Fuzzy Logic Based Condition Rating of Existing Reinforced Concrete Bridges

Fuzzy logic is a means for modeling the uncertainty involved in describing an event/result using natural language. The fuzzy logic approach would be particularly useful for remedying the uncertainties and imprecision in bridge inspectors’ observations. This study explores the possibilities of using fuzzy mathematics for condition assessment and rating of bridges, developing a systematic procedure and formulations for rating existing bridges using fuzzy mathematics. Computer programs developed from formulations presented in this paper are used for evaluating the rating of existing bridges, and the details are presented in the paper. In this approach, the entire bridge has been divided into three major components—deck, superstructure, and substructure—each of which is further subdivided into a number of elements. Using fuzzy mathematics in combination with an eigenvector-based priority setting approach, the resultant rating set for the bridge has been evaluated based on the specified ratings and importance factors for all the elements of the bridge. Then the defuzzified value of the resultant rating fuzzy set becomes the rating value for the bridge as a whole. It is argued that the methodology presented in this paper would help the decision makers/bridge inspectors immensely.     

Application of Fuzzy Sets for Remaining Life Assessment of Corrosion Affected Reinforced Concrete Bridge Girders

A methodology for remaining life assessment of reinforced concrete bridge girders affected by chloride-induced corrosion of reinforcement is proposed. The uncertainties in the values of the parameters characterizing the environment and, the variables affecting the time to corrosion initiation, and the rate of corrosion propagation are taken into account by treating them as fuzzy variables. The usefulness of the proposed methodology is illustrated through a case study, by comparing the times to reach different damage levels for a severely distressed beam, of Rocky Point Viaduct, determined using the proposed methodology with the observations from the field investigations. It is noted that the predicted times are in satisfactory agreement with the reported values. Hence, the methodology will be useful for the scheduling of inspections for reinforced concrete girders subjected to chloride-induced corrosion of reinforcement.     

Stiffness Degradation and Time to Cracking of Cover Concrete in Reinforced Concrete Structures Subject to Corrosion

Corrosion-induced cracks in reinforced concrete (RC) structures degrade the stiffness of the cover concrete. The stiffness degradation is mainly caused by the softening in the stress-strain relation in the cracked concrete. Limited efforts have been made to model the cracking and the corresponding effects on the cover concrete, despite of its importance in assessing and modeling the behavior of RC structures. This paper proposes a stiffness degradation factor to model the stiffness degradation of the cover concrete subject to cracking. The proposed factor is computed in terms of the cracking strain corresponding to the maximum opening of the concrete cracks based on an energy principle applied to a fractured RC structure. The time to cracking of the cover concrete is then determined as the time from the corrosion initiation needed by the crack front to reach the outer surface of the cover concrete. The proposed stiffness degradation factor and the method to compute the time to cracking are illustrated through two numerical examples. The times to cracking of the cover concrete that are predicted using the proposed method are in agreement with the measured values from laboratory experiments.     

Development of FRP Shear Bolts for Punching Shear Retrofit of Reinforced Concrete Slabs

A fiber-reinforced polymer (FRP) shear bolt system has been recently developed at the University of Waterloo in Canada. The system is used to protect previously built reinforced concrete (RC) slabs against brittle punching shear failure. The system requires drilling small holes in a RC slab around the perimeter of a column, inserting bolts into the holes, and anchoring the bolts at both external surfaces of the slab. Many existing RC slabs have been built without any shear reinforcement. Also, many of these slabs are in corrosive environments, e.g., parking garages, where the use of deicing salts accelerates reinforcement corrosion and concrete deterioration. Therefore, FRPs are ideal materials to be used for such retrofit. The challenge, however, is the development of mechanical end anchorages for FRP rods that are efficient, aesthetic, cost effective, and that can be installed on site. The research presented in this paper includes development of FRP bolts with mechanical anchorages and the results of testing done using the developed systems. A new anchorage technique for the FRP rods based on crimping the rod ends with the aluminum fittings was developed. The testing was done on isolated slab-column specimens representing interior slab-column connections in a continuous flat plate system. The specimens were subjected to simulated gravity loading. The developed FRP bolts worked very well in improving the performance of the slab-column connections and showing the benefits of using FRP in punching shear retrofit of reinforced concrete slabs in corrosive environments.     

