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This is the third book in a series on Computational Methods in Earthquake Engineering. The purpose of this volume is to bring together the scientific communities of Computational Mechanics and Structural Dynamics, offering a wide coverage of timely issues on contemporary Earthquake Engineering.

This volume will facilitate the exchange of ideas in topics of mutual interest and can serve as a platform for establishing links between research groups with complementary activities. The computational aspects are emphasized in order to address difficult engineering problems of great social and economic importance.



Numerical Modeling Aspects of Buried Pipeline—Fault Crossing

Onshore buried steel pipelines transporting oil and gas play a major role in the energy supply chain. Hence, when seismic areas are transversed, fault crossing might be inevitable, which may heavily endanger the pipeline integrity. Thus, the design of buried pipelines at fault crossing remains a research topic of great interest both for the industry and the academia. Experimental, analytical and numerical approaches are used for that purpose. In this chapter, the numerical modeling of pipelines subjected to faulting is addressed and the advantages and disadvantages of the available numerical approaches are highlighted. The impact of fault type on the pipeline mechanical behavior is investigated and numerical considerations, such as the geometrical nonlinearity, the ovalization and the internal pressure are evaluated using a simple, well-established and reliable numerical approach. The outcome of this study provides useful information and guidelines to practicing engineers for the analysis and design of buried pipelines at fault crossings.

Vasileios E. Melissianos, Charis J. Gantes

Determination of the Parameters of the Directivity Pulse Embedded in Near-Fault Ground Motions and Its Effect on Structural Response

Near-fault ground motions are affected by directivity phenomena, which produce important velocity pulses, mostly associated with the normal to the fault direction. Directivity pulses amplify the long period coherent component of the ground motions and are explicitly apparent in the velocity and the displacement time histories and the related response spectra. A number of methods are commonly used for the identification of the parameters of the velocity pulses, mainly their period and amplitude. Also, several mathematical expressions have been proposed for their mathematical representation, which vary from simple functions to more complicated wavelets. A very efficient wavelet is the one proposed by Mavroeidis and Papageorgiou (M&P), which, beyond the period and the amplitude, uses additional parameters related to the total duration and the phase shift of the pulse. In this chapter, a recently proposed new method is presented, which allows the explicit determination of the parameters of the pulse contained in pulse-like records. The M&P wavelet is used for the mathematical representation of the pulse but the proposed methodology can be easily modified to cover other types of wavelets as well. First, the period of the pulse is determined from the peak of the S d × S ν product spectrum, a new concept defined as the product of the velocity and the displacement response spectra. The remaining parameters of the M&P wavelet are derived from the targeted response spectrum of the ground motion applying a relationship that is established between the Cumulative Absolute Displacement (CAD) of a wavelet and its peak spectral amplitude. The method follows a well-defined procedure that can be easily implemented in a computer code for the automatic determination of the pulse parameters of a given ground motion. In the last part of the chapter, the identified pulses, inherent in a wide set of ground motions, are used to study the effect of directivity pulses on the nonlinear response of SDOF structures. It is shown that, in a wide range of periods, the seismic behavior is dominated by the presence of the pulse, since the corresponding M&P wavelet alone can capture quite satisfactorily the nonlinear response.

Petros Mimoglou, Ioannis N. Psycharis, Ioannis M. Taflampas

Numerical Simulation of Liquid Sloshing in Tanks

Sloshing waves induced by long-period components of earthquake ground motions may generate high magnitude hydrodynamic forces on liquid storage tanks. Past earthquake experience has shown that the forces generated by the sloshing waves may affect the overall safety of tanks by causing extensive damage on the tank wall and roof. Therefore, the accurate description of these forces is vital for reducing the potential risk of tank failure during an earthquake. Appropriate numerical simulation methods can be used to predict response of liquid storage tanks, as they offer a concise way of accurate consideration of all nonlinearities associated with fluid, tank and soil response in the same model. This chapter is, therefore, devoted to the Finite Element (FE) analysis of the sloshing phenomenon occurring in liquid storage tanks under external excitations. The governing equations for the fluid and structure and their solution methodologies are clarified. Current nonlinear FE modelling strategies for interactions between liquid, tank and soil are presented in great detail. The presented numerical modelling schemes are applied to analyze sloshing response of rectangular and cylindrical tanks when subjected to external excitations. Strong correlation between experimental and numerical results is obtained in terms of sloshing wave height for a rectangular tank model under resonant harmonic motion. Numerical simulations on cylindrical tanks have indicated that tank material, boundary conditions at the base and the presence of a second horizontal component in addition to one horizontal component have negligible effect on the sloshing response of cylindrical tanks when subjected to earthquake motions.

