Rocking Behavior of Irregular Free-Standing Objects Subjected to Earthquake Motion

Free-standing rigid objects and structures are dominantly found to exhibit rocking behavior and can be vulnerable to overturning during an earthquake as demonstrated by numerous past earthquake events. Such objects are typically considered to be displacement sensitive with their rocking response being well presented by the Peak Displacement Demand (PDD) parameter of the supporting floor’s motion. This in turn can be directly related to an object’s width (along the direction of motion) for assessing its vulnerability to overturn. Such findings have been sufficiently justified by refined dynamic analysis supported by experimental evaluations which were based on rigid blocks with uniform geometric format (i.e., regular in their mass distribution). However, vulnerable rocking objects can be asymmetric and accordingly their sensitivity to floor displacement cannot be directly related to their width. The key parameter which defines irregular objects’ response to rocking motion is represented by the degree of eccentricity of their center of mass. In this study, the well-known rocking equation of motion is reconfigured and devised to model the rocking responses for 280 irregular objects undergoing eight earthquake motions which included artificial and recorded earthquakes. Analytical results obtained from solving the adjusted equation of motion were evaluated with sophisticated finite element (FE) models simulating the 280 irregular cases. This experimentally validated FE modeling approach was found to be time- and cost-effective for understating the rocking behavior of asymmetric objects as well as clarifying an interesting relationship between the object’s damping level and the condition of the supporting base (i.e., whether being provided with supports at the points of rotation or not). The rocking response of irregular objects was found to be highly influenced by the level of eccentricity of the object when excited by motions with high displacement amplitudes, while such influence was not found noticeable by wider objects. Based on the developed trends between the maximum top displacement of irregular objects and the PDD, an expression for estimating the rocking amplitudes is proposed which is a function of the object’s eccentricity.     

Optimal Control of Structures under Earthquakes Including Soil-Structure Interaction

It is well known that the soil-structure interaction (SSI) changes the dynamic response of a structure supported on flexible soil. The analysis of optimally controlled SSI systems has certain difficulties due to the nature of the SSI and the optimal control problem. In this paper, a two-step iteration-based numerical algorithm is proposed to handle optimally controlled SSI systems under earthquakes. First, the optimal control forces are obtained by using a fixed-base system. Then, the optimal control forces are converted to the frequency domain by the Fourier transform technique to be used in the equations of the SSI system. The lateral displacement and the rocking of the foundation are obtained from the equations of the SSI system containing the optimal control forces in the frequency domain. The lateral displacement and rocking of the foundation are then converted to the time domain by the inverse Fourier transform technique, and the lateral accelerations and the rocking accelerations of the foundation are obtained by the forward finite difference method. During the second step, the optimal control forces are calculated again by using the lateral acceleration and the rocking acceleration of the foundation along with the earthquake ground motion. Using the method explained above, the optimal control forces obtained in the time domain are used in the equations of the soil-structure system from which the behavior of foundation and structure is obtained. In the final section of the paper, a numerical study is conducted for a controlled structure supported on flexible soil.     

Controlled Rocking CLT Walls for Buildings in Regions of Moderate Seismicity: Design Procedure and Numerical Collapse Assessment

Controlled rocking heavy timber walls are designed to rock on their foundations in response to earthquakes. For regions of moderate seismicity, it is proposed that this rocking behaviour can be adequately controlled using only post-tensioning, even with a large force-reduction factor and no supplemental energy dissipation. This article presents a force-based design procedure for controlled rocking cross-laminated timber walls without supplemental energy dissipation, including a method for estimating higher mode effects. Fragility analyses of three prototype walls demonstrate that the procedure can limit the probability of collapse to <10% during a maximum considered earthquake in a region of moderate seismicity.     

Floor Spectra of Inelastic RC Frame Buildings Considering Ground Motion Characteristics

A range of reinforced concrete frame buildings with different levels of inelasticity as well as periods of vibration is analyzed to study the floor response. The derived floor acceleration response spectra are normalized by peak ground acceleration, peak floor acceleration, and ground response spectrum. The normalization with respect to ground response spectrum leads to the lowest coefficients of variation. Based on this observation as well as previous studies, an amplification function is proposed that can be used to develop design floor spectra from the ground motion spectrum, considering the building’s dynamic characteristics and level of inelasticity.     

