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Meso-scale analysis of the aggregate size influence on the mechanical properties of heterogeneous materials using the Brazilian splitting test
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ScienceDirect Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Available Energy Procedia 00 (2017) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia
Energy (2017) 000–000 266–272 EnergyProcedia Procedia139 00 (2017) www.elsevier.com/locate/procedia
International Conference On Materials And Energy 2015, ICOME 15, 19-22 May 2015, Tetouan, Morocco, and the International Conference On Materials And Energy 2016, ICOME 16, 17-20 May 2016, La Rochelle, France The 15th International Symposium on District Heating and Cooling Meso-scale analysis of the aggregate size influence on the mechanical properties of heterogeneous materials using the Assessing the feasibility of using the heat demand-outdoor splitting test heat demand forecast temperature function Brazilian for a long-term district
AL-KHAZRAJI Haydera, b*,a BENKEMOUN Nathanba, CHOINSKA cMartaa, KHELIDJ a,b,c a a I. Andrić *, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Correc Abdelhafid a
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal a LUNAM, b Université, GeM, UMR CNRS 6183, IUT de Saint Nazaire, Université de Nantes, France Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France b Department of Civil Engineering, University of Misan, Iraq c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
Abstract Abstract The effect of the aggregate size on the behavior of the hardened concrete under splitting tensile loading is studied in this paper. The studies of Tasdemir et al., 2001 [19], Appa et al., 2011 [2], Li et al., 2014 [13] show that the behavior of heterogeneous materials which are subjected loading depends on in many fraction, aggregate type, aggregate District heating networks aretocommonly addressed the parameters literature assuch oneasofvolume the most effective solutions for and decreasing the size, etc. In gas thisemissions paper an from investigation wassector. madeThese to study the require effect of aggregate size which on thearemechanical properties of greenhouse the building systems high investments returned through the heat heterogeneous such as concrete in the context of the Brazilian splitting test. heat demand in the future could decrease, sales. Due tomaterials the changed climate conditions and building renovation policies, Five finite element simulations been carried out in this research to study the behavior of concrete under diametral prolonging the investment returnhave period. compression load.ofCylinder specimens of concrete with 50 mm ofthe thickness and 110 mm oftemperature diameters have been for regarded. Five The main scope this paper is to assess the feasibility of using heat demand – outdoor function heat demand diameters aggregate been employed analyses, ranging from to 16asmm. forecast. of The district have of Alvalade, locatedinintheLisbon (Portugal), was 4used a case study. The district is consisted of 665 This study has employed a meso-scale model (mechanical model) based upon a 3D lattice approach, representing with explicitly buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district heterogeneity and failure mechanism of the concrete. This model considers the concrete to be a two-phase material in which renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were aggregates are melt within the cement paste. Because of using a non-adapted meshing process to mesh the microstructure, a weak compared with results from a dynamicfield) heat demand model, developed and validated by the authors. discontinuity (jump in the deformation is introduced in previously the kinematics. Theresults resultsof showed that whensimulations only weather change is considered, the margin of errortocould be acceptable for some applications The the numerical show the ability of the meso-scale model evaluate the mechanical failure in the (the error in annual demand wastest. lower than for show all weather considered). introducing renovation context of the Brazilian splitting Also, the20% results that (1)scenarios the maximum tensile However, stress, (2) after the fracture energy and (3) scenarios, thecrack erroropening value increased up been to 59.5% (depending on aggregate the weather and renovation scenarios combination considered). the maximum are all have increased when the diameter was increased. The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the inAuthors. the number of heating hours of 22-139h during the heating season (depending on the combination of weather and ©decrease 2017 The Published by Elsevier Ltd. renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016. coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. Keywords: Brazilian test, heterogeneous materials, meso-scale model, weak discontinuity, strong discontinuity, aggregate size. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Keywords: Heat demand; Climate change E-mail address: Email: Forecast; [email protected] 1876-6102 © 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016 10.1016/j.egypro.2017.11.207
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1. Introduction The concrete is a widely used material in concrete structures, it is considered to be a heterogeneous material which is consisting of aggregate melts into cement paste or mortar. Designed structures need the information about the factors that influence crack initiation and propagation in the concrete. Prediction modulus of the elasticity of concrete depends on two materials: the aggregate and the cement paste. The volume of the aggregate occupies most of the concrete, therefore these information are needed for the numerical investigation of concrete behavior. The mechanical behaviour of concrete depends on many characteristics such as, volume fraction; aggregate type and aggregate size, etc. The aim of this study is to investigate the influence of aggregate size on the mechanical properties of heterogeneous material such as concrete in the context of the Brazilian splitting test. Previous