Zuhal Ozdemir, Yasin M. Fahjan, Mhamed Souli

Seismic Analysis of Structural Systems Subjected to Fully Non-stationary Artificial Accelerograms

In seismic engineering, the earthquake-induced ground motion is generally represented in the form of pseudo-acceleration or displacement response spectra. There are, however, situations in which the response spectrum is not considered appropriate, and a fully dynamic analysis is required. In this case, the most effective approach is to define artificial spectrum-compatible stationary accelerograms, which are generated to match the target elastic response spectrum. So a Power Spectral Density (PSD) function is derived from the response spectrum. However, the above approach possesses the drawback that the artificial accelerograms do not manifest the variability in time and in frequency observed from the analysis of real earthquakes. Indeed, the recorded accelerograms can be considered sample of a fully non-stationary process. In this study a procedure based on the analysis of a set of accelerograms recorded in a chosen site to take into account their time and frequency variability is described. In particular the generation of artificial fully non-stationary accelerograms is performed in three steps. In the first step the spectrum-compatible PSD function, in the hypothesis of stationary excitations, is derived. In the second step the spectrum-compatible Evolutionary Power Spectral Density (EPSD) function is obtained by an iterative procedure to improve the match with the target response spectrum starting from the PSD function, once a time-frequency modulating function is chosen. In the third step the artificial accelerograms are generated by the well-known Shinozuka and Jan (J Sound Vib 25:111–128, 1972) formula and deterministic analyses can be performed to evaluate the structural response. Once the EPSD spectrum-compatible function is derived, a method recently proposed by the authors (Muscolino and Alderucci in Probab Eng Mech 40:75–89, 2015), is adopted to evaluate the EPSD response function of linear structural systems subjected to fully non-stationary excitations by very handy explicit closed-form.

Giuseppe Muscolino, Tiziana Alderucci

Elastic and Inelastic Analysis of Frames with a Force-Based Higher-Order 3D Beam Element Accounting for Axial-Flexural-Shear-Torsional Interaction

When one of the dimensions of a structural member is not clearly larger than the two orthogonal ones, engineers are usually compelled to simulate it with refined meshes of shell or solid finite elements that typically impose a large computational burden. The alternative use of classical beam theories, either based on Euler-Bernoulli or Timoshenko’s assumptions, will in general not accurately capture important deformation mechanisms such as shear, warping, distortion, flexural-shear-torsional interaction, etc. However, higher-order beam theories are a still largely disregarded avenue that requires an acceptable computational demand and simultaneously has the potential to account for the above mentioned deformation mechanisms, some of which can also be relevant in slender members. This chapter starts by recalling the main theoretical features of a recently developed higher-order beam element, which was combined for the first time with a force-based formulation. The latter strictly verifies the advanced form of beam equilibrium expressed in the governing differential equations. The main innovative theoretical aspects of the proposed element are accompanied by an illustrative application to members with linear elastic behaviour. In particular, the ability of the model to simulate the effect of different boundary conditions on the response of an axially loaded member is addressed, which is then followed by an application to a case where flexural-shear-torsional interaction takes place. The beam performance is assessed by comparison against refined solid finite element analyses, classical beam theory results, and approximate numerical solutions. Finally, with a view to a future extension to earthquake engineering, an example of the element behaviour with inelastic response is also carried out.