Effects of Mixed Corrosion, Freeze-Thaw Cycles, and Persistent Loads on Behavior of Reinforced Concrete Beams

The effects of mixed corrosion and freeze-thaw cycles on the mechanical properties of concrete prism specimens and the effects of mixed corrosion, freeze-thaw cycles, and persistent loads on the structural behavior of reinforced concrete beams were experimentally studied. A mixed solution of NaCl and Na2SO4 was used as a corrosive medium. Results show that under alternating actions of freeze-thaw and mixed corrosive agents, increasing the number of freeze-thaw cycles decreases the compressive strength and the elastic modulus of concrete and increases the compressive strain corresponding to the maximum compressive stress. The degradation of concrete material properties accelerates with the increase of water-cement ratio. For reinforced concrete beams, a 4% reduction in the loading capacity is found when these are subjected to freeze-thaw cycles and mixed corrosion only. However, if these actions are coupled with persistent loading, as expected during the service life of reinforced concrete structures in cold regions, a more rapid drop in the strength and deformation capacity of the beams is identified. The degradation is enhanced by a larger persistent-loading ratio. The significance of an accurate simulation of service conditions in the durability study of reinforced concrete structures in cold regions is highlighted.     

Fragility Increment Functions for Deteriorating Reinforced Concrete Bridge Columns

The increased deformation and shear fragilities of corroding RC bridge columns subject to seismic excitations are modeled as functions of time using fragility increment functions. These functions can be applied to various environmental and material conditions by means of controlling parameters that correspond to the specific condition. For each mode of failure, the fragility of a deteriorated column at any given time is obtained by simply multiplying the initial fragility of the pristine/nondeteriorated column by the corresponding function developed in this paper. The developed increment functions account for the effects of the time-dependent uncertainties that are present in the corrosion model as well as in the structural capacity models. The proposed formulation is a useful tool for engineering practice because the fragility of deteriorated columns is obtained without any extra reliability analysis once the fragility of the pristine column is known. The fragility increment functions are expressed as functions of time t and a given deformation or shear demand. Unknown parameters involved in the models are estimated using a Bayesian updating framework. A model selection is conducted during the assessment of the unknown parameters using the Akaike information criterion and the Bayesian information criterion. For the estimation of the parameters, a set of data are obtained by first-order reliability method analysis using existing probabilistic capacity models for corroding RC bridge columns. Example fragilities of a deteriorated bridge column typical of current California’s practice are presented to demonstrate the developed methodology. The increment functions suggested in this paper can be used to assess the time-variant fragility for application to life cycle cost analysis and risk analysis.     

Fatigue of Reinforced Concrete Beams Strengthened with Steel-Reinforced Inorganic Polymers

Steel-reinforced polymer (SRP) composite materials are very attractive due to their low weight and high strength. The ease of installation which significantly reduces repair time and expense is another major advantage. One of the main disadvantages of SRP materials is that the matrices used for their fabrication are typically organic and thus they are susceptible to fire. In this study, a newly developed retrofit system is being used. It consists of high strength steel fibers impregnated in a fireproof inorganic matrix. The objective of this study is to examine the effects of this hybrid rehabilitation system on the fatigue performance of strengthened reinforced concrete beams. Sixteen 100?mm×150?mm×1200?mm reinforced concrete beams with enough transverse reinforcement to avoid shear failure were used in this study. Nine beams were strengthened with steel fiber sheets on their tension faces. The results from the present study indicate that the fatigue life of reinforced concrete beams, subjected to the same cycling load, can be significantly extended using externally bonded sheets. A rather important finding is that although the strengthening system increases the fatigue life of the beams, the failure mechanism remains the same in both strengthened and nonstrengthened beams. Thus, it is possible to predict the fatigue life of a cyclically loaded beam using existing fatigue models. Furthermore, no delamination failures were observed due to fatigue loading.     

Forecasting Project Status by Using Fuzzy Logic

This paper describes a forecasting method for predicting potential cost overruns and schedule delays on construction projects. The output of the forecasting method is useful in evaluating the project status at different time horizons and in quantifying the impact of the performance indicators on the profitability of the job. The method is intended for use by members of project teams in performing integrated time and cost control of construction projects. The paper addresses the effects of a number of factors, referred to in the developed method as indicators, on project cost overruns and schedule delays using fuzzy logic. The proposed forecasting method has been implemented in a prototype that operates in the World Wide Web environment. It has an open architecture that allows users to actively interact and, accordingly, makes use of their own experience and knowledge in the forecasting process. An example project is analyzed to test the developed prototype, demonstrate the use of the proposed method, and to illustrate its capabilities.     

