Influence of externally bonded FRP strengthening on compressive membrane action and robustness of concrete structures

摘要

Since robustness was first recognized as a significant issue after the progressivecollapse of Ronan Point Building in 1968, it has been recognized as one of themust-have structural properties and it is incorporated into current structural designcodes like the European Standard EN 1990 (CEN 2002). The requirementregarding robustness of a structure is prescribed as “A structure shall be designedand executed in such a way that it will not be damaged by events such as explosion,impact and the consequence of human errors to an extent disproportionate to theoriginal cause”. Following this requirement EN 1991-1-7 provides three strategiesto limit the implication of accidental situations: to design key load-bearingmembers, to limit damages via alternative load paths and to apply prescriptivemeasures. However, procedures to quantify structural robustness are not providedin Eurocodes. With respect to the second strategy, fiber reinforced polymer (FRP)strengthening can be an alternative in order to increase the structural robustness.Therefore, the influence of FRP strengthening on structural robustness is ofinterest. Moreover, although recent studies show that membrane actions havebenefits in enhancing the load carrying capacity of reinforced concrete (RC)structures, no investigations have been performed with respect to the effect ofmembrane actions on robustness of RC structures.The main objective of this Ph.D. research is to investigate the influence of FRPstrengthening and membrane actions on structural robustness of RC structureswithin the scope of the Eurocodes and the existing robustness quantificationmethodologies. Main tools including structural analysis, probabilistic modelling,Monte Carlo simulation as well as risk evaluation are adopted in the investigations.This thesis covers three main parts i.e. the investigation on membrane actions (inparticular compressive membrane action, CMA) in FRP strengthened concretestructures, the investigation of suitable frameworks for robustness quantificationand finally an application to a concrete frame structure to evaluate the influence ofFRP strengthening and CMA on structural robustness.An analytical CMA model for FRP strengthened RC one-way members is proposedby extending the Park and Gamble’s model (Park and Gamble 1980) which wasdeveloped to capture the CMA behavior in RC members. Based on structuralanalysis i.e. the requirements of compatibility and force equilibrium, it is foundthat CMA is significant in enhancing the load bearing capacity of FRP strengthenedRC one-way members if sufficient lateral restraint is available.In order to investigate the effect of CMA on structural reliability of FRPstrengthened concrete members, the probabilistic model for the tensile strength ofunidirectional FRP composites is developed since limited information regardingthis model can be found in the Probabilistic Model Code (JCSS 2001) or designguidelines. Based on experimental results reported in literature, a relatively largedatabase (in total 80 datasets) is built and the Normal, Lognormal and Weibulldistributions are selected to fit these datasets using a tail-sensitive Anderson-Darling statistic based measure of goodness-of-fit. Fitting results show that, fromthe perspective of experimental justification, the Normal, Lognormal as well asWeibull distributions can be used to model the tensile strength of FRP compositesas they are all accepted on the basis of goodness-of-fit tests on the selected datasets.In agreement with the adoption in guidelines for composites (e.g. MIL-HDBK-17-1F (2002)) and the adoption in literature, the Weibull distribution is proposed tomodel the tensile strength of unidirectional FRP composites for the reasons that ithas a theoretical justification to model composite materials and it provides moreconservativeness than either the Normal or Lognormal distributions does forstructural design. Furthermore, statistical uncertainties arising from parameterestimation are examined and the design-orientated characteristic value of thetensile strength of unidirectional FRP composites based on test results isformulated.On the basis of the proposed stochastic model for the tensile strength of FRPcomposites as well as the models recommended in the Probabilistic Model Code(2001) for properties of concrete and steel reinforcement, the extended CMA modelin FRP strengthened concrete members is further investigated in a probabilisticway by adopting Monte Carlo simulations. Reliability analysis shows that the effectof CMA on the reliability indices of FRP strengthened concrete beams issignificant. Moreover, a parametric study as well as a sensitivity analysis withrespect to uncertainty propagation are performed. The parameter study shows thatthe effect of the FRP ratio decreases with increasing values of the ratio. However,if the considered member is heavily strengthened with FRP reinforcement, suchdecrease is negligible. A similar conclusion applies to the FRP modulus and steelratio. Also, an increase of the yield strain of the steel reinforcement as well as theconcrete strength give rise to an increase of the resulting reliability index whereasan opposite conclusion applies to the effect of the ultimate compressive strain ofconcrete and the span-to-depth ratio. The sensitivity analysis shows that in generalan increase of variation of one of the variables causes a decrease of the reliabilityindex, which applies to all factors considered except for the ultimate compressivestrain of concrete. For concrete strength, FRP modulus and concrete cover, anincrease of variation significantly leads to a decrease of the reliability index; forthe ultimate strain of FRP and yield strain of steel, an increase of variationmoderately results in a decrease of the reliability index; and the effect of thelongitudinal restraint’s variation on the reliability index could be ignored. Basedon the results of the parametric study and sensitivity analysis, a design space isconstructed to calibrate