Experimental and statistical investigation of a new concrete-composite beam with encased polymer tube wrapped by FRP

Abstract

A new concrete-composite beam with high mechanical performances to weight ratio is developed in this study. The proposed design technique consists to embed a cylindrical polymer tube wrapped by a GFRP Jacket in the mechanically ineffective concrete tensile zone. An experimental investigation is carried out on composite beams under bending loads until failure to evaluate the flexural capacity and the corresponding failure mechanisms. Based on the experimental results, statistical and preliminary reliability analyses using the FORM method are performed to assess the safety margin of the new beam. The confrontation between test and simulation results shows a satisfactory agreement, and represents a promising revelation regarding the improvement in terms of strength and ductility of such design compared to conventional reinforced concrete beams with traditional one.

Keywords

design / GFRP-Jacket / polymer tube / test / reliability analysis

Introduction

Fiber reinforced polymers (FRP) are experienced significant progress in mechanical engineering fields, aeronautics, and especially in civil engineering constructions. These innovative materials have found their new applications in the rehabilitation and the strengthening of reinforced concrete members. The enhancement of mechanical performances of concrete members strengthened with composite materials was experimentally demonstrated by several authors [ 1- 9] and several approaches for reinforced and confined concrete structures by FRP composites have been developed. One of the most used strengthening methods was the bonding of external composite plates on the exposed faces to failure. In this connection, tests carried out by [ 10] on simply supported beams reinforced with FRP sheets, under four point flexural loads, showed that the reinforced beam records a significant increase in strength and a reduction in ductility compared to the reference one without FRP reinforcement. However, many works available in the literature [ 11- 13], have studied problems of the bonding interface between concrete and FRP due to the stresses concentration. These studies have showed that the adhesive failure implies sudden failure of concrete members. In conclusion the bond at FRP/Concrete interface is influenced by a number of factors such as the type of FRP reinforcement, the type of adhesive and its thickness, the compressive strength of concrete, moisture, surface preparation, workmanship, and temperature level [ 14].

To ensure safety and long lifetime of composite materials and structures, which are restricted by the dispersion of their mechanical properties, particularly in terms of their tensile strength [ 15], many reliability analyses have been performed and proposed by several researchers [ 16– 19]. These studies allow that the performance estimation of systems which exhibit notable fluctuations cannot be captured by deterministic models. Recently, structural reliability analyses have allowed significant progress in the conception phases and for maintenance programs through a more rational estimation of the risk exposure. Moreover, reliability analysis works carried by Frangopol et al. [ 20, 21] and Milton [ 22] out on reinforced concrete columns have showed the importance of the load path, the load correlation and random variables of concrete in the reliability assessment.

Our study aims to introduce new fully-composite concrete-based beams, with polymer and fiber components. Structural elements which have a reduced own weight and high mechanical performances are developed. Such design consists to integrate in the flexural concrete tensile zone a polymer tube wrapped by a GFRP fabric to improve its flexural stiffness. To testify the proposed technique, an experimental investigation is carried out, on the basis of classical experiments model used in the study of structure components under flexural loading [ 23- 29]. The average test results in terms of strength, ductility and high mechanical performances to weight ratio compared to conventional concrete and reinforced concrete beams are emphasized and discussed.

The experimental work were completed by statistical and preliminary structural reliability analyses in order to allow for a better understanding of the level of uncertainty associated with the presented experimental values and observations. In fact, these analyses based on test results was performed to assess the safe margin and also to draw complete conclusions about the interest of the proposed technology. The reliability index which reflects the risk exposure of crack initiation and propagation was assessed by the First Order reliability Method for various loading levels.

Experimental investigation

A total of twenty four (24) rectangular beams have been tested. Tests were carried out in two series. In the first one: Six (06) identical concrete-composite beams referred to as (C-C-B), with 80×160×1100 mm dimensions were casted. Reference specimens with the same geometrical characteristics were divided into three sets: Concrete beams (C-B), Concrete beams with encased polymer tube without fibers (C-T-B) and Reinforced Concrete ones referred to as (R-C-Bs), with two longitudinal deformed steel bars integrated in the tensile zone to be used for comparison purposes.