studies like Tasdemir et al. [19] and Burcu et al. [4] investigated the influence of the volume fraction of aggregate on mechanical properties of concrete depending on the meso-mechanical approach and the experimental work. App et al. [2] pointed out to the influence of the surface type of aggregate on fracture behaviour of heterogeneous materials. Another study was made by Li et al. [13] reported that the splitting tensile strength of concrete had been increased with the roughness of coarse aggregate. Hillerborg's research [12] demonstrated that the fracture energy of mortars are lower than those in the concretes. Furthermore the increasing of the aggregate size is caused by the increasing of the fracture energy according Li et al. [15] study. Elices et al. [9] concluded in their research that the average values of the initial crack opening w1 and the average values of the critical opening wc are increasing with the aggregate size. 2. Analysis and modelling 2.1 Splitting tensile test (the Brazilian test) In order to investigate the behavior of concrete during splitting tensile test, the tensile tests of concrete are classified into direct and indirect tensile tests. A direct tensile test is executed by applying an axial tension force to the concrete specimens. Cunha et al. [8] developed this test (direct tensile) by molding specimen with embedded steel bars. The bars were used to apply the tensile force to the concrete. Also, Mechtcherine et al. [16] developed this test by using (dogbone) specimen as un-notched element and prism as notched one. The experimental results compared with the notched specimens by the other studies [6, 14]. As a result of the constricts as pointed out, most of the researchers changed the test method to use the indirect tensile test techniques, i. e. flexural test and Brazilian splitting test. These tests are less complicated than other type of tests that are considered to be the test set-up procedure that has been standard in several Codes, ASTM and the Euro Code. The Brazilian splitting test set-up can be seen in the Fig. 1. A test strategy consists of a concrete cylinder specimen placed horizontally and loaded in compression (diametral load) by the loading platens of the compression testing machine along the length of the cylinder. As shown in Fig. 2, the distribution of the loading (applied load and tensile stress) are according to ASTM C496 [1], and equation 1 is the formula to be used to calculate the splitting tensile strength under diametral loading for concrete cylinder specimen. Where, f st is the splitting tensile strength in (MPa) at the failure due to the ultimate diametral loading
Pu in (N), and D is the diameter of the cylinder specimen in (mm), B is the specimen thickness in (mm).
f st = 2 Pu / π BD
(1)
AL-KHAZRAJI al. / Energy Procedia 139000–000 (2017) 266–272 AL-KHAZRAJI H.Hayder et al. / et Energy Procedia 00 (2017)
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Fig. 1. The test set-up of the Brazilian splitting test.
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Fig. 2. The description behavior of specimen cylinder under loading, distribution stress [ASTM C496] [1] (a) and applied load with crack pattern (b).
2.2 Meso-scale model mechanical-numerical model This study is based on a meso-scale model with enhanced kinematics for representing the failure of the heterogeneous materials. This type of enhancement kinematics is classified to two types of kinematics: weak discontinuity (jump in the deformation field) without any mesh adaptation and strong discontinuity (discontinuous displacement field) for measuring crack value. Furthermore, this model was considered that the concrete consists of a multi-phases material (aggregates melt into cement paste) and that the concrete is quasi-brittle material. For discretization 3D heterogeneous multi-phases material by using Enhanced Finite Element Method (E-FEM). Three sets of elements have been obtained. Fig. 3 shows three types of elements for representing the specimen cylinder concrete. The first set of elements colored in blue represents the cement paste and the second set of elements colored white are the inclusions (aggregates). The last set is colored in red, which is placed between aggregates and cement paste, and this type of elements consists of two parts; the first part has the properties of the cement paste, while the second part has the properties of the aggregates (inclusions).
Fig. 3. 3D representation of two-phase heterogeneous materials [3].
2.3 Weak discontinuity Due to the heterogeneity of materials and do not need change adapted meshes caused by splitting into parts for third set elements which placed at interface position between the aggregate and the cement paste, each part has different elastic properties. Fig. 4 shows the first enhanced kinematics with two subdomains; the first one represents the elastic properties of the cement paste, and the second one represents the elastic properties of the aggregate. Equation 2 offers the first enhancement of the elements bar at the interface between the two subdomains (two elastic properties), also by a function calculates jump in the deformation field, where l is the length of the element bar, and θ is the scalar dimensionless.
G1 = −1 / θ l , x∈ [0,θ l ] G1 = 1 / l (1 − θ ) , x ∈ [θ l , l ]
(2a) (2b)
2.4 Strong discontinuity The concrete is considered to be a quasi-brittle material for representing the softening behavior with crack width introduced second kinematic enhancement (strong discontinuity). Thanks to the strong discontinuity, approach can be
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AL-KHAZRAJI et al.Procedia / Energy Procedia (2017) 266–272 AL-KHAZRAJI H. etHayder al. / Energy 00 (2017)139 000–000
measured the opening crack value, Fig. 5 shows element bar with strong discontinuity and
269
G2 function, which consists
δ Γ placed within the interface zone and − 1 / l . The elements in this enhancement place in the interface zone and cement paste or aggregate. The function G 2 can be written as: the Dirac function
G2 = −1 / 1 + δ Γ
Fig. 4. Split truss element with weak discontinuity and
(3)
G1
function [3].
