Base uplifting analysis of flexibly supported liquid-storage tanks

An approximate method is presented for the analysis of earthquake induced uplifting in base plates of unanchored liquid-storage tanks that are supported directly on flexible soil foundations. The method takes due account of the non-linearities arising from the continuous variation of base contact area, membrane action and plastic yielding in the base plate. First, an ‘exact’ solution is presented for a uniformly loaded flexibly supported prismatic beam, uplifted by a concentrated force applied at one end. A series of such beams are later used in an approximate model of the base plate. The method is highly efficient and believed to be accurate for the level of uplifts encountered in practice. The results are presented for a range of foundation stiffness, representing loose sandy soils to rigid concrete mat. It is shown that, for the same overturning base moment, the flexibly supported tanks, in comparison with the rigidly supported tanks, experience significantly smaller axial compressive stress, but larger base uplift, foundation penetration, plastic rotation at plate boundary and hoop compressive stress in the tank wall.     

立式储液罐地震反应数值分析

本文采用大型有限元程序ANSYS对立式储液罐的地震反应进行了研究,考虑了不同罐体和内部液体的相互作用,采用3个不同容积的储罐,输入不同强度的地震动时程,进行了大量的数值计算,给出了一些结论。     

立式储液罐地震破坏快速评估方法

本文采用大型有限元程序ANSYS对立式储液罐的地震反应进行了非线性数值分析,考虑了罐体和内部液体的相互作用,得到了3个不同容积的储罐,在不同峰值的地震动时程输入下的反应结果。结合地震灾害中立式储罐的地震破坏现象和特点,以及现有的立式储罐地震破坏预测方法,提出了立式储罐的地震破坏快速评估方法。     

Probabilistic evaluation of liquefaction potential under earthquake loading

This paper presents a procedure to perform the risk analysis for ground failure by liquefaction. The first part of this study describes the differential equation of a smooth hysteretic model to characterize the behavior of the soil under random loading. The parameters of the proposed model to represent the experimental relationship are discussed. The second part of this study is to develop a method to calculate the probability that a specified volume of soil will liquefy at a given depth in the deposit. The liquefaction is defined as the result of cumulative damage caused by seismic loading. The fatigue life of soil can be determined on the basis of the N---S relationship and Miner's cumulative damage law. The rain-flow method is used to count the number of cycles of stress response of the soil deposit. Finally, the probability of liquefaction is obtained by integration over all the possible ground motion and the fragility curves of liquefaction potential. The sensitivity of the reliability against liquefaction to soil system parameters is also examined.     

Mechanisms of failure for shallow foundations under earthquake loading

It is widely known that the bearing capacity of a shallow foundation is reduced when the foundation is subjected to rocking moments and horizontal loads during an earthquake event. Analytical solutions generally require an assumption to be made of the kinematic failure mechanism in the soil, when the true failure mechanism is unknown. This paper discusses a series of experiments carried out on a new 1g shaking table at Cambridge University in order to measure the displacements of a shallow foundation due to seismic loading and also the development of the failure mechanism within the soil. The failure mechanism was studied using the technique of Particle Image Velocimetry (PIV), combined with high-speed videography and photogrammetry. In this paper, the failure mechanisms observed in these experiments will be compared with the theoretical results found from upper- and lower-bound solutions and the effects of such parameters as earthquake magnitude, frequency and embedment ratio (and hence surcharge) will be discussed.     

Centrifuge modeling of offshore wind foundations under earthquake loading

The construction of large offshore wind turbines in seismic active regions has great demand on the design of foundations. The occurrence of soil liquefaction under seismic motion will affect the stability of the foundations and consequently the operation of the turbines. In this study, a group of earthquake centrifuge tests was performed on wind turbine models with gravity and monopile foundations, respectively, to exam their seismic response. It was found that the seismic behavior of models was quite different in the dry or saturated conditions. Each type of foundation exhibited distinct response to the earthquake loading, especially in the offshore environment. In the supplementary tests, several remediation methods were evaluated in order to mitigate the relatively large lateral displacement of pile foundation (by fixed-end pile and multi-pile foundation) and excessive settlement of gravity foundation (by densification, stone column, and cementation techniques).     

