Rocking Behavior of Irregular Free-Standing Objects Subjected to Earthquake Motion

Free-standing rigid objects and structures are dominantly found to exhibit rocking behavior and can be vulnerable to overturning during an earthquake as demonstrated by numerous past earthquake events. Such objects are typically considered to be displacement sensitive with their rocking response being well presented by the Peak Displacement Demand (PDD) parameter of the supporting floor’s motion. This in turn can be directly related to an object’s width (along the direction of motion) for assessing its vulnerability to overturn. Such findings have been sufficiently justified by refined dynamic analysis supported by experimental evaluations which were based on rigid blocks with uniform geometric format (i.e., regular in their mass distribution). However, vulnerable rocking objects can be asymmetric and accordingly their sensitivity to floor displacement cannot be directly related to their width. The key parameter which defines irregular objects’ response to rocking motion is represented by the degree of eccentricity of their center of mass. In this study, the well-known rocking equation of motion is reconfigured and devised to model the rocking responses for 280 irregular objects undergoing eight earthquake motions which included artificial and recorded earthquakes. Analytical results obtained from solving the adjusted equation of motion were evaluated with sophisticated finite element (FE) models simulating the 280 irregular cases. This experimentally validated FE modeling approach was found to be time- and cost-effective for understating the rocking behavior of asymmetric objects as well as clarifying an interesting relationship between the object’s damping level and the condition of the supporting base (i.e., whether being provided with supports at the points of rotation or not). The rocking response of irregular objects was found to be highly influenced by the level of eccentricity of the object when excited by motions with high displacement amplitudes, while such influence was not found noticeable by wider objects. Based on the developed trends between the maximum top displacement of irregular objects and the PDD, an expression for estimating the rocking amplitudes is proposed which is a function of the object’s eccentricity.     

Contact Dynamics of Masonry Block Structures Using Mathematical Programming

A simple variational formulation for contact dynamics is adopted to investigate the dynamic behavior of planar masonry block structures subjected to seismic events. The numerical model is a two-dimensional assemblage of rigid blocks interacting at potential contact points located at the vertices of the interfaces. A no-tension and associative frictional behavior with infinite compressive strength is considered for joints. The dynamic contact problem is formulated as a quadratic programming problem (QP) and an iterative procedure is implemented for time integration. Applications to analytical and numerical case studies are presented for validation. Comparisons with the experimental results of a masonry wall under free rocking motion and of a small scale panel with opening subjected to in-plane loads are also carried out to evaluate the accuracy and the computational efficiency of the formulation adopted.     

Investigation of the Seismic Behavior of a Historical Masonry Minaret Considering the Interaction with Surrounding Structures

This study examines the seismic behavior of the minaret of the well-known historical structure “Sultan Ahmed Mosque” under strong earthquake motion. Despite their slenderness and height, minarets are towers with well-established earthquake resistance. In general, these structures were constructed adjacent to the main structure and/or its components. Hence, it is expected that the dynamic behavior of the minarets is influenced by the dynamic characteristics of the adjacent structures as well as the contact conditions. In the presented study, the dynamic behavior of the M6 minaret of the Sultan Ahmed Mosque, which is in contact with the portico that surrounds the courtyard of the mosque, is considered. Ambient vibration tests were conducted on site in order to identify the individual and coupled vibration modes of the minaret and the portico. A finite/discrete model was developed and seismic analysis was carried out. The comparative study reveals considerable differences in responses of different models under strong and very strong earthquake motion.     

Rocking of Non-symmetric Rigid Blocks in Buildings Considering Effects Associated with Dynamic Soil-Structure Interaction

A dynamic model for the estimation of the rocking and/or overturning response of a free-standing non-symmetric rigid block considering rotational and horizontal excitation is proposed. The block is situated at different levels of a building with flexible base subjected to earthquakes. Base flexibility introduces the rotational component of the excitation due to dynamic soil-structure interaction (DSSI). The model is used to assess the influence of the dynamic soil-structure interaction on the behavior of the block. An illustrative example of the proposed model for non-symmetric rigid blocks in 5-, 10-, and 15-story buildings located in soft soils considering earthquakes from different seismic sources is presented. Results show that it is important to consider kinematic effects as well as inertial effects of DSSI in the dynamic response of contents. The influence of base flexibility depends on the change of spectral intensities associated to the increase of the building structural period and is larger for higher building levels.     

