Horizontal Ground Excitation Research Articles

Seismic retrofit of torsionally coupled RC soft-storey building using short yielding core BRBs

This study presents seismic retrofitting of medium-rise torsionally coupled Reinforced-Concrete (RC) non-ductile building with soft ground storey. An irregular RC building with T-shaped plan is considered for the present study. In this sample building the presence of plan irregularity results in the torsional coupling of lateral modes. The location of staircase in the sample building significantly enhances the plan irregularity. Therefore, the contribution of stiffness of the staircase slabs is considered in the overall stiffness of the numerical model. Buckling Restrained Braces (BRBs) with short yielding cores are adopted to improve the seismic performance of the sample building. Short yielding core BRBs are installed in the ground storey to control the seismic lateral response induced by the soft-storey and torsional coupling of lateral modes. Displacement-based design method is adopted for the design of short yielding core BRBs to enhance the stiffness and energy dissipation of the structure so that it can endure the considered earthquake without exceeding the target drift level. Nonlinear dynamic analysis of the sample building is carried out before and after retrofit under bidirectional horizontal ground excitations applied simultaneously. The seismic performance is assessed in terms of maximum inter-storey drift, torsional response, plastic hinge distribution, residual displacement. Maximum axial force distribution of BRBs, maximum ductility and cumulative ductility demand of BRBs are discussed for a critical ground motion record. Analysis of the results reveals that the installation of BRBs decouples the torsionally coupled lateral modes of the sample building; and decreases inter-storey drift, torsional response and residual displacement in the soft ground storey. Thus, the retrofit design considered in this study, enhances the overall structural performance of the sample building reducing the lateral response due to the combined effect of the soft-storey and torsional coupling of lateral modes.

A liquid spring–magnetorheological damper system under combined axial and shear loading for three-dimensional seismic isolation of structures

This study focuses on experimental investigation of a fail-safe, bi-linear, liquid spring magnetorheological damper system for a three-dimensional earthquake isolation system. The device combines the controllable magnetorheological damping, fail-safe viscous damping, and liquid spring features in a single unit serving as the vertical component of a building isolation system. The bi-linear liquid spring feature provides two different stiffnesses in compression and rebound modes. The higher stiffness in the rebound mode prevents a possible overturning of the structure during rocking mode. For practical application, the device is to be stacked together along with the traditional elastomeric bearings that are currently used to absorb the horizontal ground excitations. An experimental setup is designed to reflect the real-life loading conditions. The 1/4th-scale device is exposed to combined dynamic axial loading (reflecting vertical seismic excitation) and constant shear force that are up to 245 and 28 kN, respectively. The results demonstrate that the device performs successfully under the combined axial and shear loadings and compare well with the theoretical calculations.

Capacity of liquid steel conical tanks under hydrodynamic pressure due to horizontal ground excitations

Steel conical tanks are widely used for liquid storage around the world and especially in North America. A number of those tanks collapsed in the last decades at different places as a result of instability of the steel shells. Despite being widely used, no specific design procedure is available for conical tanks under dynamic conditions. Most of the previous studies related to steel conical tanks focused on calculating the acting forces due to a seismic event. This study however, focuses on evaluating the capacity of conical tanks under hydrodynamic pressure resulting from horizontal ground excitation using non-linear static pushover analysis. The capacity is then compared to the seismic demand obtained using a previously developed mechanical model found in the literature for different seismic zones. This paper is a part of a larger study aiming to provide a simplified design procedure for steel conical tanks when subjected to earthquakes. The study is conducted numerically using a non-linear finite element model that accounts for the effects of large deformations and geometric imperfections on the stability of steel conical tanks.