Fig. 5. Split truss element with strong discontinuity and
G2
function [3].
2.5 Tension-softening relation The mechanical meso-scale model that deals with quasi-brittle materials to represent this feature must be determined relation between the applied tensile load and softening behavior of concrete. This relation based on yield function to activate the strong discontinuity. Yield function is written by:
Φ = t Γ − (σ u − q ) q = σ u (1 − exp(− σ u / Gu [| u |])) Where
(4) (5)
t Γ is the tensile stress at the discontinuity, and σ u is the fracture stress. This equation depends on fracture energy
Gu which is based on the total area under the tensile stress-crack opening curve in Fig. 6b.
Fig. 6. The elastic-quasi-brittle behavior.
3. Results and discussion 3.1 Numerical simulations and results In this section, the description of the numerical simulations and the results for the five cylinder specimens under the Brazilian splitting test will be given. 3.2 Discretization of two-phase materials Five cylinder specimens with the size 110 x 50 mm diameter and thickness respectively have been simulated. The parameter variable in this study is the aggregate diameter (simulated with mono-sizes aggregate) while the volume of the fraction has kept constant 20% for the five specimens. The aggregate diameters are 4, 8, 10, 14 and 16 mm respectively, also each simulation consists of one diameter. The geometry properties for each phase (cement paste, aggregate and
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5
interfaces) are summarized in Table 1. As shown in Fig. 7, 3D isometric view for five cylinder specimens are simulated with different aggregate diameters. Table 1. Mechanical Properties of Materials, (E,
σ u , Gu
Cement paste
Aggregate
Interface
=35 GPa
-
σu
=3 MPa
=100 GPa -
σu
=3 MPa
Gu
=80 J/m²
-
Gu
=80 J/m²
) Modulus of Elasticity, Tensile Stress and Fracture Energy. Volume of fraction
20 %
Fig. 7. 3D isometric view section in the five simulated cylinders.
3.3 Maximum crack opening The focus of this study is to describe the effect of aggregate size on the mechanical behavior of concrete in context of Brazilian splitting tensile test. The numerical results show the influence of aggregate diameter on the crack opening without changes in the volume of fraction. On the other hand, the increasing in the aggregate diameter leads to an increase in the maximum crack opening, Fig. 8 shows this relation for five cylinder specimens are simulated. In addition, the results show that the orientation of the cracking became more isotropic in the specimens with larger aggregate diameters. The previous study offered that the crack open is decreasing when the interface zone is strong, and this decrease is depending on the properties of cement paste and rough of crack [11], while other authors presented the increase of the critical opening wc with the aggregate size [10, 15, 17] . 3.4 Splitting tensile stress The numerical results show the relation between aggregate diameters with the maximum splitting tensile stress. Therefore the increasing of aggregate diameter tends to cause an increase in the maximum tensile stress. Otherwise, Fig. 9 shows the maximum tensile stress is a function of aggregate diameter for five cylinder specimens are simulated. One noticeable point is that the total surface area of the interface zone between the aggregate and the cement paste depends on the aggregate diameter, see Table 2. Concerning the effect of aggregate diameter, many studies have recently shown the influence of aggregate size on the mechanical behavior of concrete under loading. The increasing in the tensile stress resulted from the increasing of aggregate size [18], in addition, tensile strength for high-strengthed concrete is increasing with the aggregate size [7].
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AL-KHAZRAJI Hayder et al. / Energy Procedia 139 (2017) 266–272 AL-KHAZRAJI H. et al. / Energy Procedia 00 (2017) 000–000
Fig. 8. Maximum crack opening versus aggregate diameter.
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Fig. 9. Ultimate tensile stress versus aggregates diameters.
Table 2. Surface area of aggregates for five cylinder specimens. Specimen
Surface area of aggregates mm²
Cylinder-4 Cylinder-8 Cylinder-10 Cylinder-14 Cylinder-16
Ultimate tensile stress
43178.1 7489.6 5943.9 2764.6 1420.0
σu
MPa
1.7 1.9 1.953 2.01 2.11
3.5 Fracture energy By integrating the area under the curve (stress-crack opening) relation in Fig. 6, the total energy can be calculated for each simulation. Fig. 10 gives a clear representation of 3D heterogeneous materials mechanism that occurs during the splitting tensile loading, which is a representative of a softening behavior. The results obtained show that the fracture energy, as a function of aggregate diameter, it seems to increase as the aggregate diameter increases, which is confirmed with the standard of CEB-FIP model code [5]. As shown in Table 3, the fracture energy for many studies, which compared with the fracture energy is obtained from numerical simulations, it shows the influence of the volume of fraction and aggregate sizes on the fracture energy, i. e. the increasing of aggregate size leads to an increase in the fracture energy.
