Research on differences and correlation between tensile, compression and flexural moduli of cement stabilized macadam

Transcription

1 Research on dierences and correlation between tensile, comression and lexural moduli o cement stabilized macadam Yi Yang School o Traic and Transortation, Changsha University o Science & Technology, Hunan , China; Modern Investment Co., Ltd., Hunan , China @qq.com Jianlong Zheng School o Traic and Transortation, Changsha University o Science & Technology, Hunan , China zjl@csust.edu.cn Songtao Lv School o Traic and Transortation, Changsha University o Science & Technology, Hunan , China lstcs@126.com ABSTRACT. In order to reveal the dierences and conversion relations between the tensile, comressive and lexural moduli o cement stabilized macadam, in this aer, we develo a new test method or measuring three moduli simultaneously. By using the materials testing system, we test three moduli o the cement stabilized macadam under dierent loading rates, roose a lexural modulus calculation ormula which considers the shearing eect, reveal the change rules o the tensile, comression and lexural moduli with the loading rate and establish the conversion relationshis between the three moduli. The results indicate that: three moduli become larger with the increase o the loading rate, showing a ower unction attern; with the shear eect considered, the lexural modulus is increased by 47% aroximately over that in the current test method; the tensile and comression moduli o cement stabilized macadam are signiicantly dierent. Thereore, i only the comression modulus is used as the structural design arameter o ashalt avement, there will be a great deviation in the analysis o the load resonse. In order to achieve scientiic design and calculation, the aroriate design arameters should be chosen based on the actual stress state at each oint inside the avement structure. Citation: Yang, Y., Zheng, J., Lv, S., Research on dierences and correlation between tensile, comression and lexural moduli o cement stabilized macadam, Frattura ed Integrità Strutturale, 41 (2017) Received: Acceted: Published: Coyright: 2017 This is an oen access article under the terms o the CC-BY 4.0, which ermits unrestricted use, distribution, and reroduction in any medium, rovided the original author and source are credited. KEYWORDS. Road engineering; Cement stabilized macadam; Laboratory test; Tensile-comression-lexural modulus; Loading rate. 9

2 INTRODUCTION D ue to high intensity and rigidity and good resistance, the cement stabilized semi-rigid base can adat to heavy traic and comlex climate environment, making it become one o the major tyes o base course or highgrade highway ashalt avement in China [1]. Restricted by economic and technological conditions, or a long eriod o time, semi-rigid base will still be widely alied as a major base course o avement. Thereore, we should urther understand its characteristics and imrove and utilize them so as to give ull lay to the advantages o this semirigid base material [2]. The ashalt avement design code currently in use in China is simle, in which unconined comressive resilient modulus is used as the arameters in the structural design o ashalt mixture and semi-rigid base material [,4], and the avement material is similar to most o the engineering materials, showing dierent characteristics under dierent tensile and comression moduli. When the dierence between the tensile and comression moduli o the material is large, it is inaroriate to use a single modulus to calculate and analyze the mechanical resonse [5]. Reerence [6,7] studied the constitutive relations o materials with dierent tensile and comressive elastic moduli and the racture mechanical resonses thereo. Reerence [8-11] discussed and analyzed the alication o the elastic theory o dierent moduli like tensile and comression moduli in the theories o beam, shell and late, established elasticity solutions to beams, shells and lates with dierent tensile and comression moduli under dierent loads, and roosed a static equilibrium equation and calculation methods or stress and dislacement under external orce. For the avement material, in 1992, Changsha University o Science & Technology (ormerly Changsha Communications College) roosed a calculation method when dierences between tensile and comression moduli are considered or the rigid avement [12], then analyzed the drawbacks o lexible avement design using tensile and comression moduli as the moduli o the structural layer and deduced the basic ormula and test method o the double modulus theory [1]. The semi-rigid base is ormed through stratiied comaction, with signiicant dierences in its tensile and comressive moduli. Under the action o traic load, the neutral surace o the semi-rigid base course is not at the geometric center o the structural layer; instead, it shits towards the comressive zone. The existing ashalt avement design method does not consider the actual stress distribution o the semi-rigid base, and erorms the structural load resonse analysis according to the comressive elastic modulus, which will lead to the unbalance between the working state o the structural design arameter and the actual stress state, and urther resulting in large deviation in calculation and analysis results. In order to achieve scientiic calculation and analysis, the corresonding design arameters should be determined according to the stress state o the oints inside the avement structure. Thereore, it is necessary to set u the mechanical resonse analysis method or ashalt avement structure using the double modulus theory with dierent tensile and comressive moduli, esecially the method to obtain the corresonding material arameters. In this aer, by using the MTS (Material Test System), we roose a new test method or measuring tensile, comression and lexural moduli simultaneously. We test three moduli o the cement stabilized macadam under dierent loading rates, roose a lexural modulus calculation ormula which considers the shearing eect and reveal the change rules o the tensile, comression and lexural moduli with the loading rate and the dierences and correlations between the three moduli so as to rovide theoretical basis or the selection and otimization o material arameters in the ashalt avement structure design. SPECIMEN MOLDING AND TEST PREPARATION Secimen Molding T he cement used as the raw material o cement stabilized macadam is Xing an Hailuo ordinary ortland cement PC2.5 and its inormation are shown as Tab.1. The aggregate is the limestone aggregate manuactured by Yangjiaqiao Crushing Plant and its inormation are shown as Tab.2. The test results show that the technical indexes o these raw materials meet the requirements as seciied in the code. In the basis o ractical engineering, the gradation o CSM aggregate was designed to realize ramework-dense structure according to the Testing Methods o Material Stabilized with Inorganic Binders or Highway Engineering [14].The mineral aggregate gradation adoted is shown in Tab. : According to the mineral aggregate gradation listed in Tab., we carry out the heavy comaction test on cement stabilized macadam. First, we determine the otimum water content and maximum dry density at dierent cement dosages, and then determine the dosage o cement that meets the requirements by erorming the unconined comressive strength 40