the partial factor of the FRP strength within the scope ofEuropean guidelines. With the target reliability index being 3.8 for a referenceperiod of 50 years, a value of 1.65 is calibrated as the partial factor of FRP strengthfor the design situations in case the CMA effect is taken into account.With respect to the framework for the quantification of structural robustness, therequirements on structural robustness in current codes and guidelines and theexisting quantification methodologies are screened and analysed. The definition ofstructural robustness recommended in the European Standard EN 1990 iselaborated and the key to quantify structural robustness is pointed out in relation todamage disproportionality. On the basis of a literature review, the existingmethodologies for robustness quantification are classified into four categories i.e.the structural property based, structural performance based, probability / reliabilitybased and risk based methodologies, followed by an elaborated examination of theadvantages and limitations of these methodologies. It is found that structuralrobustness can be practically quantified from two perspectives by adoptingdifferent interpretations with respect to damage disproportionality. One way toquantify robustness is to perform a comparison of the structure between its intactand damaged states to quantify the damage disproportionality of the total damageto the initial damage due to the original cause in one way or another. Thisperspective forms the basis of the current property based, performance based aswell as probability / reliability based robustness indicators. The secondquantification perspective to carry out a comparison of the structure between itsdamaged state and its final state of interest relates to defining the damagedisproportionality as the disproportionality of the indirect consequences to thedirect consequences, which sets the basis of the risk based robustness indicator.Broadly speaking, each perspective provides useful information about robustnessand can be adopted where necessary.However, it is found that there are several limitations to the suitability andapplicability of the current methodologies for robustness quantification. Forexample, some of the current robustness indicators are deterministic and fail to takeinto account uncertainties while some of them are even not effective in robustnessquantification. One of the limitations is that the current robustness assessment doesnot quantitatively consider specific activities within the service life of a structure.Activities like health monitoring, maintenance and/or repair, deterioration,rehabilitation, strengthening, replacement and retrofitting are important in thelifetime of structures and might have significant effects on structural robustnessand should be encompassed in robustness quantifications. It is found that the riskbased methodology is promising in accounting for these activities in robustnessquantification. Therefore, these activities are modelled as time-dependent variablesand are quantitatively incorporated into the risk based methodology. A notionalexample considering deteriorations shows the efficiency of this incorporation toquantitatively evaluate the influences of the possible activities within thestructure’s service life on structural robustness.In order to assess the influence of FRP strengthening as well as CMA on structuralrobustness, a concrete frame office building is selected as an example. The exampleconsists of a plane frame structure under a central column removal scenario. Thestructure is subjected to permanent loads and imposed loads and is designedaccording to Eurocodes for a reference period of 50 years. Robustnessquantifications with respect to the original structure, the original structuresubjected to additional imposed loads, and the original structure strengthened withFRP composites and subjected to additional imposed loads are carried out. Duringthe process of robustness quantifications, the beta-unzipping method at level 1 andMonte Carlo simulations are adopted for determining the system failure probability.Robustness indicators including the probability based robustness indicators RI(redundancy) and V (vulnerability), reliability based robustness indicator  R andrisk based robustness indicator Irob were quantified and the results are comparedand analysed. It is found that for all robustness quantifications in this research therobustness indicators RI and V exhibit comparable behaviour while the indicatorsR and Irob exhibit another, but also comparable behaviour.It is found that for the concrete frame example the robustness decreasessignificantly if an increase of imposed loads is applied. After examining thecomponents (critical beams and columns), the structure is flexurally strengthenedwith FRP composites for critical beams and columns and the structural robustnessafter strengthening is quantified again. Results show that the specific strengtheningresults in an increase of the structural robustness. More specifically, compared tocases where no FRP strengthening is applied, the probability based robustnessindicators RI and V decrease by approximately 10%; the reliability basedrobustness indicator  R increases by 124%; and the risk based robustness indicatorIrob increases by 468%. This indicates that the robustness of a structure can beeffectively improved if the structure is properly strengthened with FRP composites.In addition, the CMA effect on the structural robustness is also investigated byconsidering CMA for the original structure strengthened with FRP composites andsubjected to additional imposed loads. In comparison with the structural robustnessafter strengthening, it is found that for the specific example the effect of CMA onstructural robustness is not significant. However, it is pointed out that the potentialfavourable and significant effect of CMA can only be slightly reflected in thespecified example due to the moderate size of the analysed plane frame structure.Hence, further research on structures of higher complexity is necessary to explorethe full potential of CMA.