Non-linear analytical model of composites based on basalt textile reinforced mortar under uniaxial tension

Elsevier Editorial System(tm) for Composites Part B Manuscript Draft Manuscript Number: Title: NON-LINEAR ANALYTICAL MODEL OF COMPOSITES BASED ON BASALT TEXTILE REINFORCED MORTAR UNDER UNIAXIAL TENSION Article Type: Full Length Article Keywords: A. Fabrics/textiles; B. Mechanical properties; C. Analytical modelling; D. Mechanical testing Corresponding Author: Dr. Pello Larrinaga Alonso, Ph. D. Corresponding Author's Institution: TECNALIA Research & Innovation First Author: Pello Larrinaga Alonso, Ph. D. Order of Authors: Pello Larrinaga Alonso, Ph. D.; Carlos Chastre, Assistant Professor; José Tomás SanJosé, Assistant Professor; Leire Garmendia, PhD Industrial Engineer Abstract: The recent development of inorganic based composites as low-cost materials in reinforced concrete structural strengthening and precast thin-walled components, requires the creation of models that predict the mechanical behaviour of these materials. Textile Reinforced Mortar (TRM) shows complex stress-strain behaviour in tension derived from the heterogeneity of its constituent materials. This complexity is mainly caused by the formation of several cracks in the inorganic matrix. The multiple cracking leads to a decrease in structural stiffness. Due to the severe conditions of the serviceability limit state in structural elements, the prediction of the stress-strain curve is essential for design and calculation purposes. After checking other models, a nonlinear approach, which is based on the crack control expression included in the Eurocode 2, is proposed in this paper. Following this scope, this paper presents an experimental campaign focused on thirty one TRM specimens reinforced with four different reinforcing ratios. The results are analysed and satisfactorily contrasted with the presented non-linear approach. Suggested Reviewers: Amir Si Larbi Claude Bernard University of Lyon 1, France [email protected] Dr. Si Larbi has broad experience in the field of fibre-cementitious composites, especially with Textile Reinforced Concrete (TRC), a composite very similar to the one included in this paper. Due to his research activity Dr. Si Larbi has to deal with the analysis of TRC uniaxial tensile behaviour. Hence, I consider Dr. Si Larbi a suitable revisor for this paper. Heidi Cuypers PhD Civil Engineer Vrije Universiteit Brussel [email protected] Dr. Cuypers has broad experience in the field of inorganic based composites, especially the study of matrix cracking and its durability. Thus, I consider Dr. Cuypers a suitable revisor for the presented article. This is the accept manuscript of the following article that appeared in final form in Composites Part B: Engineering 55: 518-527 (2013),which has been published in final form at https://doi.org/10.1016/j.compositesb.2013.06.043.Copyright © 2013 Elsevier Ltd. under CC BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 NON-LINEAR ANALYTICAL MODEL OF COMPOSITES BASED ON BASALT TEXTILE REINFORCED MORTAR UNDER UNIAXIAL TENSION Pello Larrinaga a, * , Carlos Chastre b, José T. San-José c, Leire Garmendia a a TECNALIA. c/Geldo, Ed. 700, Parque Tecnológico de Bizkaia, 48160, Derio, Spain b UNIC, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica – Portugal c UPV/EHU, Department of Engineering of Materials. c/Alameda Urquijo s/n, 48013 Bilbao, Spain Abstract The recent development of inorganic based composites as low-cost materials in reinforced concrete structural strengthening and precast thin-walled components, requires the creation of models that predict the mechanical behaviour of these materials. Textile Reinforced Mortar (TRM) shows complex stress-strain behaviour in tension derived from the heterogeneity of its constituent materials. This complexity is mainly caused by the formation of several cracks in the inorganic matrix. The multiple cracking leads to a decrease in structural stiffness. Due to the severe conditions of the serviceability limit state in structural elements, the prediction of the stress-strain curve is essential for design and calculation purposes. After checking other models, a nonlinear approach, which is based on the crack control expression included in the Eurocode 2, is proposed in this paper. Following this scope, this paper presents an experimental campaign focused on thirty one TRM specimens reinforced with four different reinforcing ratios. The results are analysed and satisfactorily contrasted with the presented non-linear approach. Keywords: A. Fabrics/textiles; B. Mechanical properties; C. Analytical modelling; D. Mechanical testing; 1. Introduction By means