Edited by Catherine A. Cardno, Ph.D.


Engineers at Rice University’s George R. Brown School of Engineering and Texas A&M University's College of Engineering have developed a computational modeling strategy to make more effective the planning of post-earthquake repairs of reinforced-concrete columns — which support many of the world’s bridges. The findings appeared in the paper, “Numerical modeling of repaired reinforced concrete bridge columns,” which was published in Engineering Structures (Volume 253, Feb. 15, 2022).


Civil Engineering Online spoke about the study and the modeling software’s capabilities with one of the researchers, Mohammad Salehi, Ph.D., a postdoctoral researcher in the department of civil and environmental engineering at Rice.


Civil Engineering Online: What happens to reinforced-concrete bridge supports during earthquakes?


MS: The design philosophy in the current bridge design codes is to prevent bridge collapse under a site’s maximum considered earthquake. But bridges can still sustain considerable damage under moderate to strong earthquakes. Depending on an earthquake’s intensity, the damage in reinforced-concrete bridge columns can appear in the forms of concrete cracking, cover-concrete spalling, core concrete crushing, rebar buckling, and rebar fracture. Indeed, in the RC columns of ductile (that is, flexure-dominant) design, all these forms of damage are confined to the so-called plastic hinge lengths, which occur at the column ends — i.e., where the maximum flexural moments happen during an earthquake.


Among the above damage states, the latter three are considered severe and may lead to significant lateral load resistance and stiffness losses as well as large residual displacements, thereby necessitating the replacement of the entire bridge.


What sorts of repairs are often required after a seismic event?


Mere cracks, which usually pose only serviceability issues (e.g., steel corrosion), may be repaired through epoxy or grout injection.


If damage is limited to concrete spalling, it is often repaired through concrete patching such as replacing the spalled concrete with cementitious mortar whereas deep concrete spalling may additionally need jacketing with carbon-fiber-reinforced polymer or steel to avoid the quick damage of the replaced concrete under future earthquakes.


In the event of severe, yet repairable, damage, usually it becomes necessary to turn to RC jacketing, steel jacketing, or CFRP jacketing.


All these methods involve removing damaged materials such as loose concrete and buckled/fracture rebar replacing them with new materials of similar or different properties, and adding a jacket made of RC, steel, or CFRP around the damaged regions for extra confinement.


The objective of these methods is to achieve at least a similar performance to the original RC column in terms of lateral load resistance and ductility.


How are these bridge supports analyzed currently?


Currently, the nonlinear finite element method is the most effective method to analyze any civil structure. Though 3D solid continuum-based FE models are generally more accurate than macroscopic FE models (i.e., using beam/truss elements), they are computationally much more expensive, especially when it comes to response history analyses (that is, analyses under earthquake excitations).


As a result, the latter type of FE models is usually used for the analysis of RC structures. In such models, RC beams and columns are represented via nonlinear fiber-based beam-column elements, which simulate these members by discretizing their lengths into a number of so-called fiber sections. Fiber sections represent the geometry and mechanical response of RC member cross sections through a number of concrete and steel “fibers” with appropriate uniaxial material models.


The most common modeling approach for repaired RC bridge columns is to represent them through fiber-based beam-column elements, while their fiber sections are defined in accordance with the geometry of the repaired column cross sections and the material models representing concrete and steel are modified through empirical strength/stiffness reduction factors to approximately account for their prior damage.


Such modeling approaches fail to accurately capture the effects of initial loading in a pre-repair earthquake on the non-replaced materials, rely on empirical reduction factors that are determined based on visual inspection of the damaged column, and assume zero initial stress/strain states for all the materials in the model. This is while the repaired column’s non-replaced materials are generally in non-zero initial stress/strain states.


How do your computational models improve on the current methods?


Though our proposed modeling strategy employs fiber-based beam-column elements too, it explicitly accounts for the initial damage of the RC column through a number of innovative time-dependent material models.


The developed time-dependent material models allow removing, replacing, adding, and modifying materials in the fiber sections at pre-specified times during the analyses to simulate repair changes to the cross sections. The modification material model is particularly used to modify the response of concrete materials after jacketing (due to added confinement).


The overall analysis approach comprises three phases.


