Computational Methods, Seismic Protection, Hybrid Testing and Resilience in Earthquake Engineering

Origins and development of 3D-BASIS (3-Dimensional BASe Isolated Structures) was initially envisioned by the need for an efficient tool for nonlinear dynamic analysis of three-dimensional base isolated structures, particularly in solving the highly nonlinear bidirectional stick-slip hysteretic response of a collection of sliding isolation bearings and the resulting response of the superstructure, as this was not available at that time. The primary challenge was to solve the stick-slip behavior of friction bearings—modeled using a differential equation (Bouc-Wen Model) due to its efficiency in representing constant Coulomb friction or variable velocity depended friction by using a very small yield displacement during the stick phase resulting in very high tangential stiffness followed by a very small tangential stiffness during the sliding phase—and the resulting stiff differential equations. A challenge that is compounded when biaxial-friction is modeled, wherein even the traditional method of using Gear’s method to solve stiff differential equations breaks down—a problem that was vexing the research team at University at Buffalo trying to solve the problem at that time. The answer was the development of the novel pseudo-force solution algorithm along with a semi-implicit Runge-Kutta method to solve the difficult problem. The efficient solution procedure is needed primarily for the nonlinear isolation system consisting of (1) sliding and/or elastomeric bearings, (2) fluid dampers, (3) other energy dissipation devices, while the superstructure is represented by three dimensional superstructure model appropriately condensed (where only master nodes at the center of mass of the floor are retained). This chapter describes the origins, development of 3D-BASIS and its impact.

The development of IDARC (Park et al., IDARC: Inelastic Damage Analysis of Reinforced Concrete frame shear-wall structures. Technical report NCEER 87-0008, State University of New York, Buffalo, 1987) (Inelastic Damage Analysis of Reinforced Concrete structures) was initially motivated by the need for an efficient computer program to aid the design of shaking table experiments but then evolved into a tool for seismic assessment of reinforced concrete structures. The primary modeling technique employed in the IDARC computational platform is the representation of the overall behavior of components through macromodels. The effectiveness of the macro elements is enhanced through the introduction of distributed flexibility models that account for the effects of spread plasticity. Nonlinear material behavior is specified by means of a generic hysteretic force-deformation model that incorporates stiffness degradation, strength deterioration and pinching or bond-slip effects. Solution modules for nonlinear static, monotonic, quasi-static cyclic and transient seismic loads were implemented. The final response quantities are expressed in terms of damage indices that provide engineers with a qualitative interpretation of the structural response.

Matrices with random entries are encountered in finite element/difference formulations of a broad range of mechanics problems. Monte Carlo simulation, the only general method for solving this class of problems, is usual impractical when dealing with realistic problems.

A new method is presented for solving stochastic problems with random matrices that is based on the representation of the entries of random matrices by stochastic reduced order models (SROMs) and surrogate models. SROMs are random elements with finite numbers of samples that are selected from the samples of target random elements in an optimal manner. Surrogate models are approximations for quantities of interest with known expressions. Numerical examples are used to illustrate the implementation and the performance of the SROM method. The examples include inverses and eigenvalues/eigenvectors of random matrices.

A zipper frame is a conventional braced frame with chevron type braces at all floors, connected through a zipper column linking their midpoints. Under lateral force, a 3 stories frame is expected to behave as follows: after the 1st floor braces buckle, the zipper column transmits the unbalance vertical force to the 2nd story, forcing them to buckle. The new unbalanced vertical force is then transmitted to the third story, which is designed to remain elastic. This is known as the zipper mechanism. Three shaking table tests were performed to evaluate the seismic response of a 3 story suspended zipper frame model. In every shaking table test performed, the braces buckled out of plane but the zipper mechanism did not always develop. Following the test results, a new analytical tool was developed to capture the 3 dimensional phenomena of buckling. It is based on the well known corotational formulation. Every element is described independently. The rigid body modes are removed by using a corotated coordinate system. Within the deformed shape, the element can undergo large rotations and large strains, which are evaluated respect to the corotated origin. The structural problem is solved in the state space, where displacements as well as velocities are variables. The final set of equations is a combination of differential and algebraic equations that is solved using the IDA software. This paper presents the main results of the shaking table tests as well as some general description of the proposed formulation and its capability to verify the shaking table findings.