of several research projects, the mechanical possibilities and advantages of Textile Reinforced Mortar have been proven, both as strengthening material and as precast material (in this field this composite is also called Textile Reinforced Concrete) [1-5]. However, its implementation as a regular technique is still far. One important step to reach this objective is modelling the mechanical behaviour of TRM for future applications in real situations. As TRM usually bears tensile loads, it is very relevant to * Corresponding author. Tel: +34 667 178 992/946 430 850; fax: +34 946 460 900 E-mail address: p[email protected]m *Manuscript Click here to view linked References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 2 model the behaviour of this material under pure tensile loads, i.e. to define its stressstrain relationship. In the bibliography, there is broad information referred to numerical or analytical TRM models which show excellent results [6-9]. Nevertheless, most of these analyses require the use of specific softwares [9] or are costly in terms of time. Moreover, in some cases additional information is required, which involves the development of additional tests [7,8]. For these reasons, it is convenient to produce simple and easy-to-implement models. Stress-strain mathematical expressions are usually proposed to model the materials, both for linear and non-linear analysis. These expressions are based on experimental data and can be used as constitutive equations in simple numerical models. Concrete and steel are obvious examples of stress modelling by means of mathematical expressions, in fact, both materials are modelled in design codes as the Eurocode 2. A nonlinear approach is presented in this paper to define the stress-strain relationship of Basalt Textile Reinforced Mortar (BTRM) under uniaxial tensile loads. The model is based on the concrete crack control expression included in the Eurocode 2 [10]. The developed expression is calibrated empirically with experimental data included in the article, the results of thirty one TRM specimens subjected to uniaxial tensile loads. 2. Materials. Basalt textile and mortar characterization. Basalt appears to be a material which can offer interesting opportunities in the future of the construction industry [11]. Recent studies have included basalt fabrics as reinforcement in FRP composites [11,12] and basalt textile as TRM internal core [13,14]. The basalt textile used in this study consists of rovings woven in the two principal directions, i.e. a bidirectional mesh which geometry is detailed in Table 1. Basalt rovings are covered by a bitumen coat in order to improve the bond between the mortar matrix and the textile. In addition, the coat improves the textile performance due to its capacity to transfer load directly to more roving filaments [15,16]. Table 1 Basalt textile geometry According to several previous studies, there is a considerable gap between the main mechanical properties - tensile strength, ultimate strain and Young’s modulus - of a single fibre or filament and those of the textile mesh [17]. For this reason, the mechanical characteristics of the textile were experimentally determined in tensile tests on specimens which length was 600mm. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 3 ASTM D 5034 [18] standard, used as a reference, suggests a strain rate of 300mm/min. However, in order to carry out a suitable data acquisition, a speed of 1mm/min was selected for the present test. In total, seven textile specimens of four rovings were tested. The results are summarised in Table 2. Table 2 Average results of basalt textile under pure tensile load The difference between the data given by the manufacture and the experimental results is caused by several factors, mainly the load transfer between filaments and the difficulty to exert an identical initial length and strain for all the strands of the specimens [13,17]. Hence, it was impossible to achieve a simultaneous rupture of all the rovings, so the experimental values for ultimate tensile strength and ultimate tensile strain can not be considered as reference data. However, as the tested textile presents linear behaviour until rupture, the tensile Young’s modulus values obtained in this test can be easily calculated [14] and it will be considered for the model presented in this paper. Moreover, despite the difficulties derived in this kind of tests, the obtained results presented low scattering. A non-commercial cement-based mortar was used as TRM matrix. The performance of any externally bonded strengthening system is clearly influenced by the interaction between the matrix and the inner