Description of the proposed system

The developed mechanical system is shown in Fig. 1. Geometrical characteristics, as well as the loading and boundaries condition are depicted in Fig. 1 (a). In the order to oppose to the development of lateral deformations of the tube, the composite fabric is extended along the height of the beam; and it is disposed perpendicularly to the neutral axis of the cross section as shown in Fig. 1 (b) and Fig. (2 b). The use of the GFRP fabric shown in Fig. 2 (a) is generalized because of the relative facilities of fiber fabrication, the good mechanical properties and the moderate cost and own weight. The various filaments of this fabric are arranging following two main directions (i.e., warps and wefts) in order to ensure the continuity of concrete between the compressive and the tensile zones of the beam.

Raw materials

Batches of concrete have been made according to the Dreux-Gorisse method, by mixing Portland cement; gravel with a maximum coarse aggregate diameter of 20 mm, natural sand, water and superplasticizers. (More detailed explanations are reported in Table 1). The concrete mixtures are prepared with a conventional rotary drum concrete mix, followed by a slump test according to EN 12350-2 standards. The 28-day compressive strength of the used concrete was determined using standard 160 mm by 320 mm cylinders, it was found to be 27.1 MPa.

The composite Jacket is made up of E-fibers-reinforced polymer FRP. The geometrical parameters of the used fabric are given as following: the thickness t_f = 1 mm, the filament cross section b_f = 3 mm² and the net space of each FRP mesh S_f = 15 mm. These dimensions agree with the granulometry of usual concrete works. The experimental behavior of used composite materials under tensile loading according to NF EN ISO 527-1 is shown in Fig. 3. However, the used steel bars have a 6 mm diameter and yield strength of 235 Mpa. The main mechanical properties of all reinforcement materials, used in this study are reported in Table 2.

The overall diameter of the tube was \varphi = 40 mm, and its thickness was 2 mm. Figure 4 shows the average load-deflection curve of the used polymer tube. The observed deformations and the overall behavior of this tube are in agreement with the mechanical properties of the used composite Jacket.

Manufacturing and loading procedure

Before casting the concrete, the longitudinal reinforcement steel bars and the cylindrical polymer tube wrapped by GFRP are integrated in the mold respectively for the (R-C-Bs) and the new (C-C-B). After casting, the concrete specimen was compacted using a vibrating table and consolidated. After 24 h, the specimens were demolded, and then the beams were cured in saturated limewater with 100% relative humidity for 28 days until testing. The effective span of the beams was 1000 mm and the distance between loads was 200 mm. The simply supported beams were loaded at a rate of 1 kN/min, using a universal ELE IBERTEST test machine of 200 kN capacity. Automatic statistical processing is performed at the end of each test sets. The loading rate is kept constant during the test procedure and the beams were instrumented to record load and deflection measurements.

Test results and analysis

The flexural behavior at ultimate limit state was experimentally studied by means of four-point bending tests. This part includes the analysis of the weight reduction, analysis of the load-deflection response and ductility, which enable to measure the differences in strengths between the reference reinforced concrete beam and the concrete-composite one, and also to draw the preliminary conclusions. Finally, analyses of failure modes of all studied beams that allows us to observe the failure mode of the new beam and to evaluate the contribution of the composite Jacket in observed behavior.

Weight analysis

The measured average own-weight of the reinforced concrete beams was 39.2 kg, while the concrete-composite beam weights only 30.4 kg. The concrete-composite beam weight was reduced by 20%, which can be transformed in additional dead loads. This weight reduction leads to an increasing in ductility and a reduction of the seismic stresses, which is very important for safety reasons because this cover plays the role of an alarm before overall collapse, and hence the building evacuation can be possible to save human fatalities [ 2].

Load-deflection response

Table 3 presents the details of average and standard deviation of test results, namely: crack initiation loads, ultimate loads, mid-span deflection at crack initiation and ultimate loads. Also the failure mechanisms for each test series obtained from identical six (06) specimens are reported. The control specimens based on concrete referred to as (C-B) are confronted to (C-T-B) ones, in order to quantify the loss on stiffness caused by the tensile concrete extraction and also to evaluate the stiffness recovery due to the embedded GFRP-Jacket; for more clarity the rupture loads and deflections for all tested beams are plotted in Fig. 5.

These average results confirm the effectiveness of the new design technique in terms of positive contribution in ductility and strength compared to conventional concrete and reinforced concrete beams. The confrontation of the load-deflection curves of all studied beams depicted in Fig. 6 shows that that the average strength of the composite beam is increased by an average of 60%, compared to classical reinforced concrete one.

