Evaluation of Seismic Effects on Atmospheric Pressure Liquid Storage Tanks †
Abstract
1. Introduction
1.1. Seismic Stress Modeling
1.2. Seismic Damage Characteristics
- Buckling in the upper portion of the shell (top buckling): if the depression due to the hydrodynamic effect is excessive, the tank may collapse inwards (Figure 3).
- Instability in the lower portion of the tank: if the overpressure due to hydrostatic loading and the hydrodynamic effect exceeds the yield strength of the material, even if the course is mainly stressed still in the plane (as a membrane), there is excessive deformation due to plasticization, which, with the effect of axial stress, can lead to instability. This damage is usually called elephant foot (Figure 4).
1.3. Reference Norms
2. Eurocode 8 Theoretical Bases—Part 4
2.1. Seismic Analysis Procedures for Tanks (Annex A)
- the impulsive contribution;
- the convective contribution.
2.2. Rigid Impulsive Component
2.3. Convective Contribution
2.4. Solution Method Considerations
3. Deformable Tanks
3.1. Fluid–Structural Modal Analysis
3.2. Acoustic Modal Analysis
3.3. Comparative Verification
- Radius m;
- Wetted height m coincident with the height of the freeboard;
- Liquid content: water kg/m3, GPa;
- Steel shell, GPa, , kg/m3;
- Constant thickness, m.
4. Case Study
- Earthquake Ground Motion Level 1 (DD-1): characterizes a very rare seismic event where the corresponding return period is 2475 years.
- Earthquake Ground Motion Level 2 (DD-2): characterizes a rare seismic event where the corresponding return period is 475 years.
4.1. Ideal Model
4.2. Impulsive Rigid Contribution
4.3. Convective Contribution
4.4. Deformability Contribution
4.5. Deformed Model
4.6. Setting Up Analyses
- Generic static step: in this step, the hydrostatic load and the force of gravity are applied with linear progression; in this step, it is required to update the stiffness matrix by including the geometric non-linearities, a calculation necessary in the regime of large displacements.
- Incremental non-linear static step: in this step, the hydrodynamic loads are applied and the analysis is carried out using the modified Riks method.
5. Results
- Load proportionality factor ;
- Constraining reaction of the central node of the base along the direction of the load;
- Moment modulus reaction of the central node of the base;
- Displacement of the node that exhibits the greatest displacement at the beginning of the non-linear step;
- Displacement of the node that exhibits the greatest displacement in the non-linear step.
5.1. Static Step
5.2. Non-Linear Step, Seismic Case DD1
5.3. Non-Linear Step, Seismic Case DD2
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Tank Design Data | |
---|---|
Tank diameter [m] | 27.50 |
Tank height (filling) [m] | 13.50 |
Tank height (geometric) [m] | 15.00 |
Design density of content [kg/m3] | 750.00 |
Assigned Materials | ||||||
---|---|---|---|---|---|---|
Material | [MPa] | [MPa] | [GPa] | [kg/m3] | ||
A283-gr. C | 235 | 0.11 | 236 | 210 | 8000 | 0.3 |
R-ST-37-2 | 235 | 0.11 | 236 | 210 | 8000 | 0.3 |
SA106-gr. B | 241 | 0.11 | 242 | 210 | 8000 | 0.3 |
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Chiappelloni, L.; Serraino, F.; Belardi, V.; Trupiano, S.; Gaetani, L.; Vivio, F. Evaluation of Seismic Effects on Atmospheric Pressure Liquid Storage Tanks. Eng. Proc. 2025, 85, 54. https://doi.org/10.3390/engproc2025085054
Chiappelloni L, Serraino F, Belardi V, Trupiano S, Gaetani L, Vivio F. Evaluation of Seismic Effects on Atmospheric Pressure Liquid Storage Tanks. Engineering Proceedings. 2025; 85(1):54. https://doi.org/10.3390/engproc2025085054
Chicago/Turabian StyleChiappelloni, Luca, Francesco Serraino, Valerio Belardi, Simone Trupiano, Luca Gaetani, and Francesco Vivio. 2025. "Evaluation of Seismic Effects on Atmospheric Pressure Liquid Storage Tanks" Engineering Proceedings 85, no. 1: 54. https://doi.org/10.3390/engproc2025085054
APA StyleChiappelloni, L., Serraino, F., Belardi, V., Trupiano, S., Gaetani, L., & Vivio, F. (2025). Evaluation of Seismic Effects on Atmospheric Pressure Liquid Storage Tanks. Engineering Proceedings, 85(1), 54. https://doi.org/10.3390/engproc2025085054