Tension stiffening approach for interface characterization in recycled aggregate concrete

Accepted Manuscript Tension stiffening approach for interface characterization in recycled aggregate concrete Caroline Santana Rangel, Mayara Amario, Marco Pepe, Yiming Yao, Barzin Mobasher, Romildo Dias Toledo Filho PII:

S0958-9465(16)30412-7

DOI:

10.1016/j.cemconcomp.2017.06.009

Reference:

CECO 2846

To appear in:

Cement and Concrete Composites

Received Date: 27 July 2016 Revised Date:

15 June 2017

Accepted Date: 19 June 2017

Please cite this article as: C. Santana Rangel, M. Amario, M. Pepe, Y. Yao, B. Mobasher, R.D. Toledo Filho, Tension stiffening approach for interface characterization in recycled aggregate concrete, Cement and Concrete Composites (2017), doi: 10.1016/j.cemconcomp.2017.06.009. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Tension Stiffening Approach for Interface Characterization in Recycled Aggregate Concrete

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Caroline Santana Rangel Department of Civil Engineering, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil. e.mail: [email protected]

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Mayara Amario Department of Civil Engineering, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil. e.mail: [email protected]

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Marco Pepe Department of Civil Engineering, University of Salerno, Italy e.mail: [email protected]

Yiming Yao School of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, AZ, USA email: [email protected]

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Barzin Mobasher School of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, AZ, USA email: [email protected]

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Romildo Dias Toledo Filho Department of Civil Engineering, COPPE, Federal University of Rio de Janeiro, P.O. Box 68506, CEP: 21945-970, Rio de Janeiro, Brazil. e.mail: [email protected]; Corresponding author: [email protected]

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ACCEPTED MANUSCRIPT ABSTRACT This study proposes a comprehensive analysis on the structural performance of reinforced Recycled Aggregate Concrete members. Particularly it summarizes the results of an experimental investigation aimed at analyzing the tension stiffening behavior of normal and high strength class concretes produced with Recycled Concrete Aggregates (RCAs). The

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mixtures were proportioned in order to achieve 25 and 65 MPa of compressive strength and, moreover, several recycled-to-natural coarse aggregates replacement ratios were considered: 0%, 25% and 50%. The results derived from this type of test furnish a comprehensive analysis on both the steel-to-matrix interaction and the crack formation and

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propagation on concrete elements as well as distributed cracking mechanisms. Using a finite difference numerical model, the experimental results are used to back-calculate and identify

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the steel-to-concrete bond slip law. Also, it is an alternative mean of developing the stresscrack-width law for concrete in tension. The results showed that the use of recycled concrete aggregate does not affect the resulting concrete performance and, therefore, the RCAs can be successfully employed, up to the levels analyzed herein, for the production of structural

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elements made with normal and high strength class concrete mix.

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ACCEPTED MANUSCRIPT KEYWORDS: Recycled aggregate concrete, Tension stiffening, High strength concrete,

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Steel-concrete bond, Crack propagation.

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1. INTRODUCTION The major environmental impact of construction industry extends to an exorbitant extraction of natural resources, transportation of large volume of materials, emission of pollutants, and

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consumption of high amounts of energy. The disposal of the large amount of waste generated is likely to take center stage in many construction projects [1]. In order to reduce the environmental impact, sustainable construction practices require the realization and potential

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for reducing the main cost drivers including: construction costs, net recycling, and greenhouse gas generation. Among the available opportunities, a paradigm shift in reuse and

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recycling efforts in concrete production will represent a major opportunity in the most widely used building material in the world [2]. One of the most effective alternatives from economic, environmental, and technical point of views is the recycling of concrete construction waste to produce Recycled Concrete Aggregates (RCAs) in substituting the natural aggregates [3].

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This is an attractive solution as the quality aggregate sources are becoming scarcer and the mining, transportation, and processing costs are exceeding at a higher rate compared to other construction materials. As a direct consequence, factors that influence the role of RCAs on

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the resulting Recycled Aggregate Concretes (RACs) properties need to be analyzed [4].

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Among these factors, the RCAs present different intrinsic characteristics in comparison with the ordinary natural aggregates, and considered as composites of “original” natural aggregate and Attached Mortar (AM) [5]. The presence of AM phase, generally, confers a more porous structure and, consequently, a higher water absorption capacity with a lower specific gravity. These parameters affect the RAC performance both at fresh and hardened state if an adequate design is not employed [6,7]. Although several studies demonstrate the feasible use of RCAs for concrete production, only limited studies on the structural response of RAC elements are available in literature.

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ACCEPTED MANUSCRIPT The bond behavior between RAC and steel rebars has been widely investigated and results show that the presence of RCA does not alter the adhesion of reinforcement and the surrounding RAC matrix [8-10]. In some cases, a better adhesion in the case of RAC occurred [11-13]. Moreover, it has been demonstrated that bond behavior is influenced by the

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grain size [14,15] and the processing parameters [16] of RCAs. Sadati et al. [17] demonstrated that the shear capacity of structural concrete beams produced with coarse recycled concrete aggregate was almost unaffected by the presence of RCAs. Results were

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evaluated by means of shear strength, load-deflection trends, crack patterns, and crack propagation. On the contrary, Arezoumandi et al. [18] found that the shear strength of

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concrete beams produced with 100% RCA, was 12% lower than the ordinary reference beams. In a follow-up study Arezoumandi et al. [19] found the flexural behavior of reinforced recycled aggregate concrete to be similar to the reference samples, with a smaller flexural crack spacing for the RAC beams. Moreover, concrete structures with different replacement

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ratios of coarse-recycled aggregates demonstrated a similar behavior by Pacheco et al. [20]. An overview of the potential widespread use of RACs indicates that in order to confidently specify the material for structural concrete at various proportions, additional

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information on the failure mechanisms of reinforced RAC members are needed to

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substantiate their use. One of the main opportunities offered by the present approach of developing RACs is that, by monitoring and controlling particle size distributions, optimal concrete mixtures with minimized cement content by means of particle packing models can be obtained.

The present study addresses two main aspects of the use of RACs: in terms of uniaxial full range of tensile stress-strain response (that includes the softening range) as well as the bond of RACs with reinforcing bars. Tension-stiffening tests are performed on normal and high strength reinforced RAC elements made with up to 50% RCAs content. Results of these

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ACCEPTED MANUSCRIPT tests provide a comprehensive perspective on the steel-to-matrix interaction as well as the formation and propagation of cracks on concrete elements. The results were also evaluated for distributed cracking mechanisms and through the use of a finite difference numerical model, they were used to back-calculate the steel-to-concrete bond slip law as well as an

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alternative means of developing the stress-crack-width law for concrete in tension. The

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numerical model is capable of simulating the various stages of a tension-stiffening test [21].