A simplified procedure for evaluating the seismic performance and retrofit of existing low to mid-rise reinforced concrete buildings was first presented by Bracci et al. (ASCE J Struct Eng 123(1):3–10, 1997). The procedure is derived from the well-known Capacity Spectrum Method (Freeman, Prediction of response of concrete buildings to severe earthquake motion. In: Douglas McHenry international symposium on concrete and concrete structures, SP-55. ACI, Detroit, pp 589–605, 1978) and is intended to provide practicing engineers with a relatively simple methodology for estimating the margin of safety against structural failure. The procedure consists of constructing a series of seismic story demand curves from modal superposition analyses wherein changes in the dynamic characteristics of the structure (natural frequencies, mode shapes and linear viscous damping) at various response phases ranging from elastic to full failure mechanism are considered. Then these demands are compared to the lateral story capacities as determined from an independent adaptive pushover analysis, where the distribution of lateral forces is based on stiffness dependent story shear demands. The adaptive pushover analysis forms a critical aspect of the methodology which relies on a reasonable estimate of the failure modes of the structure. The proposed technique is applied to a one-third scale three story reinforced concrete frame model building that was subjected to repeated shaking table excitations, and later retrofitted and tested again at the same intensities. This study shows that the procedure can provide reliable estimates of story demands vs. capacities for use in seismic performance and retrofit evaluation of structures.

Nonstructural components (NSC) economic impact and the extensive damages due to NSC after an earthquake motivate the research studies conducted in the past few years at the Department of Structures for Engineering and Architecture, University of Naples Federico II on this topic. The seismic qualification of continuous ceiling systems, plasterboard and brick internal partitions via shake table tests is described in the paper. The test campaign on continuous ceiling systems highlights the low fragility of the tested specimen, primarily caused by: (a) the continuous nature of the ceiling, (b) the dense suspen-sion grid, and (c) the large number of hangers being used. In order to test the internal partitions, which are mainly displacement-sensitive components, an appropriate steel test structure is designed. This structure simulates the behavior of a generic floor in a structure that exhibits an interstorey drift equal to 0.5 % for a frequent earthquake, according to Eurocode 8 prescriptions. Three possible damage states are considered in the study and correlated to an engineering demand parameter, i.e. the interstorey drift ratio, through the use of a damage scheme. Extensive tests show an excellent seismic performance of the plasterboard partition walls, which are characterized by innovative anti-seismic details. In fact, they show minor damage when subjected to interstorey drifts even larger than 1 %. The shake table tests performed at different intensity levels on hollow brick partitions, widespread in the European zone, denote significant damage in the tested specimen for 0.3 % interstorey drift and extensive damage for drift close to 1 %.

Preserving historic buildings is essential in the safeguard of the cultural heritage of any country. The need to carry out structural analyses by means of non-destructive methods has made structural monitoring ever more widespread in the diagnosis and control of historic buildings. The aim of this study is to introduce a standardized approach for the analysis of the data acquired from a monitoring system of historic buildings. This approach is based on the definition of specific reference quantities (extrapolated from the recorded time series) able to characterize the main features of the structural response and the preliminary identification of the order of magnitudes of these quantities. It is assumed that the recorded time series can be decomposed into two components: a periodical one depending on with the natural forces acting on the building and an unknown one related to the variation of the state of the structure. Exploiting the properties of periodic functions, one may identify these reference quantities, which are based on the year and the day variability and allow to monitor the evolution of the phenomena under observation. These reference quantities may be collected in a database and may become fundamental for comparing the response of similar buildings. This approach has been applied to the data obtained from the monitoring systems of two important Italian monuments: the Cathedral of Modena and the “Two Towers” of Bologna.

