Bsi bs en 12697 26 2012

BS EN 12697-26:2012 BSI Standards Publication Bituminous mixtures — Test methods for hot mix asphalt Part 26: Stiffness BS EN 12697-26:2012 BRITISH STANDARD National foreword This British Standard is the UK implementation of EN 12697-26:2012 It supersedes BS EN 12697-26:2004 which is withdrawn The UK participation in its preparation was entrusted to Technical Committee B/510/1, Asphalt products A list of organizations represented on this committee can be obtained on request to its secretary This publication does not purport to include all the necessary provisions of a contract Users are responsible for its correct application © The British Standards Institution 2012 Published by BSI Standards Limited 2012 ISBN 978 580 74079 ICS 93.080.20 Compliance with a British Standard cannot confer immunity from legal obligations This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 March 2012 Amendments issued since publication Date Text affected BS EN 12697-26:2012 EN 12697-26 EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM March 2012 ICS 93.080.20 Supersedes EN 12697-26:2004 English Version Bituminous mixtures - Test methods for hot mix asphalt - Part 26: Stiffness Mélanges bitumineux - Méthodes d'essai pour enrobés chaud - Partie 26: Rigidité Asphalt - Prüfverfahren für Heißasphalt - Teil 26: Steifigkeit This European Standard was approved by CEN on 18 September 2011 CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member This European Standard exists in three official versions (English, French, German) A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same status as the official versions CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom EUROPEAN COMMITTEE FOR STANDARDIZATION COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG Management Centre: Avenue Marnix 17, B-1000 Brussels © 2012 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members Ref No EN 12697-26:2012: E BS EN 12697-26:2012 EN 12697-26:2012 (E) Contents Page Foreword 1 Scope 2 Normative references 3 3.1 3.2 Terms, definitions and symbols Terms and definitions Symbols 4 Principle 10 5 5.1 5.2 5.3 5.4 5.5 Sample preparation 10 Age of the specimens 10 Drying of the specimen 10 Dimensions and bulk density of the specimens 10 Temperature of the specimen before testing 10 Number of test specimens 10 6 Checking of the testing equipment 10 7 7.1 7.2 7.3 Test methods 11 General 11 Tests with sinusoidal or pulse loading 11 Controlled strain rate loading 12 8 Temperatures 13 9 Expression of results 14 10 10.1 10.2 10.3 10.4 10.5 Test report 16 General 16 Information on specimen 16 Information on test method 17 Information on the test and results 17 Optional information 17 11 Precision 17 Annex A (normative) Two point bending test on trapezoidal specimens (2PB-TR) or on prismatic specimens (2PB-PR) 18 A.1 Principle 18 A.2 Equipment 18 A.3 Specimen preparation 19 A.4 Procedure 20 Annex B (normative) Three point bending test on prismatic specimens (3PB-PR) and four point bending test on prismatic specimens (4PB-PR) 21 B.1 Principle 21 B.2 Equipment 22 B.3 Specimen preparation 23 B.4 Procedure 23 Annex C (normative) Test applying indirect tension to cylindrical specimens (IT-CY) 25 C.1 Principle 25 C.2 Equipment 25 C.3 Specimen preparation 30 BS EN 12697-26:2012 EN 12697-26:2012 (E) Page C.4 Mode of operation .31 Annex D (normative) Direct tension-compression test on cylindrical specimens (DTC-CY) 33 D.1 Principle 33 D.2 Equipment 33 D.3 Specimen preparation 33 D.4 Mode of operation 34 Annex E (normative) Test applying direct tension to cylindrical specimens (DT-CY) or to prismatic specimens (DT-PR) 36 E.1 Principle 36 E.2 Equipment 36 E.3 Specimen preparation 36 E.4 Mode of operation 37 E.5 Derivation of the master-curve 38 E.6 Determination of the stiffness modulus for the fixed loading time 41 Annex F (normative) Test applying Cyclic indirect tension to cylindrical specimens (CIT-CY) 42 F.1 Principle 42 F.2 Equipment 42 F.3 Specimen preparation 44 F.4 Mode of operation 45 Annex G (informative) Derivation of the master curve 47 G.1 Principle 47 G.2 Theoretical background 48 G.3 Experimental data 49 G.4 Test report 50 BS EN 12697-26:2012 EN 12697-26:2012 (E) Foreword This document (EN 12697-26:2012) has been prepared by Technical Committee CEN/TC 227 “Road materials”, the secretariat of which is held by DIN This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by September 2012, and conflicting national