Response of a 42-storey steel-frame building to the Ms = 7.1 Loma Prieta earthquake

A set of 14 acceleration records was obtained from a 42-storey steel-frame building, the Chevron Building, in San Francisco during the M_s = 7.1 Loma Prieta earthquake of 17 October 1989. Data were analysed using a system identification method based on the discretetime linear filtering, and the least-squares estimation techniques. The results show that the response of the building is dominated by two modes: a translational mode in the weaker (southwest-northeast) principal direction of the building at 0.16 Hz with 5% damping, and a translational-torsional mode along the east-west diagonal of the building's cross-section at 0.20 Hz with 7% damping. There are significant contributions from higher modes at 0.54 Hz, 0.62 Hz, 1.02 Hz and 1.09 Hz. All the modes incorporate some torsion, but the amplitudes of torsional components are small, about 10% of translational amplitudes. Soil-structure interaction influences the vibrations near 1.0 Hz. The contribution of soil-structure interaction to the peak displacements of the building is significant, particularly at lower floors.     

应县木塔动力特性原位试验及有限元分析

为研究现有变形状态下应县木塔的动力特性,采用941B型传感器和INV3060S型采集仪对木塔各层明层柱头、柱脚东西方向和南北方向的脉动信号进行原位测试试验和数据采集.通过峰值拾取法与随机子空间法相结合的方式,分析得到了木塔前7阶的自振频率、振型及阻尼比.考虑到木塔的变形较为严重,利用大型有限元分析软件ANSYS建立损伤...     

Determining the damping factor of sedimentary rocks required for seismically designed structures

Relationships for the shear damping ratio D_s (a function of shear quality factor Q_s) and modulus decay curve G_seis/G_max as a function of shear strain for mudrocks have been developed. Field experiments to determine damping ratio and elastic moduli should be performed at frequencies as close as possible to the bandwidth (0–100 Hz) of interest for building design. Estimates of these parameters made from extrapolating laboratory core (MHz) or wireline (kHz) data to lower frequencies can be highly unreliable. Field estimates of damping ratio are very dependent on, and often totally dominated by, the effects of scattering of P and S waves by inhomogeneities in the rock mass structure. This is, particularly, the case when open fractures or cracks are present in near-surface rocks.     

Response of a tall building far from the epicenter of the 11 March 2011 M 9.0 Great East Japan earthquake and aftershocks

The 11 March 2011 M 9.0 Great East Japan earthquake generated significant long‐duration shaking that propagated hundreds of kilometers from the epicenter and affected urban areas throughout much of Honshu. Recorded responses of a tall building at 770 km from the epicenter of the mainshock and other related or unrelated events show how structures sensitive to long‐period motions can be affected by distant sources. Even when the largest peak input motions to the building is about 3% g, the strong‐shaking duration was about 140 s. The 300‐ to 1000‐s prolonged responses of the building are primarily due to a combination of site resonance (e.g. structural fundamental frequency ~0.15 Hz and site frequency ~0.13–0.17 Hz) and low damping (~1–2%) of the structure. Response modification technologies can improve the response of the building during future earthquakes. The need‐to‐consider risks to such built environments from distant sources are emphasized. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonlinear procedures for seismic evaluation of buildings

New static and dynamic displacement‐based procedures have been developed by the Federal Emergency Management Agency (FEMA) for the seismic evaluation and design of buildings. The static procedures calculate displacements in yielding buildings as the product of an elastic spectral displacement and coefficients C_i. Mean elastic and mean inelastic displacements are assumed to be equal for elastic periods, T₀, greater than the characteristic site period, T_g. The data presented in this paper and elsewhere support this assumption for values of the strength ratio greater than or equal to 0·20. For T₀ ≤ T_g, mean inelastic displacements can substantially exceed mean elastic displacements for all values of the strength ratio; FEMA 273 accounts for this observation by the coefficient C₁. However, the FEMA 273 cap on C₁ (= 1·5) is not sufficiently conservative and should be increased to 3·0 for the analysis and design of modern construction. The effects of stiffness degradation, strength deterioration and pinching are represented in FEMA 273 by the coefficient C₂. The values assigned to C₂ appear to be most reasonable. Nonlinear dynamic analysis is being widely used to estimate maximum deformations and displacements in buildings. The values calculated for the maximum deformations and displacements will be dependent upon the means used to characterize structural damping in the building frame. Although structural damping is routinely implemented through a damping constant (or matrix), such an implementation will overestimate the effects of structural damping in a yielding building and underestimate maximum deformations and displacements. Structural damping should be characterized by the target damping ratio (typically 5% of critical) at the point of maximum displacement. Copyright © 1999 John Wiley & Sons, Ltd.     

