Development of damage probability matrices based on Greek earthquake damage data

A comprehensive study is presented for empirical seismic vulnerability assessment of typical structural types, representative of the building stock of Southern Europe, based on a large set of damage statistics. The observational database was obtained from post-earthquake surveys carried out in the area struck by the September 7, 1999 Athens earthquake. After analysis of the collected observational data, a unified damage database has been created which comprises 180,945 damaged buildings from/after the near-field area of the earthquake. The damaged buildings are classified in specific structural types, according to the materials, seismic codes and construction techniques in Southern Europe. The seismic demand is described in terms of both the regional macroseismic intensity and the ratio αg/ao, where αg is the maximum peak ground acceleration (PGA) of the earthquake event and ao is the unique value PGA that characterizes each municipality shown on the Greek hazard map. The relative and cumulative frequencies of the different damage states for each structural type and each intensity level are computed in terms of damage ratio. Damage probability matrices (DPMs) and vulnerability curves are obtained for specific structural types. A comparison analysis is fulfilled between the produced and the existing vulnerability models.     

On the propagation of an in-plane shear fault with super-S-wave velocity

The speedv, especially the problem whether super S-wave velocity in the classical model (linear elasticity fracture mechanics) exists, of spontaneous propagation of a shear fault is investigated theoretically. An in-plane shear crack propagating in the crack plane is taken as the model of the shear fault. The results obtained firstly by Kostrov (1975) is extended from sub-Rayleigh wave velocity to super S-wave velocity, and the analytical expression for the stress intensity factorK ₂ in the case ofα>v>β is derived. It is proved that for Poisson mediumK ₂ is positive and real in the velocity range (β, 1.70β). This demonstrates that (β, 1.70β) is the velocity range which fulfils the conditions for spontaneous crack propagation. The existence, convergence and positiveness or negativeness ofK ₂ forv in individual sections are examined, and it is found that for an in-plane shear crack: 1. There are three sections forv, i.e., [0.v _R], (β, 1.70β), andα, respectively, and 2. There are two physically reasonable sections forv, the first is [v _R, β], and the second is [1.70β, α]. These two forbidden sections behave as barriers to fault propagation. The analytical expressions derived in this paper are not only suitable to classical model, but also to the other derivative models (e. g., the slip-weakening model and the renomalization model etc.). The model considered in this paper is more realistic than the static model employed by previous authors. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica, 15, 9–14, 1993.     

The 1986 Dharamsala earthquake of Himachal Himalaya – estimates of source parameters,average intrinsic attenuation and site amplification functions

The 26th April 1986 Dharamsala earthquake (m_b 5.5) occurred in the Kangra region of Himachal Himalaya, which lies in the rupture zone of great Kangra earthquake of 1905. This was the first moderate sized earthquake to be recorded at a few sites of the strong ground motion array in the NW Himalaya. The accelerograms of this earthquake have been used to estimate its source parameters, site amplification functions and to estimate the effective shear wave attenuation factor Q_β in the frontal region of Himachal Himalaya. A double couple fault plane solution for the earthquake has been obtained based on the spectra of the transverse component of the accelerograms. The estimated values of the source parameters are seismic moment: 2.1×10²⁴ dyne-cm, static stress drop (Δσ): 36 bars, source radius (r): 2.8 km and moment magnitude (M_w): 5.4. The estimated average values of effective shear wave attenuation factor Q_β for various sites are in the range of 125 to 300 with an overall spatial average of 239. The influence of local site effects on the observed PGA values have been examined on the basis of site amplification functions.     