3 test at each dose. The inal test results are: the dosage o cement added into the cement stabilized macadam is 4.5%, the maximum dry density is 2.5g/cm and the otimum water content is 4.5%. Test Results seciication Fineness (Sieve size 80μm) % Initial setting time (min) Final setting time (min) Stability (mm) 5 day lexural strength o cement mortar (MPa) day comressive strength o cement mortar (MPa) Table 1: The characterization o Xing an Hailuo ordinary Portland cement PC2.5. Test Coarse aggregate seciication Content o needle and late article 11.7% 20% Crushing value 19.8% 0% Liquid Liquid limit& Plasticity index o limit 28% 26.5% Particles less than 0.6mm Plasticity index Table 2: The characterization o the limestone aggregate. Mesh size (mm) Pass rate (%) Table : Synthetic Aggregate Gradation o Cement Stabilized Macadam. Based on the above data, according to the requirements in the test regulations [14], we make secimens or lexural strength and lexural modulus, whose size is 100mm 100mm 400mm. We use the static molding method in the secimen molding. Ater that, secimens are ut in a standard reservation room (temerature: 20 C±2 C; humidity 95%) or 90 days o reservation. Descrition o the tensile, comression and lexural test method We use MTS (Material Test System) or modulus testing. The test rincile is shown in Fig. 1, 2 and. The mid-san delection is measured using a micrometer laced on the uer surace o the secimen, which is used to calculate the lexural modulus o the secimen; the comressive strain o the mid-san uer surace and the tensile strain o the lower surace are measured by the strain gauges attached to the surace, resectively, which are used to calculate the comression modulus and tensile modulus o the secimen. 41