reinforcement and the capacity of the compositesubstrate interface [15]. The maximum grain size of the sand used in the mortar was 0.6mm. This factor enhances the workability of the fresh mixture and facilitates its interaction with the textile mesh. The amount of redispersable resins was lower than 5%, in order to achieve a fire-proof mortar. As can be observed in Table 3, there are not innovative products in the mortar composition because the idea is to present the TRM as a competitive material. However, special attention was paid to its composition so as to achieve appropriate workability, curing time and fire resistance. Table 3 Mortar dosage by weight (%) Matrix mortar was mechanically characterized according to. After 28-day curing, 40x40x160mm prisms were tested to determine mortar mechanical properties according to UNE-EN 1015.11:1999 [19]. Compressive strength is 19.8MPa while tensile flexural strength is 7.2MPa. 3. Uniaxial tensile test 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 4 The experimental campaign included in this paper is formed by thirty one uniaxial tensile specimens. Four series, from one to four textile layers, of seven specimens each one were defined. The effect of reinforcing ratio was therefore analysed. Specimens were tagged as TBX, where the X represents the number of internal reinforcement layers, i.e. in this paper from TB1 to TB4. Besides, three additional specimens were also manufactured without reinforcing material. 3.1.Specimens geometry and manufacturing process TRM has attracted attention for the last ten years. There has been a considerable increase in research projects and publications related to this innovative composite. However, no standard characterization tests are available in the bibliography. Thus, several test proposals have already been made [6,15,20,21] by different authors. They differ primarily in: the shape and geometry of the specimens, the connection with the test machine clamps, the strain rate and the instrumentation. Fig. 1. Uniaxial tensile TRM specimen geometry. The rectangular parallelepiped specimen is easy to manufacture and implement. For the present study it was decided to manufacture specimens with a 100x10mm crosssectional area and 600mm in length. Samples were prepared in plywood formworks. In order to promote the failure of the specimen in its middle third portion, both ends of each specimen were extra-reinforced with two layers of 200x100mm textile (Figure 1). The internal reinforcement or core layers (800x100mm) were always uniformly positioned within the cross section. In the particular case of the unreinforced specimens, only the additional reinforcement was installed at both ends. (a) (b) Fig. 2. Two steps of the TRM tensile specimens manufacturing. Specimens were cured in a saturated atmosphere for seven days, and, then, they were stored for 21 days at room temperature (18ºC and 60%RH). Tests were carried out between 28 and 34 days after the specimens were manufactured. 3.2.Test Setup TRM tensile specimens were tested in a Schenk 100kN press which was programmed to exert a deformation rate of 0.5mm/min [15]. Tensile force was applied with specially designed metallic clamps, in order to avoid any stress concentration point, which would cause premature brittle failure without reaching the ultimate tensile load. Fig. 3. Uniaxial tensile of the test setup. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 5 As the formation of cracks is promoted in the specimen central third part, two displacement transducers (LVDTs) were placed on each side of the specimen to measure the elongation of that area. The measured reference length, as can be observed in Figure 3, was 210mm. All the data was compiled by a data logger at a frequency of 5Hz. 3.3.Experimental results The purpose of testing unreinforced specimens was to characterize the behaviour of the mortar under pure tensile loads. As it was expected, only one crack was formed in the unreinforced specimens. The average results of the three specimens are displayed in Table 4. Table 4 Average results of unreinforced specimens The load-strain curves of 28 TRM tests with 1-4 layers are shown graphically in Figure 4. The results show good repeatability in contrast with the characteristic scattering of this kind of materials. Three stages are clearly differenced in each curve. This behaviour is typical in inorganic composites subjected to uniaxial tensile load [22], reinforced above the critical volume fraction. These stages are: - Stage I. Pre-cracking state. - Stage II. Multicracking process. - Stage III. Stabilized crack pattern. Only the fibres carry load. Fig. 4. Load-strain curves of TRM