Regularization of Inverse Problems in Reinforced Concrete Fracture

Reinforced concrete beams with flexural cracks are simulated by the bridged crack model. The weight function method of determining stress intensity factors has been followed to derive a transformation between the crack bridging force (the rebar force) and the crack opening displacements (CODs). The matrix of the transformation is then approximated by its finite difference equivalent within finite dimensional vector spaces. Direct problem of the transformation solves for CODs, which require a known rebar force. Alternatively, the inverse problem works out the rebar force from known CODs. However, the inverse transformations of such convolution type integral equations become ill-posed if input CODs are perturbed. The Tikhonov regularization method is followed in its numerical form to regularize the linear ill-posed inverse problem. Restoration of mathematical stability and consistency are demonstrated by specific examples, where the results of the direct and the corresponding inverse problem are cross checked. Results of the direct problem (i.e., the analytical CODs) are deliberately perturbed by adding machine generated random numbers of a certain width. The inverse problems are solved with these CODs to simulate practical situations, where measured CODs data will inevitably be noisy. Computations reveal that the inverse analysis of CODs satisfactorily determines the rebar force without cross-section information.     

Damage of Reinforced Concrete Structure due to Severe Soil Expansion

In Irbid City, Jordan, foundation designs made before 1983 were based on bearing capacity criteria with a limited knowledge of high shrink/swell soil problems. The use of wide and shallow foundation systems was generally the practice rather than the exception in this area. Lack of structural rigidity and insufficient dead load pressure of the foundation systems used in the Irbid area where soils of high shrink/swell are present often cause serious problems related to the performance of constructed facilities. This paper presents a case study typical of a severely cracked one-story reinforced concrete (RC) building constructed over the expansive clay of Irbid City. The building is founded on a mat foundation (solid RC structural slab) embedded at a shallow depth and bearing directly on expansive clay. It is unfortunate that the high shrink/swell potential of the foundation soil had not been recognized properly in the design stage. Based on field and laboratory investigations, remedial construction for the damaged building was proposed. The proposed remedial construction was performed, and more than 10 months have elapsed since the remedial work was completed, with the performance of the building in perfect condition.     

Residual Strength of Impact-Damaged CFRP Used to Strengthen Concrete Structures

Although previous research has demonstrated the improvement in performance of reinforced concrete structures enhanced with externally applied carbon fiber reinforced polymers (CFRP), the effect of transverse impact damage on the strength of the CFRP enhancements is unknown, and no guidelines have been provided that describe which impact events warrant CFRP repair or replacement. The impact events, such as dropped tools, collisions, and low-speed projectiles may cause critical damage to the epoxy matrix and fibers that is undetectable through visual inspection. The purpose of this research is to provide insight into the level of transverse impact needed to initiate critical damage in wet layup CFRP enhancements, which will serve as a guideline for inexpensive and immediate damage assessments. To simulate a variety of impact events, impactors (tups) of different sizes and shapes were dropped from several heights. The impacts were performed with a guided drop-weight apparatus, designed to achieve free-fall behavior. The results show that impacts that only cause indention of the FRP surface do not significantly affect the tensile strength, but impacts that cause crushing of the epoxy (seen as whitish areas) can indicate as much as a 63% residual tensile strength. Furthermore, for the test conditions considered, tests showed that impacts with a peak impact pressure greater than 21?MPa (3,000?psi) reduced the tensile strength of the CFRP.     

Nondestructive Assessment of Reinforced Concrete Structures Based on Fractal Damage Characteristic Factors

Nondestructive damage assessment of civil engineering structures has become a focus of increasing interest for recent decades. Its core is to extract effective damage characteristic information capable of reflecting structural damage status. In this study, fractal theory is adopted to extract the fractal damage characteristic factors of a reinforced concrete structure by characterizing its surface-crack distributions. The concentrated and even load spaces are generalized as applicable spaces for employing fractal-to-structural damage assessment. As demonstrated in the damage assessment of reinforced concrete beams under four-point bending and aged crossbeams of an operation bridge in a sluice, the surface-crack distributions of reinforced concrete structures exhibit monofractal character in the concentrated load space, and multifractal character in the even load space. The physical damage interpretations of the extracted monofractal and multifractal damage characteristic factors in the respective load spaces are then established by analyzing the correlations between the monofractal dimension and the natural frequency, and between the multifractal singular spectrum and the average carbonized depth and residual material intensity, respectively. The closely linear fitting relationships between the fractal quantities and traditional damage characteristic factors indicate that the fractal (i.e., monofractal and multifractal) quantities can serve as viable and novel damage characteristic factors in the online damage assessment of concrete structures. It is significant that the proposed fractal damage characteristic factors overcome some disadvantages of traditional damage characteristic factors in practical applications, and they extend the technique of fractal into the meaningful damage assessment of reinforced concrete materials.     