Coupled lateral-torsional behaviour of frame structures under earthquake loading

A series of parametrically defined experimental model structures has been tested under earthquake base loading using the SERC national U.K. earthquake simulator. The models have been designed with variable ratios of torsional to lateral stiffness, and with both symmetric and asymmetric mass distributions. This paper first describes the tests carried out to determine the basic dynamic model properties and the establishment of idealized analytical models which give accurate predictions of model behaviour under steady-state loading and free-vibration conditions. Secondly, a detailed discussion is made of the two highly coupled structural models having uncoupled torsional to lateral frequency ratio R_f = 1.2, commenting on the ability of the modal analysis procedures to predict accurately the maximum recorded responses. It is concluded that the theory underestimates the significance of the fundamental torsional mode of vibration in the combined structural response, and overestimates the contribution of the first lateral mode. These effects compensate each other on the side of the structure which is most severely affected by torsional response, but produce large inaccuracies on the side of the building which is commonly assumed to be affected beneficially by torsional coupling.     

Experimental behaviour of reinforced concrete walls under earthquake loading

The experimental work and first results of a recently completed experimental research programme investigating the response of reinforced concrete (RC) walls under earthquake (EQ) loading are discussed in this paper. A brief literature review is given as a prelude to the outline of research objectives. The tests are presented in two groups according to the scale of models. For the 1:5 scale tests, a modified similitude relation for small scale reinforced concrete dynamic modelling is developed. Based on the chosen model parameters, the design of the isolated RC walls is given. The test-rig set-up and the EQ input signals suitable for testing the model on the Imperial College shake-table are also discussed. Preliminary observations regarding stiffness, strength and failure modes of the RC wall models are given. Experimental results from the shake-table are compared to tests, at the same scale, under static cyclic conditions. For the scale 1:2–5 cyclic tests a different test-rig assembly is designed. The test results are given in three pairs of flexurally similar walls followed with general observations and discussion. Finally, conclusions are drawn regarding experimental procedures and behaviour patterns of the tested models.     

Ductility demands on buckling-restrained braced frames under earthquake loading

Accurate estimates of ductility demands on buckling-restrained braced frames (BRBFs) are crucial to performance-based design of BRBFs. An analytical study on the seismic behavior of BRBFs has been conducted at the ATLSS Center, Lehigh University to prepare for an upcoming experimental program. The analysis program DRAIN-2DX was used to model a one-bay, four-story prototype BRBF including material and geometric nonlinearities. The bucklingrestrained brace (BRB) model incorporates both isotropic and kinematic hardening. Nonlinear static pushover and timehistory analyses were performed on the prototype BRBF. Performance objectives for the BRBs were defined and uscd to evaluate thc time-history analysis results. Particular emphasis was placed on global ductility demands and ductility demands oa the BRBs. These demands were compared with anticipated ductility capacities. The analysis results, along with results from similar previous studics, are used to evaluate the BRBF design provisions that have been recommended for codification in the United States. Thc results show that BRB maximum ductility demands can be as high as 20 to 25. These demands significantly exceed those anticipated by the BRBF recommended provisions. Results from the static pushover and timehistory analyses are used to demonstrate why the ductility demands exceed those anticipated by the recommended provisions.The BRB qualification testing protocol contained in the BRBF recommended provisions is shown to be inadequate because it requires only a maximum ductility demand of at most 7.5. Modifications to the testing protocol are recommended.     

地震作用下结构时变物理参数识别

利用小波分析函数多尺度逼近方法,将剪切型结构在地震作用下时变的阻尼和刚度用尺度函数的线性组合表示,将时变参数的辨识问题转化为由已知的正交尺度函数和系统的输入输出来估计线性组合中的时不变系数问题,用最小二乘法对剪切型框架结构在地震作用下时变的刚度和阻尼进行了有效的辨识。此方法无需事先假定系统参数的时变规律,在有噪声情况下可以用Tikhonov正则化方法减小识别方程的不适定性对识别结果的影响。数值算例表明了该方法的有效性。     

Seismic design of flexible cylindrical liquid storage tanks

Seismic response of cylindrical storage tanks anchored to rigid base slabs is considered. Finite elements are used for the liquid and tank wall, idealized as a thin shell. For steel tanks of practical dimensions, design charts are presented for natural frequencies, maximum shear and overturning moment on the foundation, and maximum stress resultants in the tank wall. Furthermore, an analytical expression for the superelevation of the free surface is presented.     

