Earthquake-induced Hydrodynamic Pressures Research Articles

Evaluating the Seismic Resilience of Above-Ground Liquid Storage Tanks

Historical seismic events have repeatedly highlighted the susceptibility of above-ground liquid storage steel tanks, underscoring the critical need for their proper design to minimize potential damage due to seismic forces. A significant failure mechanism in these structures, which play essential roles in the extraction and distribution of various raw or refined materials—many of which are flammable or environmentally hazardous—is the dynamic buckling of the tank walls. This study introduces a numerical framework designed to assess the earthquake-induced hydrodynamic pressures exerted on the walls of cylindrical steel tanks. These pressures result from the inertial forces generated during seismic activity. The computational framework incorporates material and geometric nonlinearities and models the tanks using four-node shell elements with two-point integration, specifically Belytschko shell elements. The Arbitrary Lagrangian–Eulerian (ALE) method is employed to accommodate substantial structural and fluid deformations, enabling a full simulation of fluid–structure interaction through highly nonlinear algorithms. Experimental test data are utilized to validate the proposed modeling approach, particularly in replicating sloshing phenomena and identifying stress concentrations that may lead to wall buckling. The study further presents results from a parametric analysis that varies the height-to-radius and radius-to-thickness ratios of a typical anchored flat-bottomed tank, examining the seismic performance of this common storage system. These results provide insights into the relationship between tank properties and mechanical behavior under dynamic loading conditions.

Experimental research on dynamic responses and hydrodynamic pressures of deep-water bridge piers under seismic and wave actions

Earthquakes and extreme waves pose significant threats to the safety of offshore bridges, particularly in deep-water environments. The temporal sequence of earthquakes and waves and the specific type of earthquake are critical factors that contribute to the potential risks involved. This study aimed to fill a key knowledge gap by conducting a comprehensive series of physical tests on a deep-water bridge pier at a scale factor of 1:30. White noise tests, shaking table tests, wavemaker tests, and combined shaking table and wavemaker tests were carried out. Near-field pulsed earthquakes, far-field long-period earthquakes and earthquake-wave phase differences were examined in the tests. The test results indicate that the presence of water has a noticeable impact on the natural frequency, particularly the 2nd-order frequency, of bridge piers, which may significantly influence the dynamic responses of high bridge piers. The effects of water–pier interactions are further intensified by seismic actions such as the pulsed Loma Prieta and long-period Chi-Chi earthquakes. Moreover, the earthquake-induced hydrodynamic pressures on the upstream and downstream faces of the pier are nearly identical, whereas there is a notable difference when the pressures are caused by incident waves. The magnitude of the combined earthquake and wave responses in relation to the individual responses is influenced by the earthquake–wave phase differences, and the combined responses are less than the sum of the individual responses.

Influence of earthquake-induced hydrodynamic pressure on train-bridge interactions based on back-propagation neural network

Forecasting the behavior of the train-bridge system under strong waves is crucial in designing the cross-sea bridge. However, the influence of earthquake-induced hydrodynamic pressure on the dynamic system may be significant and need to be adequately understood. This study investigates the influence of earthquake-induced hydrodynamic force on the stochastic responses of the train-bridge interaction using the Newmark-β method. A surrogate model named back-propagation neural network is implemented by correlating wave samples with the stochastic responses of the train-bridge system. Such a model improves computation efficiency and avoids further time-step integration. The Pintan’s bridge, located in China’s Eastern Region, is selected as a case study. The results show that the earthquake-induced hydrodynamic force involves significant responses of the train-bridge system. Moreover, the maximum dynamic amplification factor of the deck and the pier are 6% and 12.5%, respectively. Finally, a significant value of the peak period minimizes the effect of the earthquake-induced hydrodynamic responses on the train-bridge system.

Analytical Solution of Earthquake-Induced Hydrodynamic Pressure on Arrays of Circular Cylinders Considering High-Order Scattered Waves

AbstractThe earthquake-induced pressures on arrays of cylinders have received less concern, although pile groups have been widely adopted in real practice. This paper develops an analytical method ...

Ocean Bottom Hydrodynamic Pressure due to Vertical Seismic Motion

Abstract Earthquake-induced hydrodynamic pressure on the ocean floor is a key factor in evaluating the surface disturbance and dynamic response of the seabed under the action of a submarine earthqu...