Reinforced Concrete Walls with Vulnerable Foundations

Moment capacities of shallow foundations are compared with those of reinforced concrete walls in order to determine the likelihood of exceeding the bearing capacity of the supporting soil in buildings subjected to strong ground motions. Recommendations are made regarding the appropriate modeling at the base of first-story walls in compliance with the moment-capacity axial load interaction of the supporting foundations.     

Analytical Model for FRP-Confined Circular Reinforced Concrete Columns

One disadvantage of most available stress–strain models for concrete confined with fiber-reinforced polymer (FRP) composites is that they do not take into consideration the interaction between the internal lateral steel reinforcement and the external FRP sheets. According to most structural concrete design codes, concrete columns must contain minimum amounts of longitudinal and transverse reinforcement. Therefore, concrete columns that have to be retrofitted (and therefore confined) with FRP sheets usually contain lateral steel. Hence, the retrofitted concrete column is under two actions of confinement: the action due to the FRP and that due to the steel ties. This paper presents a new designed-oriented confinement model for the axial and lateral behavior of circular concrete columns confined with steel ties, FRP composites, and both steel ties and FRP composites. Comparison with experimental results of confined concrete stress–strain curves shows good agreement between the test and predicted results.     

Performance of Template School Buildings during Earthquakes in Turkey and Peru

Most of the public school buildings in Turkey and Peru are built according to a small number of template plans. Over the years, these template plans are kept the same while the structural designs are varied with the seismic design codes in force. During recent strong earthquakes in Turkey and Peru, the design concepts and construction styles for these template school buildings have been put to test. In this paper, observed earthquake performances of template reinforced concrete school buildings with moment-frames or moment-frames and shear walls are compared. The comparison reveals choices in design that were successful as well as those that were not. The disastrous results of “captive columns” are demonstrated in illustrations from what has been observed in recent earthquakes in these seismically active countries. It is shown that since 1997 the Peruvian practice has been producing school buildings that perform well during strong earthquakes.     

Probabilistic Assessment of Concrete Structure Durability under Reinforcement Corrosion Attack

In the context of performance-based approaches, sustainability and whole life costing, the concrete structure durability issue has recently gained considerable attention. The present paper deals with service life assessment using durability limit states specialized for concrete structures. Both initiation and propagation periods of reinforcement corrosion are considered and a comprehensive choice of limit states is provided. The approach is based on degradation modeling and probabilistic assessment, enabling the evaluation of service life and the relevant reliability level, serving thus to facilitate the effective decision making of designers and clients. For this purpose the selected analytical models for degradation assessment are randomized and appropriate software has been developed. Three numerical examples are presented: a comparison of modeled carbonation depth with in situ measurements on a cooling tower, and analyses of crack initiation due to corrosion and loss of reinforcement cross section.     

Probabilistic Capacity Models and Fragility Estimates for Reinforced Concrete Columns Incorporating NDT Data

Knowing the ability of reinforced concrete (RC) bridges to withstand future seismic demands during their life-cycle can help bridge owners make rational decisions regarding optimal allocation of resources for maintenance, repair, and/or rehabilitation of bridge systems. The accuracy of a reliability assessment can be improved by incorporating information about the current aging and deterioration conditions of a bridge. Nondestructive testing (NDT) can be used to evaluate the actual conditions of a bridge, avoiding the use of deterioration models that bring additional uncertainties in the reliability assessment. This paper develops probabilistic deformation and shear capacity models for RC bridge columns that incorporate information obtained from NDT. The proposed models can be used when the flexural stiffness decays nonuniformly over a column height. The flexural stiffness of a column is estimated based on measured acceleration responses using a system identification method and the damage index method. As an application of the proposed models, a case study assesses the fragility (the conditional probability of attaining or exceeding a specified capacity level) of the column in the Lavic Road Overcrossing for a given deformation or shear demand. This two-span concrete box-girder bridge located in Southern California was subject to the Hector Mine Earthquake in 1999. Pre- and postearthquake estimates of the univariate shear and deformation fragilities and of the bivariate shear-deformation fragility are computed and compared. Both displacement and shear capacities are found to decrease after the earthquake event. Additionally, the results show that the damage due to the Hector Mine Earthquake has a larger impact on the shear capacity than the deformation capacity, leading to a more significant increment in the shear fragility than in the deformation fragility.     