Robust control of plate vibration via active constrained layer damping

In this paper, the theoretical modeling of a plate partially treated with active constrained layer damping (ACLD) treatments and its vibration control in an H_∞ approach is discussed. Vibration of the flat plate is controlled with patches of ACLD treatments, each consisting of a viscoelastic damping layer which is sandwiched between the piezo-electric constrained layer and the host plate. The piezo-electric constrained layer acts as an actuator to actively control the shear deformation of the viscoelastic damping layer according to the vibration response of the plate excited by external disturbances. In the first part of this paper, the Mindlin–Reissner plate theory is adopted to express the shear deformation characteristics of the viscoelastic damping layer, meanwhile GHM (Golla–Hughes–McTavish) model of viscoelastic damping material and FEM (finite element model) are incorporated to describe the dynamics of the plate partially treated with ACLD treatment. In the second part, particular emphasis is placed on the vibration control of the first four modes of the treated plate using H_∞ robust control method. For this purpose, an H_∞ robust controller is designed to accommodate uncertainties of the ACLD parameters, particularly those of the viscoelastic damping core which arise from the variation of the operation temperature and frequency. Disturbances and measurement noise are rejected in the closed loop by H_∞ robust controller. In the experimental validation, external disturbances of different types are employed to excite the treated plate. The results of the experimental clearly demonstrate that the proposed modeling method is correct and the ACLD treatments are very effective in fast damping out the structural vibration as compared to the conventional passive constrained layer damping (PCLD).     

Evaluation of the damping factor of foundation bases subjected to vertical vibrations

Conclusions 1. The damping factor b depends on the elastic properties of the soil base and the dimensions of the lower surface of the foundation. Hence, one of the values — the coefficient of uniform elastic compression C_z — makes it possible to find both the elastic and damping characteristics of the soil base. To evaluate the damping characteristics, it is expedient to use the specific damping factor introduced in this article.2. To find the maximum amplitudes of unsteady vibrations of massive foundations under the action of an instantaneous impulse, use can be made of Eqs. (21)–(23), which determine the factor b_z if the limit from which the elastic waves may be reflected (rock, soil layer with higher wave velocities, etc.) is located below the lower surface of the foundation at a depth greater thanl/2,l being calculated from Eq. (16). To find the parameters of steady vibrations of massive foundations, the damping properties of the soil base are determined by the factor b_z, calculated from Eqs. (12)–(15).3. The equations for the factor b_z are related to the mean soil conditions; however, the effect of the characteristics of the geologic morphology is exerted on this factor more strongly than on the rigidity modulus of the soil base; hence, it is desirable to gather experimental data for the systematization and processing of which use can be made of the relations obtained in this article.Scientific-Research Institute of Bases and Underground Structures. Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 5, pp. 15–18, September–October, 1981.     

Measuring fracture toughness of crystalline marbles under modes I and II and mixed mode I–II loading conditions using CCNBD and HCCD specimens

Fracture toughness of three crystalline Calcite marbles, which are different only in grain size and distribution, is determined under modes I and II and mixed mode I–II loading conditions using Cracked Chevron-Notched Brazilian Disc (CCNBD) and Hollow Centre Cracked Disc (HCCD) specimens. The results show that mode I fracture toughness (K_IC) is correlated negatively with grain size. For each marble, HCCD yields lower values of fracture toughness, compared with CCNBD. This difference is negligible under mode I loading condition; while it becomes larger as loading condition transits from mode I to mode II. Measured values of P-wave velocity (V_P), Brazilian tensile strength (σ_tB) and Schmidt hammer hardness are in direct relation with K_IC of the marbles. The obtained results are compared with three fracture criteria, in which the Minimum Strain Energy Density (MSED) criterion has provided better correlations with different critical combinations of modes I and II Stress Intensity Factors.     