Evaluation of Side Boundary Effects on Dynamic Numerical Modeling for Centrifugal Model Tests

Four different boundary conditions consisting of fixed nodes, motion of roller only in the z or the x direction, and equivalent motion of two side boundaries were applied with a finite element code to simulate seismic behavior of two foundation conditions consisting of dry loose and dense sands. Comparing numerical results with physical model tests indicates that data obtained from the finite element code when considering soil nonlinearity with a sand model based on the tij concept have acceptable agreements with those from dynamic centrifuge tests regardless of the boundary conditions. The results from the boundary conditions of roller in the x direction and equivalent motion of two side boundaries agree well with the experimental data in wave peaks. The two side boundary conditions also keep the ground middle undisturbed and provide the results that are similar to those obtained from the wave amplification experimental data. For numerical simulations of centrifuge model tests, the side boundary condition with roller in the x direction is recommended because of low computation time and high simulation quality.     

Energy-Based Similitude for Shake Table Testing of Scale Woodframe Structures

The development and refinement of performance seismic design is underway, thus understanding the dynamic behavior of woodframe structures has become critical. Although several full scale shake table tests have been performed, many details associated with load transfer/path and behavior of varying systems remains to be investigated. This short technical communication presents the results of a study whose objective was to scale a woodframe structure to one-half scale using similitude theory, something that has eluded researchers to date. It is widely felt that woodframe structures cannot be scaled because there is no way to scale a naturally occurring fibrous material with non isotropic properties. However, because the dynamic response of wood shearwalls (and thus woodframe structures) is dominated by the behavior of the sheathing-to-framing connectors, an energy-based similitude was developed at the connector/fastener (nail) level. Shake table tests were performed for both the full-scale prototype and half-scale model. Peak displacements at roof level for the prototype and model were found to be very close, i.e., within 2%, for the largest simulated ground motion and only within 30% for the smallest simulated ground motions. While the displacement time series scaled very well, the resulting damage did not scale.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (V): Discrete Element Approach

ABSTRACT

The analysis of the shaking table test of a 3-wall stone masonry structure performed with a discrete element model is presented. The numerical model, created with the code 3DEC, employed a rigid block representation and a Mohr-Coulomb joint model. Joint stiffness calibration to match the experimental natural frequencies is discussed, as well as the boundary conditions to simulate the shake table. Comparisons are made with the measured displacements at key locations, and the modes of deformation and fracture of the walls. The DEM model was able to reproduce important features of the shaking table tests. The experimental deformation and near collapse patterns were clearly identifiable in the numerical simulations, which produced displacements within the observed orders of magnitude, for the various levels of excitation.     

NUMERICAL ANALYSIS OF EMBANKMENT FOUNDATION LIQUEFACTION COUNTERMEASURES

Computational simulations are presented for a unique series of centrifuge tests conducted to assess the performance of liquefaction countermeasure techniques. In these centrifuge tests, the dynamic response of an embankment supported on a liquefiable foundation (medium sand) is investigated. The experimental series included: (i) a benchmark test without a liquefaction countermeasure, (ii) foundation densiflcation below the embankment toe, and (iii) use of a sheet-pile containment enclosure below the embankment. This series of experiments documents a wide range of practical liquefaction response mechanisms (including countermeasure implementation). In order to numerically simulate the above centrifuge tests, a new calibrated soil stress-strain constitutive model is incorporated into a two-phase (solid-fluid) fully coupled Finite Element formulation. Comparison of the computational and experimental results demonstrates: (i) importance of post-liquefaction dilative soil behavior in dictating the dynamic response and deformation characteristics of the embankment-foundation system, and (ii) capabilities and limitations of the numerical modeling procedure.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (IV): Macro and Micro FEM Based Approaches

ABSTRACT

This article presents a study on the out-of-plane response of two masonry structures without box behavior tested in a shaking table. Two numerical approaches were defined for the evaluation, namely macro-modeling and simplified micro-modeling. As a first step of this study, static nonlinear analyses were performed for the macro models in order to assess the out-of-plane response of masonry structures due to incremental loading. For these analyses, mesh size and material model dependency was discussed. Subsequently, dynamic nonlinear analyses with time integration were carried out, aiming at evaluating the collapse mechanism and at comparing it to the experimental response. Finally, nonlinear static and dynamic analyses were also performed for the simplified micro models. It was observed that these numerical techniques correctly simulate the in-plane response. The collapse mechanism of the stone masonry model is in good agreement with the experimental response. However, there are some inconsistencies regarding the out-of-plane behavior of the brick masonry model, which required further validation.     