Experimental Identification of the Dynamic Characteristics of a Flexible Rocking Structure

This article presents the results of free vibration and earthquake excitation tests to investigate the dynamic behavior of freely rocking flexible structures with different geometric and vibration characteristics. The primary objective of these tests was to identify the complex interaction of elasticity and rocking and discuss its salient effects on the rocking and vibration mode frequencies, shapes and excitation mechanisms. The variability of response is discussed, including critical investigation of the repeatability of the tests. It was found that the variability in energy dissipation and energy transfer to vibrations at impact may lead to significantly different responses to almost identical excitations.     

文物防震措施研究初探

台北故宫博物院珍藏中国历代名瓷和玉器其数量和种类居全世界博物馆之冠,目前陈列柜内瓷器及玉器的防震措施仍有改善的空间,因此运用现代科学方法和仪器研究文物防震措施,更突显其重要性和迫切性。本研究使用的方法为传统文物防震措施(使用微晶蜡固定、铁弗龙、橡胶垫和防震塑料垫衬底)、柜内型隔震台减震和电磁铁固定陈列柜功能性测试;运用台湾地震工程研究中心的人工地震台执行上述不同方法之实验。实验结果,传统方法抗震优劣顺序为:微晶蜡>铁弗龙>塑料垫>橡胶垫;柜内型隔震台消能减震功效可达60％;至于电磁铁固定陈列柜防震在加速度超过800gal时,才显现摇摆现象,未装电磁铁的陈列柜,加速度超过300gal时,即有自震现象。然而在瓷器、玉器陈列柜内实务执行防震措施的层面,宜使用微晶蜡固定最为经济有效,柜内型隔震台亦可使用,但需考量柜内可滑动空间是否充裕的实际状况执行。     

Inelastic Displacement Ratios for Nonstructural Components Subjected to Floor Accelerations

This paper describes a study on the characterization of the Inelastic Displacement Ratios (IDRs) of inelastic acceleration-sensitive nonstructural components subjected to floor accelerations obtained from the linear analysis of multistory building structures under far-field ground accelerations. Several building models having different structural systems and a number of stories were considered. IDRs were obtained from the displacement response of elastic and inelastic single-degree-of-freedom systems subjected to floor accelerations. Similarities and differences between floor acceleration IDRs and ground acceleration IDRs were identified, and efforts were made to explain the differences. Finally, a predicting equation for floor acceleration IDRs is proposed and validated.     

EVALUATION OF ACCIDENTAL ECCENTRICITY IN BUILDINGS DUE TO ROTATIONAL COMPONENT OF EARTHQUAKE

This study adopts a random procedure in the evaluation of the effect of the rotational component of earthquake on the accidental eccentricity of symmetric and asymmetric buildings. The spectral density function of the rotational component of earthquake acceleration (about the vertical axis) is obtained on the basis of the spectral density function of the horizontal component of earthquake acceleration. The rotational component of an earthquake can increase the response of the structure. The degree of the increase is highly dependent upon the dynamic characteristics of the system and the rotational component of the earthquake. To bring this increase under consideration, seismic codes represent a parameter referred to as accidental eccentricity, as a part of the design eccentricity. The purpose of the present study is to estimate the value of this increase and to make appropriate suggestions based on frequency domain analysis.     

Rocking of Non-symmetric Rigid Blocks in Buildings Considering Effects Associated with Dynamic Soil-Structure Interaction

A dynamic model for the estimation of the rocking and/or overturning response of a free-standing non-symmetric rigid block considering rotational and horizontal excitation is proposed. The block is situated at different levels of a building with flexible base subjected to earthquakes. Base flexibility introduces the rotational component of the excitation due to dynamic soil-structure interaction (DSSI). The model is used to assess the influence of the dynamic soil-structure interaction on the behavior of the block. An illustrative example of the proposed model for non-symmetric rigid blocks in 5-, 10-, and 15-story buildings located in soft soils considering earthquakes from different seismic sources is presented. Results show that it is important to consider kinematic effects as well as inertial effects of DSSI in the dynamic response of contents. The influence of base flexibility depends on the change of spectral intensities associated to the increase of the building structural period and is larger for higher building levels.     