厦门沿海某超高层建筑结构风致振动动力特性研究

现场实测是获得结构风致振动动力特性参数的一种较为可靠的手段和方法。通过对厦门沿海某超高层建筑在台风登陆时进行现场原型实测,得到了该建筑结构的第10层、18层、23层、28层、33层和36层的加速度响应时程数据和固有频率及振型等结构的动力特性。根据实测加速度数据,利用随机减量法提取结构两方向的前3阶固有频率对应的阻尼比,结果表明：由于实测时台风风速较大,导致结构风致响应较为显著,因此结构两个方向第1阶阻尼比值在7%左右,明显大于另外两阶阻尼比;两方向第1阶阻尼比与加速度呈非线性关系,阻尼比随加速度的增大而增大。采用ANSYS软件建立该超高层建筑的3D有限元分析模型并进行模态分析,提取该模型的前3阶固有频率和振型,与实测结果进行对比分析,结果较为吻合,由此说明所建立的3D有限元分析模型正确可靠。     

环境风激励下的深圳平安金融中心模态参数识别

对高度600 m的超高层建筑——深圳平安金融中心在外界环境风激励下的风振响应进行了现场实测。通过安装在塔楼118层的2组加速度传感器测得结构的风致加速度响应,采用经验模态分解法（EMD）与随机减量技术（RDT）相结合的方法计算了结构的自振频率和阻尼比。建立了深圳平安金融中心三维有限元模型,通过有限元分析得出结构的自振频率,并与实测结果进行对比。结果表明:由EMD和RDT相结合的方法计算得出结构1阶横弯自振频率约为0.12 Hz,阻尼比为0.3%~0.6%;结构1阶扭转自振频率约为0.28 Hz,阻尼比为0.8%~1.0%;深圳平安金融中心实测结构自振频率和阻尼比与其他结构高度相似的超高层建筑实测结果相近,且实测结果和有限元分析结果吻合较好,验证了EMD和RDT结合方法分析超高层建筑模态参数的有效性;测试结果可以为超高层建筑设计和相关研究提供依据。     

Decentralized robust control of building structures based on sliding mode theory

In this paper, a decentralized control algorithm is proposed for actively controlling the response of the flexible tall building structures under earthquake excitations. In the proposed approach, tall building structure was divided into some substructures in the form of state equation. The interaction of the subsystems and external excitations is conducted as bounded generalized force acting on the subsystems. A decentralized control algorithm of tall building structures is established based on the sliding model control theory. The control structure is described based on unit vector control. The control law consists of two parts: a linear control law u_L and a nonlinear law u_N. The linear control is merely a linear state feedback controller, whereas the nonlinear feedback controller incorporates the discontinuous or continuous nonlinear elements of the control law. Using the advantage of match conditions of sliding mode theory and the bounded feature of generalized force, the overall stability of decentralized control is also investigated. The actuator arrangement and matching conditions are discussed. The effectiveness of the proposed method is demonstrated by the numerical simulation of the decentralized control of a 20-story benchmark structure under seismic excitations.     

Study of ground vibrations excited during pile driving

1. When driving piles with S-330 diesel hammers, vibrations that range in frequency from 10 to 30 Hz and are extinguished in the interval between blows and with increasing distance from the pile-driving site are excited in the ground. The damping of the vibration amplitude and acceleration that occurs with increasing distance from the point of pile embedment is rather accurately described by B. Golitsyn's equation.2. The frequency of surface vibrations excited in cohesive soils with a probe resistance R=460–2400 kN/m² can be determined with an accuracy to 25% from the empirical relationship

Experimental study on seismic deformation modes of reinforced-soil walls

A series of 1-g shaking table tests were conducted on 1 m high reinforced-soil wall models. The physical models were subjected to harmonic sinusoidal-like time history input motions at frequencies of 2, 5, 8 and 10 Hz. The effects of parameters such as soil density, reinforcement length, spacing and stiffness on the seismic response of the model walls were studied. Free-sliding toe boundary and wrap-around wall facing were selected to reveal all potential deformation modes of the wall and different deformation shapes of the facing. Different deformation modes (overturning and bulging) of the facing as well as base sliding were observed. Determinant parameters in the formation of each mode were identified by introducing internal failure indexes. A bulging index was introduced to measure the bulging intensity of the wall facing. Additionally, the distribution of the shear stiffness modulus (G) and damping ratio (D) of the reinforced soil along the wall height were assessed. The effect of the confining pressure (σ_v) and shear strain on variations of G and D were traced. G proved to be dependent on σ_v and, as expected, to be incremental with depth below the crest of the wall. Based on measurements and relevant approximations, no incremental or decremental patterns for D were detected along the wall height. Moreover, at large strains of about 10⁻³, an average D of about 20% was observed. Overall, based on the results of physical model testing in this study, which confirm similar findings of previous research, it was concluded that reinforcement stiffness is a key parameter dominating the seismic response and deformation mode of a wall and not reinforcement ultimate tensile strength, which is currently used as the main parameter for wall design in existing codes.     