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2. MATERIALS AND METHODS 2.1

Materials

Quartz sand with a nominal diameter lower than 4.75 mm was used as Natural Fine

mm and 9.5 mm, was used as Natural Coarse Aggregate (NCA).

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Aggregate (NFA) while a granite type stone, with a nominal diameter ranging between 4.75

The Recycled Concrete Aggregates (RCAs) were crushed from the debris of reinforced

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concrete beams produced and tested in laboratory [22]. The compressive strength of the

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original concrete was 33-36 MPa and the water-to-cement ratio was 0.60. In the production process of the RCAs, the original concrete was crushed initially with a stone crusher and subsequently with a jaw crusher (model Queixada 200 produced by Vegedry [23]). The RCAs were then homogenized by longitudinal blending bed technique [24], and finally sieved to coarse RCAs with a nominal diameter ranging between 4.75 mm and 9.5 mm. Fig. 1

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shows the three types of aggregate used in this study. Several tests were performed on both natural and recycled aggregates with the main results summarized in Table 1. Particularly, the specific gravity and the water absorption tests

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of NCA and RCA were performed according to the NBR NM 53 [25]. Meanwhile, the

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specific gravity and the water absorption capacity of NFA were performed according to the NBR NM 52 [26] and NBR NM 30 [27], respectively. The cement used was “high initial strength Portland cement”, CPV-ARI, according to the National Brazilian Standard (NBR) 5733 [28]. The physical and chemical properties of the cement are presented in Table 2. A polycarboxilate superplasticizer (Glenium 51) with a solid concentration content of 30% and specific gravity of 1.087 g/cm³ was used in all mixes for workability control.

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ACCEPTED MANUSCRIPT Deformed steel rebar with a diameter of 20 mm, yield and ultimate strength of 540 and 705 MPa respectively, and elastic modulus of 232.9 GPa [29] was used for all the samples. 2.2

Concrete mixture composition

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The concrete mixture proportioning was performed in accordance to the Compressible Packing Model (CPM) proposed by de Larrard [30]. This model assumes that the main physical and mechanical properties of concrete are governed by the overall packing density

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of the granular skeleton. Therefore, a simultaneous combination of mechanical compression and vibration process was used to measure the experimental compactness of each granular

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compound [30]. This method was adopted for NCA, NFA and RCA and, in order to obtain a more accurate result, each aggregate type was separated into three size classes. For the coarse aggregates: class 1 – larger than 7.93 mm; class 2 – 6.30 to 7.93 mm; class 3 – smaller than 6.30 mm. For the fine aggregate: class 1 – larger than 2.36 mm; class 2 –1.18 to 2.36 mm;

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class 3 –smaller than 1.18 mm. Two measurements were performed for each of the three classes of aggregates and compactness values are reported in Table 1. Moreover, according to the CPM, it is necessary to calibrate two compressive strength

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parameters related to aggregates [30]. These are defined as “p” and “q” where, “p” represents the bond between the aggregate and the paste, while “q” identifies the intrinsic strength of the

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aggregates. Table 1 reports the experimental compactness measurements and the “p” and “q” values obtained for each aggregate used in this study. An optimization procedure was performed with the software BetonLab Pro 3 for designing the concrete mixture composition. Two different concrete class strength were considered: 25 MPa and 65 MPa. Then, for each strength class, three mixture proportions were developed: a reference concrete with only natural aggregates and two RAC mixtures with 25% and 50% of coarse RCAs replacement level (by volume). The concrete mixture compositions are summarized in Table 3. The mixtures are labelled “CXX-YY”, where "XX"

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ACCEPTED MANUSCRIPT indicates the resistance class (25 or 65) and "YY" indicates the RCA level (00 for the reference concrete, and 25 or 50 for the RACs). The superplasticizer was used in weight equal to 1% of the cement weight in all concrete mixtures. It is noted that in the RAC mixtures the NCAs were not simply replaced by RCAs. In

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fact, the CPM defines the optimal compactness for each mixture considering the individual properties of each compound in order to achieve the desired strength (i.e., 25 MPa and 65 MPa in this study).

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In order to take into account of the high porosity of RCAs, the water absorption capacity was measured for RCAs and the 10-minutes absorption (simulating the mixing time)

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was considered during the mix design and the casting process (resulting in a value equal to 5.6%) [6]. 2.3

Experimental program and testing procedures

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For each mixture, slump tests were performed [31] and cylindrical specimens (with 100 mm diameter and 200 mm height) were prepared for the mechanical characterization: compressive strength at 7 and 28 days (four samples for each age), elastic modulus (four

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samples tested at 28 days) [32] and tensile splitting strength (four samples tested at 28 days) [33]. Then, 150 x 150 x 800 mm³ prisms were prepared for the tension stiffening tests (three

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samples for each mixture tested at 28 days): the specimens were reinforced with a single deformed steel rebar (d=20 mm) with a 1200 mm length. The tension stiffening test set-up as adopted from the NBR 7477 [34] is shown in Fig. 2. The tests were conducted at a constant speed of 0.3 mm/min until the steel yield strength was reached, at that point the speed was increased to 5 mm/min. The axial strain was measured using two electrical transducers (LVDT) attached on both specimen sides, as shown in Fig. 2.

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3. MATERIAL PROPERTIES Table 4 presents the mean values (with the coefficient of variation) of the slump, 7- and 28days compressive strength (fc,7, fc,28), strain at maximum stress (εc), elastic modulus (E),

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splitting tensile strength (ftd), and ftd/fc,28 ratio. Workability

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The slump test results were approximately 100 mm for all the concrete mixtures in this study. This is a satisfactory level of workability as it allows for casting of concrete. Moreover, Table

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4 shows that concrete’s workability increased with the use of RCAs. The required cement content decreased with increasing RCA and natural sand as shown in Table 3. This reduced quantity of fines caused by the reduction of the amount of cement in mixtures with RCA may explain the slight variation of the slump test values for C25 reported in Table 4. In C65, along

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with the reduction of the amount of cement, there was also a greater increase of natural sand in the mixtures with RCA. This increase of natural sand may increase the fines content, and for this reason, the slump variation did not occur for this class. Compressive behavior

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The results in Table 4 highlight that the strength based design requirements for both normal (25 MPa) and high strength (65 MPa) mixtures for all the reference and RAC mixtures were achieved. The importance of the mix design method for concrete with RCA is noted since a direct replacement of natural aggregate by RCA does not guarantee the desired strengths since different properties of recycled material needs to be considered in the mix design [6]. Typical compressive behavior of class C25 and class C65 are presented in Fig. 3. It is observed that the normal strength concrete has similar behavior at the three RCA levels (0%, 25% and 50%), both in the ascending and the post peak branches. The final cracking pattern

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ACCEPTED MANUSCRIPT in all 25MPa concretes was identified by several diagonal cracks as the specimens maintained their initial cylindrical appearance. The high strength concretes also exhibit similar behavior under uniaxial compressive load for all RCA levels as shown by the typical curves of 0%, 25% and 50% RCA ratio in all stages. The 65 MPa concretes are different from the 25 MPa

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mixtures and exhibited an explosive rupture mechanism at the maximum load. In fact, the 65 MPa concretes did not show the descending phase due to the brittle fracture mode while the 25 MPa concrete continued to gradually deform after the peak. Moreover, the strain at

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maximum stress and the elastic modulus (Table 4) showed very similar values in each class, thus failing to register any effects by the influence of RCAs.