Hybrid simulation method in earthquake engineering, which combines physical testing and numerical simulation, was developed to evaluate seismic performance of civil structural systems. Thus, instead of constructing a full sized structural specimen, hybrid simulation allows researchers to build a complex experimental substructure tested experimentally while the relatively simple part of the structure is numerically simulated to economically obtain the full structural responses. Recently a versatile hybrid testing system was built at the Laboratory of Earthquake and Structural Simulation (LESS) at Western Michigan University. The major equipment consists of a seismic simulator (often called shake table), an actuator/reaction system and an advanced hybrid testing controller. Such testing system is capable of conducting various hybrid simulation experiments such as displacement-based pseudodynamic substructure testing as well as force-based real time dynamic hybrid testing. The benchmark scale testing system at LESS is particularly suitable for development of hybrid simulation techniques and earthquake engineering education and outreach activities. The development of this testing system including both hardware and software integration is presented. Example hybrid simulation methods that can be conducted using the developed testing system as well as its applications in the hybrid simulation method development of two NEESR projects are discussed.

The chapter is presenting a holistic framework for defining and measuring disaster resilience for a community at various scales. Seven dimensions characterizing community functionality have been identified and are represented by the acronym PEOPLES: Population and Demographics, Environmental/Ecosystem, Organized Governmental Services, Physical Infrastructure, Lifestyle and Community Competence, Economic Development, and Social-Cultural Capital. The proposed framework provides the basis for development of quantitative and qualitative models that measure continuously the functionality and resilience of communities against extreme events or disasters in any or a combination of the above-mentioned dimensions. Over the longer term, this framework will enable the development of geospatial and temporal decision-support software tools that help planners and other key decision makers and stakeholders to assess and enhance the resilience of their communities.

Earthquakes and extreme events in general cause direct and indirect economic effects on every major economic sector of a given community. These effects have grown in the last years due to the increasing interdependency of the infrastructures and make the community more vulnerable to natural and human-induced disruptive events. Therefore, there is need for metrics and models which are able to describe economic resilience, defined as the ability of a community affected by a disaster to resist at the shock and bounce back to the economy in normal operating conditions. Several attempts have been made in the past to achieve a better measurement and representation of the economic resilience and to find suitable metrics to help decision planning. The most popular methodologies are based on Computable General Equilibrium models (CGE) and Inoperability Input-Output models (IIM). In this study, we analyze these methods, showing advantages and limitations. Finally, a new method is proposed to evaluate economic resilience which is based on equilibrium growth models and compared with other approaches on a specific case study: the San Francisco Bay Area.

The chapter presents a hospital testbed which aims to help the earthquake engineering community moving another step toward the realization and implementation of resilience-based design strategies. An organizational model describing the response of the Hospital Emergency Department (ED) has been implemented using a discrete events simulation model (DES). The waiting time is the main parameter of response and it is used to evaluate the disaster resilience index of healthcare facilities. It has been considered for patients arriving in an Emergency Department after an earthquake, when no emergency plan is activated, to see the response of the hospital and observe its capacity of performing in emergency conditions. The hospital analyzed is the Mauriziano “Umberto I” Hospital, located in downtown Turin, in Italy. The DES model is an important tool in the hospital decision process either for the engineering profession or for the policy makers.

In the last couple of decades the use of energy dissipation devices for earthquake mitigation has gained much attention. Most research in that field, however, focused on frame buildings. This chapter is based on (Lavan, Earthq Eng Struct Dyn 41(12):1673–1692) and discusses the possibilities of using energy dissipation devices, or more specifically viscous dampers, in wall structures to result in viscously coupled shear walls (VCSWs). In turn, insight to their behaviour, as well as simplified approximate tools for their analysis and initial design are presented. While very simple to use, those rely on a strong theoretical background.

This paper presents a design method for calculating the supplemental damping of inelastic structures. This method is based on a balance of the mean energy dissipated per cycle by the structure and by the supplemental damping. The objective is to reduce the amplitude of the hysteretic cycles by adding the required amount of damping, so that the supplemental damping dissipates a large portion of the hysteretic energy with the reduced amplitude of vibration. The applicability of the method is shown in the design of the supplemental damping of an 8-story building highly irregular in plan and elevation. It is concluded that the use of a small amount of supplemental damping, optimally placed, considerably reduces the structural response. In this example, the added damping represents a damping ratio of 4.3 % and it was capable to dissipate more than the 80 % of the energy fed by the earthquake. The truss system of the supplemental damping took the majority of the inertial forces, realising the structure from these forces and reducing its overall response. For example, the mean reduction of the maximum interstory drifts and maximum story rotations were 46 % and 65 %, respectively. This showed that the energy-based method herein presented is a good method for designing the supplemental damping.