specimens. Table 5 includes the average main values for each series: ultimate tensile force and stress, the Young’s modulus of stage III, and the final strain at each stage. The tensile stress of the specimens is calculated dividing measured load by the area of internal reinforcement: b·tf ·n; where b is the width of the specimen (100mm), tf is the design thickness (0.0349mm) and n is the number of textile layers installed as internal reinforcement. Table 5 Average results for each TRM series The analysis of the results produces interesting interpretations. According to the bibliography, the stiffness of the third stage Et,III is slightly lower than the Young’s modulus of the textile reinforcement Ef (see Table 2). In three of the four series Et,III remained close to 60GPa, while the basalt textile Young’s modulus is 67GPa, i.e. 9% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 6 higher. This reduction has been quantified (10-30%) by other authors [22,23]. Likewise, there was good correlation in series TB2, TB3 and TB4 in terms of tensile strength and ultimate strain. The main difference between these three series is the length of the Stage II (see Table 5). The multiple cracking strain εt,II was reduced with a higher number of reinforcement layers [24]. Nevertheless, series TB1 showed a significant discrepancy when compared with the other results. The average value for Et,III was equal to 43GPa. The low amount of internal reinforcement in series TB1 can explain this discrepancy; one layer may not be enough to achieve a monolithic material which could be considered as a composite. According to Peled and Bentour [16] the critical volume content of fibres in cement composite is about 1-3%. At ratios above this level the behaviour load is characterized by multiple cracking and the TRM is able to carry the additional load applied after the matrix has cracked. However, Series TB2 presents a volume content of 0.7% and the specimens showed multiple cracking and behaved as the rest of the series with higher fibre content. These statements can be contrasted with the stress-strain results included in Figure 5. While series TB2, TB3 and TB4 presented similar behaviour after multiple-cracking, series TB1 developed a different slope at third stage. Fig. 5. Direct comparison between specimens of different series. The analysis of the crack pattern also provides interesting information. Firstly, it is noticeable how the number of cracks rises when the number of textile layers increases (see Figure 6). Moreover, the distance between cracks is reduced when more internal reinforcement is used. At series TB1 only one or three cracks were formed, being an evidence of its incapability for developing multiple cracking and behave as an inorganic based composite. Finally, as the fibre content increases, the crack pattern tends to standardize. (a) (b) (c) (d) Fig. 6. Crack pattern development. From up-left to down right: TB1, TB2, TB3 and TB4. In the following section a non-linear analytical model is presented. The obtained experimental results will be compared with those obtained in the model in order to check its validity. 4. TRM modelling 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 7 The proposed model is based on the crack control expression included in the “Eurocode 2: Design of concrete structures. Part 1-1” and the Aveston-Cooper-Kelly theory. This well-known theory was the first satisfactory explanation of multiple cracking. For this reason, the authors would like to revise the ACK theory and compare its results with the experimental data. 4.1. ACK-Theory This theory defines a theoretical tri-linear stress-strain behaviour of a composite with a brittle matrix, in which it is assumed that the fibres are held in the matrix solely by the presence of friction, and that axial sliding along a fibre-matrix interface would occur under a critical, limiting value of longitudinal shear stress [25,26]. The fibre debonding degree and crack spacing are closely linked to the maximum shear stress at the fibrematrix interface. Several models for brittle matrix composites have already been modelled considering the ACK theory, e.g. [27,28]. Basic assumptions, employed in its development, are [24]: - The fibres are only capable of carrying load along their longitudinal axis. - The matrix-fibre bond is weak. - Once the matrix and the fibre are debonded, a pure frictional shear stress η replaces the previously existing adhesion shear stress ηa. This frictional interface shear stress η is constant along the debonded interface. - Poisson effects of the fibre and matrix are neglected. - Global load sharing is assumed for the fibres. - Normal matrix