The first phase includes analysis of the column under initial, pre-repair loading.


In the second phase, repair changes are applied to the fiber sections of the fiber-based elements through the time-dependent material models without losing the effects of the initial loading on the non-replaced materials.


The third phase consists of the analysis of the repaired column under the second (post-repair) loading.


Given this approach, the proposed modeling strategy does not rely on any empirical reduction factors and considers the non-zero initial stress/strain states of the materials over the column length before the column’s post-repair analysis.


Do your models only work with reinforced-concrete bridge columns?


One of the advantages of the developed time-dependent material models is their possible application in modeling of any repaired/modified structural elements, regardless of their materials and their application. In addition, there is no restriction on the type of finite elements that can use the time-dependent material models, and thus, they can be used in truss elements too.


That said, the same strategy described above could be used to analyze any repaired/modified structure with any system and made of any materials, such as steel and RC. For example, one may use the proposed strategy to analyze a damaged building structure retrofitted through steel braces by modeling the retrofit braces through truss elements, while the material models used in the definition of truss elements are of the time-dependent addition type — i.e., the material models representing the braces will be activated in the analysis only after a pre-specified retrofit time.


Do the models only work with seismic events?


The proposed modeling strategy can be used to analyze repaired/modified structures initially damaged under any type of pre-repair loading, whether it is seismic or not, as long as the initial loading can be simulated through (the) FE method.


Examples of such loading conditions are wind, collision, and snow loads.


Moreover, analysis of repaired members after they are affected by aging and corrosion is also possible, as long as such effects could appropriately be simulated during the first phase of the analysis approach explained earlier.


How did you develop the models?


The developed time-dependent material models are not based on any existing experimental/numerical data. But the material models used to represent the nonlinear (stress versus strain) responses of concrete and steel have, however, been developed based on extensive experimental data by other researchers in the past.


The overall performance of the proposed modeling strategy was validated by comparing the model results with test results from several past experiments on repaired RC columns. The selected experiments consisted of RC columns repaired through concrete patching, RC jacketing, and CFRP jacketing.


How do your models work?


The primary information required to define a fiber-based element includes the member geometry (including its cross-section details) and its material properties (e.g., concrete’s compressive strength and longitudinal rebar’s modulus of elasticity and yield strength). Several uniaxial material models exist in various software packages to simulate concrete and reinforcing steel.


As partially explained above, fiber-based elements — which are often referred to as just fiber elements — simulate a beam/column by discretizing it into a number of fiber sections and, simply put, by integrating the responses of those fiber sections.


Each fiber section represents a certain cross section of the beam/column and consists of a number of uniaxial fibers representing the materials in that cross section (e.g., cover/unconfined concrete, core/confined concrete, and longitudinal steel bars in an RC column cross section).


Each fiber is represented through a unique uniaxial material model, which generates the axial stress for any given axial strain considering the loading history of that fiber (i.e., to capture its cyclic behavior).


What sort of data do you need to input in advance? What do you input following the earthquake?


Depending on the analysis objectives, using the proposed modeling strategy, a bridge structure with repaired RC columns may be modeled before or after any earthquakes occur.


For instance, if the objective is to determine what is the most effective approach to repair the RC columns of a bridge after a future earthquake of a certain intensity, one needs to first run a preliminary nonlinear response history analysis on the original bridge (without any repair modeling) to predict the damage in the columns.


Depending on the predicted damage, repair methods would then need to be designed and implemented within the initial FE model through the proposed time-dependent material models.


The updated FE model is then used to run a longer response history analysis, which includes both the initial earthquake excitation (prior to repair) to maintain its effects on the RC columns and the second excitation (after repair changes are made in the model via the time-dependent material models) to evaluate the performance of the repaired RC columns.


Contrarily, if the objective is to determine what is the most effective approach to repair the RC columns of a bridge after an earthquake that has already occurred, one does not need to run any preliminary analyses and may start with the design of repairs and their modeling. In this case, the repair designs can be done based on the observed damage in the actual RC columns and not based on the model’s damage predictions. The first (pre-repair) earthquake excitation applied to the bridge model should nearly match the actual excitation during the real earthquake, and the second (post-repair) excitation may represent any hazard level of interest.


