Pipeline response to random ground motion by discrete model

The response of buried pipelines to random excitation by earthquake forces is obtained using a lumped mass model. The earthquake is considered as a stationary random process characterized by a power spectral density function (PSDF). The cross spectral density function between two random inputs along the length of the pipe is defined with the help of the local earthquake PSDF which is the same for all points, and a frequency dependent exponentially decaying (with distance) function. Soil resistance to dynamic excitation along the pipelength is obtained in an approximate manner with the help of frequency independent impedance functions derived from half-space analysis and Mindlin's static stresses within the soil due to point loads. The proposed method has the advantage that it can take into consideration the cross terms in soil stiffness and damping matrices and can consider any boundary condition that needs to be satisfied at the ends of the pipe. A parametric study is also made to show the influence of cross terms in the soil stiffness and damping matrices on the response of the pipe.     

System identification estimation of soil properties at the Lotung site

Dynamic properties of the soils at the Lotung test site, Lotung, Taiwan, are estimated from seismic vertical array measurements (input–output data sets) using both time-invariant and time-variant parametric modeling methods (system identification). Soil properties are directly mapped from model parameters to an equivalent lumped mass model of the soil interval. Shear stiffness and damping ratios were calculated for 8 events with M_L ranging from 4.5 to 7.0. Shear stiffness ranged between 0.5 and 6 MN/m, inversely proportional to PGA. The equivalent viscous damping ratio varied from 2 to 30% of critical damping, proportional to PGA. Degradation of soil behavior, while less pronounced with increasing depth, consistently occurs above a peak input acceleration of 0.07 g. Although “non-linear” behavior is evident above 0.17 g, Event 7 (0.21 g) is accurately predicted using a linear constant parameter model estimated from the smaller Event 8 aftershock ground motions.     

Consistent lumped-parameter models for unbounded soil: Frequency-independent stiffness,damping and mass matrices

A systematic procedure to develop consistent (symmetric) stiffness, damping and mass matrices with real coefficients to represent any unbounded soil is developed. These property matrices are based on the lumped-parameter models of Reference 1. Either stiffness and damping matrices corresponding to first-order differential equations involving the internal degrees of freedom and those on the structure-soil interface result or, alternatively, in addition mass matrices are introduced, corresponding to second-order differential equations, which reduce the number of internal degrees of freedom by a factor 2. The stiffness, damping and mass matrices can easily be incorporated in a general-purpose structural dynamics program working in the time domain, whereby the structure can even be non-linear.     

Soil-pile interaction in horizontal vibration

Interaction between soil and an elastic pile vibrating horizontally is theoretically examined. The soil is modelled as a linear, viscoelastic layer overlying rigid bedrock. The pile is assumed to be vertical and point bearing. This study utilizes the definition of soil resistance presented in a preceding paper.¹ A direct solution is developed which yields closed form formulas for pile displacement, stiffness and damping. A parametric study clarifies the role of the parameters involved, illustrates the interaction between the soil and the pile and shows the stiffness and damping properties of the soil-pile system for typical values of the governing parameters.     

Validation of small strain properties from recorded weak seismic motions

During the last decade, there has been an increased interest in the computations of surface ground motions from known rock outcrop motions. The main advantage of the procedure is to allow for the actual variation of strength and stiffness properties of heterogeneous soil profiles, eventually accounting for non-linear soil behavior. The main questions raised against the adequacy of such a procedure lie upon the reliability of the computational scheme and in the representativity of the soil constitutive relationship. The present paper addresses both aspects by comparing the motions computed assuming standard assumptions in the state of practice of earthquake engineering. Since until now, the downhole array recorded only weak motions (horizontal peak ground accelerations smaller than 0·04 g), the paper focuses on elastic soil properties. It is demonstrated that a carefully conducted geotechnical survey yields an accurate shear wave velocity profile and that rate-independent soil damping might not be appropriate to represent the soil behavior in the small strain range.     