4 In order to eliminate the riction between the load head, the suort and the secimen, we use a cylindrical load head and a cylindrical suort and aly butter to the load head and the suort beore the test. The loading rate includes 0.1mm/min, 0.4mm/min, 0.7mm/min, 1mm/min our grades. Figure 1: Testing Princile or Tensile, Comression and Flexural moduli (1-beam secimen; 2-cylindrical suort; -micrometer; 4- strain gage). The strain gages are oil resistance strain gages, with a grid length o 80mm and a resistance o 120Ω. Due to the rough beam surace o the cement stabilized macadam secimen, it is necessary to ut cement aste on the uer and lower suraces to ill the gas in areas where strain gages will be ut on one week beore the test. While attaching 4 strain gages on the uer and lower suraces resectively, i.e. 8 strain gages in total, we measure the comressive and tensile strains o the test beam (as shown in Fig. 1 and Fig. 2). At the same time, considering the edge eect o strain, the center o the most marginal strain gage should be 20mm away rom the edge o the beam. The strain gage asting method and test device are shown in Fig. 2 and Fig.. The center o the most marginal strain gage is 20mm away rom the edge o the beam. The way the strain gage is asted and the test device are shown in Fig. 2 and Fig.. Figure 2: Schematic o Strain Gauges Pasted Figure : Installation Drawing o Modulus Test DERIVATION OF THE TENSILE, COMPRESSION AND FLEXURAL MODULI CALCULATION FORMULAS Traditional lexural modulus calculation ormula W hen the length o the bar l is much greater than the cross-sectional height h, i.e. l>5h, the analytical ormula or ure bending can be used. The current test rocedure calculates the lexural modulus without considering the shear eect [14]. The calculation and derivation rocess is as ollows: P P/2 P/2 P/2 P/2 x L/2-x P/2 L/ L/ L/ L/6 L/2 P/2 (a) (b) Figure 4: Force Analysis Diagram o Secimen 42

5 Fig. 4(a) shows the simliied orce diagram o the secimen. (b) shows the equivalent orce diagram or the right art o the secimen. The aroximate dierential line o delection equation or the beam can be exressed by section as ollows: When 0 x L/6: PL E I ω '' = (1) 6 When L/6 x L/2: PL Px E I ω '' = (2) 4 2 Where, E is the traditional lexural modulus; I is the inertia moment; w is the mid-san delection; P is the load alied; L is the secimen san. By integrating Formula (1) and (2) twice resectively, based on the boundary conditions and continuity conditions, we will know that when L/6 x L/2, 2 2 PLx Px PL x PL E I ω = + () When x=l/2, by substituting the inertia moment I=bh /12 into Formla (), we obtain the lexural modulus calculation ormula: E 2PL = 108bh ω (4) Where, h is the mid-san sectional height; b is the cross section width o the secimen; other symbols are the same meanings as above. Flexural modulus calculation correction ormula considering the shear eect When the san height o the beam is greater than 5, the ositive stress ormula or ure bending can be alied to the ositive stress calculation or transverse bending. However, or a dee beam with a san height o less than 5, i we use the ure bending theory and assumtions or slender beam in material mechanics, the error will increase raidly with the decreasing deth-san ratio [15]. In the current inorganic binder test regulation or lexural modulus, the san height ratio L/h used is, but it did not consider the shear eect on the beam delection, so the result is inconsistent with the actual situation [14]. Thereore, this aer deduces the lexural modulus calculation correction ormula considering the shear eect. (the lexural modulus mentioned later is the result considering the shear eect). P/2 P/2 P/2 P/2 Ø P/2 P/2 γ τ τ Figure 5: Force Analysis Diagram o Secimen Considering the Shear Eect As shown in Fig. 5, let the additional delection caused by the shear eect be ω. Then: L ω = γ (5) 4