Source parameters of the earthquakes of the Baikal rift system

The dynamic parameters of the earthquake source—the seismic moment, the moment magnitude, the source radius, the stress drop, and the amplitude of displacement—are determined by the amplitude Fourier spectra of the body shear waves (S-waves) for 62 earthquakes of the Baikal rift system with the energy class of K _P = 9.1–15.7. In the calculations I used the classical Brune model. The seismic moment of the earthquakes being investigated changes from 3.65 × 10¹¹ N m to 1.35 × 10¹⁸ N m, and the radii of earthquake sources vary from 390 m to 1.84 km. The values of the drop in stress Δσ grow with an increase in the seismic moment up to 1.7 × 10⁸ Pa. For the group of weak earthquakes (M _w = 1.7–3.3), extremely low values of the drop in stress 10³–10⁴ Pa are observed. The maximum amplitude of displacement in the source amounts to 5.95 m. The empirical equations between the seismic moment and the other dynamic parameters of the source are determined. The regional dependence of the seismic moment and energy class is obtained: log M ₀ ± 0.60 = 1.03K _P + 3.17. The character of the relationship between the seismic moment and the corner frequency indicates that the classical scaling law of the seismic spectrum for the earthquakes in question is not fulfilled. The obtained estimates of the dynamic parameters are in satisfactory agreement with the published data concerning the analogous parameters of the other rift zones, which reflects the general regular patterns of the destruction of the lithosphere and the seismicity in the extension zones of the lithosphere.     

Application of grey correlation method to evaluate potential groundwater recharge sites

Artificial recharge is a practical tool available for increasing the groundwater storage capacity. The efficiency of artificial recharge is related to various hydrogeological factors of the target area. In this study, a variable saturated groundwater flow model, FEMWATER, was used to evaluate the arrival times of recharged water that infiltrates from an artificial recharge pond to the groundwater table under various hydrogeological conditions. Forty-five arrival times were generated by FEMWATER. The relationships between the arrival times and hydrogeological factors used in the simulation of FEMWATER were analyzed by the grey correlation method. The results show the order of importance of the factors as they influence the arrival time. In order from high to low importance, they are α, D _g, θ _e, D _p, K _S and β. D _g and D _p are interpreted as the potential for movement of the recharge water; θ_e is the water storage capacity of soil, and K _S represents the ability of soil to transport water. α and β describe the characteristic curve of the unsaturated soil. The method was applied to evaluate a suitable site for artificial recharge in the Yun-Lin area. Grey correlation analysis was performed to obtain the grey correlation grade using the minimum arrival time as a reference sequence. An index is proposed herein to determine the recharge efficiency of 20 sampling sites. A contour mapping of index values at the 20 sampling sites identified three areas for artificial aquifer recharge in Yun-Lin. Area A in the upper plain is considered more appropriate for groundwater recharge than areas B and C in the coast.     

Alignment silkworms as seismic animal anomalous behavior (SAAB) and electromagnetic model of a fault: a theory and laboratory experiment

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Nonlinear earthquake response analysis and energy calculation for seismic slit shear wall structures

Based on the concept of structural passive control, a new type of slit shear wall, with improved seismic performance when compared to an ordinary solid shear wall, was proposed by the authors in 1996. The idea has been verified by a series of pseudo-static and dynamic tests. In this paper a macro numerical model is developed for the wall element and the energy dissipation device. Then, nonlinear time history analysis is carried out for a 10-story slit shear wall model tested on a shaking table. Furthermore, the seismic input energy and the individual energy dissipated by the components are calculated by a method based on Newmark-β assumptions for this shear wall model, and the advantages of this shear wall are further demonstrated by the calculation results from the viewpoint of energy. Finally, according to the seismic damage criterion on the basis of plastic accumulative energy and maximum response, the optimal analysis is carried out to select design parameters for the energy dissipation device.     

