Numerical Investigation of Variable Length of Seismic Damage Region for Reinforced Concrete Columns

ABSTRACT

The seldom investigation of variable length of damage region prevents the estimation of probabilistic drift limits of reinforced concrete columns at different performance levels for the performance-based seismic design. However, if using the numerical approach to predict the variability of damage region within the framework of force-based beam-column element, the current force-based beam-column element is unable to model the spreading of damage region. Therefore, a new numerical simulation method is proposed to compute the emergence, propagation and termination of damage region of reinforced concrete columns. Then, based on the developed numerical simulation method, the measured response of experimental testing is calibrated. From the calibration, it can be observed that there is a rapid increase on the variable length of damage region with the increasing of lateral displacement and then followed by a stable stage. The propagation of the longitudinal reinforcement yielding and concrete tensile cracking mainly occurs in the ascending branch of the load–displacement response. Then, based on the growth characteristic of the damage region from the numerical simulation, an empirical equation is proposed to describe the variable length of damage region by using the least-square regression analysis to fit the computed responses for its simplicity to use in engineering practices. Finally, the stable length of damage region is reinvestigated by carrying out a parametric study with the developed numerical simulation method, indicating that two critical design parameters, specifically the axial load ratio and the shear span ratio, have considerable influences on this quantity of interest.     

METHODOLOGY FOR THE PROBABILISTIC ASSESSMENT OF q FACTORS. A DAMAGE INDEX APPROACH

The objective of the present work is to present a methodology for the identification of relevant limit states, namely ultimate limit states leading to structural collapse, and for the assessment of design q factors (or force reduction factors) for reinforced concrete structures under seismic loading. It follows a probabilistic approach based on damage indices. The utilised nonlinear models, as well as the damage indices, which are those proposed by Miner and by Park and Ang, are.described. The methodology of analysis is presented emphasising its probabilistic characteristics. Some parametric studies are carried out, including the analysis of one regular plane frame reinforced concrete structure, designed for three different ductility classes (those proposed by Eurocode 8) and assuming different q factors in design. Results show how the chosen damage indices can be used as parameters to characterise the structural response and how the proposed methodology can be used to assess the design q factors. It is also shown that, for moderate seismic input, the three ductility classes are essentially equivalent in terms of maximum damage indices, but that for higher seismic levels the differences are evident, justifying the use of different q factors.     

SEISMIC RELIABILITY ASSESSMENT OF EXISTING REINFORCED CONCRETE BUILDINGS

Structures designed according to earlier codes with inadequate seismic provisions have not performed satisfactorily during recent earthquakes. The seismic performance of an existing three-storey reinforced concrete building designed according to the 1963 ACI 313-63 is evaluated and compared to the performance of a similar frame designed according to current code provisions. Non-linear static and dynamic analyses of the reinforced concrete frames are conducted. In this study, a probabilistic approach is adopted where a large number of artificially generated ground motion records is used as input motion to the structure. The results of the analysis indicated the probability of various degrees of damage to be expected when the existing frame is subjected to different ground motion levels. This information is useful in the design of the required rehabilitation scheme to provide an identified level of protection.     

A Probability-based Approach for the Definition of the Expected Seismic Damage Evaluated with Non-linear Time-History Analyses

The seismic damage evaluated through Nonlinear Time-History Analyses is significantly affected by the response quantity chosen to represent the seismic responses. Starting from the theory of tolerance regions, a generic upper limit of the seismic responses is proposed. The method is applied to a reinforced concrete structure subjected to different record combinations. For each considered damage index and record combination, the upper limit damage is compared with the average value suggested by seismic codes. The proposed method yields a higher seismic damage than the average response and an increase in the damage indices as the number of records decreases.     

Seismic Reliability of Code-Conforming Italian Buildings

ABSTRACT

This paper presents and discusses some research results related to the seismic failure risk of standard, residential and industrial, buildings designed for damage, and life-safety according to the Italian seismic code, which is somewhat similar to Eurocode 8. The five considered structural typologies are as follows: masonry, cast-in-place reinforced concrete, precast reinforced concrete, steel, and base-isolated buildings. The archetype structures have been designed according to standard practice at three sites, representative of the seismic hazard across the country. Seismic risk is defined here as the annual rate of earthquakes able to cause structural failure in terms of usability-preventing damage and global collapse. For each structure, the failure rates have been evaluated in the framework of performance-based earthquake engineering, that is, via integration of site’s probabilistic hazard and structural fragility. The former has been computed consistently with the official hazard model for Italy that is also used to define design actions in the code. The latter has been addressed via nonlinear dynamic analysis of three-dimensional numerical structural models. Results indicate that, generally, design procedures are such that seismic structural reliability tends to decrease with increasing seismic hazard of the building site, despite the homogeneous return period of exceedance of the design seismic ground-motion.     