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Finally, analysis of the data in Table 4 shows a higher elastic modulus E, for the high strength concrete than the normal strength concrete, as well as the compressive strength and the strain at maximum stress. Indirect Tensile Behavior

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The tensile splitting strength results (Table 4) present a rather constant range of values which are similar at all RCA replacement levels. The C25 class had a tensile splitting-to-

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compressive strength ratio around 11% and the C65 class had values around 7.5% (Table 4). Therefore, while the compressive strength increases, the tensile strength also increases;

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however, the ratio of the tensile splitting-to-compressive strength ratio decreases with increasing compressive strength.

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4. TENSION STIFFENING BEHAVIOR The purposes of tension stiffening tests are several folds. First, the standard tension tests are difficult to conduct as localization effects, and control parameters make it extremely difficult

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to obtain reliable test data. Second, the characteristics of the sample are of interest since when concrete is used in a reinforced concrete condition. For example in a flexural test, the strain softening helps in characterization of the distributed cracking in the tension zone.

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The tension stiffening behavior can be generally characterized in a simple 1-D reinforced concrete element using four phases (Fig. 4a): elastic pre-cracking, cracking, post-

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cracking and steel yielding [35]. The matrix stress is represented in Fig. 4 as σm. In the precracking phase (elastic line a in Fig. 4a), the load is distributed in accordance to the rule of mixtures and the relative stiffness of the two phases of the matrix and the reinforcement under the assumption of perfect bond distribute the load. This branch is governed by the

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elastic modulus (EpreAc=EsAs+EmAm), with c for composite, s for steel, and m for matrix. The appearance of the first crack does not lead to catastrophic failure, but will result in the load redistribution between the matrix and the reinforcement. With the initiation and propagation

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of the first crack, the load is distributed, transferred to the steel and returned back to concrete

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by means of the bond properties, and once the stress build up is sufficient, additional cracks occur depending on the nature of the bond. The multiple cracking phase begins (line b in Fig. 4a) starting from the first crack load (F1st) and the first crack strain (ε1st) and represents the tensile strength of the matrix. As cracking occurs in the brittle matrix, the load is transferred to the reinforcement, and additional strain will result in further cracking until the matrix is divided in several segments. As the multiple cracking phase occurs at an approximately constant stress, the matrix experiences loss in resistance and elastic modulus by the formation

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ACCEPTED MANUSCRIPT of each crack until it can no longer contribute in a substantial manner to the load-carrying capacity. When there is no further multiple cracking, and the concrete matrix is already divided by parallel cracks, any additional strain causes the debonding, slip, and stretching of the

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reinforcement. Therefore, after the cracking stage, when the steel supports the tensile loads almost entirely, the composite still withstands the increasing load (line c in Fig. 4a). At this stage, the rigidity of the reinforcement supports the ascending behavior of the load vs. axial

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strain curve in the post-cracking zone. The composite curve in the post-cracking zone also shows the isolated rebar curve as the composite behavior is governed almost entirely by the

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reinforcement in the higher strain levels and it is possible to determine the post-cracking equivalent modulus (Epost). The increase in tensile load occurs until the steel yielding phase (line d in Fig. 4a) where the final yield load (Fyield) can be obtained. Finally, the failure occurs when the reinforcement reaches its ultimate strength.

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The uncracked concrete segments still carry a portion of tensile loads in nonlinear stages due to the load transfer mechanisms between steel and matrix. Thus the contribution to the overall load by the matrix can be used to evaluate the tension stiffening effects. In the

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present study, the matrix contributions are obtained by two approaches as shown in Fig. 4b:

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1) isolate the matrix contribution from composite load-strain diagram, i.e., the matrix load is calculated by subtracting the steel force from the total force applied on a cross section based on the assumption of rule of mixture ( σ ROM ); 2) determine the average of the matrix stress (σm) from a nonlinear matrix distribution diagram with formation of cracks, which is provided by a finite difference model used in this study ( σ FDM ).

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ACCEPTED MANUSCRIPT 4.1

Properties and behavior of RAC in the tension stiffening test

Fig. 5 reports the typical curves (average of three measurements) of load vs. axial strain under tension stiffening test for normal (C25) and high strength (C65) concrete members. The tests are extended beyond the yield point of the isolated rebar. The graphs reported in

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Fig. 5 confirm, for both C25 (Fig. 5a) and C65 (Fig. 5b) class strength, the trend above described [35].

A comprehensive analysis has been performed to address the results summarized in

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Table 5. Table 5 indicates that the pre-cracking elastic modulus (Epre) of the composite is

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higher for the C65 mixtures in comparison with the C25 ones as expected. The higher modulus of the C65 mixtures is correlated to their higher strength (Table 4). Moreover, the presence of RCA does not affect the initial elastic modulus, in fact, within the same concrete strength class, the Epre values are almost constant for all the RCA replacement levels. The first crack load (F1st) and the strength (f1st) values show that an increase in the

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compressive strength causes an increase in the first crack values of the tension stiffening. This was expected as the steel-concrete adhesion increases with the concrete strength [36]. In the 25 MPa class, a small increase in first crack load value is observed for the increase of the

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RCA level compared to a marginal reduction in corresponding load value in 65 MPa class

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(Fig. 5b). It is expected that since the first crack strength is governed by the cement matrix, aggregate and ITZs strength, for a low strength class (i.e., 25 MPa) the higher porosity of the RCAs did not affect the overall strength of the composite, meanwhile, for C65 class the presence of a more porous aggregate (i.e., RCA) caused a marginal reduction in the corresponding strength. Moreover, it is worth to highlight that the variation reported by the experimental evidence is within the usual scatter of concrete mixtures. The first crack strain (ε1st) values slightly increase with the compressive strength from 25 to 65 MPa as seen in compression test results (Fig. 3). The first crack strain values within

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ACCEPTED MANUSCRIPT each class show a small increase in the values of C25 mixtures with increasing the RCA level, but this does not extend in the C65 class, in which the slightly lowest value is registered for the C65-25 mixture. This is mainly due to the overall amount of the aggregate included within the cement matrix. As a matter of the fact, the C25 mixtures present a higher

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amount of aggregates in comparison with the C65. For this reason, in the C25 mixtures the elastic properties of the composite (i.e., the concrete mixtures) are affected more by the presence of RCAs than in the case of C65 where these properties are, mainly, governed by

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the cement matrix characteristics. Similar to the previous observation on the first crack

observed for concrete mixtures.