Finite element simulations of wave propagation in soils using a Viscoelastic model

Wave propagation in soil is dependent on both the stiffness and the material damping of the soil. While some researchers have performed finite element modelling of resonant column tests and wave propagation in soil, most do not describe the methodology in detail and there is little or no verification of the correctness of the model. Viscoelastic model has been used to model wave propagation in soil. However, the determination of the parameters in the viscoelastic model is complicated and the parameters may not be related to the soil properties. This paper presents a simplified viscoelastic model with soil parameters obtainable from advanced geotechnical testing to simulate wave propagation in soil medium taking into account of material damping. The viscoelastic material model was first calibrated by replicating torsional, longitudinal and flexural modes resonant column tests. The relationships between the parameters of the simplified viscoelastic model and their corresponding stiffness and damping properties were investigated. An equation was proposed to correlate the decay constant used in the simplified viscoelastic model and the material damping ratio obtained through the application of the logarithmic decrement method on the modelled resonant column test results. The simplified viscoelastic model was then evaluated by modelling wave propagation in a semi-infinite medium. Results indicated that the viscoelastic model with parameters as proposed in this paper is able to model wave propagation in soils.     

Horizontal dynamic response of a large-diameter pipe pile considering the second-order effect of axial force

The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated. Governing equations of the pile-soil system are established based on elastodynamics. Three-dimensional wave equations of soil are decoupled through differential transformation and variable separation. Consequently, expressions of soil displacements and horizontal resistances can be obtained. An analytical solution of the pile is derived based on continuity conditions between the pile and soil, subsequently from which expressions of the complex impedances are deduced. Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile. Some conclusions can be summarized as follows: stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.     

Large scale shaking table model test and analysis on seismic response of utility tunnel in non-homogeneous soil

Underground utility tunnels are the most fundamental and reliable lifeline network in urban cities,and are widely constructed throughout the world.In urban areas,most utility tunnels usually encounter the non-homogeneity of subsoil condition due to various construction effects.Studies have shown that the damage mechanism of shallow underground structures mainly depends on the inhomogeneity of the subsoil conditions.This would become a considerable factor for the stability of the underground utility tunnel structures.However,this type of research still needs to establish the vulnerable seismic design.In this study,a series of shaking table tests were conducted on non-homogenous soils to investigate the performance of seismic interaction between utility tunnels,surrounding soils and interior pipelines.The dynamic responses measured from the test account for the boundary condition of non-homogeneous soils,the internal forces,displacement of tunnel joints,the dynamic characteristics on interior pipelines and the reasonable spring stiffness with damping in the seismically isolated gas pipeline model inside the tunnel.The vulnerability of underground utility tunnel in non-homogeneous soil zone and the mechanism of the stability of interior facilities are the main topics discussed in this paper.     

Nonlinear surface ground analysis via statistical approach

A statistical approach is proposed for nonlinear surface ground analysis. In contrast to the conventional method which deals with only a single ground motion for equivalent linearization of soil properties, a design response spectrum defined at the upper level (bottom of the surface ground) of an engineering bedrock can be handled as the target design earthquake in the present paper. The effective shear strain in each soil layer is evaluated by means of a statistical procedure in which the mean peak shear strain is computed in terms of its standard deviation and the corresponding peak factor. The stiffness and damping ratio of each soil layer are obtained iteratively from the nonlinear relation of stiffness reduction factors and damping ratios with respect to the strain level. After the evaluation of the equivalent stiffness and damping ratio of every soil layer, the ground surface response spectrum is transformed from the design response spectrum defined at the upper level of the engineering bedrock via the one-dimensional wave propagation theory. The reliability and accuracy of the proposed analysis method is examined through the comparison with the results by the conventional method (represented by the program) for many simulated spectrum-compatible ground motions.     

Evaluating foundation mass,damping and stiffness by the least‐squares method

This paper discusses how to use the three‐dimensional (3D) time‐domain finite‐element method incorporating the least‐squares method to calculate the equivalent foundation mass, damping and stiffness matrices. Numerical simulations indicate that the accuracy of these equivalent matrices is acceptable when the applied harmonic force of 1+sine is used. Moreover, the accuracy of the least‐squares method using the 1+sine force is not sensitive to the first time step for inclusion of data. Since the finite‐element method can model problems flexibly, the equivalent mass, damping and stiffness matrices of very complicated soil profiles and foundations can be established without difficulty using this least‐squares method. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic response of base-isolated buildings including soil–structure interaction

This study investigates the effect of soil–structure interaction (SSI) on the response of base-isolated buildings. The equations of motion are formulated in the frequency domain, assuming frequency-independent soil stiffness and damping constants. An equivalent fixed-base system is developed that accounts for soil compliance and damping characteristics of the base-isolated building. Closed-form expressions are derived, followed by a thorough parametric study involving the pertinent system parameters. For preliminary design, the methodology can serve as a means to assess effective use of base isolation on building structures accounting for SSI. This study concludes that the effects of SSI are more pronounced on the modal properties of the system, especially for the case of squat and stiff base-isolated structures.     