The load capacity of the (C-C-B) was around of 21.41 kN, with a corresponding mid-span deflection of 4.62 mm. While the reinforced concrete ones provide an ultimate flexural capacity of 14.12 kN, with a corresponding deflection of 3.12 mm. Control specimens (C-B) and (C-T-B) are characterized by less flexural capacities, respectively in order of 8.89 and 7.23 kN, with a corresponding ultimate deflections of 2.4 mm and 3.9 mm respectively. In addition, the load-mid span deflection curves analysis shows that the non linear behavior of the new beam can be decomposed into three phases: The first phase corresponds to low strains, the mid span deflection increases linearly with the external applied load. The second phase corresponds to the cracks initiation and the cracks propagation. The last behavior phase corresponds to the plasticization of the FRP/Polymer tube and the final failure of the beam.

Failure mechanisms analysis

The failure mechanisms of the different studied specimens are depicted in Figs. 7 and 8. The failure of the control reinforced concrete beam shown in Fig. 8(a) is achieved after the plasticization of the tensile reinforcement bars, with a bending failure mode. This failure mechanism occurs more brutally than the failure mechanism of the developed concrete composite beam, which provides an acceptable level of flexural strength and ductility that is clearly seen in Fig. 7. Whereas the reference (C-T-Bs) are characterized by a sudden failure mechanisms as shown in Fig. 8(b).

The flexural cracks propagation thorough the new developed specimen is prevented by the combination of the mechanical performances of the GFRP Jacket, which allows in one hand to increase the load corresponding to the crack initiation and in other hand to ensure a relatively ductile behavior. The propagation of stresses caused by the radial deformations of the cylindrical polymer tube is also prevented, through the mobilization of the lateral pressure due to the embedded polymer tube wrapped by FRP. Moreover, cracks concentration in the compressive zone is observed at the failure as depicted on Fig. 7(a).

Statistical and reliability assessment

The verification of structural safety consists of the validation of a number of good-standing rules, resulting from the engineering knowledge, these rules state that loading effects must be limited to a certain admissible level [ 30]. Each of these rules represents a potential failure mode, defined in terms of the system basic variables, for which uncertainties and fluctuations can be modeled by random distributions. In this connection, the second section of this paper describes a coupled approach between the experimental results and statistical analysis in order to assess the safety margin of the developed system and to complete the conclusions done in the experiments, especially to evaluate the range of structural strengths for a 95% confidence interval. In addition, a preliminary reliability modeling was performed to assess the reliability index according to the applied loading and the load ratio that allow us to describe the safe and the failure domains for different loading levels.

Random variables modeling

Table 4 summarizes the mean values, the coefficient of variation (COV) as well as the range of the mean value and the COV results for a 95% confidence interval respectively for the resistance loads obtained by the experimental analysis for all tested beams. However, the acting load statistics take values ​​from the start of loading until the ultimate failure load. In most general cases, the distribution of the experimental values of composite beam parameters is a normal law (for example, see experimental results in [ 17, 19]). In this connection, a Kolmogorov–Smirnov test for goodness of fit is performed to decide if the tested beams sample comes from a population with a normal distribution using the R statistical software.

The associated P-values given in Table 4 are higher than significance levels usually used to test statistical hypotheses (the level of significance α was 5%), we accept null hypothesis that is sample data belong form a Gaussian distribution. In addition, the range of mean value and COV result for a 95% confidence interval is lower than 15%, which is less than the normal experimental scatter. In conclusion, the random variable distribution type is assumed to be normal.

Isoprobabilistic transformation

The FORM method requires working in a standard probability space, therefore the statistics for the resisting loads summarized in Table 4 are transformed into independent standard variables; mapping to the standard normal space of normally distributed variates of zero mean and unit variance, such that the integration density function becomes a standard normal density function. Several isoprobabilistic transformations thus allow for this passage [ 31, 32]. In this study the Rosenblatt [ 33] transformation is used as given by Eq. (1).

