Seismic Behavior of L-Shaped RC Squat Walls under Various Lateral Loading Directions

Considerable progress has been made on the research of non-rectangular reinforced concrete (RC) squat walls over the past decades. However, the experimental data of L-shaped RC squat walls remain limited, especially for their seismic behaviors under non-principal bending actions. This paper presents an experimental and numerical investigation on L-shaped RC squat structural walls with an emphasis on how varying the directions of lateral cyclic loading influences the seismic responses of these walls. Four L-shaped specimens are tested under lateral cyclic displacements and low levels of axial compression The variables are axial loads and lateral loading directions. The performance of specimens is discussed in terms of cracking patterns, failure mechanisms, hysteretic responses, deformation components and strain profiles. Furthermore, three-dimensional finite element models are developed to supplement the experimental results. The direction of lateral loading is found to have a significant effect on the peak shear strength of L-shaped RC squat walls.     

Seismic Fragility Assessment of Lightly Reinforced Concrete Structural Walls

Development of fragility functions is a pertinent stage in seismic performance assessment of structures. A database of lightly Reinforced Concrete (RC) walls under simulated seismic loading is compiled from the literature to establish the drift-based seismic fragility functions. To classify the damage states experienced by RC walls, the Park-Ang Damage model is amended in this research. Then, the modified Bouc-Wen-Baber-Noori hysteresis model is implemented in ABAQUS to predict the hysteresis behavior of RC walls. Thereafter, the proposed hysteresis model is employed to develop the seismic fragility curves of low to mid-rise RC walls in Singapore using incremental dynamic analysis approach.     

Effective Stiffness of Non-Rectangular Reinforced Concrete Structural Walls

The effective stiffness of a structural wall is an important property in design, which many design codes estimate by the moment inertia of the wall section with a reduction factor. The reduction factor is typically estimated by empirical equations based on configurations of the wall. The existing methods for the reduction factor were proposed based on investigations on rectangular reinforced concrete (RC) walls. The effective stiffness of non-rectangular RC walls can be more complex than that of rectangular RC walls. As such, more research investigations are required. Based on finite element models, the effective stiffness of U-shaped and T-shaped RC walls was investigated in this paper. The numerical results were further adopted to develop methods for calculating the effective stiffness of non-rectangular wall in different loading directions. The proposed method was afterward compared with the experimental data.     

Macro-Modeling of Reinforced Concrete Structural Walls: State-of-the-Art

During the past decades, various analytical macroscopic models of structural walls have been developed for simulating the seismic behavior of reinforced concrete (RC) walls. Due to the inherently complicated characteristics of RC walls, macroscopic models that can capture all the important response characteristics with good accuracy and applicability are very challenging to establish. A thorough review of the four main types of mathematical macro models of RC walls, i.e., the vertical-line-element-model, the 2-D shear panel element model, the equivalent truss model and the fiber-based model, is presented to discuss the methodology behind each model and examine the corresponding merits and disadvantages. Suggestions are also made for the further research of the macro modeling of structural walls.     

Seismic Performance Assessment of Slender T-Shaped Reinforced Concrete Walls

T-shaped slender reinforced concrete (RC) structural walls are commonly used in medium-rise and high-rise buildings as part of lateral force resisting system. Compared to its popularity, experimental results on seismic performance of these walls are relatively sparse, especially for data regarding these walls in the non-principal bending directions. This article aims at providing additional experimental evidence on seismic performance of T-shaped RC structural walls. Experimental results of six T-shaped RC walls were presented. These walls resemble the structural walls found in existing buildings in Singapore and possess slightly inferior details compared to the requirements of modern design codes. The test variables were the loading direction and the axial load ratio. The experimental results were discussed in terms of the failure mechanisms, cracking patterns, hysteretic responses, curvature distributions, displacement components, and strain profiles. In addition, the experimental results were compared with methods commonly adopted in current design practice including the nonlinear section analyses, shear strength models and effective width of the tension flange. The experimental data illustrate that the shear lag effect not only was not accurately accounted for by the effective width method but also significantly affected the strength and stiffness of the tested specimens.     