stresses, transversal to the loading direction, are uniform in a cross section. As it has been experimentally stated, TRM tensile behaviour could be divided in three different, but complementary, stages. The ACK theory consists on three straight lines which superimposes the experimental stress-strain curve (see Figure 7). Fig. 7. Typical stress-strain curve of TRM in tension (in black) and ACK linearization (in dotted grey) According to ACK theory, at the first stage, the composite obeys the law of mixtures: mmffc VEVEE  1 (1) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 8 where Ec1 is the composite stiffness, Ef represents the tensile Young’s modulus of the fibres, Em is the matrix one, and Vf and Vm are the volumetric fraction of fibres and matrix, respectively. At the first stage, the matrix-fibre interface shear behaviour is assumed to be elastic. Stage I finishes when the matrix reaches its tensile failure stress ζmc. Matrix tensile failure stress, ζmu, (and its corresponding strain εmu) has a direct influence on ζmc: m muc mc E E   1  (2) At this value, the composite presents multiple cracking, i.e. successive cracks are formed as the composite strain increases. As has been stated, when a crack appears in the matrix and reaches a fibre, debonding of the matrix-fibre interface occurs due to weakness of the bond. Then, a constant frictional interface shear stress η is considered. This shear stress provides normal stress transfer from fibres to the inorganic matrix. The length of the debonded interface δ can be written by expressing the force equilibrium along the loading (longitudinal) axis of the fibres [25]:    2 f mum V rV  (3) where, r is the fibre radius and η represents the frictional shear stress at the matrix-fibre interface. At the multiple cracking stage, distances between cracks are no smaller than δ and no larger than 2δ. The spatial introduction of cracks occurs randomly until no space remains for new cracks, in a similar way to the geometrical car parking problem. Widom [29] determined that the average distance between cracks equals X=1.337δ. By means of this value it is possible to determine the composite strain (εmc) when the multiple cracking stops: m mu emc E   )666.01(  (4) where: ff mm eVE VE   (5) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 15 of internal reinforcement and generates a curve that shows considerable differences with the experimental ones (series TB1). The proposed simulation presents optimum results for the multiple cracking strain εmc, so there are no significant discrepancies between the analytical and experimental data on this key point. The behaviour of the model at stage III is satisfactory due to the introduced non-linearity which improves the model’s performance at the end of this stage. The Cracking Model has been successfully proven by the authors with other reinforcing materials such as glass, carbon and steel wire [14]. This fact enhances the versatility of the Cracking Model to materials that could be used as TRM reinforcing core. Moreover, this model has already been employed as a constitutive equation in numerical models developed to simulate the behaviour of reinforced concrete beams strengthened in flexure using Textile Reinforced Mortar [14]. 5. Conclusions Both as new construction material or as structural strengthening solution, inorganicbased composites, mainly TRM and TRC, have increased their relevance within the construction area and are currently focusing the efforts of several research groups. For this reason, it is important to standardize the use of the TRM. Characterization test, manufacturing and application guides or analytical models are among the aspects that should be normalized. There are studies that have developed analytical and numerical models with satisfactory results. However, most of them are very sophisticated and their application could be expensive in terms of time and budget. Therefore, it is necessary to develop models easy-to-apply. TRM, as strengthening material, usually works under tensile loads which are transferred by adherence from the strengthened element. It is essential to study the tensile behaviour of TRM to define its possibilities and failure modes. Especially after stating that these failure modes have different nature compared to those observed in other externally bonded strengthening systems. Textile Reinforced Mortar is a composite with a very complex material behaviour. In addition, its structural relevance asks for accurate model with no significant discrepancies with the real behaviour. A non-linear model is presented in this paper to describe the stress-strain behaviour of TRM under uniaxial tensile