Martin S. Williams

SEISMIC DAMAGE INDICES FOR CONCRETE STRUCTURES: A STATE-OF-THE ART REVIEW

This paper gives a review of seismic damage indices, with particular reference to their use in retrofit decision making. Damage indices aim to provide a means of quantifying numerically the damage in concrete structures sustained under earthquake loading. Indices may be defined locally, for an individual element, or globally, for a whole structure. Most local indices are cumulative in nature, reflecting the dependence of damage on both the amplitude and the number of cycles of loading. The main disadvantages of most local damage indices are the need for tuning of coefficients for a particular structural type and the lack of calibration against varying degrees of damage. Global damage indices may be calculated by taking a weighted average of the local indices throughout a structure, or by comparing the modal properties of the structure before and after (and sometimes during) the earthquake. The weighted-average indices are prone to much the same problems as the local indices. The modal indices vary widely in their level of sophistication, those capable of detecting relatively minor damage requiring the accurate determination of a large number of modes of vibration. The development and application of damage indices has until now concentrated almost exclusively on flexural modes of failure; there is a clear need to investigate the ability of the indices to represent shear damage.

The development of real-time substructure testing

Full–scale dynamic testing of civil engineering structures is extremely costly and difficult to perform. Most test methods therefore involve either a reduction in the physical scale or an extension of the time–scale. Both of these approaches can cause significant difficulties in extrapolating to the full–scale dynamic behaviour, particularly when the structure responds nonlinearly or includes highly rate–dependent components such as dampers. Real–time substructure testing is a relatively new method which seeks to avoid these problems by performing tests on key elements of the structure at full or large scale, with the physical test coupled in real time to a numerical model of the surrounding structure. The method requires a high performance of both the physical test equipment and the numerical algorithms. This paper first reviews the development of structural test methods and the emergence of real–time substructure testing. This is followed by a brief description of the equipment that is needed to implement a substructure test. Several novel developments in the numerical algorithms used in real–time substructure testing are presented, including a new, fast algorithm which allows nonlinear response of the surrounding structure to be computed in real time. Results are presented from a variety of tests which demonstrate the performance of the system at small and large scale, with either linear or nonlinear test specimens, and with varying numbers of degrees of freedom passed between the physical and numerical substructures. Finally, the usefulness and possible applications of the test method are discussed.

A review of time-frequency methods for structural vibration analysis

Abstract This paper presents a review of time-frequency distribution tools for the analysis of non-linear vibrations of structures. The theoretical basis of the moving window discrete Fourier transform (DFT), the moving window auto-regressive (AR) model, the harmonic wavelet transform, the Wigner–Ville (WV) and the Windowed Wigner–Ville (WWV) bilinear distributions are presented. The strengths and weaknesses of each technique are demonstrated by applying them to a variety of synthetic signals. Then the methods are applied to real vibration data taken from experiments on a damaged reinforced concrete beam. It is shown that, for this simple structure, the DFT and AR moving window, wavelet and WWV methods give similar estimates of the time-frequency relationship for the fundamental mode, though the AR model estimate is much noisier than the others.

Laboratory testing of structures under dynamic loads: an introductory review

This paper introduces and reviews the theme of laboratory testing of structures under dynamic loads. The emphasis is on the simulation of earthquake effects, for which three principle methods are discussed: shaking tables, pseudo–dynamic testing and real–time testing. The latest developments in these areas are discussed in depth in the subsequent papers in this issue. While shaking tables and pseudo–dynamic methods are quite well established, both techniques have undergone significant advances in recent years, including improvements in control to ensure accurate reproduction of dynamic loads, and the construction of very large facilities aimed at eliminating the significant scaling problems. Development of the substructuring method has enabled large–scale pseudo–dynamic tests of parts of structures, coupled to numerical models of the remainder. Attempts are now being made to extend this approach to shaking tables. Recently, considerable efforts have been devoted to methods of testing both at large scale and in real time. Two approaches are discussed: the real–time substructure method, in which a physical test and a numerical model interact in real time; and effective force testing, in which equivalent seismic forces are applied by actuators operating under force control. Both methods have been shown to be feasible, but require further development. Although the techniques described have been developed primarily for seismic testing of structures, there is considerable potential for their application to other load types in the fields of civil and mechanical engineering.