6 Where, τ γ = is the shear strain; is the shear stress; τ = T G A is the shear orce; = P T is the sectional area; 2 E G = is the shear modulus; μ is Poisson s ratio. We substitute this into Formula (5) and obtain 2(1 + µ ) + µ ω = 2(1 ) PL. E bh The delection ω ' under the mutual action o moment and shear can be exressed as: ω' = ω+ ω. By substituting the above equations, we obtain: 2PL 2(1 + µ ) PL ω ' = + 108E bh E bh (6) Then the lexural modulus E ' considering the shear eect can be exressed as: E 2PL 2(1 + µ ) PL ' = bh ω ' bhω ' (7) I we comare the lexural modulus ormula (7) considering the shear eect and ormula (4) without considering the shear E 2 ' E 216(1 + µ ) h eect, the change ratio o the two is: =. As the required san height ratio L/h o the cement 2 E 69L stabilized macadam beam secimen is, we know that with the shear eect taken into account, the lexural modulus is increased by about 47% (Poisson s ratio μ is 0.25). Derivation o tensile modulus calculation ormula based on lexural test The tensile and comressive stress distribution o the mid-san section is shown in Fig. 6(b). x Ò P h h 1 h 2 dx x y E E t h 1 h 2 b Ò t (a) (b) Figure 6: Stress Distribution o Secimen Mid-San Section Let the micro-area unit arallel to the neutral axis (as shown in Fig. 6(a)) da = bdx. For the mid-san section, the bending moment M caused by the internal orce can be exressed as ollows: h1 σ 2 σ = + 0 t 2 M bx dx bx dx 0 h h2 h 1 2 (8) Where, M is the bending moment; σ is the comressive stress o the uer surace; σ t is the tensile stress o the lower surace; h 1 is the vertical distance between the uer surace o the secimen and the neutral axis moved u; h 2 is the vertical distance between the lower surace o the secimen and the neutral axis; other symbols have the same meanings as above. By integrating this ormula, we obtain: 1 2 t 2 2 M = σ bh / + σ bh / (9) 44

7 That is: 1 2 t t 2 2 M = E ε bh / + E ε bh / (10) The lane hyothesis: ε / h = ε / h (11) t 2 1 Where, ε is the comressive strain o the uer surace; ε t is the tensile strain o the lower surace; other symbols have the same meanings as above. Equilibrium condition: σ σ bxdx = bxdx σ = σ h h th h h h t (12) As the tensile modulus E = σ / ε and the comression modulus E = σ / ε, by combining Formula (10), (11) and (12), we obtain: t t t t t t E = M( ε + ε )/ bε h (1) t E = M( ε + ε )/ bε h (14) Where, E t is the tensile modulus; E is the comression modulus. Thereore, the tensile - comression modulus ratio is: Et E 1 ε h = = ε h t 2 (15) The mid-san bending moment o the secimen: M = PL /6 (16) By substituting Eq. (16) into Formula (1) and Formula (14), we obtain the tensile and comression modulus calculation ormulas as ollows: E t = L( ε + ε ) t t 2bh ε (17) E = L( ε + ε ) t 2bh ε (18) ANALYSIS ON TENSILE, COMPRESSION AND FLEXURAL MODULI TEST RESULTS Analysis on the change rules o the three moduli with the loading rate ccording to the deduced tensile, comressive and lexural modulus calculation ormulas, we use the trile mean variance to eliminate the abnormal test results and calculate the test mean value o 9 grous o secimens. The test results o the three moduli under dierent loading rates are shown in Tab. 2. A 45

8 Loading rate ν /(mm/min) Flexural modulus E /MPa tensile modulus Et/MPa comression modulus E/MPa Table 2: Tensile, Comression and Flexural Modulus Test Results under Dierent Loading Rates. According to the change rules o the three moduli with the loading rate, we use a ower unction (19) to it the data: b E= a v (19) The itting results are shown in Tab. and Fig. 7. Fitting arameters Correlation coeicient R 2 a b Flexural modulus tensile modulus comression modulus Table : Summary o Three Modulus Fitting Results under Dierent Loading Rates. Flexural ModulusE / /Ma Loading ratesv/(mm/min) (a) Flexural Modulus Tensile mmoduluse t /Ma Loading ratesv/(mm/min) (b) Tensile Modulus Comressive moduluse /Ma Loading ratesv/(mm/min) (c) Comression Modulus Figure 7: Change Rules o the Three Moduli with the Loading Rates. 46