The Numerical Study of Base-Isolated Buildings Under Near-Field and Far-Field Earthquakes

The behavior of base-isolated building frame is investigated with the help of a numerical study for far-field and near-field earthquakes with directivity and fling-step effects. Both design-level and extreme-level earthquakes are considered. Selected response parameters are peak floor displacement, acceleration, base shear, and isolator displacement. Inelastic behavior of base-isolated structure during the earthquake is investigated performing nonlinear time history analysis of a ten-story building frame. This study shows that base isolation is not effective for near-field earthquakes. Even for design-level earthquake, the frame gets significantly into inelastic range for earthquakes with fling-step effect.     

Diffraction around a Semi-Parabolic Canyon in an Elastic Half-Space by Out-of-Plane SH-Waves,II: Rocking and Resultant Rotations

This paper is the second of the two papers, discussing the rocking and resultant component of rotations, with the torsional components of motions presented earlier in the first paper for the case of out-of-plane SH waves excitation on a semi-parabolic canyon. The rotational motions are gaining importance in recent years in the field of strong-motion seismology and earthquake engineering. Many previous papers on out-of-plane SH waves excitation presented the associated torsion rotational motions, when in fact there is also a rocking rotational component of motions. Both the rocking and torsion rotational motions, in as much as the translational motions, had shown to play an important role in structural responses, even though rotations are not incorporated into building design codes at present. Studying the rotational motions can thus help to a better understanding of the behavior of surface topographies that are in the vicinity of structures in the event of seismic excitation. This paper included, besides the additional rocking motions, also the resultant rotational motions combining torsion and rocking.     

A Simplified Model to Evaluate the Dynamic Rocking Behavior of Irregular Free-Standing Rigid Bodies Calibrated with Experimental Shaking-Table Tests

A simplified model to evaluate the dynamic rocking behavior of free-standing irregular rigid bodies under earthquake-induced forces is proposed. The model analyzes the response of a three-dimensional irregular rigid body using a numerical approach that considers a critical section and two equivalent rectangular rigid blocks. Experimental shaking-table tests were carried out on modular prototypes, which allow the replication of representative mass distributions, sizes, and/or slenderness ratios for typical objects. The tests were used to calibrate the numerical model. It was found that the dynamic behavior under irregular conditions (asymmetrical shape and/or non-uniform mass distribution) can be estimated with the appropriate geometric and density considerations.     

Seismic Rotational Displacements of Gravity Quay Walls Considering Excess Pore Pressure in Backfill Soils

The effect of excess pore pressure developed in backfill soil during earthquake is an important consideration in rotational displacement prediction of gravity quay walls. Based on Newmark’s sliding block concept and stress-based excess pore pressure model, a new method is proposed to predict the critical rotational acceleration and angular acceleration time histories considering the development process of excess pore pressure in earthquake events. Then, the rotational displacement of gravity quay walls is predicted according to the calculated angular acceleration time histories. By using the proposed method, the effects of various parameters involved in the calculation have been studied by carrying out a parameter study. Analysis results reveal that the influence of excess pore pressure on the rotational displacement of gravity quay walls with saturated backfill soil is significant, so, can not be ignored; and rotational displacement is sensitive to the magnitude of earthquake, horizontal and vertical seismic accelerations of ground motion, wall and soil friction angle, and soil relative density. When the rotation and sliding of wall occur simultaneously, rotation and sliding will be inhibited by each other.     

Influence of Frequency Content and Peak Intensities in the Rocking Seismic Response of Rigid Bodies

The rocking response of a family of bodies given by its width and height due to synthetic and recorded strong ground motions is presented; this allow us to identify the main parameters that govern their response: peak acceleration and velocity, dominant frequency, and acceleration time-history. Recorded strong ground motions were scaled to the same peak acceleration and also to the same peak velocity to analyze the effect of both parameters in the response of rigid bodies. These three parameters were used to build an equation to obtain the height/width overturning plots. The proposed equation was tested for many well-known strong ground motions and the results were compared to other methods shown to be more accurate. This parametric equation does not need iterations or numerical approximations to be solved and can provide engineers, in a very practical way, minimum design requirements or particular specifications to protect non structural elements.     

