The topic involves a wide coverage of timely issues on contemporary Earthquake Engineering focusing on the computational aspects in order to address engineering problems of great social and economic importance. It provides an insight on advanced methods and concepts for the design and analysis of structures against earthquake loading. Emphasis is given on the current state-of-the-art methods and concepts in computing methods and their application in engineering practice. Due to the devastating socioeconomic consequences of seismic events, the topic is of great scientific interest and is expected to be of valuable help to scientists and engineers.

Qatar University

Computational Mechanics Laboratory, Department of Civil Engineering Educators, School of Pedagogical & Technological Education

Frontiers in Built Environment

Earthquake Engineering

Computational Methods in Earthquake Engineering

A new optimization concept is introduced which involves the optimization of non-linear planar shear buildings by using gradients based on equivalent linear structures, instead of the traditional practice of calculating the gradients from the non-linear objective function. The optimization problem is formulated as an equivalent linear system of equations in which a target fundamental eigenfrequency and equal dissipated energy distribution within the storeys of the building are the components of the objective function. The concept is applied in a modified Newton–Raphson algorithm in order to find the optimum stiffness distribution of two representative linear or non-linear MDOF shear buildings, so that the distribution of viscously damped and hysteretically dissipated energy, respectively, over the structural height is uniform. A number of optimization results are presented in which the effect of the earthquake excitation, the critical modal damping ratio, and the normalized yield inter-storey drift limit on the optimum stiffness distributions is studied. Structural design based on the proposed approach is more rational and technically feasible compared to other optimization strategies (e.g., uniform ductility concept), whereas it is expected to provide increased protection against global collapse and loss of life during strong earthquake events. Finally, it is proven that the new optimization concept not only reduces running times by as much as 91% compared to the classical optimization algorithms but also can be applied in other optimization algorithms which use gradient information to proceed to the optimum point.

A new optimization concept is introduced which involves the optimization of non-linear planar shear buildings by using gradients based on equivalent linear structures, instead of the traditional practice of calculating the gradients from the non-linear objective function. The optimization problem is formulated as an equivalent linear system of equations in which a target fundamental eigenfrequency and equal dissipated energy distribution within the storeys of the building are the components of the objective function. The concept is applied in a modified Newton&#x2013;Raphson algorithm in order to find the optimum stiffness distribution of two representative linear or non-linear MDOF shear buildings, so that the distribution of viscously damped and hysteretically dissipated energy, respectively, over the structural height is uniform. A number of optimization results are presented in which the effect of the earthquake excitation, the critical modal damping ratio, and the normalized yield inter-storey drift limit on the optimum stiffness distributions is studied. Structural design based on the proposed approach is more rational and technically feasible compared to other optimization strategies (e.g., uniform ductility concept), whereas it is expected to provide increased protection against global collapse and loss of life during strong earthquake events. Finally, it is proven that the new optimization concept not only reduces running times by as much as 91% compared to the classical optimization algorithms but also can be applied in other optimization algorithms which use gradient information to proceed to the optimum point.

A New Energy-Based Structural Design Optimization Concept under Seismic Actions

An accurate evaluation of the non-linear behavior of masonry structural elements in existing buildings still represents a complex issue that rigorously requires non-linear finite element strategies difficult to apply to real large structures. Nevertheless, for the static and seismic assessment of existing structures, involving the contribution of masonry materials, engineers need reliable and efficient numerical tools, whose complexity and computational demand should be suitable for practical purposes. For these reasons, the formulation and the validation of simplified numerical strategies represent a very important issue in masonry computational research. In this paper, an innovative macroelement approach, developed by the authors in the last decade, is presented. The proposed macroelement formulation is based on different, plane and spatial, macroelements for the simulation of both the in-plane and out-of-plane behavior of masonry structures also in presence of masonry elements with curved geometry. The mechanical response of the adopted macroelement is governed by non-linear zero-thickness interfaces, whose calibration follows a straightforward fiber discretization, and the non-linear internal shear deformability is ruled by equivalence with a corresponding geometrically consistent homogenized medium. The approach can be considered as “parsimonious” since the kinematics of the adopted elements is controlled by very few degrees of freedom, if compared to a corresponding discretization performed by using non-linear finite element method strategies. This innovative discrete element strategy has been implemented in two user-oriented software codes 3DMacro (Caliò et al., <xref ref-type="bibr" rid="B19">2012b</xref>) and HiStrA (Historical Structures Analysis) (Caliò et al., <xref ref-type="bibr" rid="B16">2015</xref>), which simplify the modeling of buildings and historical structures by means of several wizard generation tools and input/output facilities. The proposed approach, that represents a powerful tool for the structural assessment of structures in which the masonry plays a key role, is here validated against experimental results involving typical masonry monumental substructural elements and numerical results involving real-scale structures.