A comparison of viscous damper placement methods for improving seismic building design

This article compares the effectiveness of five viscous damper placement techniques, two standard and three advanced, for reducing seismic performance objectives, including peak interstory drifts, absolute accelerations, and residual drifts. The techniques are evaluated statistically for two steel moment-resisting frames under varying seismic hazard levels, employing linear viscous dampers and nonlinear time history analyses. Usability of the methods is also assessed. All the placement methods meet the desired drift limit but advanced techniques achieve additional improvement in drift reduction and distribution. Performance differences between the advanced techniques are minor, making usability a significant selection factor amongst the methods.

Modeling of Local Impact Effects on Plain and Reinforced Concrete

A review is given of models of localized concrete behavior when impacted by undeformable missiles at a wide range of incident velocities. First, experimental and empirical studies of strain rate effects on concrete are discussed. Omission of rate effects may cause substantial errors in prediction of both the mode and magnitude of impact response. A critical review of empirical equations shows that they are able to give reliable predictions of penetration depth and of perforation and scabbing thicknesses over a wide range of parameters. Analytical and computational models are capable of providing very detailed information about the impact process, including stress and deformation histories, but their application is being held back by the need for realistic constitutive relations, especially the modeling of crack formation and propagation.

Non-linear dynamic analysis of offshore jack-up units

Abstract A two-dimensional finite element program for the non-linear dynamic analysis of offshore jack-up units under storm loading is described. The program aims to incorporate consistent and reasonable levels of approximation of all the major system parameters; this is in contrast to many previous approaches, which have tended to model some aspects of the problem in great detail while adopting a very simplified approach to others. Accurate modelling of the jack-up legs is achieved using an Eulerian formulation of beam–column theory. The complex non-linear behaviour of the spudcan footings is represented by a recently developed work-hardening plasticity model, which represents a considerable advance over the simple pinned footing assumption which is most frequently used for jack-up analysis. Several options for calculating wave kinematics are available, including Stokes’ fifth order wave theory. The resulting non-linear equations are solved in the time domain using implicit integration algorithms. Results for some representative test cases are presented.

Evaluation of seismic damage indices for concrete elements loaded in combined shear and flexure

Damage indices have the potential to play a vital role in retrofit decision-making and disaster planning in earthquake regions. However, a major limitation of existing indices is that they have been formulated and validated almost exclusively on the basis of flexural response, neglecting the importance of shear as a cause of seismic damage. In this paper, eight damage indices are evaluated by comparison with a series of single-component tests using a variety of moment to shear ratios and stirrup spacings. On the basis of these comparisons, it appears that the more sophisticated indices which attempt to take account of the damage caused by repeated cycling give no more reliable an indication of damage than simple measures such as ductility and stiffness degradation.

Non-linear behaviour of reinforced concrete beams under low-amplitude cyclic and vibration loads

Abstract Recently, there has been increased interest in using non-linear vibration techniques to detect damage in reinforced concrete beams. To understand better the non-linear behaviour of damaged concrete beams during low-amplitude vibration, modelling is necessary. This could be achieved with knowledge of the moment–relative rotation relationship of a section of beam within the damaged region. An experimental method of studying the static moment–rotation relationship over a short subsection of the beam is presented here. Tests are conducted at the mid-span of a beam, damaged by overload. Initially the stiffness of the damaged section decreases rapidly with increased damage but above 27% of failure load the change with increased damage is very small. Several possible non-linear crack mechanisms are then discussed, two of which may be assessed using the experimental data.

Compensation of actuator dynamics in real-time hybrid tests:

Abstract Real-time hybrid testing is a novel approach to the dynamic testing of structures, in which the system under test is split into physical and numerical substructures which are tested and analysed in parallel, with data passed between them in real time. The success of a test is highly dependent on the performance of the actuators which provide the interface forces and displacements between the two substructures. This paper presents several numerical schemes to compensate for the non-ideal dynamics of typical servohydraulic actuators and evaluates them through a series of real-time hybrid tests on simple mass-spring systems. It is shown that effective schemes can be developed on the basis of a simple representation of the actuator response as combination of a delay and an amplitude error, both of which can vary during a test. The use of a modified online delay estimator, together with one of three simple forward extrapolation schemes, is found to be highly effective in minimizing experimental errors related to the actuator dynamics.