• Journal of the Korean GEO-environmental Society
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• v.24 no.2
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• pp.13-24
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• 2023

Tunnels may undergo a larger or a smaller response compared with the free-field soil. In the pseudo-static procedure, the response of the tunnel is most often characterized by a curve that relates the racking ratio (R) with the flexibility ratio (F), where R represents the ratio of the tunnel response with respect to the free-field vibration and F is the relative stiffness of the tunnel and the surrounding soil. A set of analytical and empirical curves that do not account for the depth and the aspect ratio of the tunnel are typically used in practice. In this study, a series of dynamic analyses are conducted to develop a set of F-R_m relations for use in a frame analysis method. R_m is defined as an adjusted R where the rocking mode of deformation is removed and only the racking deformation is extracted. The numerical model is validated against centrifuge test recordings. The influence of aspect ratio, buried depth of tunnel on results is investigated. The results show that R_m increases with the increase of the buried depth and the aspect ratio. The widely used F-R relations are highlighted to be different compared with the obtained results in this study. Therefore, the updated F-R_m relations with proposed equations are recommended to be used in practice design. The rocking response decreases with either the decrease of the difference of stiffness between surrounding soil and tunnel or the larger aspect ratio of the tunnel section.

• Structural Engineering and Mechanics
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• v.9 no.1
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• pp.1-16
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• 2000

To study the dynamic response of a rigid block standing unrestrained on a rigid foundation which shakes horizontally, four modes of motion can be identified, i.e., rest, slide, rock, and slide and rock. The occurrence of each of these four modes and the transition between any two modes depend on the parametric values specified, the initial conditions, and the magnitude of ground acceleration. In this paper, a general two-dimensional theory is presented for dealing with the various modes of a free-standing rigid block, considering in particular the impact occurring during the rocking motion. Through selection of proper values for the system parameters, the occurrence of each of the four modes and the transition between different modes are demonstrated in the numerical examples.

• Earthquakes and Structures
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• v.19 no.3
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• pp.215-226
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• 2020

A self-centering wall (SCW) is a lateral resistant rocking system that incorporates posttensioned (PT) tendons to provide a self-centering capacity along with dampers to dissipate energy. This paper investigates the rocking responses of a SCW with base viscous dampers under a sinusoidal-type pulse considering yielding and fracture behaviour of the PT tendon. The differences in the overturning acceleration caused by different initial forces in the PT tendon are computed by the theoretical method. The exact analytical solution to the linear approximate equation of motion is also provided for slender SCWs. Finally, the effects of the ductile behaviour of PT tendons on the rocking response of a SCW are analysed. The results demonstrate that SCWs exhibit two overturning modes under pulse excitation. The overturning region with Mode 1 in the PT force cases separates the safe region of the wall into two parts: region S1 with an elastic tendon and region S2 with a fractured tendon. The minimum overturning acceleration of a SCW with an elastic-brittle tendon becomes insensitive to excitation frequency as the PT force increases. After the plastic behaviour of the PT tendon is considered, the minimum overturning acceleration of a SCW is increased significantly in the whole range of the studied w_g/p.

• Coupled systems mechanics
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• v.8 no.4
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• pp.351-375
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• 2019

The present work investigates the use of a rigid rocking block as a tool to reduce vibrations in a frame structure. The study is based on a simplified model composed by a 2-DOF linear system, meant to represent a general M-DOF frame structure, coupled with a rocking rigid block through a linear visco-elastic device, which connects only the lower part of the 2-DOF system. The possibility to restrain the block directly to the ground, by means of a second visco-elastic device, is investigated as well. The dynamic response of the model under an harmonic base excitation is then analysed in order to evaluate the effectiveness of the coupling in reducing the displacements and the drift of the 2-DOF system. The nonlinear equations of motion of the coupled assemblage 2-DOF-block are obtained by a Lagrangian approach and then numerically integrated considering some reference mechanical and geometrical quantities as variable parameters. It follows an extensive parametric analysis, whose results are summarized through behaviour maps, which portray the ratio between the maximum displacements and drifts of the system, with and without the coupling with the rigid block, for several combinations of system's parameters. When the ratio of the displacements is less than unity, the coupling is considered effective. Results show that the presence of the rocking rigid block improves the dynamics of the system in large ranges of the characterizing parameters.

• Geomechanics and Engineering
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• v.19 no.5
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• pp.407-420
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• 2019

This paper illustrates the results of a series of seismic geotechnical centrifuge experiments to explore dynamic structure-soil-structure interaction (SSSI) of two structures (named S1 and S2) installed on ground surface. A dense homogeneous ground is prepared in an equivalent shear beam (ESB) container. Two structural models are designed to elicit soil-foundation-structure interaction (SFSI) with different masses, heights, and dynamic characteristics. Five experimental tests are carried out for: (1) two reference responses of the two structures and (2) the response of two structures closely located at three ranges of distance. It is found that differential settlements of both structures increase and the smaller structure (S2) inversely rotates out of the other (S1) when they interact with each other. S2 structure experiences less settlement and uplift when at a close distance to the S1 structure. Furthermore, the S1 structure, which is larger one, shows a larger rocking and a smaller sliding response due to the SSSI effects, while S2 structure tends to slide more than that in the reference test, which is illustrated by an increase in sliding response and rocking stiffness as well as a decrease in moment-to-shear ratio (M/H·L) of the S2 structure.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.383-389
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• 2005

This research is to develop a seismic response analysis method for a spent fuel storage cask. FEM model is built for the test model of 1/8 scale spent fuel dry storage cask using available 3D contact conditions in ABAQUS/Explicit. Input load for this analysis os a seismic wave of El-centro earthquake, and the friction and damping coefficients in the analysis condition we obtained from the test result. Penalty and kinematic contact methods of ABAQUS are used for mechanical contact formulation. The analysis method was verified for rocking angle obtained by seismic response tests. The kinematic contact method with an adequate normal contact stiffness showed a good agreement with tests.