平面P波入射下深埋圆形复合式衬砌隧道抗减震机理研究

基于Fourier-Bessel级数展开法,研究深埋圆形三层复合式衬砌洞室在平面P波入射下的动应力集中问题,并给出三层衬砌洞室动应力集中系数级数解析解;依托某IX度地震区管道隧道实际工程,分析不同衬砌刚度组合和厚度组合对洞室动应力集中系数的影响。研究表明:注浆加固洞室围岩和设置减震层都可以降低二次衬砌动应力集中系数;增大围岩注浆区弹性模量和厚度,有利于减小衬砌动应力集中系数,最优围岩注浆区厚度为1倍洞室净空半径;减震层弹性模量降低,减震层厚度增大,二次衬砌动应力集中系数变小,减震层弹性模量宜低于围岩弹模1/20,最优减震层厚度宜取1/50的洞室内净空半径。最后针对实际管道隧道抗减震技术,考虑围岩稳定性,提出"围岩-加固圈-减震层-衬砌"新型减震结构,分析结果表明:对比其他三种抗减震措施,新型减震结构的减震效果最好。     

Natural vibration frequency and damping of slender structures founded on monopiles

Offshore wind turbine (OWT) is a typical example of a slender engineering structure founded on large diameter rigid piles (monopiles). The natural vibration characteristics of these structures are of primary interest since the dominant loading conditions are dynamic. A rigorous analytical solution of the modified SSI eigenfrequency and damping is presented, which accounts for the cross coupling stiffness and damping terms of the soil–pile system and is applicable but not restrictive to OWTs. A parametric study was performed to illustrate the sensitivity of the eigenfrequency and damping on the foundation properties, the latter being expressed using the notion of dimensionless parameters (slenderness ratio and flexibility factor). The application of the approximate solution that disregards the off diagonal terms of the dynamic impedance matrix was found to overestimate the eigenfrequency and underestimate the damping. The modified SSI eigenfrequency and damping was mostly affected by the soil–pile properties, when the structural eigenfrequency was set between the first and second eigenfrequency of the soil layer. Caution is suggested when selecting one of the popular design approaches for OWTs, since the dynamic SSI effects may drive even a conservative design to restrictive frequency ranges, nonetheless along with advantageous – from a designers perspective – increased damping.     

Dynamics of seismic impacts in base-isolated buildings

A systematic study is made of the effects of seismic impacts between the base of an isolated building and the surrounding retaining wall. The analysis is performed without using gap elements or assuming values of the coefficient of restitution and the duration of impact. The analysis captures the effects of wave travel along the height of the building and of the associated energy loss. It poses no numerical difficulties. Results show that for elastic systems the base shear generated by impacts can be higher than the weight of the building; base shear increases with increase in the stiffness of the retaining wall, stiffness of the building and the mass of the base mat. A significant fraction of the initial kinetic energy of the system is lost by impacts; energy loss increases with increase in the stiffness of the retaining wall, system damping and mass of the base mat. © 1997 John Wiley & Sons, Ltd.     

Soil–pile–structure interaction under SH wave excitation

A continuum model for the interaction analysis of a fully coupled soil–pile–structure system under seismic excitation is presented in this paper. Only horizontal shaking induced by harmonic SH waves is considered so that the soil–pile–structure system is under anti‐plane deformation. The soil mass, pile and superstructure were all considered as elastic with hysteretic damping, while geometrically both pile and structures were simplified as a beam model. Buildings of various heights in Hong Kong designed to resist wind load were analysed using the present model. It was discovered that the acceleration of the piled‐structures at ground level can, in general, be larger than that of a free‐field shaking of the soil site, depending on the excitation frequency. For typical piled‐structures in Hong Kong, the amplification factor of shaking at the ground level does not show simple trends with the number of storeys of the superstructure, the thickness and the stiffness of soil, and the stiffness of the superstructure if number of storeys is fixed. The effect of pile stiffness on the amplification factor of shaking is, however, insignificant. Thus, simply increasing the pile size or the superstructure stiffness does not necessarily improve the seismic resistance of the soil–pile–structure system; on the contrary, it may lead to excessive amplification of shaking for the whole system. Copyright © 2003 John Wiley & Sons, Ltd.     