This paper investigates the planar rocking response of an array of free-standing columns capped with a freely supported rigid beam in an effort to explain the appreciable seismic stability of ancient free-standing columns which support heavy epistyles together with the even heavier frieze atop. Following a variational formulation the paper concludes to the remarkable result that the dynamic rocking response of an array of free-standing columns capped with a rigid beam is identical to the rocking response of a single free-standing column with the same slenderness; yet with larger size – that is a more stable configuration. Most importantly, the study shows that the heavier the freely supported cap-beam is (epistyles with frieze atop), the more stable is the rocking frame regardless the rise of the center of gravity of the cap-beam; concluding that top-heavy rocking frames are more stable than when they are top-light. This “counter intuitive” finding renders rocking isolation a most attractive alternative for the seismic protection of bridges with tall piers; while its potential implementation shall remove several of the concerns associated with the seismic connections of prefabricated bridges.

The correct estimation of the compressive concrete strength plays a key role in the evaluation of the structural performance of existing RC buildings. Both Italian (NTC 2008) and European (EC8) Standards define different levels of knowledge according to the number of tests carried out on a building. They indicate a reduced value to assume in the analysis, defined as the mean value of the compressive strength, divided by a confidence factor. However, such a procedure completely neglects the dispersion of the test data, as represented by the high values of the coefficient of variation. Instead, this aspect is treated by FEMA 356 where a limit to the coefficient of variation was introduced. In this paper, with reference to a significant number of existing buildings located in Tuscany, the coefficient of variation (cov) of concrete strength is evaluated and the frequency of high cov values is determined. The dispersion of compressive strength, obtained by SonReb method, using correlation curves calibrated ad hoc on single building, shows that increasing the number of data for each building the coefficient of variation does not necessary decrease. Moreover, the strength value considered by EC8 in the analysis for a single building, i.e. the mean value of compressive strength, is often not conservative, while the approach provided by FEMA 356 is safer since it dependent on the cov itself.

Mechanical properties of concrete can consistently affect the seismic performance of RC buildings. A proper determination of the concrete strength is therefore essential for a reliable modeling of the structure. The current European Technical Code, Eurocode 8, provides a criterion for the strength assumption related to the knowledge level of the structure, which does not take into account the variability of the strength. If the concrete strength is affected by a large variability, the conventional value suggested by Eurocode 8 can be not conservative, since it does not consider the increase in the demand due to a not homogeneous strength distribution and the reduced capacity of the weaker members. In this paper the concrete strength variability is investigated as a source of in-plan and in-elevation irregularity. The effects of the strength variability on the seismic response and performance are evaluated on a case study, that is a 4-storeys 3D framed building. The seismic response of the case study has been represented by performing a nonlinear static analysis, while the seismic performance has been measured in terms of chord rotation. Results obtained from the analysis have been compared with the Eurocode 8 previsions.

The Seismic Assessment of an asymmetric plan building is performed through an assemblage of recent Nonlinear Static Procedures (NSPs); some of them are extensions of known NSPs. Among these methods are included two multi-mode methods: Modal Pushover Analysis (MPA) and Improved Modal Pushover Analysis (iMPA); the Extended N2 which considers the higher modes effects in both plan and elevation; and the 3D Pushover wherein each step derives from a different known NSP in order to obtain the most reliable results.

The seismic response of an asymmetric plan building is studied considering both components of ground motion acting simultaneously. The seismic assessment of the building is performed in terms of pushover curves, top displacement ratios, lateral displacements profiles, interstorey drifts, normalized top displacements and shear forces. Such seismic quantities are compared with the results obtained by means of Nonlinear Dynamic Analysis (NDA).