RESPONSE OF UNREINFORCED MASONRY BUILDINGS

Abstract

A summary of dynamic measurements are presented that illustrate relations between linear seismic demand and true nonlinear response of unreinforced masonry buildings with flexible diaphragms and rocking piers subjected to a series of simulated earthquake motions.     

Experimental Study on the Seismic Performance of Superimposed RC Shear Walls with Enhanced Horizontal Joints

The seismic performance of superimposed reinforced concrete (RC) shear walls is decreased by rocking behavior and damage concentration at the horizontal joint. An enhanced horizontal joint method is proposed to improve the corresponding seismic performance. To validate the reliability of the proposed method, three full-scale superimposed walls and a cast-in-place shear wall (for comparison) are designed and tested under the quasi-static load. The test results indicate that the rocking phenomenon can be prevented using the proposed method, and the seismic performance of superimposed RC shear walls with enhanced horizontal joints is comparable to that of the cast-in-place RC shear walls.     

Shake-Table Tests of Confined-Masonry Rocking Walls with Supplementary Hysteretic Damping

A shake-table investigation is conducted on a 40% scale model frame-wall system to validate the concept of rocking walls as primary seismic systems. The rocking wall concept was implemented on confined masonry walls, but the findings can be extended to any rocking wall system. As the inherent damping of this system is low, a pair of supplemental steel hysteretic energy dissipating dampers is used at the base of the wall. It is concluded that with careful detailing, damage is not only eliminated but the structure re-centers itself following a large earthquake.     

Seismic Fragility Evaluation of RC Frame Structures Retrofitted with Controlled Concrete Rocking Column and Damping Technique

Acceleration response of simple yielding structure is proportional to its own weight, but it is limited by yield strength. Thus, using rocking columns that reduces global yield strength, a limited acceleration is achieved. However, the displacement becomes large due to lower strength and higher inelasticity, but it can be controlled by adding damping. Performing fragility analyses, the seismic response of R/C frame structures with rocking columns and viscous dampers is investigated. Near field MCEER ground motions are considered. The analyses show that the story accelerations are reduced by using rocking columns, while the story displacements are controlled by using viscous dampers.     

Contact Dynamics of Masonry Block Structures Using Mathematical Programming

A simple variational formulation for contact dynamics is adopted to investigate the dynamic behavior of planar masonry block structures subjected to seismic events. The numerical model is a two-dimensional assemblage of rigid blocks interacting at potential contact points located at the vertices of the interfaces. A no-tension and associative frictional behavior with infinite compressive strength is considered for joints. The dynamic contact problem is formulated as a quadratic programming problem (QP) and an iterative procedure is implemented for time integration. Applications to analytical and numerical case studies are presented for validation. Comparisons with the experimental results of a masonry wall under free rocking motion and of a small scale panel with opening subjected to in-plane loads are also carried out to evaluate the accuracy and the computational efficiency of the formulation adopted.     

Implications of Thrown-Out Boulders for Earthquake Shaking

In the source areas of some large shallow earthquakes, we have found many dislodged boulders struck by severe ground shaking. Some boulders were located at quite distances from the former sockets, which remained undisturbed with surrounding clear edges. This fact indicates the possibility that vertically upward seismic acceleration exceeded the earth's gravity (1g). This phenomenon of upthrown boulders is investigated herein by examining the effects of waves, which emanate deep in the ground due to an earthquake, propagate through the ground and boulder, and reflect back to the ground, involving a variety of their interaction. An elastic dynamic analysis is carried out on the basis of a one-dimensional continuum model consisting of the ground and boulder. It is subjected to the input of the Ricker wave, which is intended to simulate an earthquake-generated wave, emanating from the bottom of the model ground. The upthrow of a boulder is taken to occur when the dynamic response at the bottom of the boulder satisfies certain conditions. It turns out that the possibility of upthrow occurrence is high when the period of the Ricker wave coincides with the fundamental period of the ground vibration. It leads to the conclusion that the upthrow takes place due to resonance in the response of the system of the ground and boulder to the external wave input. The upthrow possibility increases as the input acceleration increases. Trial is made of predicting the maximum acceleration and velocity of an earthquake, based on this consideration of the up throw phenomenon.