Among the most effective seismic protection devices, friction pendulum (FP), whose conceptual basis lies in the pendulum motion and its simple analytical description, has now gained a widespread acceptance. All the studies carried out so far have explored almost all the remarkable features of this device. Among the most appealing are constant stiffness, constant oscillation period, and recentering capability. These studies - and the authors found no exception - have systematically made reference to the classical gravity pendulum equation, whose motion occurs only in one dimension (1D), according to one DOF: the polar angle θ. When the presence of bi-directional seismic excitation required a 2D model, authors have resorted to the vector combination of the response of two orthogonal 1D pendulums, which we refer to as '1.5D' pendulum. Actually, FP is more correctly described as a 2D spherical pendulum, consisting of a mass moving on a sphere with friction, according to two DOFs: the polar angle θ and the azimuth angle φ. The relevant analytical equations of motion are presented in this paper, also accounting for thermo-mechanical coupling, to model the friction-induced temperature on the contact surface. The so-developed equations have been the object of an ample parametric study. This has allowed to observe some - sometimes notable - features in the FP response, both in free oscillation state and under bi-directional or tri-directional earthquake-like action, which in some cases lead to a different response with respect to what is generally computed - and designed - under the simplified assumptions of 1D or '1.5D' pendulum motion.

A simple procedure to calibrate the safety factor of capacity models is presented. The calibration can be carried out based on any available database of experimental tests, even of limited size. The procedure aims to assess the model capability of predicting the test results and to calibrate the safety factor so that the capacity equation meets the target reliability level required by the code or sought by the calibrator. After predicting each test of the database with the capacity equation under consideration, the test-prediction pairs are checked for the property of linearity, and the relative error for the properties of homoscedasticity and normality. Once these properties are fulfilled - which may require a nonlinear transformation of the test values and/or the predictions - the closed-form equation proposed in this paper is employed to compute a target design value. The model safety factor is finally obtained by comparing such target design value with the design value obtained from the code. The paper also proposes two approximate analytical equations to compute the tolerance factor, used to attain any given fractile, as a function of the (even small) number of tests, with any assigned confidence level. A fundamental outcome of the procedure is that it yields an objective indicator of the model accuracy, measured by the standard deviation of its error, which may be regarded as a parameter useful for selecting the most reliable model among different competing ones. In the long run, the application of the proposed procedure will allow achieving a uniform reliability level throughout all capacity models used in codes and guidelines. A further advantage is that the partial safety factors so derived can be straightforwardly updated when more experiments become available. As an example, the proposed procedure is herein applied to the ACI 318 shear design capacity equation for concrete members unreinforced in shear.

The progressive collapse analysis of reinforced concrete (RC) moment-frame buildings under extreme loads is discussed from the perspective of modeling issues. A threat-independent approach or the alternate path method forms the basis of the simulations wherein the extreme event is modeled via column removal scenarios. Using a prototype RC frame building, issues and considerations in constitutive modeling of materials, options in modeling the structural elements and specification of gravity loads are discussed with the goal of achieving consistent models that can be used in collapse scenarios involving successive loss of load-bearing columns at the lowest level of the building. The role of the floor slabs in mobilizing catenary action and influencing the progressive collapse response is also highlighted. Finally, an energy-based approach for identifying the proximity to collapse of regular multi-story buildings is proposed.

Ground-motion simulations generated from physics-based wave propagation models are gaining increasing interest in the engineering community for their potential to inform the performance-based design and assessment of infrastructure residing in active seismic areas. A key prerequisite before the ground-motion simulations can be used with confidence for application in engineering domains is their comprehensive and rigorous investigation and validation. This article provides a four-step methodology and acceptance criteria to assess the reliability of simulated ground motions of not historical events, which includes (1) the selection of a population of real records consistent with the simulated scenarios, (2) the comparison of the distribution of Intensity Measures (IMs) from the simulated records, real records, and Ground-Motion Prediction Equations (GMPEs), (3) the comparison of the distribution of simple proxies for building response, and (4) the comparison of the distribution of Engineering Demand Parameters (EDPs) for a realistic model of a structure. Specific focus is laid on near-field ground motions (<10km) from large earthquakes (Mw7), for which the database of real records for potential use in engineering applications is severely limited. The methodology is demonstrated through comparison of (2490) near-field synthetic records with 5 Hz resolution generated from the Pitarka et al (2019) kinematic rupture model with a population of (38) pulse-like near-field real records from multiple events and, when applicable, with NGA-W2 GMPEs. The proposed procedure provides an effective method for informing and advancing the science needed to generate realistic ground-motion simulations, and for building confidence in their use in engineering domains.