长周期地震动输入下大型建筑剪力墙振动台试验

为优化处于长周期地震动输入下的大型建筑剪力墙结构,进行了振动台试验。分析普通地震动与长周期地震动波的区别,证明了长周期地震波具有显著长周期分量的特性。将某一高层酒店剪力墙作为研究案例,设计模拟实验台的构建流程与传感器布局,将建筑模型缩尺比例设置为1∶10。选择CA波、RG波、EL波作为实验用地震波,从位移与结构周期、层间剪力与位移比、易损性以及损失评估等方面对大型建筑剪力墙的抗震性能进行了评估。振动台试验结果表明,在位移相同的情况下,长周期地震波下的建筑极限承载力最小;在经历CA波、RG波、EL波后,模型的自振周期均发生变化,而EL波作用下模型的自振周期始终比基本周期略长;不同地震波下,X、Y向层间剪力变化基本趋于一致;CA波、EL波作用下,X向位移比较为接近,而剪力墙Y向上位移比在三种地震波作用下具有较大差异性;在长周期地震波作用下,大型建筑剪力墙损伤最为严重。     

Dependence of the energy released during earthquake on ambient shear stress

Starting with dislocation model, using the result of the fracture mechanics: the slip displacement at the crack tip is proportional to the length of the crack and the applied ambient shear stressτ ₀ ² , we consider the dislocation in the earthquake to be the slip displacement at the crack tip and have obtained the analysis expresses of displacement and velocity pulse for the circular crack and have calculated the seismic wave energy radiated by earthquake. The seismic wave energyE ∞M ₀ τ ₀ ² f(v) _r , i. e.E is proportional to the seismic momentM ₀ and the square of the ambient shear stressτ ₀ ² and increases with the rupture velocityv _r . In frequency domain, integrating the square of source velocity spectrum derived from our the scaling law model, we have also obtained the seismic wave energyE released by earthquake and earthquake radiated effficiencyη.E ∞M ₀ τ ₀ ² also. If takingτ ₀ = 10.0 MPa, E=4.79M ₀. This result is consistent with the estimate by Vassiliou and Kanamori (1982). Theη=5.26%. The distribution of the seismic wave energy is that most of the energy contains in the frequency range between the first corner frequencyf _c1 and thirdf _c3, amount to 92.3% the energy in the rangef<f _c1 is about 3.85% and 3.85% whenf>f _c3. Thef _c3 is about 8Hz forM ⩾ 6, thus most of radiated energy is below 2Hz. This phenomenon had been verified by Vassiliou Kanamori. Previous results show the energy radiated by earthquake to be strongly dependent on ambient shear stress. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 146–152, 1993. This work was supported by the Deutsche Forschungsgemeinschaft, Bonn, F. R. Germany. The support is grateful acknowledged. The authors are also grateful to Professor Klussmann and Mr. Hasthoff for their lots of help.     

Performance-based methodology for assessing seismic vulnerability and capacity of buildings

This paper presents a performance-based methodology for the assessment of seismic vulnerability and capacity of buildings. The vulnerability assessment methodology is based on the HAZUS methodology and the improved capacity- demand-diagram method. The spectral displacement (Sd) of performance points on a capacity curve is used to estimate the damage level of a building. The relationship between Sd and peak ground acceleration (PGA) is established, and then a new vulnerability function is expressed in terms of PGA. Furthermore, the expected value of the seismic capacity index (SCev) is provided to estimate the seismic capacity of buildings based on the probability distribution of damage levels and the corresponding seismic capacity index. The results indicate that the proposed vulnerability methodology is able to assess seismic damage of a large number of building stock directly and quickly following an earthquake. The SCev provides an effective index to measure the seismic capacity of buildings and illustrate the relationship between the seismic capacity of buildings and seismic action. The estimated result is compared with damage surveys of the cities of Dujiangyan and Jiangyou in the M8.0 Wenchuan earthquake, revealing that the methodology is acceptable for seismic risk assessment and decision making. The primary reasons for discrepancies between the estimated results and the damage surveys are discussed.     