Equivalent mechanical model for structural dynamic analysis of elevated tank like AP1000 PCCWST

This study is motivated by a lack of information regarding the seismic analysis and design of AP1000 passive containment cooling system water storage tank (PCCWST). The major challenge faced in this specific type of fluid–structure interaction (FSI) problem is the estimation of the forces associated with the hydrodynamic pressure. In this paper, an equivalent mechanical model for the water tank of PCCWST was developed regarding the hydrodynamic pressure. Parameters of this newly-developed mechanical model, which was evaluated by finite element method (FEM), were given in chart form as functions of geometrical parameters including ratio of inner and outer tank radii, tank bottom’s inclination angle, and tank height. The values of impulsive mass were compared between the proposed model and the cylindrical tanks reported in the literature when their inclination angle approaches zero. The agreement shown by this comparison confirmed the validity of the proposed mechanical model. Shaking table experiments of a scaled PCCWST were also carried out to verify the feasibility of the proposed model. Finally, the transient response of PCCWST subjected to horizontal ground excitation was provided to illustrate the application of the proposed model. Therefore, the study shows that the equivalent mechanical model can provide an effective method for the design of PCCWST.

Multiple support excitations of open-plane frames by a filtered white noise and soil–structure interaction

Seismic structural design is essentially the estimation of structural response to a forced motion, which may be deterministic or stochastic, imposed on the ground. The assumption that the same ground motion acts at every point of the base of the structure (or at every support) is not always justifiable; particularly in case of very large structures when considerable spatial variability in ground motion can exist over significant distances—example long span bridges. This variability is partly due to the delay in arrival of the excitation at different supports (which is called the wave passage effect) and due to heterogeneity in the ground medium which results in incoherency and local effects. The current study examines the influence of the wave passage effect (in terms of delay in arrival of horizontal ground excitation at different supports and neglecting transmission through the structure) on the response of a few open-plane frame building structures with soil–structure interaction. The ground acceleration has been modeled by a suitably filtered white noise. As a special case, the ground excitation at different supports has also been treated as statistically independent to model the extreme case of incoherence due to local effects and due to modifications to the ground motion resulting from wave reflections and refractions in heterogeneous soil media. The results indicate that, even for relatively short spanned building frames, wave passage effect can be significant. In the absence of soil–structure interaction, it can significantly increase the root mean square (rms) value of the shear in extreme end columns for the stiffer frames but has negligible effect on the flexible frames when total displacements are considered. It is seen that pseudo-static displacements increasingly contribute to the rms value of column shear as the time delay increases both for the stiffer and for the more flexible frames. When soil–structure interaction is considered, wave passage effect (in terms of total displacements) is significant only for low soil shear modulus, G s , values (where soil–structure interaction significantly lowers the fundamental frequency) and for stiff frames. The contribution of pseudo-static displacement to these rms values is found to decrease with increase in G s . In general, wave passage effect for most interactive frames is insignificant compared to the attenuating effect a decrease in G s has on the response of the interactive structure to uniform support excitation. When the excitations at different supports are statistically independent, it is seen that for both the stiff and flexible frames, the rms value of the column shear in extreme end columns is several times larger (more for the stiffer frames) than the value corresponding to uniform base excitation with the pseudo-static displacements contributing over 99% of the rms value of column shear. Soil–structure interaction has an attenuating effect on the rms value of the column shear, the effect decreasing with increase in G s . Here too, the pseudo-static displacements contribute very largely to the column shear. The influence of the wave passage effect on the response of three 2-bay frames with and without soil–structure interaction to a recorded horizontal accelerogram is also examined.

Equivalent mechanical analog for dynamic analysis of pure conical tanks

This study is motivated by the lack of information regarding seismic analysis and design of liquid-filled conical tanks. The main challenge in this type of fluid–structure interaction problem is the estimation of the forces associated with the hydrodynamic pressure resulting from the vibration of the structure. A simplified mechanical analog that can be used to estimate the forces associated with horizontal ground excitation is developed in this study. The proposed mechanical analog takes into account the flexibility of the tank walls and simulates both the impulsive and sloshing components of the hydrodynamic pressure. Parameters of this analog are displayed in chart form as functions of the geometrical parameters of the tanks including the angle of inclination of the tanks’ walls. Finally, an example is provided to illustrate the application of the developed analog for evaluation of the response of liquid-filled conical tanks to horizontal ground excitation.