Newmark sliding block model for pile-reinforced slopes under earthquake loading

Recent studies have demonstrated that the use of a discretely-spaced row of piles can be effective in reducing the deformations of slopes in earthquakes. In this paper, an approximate strain-dependant Newmark sliding-block procedure for pile-reinforced slopes has been developed, for use in analysis and design of the piling scheme, and the model is validated against centrifuge test data. The interaction of the pile within the slipping soil was idealised using a non-linear elasto-plastic (P–y) model, while the interaction within the underlying stable soil was modelled using an elastic response model in which (degraded) soil stiffness is selected for an appropriate amount of shear strain. This combined soil–pile interaction model was incorporated into the improved Newmark methodology for unreinforced slopes presented by Al-defae et al. [1], so that the final method additionally incorporates strain-dependent geometric hardening (slope re-grading). When combined with the strain-dependent pile resistance, the method is therefore applicable to analysis of both the mainshock and subsequent aftershocks acting on the deformed slope. It was observed that the single pile resistance is mobilised rapidly at the start of a strong earthquake and that this and the permanent slope deformation are therefore strongly influenced by pile stiffness properties, pile spacing and the depth of the slip surface. The model shows good agreement with the centrifuge test data in terms of the prediction of permanent deformation at the crest of the slope (important in design for selecting an appropriate pile layout/spacing i.e. S/B) and in terms of the maximum permanent bending moments induced in the piles (important for appropriate structural detailing of the piles), so long as the slip surface depth can be accurately predicted. A method for doing this, based on limit analysis, is also presented and validated.     

Numerical analysis of deformation behaviour of quay walls under earthquake loading

In the last 50 years, there have been many incidences of failure of gravity quay walls. These failures are often associated with significant deformation of liquefiable soil deposits. Gravity quay wall failures have stimulated great progress in the development of deformation-based design methods for geotechnical structures. In this paper, the effective-stress analysis method has been used in conjunction with a generalised elasto-plasticity constitutive model implemented into a finite element procedure. Various monotonic and cyclic triaxial paths are simulated in order to demonstrate the capabilities of the constitutive model. The FEM is validated by back analysis of a typical Port Island PC1 caisson type quay wall, which was damaged during the 1995 Hyogoken-Nanbu earthquake. The numerical results are compared with the observed data obtained consisting of seaward displacement, settlement and tilting. In addition, both the influence of permeability, on the generation of pore water pressure and the influence of the relative density of the backfill and foundation layers, on the residual deformation of gravity quay walls are investigated.     

Numerical analysis of the interaction of soil-structure under earthquake loading

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Vibration control of structures under earthquake loading by three-stage friction-grip elements

The behaviour of a building subjected to a strong-motion earthquake depends highly on its energy dissipation capacity. By introducing three-stage friction-grip elements, the energy dissipation within each storey can be ‘designed’ according to definable stages (e.g. serviceability, medium- and strong-motion earthquake). Tests on simple steel-concrete- and steel-steel-friction-grip connections have proved their very satisfactory behaviour under high dynamic loading, showing no considerable damage when well designed. Examples of horizontal stiffening elements are given to illustrate the construction of three-stage elements with either steel-steel- or steel-concrete-friction-grip joints. By computing the response of a seven storey building designed as a steel frame (‘ductile system’ philosophy), concrete core (‘stiff system’-philosophy) and three-stage truss and being subjected to the 1940 El Centre earthquake, the superior performance of three-stage elements and its economic advantage over the other two systems becomes apparent. Although this is just one illustrative example, it is nevertheless an important one, because it resembles the type of building that would respond best to the application of three-stage building brakes. Finally, the result of an online test on a three-stage element is given. This realistic earthquake simulation proved the behaviour to be adequately close to the basic philosophy and yielded important design implications for three-stage elements.     