Fig. 10. Energy versus time step for five cylinder specimens are simulated. Table 3. Increasing of fracture energy with aggregate size. Authors
Volume of fraction %
Increasing of fracture energy %
Petersson, 1980 Mihashi, 1989, 1991 Tasdemir et al., 1996 Rao and Prasad, 2002 Numerical simulations
50 40 49 44 20
13 50 34 35 25
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4. Conclusions From this study it can concluded that the increasing of aggregates size led to an increase the ultimate tensile stress, the maximum crack opening and fracture energy for example the ultimate tensile stresses were increased from 1.7 to 2.11 MPa with aggregate diameters 4 and 16 mm respectively. Also, the maximum crack opening varied from 0.391 to 1.159 mm when the aggregates size increased from 4 to 16 mm in addition, the fracture energy increased by 25 %. References [1] ASTM C496, Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens, ASTM Book of Standards. [2] App Rao, G. and Raghu Prasad, B. K, 2011, Influence of interface properties on fracture behaviour of concrete, Indian Academy of Sciences, Res 36 (2) pp. 193-208. [3] Benkemoun N., Hautefeuille M., Colliat JB. ,Ibrahimbegovic A., 2010, Failure of heterogeneous materials: 3D meso-scale FE models with embedded discontinuities. International Journal of Numerical Methods in Engineering 82: 1671-1688. [4] Burcu A., Ayda S. A., Fikret B., Hakan N. A., Cengiz S., 2012, Interpretation of aggregate volume fraction effects on fracture behavior of concrete, Construction and Building Materials 28 pp. 437-443. [5] CEB-FIP Model Code, 1990, Comité Euro-International du Béton (CEB), Bulletin d'Information 195, Lausanne, Switzerland. [6] Cedolin L., Poli S.D., Iori I., 1987, Tensile behavior of concrete, ASCE J. Eng. Mech.113 pp. 431–449. [7] Chen B., Liu J., 2004, Effect of aggregate on the fracture behavior of high strength concrete. Construction and Building Materials ;18 pp. 585–90. [8] Cunha V.M.C.F., Barros J.A.O., Senna-Cruz J.M., 2011, An integrated approach for modeling the tensile behavior of steel reinforced selfcompacting concrete, Cement and Concrete Research 41 pp. 64–76. [9] Elices A., and Rocco C. G., 2008, Effect of aggregate size on the fracture and mechanical properties of a simple concrete, Engineering Fracture Mechanics 75 pp. 3839-3851. [10] Grassl P., Wong H.S., Buenfeld N.R., 2010, Influence of aggregate size and volume fraction on shrinkage induced micro-cracking of concrete and mortar. Cement Concrete Research 40(1) pp. 85–93. [11] Guinea G.V., El-Sayed, Rocco C.G., Elices M., Planas J., 2002, The effect of the bond between the matrix and the aggregates on the cracking mechanism and fracture parameters of concrete ,Cement and Concrete Research 32 pp. 1961– 1970. [12] Hillerborg A., 1985, results of three comparative test seriesfor determining the fracture energy of concrete, Materials and Structures 18 (107) pp. 407-13. [13] Li H., Xianglin G., Feng L., 2014, Influence of aggregate surface roughness on mechanical properties of interface and concrete, Construction and Building Materials 65 pp. 338-349. [14] Li Q., Ansari F., 2000, High-strength concrete inuniaxial tension, ACI Mat. J. 97 pp. 49–55. [15] Li Q., Deng Z., Fu H., 2004, Effect of aggregate type on mechanical behavior of dam concrete, ACI materials Journal 101 (6) pp. 483-92. [16] Mechtcherine V., Muller H.S., 1998, Effect of test set-up on fracture mechanical parameters of concrete, in: Proc. FRAMCOS-3 Fracture Mech and Concrete Struct., Germany, pp. 377-386. [17] Mihashi H., Nomura N., Izumi M., 1989, Influence of matrix strength and gravel size on fracture properties of concrete. In: Shah SP, Swartz SE, Barr B, editors. Fracture of concrete and rock. Elsevier;. pp. 503–12. [18] Rao G. A., Raghu Prasad B. K., 2002, Fracture energy and softening behavior of high-strength concrete. Cement Concrete Research, 32 pp. 247–52. [19] Tasdemir C., Tasdemir M.A., Lydon F.D., Barr B.I.G., 1996, Effects silica fume and aggregate size on the brittleness of concrete. Cement Concrete Research; 26(1) pp. 63–8.