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strength, the variations in the experimental results are within the conventional scatter

The values of final crack strain (εfinal) show a wide range of differences between the C25 and C65 classes which is attributed to the higher number of cracks in the higher strength class. The graphs in Fig. 5a show two or three oscillations in the force response in the

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multiple cracking phase for the C25 class which indicate cracks formation which for the higher strength class the number of oscillations increases in the typical curves shown in (Fig. 5b) to about six to seven. These oscillations are characteristic tension stiffening distributed

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cracking in the response of load vs. axial strain in the multiple cracking phase. In some

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specimens, it was observed that cracks opened at the same time and therefore they appear in the graph load vs. axial strain in the same force discontinuity. For the C25 class, as shown in in Table 5, there was an increase in the final crack strain value with the increasing of the RCA percentage, but no relation between the use of RCA and the final crack strain value was found for the C65 class. As straining progresses, the post-cracking elastic modulus (Epost) approaches the steel elastic modulus (which is obtained in the tensile test with isolated bar) with EsVs = 3.25 GPa, where Vs is the (dimensionless) volume content of the isolated steel rebar. The values in

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ACCEPTED MANUSCRIPT Table 5 associate the increase of RCA content with a small increase in the post crack modulus for both C25 and C65 classes, indicating that the use of the recycled concrete aggregates improves the post-cracking elastic modulus. The difference between the composite curve and the isolated rebar throughout the entire graph indicates the existence and

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level of matrix contribution throughout the entire tension stiffening test, even when the concrete contains several cracks.

Finally, the final yield load (Fyield) of the tension stiffening indicates a composite

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behavior governed almost entirely by the steel which yields at about 172 kN, which is statistically similar for all the cases. The final yield load of all composites was higher than the

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results for the isolated rebar since the matrix still contributes to the tensile stresses. Multiple cracking process of RAC

Typical transverse cracking of the tension stiffening of C25 and C65 classes are shown in

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Fig. 6 and Fig. 7, respectively. For C25 mixtures, a pattern of three large and one to two fine cracks was observed (Fig. 6), whereas, for C65 class, the specimens showed a larger number of finer cracks (Fig. 7). For both C25 and C65 the cracking patterns are in accordance with

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force discontinuities registered in the multiple cracking phases reported in Fig. 5. The presence of RCAs does not interfere in the cracking patterns for both normal and high

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strength concretes.

The sequence cracking throughout the test for each mixture is shown in Fig. 8. The average crack spacing vs. axial strain decreases with new cracks until it reaches a constant value, indicating the saturation cracking level. As the crack spacing stabilizes, the strain increases only due to the opening of existing cracks or deboning. The final spacing magnitudes are similar within each class, but a slight increase is measured in the case of C65 with 50% of RCAs. The C65 class has a lower final value of average spacing between cracks

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ACCEPTED MANUSCRIPT because high strength concrete specimens had a larger number of cracks at the end of the test than the normal strength concrete specimens, as seen in Fig. 6 and Fig. 7. Moreover, crack width measurements were conducted at seven locations along each crack as shown in Fig. 9. The crack openings for class C25 are larger than for class C65 and

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some slight increases were registered for the crack width values in cases of RACs.

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5. TENSION STIFFENING MODELING A finite difference method developed by Soranakom and Mobasher [21] was used to model the tension stiffening behavior in themembers. A tension specimen is idealized as a series of

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1-D segments consisting of rebar, matrix, and interface elements. The matrix is treated as brittle with no strain-softening response. One end of the sample is fixed and an increasing load is applied at the other end such that as the cracking stress of the matrix is exceeded and

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it cracks, however the load is now carried by the rebar through the interface elements. The individual pullout segments continue to transfer the load back and forth between the steel and

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matrix. Fig. 10a presents the discretized finite difference model of the cracked specimen with the total embedded length L discretized into N nodes of equal spacing, h. Once cracking takes place, the specimen is divided into smaller segments Ls(1), Ls(2),… Ls(q) with each segment containing n(q) number of local nodes, where q is the segment index. Free body diagrams of

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representative nodes are shown in Fig. 10b, where si = nodal slip, Fi = nodal rebar force, Bi = nodal bond force, Gi = nodal spring force. The equilibrium equations can be derived in terms of the primary unknown variable slip s, defined as the difference between the deformations of

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the rebar with respect to the matrix. Nodal equilibrium equations are constructed and each

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nodal force is expressed as the product of slip by stiffness. A global system of equations including stiffness matrix [C], nodal slip vector {S}, and force vector {T} was subsequently obtained as follows:

[C]n,n{S}n = {T}n

(1)

In nonlinear analysis, an iterative solution algorithm is used to enforce material constitutive laws and obtain load-deformation curves. Once the solution of nodal slip values is obtained, the corresponding stress, strain and crack spacing can be subsequently computed.

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ACCEPTED MANUSCRIPT Set up, assembly, as well as the solution algorithm of equilibrium equations based on several parametric studies were discussed [38]. Studies [39-41] have shown that initial shrinkage in concrete specimen prior to loading can lead to a change of member length and reduction in cracking strength. In the data analysis, the effect can be taken into account by offsetting the

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member response such that the yield strain of the rebar is matched with the observed yield point of composite response. In the finite difference model, free shrinkage strain can be applied as initial boundary condition by introducing an initial slack in the steel tensile model.