Accurate measurements of the time-dependent deformations of a building during earthquake excitation are essential for interpretation of the dynamic response of the as-built system and for quantifying the seismic demands. Traditional approaches for monitoring building systems are based on strong motion accelerometers mounted at selected elevations. However, accelerometer-based systems do not directly measure the deformations of the structure, and can have significant limitations that make it challenging to correctly measure deformations, particularly permanent deformations from inelastic response. In the study described herein, computational simulations and experiments were combined to evaluate the potential of a new optically based sensor to directly measure time-dependent deformations of a building, including inelastic deformations. The sensor methodology includes corrections for localized structural member rotations and can provide estimates of the absolute accelerations at each floor. A laser-based system utilizing a recently developed discrete diode position sensor (DDPS) is evaluated, and the ability of such a system to measure earthquake induced transient deformations characterized by building interstory drift is demonstrated.

Interstory drift (ID) is a key response parameter for buildings subjected to lateral loads and is used to define performance-based limit states, allowable deformations and damage states in a number of seismic design codes and standards. An ability to rapidly and accurately measure both transient and residual ID during an earthquake would provide important observables for understanding the seismic demands and post-earthquake condition of a building. Accurate retrieval of ID from accelerometer-based instrumentation systems can be very challenging, if not impossible, as a result of instrumentation limitations and the post-processing associated with strong motion accelerometer data. This is particularly true for the case in which residual drifts occur during inelastic building response. In the study presented herein, a newly developed optical sensor system, designed specifically for directly measuring both transient and residual ID, was experimentally evaluated through shake table testing and computational simulations. The ability of the sensor to accurately measure ID is demonstrated and key operational considerations for sensor system deployment are examined through a model-based investigation.

The existing observational database of the regional-scale distribution of strong ground motions and measured building response for major earthquakes continues to be quite sparse. As a result, details of the regional variability and spatial distribution of ground motions, and the corresponding distribution of risk to buildings and other infrastructure, are not comprehensively understood. Utilizing high-performance computing platforms, emerging high-resolution, physics-based ground motion simulations can now resolve frequencies of engineering interest and provide detailed synthetic ground motions at high spatial density. This provides an opportunity for new insight into the distribution of infrastructure seismic demands and risk. In the work presented herein, the EQSIM fault-to-structure computational framework described in a companion paper, McCallen et al., is employed to investigate the regional-scale response of buildings to large earthquakes. A representative M = 7.0 strike-slip event is used to explore the distribution and amplitude of building demand, and comparisons are made between building response computed with fault-to-structure simulations and building response computed with existing measured near-fault earthquake records. New information on the distribution and variability of building response from high-performance parallel simulations is described and analyzed, and favorable first comparisons between building response predicted with both fault-to-structure simulations and real ground motions records are presented.

Computational simulations have become central to the seismic analysis and design of major infrastructure over the past several decades. Most major structures are now “proof tested” virtually through representative simulations of earthquake-induced response. More recently, with the advancement of high-performance computing (HPC) platforms and the associated massively parallel computational ecosystems, simulation is beginning to play a role in increased understanding and prediction of ground motions for earthquake hazard assessments. However, the computational requirements for regional-scale geophysics-based ground motion simulations are extreme, which has restricted the frequency resolution of direct simulations and limited the ability to perform the large number of simulations required to numerically explore the problem parametric space. In this article, recent developments toward an integrated, multidisciplinary earth science-engineering computational framework for the regional-scale simulation of both ground motions and resulting structural response are described with a particular emphasis on advancing simulations to frequencies relevant to engineered systems. This multidisciplinary computational development is being carried out as part of the US Department of Energy (DOE) Exascale Computing Project with the goal of achieving a computational framework poised to exploit emerging DOE exaflop computer platforms scheduled for the 2022–2023 timeframe.