9 From the above itting results, it can be seen that the tensile modulus, comression modulus and lexural modulus increase with the increase o the loading rate, showing a good ower unction relationshi. It has been roved in the existing research that when the loading rate increases, the stress state inside the secimen is not exactly one-dimensional stress state, but rather a mechanical resonse characteristic towards the one-dimensional strain state. In articular, in the middle art o the secimen, under a higher loading rate, due to the inertia o the material, the lateral strain o the secimen is restricted, and the higher the strain rate is, the more obvious the restriction will be, showing an obvious strain ratio eect, which causes the material modulus and strength to increase with the growth o loading rate [16]. The modulus and strength o ashalt mixture has a similar change attern [17-20]. In the same way, in this aer, the change rule that the modulus o the cement stabilized macadam material changes with the loading rate also roves this conclusion. Comarison and analysis o the three moduli According to the test results in Tab. 2, we get to know: (1) Under dierent loading rates, the ratio between the comression and tensile moduli is 1.71, 1.78, 1.81 and 1.80, with an average value o The cement stabilized macadam material shows signiicant dierences between the tensile and comression moduli, and the comression modulus is greater than the tensile modulus, it roved the dierences between the tensile and comressive modulus o cement stabilized macadam material. (2) The tensile modulus is resectively about.97,.77,.65 and.6 times the lexural modulus, with a mean value o.76; the comression modulus is about 6.81, 6.71, 6.6 and 6.54 times the lexural modulus, resectively, with a mean o In other words, the tensile and comression moduli are much greater than the lexural modulus. It can be seen that, regardless o the stress state inside the cement stabilized macadam semi-rigid base structure, it is obviously inaroriate to simly use the unconined comressive resilient modulus to calculate the structural load resonse. As the comressive resilient modulus is the largest among the three moduli, the structural deormation resonse calculated based on this modulus will be the smallest. As a result, the ashalt avement structure, which takes the surace delection as the indicator, will be thin and unsae, and the road avement is likely to be damaged at an early stage. () Under dierent loading rates, the ratios between each two o the tensile, comressive and lexural moduli, are stable, showing that even the loading rate has direct imact on the moduli o cement stabilized macadam material, but it does not aect the ratio relationshi between the three moduli[19]. This rovides basis and convenience or the conversion between the three moduli. Conversion relations between the three moduli With the loading rate as the intermediate variable, according to Formula (19) and the itting results in Tab., we can establish the conversion relations between the three moduli. (1) Conversion relation between the tensile modulus and the lexural modulus: 0.27 E = E (20) t (2) Conversion relation between the comression modulus and the lexural modulus: 0.7 E = 72.04E (21) () Conversion relation between the tensile modulus and the comression modulus: 0.9 E = E (22) t According to the conversion relations between the three moduli in Formula (20), (21) and (22), as long as we can get one modulus value, we can easily calculate the other two modulus, which acilitates the selection o modulus design arameters based on the stress state inside the avement structure. CONCLUSIONS (1) When the shear eect is considered, the lexural modulus o the beam secimen o cement stabilized macadam will be greatly increased. Thereore, when measuring the modulus o the indoor middle beam made o semi-rigid material, we should consider the shear eect. 47