João P. Almeida, António A. Correia, Rui Pinho

Improved Method for the Calculation of Plastic Rotation of Moment-Resisting Framed Structures for Nonlinear Static and Dynamic Analysis

Given the vast advancements in computing power in the last several decades, nonlinear dynamic analysis has gained wide acceptance by practicing engineers as a useful way of assessing and improving the seismic performance of structures. Nonlinear structural analysis software packages give engineers the ability to directly model nonlinear component behavior in detail, resulting in improved understanding of how a building will respond under strong earthquake shaking. One key component, in particular, for understanding the behavior of moment-resisting frames is the plastic rotation of the flexural hinges. Performance-based standards typically use plastic rotation as the primary parameter for defining the acceptance criteria in moment-resisting frames. Since plastic rotation is a key parameter in the seismic damage assessment, the concept as well as the method to calculate this quantity must be understood completely. Though engineers rely on the plastic rotation output from seismic structural analysis software packages to determine acceptable performance, the actual calculation methods used in achieving such plastic rotation quantities usually lay within a so-called “black box”. Based on the outputs obtained from most structural analysis software packages, it can be shown that running an algorithm considering material nonlinearity by itself will produce reasonably accurate results. Moreover, separately running an algorithm considering geometric nonlinearity also can produce accurate results. However, when material nonlinearity is combined with geometric nonlinearity in an analysis, obtaining accurate results or even stable solutions is more difficult. The coupling effect between the two nonlinearities can significantly affect the global response and the local plastic rotation obtained from the analysis and therefore needs to be verified through some analytical means. Yet, the verification process is difficult because a robust analytical framework for calculating plastic rotation is currently unavailable and urgently needed. In view of this gap, an improved analytical approach based on small displacement theory is derived to calculate the plastic rotations of plastic hinges at various locations of moment-resisting frames. Both static and dynamic analysis with nonlinear geometric effects will be incorporated in the derivation. Here the element stiffness matrices are first rigorously derived using a member with plastic hinges in compression, and therefore the coupling of geometric and material nonlinearity effects is included from the beginning of the derivation. Additionally, plastic rotation is handled explicitly by considering this rotation as an additional nonlinear degree-of-freedom. Numerical simulation is performed to calculate the nonlinear static and dynamic responses of simple benchmark models subjected to seismic excitations. Results are compared with various software packages to demonstrate the feasibility of the proposed method in light of the output results among software packages in calculating plastic rotations.

Kevin K.F. Wong, Matthew S. Speicher

Seismic Demand on Acceleration-Sensitive Nonstructural Components

Nonstructural components should be subjected to a careful and rational seismic design, in order to reduce economic loss and to avoid threats to the life safety, as well as what concerns structural elements. The design of nonstructural components is based on the evaluation of the maximum inertial force, which is related to the floor spectral accelerations. The question arises as to whether the European Building Code, i.e. Eurocode 8, is able to predict actual floor response spectral accelerations occurring in structures designed according to its provisions. A parametric study is therefore conducted on five RC frame structures designed according to Eurocode 8. It shows that Eurocode formulation for the evaluation of the seismic demand on nonstructural components does not well fit the analytical results for a wide range of periods, particularly in the vicinity of the higher mode periods of vibration of the reference structures. The inconsistent approach of current European building codes to the design of nonstructural components is also highlighted. For this reason a parametric study is conducted in order to evaluate the seismic demand on light acceleration-sensitive nonstructural components caused by frequent earthquakes. The above mentioned RC frame structures are therefore subjected to a set of frequent earthquakes, i.e. 63 % probability of exceedance in 50 years. A novel formulation is proposed for an easy implementation in future building codes based on the actual Eurocode provisions.

Gennaro Magliulo, Crescenzo Petrone, Gaetano Manfredi

Design of RC Sections with Single Reinforcement According to EC2-1-1 and the Rectangular Stress Distribution

Nowadays, the design of concrete structures in Europe is governed by the application of Eurocode 2 (EC2). In particular, EC2—Part 1-1 deals with the general rules and the rules for concrete buildings. An important aspect of the design is specifying the necessary tensile (and compressive, if needed) steel reinforcement required for a Reinforced Concrete (RC) section. In this study we take into account the equivalent rectangular stress distribution for concrete and the bilinear stress-strain relation with a horizontal top branch for steel. This chapter presents three detailed methodologies for the design of rectangular cross sections with tensile reinforcement, covering all concrete classes, from C12/15 up to C90/105. The purpose of the design is to calculate the necessary tensile steel reinforcement. The first methodology provides analytic formulas and an algorithmic procedure that can be easily implemented in any programming language. The second methodology is based on design tables that are provided in Appendix A, requiring less calculations. The third methodology provides again analytic formulas that can replace the use of tables and even be used to reproduce the design tables. Apart from the direct problem, the inverse problem is also addressed, where the steel reinforcement is given and the purpose is to find the maximum bending moment that the section can withstand, given also the value and position of the axial force. For each case analytic relations are extracted in detail with a step-by-step procedure, the relevant assumptions are highlighted and results for four different cross section design examples are presented.