Hydrodynamic Forces Acting on Arbitrary-Shaped Offshore Structures Subjected to Seismic Excitation

A general-purpose numerical method utilizing the Green function is proposed for evaluating hydrodynamic forces acting on offshore structures due to seismic horizontal ground excitation. This model can be applied to arbitrary-shaped structures and considers the effects of fluid compressibility and wave generation. In the proposed method, the Green function and its gradient are precisely evaluated by employing approximation formulas for infinite series efficiently. Its validity and applicability to actual structures are demonstrated through numerical experiments.

Fluid-structure interaction analysis of 3-D rectangular tanks by a variationally coupled BEM-FEM and comparison with test results

A variationally coupled BEM–FEM is developed which can be used to analyse dynamic response, including free-surface sloshing motion, of 3-D rectangular liquid storage tanks subjected to horizontal ground excitation. The tank structure is modelled by the finite element method and the fluid region by the indirect boundary element method. By minimizing a single Lagrange function defined for the entire system, the governing equation with symmetric coefficient matrices is obtained. To verify the newly developed method, the analysis results are compared with the shaking-table test data of a 3-D rectangular tank model and with the solutions by the direct BEM–FEM. Analytical studies are conducted on the dynamic behaviour of 3-D rectangular tanks using the method developed. In particular, the characteristics of the sloshing response, the effect of the rigidity of adjacent walls on the dynamic response of the tanks and the orthogonal effects are investigated. © 1998 John Wiley & Sons, Ltd.

Earthquake response of tension‐leg‐platforms in steady currents

AbstractDynamic response of tethers of tension‐leg‐platforms to current and horizontal earthquake excitations is investigated. The static deflected shape of tether under a steady current is firstly identified. Next dynamic analysis for earthquake input is carried out for this deflected tether. The fluid loading due to surrounding water is included in the analysis as an added mass term and a hydrodynamic damping term. The tether is discretized by lumping masses at selected nodes. The platform is represented by a mass at the top end of the tether. The effect of pretension in the tether is taken into account in the form of a geometric stiffness term. At each node three degrees of freedom corresponding to surge, heave and pitch motion are considered. As the vibration modes and hence the responses are likely to be affected by the foundation characteristics, the study is extended to include the dynamic soil–structure interaction. The dynamic equations of motion for the tether–pile–soil system are derived using the substructure method. The natural frequencies and the vibration mode shapes of the total system are determined by eigenvalue analysis. The input ground acceleration is represented by Tajimi–Kanai's power spectrum for stationary conditions. The response analysis is carried out using the frequency‐domain random‐vibration approach. The coupled axial and lateral responses are evaluated for horizontal ground excitations. Numerical results indicate that the horizontal displacements of the tether increase with the input ground acceleration, but are nearly equal for all the cases of current velocities considered in the study; the vertical displacements however increase rapidly with the increase in current velocity. For the model considered in the present study, the responses are reduced when soil–structure interaction is included in the analysis.

Buckling of Force-Excited Liquid-Filled Shells

The matrix equation of motion for liquid-filled shells with a particular reference to the influence of ground excitation are derived through a Galerkin/finite element discretization procedure. The modal coupling among the various combinations of axial and circumferential modes are identified. The equations for the dynamic buckling analysis of liquid-filled shells are presented. The buckling criteria of liquid-filled shells subjected to horizontal ground excitation are established. A comparison to available experimental results gives strikingly good agreement. The importance of modal interaction in the axial as well as circumferential directions is also demonstrated. This provides guidelines for a better understanding of dynamic buckling of liquid-filled shells.