Assessment indices for the seismic vulnerability of existing R.C. buildings

The seismic vulnerability of old multi‐storey reinforced concrete (R.C.) buildings reinforced with substandard details is assessed as a function of interstorey drift demand imposed by the design earthquake while considering brittle termination of elastic response of the critical members of the structure due to a premature shear failure. Interstorey drift demand is related to column and wall translational stiffnesses which are expressed through analytical derivations in terms of the floor area ratios of gravity and lateral load bearing members in the critical floor. Interstorey drift capacity is related to the available transverse reinforcement and the axial load ratio of the vertical members. The significance of the area ratio of vertical members in the typical floor as an index of vulnerability is explored with reference to the limitations in the value of axial load ratio used in R.C. design in order to secure ductile flexural behavior, and also with reference to the stability index of gravity load bearing members. Interstorey Drift Spectra are derived for the existing R.C. buildings suitable for rapid seismic vulnerability screening but also as a guide for rehabilitation of the existing structures. Lightly reinforced or substandard reinforced concrete buildings that reportedly collapsed during previous earthquakes are used as example case studies in order to calibrate the proposed methodology. Copyright © 2010 John Wiley & Sons, Ltd.     

IM‐based and EDP‐based decision models for the verification of the seismic collapse safety of buildings

Decision models for the verification of seismic collapse safety of buildings are introduced. The derivations are based on the concept of the acceptable (target) annual probability of collapse, whereas the decision making involves comparisons between seismic demand and capacity, which is familiar to engineering practitioners. Seismic demand, which corresponds to the design seismic action associated with a selected return period, can be expressed either in terms of an intensity measure (IM) or an engineering demand parameter (EDP). Seismic capacity, on the other hand, is defined by dividing the near‐collapse limit‐state IM or EDP by an appropriate risk‐targeted safety factor (γ _im or γ _edp ), which is the only safety factor used in the proposed decision model. Consequently, the seismic performance assessment of a building should be based on the best possible estimate. For a case study, it is shown that if the target collapse risk is set to 10^?4 (0.5% over a period of 50 years), and if the seismic demand corresponds to a return period of 475 years (10% over a period of 50 years), then it can be demonstrated that γ _im is approximately equal to 2.5 for very stiff buildings, whereas for buildings with long periods the value of γ _im can increase up to a value of approximately 5. The model using γ _edp is equal to that using γ _im only if it can be assumed that displacements, with consideration of nonlinear behavior, are equal to displacements from linear elastic analysis.     

Estimation of the quality factor in shallow soil using surface waves

IntroductionVelocityanditsattenuationinformationiscloselylinkedwiththeoreticalstudiesonthegroundmovementsduringearthquake.Therecentstudy(Malagnini,1996)showedthatthevelocitystructureofshearwaveinshallowsoilabove30mplaysanimpoftantroletoestimatestfonggroundmotionofsite.However,itishardtopreciselymeasurethesoilstructuresanddynamiccharacteristics.First,theloosesoilabsorbstheseismicwaveswithhighfrequencies;Second,theeffectsoffocusinganddispersioncausedbylocallyinhomogeneoussitecannotbeneglectedin…     

夯土墙在单调和反复水平荷载下的试验研究

通过对不同类型的夯土墙在单调荷载和反复荷载作用下的试验研究,分析了不同添加材料对夯土墙抗剪性能、抗震性能的影响,得到了夯土墙的裂缝开展规律、破坏特征、承载能力、延性及滞回性能。借用砌体结构的抗震承载力计算公式,给出了夯土墙抗剪、抗震计算的简化公式。     

Lateral variations of coda Q and attenuation of seismic waves in Southwest Anatolia

The seismic quality factor (Q _c) and the attenuation coefficient (δ) in the earth’s crust in southwest (SW) Anatolia are estimated by using the coda wave method based on the decrease of coda wave amplitude by time on the seismogram. The quality factor Q _o, the value of Q _c at 1 Hz, and its frequency dependency η are determined from this method depending on the attenuation properties of scattered coda waves. δ is determined from the observations of amplitude variations of seismic waves. In applying the coda wave method, firstly, a type curve representing the average pattern of the individual coda decay curves for 0.75, 1.5, 3.0, 6.0, 12.0, and 24.0 Hz values was estimated. Secondly, lateral variation of coda Q and the attenuation coefficients for three main tectonic patterns are estimated. The shape of the type curve is controlled by the scattering and attenuation in the crustal volume sampled by the coda waves. The Q _o and η values vary from 30 to 180 and from 0.55 to 1.25, respectively for SW Anatolia. In SW Anatolia, coda Q–f relation is described by and δ = 0.008 km⁻¹. These results are expected to help in understanding the degree of tectonic complexity of the crust in SW Anatolia.     