standards shall be withdrawn at the latest by September 2012 This document will supersede EN 12697-26:2004 Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights The main changes deal with putting similar procedures in all the test in the general part of the standard Also the correct wording is applied within all the test procedures This document is one of a series of standards as listed below: EN 12697-1, Bituminous mixtures — Test methods for hot mix asphalt — Part 1: Soluble binder content EN 12697-2, Bituminous mixtures — Test methods for hot mix asphalt — Part 2: Determination of particle size distribution EN 12697-3, Bituminous mixtures — Test methods for hot mix asphalt — Part 3: Bitumen recovery: Rotary evaporator EN 12697-4, Bituminous mixtures — Test methods for hot mix asphalt — Part 4: Bitumen recovery: Fractionating column EN 12697-5, Bituminous mixtures — Test methods for hot mix asphalt — Part 5: Determination of the maximum density EN 12697-6, Bituminous mixtures — Test methods for hot mix asphalt — Part 6: Determination of bulk density of bituminous specimens EN 12697-7, Bituminous mixtures — Test methods for hot mix asphalt — Part 7: Determination of bulk density of bituminous specimens by gamma rays EN 12697-8, Bituminous mixtures — Test methods for hot mix asphalt — Part 8: Determination of void characteristics of bituminous specimens EN 12697-10, Bituminous mixtures — Test methods for hot mix asphalt — Part 10: Compactability EN 12697-11, Bituminous mixtures — Test methods for hot mix asphalt — Part 11: Determination of the affinity between aggregate and bitumen EN 12697-12, Bituminous mixtures — Test methods for hot mix asphalt — Part 12: Determination of the water sensitivity of bituminous specimens EN 12697-13, Bituminous mixtures — Test methods for hot mix asphalt — Part 13: Temperature measurement EN 12697-14, Bituminous mixtures — Test methods for hot mix asphalt — Part 14: Water content BS EN 12697-26:2012 EN 12697-26:2012 (E) EN 12697-15, Bituminous mixtures — Test methods for hot mix asphalt — Part 15: Determination of the segregation sensitivity EN 12697-16, Bituminous mixtures — Test methods for hot mix asphalt — Part 16: Abrasion by studded tyres EN 12697-17, Bituminous mixtures — Test methods for hot mix asphalt — Part 17: Particle loss of porous asphalt specimen EN 12697-18, Bituminous mixtures — Test methods for hot mix asphalt — Part 18: Binder drainage EN 12697-19, Bituminous mixtures — Test methods for hot mix asphalt — Part 19: Permeability of specimen EN 12697-20, Bituminous mixtures — Test methods for hot mix asphalt — Part 20: Indentation using cube or Marshall specimens EN 12697-21, Bituminous mixtures — Test methods for hot mix asphalt — Part 21: Indentation using plate specimens EN 12697-22, Bituminous mixtures — Test methods for hot mix asphalt — Part 22: Wheel tracking EN 12697-23, Bituminous mixtures — Test methods for hot mix asphalt — Part 23: Determination of the indirect tensile strength of bituminous specimens EN 12697-24, Bituminous mixtures — Test methods for hot mix asphalt — Part 24: Resistance to fatigue EN 12697-25, Bituminous mixtures — Test methods for hot mix asphalt — Part 25: Cyclic compression test EN 12697-26, Bituminous mixtures — Test methods for hot mix asphalt — Part 26: Stiffness EN 12697-27, Bituminous mixtures — Test methods for hot mix asphalt — Part 27: Sampling EN 12697-28, Bituminous mixtures — Test methods for hot mix asphalt — Part 28: Preparation of samples for determining binder content, water content and grading EN 12697-29, Bituminous mixtures — Test methods for hot mix asphalt — Part 29: Determination of the dimensions of a bituminous specimen EN 12697-30, Bituminous mixtures — Test methods for hot mix asphalt — Part 30: Specimen preparation by impact compactor EN 12697-31, Bituminous mixtures — Test methods for hot mix asphalt — Part 31: Specimen preparation by gyratory compactor EN 12697-32, Bituminous mixtures — Test methods for hot mix asphalt — Part 32: Laboratory compaction of bituminous mixtures by a vibratory compactor EN 12697-33, Bituminous mixtures — Test methods for hot mix asphalt — Part 33: Specimen prepared by roller compactor EN 12697-34, Bituminous mixtures — Test methods for hot mix asphalt — Part 34: Marshall test EN 12697-35, Bituminous mixtures — Test methods for hot mix asphalt — Part 35: Laboratory mixing EN 12697-36, Bituminous mixtures — Test methods for hot mix asphalt− Part 36: Determination of the