Successful performance of a base-isolated hospital building during the 17 January 1994 Northridge earthquake

The purpose of this paper is to examine the response records and thereby the performance of the base-isolated University of Southern California (USC) hospital building during the M_s = 6·8 Northridge (California) earthquake of 17 January 1994. The data retrieved from the building is the first set of data from any base-isolated building that (a) was tested to acceleration levels at the free-field similar to the zero period acceleration (ZPA) level postulated in the seismic design criteria of the building and (b) exhibits levels of relative displacement excursions which puts the isolators into the nonlinear range. The variation of the fundamental frequency as a function of changing instantaneous stiffness of the isolators is identifiable. During the shaking, the isolators (a) performed well and, having attained up to 10% hysteretic damping, effectively dissipated the incoming energy of motions and (b) reduced the drift ratios of the superstructure of the building to a maximum of 10% of the allowable, which should explain the fact that there was no damage to the structure or its contents. The primary conclusion of this study is that this base-isolated building performed well during the Northridge earthquake of 17 January 1994 when only approximately 10% of the displacement capability of the isolators were utilized. Therefore, there is every reason to believe that the building will perform well during future earthquakes in the region.     

Investigation of block foundations resting on soil–rock and rock–rock media under coupled vibrations

In the present study,the dynamic response of block foundations of different equivalent radius to mass(R_o/m) ratios under coupled vibrations is investigated for various homogeneous and layered systems.The frequency-dependent stiffness and damping of foundation resting on homogeneous soils and rocks are determined using the half-space theory.The dynamic response characteristics of foundation resting on the layered system considering rock-rock combination are evaluated using finite element program with transmitting boundaries.Frequencies versus amplitude responses of block foundation are obtained for both translational and rotational motion.A new methodology is proposed for determination of dynamic response of block foundations resting on soil-rock and weathered rock-rock system in the form of equations and graphs.The variations of dimensionless natural frequency and dimensionless resonant amplitude with shear wave velocity ratio are investigated for different thicknesses of top soil/weathered rock layer.The dynamic behaviors of block foundations are also analyzed for different rock-rock systems by considering sandstone,shale and limestone underlain by basalt.The variations of stiffness,damping and amplitudes of block foundations with frequency are shown in this study for various rock—rock combinations.In the analysis,two resonant peaks are observed at two different frequencies for both translational and rotational motion.It is observed that the dimensionless resonant amplitudes decrease and natural frequencies increase with increase in shear wave velocity ratio.Finally,the parametric study is performed for block foundations with dimensions of 4 m × 3 m × 2 m and 8m×5m×2m by using generalized graphs.The variations of natural frequency and peak displacement amplitude are also studied for different top layer thicknesses and eccentric moments.     

Seismic fragility assessment of effectiveness of viscous dampers in R/C buildings under scenario earthquakes

Fragility curves are used to represent the probabilities that the structural damages, under various level of seismic excitation, exceed specified damage states by means of earthquake intensity–damage relations. In this study, the fragility curves have been developed for comparative seismic evaluation of several retrofitting measures by incorporation of fluid viscous (VS) dampers applied to a representative high-rise reinforced concrete (R/C) office building located in Istanbul. In the retrofitting strategies considered, similar type of VS dampers was used and designed to provide the structure with three different effective damping ratios of 10%, 15%, and 20%. In the fragility analysis, a set of 240 artificially generated earthquake ground motions compatible with the design spectrum selected to represent the variability in ground motion was employed to study nonlinear dynamic responses of the structures before and after retrofit. Four damage states: slight, moderate, major, and collapse were defined to express the condition of damage. The fragility curves in this study are represented by lognormal distribution functions with two parameters and developed as a function of peak ground acceleration (PGA), spectral acceleration (S_a), spectral displacement (S_d). Comparison of the fragility curves indicated that the VS dampers were very effective in attenuating seismic structural response under various earthquake ground motions. It was also found that a two-fold reduction in the probability of exceeding damage states might be achieved by introducing passive VS damper systems.     