地基半空间等效集总体系的比拟法与实测分析

先略述莱斯默比拟法的形成;再由半空间理论等效为质弹体系,得出辐射阻尼比、刚度及参振土质量,并论述两体系的结合;最后经实测、分析和使用,考虑土体非匀质性折减阻尼比以作修正,使其更为实用。这有助于消除在我国长期认为阻尼比大而不安全、不便使用的疑虑,以便推动半空间理论在我国的实用化。     

辽东湾近海海底土小应变动力特性试验研究

开展场地地震动反应分析是众多海洋工程活动顺利实施和长期安全运行的重要保障,其中查明海底土小应变动力特性是十分关键的。文章借助海上原位钻孔取样和室内共振柱仪对辽东湾近海海底土小应变动力特性开展试验研究,探讨前人总结提出的滨海海底土初始动剪切模量G_max预测经验公式在辽东湾海域的适用性,对比文章试验结果与周边海域已有海底土剪切波速测试结果,分析小应变范围内海底土动剪切模量的衰减特征和阻尼比发展演变趋势,并同时进行定量化模拟预测,评价海底土动剪切模量衰减曲线的归一化特征。研究结果表明：(1)共振柱试验得到的原状海底土剪切波速与周边海域已有海底土剪切波速测试结果吻合良好;(2)相比起陆地土,海洋土在小应变范围内归一化动剪切模量G/G_max衰减得更慢,阻尼比增长得也更慢;(3)通过引入临界剪应变,不同土类和埋深对应的海底土小应变动剪切模量衰减曲线可以进行归一化。研究成果对合理开展海洋工程场地地震动反应分析评价具有一定的指导意义。     

Delay-dependent stability and added damping of SDOF real-time dynamic hybrid testing

It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing (RTDHT).This paper focuses on the delay-dependent stability and added damping of SDOF systems in RTDHT.The exponential delay term is transferred into a rational fraction by the Padé approximation, and the delay-dependent stability conditions and instability mechanism of SDOF RTDHT systems are investigated by the root locus technique.First, the stability conditions are discussed separately for the cases of stiffness, mass, and damping experimental substructure.The use of root locus plots shows that the added damping effect and instability mechanism for mass are different from those for stiffness.For the stiffness experimental substructure case, the instability results from the inherent mode because of an obvious negative damping effect of the delay.For the mass case, the delay introduces an equivalent positive damping into the inherent mode, and instability occurs at an added high frequency mode.Then, the compound stability condition is investigated for a general case and the results show that the mass ratio may have both upper and lower limits to remain stable.Finally, a high-emulational virtual shaking table model is built to validate the stability conclusions.     

Constant-ductility inelastic displacement ratios for displacement-based seismic design of self-centering structures

This paper focuses on constant-ductility inelastic displacement ratios of self-centering single-degree-of-freedom (SDF) systems with two different levels of energy dissipation capacity, in the presence of 5% viscous damping ratio. A statistical analysis is developed considering an earthquake database composed of 228 ground motions recorded in California with magnitudes greater than six and organized for NEHRP soil class, ground motion duration, and peak ground acceleration. The response of self-centering SDF systems with large variability of initial periods, ductility levels, and postyield stiffness ratios is investigated and compared with the responses of SDF systems with bilinear plastic, Clough, and Takeda hysteresis. The inelastic demand variation with soil class, initial period, postyield stiffness ratio, unloading stiffness degradation, ductility level, and hysteretic behavior is highlighted. Simple and conservative analytical estimates of constant-ductility inelastic displacement ratios for mean and 90th percentile values in terms of initial period, ductility level, and postyield stiffness ratio are proposed to allow the extension of the Displacement-Based Design via Inelastic Displacement Ratio (C_μDBD) to self-centering structural systems.     

Effect of soil on structural response to wind and earthquake

An approximate analytical approach is presented which makes it possible to consider soil properties and footing embedment in the analysis of the response of structures to external excitation such as wind and earthquake. The approach is based on modal analysis and the definition of stiffness and damping due to soil pertinent to each vibration mode. The approach also facilitates the analysis of coupled motions of a footing alone. The analysis of a tall chimney for the effects of gusting wind, vortex shedding and earthquake is used as an example.