The approximate method for reconstructing the potential fields

Numerical algorithms are suggested for reconstructing the potential field in the region Ω = {0 ≤ R ₀ ≤ ρ ≤ R, 0 ≤ θ ≤ π, 0 ≤ φ ≤ 2π} from its values on the surface Γ₁ = {R,0 ≤ α₁ ≤ θ ≤ α₂ ≤ π, 0 ≤ β₁ ≤ φ ≤ β₂ ≤ π}.     

带暗支撑双肢短肢剪力墙抗震性能试验研究

钢筋混凝土短肢剪力墙结构是一种新型的中高层住宅结构体系,已有较多的工程应用,但是短肢剪力墙的抗震性能较差,如何提高短肢剪力墙的抗震性能是目前工程界十分关注的问题。本文提出了带暗支撑短肢剪力墙,并以典型的双肢短肢剪力墙为例,选择了4个1/3缩尺的双肢短肢剪力墙试验模型,2个为普通双肢短肢剪力墙模型,2个为带暗支撑双肢剪力墙模型,进行了对比性的抗震性能试验研究,较系统地分析了带暗支撑双肢短肢剪力墙的承载力、刚度、延性、耗能能力及破坏特征,建立了承载力计算模型,计算结果与实测结果符合较好。试验表明,带暗支撑双肢短肢剪力墙的抗震能力比普通双肢短肢剪力墙显著提高。     

Cooling rates in the shock veins of chondrites: constraints on the (Mg, Fe)2SiO4 polymorph transformations

The occurrence of γ-phase, a high-pressure polymorph of olivine (α-phase), in the shock veins of Sixiangkou chondrite was due to a greater cooling rate (> 10 000°C·s^-1) in the veins. Because γ-phase partially reverted to β-phase and no back-transformation from β-phase to α-phase took place, the shock veins of Peace River chondrite with a cooling rate of 1 000–2 000δC·s^-1 contain a great amount of β-phase. In the shock veins of Mbale chondrite with a cooling rate of <500°C·s^-1, the majority of γ-phase reverted to α-phase. The heat dissipation in shock veins took place after a stage of shock compression of chondrite parent body, and the parent body was broken into fragmental pieces. Cooling rate in the shock veins constrained the back-transformations of (Mg, Fe)₂SiO₄ high-pressure polymorphs. Project of Chen and Xie supported by the National Natural Science Foundation of China (Grant No. 496720981, Natural Science Foundation of Guangdong Province (Grant No. 960500), and the Science Foundation of Academia Sinica for the returned scholars.     

高轴压比下钢管混凝土边框组合剪力墙抗震性能试验研究

钢管混凝土边框组合剪力墙是一种适用于高层及超高层建筑的新型组合剪力墙。轴压比是影响剪力墙抗震性能的一个主要因素,高层建筑底部轴压比较大。本文进行了1/4缩尺的1个普通钢筋混凝土剪力墙模型和1个钢管混凝土边框组合剪力墙模型在高轴压比下的低周反复荷载试验。在试验研究基础上,对比分析了剪力墙的承载力、延性、刚度及其衰减过程、滞回特性、耗能能力及破坏特征,建立了钢管混凝土边框组合剪力墙的承载力计算模型,计算结果与实测结果符合较好。研究表明:在高轴压比下钢管混凝土边框组合剪力墙与普通剪力墙相比抗震性能显著提高。