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Fig. 10c schematically presents the distributions of slip, matrix stress (σm), rebar stress (σf) and bond stress (τ) in cracked segments. The tension force in both steel rebar and matrix have

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positive values, while the distribution of the stress in matrix and steel change in accordance with the placement of cracks. However, the load-carrying capacity of the matrix in the uncracked segments does not diminish as a sign of tension stiffening effect. The load carried by the steel rebar is transferred back to the matrix and σm is maximized at the center line of

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each cracked segment. As the load increases and σm reaches matrix cracking strength σm,cr, new cracks form. The following a shear lag pattern, the bond stress varies from its maximum at the crack to a value of zero at bonded region. Specifically, as an indicator of the tension

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stiffening effects of post-cracking stage, an average stress σm,ave can also be obtained as by

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normalizing the numerical integration of the matrix stress:

σ m,ave =

L

1 σ m dx L ∫0

(2)

The numerical simulations have been carried on C25 and C65 specimens. Steel stressstrain and interface bond-slip models used for simulations are illustrated in Fig. 11, where the initial slack is applied to the steel model of C65 to address the more apparent shrinkage effects in high strength concrete. Fig. 12 and Fig. 13 compare the experimental and simulated load-strain responses of C25 and C65 samples where the other model parameters are

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ACCEPTED MANUSCRIPT indicated. The model was able to simulate the experimental responses accurately up to the peak in three stages, i.e., linear elastic, multiple cracking, and crack widening/rebar pull out. The responses of different sample groups exhibit similar behaviors while the marginal variabilities can be captured mainly by the cracking strength of the concrete matrix. The

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higher cracking force of C65 is captured by the higher matrix cracking strength ranging from 4.22-4.47 MPa used in the model as against to C25 sample where 1.97–2.27 MPa is used. The crack spacing-strain responses are illustrated in Fig. 12 and Fig. 13, where a

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smaller saturated crack spacing is observed in high strength concrete (C65). The differences in the final crack pattern can be explained by different rebar-matrix bond characteristics in

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the two mixes. The force carried by the intact matrix segments between two parallel cracks are transferred from the rebar through the interface. A higher bond strength corresponding to a steeper slope of the bond–slip model proportionally decreases the force transfer rate (Force/Length) to the matrix. As a result, less development length is required to achieve the

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cracking strength which results in smaller final crack spacing [42]. Experimental study conducted by Dancygier et al. [43] has shown a dramatic increase in the bond strength from normal strength concrete (NSC) to high strength concrete (HSC) matrix. For the 20 mm

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diameter rebar, the average bond strength in NSC was 13.2 MPa while the value in HSC was

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almost two times higher (35.2 MPa). In the present study, bond strength of 13.0 MPa is used to predict the responses of C25 specimens while 35.1, 33.7 and 32.43 MPa are employed for C65-00, C65-25 and C65-50, respectively (Fig. 11b). Moreover, Fig. 14 shows the existing correlation between the concrete compressive strength and the corresponding steel-to-concrete bond strength. Particularly, it summarizes some experimental results obtained in literature for the case of RAC mixtures [8-16 ,44,45] such as the correlations proposed by fib [36,46]. The values reported in the Fig. 14 where collected by employing different test methods: direct pullout test (P) and beam test (B). The

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ACCEPTED MANUSCRIPT results indicate that the bond strength is more influenced by the compressive strength of the matrix than the recycled aggregate replacement ratio. In addition, a large scatter of the results is registered and this can be mainly attributed to the test methodology adopted. In fact, when a direct pullout test is performed, the measured bond strength increases due to the

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compression stress around the steel rebar embedded within the matrix. For these reasons, the identification of the bond strength through the tension stiffening modelling can represent a more reliable result due to the fact that in the real condition the concrete matrix is subjected

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to tensile stress.

On the other hand, the crack evolutions in the C65 specimens vary slightly as the

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percentage of RCA replacement increases. Even though the saturated crack spacing values are similar, the multiple cracking of low percentage replacement forms at lower strain values prior to saturation. The higher cracking strength and earlier formation of multiple cracks indicate higher rebar bond strengths in the specimens with lower RCA content. Therefore,

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higher bond strength is used to simulate the C65-00 specimens while the lowest bond-slip responses predict the C65-50 samples, as shown in Fig. 11b. The tension stiffening effect can also be evaluated by isolating the matrix contribution

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from the load-strain diagram. In the present study, the matrix stress is obtained by subtracting

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the steel rebar isolated behavior from the composite. As a comparison, the matrix stress-strain responses are also calculated by finite difference model using eqn. (2). The matrix contribution diagrams for the mixture considered in this study are reported in Fig.15. In addition, stresses are evaluated at different levels of deformation including the peak stress, terminate of multiple cracking/saturation, onset of steel yielding, and ultimate stage (strain value of 4000 µε). The stress values (with the coefficient of variation) are summarized in Table 6. Results indicate that for both classes the ascending region of the stress-strain curves is affected by the strength class until the first crack opening, as expected by the behavior seen

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ACCEPTED MANUSCRIPT in Fig. 5. After the first crack, both classes go through the multiple cracking phase with a rapid decreasing level of matrix contribution as the tensile loads are transferred to the steel reinforcement. As the multiple cracking is finished, matrix stress decreases slightly and this stage is dominated by crack widening and rebar pull out. The yielding stages of rebar are

stresses is observed in the matrix up to the maximum strain.

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consisted of strain hardening and necking, where approximately constant level of residual

The matrix stress-strain curves obtained by numerical model agree well with the C25

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specimens both in pre- and post-crack stages. However, the residual stresses of model results for C65 samples overestimate the experimental data for approximately one time higher,

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which may be explained by the aggregate interlock mechanisms. It is known that the bond strength between aggregates and cement matrix is much higher in high strength concrete, such that the cracks tend to propagate through the aggregates instead of crack deflection usually observed in normal strength concrete. Therefore, the interlock mechanisms are less

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pronounced in the high strength concrete which leads to relatively lower residual matrix stress. In finite difference model, however, the matrix cracking is only determined by the tensile strength of concrete, i.e., the peak stress in matrix contribution. Higher matrix strength

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corresponds to a higher average stress as illustrated in Fig.15. Variations in aggregate

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interlock behaviors are not considered in this model, which may explain the discrepancies between the model simulation and experiment. No pronounced decrease in the matrix contribution stress during the steel yielding phase was observed: this evidence proves that the uncracked concrete segments contribute in the support of tensile stresses, even in the steel yielding phase. Furthermore, the matrix contribution stress values at the end phase for both classes are similar, indicating that in this test both normal strength concrete as high strength concrete have a contribution from the

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ACCEPTED MANUSCRIPT concrete matrix around 0.6-0.7 MPa, and the quantity of RCA does not affect this property of

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the concrete.