Vagelis Plevris, George Papazafeiropoulos

Multi-storey Structures with Seismic Isolation at Storey-Levels

Through increasing international research and application activities in the last years, seismic isolation has proven to be an innovative passive control technique in the area of performance-based design of buildings. Seismic isolation is principally based on the incorporation of flexible isolators at the base of low-rise buildings in order to shift the fundamental period outside of the dangerous for resonance, range of periods. In extending the concept of base isolation, the present contribution refers to the control of multi-storey structures under earthquake actions by means of introducing seismic isolation at different elevations of the structure. Thus, the structural response is influenced decisively by the vertically distributed seismic isolation, which at the respective storey-levels is alone capable of controlling the partial and overall stiffness, the force transmission and the energy dissipation process of the respective dynamic adaptable system. During strong earthquakes the effectiveness of the system in further enlarging the period of the building, compared to the classical method of seismic isolation at a unique level, is achieved, most often with decreased inter-storey deflections, and without introducing extensive displacements at the building base, which are often limited by practical constraints. The effectiveness of the proposed control system is investigated in parametric studies, in the time-history range, for a 6-storey building under ten selected earthquakes of the Greek-Mediterranean region, scaled to a maximum ground acceleration of 0.25 g. Most effective vertical distribution of seismic isolation at various storey-levels is proposed, based on the earthquake, structural and isolation characteristics used in the numerical study.

Marios C. Phocas, George Pamboris

Integration Step Size and Its Adequate Selection in Analysis of Structural Systems Against Earthquakes

True behaviour of an arbitrary structural system is dynamic and nonlinear. To analyze this behaviour in many real cases, e.g. structures in regions under high seismic risk, a versatile approach is to discretize the mathematical model in space, and use direct time integration to solve the resulting initial value problem. Besides versatility in application, simplicity of implementation is an advantage of direct time integration, while, inexactness of the response and the high computational cost are the weak points. Considering the sizes of the integration steps as the main parameters of time integration, and concentrating on transient analysis against ground acceleration, this chapter presents discussions on: (1)the role of integration step size in time integration analysis, specifically, from the points of view of accuracy and computational cost,(2)conventionally accepted comments, codes/standards’ regulations, and some modern methods for assigning adequate values to the integration step sizes in constant or adaptive time integration,and concludes with some challenges on time integration analysis and integration step size selection in structural dynamics and earthquake engineering.

Aram Soroushian

Seismic Fragility Analysis of Faulty Smart Structures

In this chapter, seismic vulnerability of smart structures is assessed using fragility analysis framework. The fragility analysis framework is effective to evaluate the performance and the vulnerability of structures under a variety of earthquake loads. To demonstrate the effectiveness of the seismic fragility analysis framework, a three-story steel frame building employing the nonlinear smart damping system is selected as a case study structure. To investigate the impact of sensor failures, various sensor damage case scenarios are considered. The seismic capacity of the smart building is determined based on the typical structural performance levels used in the literature. The unknown parameters for the seismic demand models are estimated using a Bayesian updating algorithm. Finally, the fragility curves of the smart structures under a variety of sensor damage cases are compared. It is proved from the extensive simulations that the proposed seismic fragility analysis framework is very effective in estimating the control performance of smart structures with sensor faults.