Shake Table Test and Numerical Analysis of a Bridge Model Supported on Elastomeric Pad Bearings

Elastomeric pad bearings are widely applied in short- to medium-span girder bridges in China, with the superstructure restrained by reinforced concrete (RC) shear keys in the transverse direction. Field investigations after the 2008 Wenchuan earthquake reveal that bearing systems had suffered the most serious damage, such as span falling, bearing displaced, and shear key failure, while the piers and foundations underwent minor damage. As part of a major study on damage mechanism and displacement control method for short- to medium-span bridges suffered in Wenchuan earthquake, a 1:4 scale, two-span bridge model supported on elastomeric pad bearings were recently tested on shake tables at Tongji University, Shanghai. The bridge model was subjected to increasing levels of four seismic excitations possessing different spectral characteristics. Two restraint systems with and without the restraint of RC shear keys were tested. A comprehensive analytical modeling of the test systems was also performed using OpenSees. The experimental results confirmed that for the typical bridges on elastomeric pad bearings without RC shear keys, the sliding effect of the elastomeric pad bearings plays an important role in isolation of ground motions and, however, lead to lager bearing displacement that consequently increases the seismic risk of fall of span, especially under earthquakes that contain significant mid-period contents or velocity pulse components. It is suggested from the test results that RC shear keys should be elaborately designed in order to achieve a balance between isolation efficiency and bearing displacement. Good correlation between the analytical and the experimental data indicates that the analytical models for the bearing and RC shear key as well as other modeling assumptions were appropriate.     

SEISMIC RISK ASSESSMENT OF RC STRUCTURES WITH THE “2000 SAC/FEMA” METHOD

The applicability of a new, fully probabilistic approach to seismic design and assessment of reinforced concrete (RC) structures is investigated. Fundamental advantages of the method are mathematical simplicity and comparatively light computational effort. The original formulation, which was developed for steel structures, is first illustrated; ah extension which allows consideration of multiple failure mechanisms, typical of RC structures, is then proposed. The applicability of the method is demonstrated through an example: the seismic risk of a four storey RC building that was not designed for seismic resistance is evaluated. Three failure mechanisms are considered: joint failure, column shear failure and drift failure.     

Real-time Seismic Damage Detection of Concrete Shear Walls Using Artificial Neural Networks

Concrete shear walls are widely employed in buildings as a main resistance system against lateral loads. Early identification of seismic damage to concrete shear walls is vital for deciding post-earthquake occupancy in these structures. In this article, a method based on artificial neural networks for real-time identification of seismic damage to concrete shear walls was proposed. Inter-story drifts and plastic hinge rotation of concrete walls were used as the inputs and outputs of a MLP neural network. Modal Pushover Analysis was employed to prepare well-distributed data sets for training the neural network. The proposed method was applied to a five-story concrete shear wall building. The results from the network were compared with those obtained from Nonlinear Time History Analysis. It was observed that the trained neural network successfully detected damage to concrete shear walls and accurately estimated the severity of seismic-induced damage.     

Seismic Retrofitting of Non-Seismically Designed RC Beam-Column Joints using Buckling-Restrained Haunches: Design and Analysis

Many existing reinforced concrete (RC) structures around the world have been designed to sustain gravity and wind loads only. Past earthquake reconnaissance showed that strong earthquakes can lead to substantial damage to non-seismically designed RC buildings, particularly to their beam-column joints. This paper presents a novel retrofit method using buckling-restrained haunches (BRHs) to improve the seismic performance of such joints. A numerical model for RC joints is introduced and validated. Subsequently, a new seismic retrofit strategy using BRHs is proposed, aimed at relocating plastic hinges and increasing energy dissipation. The results indicate the retrofit method can effectively meet the performance objectives.     

Shake-Table Tests of Confined-Masonry Rocking Walls with Supplementary Hysteretic Damping

A shake-table investigation is conducted on a 40% scale model frame-wall system to validate the concept of rocking walls as primary seismic systems. The rocking wall concept was implemented on confined masonry walls, but the findings can be extended to any rocking wall system. As the inherent damping of this system is low, a pair of supplemental steel hysteretic energy dissipating dampers is used at the base of the wall. It is concluded that with careful detailing, damage is not only eliminated but the structure re-centers itself following a large earthquake.     

Quasi-Static Cyclic Tests of Two U-Shaped Reinforced Concrete Walls

U-shaped or channel-shaped walls are frequently used as lateral strength providing members in reinforced concrete (RC) buildings since their form does not only provide strength and stiffness in any horizontal direction but is also well suited to accommodate elevator shafts or staircases. Despite this popularity, experimental results on the seismic behavior of U-shaped walls are scarce. For this reason a research program with the objective to provide additional experimental evidence for such walls under seismic loading was developed. It included quasi-static cyclic testing of two U-shaped walls at the structural engineering laboratories of the ETH Zurich. The walls were built at half-scale and designed for high ductility. The main difference between the two walls was their wall thickness. The project was chiefly focusing on the bending behavior in different directions and therefore the walls were subjected to a bi-directional loading regime. This article discusses the design of the test units, the test setup and the test predictions. Finally the main results are summarized in terms of failure mechanisms and force-displacement hystereses.     