Minaret behavior under earthquake loading: The case of historical Istanbul

Minarets are very slender structures with an old existence. The historical ones are made of cut‐stone‐block masonry assembled in peripheral cylindrical wall with an interior helicoidal stair supported on a central core and on the wall. They are spread throughout the Islamic world and constitute an important heritage not only of religious value, but also of great cultural interest. Throughout the times, these structures as part of a mosque, have suffered significant damage during the earthquakes. Istanbul presents interesting characteristics to evaluate their dynamic behavior, as they are in great number, in an area where a large event in the next 30 years has been predicted. In this paper, we performed a series of in situ ambient vibration tests to old minarets of various sizes and compared results of frequencies with numerical modeling of the same structures. For the low‐amplitude motion, the frequency values of the first modes can be obtained from an empirical formulae function of the inertia of the cross‐section and of the height of the main ‘body.’ Damping ratios for these amplitudes are of the order of 0.5–1.0%. Dynamic linear analyses of these structures indicate that for most cases very high stresses develop for PGA above 0.5 g, an input with a reasonable chance of occurring in the next 30 years. These high stresses are expected to cause the toppling of the minarets in the form that has been observed in the recent past events. Copyright © 2011 John Wiley & Sons, Ltd.     

双向地震激励下储罐隔震计算模型对比分析

铅芯橡胶垫基础隔震浮顶储罐在双向地震激励下,采用不同的隔震层恢复力计算模型计算所得的地震响应存在差异.不同工况下,若不加区别地选取将给储罐设计带来不利影响.通过分析高径比、阻尼比、隔震周期以及屈服强度参数对计算结果的影响得出,特定高径比时等效线性模型计算所得波高偏小,基底剪力和位移偏大,因此设计时应综合权衡各模型的计算...     

Inelastic spectra to predict period elongation of structures under earthquake loading

Period lengthening, exhibited by structures when subjected to strong ground motions, constitutes an implicit proxy of structural inelasticity and associated damage. However, the reliable prediction of the inelastic period is tedious and a multi‐parametric task, which is related to both epistemic and aleatory uncertainty. Along these lines, the objective of this paper is to investigate and quantify the elongated fundamental period of reinforced concrete structures using inelastic response spectra defined on the basis of the period shift ratio (T_in/T_el). Nonlinear oscillators of varying yield strength (expressed by the force reduction factor, R_y), post‐yield stiffness (a_y) and hysteretic laws are examined for a large number of strong motions. Constant‐strength, inelastic spectra in terms of T_in/T_el are calculated to assess the extent of period elongation for various levels of structural inelasticity. Moreover, the influence that structural characteristics (R_y, a_y and degrading level) and strong‐motion parameters (epicentral distance, frequency content and duration) exert on period lengthening are studied. Determined by regression analyses of the data obtained, simplified equations are proposed for period lengthening as a function of R_y and T_el. These equations may be used in the framework of the earthquake record selection and scaling. Copyright © 2015 John Wiley & Sons, Ltd.     

Dynamic fluid effects in liquid-filled flexible cylindrical tanks

The velocity potential of a compressible fluid is found by Galerkin's method. Free surface displacements and a flexible tank wall are assumed. Explicit expressions for the impulsive mass, the impulsive moment and the overturning moment are derived for wave number m = 1. In the case of m ≥ 1 the dynamic effect of the fluid is represented by a fictitious apparent mass in explicit form.     

Dynamic response of cylindrical structures considering coupled soil-structure interaction under seismic loading

This paper attempts to develop a mathematical model for estimating the seismic response of a cylindrical shaped nuclear reactor building resting in an elastic halfspace considering foundation compliance. Most of the research carried out on this topic has either been carried out by resorting to finite element method (FEM) which makes the computational cost expensive or based on the simplifying assumption of assuming the cylindrical structure as a multi degree lumped mass stick model with soil coupled as boundary springs. In the present paper an analytical model has been developed in which the deformation of the cylindrical body (including its shear deformation characteristics) has been taken into cognizance and then coupling with foundation stiffness a comprehensive solution has been sought based on Galerkin’s weighted residual technique. The results are finally compared with FEM to check the reliability of the same. The results are found to be in good agreement with the detailed finite element analysis.