A unified formulation of the piecewise exact method for inelastic seismic demand analysis including the P‐delta effect

The non‐linear analysis of single‐degree‐of‐freedom (SDOF) systems provides the essential background information for both strength‐based design and displacement‐based evaluation/design methodologies through the development of the inelastic response spectra. The recursive solution procedure called the piecewise exact method, which is efficiently used for the response analysis of linear SDOF systems, is re‐formulated in this paper in a unified format to analyse the non‐linear SDOF systems with multi‐linear hysteresis models. The unified formulation is also capable of handling the P‐delta effect, which generally involves the negative post‐yield stiffness of the hysteresis loops. The attractiveness of the method lies in the fact that it provides the exact solution when the loading time history is composed of piecewise linear segments, a condition that is perfectly satisfied for the earthquake excitation. Based on simple recursive relationships given for positive, negative and zero effective stiffnesses, the unified form of the piecewise exact method proves to be an extremely powerful and probably the best tool for the SDOF inelastic time‐history and response spectrum analysis including the P‐delta effect. A number of examples are presented to demonstrate the implementation of the method. Copyright © 2003 John Wiley & Sons, Ltd.     

A rooftop tuned mass damper frame

This article documents the analytical study and feasibility of placing a tuned mass damper in the form of a limber rooftop moment frame atop relatively stiff structures to reduce seismic acceleration response. Six existing structures were analytically studied using a suite of time history and response spectra records. The analyses indicate that adding mass in conjunction with a limber frame results in an increase in the fundamental period of each structure. The fundamental period increase generally results in a decrease in seismic acceleration response for the same time history and response spectra records. Owing to the limber nature of the rooftop frames, non‐linear analysis methods were required to evaluate the stability of the rooftop tuned mass damper frame. The results indicate the addition of a rooftop tuned mass damper frame reduces the seismic acceleration response for most cases although acceleration response can increase if the rooftop frame is not tuned to accommodate the specific structure's dynamic behaviour and localized soil conditions. Appropriate design of the rooftop tuned mass damper frame can result in decreased seismic acceleration response. This translates to safer structures if used as a retrofit measure or a more economical design if used for new construction. Copyright © 2003 John Wiley & Sons, Ltd.     

Statistical performance analysis of seismic‐excited structures with active interaction control

This paper presents a statistical performance analysis of a semi‐active structural control system for suppressing the vibration response of building structures during strong seismic events. The proposed semi‐active mass damper device consists of a high‐frequency mass damper with large stiffness, and an actively controlled interaction element that connects the mass damper to the structure. Through actively modulating the operating states of the interaction elements according to pre‐specified control logic, vibrational energy in the structure is dissipated in the mass damper device and the vibration of the structure is thus suppressed. The control logic, categorized under active interaction control, is defined directly in physical space by minimizing the inter‐storey drift of the structure to the maximum extent. This semi‐active structural control approach has been shown to be effective in reducing the vibration response of building structures due to specific earthquake ground motions. To further evaluate the control performance, a Monte Carlo simulation of the seismic response of a three‐storey steel‐framed building model equipped with the proposed semi‐active mass damper device is performed based on a large ensemble of artificially generated earthquake ground motions. A procedure for generating code‐compatible artificial earthquake accelerograms is also briefly described. The results obtained clearly demonstrate the effectiveness of the proposed semi‐active mass damper device in controlling vibrations of building structures during large earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

Predictive instantaneous optimal control of elastic structures during earthquakes

A predictive instantaneous optimal control (PIOC) algorithm is proposed for controlling the seismic responses of elastic structures. This algorithm compensates for the time delay that happens in practical control applications by predicting the structural response over a period that equals the time delay, and by substituting the predicted response in the instantaneous optimal control (IOC) algorithm. The unique feature of this proposed PIOC algorithm is that it is simple and at the same time compensates for the time delay very effectively. Numerical examples of single degree of freedom structures are presented to compare the performance of PIOC and IOC systems for various time delay magnitudes. Results show that a time delay always causes degradation of control efficiency, but PIOC can greatly reduce this degradation compared to IOC. The effects of the structure's natural periods and the choice of control gains on the degradation induced by the time delay are also analyzed. Results show that shorter natural periods and larger control gains are both more sensitive and more serious to the degradation of control efficiency. Finally, a practical application of PIOC is performed on a six‐story moment‐resisting steel frame. It is demonstrated that PIOC contributes significantly to maintain stability in multiple degree of freedom structures, and at the same time PIOC has a satisfactory control performance. Copyright © 2003 John Wiley & Sons, Ltd.     