loading. The model is based on the RC crack control expression included in the Eurocode 2, but takes into account the nature of the composite constituent materials. The goal of this study is to verify the simulation, called Cracking Model, contrasting its results with those obtained in an experimental campaign also included in this paper. In addition, a well-known model as ACK theory is 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 16 also discusses in this document and its simulations compared with the experimental results. Due to the good fit between the calculated and the experimental values, the Cracking Model might be employed in numerical models as TRM constitutive equations. Nevertheless, due to the nature and the thoroughness of the structural calculus within construction sector, it is necessary to support this model by means of more experimental data. Future research lines are focused on testing new reinforcing materials, more effective matrices and different reinforcing rates. Acknowledgments This research work was funded through the research projects DFB 7-12-TK-2009-10 and BIA2010-20789-C04-03/04; and the scholarship programme of the Iñaki Goenaga Foundation. References [1] Ombres L. Flexural analysis of reinforced concrete beams strengthened with a cement based high strength composite materials. Composite Structures, 94, pp. 143-155. 2011. [2] Si Larbi A, Contamine R, Hamelin P. TRC and hybrid solutions for repairing and/or strengthening reinforced concrete beams. Engineering Structures, 45, pp.12-20. 2012. [3] Larrinaga P, San-José JT, García D, Garmendia L, Díez J. Experimental study of the flexural behaviour of low performance rc beams strengthened with Textile Reinforced Mortar. Proceedings of the International RILEM Conference on Material Science (MatSci). Aachen, Germany. Vol. 1, pp. 235-244. 2010. [4] Triantafillou TC, Papanicolau CG. Shear strengthening of RC members with Textile Reinforced Mortar (TRM) jackets. Materials and Structures, 39, pp.85-93. 2007. [5] Bournas D, Lontou P, Papanicolau CG, Triantafillou TC. Textile-Reinforced Mortar (TRM) versus FRP confinement in reinforced concrete columns. ACI Structural Journal, 104(6), pp. 740-748. 2007. [6] Haüßler-Combe U, Hartig J. Bond and failure mechanism of Textile Reinforced Concrete (TRC) under uniaxial tensile loading. Cement & Concrete Composites, 29, pp. 279-289. 2007. [7] Ritcher M, Zastrau BW. On the nonlinear elastic properties of textile reinforced concrete under tensile loading including damage and cracking. Materials Science and Engineering A, 422, pp. 278-284. 2006. [8] Chudoba R, Konrad M, Schleser M, Meskouris K, Reisgen U. Parametric study of tensile response of TRC specimens reinforced with epoxy-penetrated multi.filament yarns. Proceedings of the 4th Colloquium on Textile Reinforced Structures, CTRS4, Dresden, Germany. pp. 87-98. 2006. [9] Chudoba R, Vořechovský M, Konrad M. Stochastic modelling of multi-filament yarns. I. Random properties within the cross-section and size effect. International Journal of Solids and Structures, 43, pp. 413-434. 2006. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 17 [10] Eurocode 2: Design of concrete structures – Part 1: Common rules for building and civil engineering structures. prEN 1992-1, CEN (Comité Européen de Normalisation), European Committee for Standardisation, Central Secretariat, Brussels. 2004. [11] Sim J, Park C, Moon DY. Characteristics of basalt fiber as a strengthening material for concrete structures. Composites: Part B, 36, pp. 504-512. 2005. [12] Lopresto V, Leone C, De Iorio I. Mechanical Characterisation of Basalt Fibre Reinforced Plastic. Composites: Part B, 42, Issue 4, pp.717-723. 2011. [13] Garmendia L, San-José JT, García D, Larrinaga P. Rehabilitation of Masonry Arches with Compatible Advanced Composite Material. Construction and Building Materials, Volume 25, Issue 12, pp. 4374-4385. 2011. [14] Larrinaga P. Flexural Strengthening of Low Grade Concrete Through the Use of New Cement-Based Composite Materials. PhD Thesis, University of the Basque Country, Spain. 2011. [15] Keil A, Cuypers H, Raupach M, Wastiels J. Study of the Bond in Textile Reinforced Concrete: Influence of Matrix and Interface Modification. Proceedings of the Challanges for Civil Construction – CCC2008. Torres Marques et al (Eds.). FEUP, Porto, Portugal. 2008. [16] Peled A, Bentur A. Fabric Structure and its Reinforcing Efficiency in Textile Reinforced Cement Composites. Composites: Part A, 34, pp. 107-118. 2003. [17] Curbach M. Textile Reinforced Structures. Proceedings of the 2nd Colloquium of Textile Reinforced Structures (CTRS2), Dresden, 29-9. 