• Journal of the Korea Concrete Institute
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• v.24 no.3
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• pp.285-292
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• 2012

Fixed connection is generally used for beam and column connections of concrete structures, but significant damages at the connection due to severe earthquakes have been reported. In order to reduce damages of the connection and improve seismic performance of the connection, several innovative connections have been suggested. One newly proposed connection type allows a rotation of the connection for applications in rotating or rocking beams, columns, and shear walls. Such structural elements would provide a nonlinear lateral force-displacement response since their contact depth developed during rotation is gradually reduced and the stress across the sections of the elements is non-linearly distributed around a contact area, which is called an elastic hinge region in the present study. The purpose of the present study is to define the elastic hinge region or length for the rocking columns, through investigating the cross-sectional stress distribution during their lateral behavior. Performing a finite element analysis (FEA), several parameters are considered including axial load levels (5% and 10% of nominal strength), different boundary conditions (confined-ends and cantilever types), and slenderness ratios (length/depth = 5, 7, 10). The FEA results showed that the elastic hinge length does not directly depend on the parameters considered, but it is governed by a contact depth only. The elastic hinge length started to develop after an opening state and increased non-linearly until a rocking point(pre-rocking). However, the length did not increase any more after the rocking point (post-rocking) and remained as a constant value. Half space model predicting the elastic hinge length is adapted and the results are compared with the numerical results.

• Journal of the Earthquake Engineering Society of Korea
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• v.21 no.3
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• pp.125-135
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• 2017

Various seismic isolation methods are being applied to bridges and buildings to improve their seismic performance. Most seismic isolation systems are the structural seismic isolation systems. In this study, the seismic performance of geotechnical seismic isolation system capable of isolating the lower foundation of the bridge structure from ground was evaluated. The geotechnical seismic isolation system was built with teflon, and the model structure was made by adopting the similitude law. The response acceleration for sinusoidal waves of various amplitudes and frequencies and seismic waves were analyzed by performing 1-G shaking table experiments. Fixed foundation, Sliding foundation, and Rocking foundation were evaluated. The results of this study indicated that the Teflon-type seismic foundation isolation system is effective in reducing the acceleration transmitted to the superstructure subject to large input ground motion. Response spectrum of the Rocking and Sliding foundation structures moves to the long period, while that of Fixed foundation moves to short period.

• Earthquakes and Structures
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• v.15 no.6
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• pp.639-654
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• 2018

Rocking motion have been used for achieving the 'resilient buildings' against earthquakes in recent studies. Low-rise buildings, unlike the tall ones, because of their small aspect ratio tend to slide rather than move in rocking mode. However, since rocking is more effective in seismic response reduction than sliding, it is desired to create rocking motion in low-rise buildings too. One way for this purpose is making the building's structure rock on its internal bay(s) by reducing the number of bays at the lower part of the building's skeleton, giving it a mushroom form. In this study 'mushroom skeleton' has been used for creating multi-story rocking regular steel buildings with square plan to rock on its one-by-one bay central lowest story. To show if this idea is effective, a set of mushroom buildings have been considered, and their seismic responses have been compared with those of their conventional counterparts, designed based on a conventional code. Also, a set of similar buildings with skeleton stronger than code requirement, to have immediate occupancy (IO) performance level, have been considered for comparison. Seismic responses, obtained by nonlinear time history analyses, using scaled three-dimensional accelerograms of selected earthquakes, show that by using appropriate 'mushroom skeleton' the seismic performance of buildings is upgraded to mostly IO level, while all of the conventional buildings experience collapse prevention (CP) level or beyond. The strong-skeleton buildings mostly present IO performance level as well, however, their base shear and absolute acceleration responses are much higher than the mushroom buildings.

• Earthquakes and Structures
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• v.17 no.3
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• pp.245-256
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• 2019

An experimental study was conducted to evaluate the dynamic behavior of a free-standing frame equipped with a movable base system using cast iron and mortar as the bearing materials. The preliminary friction test indicated that a graphite layer developed on the interface and exhibited stable friction behavior. The friction coefficient ranged from 0.33 to 0.36 when the applied normal compression stress ranged from 2.6 to 5.2 MPa. The effect of the variation of normal compression stress would be small. Shaking table tests on the free-standing frame showed that rock, slide, and rock-slide responses occurred. The cumulative slide distance reached 381 mm under JMA Kobe wave excitation; however, only a few cyclic slides occurred at the same locations along the moving track. Most surfaces sustained single slides. Similar results can be observed in other shaking conditions. The insufficient cyclic sliding and significant rocking resulted in a few graphite layers on the mortar surfaces. Friction coefficients were generally similar to those obtained in the preliminary friction tests; however, the values fluctuated when the rocking became significant. The collisions due to rocking caused strong horizontal acceleration responses and resulted in high friction coefficient. In addition, the strong horizontal acceleration responses caused by the collisions made the freestanding specimen unable to reduce the input horizontal acceleration notably, even when slippage occurred. Compared with the counterpart fixed-base specimen, the specimen equipped with the iron-mortar base could reduce the horizontal acceleration amplification response and the structural deformation, whereas the vertical acceleration response was doubled due to collisions from rocking.