ScienceDirect Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Available Energy Procedia 00 (2017) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia
Energy (2017) 000–000 266–272 EnergyProcedia Procedia139 00 (2017) www.elsevier.com/locate/procedia
International Conference On Materials And Energy 2015, ICOME 15, 19-22 May 2015, Tetouan, Morocco, and the International Conference On Materials And Energy 2016, ICOME 16, 17-20 May 2016, La Rochelle, France The 15th International Symposium on District Heating and Cooling Meso-scale analysis of the aggregate size influence on the mechanical properties of heterogeneous materials using the Assessing the feasibility of using the heat demand-outdoor splitting test heat demand forecast temperature function Brazilian for a long-term district
AL-KHAZRAJI Haydera, b*,a BENKEMOUN Nathanba, CHOINSKA cMartaa, KHELIDJ a,b,c a a I. Andrić *, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Correc Abdelhafid a
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal a LUNAM, b Université, GeM, UMR CNRS 6183, IUT de Saint Nazaire, Université de Nantes, France Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France b Department of Civil Engineering, University of Misan, Iraq c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
Abstract Abstract The effect of the aggregate size on the behavior of the hardened concrete under splitting tensile loading is studied in this paper. The studies of Tasdemir et al., 2001 [19], Appa et al., 2011 [2], Li et al., 2014 [13] show that the behavior of heterogeneous materials which are subjected loading depends on in many fraction, aggregate type, aggregate District heating networks aretocommonly addressed the parameters literature assuch oneasofvolume the most effective solutions for and decreasing the size, etc. In gas thisemissions paper an from investigation wassector. madeThese to study the require effect of aggregate size which on thearemechanical properties of greenhouse the building systems high investments returned through the heat heterogeneous such as concrete in the context of the Brazilian splitting test. heat demand in the future could decrease, sales. Due tomaterials the changed climate conditions and building renovation policies, Five finite element simulations been carried out in this research to study the behavior of concrete under diametral prolonging the investment returnhave period. compression load.ofCylinder specimens of concrete with 50 mm ofthe thickness and 110 mm oftemperature diameters have been for regarded. Five The main scope this paper is to assess the feasibility of using heat demand – outdoor function heat demand diameters aggregate been employed analyses, ranging from to 16asmm. forecast. of The district have of Alvalade, locatedinintheLisbon (Portugal), was 4used a case study. The district is consisted of 665 This study has employed a meso-scale model (mechanical model) based upon a 3D lattice approach, representing with explicitly buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district heterogeneity and failure mechanism of the concrete. This model considers the concrete to be a two-phase material in which renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were aggregates are melt within the cement paste. Because of using a non-adapted meshing process to mesh the microstructure, a weak compared with results from a dynamicfield) heat demand model, developed and validated by the authors. discontinuity (jump in the deformation is introduced in previously the kinematics. Theresults resultsof showed that whensimulations only weather change is considered, the margin of errortocould be acceptable for some applications The the numerical show the ability of the meso-scale model evaluate the mechanical failure in the (the error in annual demand wastest. lower than for show all weather considered). introducing renovation context of the Brazilian splitting Also, the20% results that (1)scenarios the maximum tensile However, stress, (2) after the fracture energy and (3) scenarios, thecrack erroropening value increased up been to 59.5% (depending on aggregate the weather and renovation scenarios combination considered). the maximum are all have increased when the diameter was increased. The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the inAuthors. the number of heating hours of 22-139h during the heating season (depending on the combination of weather and ©decrease 2017 The Published by Elsevier Ltd. renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016. coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. Keywords: Brazilian test, heterogeneous materials, meso-scale model, weak discontinuity, strong discontinuity, aggregate size. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Keywords: Heat demand; Climate change E-mail address: Email: Forecast; [email protected] 1876-6102 © 2017 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016 10.1016/j.egypro.2017.11.207
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AL-KHAZRAJI et al.Procedia / Energy Procedia (2017) 266–272 AL-KHAZRAJI H. etHayder al. / Energy 00 (2017)139 000–000
267