An accurate evaluation of the non-linear behavior of masonry structural elements in existing buildings still represents a complex issue that rigorously requires non-linear finite element strategies difficult to apply to real large structures. Nevertheless, for the static and seismic assessment of existing structures, involving the contribution of masonry materials, engineers need reliable and efficient numerical tools, whose complexity and computational demand should be suitable for practical purposes. For these reasons, the formulation and the validation of simplified numerical strategies represent a very important issue in masonry computational research. In this paper, an innovative macroelement approach, developed by the authors in the last decade, is presented. The proposed macroelement formulation is based on different, plane and spatial, macroelements for the simulation of both the in-plane and out-of-plane behavior of masonry structures also in presence of masonry elements with curved geometry. The mechanical response of the adopted macroelement is governed by non-linear zero-thickness interfaces, whose calibration follows a straightforward fiber discretization, and the non-linear internal shear deformability is ruled by equivalence with a corresponding geometrically consistent homogenized medium. The approach can be considered as “parsimonious” since the kinematics of the adopted elements is controlled by very few degrees of freedom, if compared to a corresponding discretization performed by using non-linear finite element method strategies. This innovative discrete element strategy has been implemented in two user-oriented software codes 3DMacro (<a href="#B19">Caliò et al., 2012b</a>) and HiStrA (Historical Structures Analysis) (<a href="#B16">Caliò et al., 2015</a>), which simplify the modeling of buildings and historical structures by means of several wizard generation tools and input/output facilities. The proposed approach, that represents a powerful tool for the structural assessment of structures in which the masonry plays a key role, is here validated against experimental results involving typical masonry monumental substructural elements and numerical results involving real-scale structures.

New Frontiers on Seismic Modeling of Masonry Structures

At present, many of the historic masonry structures in the most important seismic zone of Argentina present damages due to the actions to which they have been subjected. Therefore, it is necessary to study the behavior of walls of ceramic masonry of great thickness. This work presents the comparison between the results obtained from the numerical simulation of ceramic masonry walls subjected to compression and shear strength, through the use of interaction surfaces using commercial software ABAQUS, versus the data obtained from physical–mechanical tests performed in 1:1 scale on the laboratory of the CeReDeTeC. Tested walls were made of solid masonry bricks with cement and lime mortar of 26 and 45 cm thick, respectively. These were compared with the obtained results by the analysis software, considering mortar joints as interaction surfaces, trying to obtain the modeling that represents the behavior of the union of the elements mortar and masonry. The conclusions of the work detail the strengths and weaknesses of this type of masonry modeling and the desirability of developing models that allow to simulate the behavior of great thickness masonry.

At present, many of the historic masonry structures in the most important seismic zone of Argentina present damages due to the actions to which they have been subjected. Therefore, it is necessary to study the behavior of walls of ceramic masonry of great thickness. This work presents the comparison between the results obtained from the numerical simulation of ceramic masonry walls subjected to compression and shear strength, through the use of interaction surfaces using commercial software ABAQUS, versus the data obtained from physical&#x2013;mechanical tests performed in 1:1 scale on the laboratory of the CeReDeTeC. Tested walls were made of solid masonry bricks with cement and lime mortar of 26 and 45 cm thick, respectively. These were compared with the obtained results by the analysis software, considering mortar joints as interaction surfaces, trying to obtain the modeling that represents the behavior of the union of the elements mortar and masonry. The conclusions of the work detail the strengths and weaknesses of this type of masonry modeling and the desirability of developing models that allow to simulate the behavior of great thickness masonry.

Surface Interaction Model for Great Thickness Masonry

In this paper, the authors summarize the results of a parametric study devoted to evaluate the seismic behavior of low to medium rise regular special moment-resisting steel frames with hysteretic energy dissipation devices mounted on chevron steel bracing. For that purpose, 270 different building models were designed considering typical story heights and bay widths used in Mexican practice. The parameters under study were (1) number of stories: 5, 10, 15, 20, and 25, (2) elastic stiffness ratios (α) between the moment frame system and the whole structure (frame-bracing-hysteretic device system): α = 0.25, 0.50, and 0.75, (3) different elastic stiffness balances (β) between the hysteretic device and the supporting braces: β = 0.25, 0.50, and 0.75, (4) post- to pre-yielding stiffness ratios (K2/KELD) for the hysteretic devices of 0.0 (elastic-perfectly plastic), 0.03, and 0.05, and (5) two angles of inclination of the chevron braces with respect to the horizontal axis (θ): 40° and 45°. From the results obtained in this study, optimal stiffness balances α and β are defined to obtain a suitable mechanism where the hysteretic devices yield first and develop their maximum local displacement ductility μ, whereas incipient yielding is only formed at beam ends of the moment frame. Observations are done with respect to: (a) the global ductility capacity for the structure and its relationships with the local displacement ductility capacity for the hysteretic devices for a given combination of α, β, K2/KELD, and θ and (b) overstrength factors (Ω) for design purposes.