(1) U_i={\displaystyle \frac{X_i-u_i}{{\sigma }_i}},

where {\mu }_i and {\sigma }_i are respectively the mean value and the standard deviation. Figure 9 (a) shows the analytical superimposed normal distribution of the generated sample for the resisting load (M_R), corresponding to the developed concrete composite beam (C-C-B), in which the statistics are experimentally assessed. As regards the statistics of applied force, the authors take into account the physical reality of the loading procedure, since that includes the external load applied at the beam end (live load) as well as its own weight (dead load) which exhibit notable uncertainties due mainly to the unit weight of concrete and composites and also the geometrical characteristics of the beams, hence the total acting loads are subjected to certain errors. In addition, the acting force takes values ​​from the loading start until the ultimate failure load and on the basic of the reliability work carried out on composite based beams by Ribeiro et al. [ 34] the acting loads was assumed to follow a normal distribution, with a Coefficient of variation of 10%. Therefore, Fig. 9 (b) shows the analytical distribution of the generated sample for the acting load, corresponding to an applied load of 13 kN.

Safety margins calculations

The failure scenario of all beams defined in this reliability analysis is related to the ultimate failure mechanism obtained by the experimental campaign. The safety margin of the concrete-composite beam is canceled when the crack opening exceeds the limit state defined by the limit state function given in Eq. (2), in which X is the realization of the random variables vector. When the ultimate limit state is achieved, the failure will occur when the resisting load M_R equals the acting load M_S, in other words, when the safety margin goes to zero.

(2) G(\{X\})=M_R-M_S,

The reliability theory aims to determine the probability of failure of a structural system using a random formulation of the problem and the modeling of the failure mode through a mechanical reliability coupling. In this study, the reliability index β was assessed for different load ratios by an optimization process using the first order reliability method.

Preliminary reliability results

Preliminary reliability results were emphasized to assess the safety margin and the mechanical performances of the new beam. The evolution of the reliability index of the system as a function the applied external loading using the FORM method is emphasized and discussed to provide an interesting complement to the load-deflection response given in the experimental part. Figures 10 and 11 show respectively the confrontation of the reliability index evolutions according to the load effects and to the load ratio for all specimens considered in this study.

The reliability index which reflects the crack initiation risks exposure decreases significantly as a function the load ratio. This is causes by the cracks propagation in the beam elements until the limit state defined by the reliability model. The failure of the R-C-B is achieved for an ultimate flexural capacity of 13.12 kN, while, the safety margin of the developed beam achieves for a load capacity of 22.32 kN. Control specimens (C-B) and (C-T-B) are characterized by less reliability values and also moderate flexural capacities, respectively in order of 9.89 and 7.93 kN.

The confrontation shows a satisfactory agreement between the experimental and the numerical results and highlights the effectiveness in terms of reliability assessment and failure mechanisms of the new proposed design. In addition, these results confirm the improvement in terms of mechanical performances, particularly in terms of load ratio. Again, based on reliability results the enhancement in terms of flexural capacity of the composite beam compared to the conventional reinforced concrete one is estimated at 65%.

Conclusion

The main objective of this investigation is to study the non linear behavior concrete composite beams designed in order to reduce the structure weight and to improve the mechanical performances. The new design recommendation consists to incorporate in the tensile zone, a cylindrical polymer tube wrapped by a GFRP-Jacket. Test results show the effectiveness of this design technique in terms of positive contribution in strength and ductility, and in terms of weight reducing compared to conventional reinforced concrete beams. This investigation showed that this technology allows to reduce 20% of the structure weight and to increase the strength around of 60%.

The preliminary reliability and statistical results provide an interesting complement to the experimental study, through an explicit model applied on concrete composite beams under 04-points flexural load. The reliability model allows us to represent the reliability index evolutions according to the applied load and the load ratio. Again, the contribution in terms safety margin, compared to reinforced concrete beams are estimated around 65%.

The confrontation between test results and the preliminary reliability analysis ones shows a satisfactory correlation, and they agree on the contribution of the GFRP Jacket to decrease the flexural crack initiation and the cracks propagation in the considered beam. Results analysis suggests the interest of the use of composite materials to improve mechanical performances, in particular flexural capacity and ductility of concrete composite beams. Future work will focus on a coupling with theoretical modeling to highlight the influence of the variability of the parameters related to the geometrical characteristics, the mechanical properties, and the loading path in the reliability assessment, and also to determine the importance of each beam parameters. Authors believe that this process is revolutionary through its structure which takes account for the physical reality of all materials. More experiments and numerical simulations are necessary to draw complete conclusions about the interest of the proposed technology.

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