1. Introduction The concrete is a widely used material in concrete structures, it is considered to be a heterogeneous material which is consisting of aggregate melts into cement paste or mortar. Designed structures need the information about the factors that influence crack initiation and propagation in the concrete. Prediction modulus of the elasticity of concrete depends on two materials: the aggregate and the cement paste. The volume of the aggregate occupies most of the concrete, therefore these information are needed for the numerical investigation of concrete behavior. The mechanical behaviour of concrete depends on many characteristics such as, volume fraction; aggregate type and aggregate size, etc. The aim of this study is to investigate the influence of aggregate size on the mechanical properties of heterogeneous material such as concrete in the context of the Brazilian splitting test. Previous studies like Tasdemir et al. [19] and Burcu et al. [4] investigated the influence of the volume fraction of aggregate on mechanical properties of concrete depending on the meso-mechanical approach and the experimental work. App et al. [2] pointed out to the influence of the surface type of aggregate on fracture behaviour of heterogeneous materials. Another study was made by Li et al. [13] reported that the splitting tensile strength of concrete had been increased with the roughness of coarse aggregate. Hillerborg's research [12] demonstrated that the fracture energy of mortars are lower than those in the concretes. Furthermore the increasing of the aggregate size is caused by the increasing of the fracture energy according Li et al. [15] study. Elices et al. [9] concluded in their research that the average values of the initial crack opening w1 and the average values of the critical opening wc are increasing with the aggregate size. 2. Analysis and modelling 2.1 Splitting tensile test (the Brazilian test) In order to investigate the behavior of concrete during splitting tensile test, the tensile tests of concrete are classified into direct and indirect tensile tests. A direct tensile test is executed by applying an axial tension force to the concrete specimens. Cunha et al. [8] developed this test (direct tensile) by molding specimen with embedded steel bars. The bars were used to apply the tensile force to the concrete. Also, Mechtcherine et al. [16] developed this test by using (dogbone) specimen as un-notched element and prism as notched one. The experimental results compared with the notched specimens by the other studies [6, 14]. As a result of the constricts as pointed out, most of the researchers changed the test method to use the indirect tensile test techniques, i. e. flexural test and Brazilian splitting test. These tests are less complicated than other type of tests that are considered to be the test set-up procedure that has been standard in several Codes, ASTM and the Euro Code. The Brazilian splitting test set-up can be seen in the Fig. 1. A test strategy consists of a concrete cylinder specimen placed horizontally and loaded in compression (diametral load) by the loading platens of the compression testing machine along the length of the cylinder. As shown in Fig. 2, the distribution of the loading (applied load and tensile stress) are according to ASTM C496 [1], and equation 1 is the formula to be used to calculate the splitting tensile strength under diametral loading for concrete cylinder specimen. Where, f st is the splitting tensile strength in (MPa) at the failure due to the ultimate diametral loading
Pu in (N), and D is the diameter of the cylinder specimen in (mm), B is the specimen thickness in (mm).
f st = 2 Pu / π BD
(1)
AL-KHAZRAJI al. / Energy Procedia 139000–000 (2017) 266–272 AL-KHAZRAJI H.Hayder et al. / et Energy Procedia 00 (2017)
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Fig. 1. The test set-up of the Brazilian splitting test.
3
Fig. 2. The description behavior of specimen cylinder under loading, distribution stress [ASTM C496] [1] (a) and applied load with crack pattern (b).
2.2 Meso-scale model mechanical-numerical model This study is based on a meso-scale model with enhanced kinematics for representing the failure of the heterogeneous materials. This type of enhancement kinematics is classified to two types of kinematics: weak discontinuity (jump in the deformation field) without any mesh adaptation and strong discontinuity (discontinuous displacement field) for measuring crack value. Furthermore, this model was considered that the concrete consists of a multi-phases material (aggregates melt into cement paste) and that the concrete is quasi-brittle material. For discretization 3D heterogeneous multi-phases material by using Enhanced Finite Element Method (E-FEM). Three sets of elements have been obtained. Fig. 3 shows three types of elements for representing the specimen cylinder concrete. The first set of elements colored in blue represents the cement paste and the second set of elements colored white are the inclusions (aggregates). The last set is colored in red, which is placed between aggregates and cement paste, and this type of elements consists of two parts; the first part has the properties of the cement paste, while the second part has the properties of the aggregates (inclusions).
Fig. 3. 3D representation of two-phase heterogeneous materials [3].
2.3 Weak discontinuity Due to the heterogeneity of materials and do not need change adapted meshes caused by splitting into parts for third set elements which placed at interface position between the aggregate and the cement paste, each part has different elastic properties. Fig. 4 shows the first enhanced kinematics with two subdomains; the first one represents the elastic properties of the cement paste, and the second one represents the elastic properties of the aggregate. Equation 2 offers the first enhancement of the elements bar at the interface between the two subdomains (two elastic properties), also by a function calculates jump in the deformation field, where l is the length of the element bar, and θ is the scalar dimensionless.