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6. CONCLUSIONS This study analyzed the mechanical behavior of normal and high strength recycled aggregate concrete under tension stiffening loading and the following main conclusions can be stated:

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- The results highlighted the importance of using a rational and adequate mixture proportioning method for RAC mixtures (CPM in the present study). As a matter of fact, in all the cases the desired compressive strength was achieved and, consequently, this

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demonstrates that performing a direct replacement of natural aggregate by RCAs does not always guarantee the control and the predictability of the required mechanical performance

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(i.e., strength and elastic modulus) since the recycled aggregates are characterized by different intrinsic characteristics in comparison with ordinary ones; - The C65 concretes presented higher resistance under the tension stiffening loads than the C25 mixtures. Moreover, the presence of RCAs seems to not affect the resulting tensile

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behavior of the matrices and the steel-to-concrete interaction. This was more evident in the case of C25 while some slight changes were registered in the case of C65 with RCAs; - The RCA content does not interfere also in cracking pattern for both normal and high

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strength concrete: the C25 class showed a pattern of smaller number of cracks (three large

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cracks and one or two fine cracks) than the C65 (up to seven to eight fine cracks) and, in all the cases, the cracks are formed transversely to the length of the specimen with an almost equidistant spacing between cracks; - The C65 concretes exhibited lower values of crack spacing and width than the C25 ones. Moreover, the results highlighted that the presence of RCAs caused a slight increase in both cracks spacing and cracks width; - The finite difference model adopted in this study, already proposed in literature for ordinary concretes, can be successfully applied also in the case of RCAs for the tension

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ACCEPTED MANUSCRIPT stiffening simulation. It allowed to back-calculate and identify the steel-to-concrete bond slip law as well as it represents an alternative means for the development of the stress-crack-width law for concrete under tensile loads; - The constitutive laws (i.e., steel-to-concrete bond and the matrix stress-strain tensile

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behavior) identified in this study with the proposed approach can represent more reliable models describing the concrete elements’ behavior than those ones, generally, obtained by performing “ordinary” standard tests (i.e., direct pull-out and direct tensile tests): this is

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mainly due to the fact the tension stiffening tests better reproduces the real load conditions

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for reinforced concrete members.

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7. REFERENCES O. Ortiz, F. Castells, G. Sonnemann, Sustainability in the construction industry: A review of recent developments based on LCA, Construction and Building Materials 23(1) (2009) 28-39.

[2]

C. Meyer, The greening of the concrete industry, Cement and concrete composites 31(8) (2009) 601-605.

[3]

P. Van den Heede, N. De Belie, Environmental impact and life cycle assessment (LCA) of traditional and ‘green’concretes: literature review and theoretical calculations, Cement and Concrete Composites 34(4) (2012) 431-442.

[4]

M. Behera, S.K. Bhattacharyya, A.K. Minocha, R. Deoliya, S. Maiti, Recycled aggregate from C&D waste & its use in concrete–A breakthrough towards sustainability in construction sector: A review, Construction and building materials 68 (2014) 501-516.

[5]

K. McNeil, T.H.K. Kang, Recycled concrete aggregates: A review, International Journal of Concrete Structures and Materials 7(1) (2013) 61-69.

[6]

M. Pepe, R.D. Toledo Filho, E.A. Koenders, E. Martinelli, A novel mix design methodology for Recycled Aggregate Concrete, Construction and Building Materials 122 (2016) 362-372.

[7]

C. Faella, C. Lima, E. Martinelli, M. Pepe, R. Realfonzo, Mechanical and durability performance of sustainable structural concretes: An experimental study, Cement and Concrete Composites 71 (2016) 85-96.

[8]

A. Ajdukiewicz, A. Kliszczewicz, Influence of recycled aggregates on mechanical properties of HS/HPC, Cement and concrete composites 24(2) (2002) 269-279.

[9]

S.W. Kim, H.D. Yun, W.S. Park, Y.I. Jang, Bond strength prediction for deformed steel rebar embedded in recycled coarse aggregate concrete, Materials & Design 83 (2015) 257-269.

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[1]

[10] J. Xiao, H. Falkner, Bond behaviour between recycled aggregate concrete and steel rebars. Construction and Building Materials 21(2) (2007) 395-401. [11] V. Corinaldesi, G. Moriconi, Influence of mineral additions on the performance of 100% recycled aggregate concrete, Construction and Building Materials 23(8) (2009) 2869-2876. [12] I. Fernandez, M. Etxeberria, A.R. Marí, Ultimate bond strength assessment of uncorroded and corroded reinforced recycled aggregate concretes, Construction and Building Materials 111 (2016) 543-555. [13] H. Yang, W. Lan, Y. Qin, J. Wang, Evaluation of bond performance between deformed bars and recycled aggregate concrete after high temperatures exposure, Construction and Building Materials 112 (2016) 885-891.

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ACCEPTED MANUSCRIPT [14] S.W. Kim, H.D. Yun, Influence of recycled coarse aggregates on the bond behavior of deformed bars in concrete, Engineering Structures 48 (2013) 133-143. [15] S.W. Kim, H.D. Yun, Evaluation of the bond behavior of steel reinforcing bars in recycled fine aggregate concrete, Cement and Concrete Composites 46 (2014) 8-18.

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[16] K. Pandurangan, A. Dayanithy, S.O. Prakash, Influence of treatment methods on the bond strength of recycled aggregate concrete, Construction and Building Materials 120 (2016) 212-221. [17] S. Sadati, M. Arezoumandi, K.H. Khayat, J.S. Volz, Shear performance of reinforced concrete beams incorporating recycled concrete aggregate and high-volume fly ash, Journal of Cleaner Production 115 (2016) 284-293.

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[18] M. Arezoumandi, A. Smith, J.S. Volz, K.H. Khayat, An experimental study on shear strength of reinforced concrete beams with 100% recycled concrete aggregate, Construction and Building Materials 53 (2014) 612-620.

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[19] M. Arezoumandi, A. Smith, J.S. Volz, K.H. Khayat, An experimental study on flexural strength of reinforced concrete beams with 100% recycled concrete aggregate, Engineering Structures 88 (2015) 154-162. [20] J. Pacheco, J. de Brito, J. Ferreira, D. Soares, Flexural load tests of full-scale recycled aggregates concrete structures, Construction and Building Materials 101 (2015) 65-71. [21] C. Soranakom, B. Mobasher, Modeling of tension stiffening in reinforced cement composites: part I - Theoretical modeling, Materials & Structures 43 (2010) 1217-30.

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[22] A.P.R.Vaz, Comportamento de vigas reforçadas submetidas a carregamento cíclico, PhD Thesis (In portugues), Federal University of Rio de Janeiro, COPPE/UFRJ, Brazil, 2013. [23] www.vegedry.com.br Accessed [14.04.2016]

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[24] A.B. Da Luz, J.Á. Sampaio, S.C. Alves França (Eds.), Tratamento de Minérios., 5ª Edição. (In Portugues), CETEM/MCT, Rio de Janeiro, Brazil, 2010.

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[25] NBR NM 53: Coarse aggregate - Determination of the bulk specific gravity, apparent specific gravity and water absorption. Associação Brasileira de Normas Técnicas, 2009. [26] NBR NM 52: Fine aggregate - Determination of the bulk specific gravity and apparent specific gravity. Associação Brasileira de Normas Técnicas, 2009. [27] NBR NM 30: Fine aggregate - Test method for water absorption. Associação Brasileira de Normas Técnicas, 2001. [28] NBR 5733: High early strength Portland cement - Specification. Associação Brasileira de Normas Técnicas,1991. [29] NBR ISO 6892-1: Metallic materials — Tensile testing Part 1: Method of test at room temperature. Associação Brasileira de Normas Técnicas, 2015. [30] F. de Larrard, Concrete mixture proportioning: a scientific approach, E&FN Spon, London and New York, 1999.