Vibrations of orthotropic annular plates subjected to non-uniform boundary conditions over different sections of the inner and outer circumferences

The free vibrational response of homogeneous or symmetrically laminated polar orthotropic annular plates subjected to non-uniform boundary conditions on the inner and outer rims is scrutinized in detail, using a finite-difference method. Although the same sets of boundary conditions are considered, the angular location at which the altered boundary conditions are applied and the segments that they cover are allowed to be different on the inner and outer circumferences. The sensitivity of vibrational frequencies to the extent and relative location of the non-uniformities is investigated and shown to be strongly influenced by the material properties with the orthotropy ratio for the plate (defined here by D_rr/D_θθ) being the predominant parameter for indicating the sensitivity to non-uniformity. The behavior of higher modes of vibration is also discussed and the phenomenon of crossover, whereby two modes having the same frequency exist, is found to occur. Unlike the crossover previously reported in the literature, for which only higher modes of frequency were involved, in the current context, it was discovered that the phenomenon may also be associated with the lowest mode of vibration. The circumstances under which crossover transpires are dependent on the relative location of the boundary non-uniformities, the relative length over which the non-uniformities are applied and the orthotropy ratio.     

Structural dynamic parameter identification of Saige building based on distributed synchronous acquisition method

在大型复杂工程结构上进行现场模态测试时，由于结构规模体量大并存在空间隔断，导致数据采集设备与传感器之间快速布设数据传输线困难。因此，有必要解决不同位置分布式同步采集设备时间精确同步问题，研发易于快速安装的分布式数据采集和无线传输设备。为此，提出基于“北斗”卫星授时的结构振动分布式同步采集算法，集成分布式同步采集硬件与研发数据在线采集和无线传输软件，获取大型复杂工程结构不同空间位置时间同步动态响应，基于随机子空间算法自[JP2]动识别工程结构服役状态下真实的模态参数。在赛格大厦振动事件溯源工作中，该系统成功捕捉到5月20日12:00—13:00[JP]结构共振时第69层与桅杆底部的加速度响应，发现四次共振均以频率2.12 Hz振动主导。基于该系统在环境激励条件下的现场模态测试，识别结构前19阶动力学参数，发现频率2.12 Hz是主体结构弯扭耦合和桅杆面内对称振动模态。基于现场激振测试识别频率2.12 Hz对应的阻尼比，发现阻尼比随着振幅的增加突然减小然后逐步增加，较低的阻尼比是导致赛格大厦发生共振的原因之一。     

基于分布式同步采集的赛格大厦结构动力学参数识别

在大型复杂工程结构上进行现场模态测试时,由于结构规模体量大并存在空间隔断,导致数据采集设备与传感器之间快速布设数据传输线困难。因此,有必要解决不同位置分布式同步采集设备时间精确同步问题,研发易于快速安装的分布式数据采集和无线传输设备。为此,提出基于“北斗”卫星授时的结构振动分布式同步采集算法,集成分布式同步采集硬件与研发数据在线采集和无线传输软件,获取大型复杂工程结构不同空间位置时间同步动态响应,基于随机子空间算法自动识别工程结构服役状态下真实的模态参数。在赛格大厦振动事件溯源工作中,该系统成功捕捉到5月20日12:00—13:00结构共振时第69层与桅杆底部的加速度响应,发现四次共振均以频率2.12 Hz振动主导。基于该系统在环境激励条件下的现场模态测试,识别结构前19阶动力学参数,发现频率2.12 Hz是主体结构弯扭耦合和桅杆面内对称振动模态。基于现场激振测试识别频率2.12 Hz对应的阻尼比,发现阻尼比随着振幅的增加突然减小然后逐步增加,较低的阻尼比是导致赛格大厦发生共振的原因之一。     

Variability in seismic response of secondary systems due to uncertain soil properties

A mode acceleration formulation is presented to investigate the variability in the response of a secondary system which is supported on a flexible-base primary system at multiple attachment points. The response functions are considered to be uncertain due to uncertainties in the values of shear wave velocity and Poisson’s ratio of the foundation soil. Both soil parameters are assumed to be statistically independent variables with Gaussian distributions. A numerical study with the help of an example primary-secondary (P–S) system shows that dynamic response should be ignored only for very stiff secondary modes, say > 7 times as stiff as the dominant mode of the primary system, for the proposed formulation to work well. It is also seen that uncertainty in shear wave velocity can be ignored in case of limited soil-structure interaction, while uncertainty in Poisson’s ratio should be considered only when soil damping is sensitive to the Poisson’s ratio and there is significant soil-structure interaction.