A three-dimensional rotational failure mechanism for earth slope is extended from toe failure to include face failure and base failure. An efficient optimisation method is simultaneously employed to find the least upper bounds to the critical height in order to avoid missing the global minimum. Compared with the results from analysis based on toe failure alone, best estimates of the critical height and the critical failure mechanism are obtained. The calculated results are given in the form of graphs and tables for a wide range of parameters. The critical failure surfaces are also investigated to assess the influences of geometrical constraint and soil property on failure mechanism.

The vibration responses of structures under controlled or ambient excitation can be used to detect structural damage by correlating changes in structural dynamic properties extracted from responses with damage. Typical dynamic properties refer to modal parameters: natural frequencies, mode shapes, and damping. Among these parameters, natural frequencies and mode shapes have been investigated extensively for their use in damage characterization by associating damage with reduction in local stiffness of structures. In contrast, the use of damping as a dynamic property to represent structural damage has not been comprehensively elucidated, primarily due to the complexities of damping measurement and analysis. With advances in measurement technologies and analysis tools, the use of damping to identify damage is becoming a focus of increasing attention in the damage detection community. Recently, a number of studies have demonstrated that damping has greater sensitivity for characterizing damage than natural frequencies and mode shapes in various applications, but damping-based damage identification is still a research direction ‘in progress’ and is not yet well resolved. This situation calls for an overall survey of the state-of-the-art and the state-of-the-practice of using damping to detect structural damage. To this end, this study aims to provide a comprehensive survey of uses and features of applying damping in structural damage detection. First, we present various methods for damping estimation in different domains including the time domain, the frequency domain, and the time-frequency domain. Second, we investigate the features and applications of damping-based damage detection methods on the basis of two predominant infrastructure elements, reinforced concrete structures and fiber-reinforced composites. Third, we clarify the influential factors that can impair the capability of damping to characterize damage. Finally, we recommend future research directions for advancing damping-based damage detection. This work holds the promise of (a) helping researchers identify crucial components in damping-based damage detection theories, methods, and technologies, and (b) leading practitioners to better implement damping-based structural damage identification.

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