Simplified 3D model for the uplift analysis of liquid storage tanks

Vertical uplifting of the tank base is perhaps the most relevant characteristic of the seismic behaviour of unanchored cylindrical liquid storage tanks made of steel. When an unanchored tank is subjected to lateral loads due to the earthquake-induced hydrodynamic pressures, a portion of the base plate tends uplift locally. Analysis of the base plate uplifting of unanchored tanks implies many sources of nonlinear behaviour mechanisms such as the varying contact of the base plate with the foundation, large deflections, the material yielding and the plastic rotation of the base plate. This paper presents a comprehensive analysis of the partially uplifted base plate of two thin-walled cylindrical tanks (one slender and one broad). First, a nonlinear quasi-static cyclic analysis with a finite element model and a simplified model is carried out for each tank. Next, an efficient method for three-dimensional dynamic analysis is proposed and used in order to obtain the nonlinear time history response of each tank. The simplified non-linear model proposed in this paper was capable to provide a good estimation of both the rocking resistance of the liquid-loaded base plate and the stress distribution on the tank wall in contact with the foundation. A set of seven seismic ground motions was used for the time history analysis. Finally, the distribution of the tank wall stresses and the critical responses of the tanks are discussed. Both anchored and unanchored tanks may present a high compressive axial stress due to the seismic effect.

Simplified Formula for Earthquake-Induced Hydrodynamic Pressure on Round-Ended and Rectangular Cylinders Surrounded by Water

AbstractAn accurate and efficient numerical model is developed to calculate the earthquake-induced hydrodynamic pressure on uniform vertical cylinders with an arbitrary cross section surrounded by ...

Simplified evaluation of earthquake-induced hydrodynamic pressure on circular tapered cylinders surrounded by water

Dynamic response of offshore structures can be influenced due to the water-structure interaction. The water-structure interaction can be simply represented by added mass in earthquake response analysis. The added mass for a circular cylinder can be obtained by analytical method. However, the added mass for an arbitrary shape of structure is rather difficult to be solved by analytical method. In this study, a substructure method for analysis of the seismic response of an arbitrary shape of structure is presented. The finite element technique incorporating the exact artificial boundary condition presented for simulating the far field of the infinite water is applied to the evaluation of added mass for offshore structures, where the exact added mass matrix is fully populated and symmetrical. The structure is idealized as a three-dimensional finite element model system. Firstly, the presented method is to investigate the seismic response of circular tapered cylinder vibrating in water. Secondly, a lumped added mass matrix is adopted to replace the exact added mass matrix. Thirdly, a simplified formula is presented to evaluate the added mass of the circular tapered cylinder.

Experimental study on the applicability of Westergaard\u2019s formula for calculating earthquake-induced hydrodynamic pressure in small lake

Moraine-dammed lake outbursts usually threaten highways, railways, and key facilities in alpine regions. The varying amplitudes and distribution of hydrodynamic pressures significantly affect the stability of the dam. We utilize a shaking table to investigate the development of hydrodynamic pressure caused by different sinusoidal waves and seismic Wolong wave. A series of shaking table tests indicate that the hydrodynamic pressure variation significantly follows seismic acceleration wave motion. The maximum hydrodynamic pressures calculated by Westergaard’s equation are compared with the experimental values under different waves. It is shown that the Westergaard’s values are lower than the experimental ones under the sinusoidal waves. However, the Westergaard’s method is able to predict the earthquake-induced hydrodynamic pressure caused by Wolong wave in small lake with desirable accuracy.

Effects of surface waves on hydrodynamic pressures on rigid dams with arbitrary upstream face

AbstractThe effects of surface gravity waves on earthquake‐induced hydrodynamic pressures on rigid dams with nonvertical upstream face are examined, taking the compressibility and viscosity of water into account. A simple closed‐form solution is obtained by using the Trefftz numerical method. The boundary under study is reduced to the upstream face only and the degrees of freedom of the problem are restricted to the number of trial functions used for analysis. For harmonic base excitation, a number of numerical examples for various geometries of the upstream face are presented. The hydrodynamic pressure distribution, the resultant lateral force and its effective height of application are evaluated. The results are strongly influenced by the upstream shape and, in a lesser degree, by the consideration of surface waves. Copyright © 2009 John Wiley & Sons, Ltd.