thickness of a bituminous pavement EN 12697-37, Bituminous mixtures — Test methods for hot mix asphalt — Part 37: Hot sand test for the adhesivity of binder on precoated chippings for HRA BS EN 12697-26:2012 EN 12697-26:2012 (E) EN 12697-38, Bituminous mixtures — Test methods for hot mix asphalt — Part 38: Common equipment and calibration EN 12697-39, Bituminous mixtures — Test methods for hot mix asphalt — Part 39: Binder content by ignition EN 12697-40, Bituminous mixtures — Test methods for hot mix asphalt — Part 40: In situ drainability EN 12697-41, Bituminous mixtures — Test methods for hot mix asphalt — Part 41: Resistance to de-icing fluids EN 12697-42, Bituminous mixtures — Test methods for hot mix asphalt — Part 42: Amount of foreign matters in reclaimed asphalt EN 12697-43, Bituminous mixtures — Test methods for hot mix asphalt — Part 43: Resistance to fuel EN 12697-44, Bituminous mixtures — Test methods for hot mix asphalt — Part 44; Crack propagation by semi-circular bending test prEN 12697-45, Bituminous mixtures — Test methods for hot mix asphalt — Part 45: Saturation ageing tensile stiffness (SATS) conditioning test prEN 12697-46, Bituminous mixtures — Test methods for hot mix asphalt — Part 46: Low temperature cracking and properties by uniaxial tension tests EN 12697-47, Bituminous mixtures — Test methods for hot mix asphalt — Part 47: Determination of the ash content of natural asphalts prEN 12697-48, Bituminous mixtures — Test methods for hot mix asphalt — Part 48: Inter-layer bond strength1) prEN 12697-49, Bituminous mixtures — Test methods for hot mix asphalt — Part 49: Skid resistance of asphalt in the laboratory1) prEN 12697-50, Bituminous mixtures — Test methods for hot mix asphalt — Part 50: Scuffing resistance of surface course1) According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom 1) In preparation BS EN 12697-26:2012 EN 12697-26:2012 (E) Scope This European Standard specifies the methods for characterising the stiffness of bituminous mixtures by alternative tests, including bending tests and direct and indirect tensile tests The tests are performed on compacted bituminous material under a sinusoidal loading or other controlled loading, using different types of specimens and supports The procedure is used to rank bituminous mixtures on the basis of stiffness, as a guide to relative performance in the pavement, to obtain data for estimating the structural behaviour in the road and to judge test data according to specifications for bituminous mixtures As this standard does not impose a particular type of testing device the precise choice of the test conditions depends on the possibilities and the working range of the used device For the choice of specific test conditions, the requirements of the product standards for bituminous mixtures should be respected The applicability of this document is described in the product standards for bituminous mixtures Normative references The following referenced documents are indispensable for the application of this document For dated references, only the edition cited applies For undated references, the latest edition of the referenced document (including any amendments) applies EN 12697-6, Bituminous mixtures — Test methods for hot mix asphalt — Part 6: Determination of bulk density of bituminous specimens EN 12697-27, Bituminous mixtures — Test methods for hot mix asphalt — Part 27: Sampling EN 12697-29, Bituminous mixtures — Test methods for hot mix asphalt — Part 29: Determination of the dimensions of a bituminous specimen EN 12967-31, Bituminous mixtures — Test methods for hot mix asphalt — Part 31: Specimen preparation by gyratory compactor EN 12967-33, Bituminous mixtures — Test methods for hot mix asphalt — Part 33: Specimen prepared by roller compactor Terms, definitions and symbols 3.1 Terms and definitions For the purposes of this document, the following terms and definitions apply 3.1.1 stiffness E= σ ε BS EN 12697-26:2012 EN 12697-26:2012 (E) 3.1.2 complex modulus relationship between stress and strain for a linear visco-elastic material submitted to a sinusoidal load wave form at time, t, where applying a stress σ × sin ( ω × t) results in a strain ε × sin (ω × (t − Φ)) that has a phase angle, Φ, with respect to the stress NOTE The amplitude of strain and the phase angle are functions of the frequency, f, and the test temperature, Θ NOTE The stress strain ratio defines the complex modulus E* as: E * = E * × (cos (Φ ) + i × sin (Φ )) (1) The complex modulus is characterised by a pair of two components This pair can be expressed in two ways: the real component E1 and the imaginary components E2: E1 = E * × cos (Φ ) (2) E2 = E * × sin (Φ ) (3) the absolute value of the complex modulus E* and the phase angle, Φ: E* = E12 + E2 E  Φ = arctan    E1  (4) (5) NOTE This second characterisation is more often used in practice In linear elastic multi-layer calculations for instance the E* modulus is generally used as input value for Young's modulus NOTE For purely elastic materials, the phase angle is zero and then the complex modulus reduces to the Young's modulus This happens when bituminous materials are at very low temperatures Then the complex modulus reaches its highest possible value noted E∞ 3.1.3 secant modulus relationship between stress and strain at the loading time, t, for a material subjected to controlled strain rate loading: E (t ) = σ (t ) ε (t ) (6) with stress, σ(t), and strain, ε(t), at time t NOTE The strain law is: ε (t ) = α i × t n (7) where αi and n are constants NOTE Several successive tests may be carried out on the same specimen for different values αi For linear viscoelastic materials, the secant modulus obtained for different values of αi at the same temperature depends on the loading time, t, only BS EN 12697-26:2012 EN 12697-26:2012 (E) E.4.2 Procedure E.4.2.1 An element test shall be defined by choosing:  the test temperature Θj;  the level of strain;  the loading time ti (with precision of %) E.4.2.2 The element test shall be carried out and the stress σ (ti, Θj) determined for the deformation εj E.4.2.3 Figure E.1 shows the principle of the test Key sample measurement area force sensor (1 of 3) transitory period Figure E.1 — Principle of the DT-CY test E.5 Derivation of the master-curve E.5.1 Isotherms At least four loading times are necessary for at least one test temperature and at least two loading times for other test temperatures (see Figure E.2) The values of the stiffness are presented graphically in a logarithmic scale under a form of isotherms of the stiffness in function of loading times following the principle of Annex G using loading time instead of frequency 38 BS EN 12697-26:2012 EN 12697-26:2012 (E) Key Y X stiffness, in MPa loading time, in s - °C °C + 10 °C + 15 °C Figure E.2 — Example of isotherms E.5.2 Master curve at a fixed temperature The master curve at a fixed temperature shall be built up by shifting the isotherms drawn at other temperatures by a translation strictly along the loading time scale The shifting factor between isotherm at temperature θ1 and isotherm at temperature θ2, shall be determined by calculation as indicated Figure E.3 in order to obtain a continuous curve at the required temperature 39 BS EN 12697-26:2012 EN 12697-26:2012 (E) Key Y X stiffness, in MPa loading time, in s Figure E.3 — Determination of the shift factor 40 BS EN 12697-26:2012 EN 12697-26:2012 (E) E.6 Determination of the stiffness modulus for the fixed loading time The stiffness modulus for the required loading time is determined on the master-curve at the required temperature (see Figure E.4) Key Y X - stiffness, in MPa loading time, in s - °C °C + 10 °C + 15 °C master curve at + 15 °C Figure E.4 — Example of stiffness modulus for a loading time of 0,02 s and a temperature of 15 °C 41 BS EN 12697-26:2012 EN 12697-26:2012 (E) Annex F (normative) Test applying Cyclic indirect tension to cylindrical specimens (CIT-CY) F.1 Principle This annex describes a test method to characterise the stiffness of bituminous mixtures under sinusoidal loading using Cyclic Indirect Tensile Test (CITT) The method is applicable to cylindrical specimens, manufactured in the laboratory or cored from a road layer During multistage tests different temperatures and loading frequencies are applied on the specimens in order to determine the master curve F.2 Equipment F.2.1 Test machine A test apparatus which enables a sinusoidal loading of the specimen within the required accuracy shall be applied A PC and software for measuring and saving the data is necessary F.2.2 Loading For the acquisition of the loading a measuring unit is required The measuring range should be 50 kN with a accuracy of ± 50 N NOTE The maximum load capacity required depends on the size of the specimen, the testing temperature and character of the material F.2.3 Displacement The measurement system to record the horizontal deformation of the specimen should