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ACCEPTED MANUSCRIPT [31] NBR NM 67: Concrete - Slump test for determination of the consistency. Associação Brasileira de Normas Técnicas, 1998. [32] NBR 5739: Concrete - Compression test of cylindric specimens - method of test. Associação Brasileira de Normas Técnicas, 2007.

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[33] NBR 7222: Concrete and mortar - Determination of the tension strength by diametrical compression of cylindrical test specimens. Associação Brasileira de Normas Técnicas, 2011. [34] NBR 7477: Determinação do coeficiente de conformação superficial de barras e fios de aço destinados à armadura de concreto armado (in Portugues). Associação Brasileira de Normas Técnicas, 1982.

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[35] J. Aveston, G.A. Cooper, A. Kelly, The properties of fiber composites. In: Conference Proceedings of the National Physical Laboratory, Guildford: IPC Science and Technology Press Ltd., 1971, 15–26.

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[36] Fib (CEB-FIP) Bulletin No. 10: Bond of reinforcement in concrete, Stage-of-art report. International Federation of Structural Concrete/Féderation Internationale du Béton (fib), 2000. [37] A. Bentur, S. Mindess, Fibre reinforced cementitious composites. 2 ed. London: Taylor & Francis, 2007. [38] C. Soranakom, B. Mobasher, Geometrical and mechanical aspects of fabric bonding and pullout in cement composites. Matererials & Structtures 42(6) (2009) 765-777.

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[39] P.H. Bischoff, Tension stiffening and cracking of steel fiber-reinforced concrete, Journal of materials in civil engineering 15(2) (2003) 174-182. [40] G. Kaklauskas, V. Gribniak, D. Bacinskas, P. Vainiunas, Shrinkage influence on tension stiffening in concrete members, Engineering Structures 31(6) (2009) 13051312.

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[41] V. Gribniak, G. Kaklauskas, L. Torres, A. Daniunas, E. Timinskas, E. Gudonis, Comparative analysis of deformations and tension-stiffening in concrete beams reinforced with GFRP or steel bars and fibers, Composites Part B: Engineering 50 (2013) 158-170. [42] Y. Yao, F.A. Silva, M. Butler, V. Mechtcherine, B. Mobasher, Tension stiffening in textile-reinforced concrete under high speed tensile loads, Cement and Concrete Composites 64 (2015) 49-61. [43] A.N. Dancygier, A. Katz, U. Wexler, Bond between deformed reinforcement and normal and high-strength concrete with and without fibers, Materials and Structures 43(6) (2010) 839-856. [44] C. Lima, A. Caggiano, C. Faella, E. Martinelli, M. Pepe, R. Realfonzo, Physical properties and mechanical behaviour of concrete made with recycled aggregates and fly ash, Construction and Building Materials 47 (2013) 547-559.

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ACCEPTED MANUSCRIPT [45] Z. Dahou, A. Castel, A. Noushini, Prediction of the steel-concrete bond strength from the compressive strength of Portland cement and geopolymer concretes, Construction and Building Materials 119 (2016) 329-342.

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[46] International Federation for Structural Concrete (fib). The fib Model Code for Concrete Structures 2010. Federal Institute of Technology Lausanne–EPFL, Section Génie Civil, Switzerland, 2013.

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ACKNOWLEDGEMENTS The present study is part of the activities carried out by the Authors within the “SUPERCONCRETE″ Project (www.superconcrete-h2020.unisa.it) funded by the European

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Union's Horizon 2020 Research and Innovation Programme under Grant Agreement No 645704 (H2020-MSCA-RISE-2014) and within the Science Without Border project funded

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by CNPq.

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1 2

Fig. 1. Natural and recycled aggregates.

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3

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31

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2

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1

Fig. 2. Prismatic specimen test set-up and dimensions.

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3

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1

Fig. 3. Typical curves of compressive strength at 28 days vs. axial strain for normal and high strength concretes.

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2 3

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4

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(a)

1 2

(b)

Fig. 4. (a) Schematic description of the typical behavior of the composite in the tension stiffening test [35], (b) matrix contribution.

3

34

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Fig. 5. Typical curves of load vs. axial strain at tension stiffening test for (a) normal strength concretes (C25) and (b) high strength concretes (C65), beyond the typical behavior of isolated rebar in tensile test.

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2 3 4

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1

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5

35

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1

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Fig. 6. Typical cracking process of the tension stiffening concrete specimen of C25 class under tensile stresses, with numbering order of cracks.

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2 3

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4

36

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1

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Fig. 7. Typical cracking process of the tension stiffening concrete specimen of C65 class under tensile stresses, with numbering order of cracks.

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2 3

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4

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(a)

(b)

1 2 3

Fig. 8. Typical curves of the average spacing between cracks vs. axial strain at tension stiffening test for (a) normal strength concretes (C25) and (b) high strength concretes (C65), compared with the typical behavior of load vs. axial strain.

4

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(a)

(b) 1 2 3

Fig. 9. Typical curves of the crack width vs. axial strain at tension stiffening test for (a) normal strength concretes (C25) and (b) high strength concretes (C65), compared with the typical behavior of load vs. axial strain.

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1

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5

Fig. 10. Finite difference model: (a) cracked concrete member, (b) free body diagram of six representative nodes labeled as “A”-“F”, (c) distributions of slip, matrix stress, rebar stress and bond stress.

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2 3 4

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(a)

(b)

Fig. 11. (a) Rebar stress-strain model and (b) interface bond-slip model used to simulate the tensile responses of normal strength concretes (C25) and high strength concretes (C65).

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1 2

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Bond stress (MPa)

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3

41

(b)

(d)

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(c)

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(a)

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Crack spacing (mm)

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(e) 1 2

(f)

Fig. 12. Comparison between experimental and simulated results of load-strain and crack spacing-strain for (a)&(b): C25-00, (c)&(d): C25-25, (e)&(f): C25-50.

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(b)

1 2

(d)

Crack spacing (mm)

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Load (kN)

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Load (kN)

Crack spacing (mm)

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(a)

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Load (kN)

Crack spacing (mm)

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(e) (f) Fig. 13.Comparison between experimental and simulated results of load-strain and crack spacing-strain for (a)&(b): C65-00, (c)&(d): C65-25, (e)&(f): C65-50.

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3

Fig. 14. Bond strength for steel rebars in Recycled Aggregate Concrete.