Validity of SDOF Models for Analyzing Two-Way Reinforced Concrete Panels under Blast Loading

The combined manual TM 5-1300/NAVFAC P-397/AFR 88-22, Structures to Resist the Effects of Accidental Explosions, published by the joint departments of the Army, the Navy, and the Air Force, has been used in all NATO countries for the past 50 years for protective design applications. The manual was recently reformatted to meet the Department of Defense Unified Facility Criteria (UFC). As a first step, the current production of the new document, UFC 3-340-02, focused on making the original TM 5-1300 available in a more functional format so that future technical updates can be facilitated. In this study, a single-degree-of-freedom (SDOF) model, based on the guidelines of the UFC 3-340-02, was used to formulate a FORTRAN code to predict the response of SDOF systems under blast. The code was used to generate pressure-impulse (P-I) diagrams for a series of two-way reinforced concrete (RC) panels with different dimensions, aspect and reinforcement ratios, and support conditions. The P-I diagram predictions were compared to the results of experimentally validated nonlinear explicit finite-element (FE) analyses and significant differences in deflection and shear predictions were observed. The general trend of results and the major characteristics of the P-I diagrams were discussed in terms of the discrepancies between the SDOF and the FE predictions. The work presented in this paper is expected to contribute to improving the modeling provisions of the two-way RC panels in the future edition of the UFC 3-340-02 by understanding the limitations of SDOF models using advanced FE analysis techniques.     

Simplified Methodology for the Evaluation of the Residual Strength of Corroded Reinforced Concrete Beams

Steel corrosion in reinforced concrete (RC) structures leads to change of steel mechanical properties, longitudinal cracking in the concrete cover, and other related effects that weaken the serviceability and load capacity of the composites. It is therefore extremely important to have methods targeted to the evaluation of the structural damage induced by corrosion for estimating the residual load capacity of a structure, and then for inspection procedures and strengthening the maintenance interventions. This paper presents a simplified methodology capable of providing estimates of the residual life of corroded RC beams. The proposed method uses damaged material properties, and accounts for the length of partial corrosion and the amount of corrosion, concrete loss and change of bond strength within this specified length. A comparison of the model predictions with the experimental results published in the literature shows the validity of the model. It is also concluded that the ultimate flexural moment of corroded RC beam will not significantly influenced by the partially corroded or unbonded length and the bond characteristics over this partial length as long as the tensile steel of the beam can reach its yield strength. In addition, although complete loss of bond over the partial length is assumed to asses the residual strength of corrosion-damaged RC beam, neglecting the influence of bond strength within the corroded length may lead to underestimate the ultimate flexural capacity of the damaged beam, especially when the corrosion level of tensile steel of the RC beam is not very high.     

Bond Strength of Fiber Reinforced Polymer Rebars in Normal Strength Concrete

The bond behavior of reinforcing bars in concrete is a critical issue in the design of reinforced concrete structures. This study focuses on the bond strength of fiber reinforced polymer (FRP) rebars in normal strength concrete. Four different types of rebars were tested using the pullout method: aramid FRP (AFRP); carbon FRP (CFRP); glass FRP (GFRP), and steel. This involved a total of 151 specimens containing 6, 8, 10, 16, and 19?mm rebars embedded in a 203?mm concrete cube. The test embedment lengths were five, seven, and nine times the rebar diameter (db). For each rebar, the test results include the bond stress–slip response and the mode of failure. The test results showed that the bond strength of an FRP rebar is, on average, 40–100% the bond strength on a steel rebar for pullout failure mode. Based on this research, a proposal for the average bond strength of straight FRP rebars in normal strength concrete is made, which verifies an existing bond strength relationship (GFRP) and extends its application to AFRP and CFRP. It is an expression that is a function of the rebar diameter, and the concrete compressive strength.