Seismic Analysis of Masonry Gravity Dams Using the Discrete Element Method: Implementation and Application

Much research in recent years has focused on the seismic analysis of concrete and earthfill dams, and few works have addressed the case of masonry dams. The structural behavior of masonry dams is controlled essentially by its discontinuous nature, which may induce significant nonlinear response during an intense earthquake. In this article, a numerical tool based on the Discrete Element Method is presented, aimed at the static, dynamic, and hydromechanical analysis of masonry gravity dams. The use of discontinuous models is mandatory for the study of failure mechanisms involving the masonry discontinuities, the dam-rock interface or the rock mass joints. The Discrete Element Method is able to assemble continuous and discontinuous meshes simultaneously in the same model, providing a versatile tool to consider various assumptions and levels of analysis, ranging from simplified to detailed structural representations. A comprehensive study of the seismic behavior of Lagoa Comprida Dam, located in Portugal, is presented. Both continuous and discontinuous models were developed to assess the main failure mechanisms, including overstress, partial and global sliding, and overturning.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (VI): Discrete Element Approach

ABSTRACT

Although many experimental tests and numerical models are available in the literature, the numerical simulation of the seismic response of existing masonry buildings is still a challenging problem. While the nonlinear behavior of masonry structures is reasonably predictable when the out-of-plane behavior can be considered inhibited, when the in-plane and out-of-plane responses coexist and interact, simplified models seem unable to provide reliable numerical predictions. In this article, taking advantage of the experimental tests carried out in a shaking table on two masonry prototypes at LNEC, a macro-element approach is applied for the numerical simulations of their nonlinear response. The adopted approach allows simulating the nonlinear behavior of masonry structures considering the in-plane and out-of-plane responses. Since it is based on a simple mechanical scheme, explicitly oriented to representing the main failure mechanisms of masonry, its computational cost is greatly reduced with respect to rigorous solutions, namely nonlinear FEM approaches. Two modeling strategies are adopted, namely a regular mesh independent from the real texture of the prototypes and a detailed one coherent with the units disposal. The numerical results are discussed and the correlation between the nonlinear static analyses and the dynamic response is provided.     

Experimental Dynamic Testing and Numerical Modeling of Historical Belfry

The experimental characterization of historical bell towers and wall belfries can provide important information for the calibration of numerical models as well as to implement proper restoration strategies. Within this framework, the presented study is concerned with the experimental dynamic assessment of an ancient belfry dating back to 1537. The structure is part of the “Santa Maria in Aracoeli Church” (Rome, Italy), an important heritage construction placed on the summit of the Capitoline Hill, close to the building that hosts the Major’s office. Several field tests have been conducted using accelerometers, and records obtained under different dynamic loading scenarios have been examined. Moreover, experimental accelerations have been elaborated to estimate the most important modal features of the structure and to validate a finite element model. Field tests have confirmed that severe vibrations are induced when the bells swing, and thus a slight reduction of the swing angle has been suggested in order to provide an immediate and inexpensive benefit to the structure. A new set of field tests demonstrates that the new swing angle is sufficient to reduce the induced vibrations while preserving the original sound.     

Numerical Simulation and Seismic Fragility Analysis of a Self-Centering Steel MRF with Web Friction Devices

This article presents the seismic fragility analysis of a self-centering steel moment-resisting frame (SC-MRF) with web friction devices. A detailed numerical model of the SC frame was developed using the Open System for Earthquake Engineering Simulation (OpenSees) and the elastoplastic responses of the SC-MRF were studied, including the strength degradation under cyclic loading, tendon rupture, beam buckling, bolt bearing and friction loss, etc. The proposed simulation approach is validated by comparing the simulated results with those in existing hybrid-simulation tests, quasi-static pushover test and low cyclic tests, where good agreement is observed. In addition to the well-established performance limit states (i.e., immediate occupancy, collapse prevention and global dynamic instability), two unique performance limit states (i.e., the recentering and repairable limit states) are defined for the SC-MRF. Finally, incremental dynamic analyses are conducted to evaluate the seismic fragilities regarding the five performance limit states.     

Calibration of an Advanced Constitutive Model for Babolsar Sand Accompanied by Liquefaction Analysis

In our research, we apply numerical modeling for prediction of liquefaction of sands during and after dynamic loading. In numerical modeling, to properly simulate the generation, redistribution, and dissipation of excess pore water pressure during and after dynamic loading, it is important to use a suitable constitutive model for soil. In this article, Dafalias and Manzari’s model [2004] (a critical state bounding surface plasticity model) was used to model the behavior of saturated sand due to relatively simple of formulations and a unique set of input parameters for a wide range of initial stress and void ratio. The attention in this article is on Babolsar sand. After calibration model parameters for Babolsar sand, the analysis of liquefaction using the modeling of a centrifuge test and predictions of model was carried out. The results indicate a reasonable performance of the model for prediction of behavior of types of sands. Also, Babolsar sand has more prone to dilatancy than Nevada and Toyoura sands.     