G1 = −1 / θ l , x∈ [0,θ l ] G1 = 1 / l (1 − θ ) , x ∈ [θ l , l ]
(2a) (2b)
2.4 Strong discontinuity The concrete is considered to be a quasi-brittle material for representing the softening behavior with crack width introduced second kinematic enhancement (strong discontinuity). Thanks to the strong discontinuity, approach can be
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measured the opening crack value, Fig. 5 shows element bar with strong discontinuity and
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G2 function, which consists
δ Γ placed within the interface zone and − 1 / l . The elements in this enhancement place in the interface zone and cement paste or aggregate. The function G 2 can be written as: the Dirac function
G2 = −1 / 1 + δ Γ
Fig. 4. Split truss element with weak discontinuity and
(3)
G1
function [3].
Fig. 5. Split truss element with strong discontinuity and
G2
function [3].
2.5 Tension-softening relation The mechanical meso-scale model that deals with quasi-brittle materials to represent this feature must be determined relation between the applied tensile load and softening behavior of concrete. This relation based on yield function to activate the strong discontinuity. Yield function is written by:
Φ = t Γ − (σ u − q ) q = σ u (1 − exp(− σ u / Gu [| u |])) Where
(4) (5)
t Γ is the tensile stress at the discontinuity, and σ u is the fracture stress. This equation depends on fracture energy
Gu which is based on the total area under the tensile stress-crack opening curve in Fig. 6b.
Fig. 6. The elastic-quasi-brittle behavior.
3. Results and discussion 3.1 Numerical simulations and results In this section, the description of the numerical simulations and the results for the five cylinder specimens under the Brazilian splitting test will be given. 3.2 Discretization of two-phase materials Five cylinder specimens with the size 110 x 50 mm diameter and thickness respectively have been simulated. The parameter variable in this study is the aggregate diameter (simulated with mono-sizes aggregate) while the volume of the fraction has kept constant 20% for the five specimens. The aggregate diameters are 4, 8, 10, 14 and 16 mm respectively, also each simulation consists of one diameter. The geometry properties for each phase (cement paste, aggregate and
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5
interfaces) are summarized in Table 1. As shown in Fig. 7, 3D isometric view for five cylinder specimens are simulated with different aggregate diameters. Table 1. Mechanical Properties of Materials, (E,
σ u , Gu
Cement paste
Aggregate
Interface
=35 GPa
-
σu
=3 MPa
=100 GPa -
σu
=3 MPa
Gu
=80 J/m²
-
Gu
=80 J/m²
) Modulus of Elasticity, Tensile Stress and Fracture Energy. Volume of fraction
20 %
Fig. 7. 3D isometric view section in the five simulated cylinders.
3.3 Maximum crack opening The focus of this study is to describe the effect of aggregate size on the mechanical behavior of concrete in context of Brazilian splitting tensile test. The numerical results show the influence of aggregate diameter on the crack opening without changes in the volume of fraction. On the other hand, the increasing in the aggregate diameter leads to an increase in the maximum crack opening, Fig. 8 shows this relation for five cylinder specimens are simulated. In addition, the results show that the orientation of the cracking became more isotropic in the specimens with larger aggregate diameters. The previous study offered that the crack open is decreasing when the interface zone is strong, and this decrease is depending on the properties of cement paste and rough of crack [11], while other authors presented the increase of the critical opening wc with the aggregate size [10, 15, 17] . 3.4 Splitting tensile stress The numerical results show the relation between aggregate diameters with the maximum splitting tensile stress. Therefore the increasing of aggregate diameter tends to cause an increase in the maximum tensile stress. Otherwise, Fig. 9 shows the maximum tensile stress is a function of aggregate diameter for five cylinder specimens are simulated. One noticeable point is that the total surface area of the interface zone between the aggregate and the cement paste depends on the aggregate diameter, see Table 2. Concerning the effect of aggregate diameter, many studies have recently shown the influence of aggregate size on the mechanical behavior of concrete under loading. The increasing in the tensile stress resulted from the increasing of aggregate size [18], in addition, tensile strength for high-strengthed concrete is increasing with the aggregate size [7].
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Fig. 8. Maximum crack opening versus aggregate diameter.
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Fig. 9. Ultimate tensile stress versus aggregates diameters.
Table 2. Surface area of aggregates for five cylinder specimens. Specimen
Surface area of aggregates mm²
Cylinder-4 Cylinder-8 Cylinder-10 Cylinder-14 Cylinder-16
Ultimate tensile stress
43178.1 7489.6 5943.9 2764.6 1420.0
σu
MPa
1.7 1.9 1.953 2.01 2.11
3.5 Fracture energy By integrating the area under the curve (stress-crack opening) relation in Fig. 6, the total energy can be calculated for each simulation. Fig. 10 gives a clear representation of 3D heterogeneous materials mechanism that occurs during the splitting tensile loading, which is a representative of a softening behavior. The results obtained show that the fracture energy, as a function of aggregate diameter, it seems to increase as the aggregate diameter increases, which is confirmed with the standard of CEB-FIP model code [5]. As shown in Table 3, the fracture energy for many studies, which compared with the fracture energy is obtained from numerical simulations, it shows the influence of the volume of fraction and aggregate sizes on the fracture energy, i. e. the increasing of aggregate size leads to an increase in the fracture energy.