Seismic Vulnerability Analysis of RC Bridges Based on Kriging Model

This paper presents a Kriging model-based method for seismic vulnerability analysis of reinforced concrete (RC) bridges. It aims at reducing the computational effect when the Monte Carlo technique is used for establishing the structural vulnerability curves. The general procedure of the proposed method is put forward firstly. In the procedure, the uncertainties existing in the structures and ground motions are both taken into account, and the uniform design (UD) technique is adopted for generating the random samples. The reliability of the proposed method is demonstrated by the vulnerability analysis of an single degree of freedom (SDOF) system using the Latin hypercube simulation (LHS) method. Vulnerability analysis of an RC bridge system is then carried out using the proposed method. The vulnerability curves of the bridge obtained by the Kriging model-based method are compared with those obtained by the LHS method. Additionally, three simulation schemes adopting different UD tables are employed to investigate the convergence and stability of the proposed method. The results show that the proposed method used for the seismic vulnerability analysis of RC bridges can reduce the computational effort and time to a large extent without much compromise on the accuracy.     

Ductility of a Structural Wall with Spread Rebars Tested in Full Scale

The experimental work focuses on the ductility of the reinforced concrete (RC) seismic structural walls in buildings of mid-rise height. A full-scale five-story structural wall was tested to obtain results, still scarce in literature, without the influence of size effect. An unusual detailing with large diameter longitudinal rebars uniformly distributed in the wall length was adopted to prevent premature web rebar fracture and shear sliding. The plastic hinge length and deformations were evaluated in detail. The results show the high ductility of the wall that reached a total drift of 2.5%, larger than those usually required in design.     

Displacement-Based Seismic Design Approach for Prestressed Precast Concrete Shear Walls and its Application

ABSTRACT

Prestressed precast concrete shear wall (PPCW) is a new kind of shear wall utilizing a combination of unbonded post-tensioning steel and mild steel for flexural resistance across horizontal joints. A simple procedure of direct displacement-based design approach for PPCW based on concept of inelastic design spectra is proposed. Section design is then carried out according to base overturning moment. A detailed design example demonstrating a step-by-step application of the design procedure is also provided. Nonlinear time-history analysis verified that this approach is applicable to control the target displacement to the performance acceptable limit.     

A PRACTICAL MODEL FOR SEISMIC ANALYSIS OF REINFORCED CONCRETE SHEAR WALL BUILDINGS

A simple macro-model for reinforced concrete shear walls is proposed, which consists of spring elements representing flexure and shear behaviour. The model for flexural behaviour is based on section analysis, while the model for shear behaviour is based on key parameters of the flexural behaviour. Four wall test specimens are selected to evaluate the reliability of the model. Modelling parameters for the backbone curves and the hysteretic rules are examined by conducting static and time history analyses, with the hysteretic response of a test specimen compared to that calculated using the proposed model. Results show some differences between measured and calculated shear force versus shear distortion relationships, but the model is acceptable because the differences do not significantly affect calculated global response. Parametric studies are also conducted to examine the influence of modelling parameters on seismic demand and capacity, which are the major design parameters for structural performance evaluation. Differences due to variation in modelling parameters are not significant, further indicating that the proposed model is reasonable.     

Seismic Overstrength of Shear Walls in Parking Structures with Flexible Diaphragms

The objective in current design practice for parking structures is that energy is dissipated through the formation of plastic hinges at the base of shear walls while floor diaphragms remain elastic and are vertically supported by a combination of shear walls and gravity resisting columns. Unfortunately, this objective is not always achieved due to inaccuracies in current methods for calculating demands on shear walls and in calculating the capacity of shear walls (IBC 2003 International Building Code. International Conference of Building Officials. Whittier, CA.  [Google Scholar], ACI code). When demands are overestimated and capacity underestimated, then diaphragm can fail prior to flexural yield of shear walls as was observed in several parking structures in the 1994 Northridge earthquake.

Eigenvalue and inelastic dynamic response analyses were performed in order to investigate the effects of diaphragm flexibility on wall responses and of wall overstrength on diaphragm responses. The elongated periods of parking structures due to diaphragm flexibility were found to significantly decrease seismic force demand on shear walls relative to what is calculated using codes of practice in which diaphragms are assumed to be rigid. This leads to the over design of shear walls, which further compounds the problem by preventing the flexural yielding of these walls and thereby driving inelastic response to diaphragms. Various degrees of diaphragm flexibility, shear wall layout, seismic zone, and the number of stories were considered in these analyses.

