Protecting Against Sudden Shakings: From a Cup to a Full-Scale Tank Without a Single Internal Baffle
This study investigates whether the seismic sloshing protection of large liquid storage tanks can be achieved solely through geometric redesign, without recourse to a single internal baffle, base isolator, or supplementary damping device. Motivated by the persistent vulnerability of conventional circular cylindrical tanks to earthquake-induced sloshing damage—documented in failures ranging from elephant-foot buckling to floating roof collapse—the research challenges the century-old design canon that treats the circular cross-section as the default and immutable choice for liquid containment. Drawing inspiration from the commonplace observation that a square cup dampens liquid oscillations more rapidly than a round one, the investigation scales this intuition to industrial dimensions through a dual-methodology architecture that tightly couples small-scale shaking table experiments with high-fidelity computational fluid dynamics simulations. The experimental program tested a full factorial matrix of 400-millimeter scale models encompassing four geometric variables: cross-sectional polygonality (square, hexagonal, octagonal), wall inclination (vertical versus 7.5- and 15-degree inward taper), floor topography (flat versus domed with a central rise of one-tenth the liquid depth), and internal surface texture (smooth versus longitudinally grooved). These models were subjected to a curated suite of seven recorded earthquake ground motions scaled to a uniform peak ground acceleration of 0.5g. The computational model, developed in OpenFOAM using the volume-of-fluid method with k-omega SST turbulence closure, was validated against the experimental data to within 1.8 percent for fundamental frequency and 6.2 percent for peak wave height. The validated solver was then extrapolated, using Froude similarity, to a full-scale 100,000-barrel prototype. A Taguchi design-of-experiments framework efficiently surveyed the four-dimensional geometric parameter space through 18 full-scale simulations. The results demonstrate that the synergistic combination of a square cross-section, a 15-degree inward wall taper, a domed floor rising to 10 percent of the liquid depth, and heavy longitudinal surface striations achieves an 80 percent reduction in normalized peak convective wave height (from 0.187 to 0.038 of the liquid depth), a near-tripling of the convective damping ratio (from 0.42 to 1.24 percent), and a 99 percent increase in the fundamental sloshing frequency (from 0.126 to 0.251 Hz) relative to an unbaffled circular baseline. When compared directly to a conventionally baffled circular tank designed according to API 650 recommendations, the optimized geometric tank exhibited a 7 percent lower peak wave height, a 5 percent higher damping ratio, and an 86 percent higher fundamental frequency, at the expense of an 18 percent increase in peak wall stress that remains within code-allowable limits. The four geometric mechanisms operate synergistically: the square cross-section provides preventive frequency detuning, the inward taper constrains convective mass participation kinematically, the domed floor scatters the standing wave pattern through topographic refraction, and the textured surface contributes distributed skin-friction damping. All five research hypotheses were confirmed, and the central proposition—that pure geometric redesign can match or exceed the performance of internal baffles—is supported by the numerical evidence. The findings establish a new paradigm of intrinsic, passive, shape-driven seismic protection that eliminates the lifecycle costs, inspection burdens, and corrosion vulnerabilities associated with internal baffles, offering a resilient and maintenance-free alternative for critical liquid storage infrastructure.
