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Tsunamis are rare destructive phenomena caused by the sudden displacement of a large amount of water in the ocean and can result in enormous losses to coastal communities. The resilience of coastal communities to tsunamis can be improved through the use of risk-informed decision making tools. Performance-Based Engineering (PBE) approaches have been developed for different natural hazards including earthquake, fire, hurricane, and wind to perform probabilistic risk assessment for structures. In this study, a probabilistic Performance-Based Tsunami Engineering (PBTE) framework based on the total probability theorem is proposed for the risk assessment of structures subject to tsunamis. The proposed framework can be disaggregated into the different basic analysis phases of hazard analysis, foundation and structure characterization, interaction analysis, structural analysis, damage analysis, and loss analysis. An application example consisting of the risk assessment of a three-story steel moment frame structure was performed using the proposed framework. The probability of exceedance of the total replacement cost including structural, nonstructural, and content losses were computed.

SUMMARYA new passive seismic response control device has been developed, fabricated, and tested by the authors and shown to be capable of producing negative stiffness via a purely mechanical mechanism, thus representing a new generation of seismic protection devices. Although the concept of negative stiffness may appear to be a reversal on the desired relationship between the force and displacement in structures (the desired relationship being that the product of restoring force and displacement is nonnegative), when implemented in parallel with a structure having positive stiffness, the combined system appears to have substantially reduced stiffness while remaining stable. Thus, there is an 'apparent weakening and softening' of the structure that results in reduced forces and increased displacements (where the weakening and softening is of a non-damaging nature in that it occurs in a seismic protection device rather than within the structural framing system). Any excessive displacement response can then be limited by incorporating a damping device in parallel with the negative stiffness device. The combination of negative stiffness and passive damping provides a large degree of control over the expected performance of the structure. In this paper, a numerical study is presented on the performance of a seismically isolated highway bridge model that is subjected to various strong earthquake ground motions. The Negative Stiffness Devices (NSDs) are described along with their hysteretic behavior as obtained from a series of cyclic tests wherein the tests were conducted using a modified design of the NSDs (modified for testing within the bridge model). Using the results from the cyclic tests, numerical simulations of the seismic response of the isolated bridge model were conducted for various configurations (with/without negative stiffness devices and/or viscous dampers). The results demonstrate that the addition of negative stiffness devices reduces the base shear substantially, while the deck displacement is limited to acceptable values. This assessment was conducted as part of a NEES (Network for Earthquake Engineering Simulation) project which included shaking table tests of a quarter-scale highway bridge model.

Researchers worldwide have developed various semi-active control devices for seismic protection of structures. Most of these devices are electromechanical in nature and thus require a power source for their operation. In this paper, a newly developed rotation-based mechanical adaptive passive device is presented. These unique devices are able to mechanically change stiffness, either by adding positive or negative stiffness, by using different types of rotational elements. The devices are compact due to their use of rotational elements, facilitating their implementation in structures. The conceptual development of these devices is presented herein along with analytical models and numerical simulation results that demonstrate their potential for providing seismic protection. In addition, an extension of the stiffness modulation concept is introduced wherein damping is modulated.

Implementation of a mechanical Negative Stiffness Device (NSD) within a reduced-scale highway bridge model and its performance under seismic loading conditions is evaluated via shaking table tests. Four different isolation system configurations are considered: isolated bridge (IB), IB with viscous dampers, IB with NSDs and IB with viscous dampers and NSDs. In addition, two bridge pier configurations were considered, one with flexible piers (mimicking a middle span of a multi-span bridge) and one with braced piers (mimicking a single span bridge supported on abutments). The main feature of the NSD is a large pre-compressed spring, which can push the structure away from its initial undeformed position and thus induce negative stiffness behavior. The experimental results clearly demonstrate the effectiveness of the NSDs in limiting the seismic response of the bridge and provide validation of numerical simulation results wherein numerical models of the bridge model components were calibrated via system identification testing.

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