include at least two displacement transducers or one extensometer that need to be attached directly to the specimen or strain gauges glued to the surface of the specimen The displacement transducers shall be placed centric on the cross sectional area of the specimen The minimum measuring range for displacement transducers shall be mm (each displacement transducer 2,0 mm) with a accuracy of 0,1 µm The accuracy class of the displacement transducers (minimum 0,3) and the extensometer (minimum 0,2) respectively shall be reported in the test report In addition, the vertical specimen deformation can be measured by displacement transducers in order to determine the Poisson’s ratio and the phase angle The displacement transducers shall be placed on the upper loading strip Any measurement at the loading cylinder or on the loading bars is not allowed The measuring range for displacement transducers shall be at least mm with an accuracy of at least µm 42 BS EN 12697-26:2012 EN 12697-26:2012 (E) Key LVDT frame set screws to fix the frame to the specimen Figure F.1 — Example for the measurement of the horizontal deformation – frame with LVDTs Key loading piston test specimen extensometer deflection strip loading strips Figure F.2 — Example for the measurement of the horizontal deformation — strain gauges with extensometer 43 BS EN 12697-26:2012 EN 12697-26:2012 (E) F.2.4 Thermostatic chamber Thermostatic chamber, in which the required test temperature can be maintained within an accuracy of ± 0,5 °C in the vicinity of the specimens NOTE It is recommended that a sufficiently large thermostatic chamber is chosen, so that additional specimens can be acclimatised during testing F.2.5 Recording and measuring system Recording and measuring devices for determining the compressive load and the horizontal deformations which shall be capable of measurement at least 10 measuring points for each load cycle The load and displacement should be measured and registered synchronically at the same time F.2.6 Loading strips For the tests loading strips made out of tempered steel (recommendation: Rockwell hardness HRC 56 to 58) with a concave segment are required The radius of curvature and the width of the loading strips b should be chosen in dependence on the specimen radius The dimensions of loading strips are listed in Figure F.3 Upper and lower loading strips shall form one plane The loading strips shall be fixed to the loading frame and the loading piston without any hinges Nominal specimen ∅ 100 mm Loading strips Nominal specimen ∅ 150 mm r = (50 ± 1,0) mm r = (75 ± 1,0) mm b = (12,7 ± 0,2) mm b = (19,1 ± 0,2) mm Lengths > h + 20 mm Lengths > h + 20 mm Figure F.3 — Dimensions of loading strips F.3 Specimen preparation F.3.1 Test specimen At each test temperature specimens shall be tested An additional specimen may be needed for estimating the required loading condition The cylindrical specimens subject to the test shall be obtained in accordance with:  test specimen drilled from laboratory-prepared slab of asphalt according to EN 12697-33;  test specimen prepared from drilled core taken from the road according to EN 12697-27 The cores shall be taken from the pavement in vertical direction The layers need to be separated by sawing if the cores are taken from the pavement consisting of different layers 44 BS EN 12697-26:2012 EN 12697-26:2012 (E) The specimen dimensions should comply with the requirements listed in Table F.1 Any damage on the specimens shall be avoided Only undamaged specimens shall be tested F.3.2 Specimen dimensions Each specimen shall form a nominal cylinder The specimen dimensions required are listed in Table F.1 Table F.1 — Specimen dimensions Maximum grain size mm Specimen diameter mm Specimen height mm ≤ 16 100 ± 40 ± > 16 to < 32 150 ± 60 ± ≥ 32 150 ± 90 ± The height and diameter of the specimens shall be measured in accordance with EN 12697-29 The deviation from the right angle should be less than 3° The lateral area of the specimen should have an even surface F.4 Mode of operation F.4.1 Test temperature In minimum, the following test temperatures shall be chosen: −10 °C, °C, 10 °C and 20 °C If required, more test temperatures can be chosen between −10 °C and 20 °C The test temperature shall be within ± 0,5 °C of the target temperature F.4.2 Mounting the specimen The loading strips shall be wiped clean using a solvent if necessary A conditioned specimen shall be placed between the loading strips that it seats itself