Yeesock Kim, Jong-Wha Bai

Actuating Connections for Substructure Damage Identification and Health Monitoring

Vibration-based damage detection and localization are often performed aiming to relate modal analysis’ results with appropriate metrics that express structural damages. The problem of structural damage identification is generally formulated as an inverse problem aiming to detect changes encountered on the global stiffness matrix of the structure’s model. In most cases, the measured quantities are less than the damage parameters to be identified, thus an infinite number of possible damage configurations is expected to satisfy the measurements. Therefore, damage identification problems are often proven to be ill-conditioned. In addition, as in situ measurements are interpreted by a computer model, a number of uncertainties play an important role in the success of the identification procedure. The class of uncertainties consist of model, discretization, material and measurement errors. Furthermore, a large number of parameters need to be identified in order to assess arbitrary damage scenario and time consuming structure monitoring need to be implemented. In the majority of the developed methods the tendency is to use measurements from sensors while the vibrations are caused either by random (e.g. wind, earthquake etc.) causes or from force actuators in one or more points of the structure. In this work the implementation of actuator connections that divide a structure in several substructures is proposed. These connections can be installed on the structure during construction or retrofit. As it will be demonstrated, these connections can be controlled and excite each substructure separately and record its fundamental frequencies. In this way, each substructure can be monitored in arbitrary time while the complexity and often ill-conditioning of damage localization for large structures can be drastically reduced.

Stavros Chatzieleftheriou, Nikos D. Lagaros

Fuzzy Neural Network Based Response of Uncertain System Subject to Earthquake Motions

Earthquakes are one of the most destructive natural phenomena which consist of rapid vibrations of rock near the earth’s surface. Because of their unpredictable occurrence and enormous capacity of destruction, they have brought fear to mankind since ancient times. Usually the earthquake acceleration is noted from the equipment in crisp or exact form. But in actual practice those data may not be obtained exactly at each time step, rather those may be with some error. So those records at each time step are assumed here as fuzzy. Using those fuzzy acceleration data, the structural response is found. The primary aim of the present study is to model Fuzzy Neural Network (FNN) and to compute structural response of a structural system by training the model for Indian earthquakes at Chamoli and Uttarkashi using fuzzified ground motion data. The neural network is first trained here for real fuzzy earthquake data. The trained FNN architecture is then used to simulate earthquakes by feeding various intensities and it is found that the predicted responses given by FNN model are good for practical purposes. The above may give an idea about the safety of the structural system in case of future earthquakes. The present chapter demonstrates the procedure for an example case of a simple shear structure (SDOF) but the procedure may easily be generalized for higher storey structures as well.

S. Chakraverty, Deepti Moyi Sahoo

Smart Control of Seismically Excited Highway Bridges

This chapter proposes a novel smart fuzzy control algorithm for mitigation of dynamic responses of seismically excited bridge structures equipped with control devices. The smart fuzzy controller is developed through the combination of discrete wavelet transform, backpropagation neural networks, and Takagi-Sugeno fuzzy model. To demonstrate the effectiveness of the proposed smart fuzzy controller, it is tested on a highway bridge equipped with magneto rheological (MR) dampers. It controls the smart dampers installed on the abutments of the highway bridge structure. The 1940 El-Centro and Kobe earthquakes are used as disturbance signals. It is demonstrated that the smart fuzzy controller is effective in reducing the structural responses of the highway bridge under a variety of seismic excitations.

Yeesock Kim, Aniket Anil Mahajan

A Real-Time Emergency Inspection Scheduling Tool Following a Seismic Event

Emergency infrastructure inspections are of the essence after a seismic event as a carefully planned inspection in the first and most critical hours can reduce the effects of such an event. Metaheuristics and more specifically nature inspired algorithms have been used in many hard combinatorial engineering problems with significant success. The success of such algorithms has attracted the interest of many researchers leading to an increased interest regarding metaheuristics. In the present literature many new and sophisticated algorithms have been proposed with interesting performance characteristics. On the other hand, up to date developments in the field of computer hardware have also had a significant influence on algorithm design. The increased computational abilities that are available to researchers through parallel programming have opened new horizons in architecture of algorithms. In this work, a methodology for real-time planning of emergency inspections of urban areas is presented. This methodology is based on two nature inspired algorithms, Harmony Search Algorithm (HS) and Ant Colony Optimization (ACO). HS is used for dividing the area into smaller blocks while ACO is used for defining optimal routes inside each created block. The proposed approach is evaluated in an actual city in Greece, Thessaloniki.

Nikos Ath. Kallioras, Nikos D. Lagaros
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