Performance-Based Vulnerability Assessment of Multi-Story Reinforced Concrete Structures Exposed to Pre- and Post-Earthquake Fire

Post-earthquake fire can potentially bring about much more damage than the earthquake itself. Performing a vulnerability assessment for a structure that has already sustained damage in an earthquake and is then exposed to fire is therefore of importance. This paper describes a performance-based investigation in which applied loads to a structure are appropriately quantified. To do so, a sequential structural analysis is performed on the Life Safety performance level of a three-story reinforced concrete frame selected from a building. For the analysis to be more realistic, the slab is also included in the frame analysis through the concept of effective length. The frame is first subjected to an earthquake load with the PGA of 0.30 g followed by a fire analysis, using the ISO834 fire curve and the iBMB fire curve. The time needed for the structure weakened by the earthquake to collapse under fire is then calculated. As a benchmark, fire-only analysis is also performed for the undamaged frame. Moreover, the effect of thermal spalling is considered in the slabs. The selected frame is evaluated under various failure criteria such as load capacity, displacement, and rate of displacement. The results show that no failure is observed when the frame is exposed to fire alone, either when using the ISO curve or the iBMB curve under various failure criteria. It is also shown that while the PEF resistance based on load capacity criteria under the ISO curve is around 120 minutes, it reduces to about 95 min under the iBMB curve. However, considering the rate of deflection failure criteria, the PEF resistance is around 103 min and 75 min under the ISO and the iBMB curves, respectively. It is then concluded that in the PEF analysis, the iBMB curve is more compatible with the concept of performance-based design than the ISO curve is.     

Seismic Vulnerability Assessment of an Infilled Reinforced Concrete Frame Structure Designed for Gravity Loads

In the last decades, particular attention has been paid to the seismic vulnerability of existing reinforced concrete buildings designed for gravity loads only. Such buildings, designed before the introduction of capacity design in modern seismic codes, are very common, particularly in seismic prone countries of the Mediterranean area. Due to poor detailing and lacking of capacity design principles, high vulnerability has been highlighted in several past studies. In this article, inadequate seismic response and peculiar damage pattern are investigated by means of shake table tests performed on a 1:2 scaled 3-story infilled prototype. Particular attention is given to the role of beam-column joints and frame-panel interaction. The effectiveness of the EC8-based assessment approach is then evaluated; both linear and nonlinear numerical models, with different levels of sophistication, have been implemented in order to explore their behavioral aspects.     

Experimental Study on the Seismic Performance of Superimposed RC Shear Walls with Enhanced Horizontal Joints

The seismic performance of superimposed reinforced concrete (RC) shear walls is decreased by rocking behavior and damage concentration at the horizontal joint. An enhanced horizontal joint method is proposed to improve the corresponding seismic performance. To validate the reliability of the proposed method, three full-scale superimposed walls and a cast-in-place shear wall (for comparison) are designed and tested under the quasi-static load. The test results indicate that the rocking phenomenon can be prevented using the proposed method, and the seismic performance of superimposed RC shear walls with enhanced horizontal joints is comparable to that of the cast-in-place RC shear walls.     

Modeling the Seismic Response of Modern URM Buildings Retrofitted by Adding RC Walls

Modern unreinforced masonry buildings with reinforced concrete slabs are often retrofitted by inserting reinforced concrete walls. The main advantages of this technique are the increase in strength and displacement capacity with respect to masonry structures. This article presents two modeling approaches for evaluating such structures: a shell-element model and a macro-element one. The objective is to formulate practical recommendations for setting up a macro-element model using as input the geometry of the structure and results from standard material tests. Structural configurations of masonry buildings, in which the insertion of reinforced concrete walls is an efficient retrofit technique, are also investigated.     

Towards Damage-Based Design Approach for RC Bridge Columns Under Combined Loadings Using Damage Index Models

This article investigates a damage-based design approach for circular reinforced concrete (RC) columns under combined bending, shear, and torsion using decoupled damage index models. The combination of bending moment, shear, axial, and torsional loading affects the structural performance of bridge columns with respect to strength, deformation capacity and progression of damage. The damage index model proposed here permits decoupling these combined actions according to various damage limit states. This work evaluates the interaction between bending and torsional damage indices in terms of progression of damage. It also investigates the effects of the transverse reinforcement ratios and shear span. Based on experimental and analytical results increase of torsion amplified the progression of damage. The increase in transverse reinforcement ratio was found to have delayed the progression of damage and to have changed the torsional dominated behavior to flexural dominated behavior under combined bending and torsion.     

Seismic Performance Assessment of Non-Compliant SMRF-Reinforced Concrete Frame: Shake-Table Test Study

Seismic performance assessment is carried out for reinforced concrete structure built in low-strength concrete lacking confining ties in beam-column joint. Shake-table tests were performed on 1/3rd scaled two-story frame using design-spectrum-compatible accelerogram, scaled to various target levels. The frame is observed with beam longitudinal bar slip and pullout. Joints with no confining ties experienced extensive damage, observed with cover/core concrete spalling. The frame could resist 70% of the design ground motion to remain within the code-specified drift limit. The code requirement for minimum column depth will not avoid joint damageability in case of low-strength concrete and joints lacking confining ties.     