A closed-form formulation for earthquake-induced hydrodynamic pressure on gravity dams

A closed-form formulation for earthquake-induced hydrodynamic pressure on gravity dams

Earthquake‐induced hydrodynamic pressures on a 3D rigid dam–reservoir system using DRBEM and a radiation matrix

AbstractThe dual reciprocity method is applied to determine the hydrodynamic pressure distribution in a three‐dimensional dam–reservoir system subjected to earthquake excitation. The reservoir domain is idealized as a finite region of irregular geometry adjacent to the dam followed by an infinite domain of uniform cross‐section in the upstream direction. The reservoir hydrodynamic pressure response is governed by the Helmholtz equation subject to free surface, dam–reservoir interface, absorbing bottom/banks and radiation boundary conditions. A three‐dimensional (3D) dual reciprocity model is developed to determine the hydrodynamic pressure in the finite reservoir domain. A radiation matrix is developed and introduced to relate the hydrodynamic pressure and its normal derivative on the interface between the finite and infinite domains. The three‐dimensional radiation model used is developed by applying a two‐dimensional dual reciprocity formulation along the interface of the finite and infinite reservoirs together with a continuum solution in the upstream direction of the infinite domain. The model is compared for the hydrodynamic response of a three‐dimensional rectangular reservoir and found to be in excellent agreement with results obtained from a model based on the analytical formulation existing in the literature. Copyright © 2003 John Wiley & Sons, Ltd.

Hydrodynamic forces on concrete sea wall and breakwater during earthquakes: effects of bottom sediment layers and back-fill soil

The objective of this paper is to present the effect of sediment characteristics on the dynamic response of sea walls and breakwaters during earthquakes. A finite-difference method is used to calculate the earthquake-induced hydrodynamic pressures of seawater and the pore water in seabed sediment. The water-filled soil mixture is used to model sediment and back-fill soil. The dynamic response of a rigid coastal structure induced by constant ground acceleration is studied, using variable sediment depths and porosity. The dynamic characteristics of the water–embankment–sediment system are investigated, applying four earthquake-records as exciting forces. The result of a quay-walled caisson demonstrates the significance of the seismic-induced dynamic force and the seismic effects should be considered for the design of coastal structures in seismic zone. The damaged wharves of Taichung Port during Chi-Chi earthquake, 21 September 1999 is also reported in the paper.

Hydrodynamic pressures on axisymmetric offshore structures considering seabed flexibility

A special boundary method for earthquake-induced hydrodynamic pressures on rigid axisymmetric offshore structures of arbitrary shape is presented, including both the water compressibility and seabed flexibility. This method makes use of a complete set of Trefftz functions, which satisfy all boundary conditions except that at the structural surface. An azimuthal decomposition of the solution allows us to reduce the three-dimensional problem to a two-dimensional one. The pressure distribution is expressed as a linear combination of natural modes of water and participation factors. Such coefficients are determined by using the Mikhlin approach, with which the remaining boundary condition is satisfied in the least-squares sense. Numerical results are computed for different geometries of the structural surface. The effects of water compressibility and seabed flexibility are examined over wide ranges of practical interest. The efficiency of this technique is validated by comparison with analytical and numerical solutions.

Effects of Ice Layer on Hydrodynamic Pressure of Structures

The horizontal earthquake-induced hydrodynamic pressure acting on the surface of axisymmetric offshore and coastal structures constructed in the freeze area is explored by a special semianalytical and seminumerical approach. The seawater is considered as inviscid and compressible, and the motion of the water is limited to small amplitudes during an earthquake. The surface of the seawater is assumed to be covered by a floating broken ice layer. The numerical examples are presented to illustrate the results obtained from this method. Accuracy of numerical computation is discussed in the paper. Results are provided for the rigid structures with sloping surface and sharp corners in the condition that water surface is covered by a floating ice layer. Attention is given to the effects of the floating ice layer on vertical distribution of the hydrodynamic pressure. The influence of ice layer to the frequency response of hydrodynamic pressure is investigated. The effects of geometrical shape of the structural surface on hydrodynamic pressure and the application of the proposed method to typical offshore structures subject to base motion are also discussed.

Earthquake-induced hydrodynamic pressures on submerged cylindrical storage tanks

The boundary integral method is utilized to calculate the hydrodynamic pressure distribution on a rigid submerged cylindrical storage tank subjected to horizontal or vertical harmonic ground excitation. The fluid is assumed to be linearly compressible and to undergo small-amplitude, irrotational motion. The vertical axisymmetry of the structure is exploited utilizing a fluid Green's function which is separable in the cylindrical polar coordinate system and so leads in each case to a line integral equation for the fluid velocity potential on the surface of the structure. Numerical results are presented which illustrate the influence of the direction and frequency of ground motion and the body dimensions on the hydrodynamic pressure distribution. For both horizontal and vertical ground excitation, the numerical values from the boundary integral method have been verified by a comparison with those obtained by an eigenfunction expansion approach.