Analysis of the base-excited response of intake-outlet towers by a Green's function approach

The dynamic response of a circular, intake-outlet tower structure subjected to high-frequency horizontal ground excitation is investigated theoretically. The tower is idealized as a one-dimensional beam of uniform flexural rigidity and mass per unit length, the fluid is assumed to be linearly compressible and to undergo small-amplitude irrotational motion. The presence of the fluid contained within, as well as the surrounding the structure, is considered in a consistent manner. Both the structural and fluid motions are expressed in terms of appropriate Green's functions leading to a pair of coupled line integral equations which are solved numerically for the fluid velocity potentials on the structure. It is found that the presence of both the interior and exterior fluids can significantly influence the dynamic response, especially for those structures possessing larger diameter to water depth ratios (squatty towers).

Transverse response of offshore pipelines to random ground motion

AbstractA method is presented for the determination of the transverse response of the idealized suspended span of an offshore pipeline to random seismic input. The method is based on spatial discretization of the pipe with nodal lumped masses. The earthquake is assumed to be a stationary random process characterized by a power spectral density function. The cross spectral density function between two random seismic excitations along the pipe length is defined with the help of a local earthquake power special density function, which is assumed to be the same for the two end supports of the pipeline, and a frequency dependent weighted function which decays exponentially with distance from the pipe supports. The solution is obtained in the frequency domain using the spectral approach and is presented in terms of r.m.s. displacements and stresses. The formulation adequately includes the pressure drag effect which tends to dampen the pipe motions. Utilizing this method of analysis, several idealized pipe sea bed configurations, in which the pipe is anchored between two end blocks and subjected to horizontal ground excitations normal to the pipe axis, have been analysed to predict the influence of certain important parameters on the response.

An Analytical Model for Unanchored Fluid-Filled Tanks Under Base Excitation

A set of equations is derived describing the dynamic response of cylindrical liquid storage tanks under horizontal ground excitation. The structure consists of a flexible cylindrical tank with a roof and a bottom plate and rests on a flexible ground through a rigid foundation. Portion of the base of the tank may separate from and lift off the foundation during ground motion. The solution of the hydrodynamic problem is first found in closed form. Then, Hamilton’s principle is applied and the equations governing the behavior of the coupled fluid/structure/ground system are derived. During this procedure, the base uplifting is modeled by an appropriate rotational nonlinear spring placed between the base of the tank and the foundation.

Buckling at the Top of a Fluid-Filled Tank During Base Excitation

An explanation is provided for the earthquake-induced damage observed at the top of liquid storage tanks. An analysis is developed and the results are compared with experimental work. The basic steps of the analysis, which is developed for the general dynamic response of fluid-filled tanks under horizontal ground excitation, are first presented. In this analysis, the structural displacements are expanded in appropriate series forms which involve both rigid body and flexible components. The latter components are expressed as linear combinations of terms, each of which is a product of a function with assumed spatial dependence and an unknown time-dependent function. These time functions are then determined from the solution of the fluid/structure system equations, which are set up by employing Hamilton’s principle. In the present work, results are obtained and compared with model tests carried out at Caltech, during which buckling was observed at the top of the tank under a known base excitation history. Computing analytically the corresponding pressure distribution and using the BOSOR computer code for the buckling computations, a value for the amplitude of the ground acceleration which results in buckling at the top of the tank is calculated. Good correlation with the test work is obtained.

Earthquake response of submerged circular cylinder

The boundary integral method is utilized to calculate the dynamic response of a surface-piercing, vertical, circular cylinder subjected to high-frequency horizontal ground excitation. The cylinder is idealized as a one-dimensional beam of uniform flexural rigidity and uniform mass per unit length, the fluid is assumed linearly compressible and to undergo small-amplitude irrotational motion. The axisymmetry of the structure is exploited by utilizing a new Green's function for linearly compressible fluid flow which is separable in the cylindrical polar coordinate system, thus reducing the surface integral equation to a series of line integral equations. The motion of the cylinder may also be described in terms of a line integral equation through an appropriate Green's function. These two coupled line integral equations are then solved approximately by a numerical approach which involves discretising the region of integration and replacing the continuous problems by systems of algebraic equations which are then solved by standard matrix inversion techniques. Numerical examples are presented which show the influence of the frequency of ground excitation and the various geometric and material parameters on the hydrodynamic force and associated dynamic response of the cylinder.