Probabilistic Calibration and Experimental Validation of the Seismic Design Criteria for One-Story Concrete Frames

This article investigates the seismic performance of one-story reinforced concrete structures for industrial buildings. To this aim, the seismic response of two structural prototypes, a cast-in-situ monolithic frame and a precast hinged frame, is compared for four different levels of translatory stiffness and seismic capacity. For these structures an incremental nonlinear dynamic analysis is performed within a Monte Carlo probabilistic simulation. The results obtained from the probabilistic analysis prove that precast structures have the same seismic capacity of the corresponding cast-in-situ structures and confirm the overall goodness of the design criteria proposed by Eurocode 8, even if a noteworthy dependency of the actual structural behavior from the prescribed response spectrum is pointed out.

The experimental verification of these theoretical results is searched for by means of pseudodynamic tests on full-scale structures. The results of these tests confirm the overall equivalence of the seismic behavior of precast and cast-in-situ structures. Moreover, two additional prototypes have been designed to investigate the seismic behavior of precast structures with roof elements placed side by side. The results of these further tests show that an effective horizontal diaphragm action can be activated even if the roof elements are not connected among them, and confirm the expected good seismic performance of these precast systems. Finally, the results of the experimental tests are compared with those obtained from nonlinear structural analyses. The good agreement between numerical and experimental results confirms the accuracy of the theoretical model and, with it, the results of the probabilistic investigation.     

Development of Neural Network Based Hysteretic Models for Steel Beam-Column Connections Through Self-Learning Simulation

Beam-column connections are zones of highly complex actions and deformations interaction that often lead to failure under the effect of earthquake ground motion. Modeling of the beam-column connections is important both in understanding the behavior and in design. In this article, a framework for developing a neural network (NN) based steel beam-column connection model through structural testing is proposed. Neural network based inelastic hysteretic model for beam-column connections is combined with a new component based model under self-learning simulation framework. Self-learning simulation has the unique advantage in that it can use structural response to extract material models. Self-learning simulation is based on auto-progressive algorithm that employs the principles of equilibrium and compatibility, and the self-organizing nature of artificial neural network material models. The component based model is an assemblage of rigid body elements and spring elements which represent smeared constitutive behaviors of components; either nonlinear elastic or nonlinear inelastic behavior of components. The component based model is verified by a 3-D finite element analysis. The proposed methodology is illustrated through a self-learning simulation for a welded steel beam-column connection. In addition to presenting the first application of self-learning simulation to steel beam-column connections, a framework is outlined for applying the proposed methodology to other types of connections.     

Seismic Tests and Numerical Modeling of a Rolling-ball Isolation System

For the seismic isolation of light structures, the use of laminated rubber bearings is neither economical nor, for most cases, technically suited. For the isolation of this type of structure a new system, consisting of steel balls rolling on rubber tracks, has been developed at TARRC (Tun Abdul Razak Research Centre).

This article presents the results of experimental tests carried out for the characterization of the behavior of this new device. A numerical model is also proposed that can be used to assess the seismic response of structures with this isolation system.

Comparison of the predictions of the numerical model with the experimental data shows that the model is adequate to perform the correct assessment of the seismic response of isolated structures. The results of the experimental campaign of shaking-table tests, as well as the numerical simulations, show that there is an effective reduction of the acceleration levels induced in the isolated structures.     

Numerical Evaluation of Seismic Soil Pressures on Rigid Walls Fixed to the Bedrock

Seismic soil pressures developed on a 7 m rigid retaining wall fixed to the bedrock are investigated using a finite element model that engages nonlinear soil intended materials available in OpenSees. This allows incorporation of the inelastic behavior of the soil and wave propagation effects in the soil-wall system seismic response. The nonlinear response of the soil was validated using the well-stablished, frequency-domain, linear-equivalent approach. An incremental dynamic analysis was implemented to comprehensively examine the effect of soil nonlinearity and input motion on the induced seismic pressures and to evaluate current code equations/methodologies at different levels of earthquake intensity. The results show that soil nonlinearity and seismic wave amplification may play an important role in the response of the soil-wall system. Therefore, methodologies that rely only on peak ground acceleration may introduce large bias on the estimated seismic pressures in scenarios where high nonlinearity and site amplification are expected.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (III): Two-Step FEM Approach

ABSTRACT

This article presents numerical simulations of two full-scale masonry structures which were tested on the shaking table within the scope of the workshop “Methods and challenges on the out-of-plane assessment of existing masonry buildings”. The numerical models have been developed on the basis of the blind-prediction models which have been improved after the publication of the test results. The solution procedure is divided into two steps with separate numerical simulations for each one. In the first step the collapse mechanism of the structure is determined by means of pushover analysis using a continuum, plasticity-based model. In the second step the dynamic response of the structure is simulated using a multibody model approach and frictional contacts. Results of the tests show reasonable, yet far from perfect predictive capabilities of the used numerical methods.