10 (2) The tensile, comression and lexural moduli o the cement stabilized macadam increase with the increase o the loading rate, showing a ower unction growth attern. () The tensile and comression moduli o cement stabilized macadam are signiicantly dierent. I only the comression modulus is used as the structural design arameter o ashalt avement, there will be unbalance between the working state o the structural design arameter and the actual stress state, and urther resulting in large deviation in load resonse analysis and aecting the saety o the design results. In order to imrove the accuracy o the design calculation, we should select the corresonding design arameters according to the stress state o the oints inside the avement structure. (4) This aer reveals the dierences between the tensile, comression and lexural moduli o cement stabilized macadam and their conversion relations, but it does not consider the imacts o dierent mineral aggregate gradations, which, however, are rather signiicant on the moduli o cement stabilized macadam. In order to imrove the resistance o the semi-rigid base material against load damages, the gradation otimization will be one o the ocuses in our uture research. REFERENCES [1] Sha, Q.L., The Design and Construction o Long Lie Semi-Rigid Pavement or Heavy Traic with Heavy Wheel- Load, Beijing: China Communications Press, (2011). [2] Sha, A.M., Material Characteristics o Semi-Rigid Base, China Journal o Highway & Transort, 1 (2008) 21. [] Yao, Z.K., Ashalt Pavement Structure Design, Beijing: China Communications Press, (2011). [4] JTG D , Seciications or Design o Highway Ashalt Pavement [S]. [5] Wu, X., Zhao, H.J., Huang, Z.G., Yang, L.J., Thermal Bending and Buckling Calculations Bimodulous Plate, Journal o Chang an University (Natural Science Edition), 4(6) (2014) [6] Patel, B.P., Khan, K., Nath, Y.A., New Constitutive Model or Bimodular Laminated Structures: Alication to Free Vibrations o Conical/Cylindrical Panels, Comosite Structures, 110(1) (2014) [7] Luo, Z.Y., Xia, J.Z., Gong, X.N., Uniied Solution or Exansion o Cylindrical Cavity in Strain-Sotening Materials with Dierent Elastic Moduli in Tension and Comression, Engineering Mechanics, 25(9) (2008) [8] He, X.T., Chen, S.L., Elasticity Solution o Simle Beams with Dierent Modulus under Uniormly Distributed Load, Engineering Mechanics, 24(10) (2007) [9] Kong, J., Yuan J.Y., Pan, X.M., Elasto-Plastic Analysis o Thick Sheric Shell with Dierent Elastic Moduli or Tensile and Comressive Deormations, Mechanics in Engineering, 2 (1) (2010) [10] Wu, X.., Yang, L.L., Huang C., Sun. J., Large delection Bending Calculation and Analysis o Bimodulous Rectangular Plate, Engineering Mechanics, 27(1) (2010) [11] He, X.T., Chen, S.L., Sun, J.Y., Alying the equivalent Section Method to Solve Beam Subjected Lateral Force and Bending-Comression Column with Dierent Moduli, International Journal o Mechanical Sciences, 49 (2007) [12] Zhang, Q.S., Zheng, J.L., The Double Moduli Calculation Method o Rigid Pavements, Journal o Changsha Communications Institute, 8() (1992) [1] Liu, J.L., Ying, R.H., The Alication Research o Double Modulus Theory in Flexible Pavement Design, Hunan Communication Science and Technology, 1(27) (2001) [14] JTG E , Test Methods o Materials Stabilized with Inorganic Binders or Highway Engineering [S]. [15] Wang, Z.Z., Zhu J.Z., Chen, L., Guo, J.L., Tan, D.Y., Mi, W.J., The Stress Calculation Method or Dee Beams with the Shear-Bending Couling Distortion under Concentrated Load, Engineering Mechanics, 25(4) (2008) [16] Wang, D.R., Hu S.S., Inluence o Aggregate on the Comression Proerties o Concrete under Imact, Journal o Exerimental Mechanics, 17(1) (2002) [17] Zheng, J.L., New Structure Design o Durable Ashalt Pavement Based on Lie Increment, China Journal o Highway and Transort, 27(1) (2014) 1-7. [18] Zheng, J.L., Lv S.T., Nonlinear Fatigue Damage Model or Ashalt Mixtures, China Journal o Highway and Transort, 22(5) (2009) [19] Lv S.T., Fatigue Equation o Ashalt Mixture Considering the Inluence o Loading Rate, Engineering Mechanics, 29(8) (2012) [20] Mannan, U.A., Islam, M.R., Tareder, R.A., Eects o Recycled Ashalt Pavements on the Fatigue Lie o Ashalt under Dierent Strain Levels and Loading Frequencies, International Journal o Fatigue, 78 (2015)

11 NOMENCLATURE L Test beam san P Test load alied ω Mid-san delection o the secimen under ure bending h Mid-san sectional height o the secimen b Mid-san sectional width o the secimen E Resilient modulus o the secimen I Mid-san sectional inertia moment o the secimen E Flexural modulus without the shear eect taken into account ω Change in the mid-san delection o the secimen caused by the shear eect γ Shear strain τ Shear stress T Shear orce A Mid-san sectional area o the secimen G Shear modulus µ Poisson s ratio ω ' Mid-san delection o the secimen under the mutual action o moment and shear E Flexural modulus with the shear eect considered h Vertical distance rom the uer surace o the secimen to the neutral axis h 1 2 σ σ t ε ε t E E t M ν R 2 Vertical distance rom the lower surace o the secimen to the neutral axis Comressive stress o the uer surace o the secimen Tensile stress o the lower surace o the secimen Comressive strain o the uer surace o the secimen Tensile strain o the lower surace o the secimen Comression modulus Tensile modulus Mid-san bending moment o the secimen Loading rate Correlation coeicient 49