NONLINEAR ANALYSIS OF REINFORCED CONCRETE SHEAR WALL UNDER EARTHQUAKE LOADING

A constitutive model for predicting the cyclic response of reinforced concrete structures is proposed. The model adopts the concept of a smeared crack approach with orthogonal fixed cracks and assumes a plane stress condition. Predictions of the model are compared firstly with existing experimental data on shear walls which were tested under monotonic and cyclic loading. The same model is then used in the finite element analysis of a complete shear wall structure which was tested under a large number of cyclic load reversals due to earthquake loading at NUPEC's Tadotsu Engineering Laboratory. Two different finite element approaches were used, namely a two-dimensional and a three-dimensional representation of the test specimen. The ability of the concrete model to -reproduce the most important characteristics of the dynamic behaviour of this type of structural element was evaluated by comparison with available experimental data. The numerical results showed good correlation between the predicted and the actual response, global as well as local response being reasonable close to the experimental one.     

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.     

Lightly Reinforced Walls Subjected to Seismic Excitations: Interpretation of CAMUS 2000–1 and 2000–2 Dynamic Tests

In this article a study is presented of the inelastic seismic performance of two 5-story reinforced concrete wall specimens, which were tested in the context of the CAMUS 2000 program. The structure has been sized and detailed following the French PS92 code. To investigate the simplifying assumptions made in design, a 3-D refined nonlinear analysis was conducted. Particular aspects of the behavior of the two tested specimens are presented and then test results are compared with numerical predictions. The experimental-analytical comparisons not only demonstrate the accuracy of the time-history analysis model, but also allow obtaining more detailed information about the behavior of the specimen when it is subjected to seismic excitation. The significant effect of degradation of the stiffness and strength of the wall suggests that it is always important that design procedures are derived from numerical modeling and experimental observations.     

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.     

Computational Modeling of the Seismic Performance of Beam-Column Subassemblies

Analytical studies are carried out to investigate the effectiveness of finite element modeling procedures in accurately capturing the nonlinear cyclic response of beam-column subassemblies. The analyses are performed using program VecTor2, employing only default or typical material constitutive models and behavior mechanisms in order to assess analysis capabilities without the need for special modeling techniques or program modifications. The specimens considered cover a wide range of conditions, and include interior and exterior seismically and non seismically designed beam-column subassemblies. It is shown that finite element analyses can achieve good accuracy in determining the strength, deformation response, energy dissipation, and failure mode of reinforced concrete beam-column subassemblies under seismic loading conditions.     

SIMULATION OF THE CYCLIC BEHAVIOUR OF R/C RECTANGULAR HOLLOW SECTION BRIDGE PIERS VIA A DETAILED NUMERICAL MODEL

In the search for robust constitutive models suitable for reproducing the performance of bridge piers during a seismic event, this paper details the simulation of the cyclic responses of four rectangular hollow section R/C bridge piers. These four R/C bridge piers were built at scale 1/2.5 and tested experimentally. Both tall and short piers are considered, covering situations where bending or shear are of relevance. Furthermore, the four piers were reinforced according to rather different design strategies: (I) the first is a 30-year-old bridge designed without allowance to the seismic action, and (ii) the second is a bridge fulfilling the EC8 provisions. The detailed constitutive model that provides the numerical predictions includes two submodels: one with two scalar damage variables, reproducing the tensile and compressive degradations of concrete, and the other is based on the Giuffre-Menegotto-Pinto formulation, simulating the cyclic behaviour of the re-inforcement. The Damage Mechanics submodel is implemented at the Gauss points of the finite elements that discretize the concrete, whereas the steel submodel is implemented on the 2-noded truss elements adopted for the rebars. A comparison between the numerical and the experimental results is discussed in detail in this paper.     

SEISMIC REHABILITATION OF SHORT RECTANGULAR RC COLUMNS

Non-ductile response of structural elements, particularly columns, has been the cause of numerous documented failures during earthquakes. The objective of this experimental study was to evaluate the non-linear behaviour of non-ductile reinforced concrete short columns under lateral cyclic deformations and to evaluate rehabilitation schemes. Three reinforced concrete short columns were tested under cyclic lateral loads and constant axial load. The behaviour and effectiveness of different rehabilitation systems using carbon fibre reinforced polymers (CFRP) were investigated. Two different techniques to improve concrete confinement were used in the two rehabilitated specimens. It was found that it is possible to eliminate the non-ductile modes of failure of short column using anchored CFRP wraps. In addition, an analytical model to predict the confining effect and the total shear resistance of rectangular reinforced concrete columns with anchored fibre wraps was introduced. The confinement model is an extension to an available model for concrete confined by steel reinforcement. The model was used to predict the shear capacity of the tested specimens and has shown good results.