In this paper, the authors summarize the results of a parametric study devoted to evaluate the seismic behavior of low to medium rise regular special moment-resisting steel frames with hysteretic energy dissipation devices mounted on chevron steel bracing. For that purpose, 270 different building models were designed considering typical story heights and bay widths used in Mexican practice. The parameters under study were (1) number of stories: 5, 10, 15, 20, and 25, (2) elastic stiffness ratios (α) between the moment frame system and the whole structure (frame-bracing-hysteretic device system): α = 0.25, 0.50, and 0.75, (3) different elastic stiffness balances (β) between the hysteretic device and the supporting braces: β = 0.25, 0.50, and 0.75, (4) post- to pre-yielding stiffness ratios (K2/KELD) for the hysteretic devices of 0.0 (elastic-perfectly plastic), 0.03, and 0.05, and (5) two angles of inclination of the chevron braces with respect to the horizontal axis (θ): 40° and 45°. From the results obtained in this study, optimal stiffness balances α and β are defined to obtain a suitable mechanism where the hysteretic devices yield first and develop their maximum local displacement ductility μ, whereas incipient yielding is only formed at beam ends of the moment frame. Observations are done with respect to: (a) the global ductility capacity for the structure and its relationships with the local displacement ductility capacity for the hysteretic devices for a given combination of α, β, K2/KELD, and θ and (b) overstrength factors (Ω) for design purposes.

Code-Oriented Global Design Parameters for Moment-Resisting Steel Frames with Metallic Structural Fuses

We propose a circular path and linear momentum method for the seismic response analysis of vehicles. This method considers the momentum induced by earthquake excitation and applies the concept of centripetal force acting laterally on the vehicle in addition to longitudinal forces. This method is valid for vehicles at rest as well as those moving at a range of speeds. The vertical responses are calculated using a quarter vehicle model. We also calculate the translational motion of the vehicle using a model with six degrees of freedom. Three vehicle types (car, bus, and truck) were used in the analysis. We compared the result with analysis of the response of a shaking vehicle from video footage recorded during the Gorkha earthquake. We used the input ground motion from 10 large earthquakes of moment magnitudes 6.7–9.0. All three components of the ground motion were used in the analysis. Vehicles at rest and moving at various speeds were analyzed. The lateral and longitudinal responses of the vehicles were calculated for different vehicle speeds ranging from 0 to 30.0 m/s, PGA excitations and orientations of the vehicle.

We propose a circular path and linear momentum method for the seismic response analysis of vehicles. This method considers the momentum induced by earthquake excitation and applies the concept of centripetal force acting laterally on the vehicle in addition to longitudinal forces. This method is valid for vehicles at rest as well as those moving at a range of speeds. The vertical responses are calculated using a quarter vehicle model. We also calculate the translational motion of the vehicle using a model with six degrees of freedom. Three vehicle types (car, bus, and truck) were used in the analysis. We compared the result with analysis of the response of a shaking vehicle from video footage recorded during the Gorkha earthquake. We used the input ground motion from 10 large earthquakes of moment magnitudes 6.7&#x2013;9.0. All three components of the ground motion were used in the analysis. Vehicles at rest and moving at various speeds were analyzed. The lateral and longitudinal responses of the vehicles were calculated for different vehicle speeds ranging from 0 to 30.0 m/s, PGA excitations and orientations of the vehicle.

Circular Path and Linear Momentum Method for Seismic Response Analysis of Vehicles

During strong earthquake excitations, base-isolated buildings may collide, either with the surrounding moat wall or with adjacent buildings if the available clearance is exceeded. This undesirable possibility has been recently investigated by several researchers, adopting various types of force-based impact models. Evidently, an important issue that arises regarding such numerical studies is the way of taking into account potential impacts. This paper parametrically investigates the effects of impact modeling characteristics on the computed overall peak response of a base-isolated building that experiences structural pounding. Specifically, the Kelvin–Voigt impact model and various other modifications of this linear viscoelastic impact model are considered in the conducted analyses. In order to efficiently conduct this investigation, a specially developed software is used. The results indicate that the excitation’s and isolator’s characteristics do not significantly influence the variation in the normalized peak response of the superstructure. In contrast, the impact parameters can have a significant effect on the superstructures’ peak accelerations with overestimations up to 70%. In general, the normalized peak response ratios of the interstory drifts tend to increase as the available seismic gap and the coefficient of restitution decrease, although the magnitude of the deviations is within 5%, which can be considered insignificant.

During strong earthquake excitations, base-isolated buildings may collide, either with the surrounding moat wall or with adjacent buildings if the available clearance is exceeded. This undesirable possibility has been recently investigated by several researchers, adopting various types of force-based impact models. Evidently, an important issue that arises regarding such numerical studies is the way of taking into account potential impacts. This paper parametrically investigates the effects of impact modeling characteristics on the computed overall peak response of a base-isolated building that experiences structural pounding. Specifically, the Kelvin&#x2013;Voigt impact model and various other modifications of this linear viscoelastic impact model are considered in the conducted analyses. In order to efficiently conduct this investigation, a specially developed software is used. The results indicate that the excitation&#x2019;s and isolator&#x2019;s characteristics do not significantly influence the variation in the normalized peak response of the superstructure. In contrast, the impact parameters can have a significant effect on the superstructures&#x2019; peak accelerations with overestimations up to 70%. In general, the normalized peak response ratios of the interstory drifts tend to increase as the available seismic gap and the coefficient of restitution decrease, although the magnitude of the deviations is within 5%, which can be considered insignificant.