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44

1

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Fig.15.

Matrix contribution (MPa)

Matrix contribution (MPa)

matrix

Matrix contribution (MPa)

measurement

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experimental

Matrix contribution (MPa)

and

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between

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responses

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stress-strain

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of

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Comparison Matrix contribution (MPa)

Matrix contribution (MPa)

numerical model.

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ACCEPTED MANUSCRIPT Table 1: Properties of fine and coarse aggregates. Fine aggregate

Coarse aggregate

Property

Specific gravity (kg/m³) Water absorption (%)

NCA

RCA

4.75

9.5

9.5

2405.0

2639.5

2571.2

0.45

1.2

8.0

Water absorption in 10 minutes (%) Class 1

0.671

0.570

0.501

Class 2

0.753

0.558

0.488

Class 3

0.741

0.678

0.506

“p”

0.8092

0.9885

0.9665

“q” (MPa-1)

0.00000

0.00466

0.00666

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CPM parameters

5.6

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Compactness

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Maximum grain size (mm)

NFA

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ACCEPTED MANUSCRIPT Table 2: Physical and chemical properties of the Portland cement. 31.8

7 days

42.6

28 days

49.9

CaO

70.4

SiO2

14.3

SO3 Al2O3 Fe2O3 K 2O Others

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Chemical composition (%)

3 days

5.2

4.9 3.5

0.8

0.9

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Compressive strength (MPa)

0.53

Compactness

3170.9

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Specific gravity (kg/m³)

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ACCEPTED MANUSCRIPT Table 3: Mix proportions of normal and recycled aggregate concretes. Mix

25 MPa

65 MPa

C25-25

C25-50

C65-00

C65-25

C65-50

RCA ratio (%)

0

25

50

0

25

50

NCA (kg/m³)

923

695

468

883

639

432

RCA (kg/m³)

0

195

394

0

179

364

NFA (kg/m³)

841

845

852

742

776

787

Cement (kg/m³)

304

301

294

531

522

503

Free water (kg/m³)

193

190

184

175

173

167

Abs. water (kg/m³)

13

21

29

10

18

26

Total water (kg/m³)

206

211

213

185

191

193

Effective w/c

0.63

0.63

0.63

0.33

0.33

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C25-00

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0.33

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ACCEPTED MANUSCRIPT Table 4: Properties of concrete mixtures at fresh and hardened state. Mix

Slump (mm)

Splitting tensile test

Compressive test fc,7 (MPa)

fc,28 (MPa)

εc (µε)

E (GPa)

ftd (MPa)

ftd/fc,28 (%)

80

22.0(±3.0%)

27.7(± 4.9%)

2305(± 1.9%)

20.7(± 4.2%)

2.98(± 7.7%)

10.8

C25-25

80

20.9(± 0.9%)

26.7(± 2.1%)

2120(± 4.8%)

21.6(± 4.0%)

2.88(± 7.9%)

10.8

C25-50

130

21.9(± 1.2%)

27.2(± 4.5%)

2304(± 3.6%)

21.1(± 5.5%)

3.02(± 5.6%)

11.1

C65-00

70

61.9(± 1.1%)

68.3(± 3.0%)

3061(± 1.3%)

29.1(± 1.9%)

5.05(± 3.0%)

7.4

C65-25

90

62.5(± 0.9%)

66.8(± 3.2%)

3015(± 3.8%)

31.3(± 4.2%)

5.09(± 3.3%)

7.6

C65-50

80

61.4(± 2.6%)

66.5(± 1.8%)

3109(± 5.4%)

32.1(± 4.1%)

5.16(± 2.6%)

7.8

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C25-00

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ACCEPTED MANUSCRIPT Table 5: Properties of concrete mixtures in the tension stiffening tests. Pre-cracking phase

Post-cracking phase

Mix F1st (kN)

f1st (MPa)

ε1st (µε)

εfinal (µε)

Epost (GPa)

Fyield (kN)

C25-00

23.0(± 6.3%)

44.4(± 6.6%)

1.97(± 6.5%)

92.8(± 1.4%)

384.7(± 9.2%)

3.03(± 2.5%)

183.0(± 1.4%)

C25-25

22.9(± 7.5%)

49.3(± 6.8%)

2.19(± 6.8%)

96.0(± 4.6%)

442.4(± 7.5%)

3.04(± 6.5%)

183.9(± 0.2%)

C25-50

22.0(± 2.9%)

51.1(± 3.4%)

103.3(± 6.4%)

451.8(± 8.6%)

3.13(± 1.6%)

184.1(± 0.4%)

C65-00

31.0(± 5.8%)

100.6(± 1.9%)

4.47(± 1.9%)

115.0(± 5.0%)

1171.9(± 8.7%)

2.98(± 4.0%)

184.4(± 0.9%)

C65-25

32.0(± 4.0%)

97.0(± 4.9%)

4.31(± 4.9%)

105.4(± 7.0%)

1066.0(± 5.1%)

3.06(± 6.5%)

183.2(± 0.1%)

C65-50

31.8(± 7.1%)

95.0(± 4.2%)

4.22(± 4.2%)

111.1(± 4.3%)

1068.0(± 2.4%)

3.08(± 6.8%)

182.8(± 0.7%)

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2.27(± 3.4%)

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Epre (GPa)

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ACCEPTED MANUSCRIPT Table 6: Matrix contribution of RAC in the tension stiffening tests. f1st (MPa)

ε1st (µε)

fsat (MPa)

εsat (µε)

fyield (MPa)

fultimate (MPa)

C25-00

1.75(± 10.3%)

78(± 12.6%)

0.85(± 2.7%)

388(± 8.8%)

0.67(± 4.4%)

0.62(± 15.1%)

C25-25

1.87(± 12.0%)

92(± 19.2%)

0.75(± 23.1%)

468(± 7.5%)

0.63(± 12.3%)

0.62(± 1.8%)

C25-50

1.89(± 4.0%)

108(± 7.6%)

0.67(± 14.9%)

492(± 15.0%)

0.85(± 11.3%)

0.67(± 4.3%)

C65-00

4.18(± 3.3%)

87(± 28.6%)

0.59(± 6.8%)

1215(± 3.8%)

C65-25

3.98(± 1.5%)

91(± 35.6%)

0.81(± 20.4%)

1076(± 4.3%)

C65-50

3.85(± 3.2%)

110(± 21.1%)

0.89(± 15.2%)

973(± 6.7%)

RI PT

Mix

0.68(± 9.0%)

0.55(± 4.7%)

0.63(± 0.8%)

0.58(± 11.3%)

0.61(± 7.8%)

AC C

EP

TE D

M AN U

SC

0.44(± 15.3%)

51