2003. [18] ASTM D 5034 (2001). Standard Test Method for Breaking Strength and Elongation of Textile Fabrics. 2001. [19] UNE-EN 1015-11:1999. Métodos de ensayo para morteros de albañilería. Parte 11: Determinación de la resistencia a flexión y a compresión del mortero endurecido. 1999. [20] Contamine R, Si Larbi A, Hamelin P. Contribution to direct tensile testing of textile reinforced concrete (TRC) composites. Material Science and Engineering A, 528, pp. 8589-8598. 2011. [21] Hegger J, Voss S. Investigations on the Bearing Behaviour and Application Potential of Textile Reinforced Concrete. Engineering Structures, 30, pp. 2050-2056. 2008. [22] Hegger J, Will N, Bentur A, Curbach M, Mobasher B, Pelled A, Wastiels J. Mechanical Behaviour of Textile Reinforced Concrete. Textile Reinforced Concrete. State-of-the-art Report of RILEM TechnicalCimittee 201-TRC. pp. 133-186. 2006. [23] Jesse F. Tragverhalten von Filamentgarnen in Zementgebundener Matrix. PhD Thesis, Dresden: Fakulty of Civil Engineering, Technische Universität Dresden. 2005. [24] Cuypers H, Wastiels J. A Stochastic Cracking Theory for the Introduction of Matrix Multiple Cracking in Textile Reinforced Concrete under Tensile Loading. Proceedings of the 1st International RILEM Symposium. RILEM Technical Committee 201-TRC. Aachen, Germany, pp. 193-202. 2006. [25] Aveston J, Cooper GA, Kelly A. Single and Multiple Fracture, the Properties of Fibre Composites. Proceedings of the Conference National Physical Laboratories, IPC Science and Technology Press Ltf. London, pp. 15-24. 1971. [26] Aveston J, Kelly A. Theory of Multiple Fracture of Fibrous Composites. J. Mat. Sci. 8, pp. 411-461. 1973. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 18 [27] Da Silva ARC. Probabilistic Approach to Predict Cracking in Lightly Reinforced Microconcrete panels. Journal of Engineering Mechanics 8 (130), pp. 931-941. 2004. [28] Mobasher B, Pahilajani J, Peled A. Analytical Simulation of Tensile Response of Fabric Reinforced Cement Based Composites. Cement and Concrete Composites, 28, pp. 77-89. 2006. [29] Widom B. Random sequential addition of hard spheres to a volume. J. Chem. Phys. 44, pp. 38883894. 1966. [30] Chastre Rodrigues C, Silva MAG. Monotonic Axial Behavior and Modelling of RC Circular Columns Confined with CFRP. Engineering Structures, 32, pp.2268-2277. 2010. [31] Richard RM, Abbot BJ. Versatile Elastic-Plastic Stress-Strain Formula. Journal of Engineering Mechanics, ASCE 101, 4, pp.511-515. 1975. Table 1 Basalt textile geometry Design thickness, tf 0.0349 mm Opening size 25x25 mm Weight of the dry sheet 233 g/m2 Density 2.75 g/cm3 Table 2 Average results of basalt textile under pure tensile load Filament - Given by the manufacturer Textile – Experimental* Ultimate tensile strength, σfu [MPa] 2100 1160 (0.025) Young’s Modulus, Ef [GPa] 89 67 (0.054) Ultimate tensile strain, εf [%] 3.14 1.82 (0.054) *COV between brackets Table 3 Mortar dosage by weight (%) W/C ratio 0.2 Sand (grain size < 0.6mm) 60-70 Grey cement type II 42.5R 30-40 Polymeric chopped fibres 3-5 Redispersable resins 1-3 Table 4 Average results of unreinforced specimens Fmu [N] σmu 1 [MPa] εmu [%] Em [GPa] 2480 2.48 0.03 8.25 1 σmu = Fmu / (10·100) Table 5 Average results for each TRM series Series Ftr (N) σtr 1 (MPa) Et,III (GPa) εt,I (%) εt,II (%) εt,III (%) TB1 3797 1088 43 0.034 0.40 2.15 TB2 8772 1256 59 0.041 0.29 1.96 TB3 12515 1195 57 0.028 0.21 2.10 TB4 16679 1194 61 0.028 0.15 2.07 1 σtr = Ftr / (0.0349·100·n) Table Table 6 ACK Theory results Series Vm [-] Vf [-] Ec1 [GPa] σmc [MPa] εmc [%] TB1 0.9965 0.0035 8.46 2.54 0.734 TB2 0.9930 0.0070 8.66 2.60 0.381 TB3 0.9895 0.0105 8.87 2.67 0.263 TB4 0.9860 0.0140 9.07 2.73 0.204 Table 7 Cracking Model data and results Series Vm [-] Vf [-] Ec1 [GPa] σmc [MPa] εmc [%] TB1 0.9965 0.0035 8.46 2.54 0.896 TB2 0.9930 0.0070 8.66 2.60 0.473 TB3 0.9895 0.0105 8.87 2.67 0.332 TB4 0.9860 0.0140 9.07 2.73 0.261 Figure1 Click here to download high resolution image Figure2a Click here to download high resolution image Figure2b Click here to download high resolution image Figure3 Click here to download high resolution image Figure7 Click here to download high resolution image Figure8 Click here to download high resolution image Figure9 Click here to download high resolution image Figure10 Click here to download high resolution image Figure11 Click here to download high resolution image Figure12a Click here to download high resolution image Figure12b Click here to download high resolution image Figure13 Click here to download high resolution image Figure14 Click here to download high resolution image Figure15 Click here to download high resolution image Figure22 Click here to download high resolution image