青藏铁路抛石路基的温度特性研究

铁路道渣和片石铺层的对流换热为多孔介质的热传导问题，根据多孔介质中流体热对流的连续性方程、动量方程和能量方程，应用伽辽金法导出了多孔介质对流换热的有限元公式，并对抛石路基和传统道渣路基在未来25a创温度变化进行了预报分析和比较．计算结果表明，在150cm的抛石厚度，片石直径为10cm，年温度较差30℃的倩况下，在路基中心线y＝一5m处，抛石路基下的冻土温度要比传统路基的温度低2．45℃，抛石路基有对其下面的冻土提供冷能的制冷作用，可以保证冻土路基的稳定．因此，推荐该种路基作为青藏铁路高温冻土区的路基结构，可以最大限度地保护冻土区的铁路．     

冻土路基表面的融化指数与冻结指数

在冻土层之上筑路，由于会改变地-气界面的热物理特性，进而影响冻土层的热力→动力稳定性，故而修筑一定高度的路基成为保护冻土层所采取的一种常规措施．在修筑路基之后，与路基边坡的朝向有关的热效应是冻土路基工程保护措施必须考虑的问题．在数理分析与数值模拟分析的基础上，给出了可根据气温的年最大和最小月平均值计算路基表面的融化指数与冻结指数以及有关热状况参数的方法，并以青藏铁路北麓河段2002年为例进行了计算分析．实例分析表明，即便是没有修筑道路，北麓河地区的冻土也已经处于临界状态；路基相对的两个坡面，由于朝向不同会造成温度分布的强非均匀性，其中南和偏南方向与北和偏北方向的路基坡面热状况差异最大，有必要对路基相对的两个坡面采用不同的防护措施，一方面改善就地取土修筑路基对其下伏冻土层的直接不良影响，同时也尽可能减小路基表面温度分布的非均匀性，以避免纵向裂缝的发生。     

青藏铁路管道通风试验路基地温变化及热状况分析

基于青藏铁路北麓河试验段管道通风路基在2个冻融循环周期内的地温监测资料，分析了路基温度的发展、温度场分布特征及多年冻土的热流量变化．结果表明：通风管埋设于路堤中部的路基温度变化和发展情况与一般路基类似，路基在施工后的2个冻融周期内仍处于整体升温的过程；通风管埋设于路堤下部的路基，虽然前2个冻融循环周期内土体温度与原始状态相比同样有所升高，但开始出现逐渐降低的趋势，同时地温场的分布在横向上的对称性也比较好，在热交换方面，一般填土路基和通风管位于路堤中部的路基在施工后的前2个冻融循环周期内一直处于吸热过程，而通风管位于路堤下部的路基在经历了第1个周期的持续吸热过程后，在第2个冻融循环周期内已经开始放热。     

地震荷载作用下温度和围压对冻土强度影响的试验研究

通过对重塑冻结兰州黄土的动三轴试验，较系统研究了地震荷载作用下冻土的动强度特性，并且定量研究了其在不同温度(-2℃、-5℃、-7℃)和围压(1MPa、3MPa、5MPa)条件下的变化规律．结果发现：冻结黄土的动抗剪强度随围压的增大、温度的降低、振次的减少而增大；动粘聚力Cd随振次的减小和温度的降低而增大；动内摩擦角吼随振次的增大和温度的降低而增大。     

慕士塔格冰芯钻孔温度测量结果

2002年8月对慕士塔格冰川累积区海拔6300m左右的两根冰芯钻孔(其中—根达到冰川底部基岩)进行了温度测量，揭示了该处冰川的温度分布特征．结果表明：慕士塔格冰芯的冰温是目前中低纬地区山地冰川中最低的，达-21．79℃，该最低温度出现的位置在35m以下；冰床底部的温度为-20．76℃，也远低于其它山地冰川的冰床温度，极低的温度对成冰过程有重要影响，并有利于获得可靠的冰芯记录。     

A hybrid indirect boundary element—discrete wave number method applied to simulate the seismic response of stratified alluvial valleys

A hybrid indirect boundary element – discrete wavenumber method is presented and applied to model the ground motion on stratified alluvial valleys under incident plane SH waves from an elastic half-space. The method is based on the single-layer integral representation for diffracted waves. Refracted waves in the horizontally stratified region can be expressed as a linear superposition of solutions for a set of discrete wavenumbers. These solutions are obtained in terms of the Thomson–Haskell propagators formalism. Boundary conditions of continuity of displacements and tractions along the common boundary between the half-space and the stratified region lead to a system of equations for the sources strengths and the coefficients of the plane wave expansion. Although the regions share the boundary, the discretization schemes are different for both sides: for the exterior region, it is based on the numerical and analytical integration of exact Green's functions for displacements and tractions whereas for the layered part, a collocation approach is used. In order to validate this approach results are compared for well-known cases studied in the literature. A homogeneous trapezoidal valley and a parabolic stratified valley were studied and excellent agreement with previous computations was found. An example is given for a stratified inclusion model of an alluvial deposit with an irregular interface with the half-space. Results are displayed in both frequency and time domains. These results show the significant influence of lateral heterogeneity and the emergence of locally generated surface waves in the seismic response of alluvial valleys.