Robert G. Sexsmith

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.

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.

Probability-based safety analysis — value and drawbacks

Abstract Probability-based safety analysis of structures has been under development for about 50 years. While there are many advantages, and much progress over that time, there remains a lack of widespread acceptance by the design community and by many researchers in the field of structural engineering. This discussion aims to identify the advantages and difficulties with the methodology of probability-based safety as currently practised, with the hope that this will help to spur some advances that will overcome the difficulties. The term “probability-based safety analysis” in this discussion includes the mathematical treatment of reliability analysis, as well as the various approaches to decision analysis such as code safety factor decisions and optimum design where the objective includes safety and cost. This author fully subscribes to the notions of subjective probability, hence the ideas include applications where probabilities are not based on statistics.

A Proposed Damage Model for RC Bridge Columns under Cyclic Loading

This paper defines a damage index based on the predicted hysteretic behavior of a concrete column. The model yields a damage index at a point in the time history for the element, based on the predicted monotonic response from the point in time to failure. The model takes into account the parameters that describe the hysteretic behavior: stiffness degradation, strength deterioration, and ultimate displacement reduction. Therefore, the damage model is accumulative and it combines energy, ductility, and low-cycle fatigue. The model is based on the work needed to fail a reinforced concrete column monotonically after it experiences a cyclic loading. The model modifies the ultimate displacement that the column can achieve, due to low-cycle fatigue in the longitudinal reinforcement using the Coffin-Manson rule in combination with Miners hypothesis. The proposed model is applied to bridge columns tested by others, and compared to existing damage indices. The proposed model gives a realistic prediction of damage throughout the loading cycles for several test specimens investigated.

Seismic assessment of concrete bridges using inelastic damage analysis

As increasing numbers of structures are considered as candidates for seismic retrofit, there is a need for simple and objective methods for assessing structures, for making decisions between competing structures, and for comparing different retrofit schemes. The accuracy and objectivity of the assessment process may be enhanced by the use of sophisticated inelastic analysis programs and seismic damage indices, but only if these tools can be shown to be very reliable; currently they are not sufficiently widely used for engineers to have complete confidence in them. Using extensive comparisons with laboratory test results, it is shown that inelastic analysis procedures, together with damage indices, can provide accurate and robust predictions of structural capacity. Recommendations are made for the selection and calibration of damage indices appropriate for use in seismic assessment and retrofit design.

CYCLIC BEHAVIOR OF CONCRETE BRIDGE BENTS

During the planning of the seismic retrofit of Vancouvers 40-year-old Oak Street Bridge, it became evident that a test program of a typical bridge pier under slow cyclic loading would assist in the determination of appropriate retrofit techniques. A series of 0.45 scale models of an as-built pier were constructed. One was tested in the as-built condition, while the others received various retrofits. Slow cyclic lateral load was applied at the model deck elevation. Hysteretic behavior of the bents and the output from numerous strain gages and displacement transducers were recorded. The test program provided significant design information for the retrofit of the bridge and for the many similar bridge bents currently in use and needing seismic retrofit.

Reliability during temporary erection phases

Abstract While design codes regulate the safety of permanent works, erection engineering of temporary works often requires a choice of safety factors. Such choices should be made on the basis of optimization of the present expected value of construction and consequence costs. This paper illustrates the choice of reliability level in terms of load factors for typical situations encountered in erection engineering. Reliability level depends on the exposure time to the temporary load, the costs of construction of the temporary work, and the consequences of failure. Reliability issues regarding personnel are briefly addressed. Safety decisions about the individual workers will not normally affect the design criteria because the requirement of the contractor, who must bear the risk of many workers, will be more conservative than that of the worker. In the case of exposure over a very short time period, it seems reasonable to accept a higher-than-normal risk. This may affect the design of temporary bracing and similar structures where they are needed for seismic risk, for example.

Safety factors for bridge falsework by risk management

Determination of safety factors logically depends upon the cost of providing safety, the consequences of failure, the failure probability or rate, and the time of exposure to load. In the case of conventional structures these are indirectly accounted with safety factors prescribed by codes, and based on probabilistic studies and calibration. Bridge falsework may consist of structural systems that support relatively costly construction (with high consequences of failure) for very short time periods. Structural design codes generally do not prescribe safety factors for such temporary works. In the absence of prescriptive codes, contractors are left with decisions about safety factors. Some common policies are: to use factors or stresses and loads the same as for permanent construction; to use increased allowable stresses; or to use reduced return periods for environmental loads. This investigation applies basic principles of decision analysis and risk management to determine safety factors for several common bridge falsework or erection situations. The results indicate that substantial differences in the appropriate safety factors can be found, especially when low cost falsework supports costly permanent structure. In particular, the common practice of using increased allowable stresses or reduced load return periods can be seriously unconservative.