Fig. 10. Energy versus time step for five cylinder specimens are simulated. Table 3. Increasing of fracture energy with aggregate size. Authors
Volume of fraction %
Increasing of fracture energy %
Petersson, 1980 Mihashi, 1989, 1991 Tasdemir et al., 1996 Rao and Prasad, 2002 Numerical simulations
50 40 49 44 20
13 50 34 35 25
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4. Conclusions From this study it can concluded that the increasing of aggregates size led to an increase the ultimate tensile stress, the maximum crack opening and fracture energy for example the ultimate tensile stresses were increased from 1.7 to 2.11 MPa with aggregate diameters 4 and 16 mm respectively. Also, the maximum crack opening varied from 0.391 to 1.159 mm when the aggregates size increased from 4 to 16 mm in addition, the fracture energy increased by 25 %. References [1] ASTM C496, Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens, ASTM Book of Standards. [2] App Rao, G. and Raghu Prasad, B. K, 2011, Influence of interface properties on fracture behaviour of concrete, Indian Academy of Sciences, Res 36 (2) pp. 193-208. [3] Benkemoun N., Hautefeuille M., Colliat JB. ,Ibrahimbegovic A., 2010, Failure of heterogeneous materials: 3D meso-scale FE models with embedded discontinuities. International Journal of Numerical Methods in Engineering 82: 1671-1688. [4] Burcu A., Ayda S. A., Fikret B., Hakan N. A., Cengiz S., 2012, Interpretation of aggregate volume fraction effects on fracture behavior of concrete, Construction and Building Materials 28 pp. 437-443. [5] CEB-FIP Model Code, 1990, Comité Euro-International du Béton (CEB), Bulletin d'Information 195, Lausanne, Switzerland. [6] Cedolin L., Poli S.D., Iori I., 1987, Tensile behavior of concrete, ASCE J. Eng. Mech.113 pp. 431–449. [7] Chen B., Liu J., 2004, Effect of aggregate on the fracture behavior of high strength concrete. Construction and Building Materials ;18 pp. 585–90. [8] Cunha V.M.C.F., Barros J.A.O., Senna-Cruz J.M., 2011, An integrated approach for modeling the tensile behavior of steel reinforced selfcompacting concrete, Cement and Concrete Research 41 pp. 64–76. [9] Elices A., and Rocco C. G., 2008, Effect of aggregate size on the fracture and mechanical properties of a simple concrete, Engineering Fracture Mechanics 75 pp. 3839-3851. [10] Grassl P., Wong H.S., Buenfeld N.R., 2010, Influence of aggregate size and volume fraction on shrinkage induced micro-cracking of concrete and mortar. Cement Concrete Research 40(1) pp. 85–93. [11] Guinea G.V., El-Sayed, Rocco C.G., Elices M., Planas J., 2002, The effect of the bond between the matrix and the aggregates on the cracking mechanism and fracture parameters of concrete ,Cement and Concrete Research 32 pp. 1961– 1970. [12] Hillerborg A., 1985, results of three comparative test seriesfor determining the fracture energy of concrete, Materials and Structures 18 (107) pp. 407-13. [13] Li H., Xianglin G., Feng L., 2014, Influence of aggregate surface roughness on mechanical properties of interface and concrete, Construction and Building Materials 65 pp. 338-349. [14] Li Q., Ansari F., 2000, High-strength concrete inuniaxial tension, ACI Mat. J. 97 pp. 49–55. [15] Li Q., Deng Z., Fu H., 2004, Effect of aggregate type on mechanical behavior of dam concrete, ACI materials Journal 101 (6) pp. 483-92. [16] Mechtcherine V., Muller H.S., 1998, Effect of test set-up on fracture mechanical parameters of concrete, in: Proc. FRAMCOS-3 Fracture Mech and Concrete Struct., Germany, pp. 377-386. [17] Mihashi H., Nomura N., Izumi M., 1989, Influence of matrix strength and gravel size on fracture properties of concrete. In: Shah SP, Swartz SE, Barr B, editors. Fracture of concrete and rock. Elsevier;. pp. 503–12. [18] Rao G. A., Raghu Prasad B. K., 2002, Fracture energy and softening behavior of high-strength concrete. Cement Concrete Research, 32 pp. 247–52. [19] Tasdemir C., Tasdemir M.A., Lydon F.D., Barr B.I.G., 1996, Effects silica fume and aggregate size on the brittleness of concrete. Cement Concrete Research; 26(1) pp. 63–8.