Inelastic static pushover analyses were preformed to investigate the design and capacity evaluation of shear walls. The results illustrate that the shear capacity of walls may be close to twice that calculated by codes of practice. The largest overstrengths were observed in shear walls with low height-to-length ratios in which a significant portion of the lateral load was taken by direct strut action to the foundation and without placing demands on the longitudinal tension reinforcement in the shear walls. The article concludes that methods in codes of practice for calculating shear wall demands and capacities need to be improved if good seismic performance of parking structures is to be achieved.     

MODELLING OF RC BEAM-COLUMN JOINTS AND STRUCTURAL WALLS

The deformation of beam-column joints may contribute significantly to drift of reinforced concrete (RC) frames. In addition, failure may occur in the joints due to cumulative concrete crushing from applied beam and column moments, bond slip of embedded bars or shear failure as in the case of existing frames with nonductile detailing. When subjected to earthquake loading, failure in RC structural wall is similar to failure of frame joints as it may occur due to cumulative crushing from high flexural stresses, bond slip failure of lap splice, shear failure or a combination of various mechanisms of failure. It is important to include these behavioural characteristics in a simple model that can be used in the analysis of RC frames and RC walls to predict their response under earthquake loading and determine their failure modes.

Global macro models for the beam-column joint and for RC structural walls are developed. The proposed models represent shear and bond slip deformations as well as flexural deformations in the plastic hinge regions. The models are capable of idealising the potential failure mechanism due to crushing of concrete, bond slip or shear with allowance for the simultaneous progress in each mode. The model predictions are compared with available experimental data and good correlation is observed between analytical results and the test measurements.     

Quasi-Static Testing of RC Infilled Frames and Confined Stone-Concrete Bearing Walls

This article presents an experimental investigation of the seismic performance of gravity load-designed RC infilled frames and confined bearing walls of limestone masonry backed with plain concrete. Five infilled frames and two bearing walls were constructed at one-third scale and tested using reversed cyclic lateral loading and constant axial loads. Effects of openings, axial loading, and infill interface conditions were examined using quasi-static experimentation. The two structural systems exhibited similar lateral resistance and energy dissipation capacities with higher global displacement ductility for the infilled frames. Hysteretic behavior of the infilled frame models exhibited pinching of the hysteretic loops accompanied by extensive degradation of stiffness whereas loops of the bearing walls were free of pinching. Test results confirmed the beneficial effect of axial loading on lateral resistance, energy dissipation, and ductility of the bearing walls. Higher axial loading resulted in a substantial decrease in ductility with no significant effect on lateral resistance of the infilled frames. Openings within the infill panel reduced significantly the lateral resistance of infilled frames. Using dowels at the infill panel interfaces with the base block and bounding columns enhanced the maximum load-carrying capacity of infilled frames without impairing their ductility.     

A High-Performance Quadrilateral Flat Shell Element for Seismic Collapse Simulation of Tall Buildings and Its Implementation in OpenSees

Shear walls are important lateral force-resistant components of tall buildings. Hence, a reliable numerical model that can accurately represent the mechanical characteristics and large deformations of shear walls is critical for realistic collapse simulation of tall buildings. Based on the theory of generalized conforming element, a high-performance quadrilateral flat shell element, NLDKGQ, accounting for the large deformation using the updated Lagrangian formulation, is proposed herein and implemented in OpenSees. The reliability of NLDKGQ is validated using classical benchmark problems and reinforced concrete specimens. In addition, its capability in simulating the collapse of a tall building is also demonstrated.     

Simplification and Assessment of Modal-Based Story Damage Index for Reinforced Concrete Frames Subjected to Seismic Excitations

Different relations have been represented for the local damage index of structures to date, while the same application is defined for them as can be an indicator of relative sustained damage by the components or stories. Since different force-resisting systems subjected to the ground motions can behave differently, some well-known story damage indices are evaluated for the reinforced concrete frames with regards to their operation during nonlinear time history analysis. Two general concepts of story damage determination are selected for this purpose. SDI is a modal-based story damage index, which is calculated by the modal frequency and mode shapes. The behavior of this local index is evaluated during the seismic excitations. The results were compared with Park-Ang and modal flexibility story damage indices. Based on analytical study on seismic responses of some RC frames subjected to a suit of earthquake records a new story damage index has been developed. It has been derived from a simple global damage equation (softening index) using a normalized ratio of inelastic story shear to its drift. A procedure is recommended to use the proposed equation without any requirement to perform nonlinear dynamic analysis, which can significantly reduce the computational efforts. Distribution of the new represented SDI along the structural height shows a good agreement with damaged state of the RC frames after seismic excitations.