163 0.233 0.201 0.466 1.504 0.586
A-50% β1 0.064 0.154 0.370 0.261 0.441 0.559 0.807
hT 0.036 0.087 0.209 0.148 0.249 0.316 0.456
hA 0.109 0.203 0.487 0.348 0.589 0.736 0.946
A-70% β1 0.082 0.148 0.377 0.344 0.609 1.020 0.721
hT 0.046 0.083 0.213 0.194 0.344 0.576 0.407
hA 0.115 0.151 0.461 0.393 0.860 1.259 0.910
B-70% β1 0.149 0.142 0.497 0.307 0.335 0.944 1.233
hT 0.054 0.051 0.179 0.111 0.121 0.340 0.444
hA 0.113 0.114 0.398 0.220 0.484 0.943 1.075
C-70% β1 0.062 0.111 0.074 0.061 0.104 0.377 0.261
hT 0.070 0.125 0.084 0.068 0.118 0.426 0.295
hA 0.158 0.259 0.267 0.223 0.275 0.958 0.717

Basic information of the selected seismic ground motions.

Name Site condition Collecting stations Epicentral distance (km) Peak acceleration (gal) The moment of peak acceleration (s) Predominant period (s)
HSDB-EW II class Sichuan Province 125.9 −102.643 6.160 0.095
JZGYF-NS II class 263.3 100.224 18.425 0.168
PJW-NS II class 81.0 101.149 10.105 0.297
BJ-EW III class Shanxi Province 513.1 120.292 15.720 0.611
CC-NS III class 528.6 107.719 14.980 1.138
YL-NS III class 569.9 −94.005 16.730 1.862
HX-NS III class 599.0 92.090 13.835 4.096

Damping ratio correction coefficient C of the design response spectrum.

Damping ratio ξ 30% 20% 10% 5% 3% 2% 1% 0.5%
Correction coefficient C 0.44 0.56 0.78 1.00 1.18 1.32 1.53 1.79

Soil profile coefficient S.

Type Soil profile description Coefficient
A A soil profile with either: (a) a rock-like material characterised by a shear wave velocity >2500 ft/s (762 m/s), or by other suitable means of classification; or (b) medium-dense to dense or medium-stiff to stiff soil conditions where the soil depth is <200 ft (60,960 mm) 1.0
B A soil profile with predominantly medium-dense to dense or medium-stiff to stiff soil conditions, where the soil depth exceeds 200 ft (60,960 mm) 1.2
C A soil profile containing >20 ft (6096 mm) of soft to medium-stiff clay but not >40 ft (12,192 mm) of soft clay 1.5
D A soil profile containing >40 ft (12,192 mm) of soft clay characterised by a shear wave velocity <500 ft/s (152.4 m/s) 2.0
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