The proposed modeling strategy was validated through comparison of its response predictions with those of experimental tests on RC bridge columns before and after their repairs through various methods.


The experimental tests were all under quasi-static cyclic loading, and none of them involved dynamic excitation (e.g., through shake tables).


How are bar-slip and -buckling modeling tools integrated into the software?


The slippage of reinforcing steel bars in concrete and their buckling, which usually occurs following large tensile strains in the steel bars and after the loss of their surrounding concrete and the yielding of transverse bars, significantly affect the seismic performance of RC bridge columns.


However, such phenomena are often ignored in modeling of RC columns or accounted for through simplified material models.


Aside from the time-dependent material models, in this study, an innovative bar-buckling model and a novel bar-slip model were developed to enable the accurate simulation of bar buckling and slip in RC bridge columns.


The unique characteristic of the proposed bar-buckling model is its ability to account for the axial-flexural response interactions at steel bar cross sections. The bar-slip model explicitly considers the local bond-slip response of concrete and the cyclic behavior of steel bars, making it capable of predicting the variations of slip and axial strain over the rebar length. Both of the above models are designed as uniaxial material models and can be used within fiber sections. These material models have been validated using the results of past bar-slip and bar-buckling tests.


What aspects of the columns will the models simulate?


The current models are capable of capturing compressive concrete damage; yielding, low-cycle fatigue, and buckling of steel bars; and added concrete confinement due to CFRP and steel jackets.


The utilized fiber-based beam-column elements can reasonably accurately predict both global and local column responses, including force-displacement response, section strain (e.g., axial strain and curvature) distributions, section force (e.g., axial force and moment) distributions, and local axial strains/stresses at any point across the column. Such response parameters can be used to predict the level of damage over the entire volume of the simulated column, e.g., by comparing the computed axial strains at appropriate locations with the strain limits corresponding to concrete cover spalling and core concrete crushing to identify concrete damage.


The proposed modeling strategy is mainly applicable to flexure-critical RC columns — i.e., it is unsuitable to model shear- and shear-flexure-critical RC columns. In addition, the current modeling strategy does not explicitly simulate transverse reinforcement (although it considers it in the material models representing confined concrete) and cannot directly account for its effects on bar buckling.


Finally, since the behavior of pre-damaged concrete after additional confinement via steel or CFRP jacketing (i.e., after repair) is not well understood, the proposed modeling strategy does not accurately simulate their behavior.


How can engineers apply the information from the models to the actual bridge columns?


The fiber-based beam-column elements can be used to model RC columns within the larger FE models of bridge structures to more accurately predict the responses of the bridges in general and the performance of their RC columns specifically.


Such models allow damage prediction directly based on local response parameters (i.e., strains) rather than global response parameters (e.g., base shear or curvature), which are rather difficult to interpret.


The proposed modeling strategy enables the evaluation of repair methods both before and after any seismic event occurs.


For example, before any earthquake occurs, through appropriate response history analyses, one may predict the level of damage to the original bridge under earthquakes of various intensities, select potentially suitable repair methods, implement them through the numerical model, and examine how the bridge with repaired columns performs under future earthquakes of various intensities.


Such early analyses could let the decision-makers more quickly make decisions regarding the repair of damaged bridges and speed up the post-event recovery of transportation networks.


How much expertise in computer modeling do engineers need to use your models?


The proposed modeling strategy can be used by any engineer with a basic knowledge of structural analysis and FE modeling. Indeed, training/courses on nonlinear FE analysis could significantly enhance the overall ability of structural engineers in using such tools.


Are the models available for others to use?


The fiber-based beam-column elements employed in this study (referred to as “gradient inelastic” beam-column elements and formulated by the paper’s first two authors in the past) have already been implemented in an open-source structural analysis software and could be used to model any structural beams/columns whose responses are dominated by flexure (i.e., rather than shear).


The time-dependent material models developed in this study to enable modeling of repaired structural members as well as the bar-slip and bar-buckling material models are available by contacting us at [email protected].


What comes next?


At this point, we do not have any updates, and we are not planning to add any new capabilities to the proposed models in the near future. In the long run, we would like to incorporate shear-flexure interactions in the employed fiber-based beam-column element formulation to allow modeling of shear- and shear-flexure-critical RC columns.