properly without extensive movement and so that the two faces of the specimen are nominally perpendicular to the loading strip Place the upper loading strip on the top of the specimen and seat it such that there is no excessive movement Adjust the system to measure the horizontal deformation NOTE It is important that, in the case of LVDT, the mounting frame is clamped evenly and securely to the specimen Care should be taken to ensure that no over-tightening of the securing clamps occurs One way of achieving this is to apply a constant torque to each of the securing clamps F.4.3 Procedure F.4.3.1 General The specimen is usually subjected to a force controlled harmonic sinusoidal loading without rest periods Table F.2 shows the load frequencies spectrum as well as the number of load cycles required for the multistage tests Table F.2 — Load cycles required for the multistage-tests Load frequency Number of load cycles Analysis of load cycle 45 BS EN 12697-26:2012 EN 12697-26:2012 (E) F.4.3.2 10 Hz 110 98 to 102 Hz 100 93 to 97 Hz 20 13 to 17 0.1 Hz 10 to Load frequency The tests shall be conducted at a constant load at different load frequencies in a range between 0,1 Hz and 10 Hz in minimum (preferable 60 Hz) for each specimen and test temperature F.4.3.3 Definition of the lower load level The lower stress level for the tests shall be 0,035 MPa F.4.3.4 Definition of the upper load level The upper load limits shall be determined in that manner that the initial horizontal strains in the specimen centre are in a range between 0,05 ‰ to 0,10 ‰ To determine the upper load limit the following procedure might be applied for every testing temperature NOTE Reasonable stress amplitudes can be determined by testing a single specimen with CITT in a force-sweep test Each stress amplitude shall be applied for a limited number of load cycles F.4.4 Checking of specimen deterioration The test conditions should be chosen to avoid any damage of the specimen during testing This can be check by applying the same test conditions for the first and last single test If the test results differ more than 15 %, the results of this multistage test should not be used The test shall be repeated by using a new specimen However, the test conditions should be modified (reduction of the stress level) In minimum three specimens should be tested at each temperature 46 BS EN 12697-26:2012 EN 12697-26:2012 (E) Annex G (informative) Derivation of the master curve G.1 Principle The stiffness modulus of bituminous mixes obey the frequency-temperature superposition principles This means that a master curve of the complex modulus can be constructed for a reference temperature from experimental data over a limited range of frequencies and temperatures, provided that a shift factor is used to calculate the reference frequency Key A B experimental range range covered by the master curve Figure G.1 — Derivation of the master curve The aim of the master curve is to determine the stiffness modulus at any arbitrary combination of loading frequency and test temperature For this purpose, the stiffness has to measured at various frequencies and temperatures These results are used to determine the parameters in an Arrhenius equation, which is used often in this case In this annex, the determination of the master of the stiffness is based on the approach of Arrhenius Alternative approaches can also be used, e.g the Christensen-Anderson model In all cases in the report on the determination of the mastercurve, the theoretical background of the used model shall be incorporated 47 BS EN 12697-26:2012 EN 12697-26:2012 (E) G.2 Theoretical background The basis form of the master curve is: 1  f     = lg (α T ) = C ⋅  − lg  T TS   fs  (G.1) with C = lg (e ) ⋅ ∆H ∆H b = = R ,303 ⋅ R ,303 (G.2) where C is the experimental constant, in K; T is the actual temperature, in K; Ts is the arbitrary chosen reference temperature, in K; R is the Universal gas constant = 8,314 J/K/mole; ∆H is the activation energy, in kJ/mole; αT is the shift factor; f is the loading frequency at temperature T, in Hz; fs is the loading frequency at temperature Ts, in Hz Equation G.1 is called the Arrhenius Equation In literature, various values for C are mentioned The C-value depends on the activation energy which depends on the characteristics oh the bitumen and filler The C-value for a specific asphalt mix can be determined with the following equation: lg (S mix ) = lg (η ) + b lg (e ) − lg (t ) T (G.3) where Smix is the stiffness modulus E as a function of loading time and temperature, in MPa; η0 is the dynamic viscosity, in Pa⋅s; b is the constant, depending on the shift factor αT; t is the loading time, in s; T is the test temperature, in K The value of the parameter b can be calculated with the stiffness modulus at temperature Tx which is determined by shifting the stiffness modulus measured at temperature Ty at the same loading time (or frequency) Equalising the stiffness modulus Smix,A determined at a loading time t1 and temperature TX to a stiffness modulus Smix,B determined at a loading time t2 and temperature TY finally results in: 48 BS EN 12697-26:2012 EN 12697-26:2012 (E) b ,303  1  −  TY TX t   = lg (t ) − lg (t1 ) = lg   t1   f   = lg   f2     (G.4) The shift factor log(αT) corresponds with lg (f1/f2) The constant C can now easily be determined At any combination of loading time and temperature, the C-value will be different For this reason, the C-value shall be determined at a combination of low temperature and high loading frequency, a combination of high temperature and low loading frequency and a middle combination of frequency and temperature After determination of the C-value, the stiffness, temperature and loading frequency can be gathered in a fictive temperature Tfict Tfict = lg ( f char / f − T a + 273 C ) − 273 (G.5) where Tfict is the fictive asphalt concrete temperature where the stiffness shall be determined, in °C; Ta is the actual temperature, in °C; fchar is the characteristic loading frequency which is used to determine the master curve, in Hz; f is the loading frequency, in Hz Using linear regression the coefficients of Equation (6) can be determined for a chosen characteristic loading frequency: ln (S mix ) = c1 + c ⋅ Tfict + c3 ⋅ Tfict + c ⋅ Tfict (G.6) G.3 Experimental data To determine a mastercurve of the stiffness, a frequency spectrum of initial complex (stiffness) moduli at several test temperatures shall be performed This test shall consist of response measurements at a range of nominal frequencies (e.g Hz, Hz, Hz, Hz, 10 Hz, 20 Hz, 30 Hz and 60 Hz and subsequently again at Hz) The loading mode in this pre-test shall be constant deflection representative for a maximum strain amplitude of less than 50 µm/m At each frequency, a representative number of load repetitions shall be applied in order to measure the stiffness modulus accurately For lower frequencies 50 load repetitions are enough; at higher frequencies 200 load cycles shall be applied In order to avoid premature fatigue damage, the total number of applications for all frequencies together shall not exceed 000 At low temperatures (Θ ≤ 10 °C), there shall be a short rest period of about 10 before the actual fatigue test starts In order to develop a representative master curve, at least specimens shall be tested From each specimen, the stiffness modulus of the mix shall be measured at temperatures and at each temperature at 10 frequencies The difference between various temperatures shall be at least 10 °C The combination of frequency and temperature shall be chosen in such a way that the resulting stiffness moduli at various temperatures have an overlap NOTE Typical test temperature are -15 °C, °C, 15 °C and 30 °C and typical loading frequencies are 0,1; 0,2; 0,5; 1; 2; 5; 8;10; 20; 30 and 50 Hz For an AC 16 bin/base 40/60, the following parameters are found assuming Ts = 20 °C and fchar = Hz: 49 BS EN 12697-26:2012 EN 12697-26:2012 (E)  C = 175 K  c1 = 10,139 533 26  c2 = −0,023 403 44  c3 = −0,001 008 16  c4 = 0,000 000 55 G.4 Test report The test report includes the following information:  characteristics of the mix;  loading conditions (type of test, test temperatures and frequencies);  numerical values of the parameters including graphical representations;  temperature or frequency range covered by the master curve;  reference to this standard 50 This page deliberately left blank NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAW British Standards Institution (BSI) BSI is the national body responsible for preparing British Standards and other standards-related publications, information and services BSI is incorporated by Royal Charter British Standards and other standardization products are published by BSI Standards Limited About us Revisions We bring together business, industry, government, consumers, innovators and others to shape their combined 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