Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4459

Search results for: complex modulus

4459 Study on the Application of Lime to Improve the Rheological Properties of Polymer Modified Bitumen

Authors: A. Chegenizadeh, M. Keramatikerman, H. Nikraz


Bitumen is one of the most applicable materials in pavement engineering. It is a binding material with unique viscoelastic properties, especially when it mixes with polymer. In this study, to figure out the viscoelastic behaviour of the polymer modified with bitumen (PMB), a series of dynamic shearing rheological (DSR) tests were conducted. Four percentages of lime (i.e. 1%, 2%, 4% and 5%) were mixed with PMB and tested under four different temperatures including 64ºC, 70ºC, 76ºC and 82ºC. The results indicated that complex shearing modulus (G*) increased by increasing the frequency due to raised resistance against deformation. The phase angle (δ) showed a decreasing trend by incrementing the frequency. The addition of lime percentages increased the complex modulus value and declined phase angle parameter. Increasing the temperature decreased the complex modulus and increased the phase angle until 70ºC. The decreasing trend of rutting factor with increasing temperature revealed that rutting factor improved by the addition of the lime to the PMB.

Keywords: rheological properties, DSR test, polymer mixed with bitumen (PMB), complex modulus, lime

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4458 Numerical Study on Ultimate Capacity of Bi-Modulus Beam-Column

Authors: Zhiming Ye, Dejiang Wang, Huiling Zhao


Development of the technology demands a higher-level research on the mechanical behavior of materials. Structural members made of bi-modulus materials have different elastic modulus when they are under tension and compression. The stress and strain states of the point effect on the elastic modulus and Poisson ratio of every point in the bi-modulus material body. Accompanied by the uncertainty and nonlinearity of the elastic constitutive relation is the complicated nonlinear problem of the bi-modulus members. In this paper, the small displacement and large displacement finite element method for the bi-modulus members have been proposed. Displacement nonlinearity is considered in the elastic constitutive equation. Mechanical behavior of slender bi-modulus beam-column under different boundary conditions and loading patterns has been simulated by the proposed method. The influence factors on the ultimate bearing capacity of slender beam and columns have been studied. The results show that as the ratio of tensile modulus to compressive modulus increases, the error of the simulation employing the same elastic modulus theory exceeds the engineering permissible error.

Keywords: bi-modulus, ultimate capacity, beam-column, nonlinearity

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4457 On Definition of Modulus of Deformation of Ground by Laboratory Method

Authors: Olgha Giorgishvili


The work is mainly concerned with the determination of modulus of deformation by laboratory method. It is known that a modulus of deformation is defining by laboratory and field methods. By laboratory method the modulus of deformation is defined in the compressive devices. Our goal is to conduct experiments by both methods and finally make to interpret the obtained results. In this article is considered the definition by new offered laboratory method of deformation modulus that is closer to the real deformation modulus. Finally, the obtained results gives the possibility to us to raise the issue of change the state norms for determining ground by laboratory method.

Keywords: building, soil mechanic, deformation moulus, compression methods

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4456 An Atomic Finite Element Model for Mechanical Properties of Graphene Sheets

Authors: Win-Jin Chang, Haw-Long Lee, Yu-Ching Yang


In this study, we use the atomic-scale finite element method to investigate the mechanical behavior of the armchair- and zigzag-structured nanoporous graphene sheets with the clamped-free-free-free boundary condition under tension and shear loadings. The effect of porosity on Young’s modulus and shear modulus of nanoporous graphene sheets is obvious. For the armchair- and zigzag-structured nanoporous graphene sheets, Young’s modulus and shear modulus decreases with increasing porosity. Young’s modulus and shear modulus of zigzag graphene are larger than that of armchair one for the same porosity. The results are useful for application in the design of nanoporous graphene sheets.

Keywords: graphene, nanoporous, Young's modulus, shear modulus

Procedia PDF Downloads 307
4455 Evaluation of Static Modulus of Elasticity Depending on Concrete Compressive Strength

Authors: Klara Krizova, Rudolf Hela


The paper is focused on monitoring of dependencies of different composition concretes on elastic modulus values. To obtain a summary of elastic modulus development independence of concrete composition design variability was the objective of the experiment. Essential part of this work was initiated as a reaction to building practice when questions of elastic moduli arose at the same time and which mostly did not obtain the required and expected values from concrete constructions. With growing interest in this theme the elastic modulus questions have been developing further.

Keywords: concrete, compressive strength, modulus of elasticity, EuroCode 2

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4454 Experimental Research on the Elastic Modulus of Bones at the Lamellar Level under Fatigue Loading

Authors: Xianjia Meng, Chuanyong Qu


Compact bone produces fatigue damage under the inevitable physiological load. The accumulation of fatigue damage can change the bone’s micro-structure at different scales and cause the catastrophic failure eventually. However, most tests were limited to the macroscopic modulus of bone and there is a need to assess the microscopic modulus during fatigue progress. In this paper, nano-identation was used to investigate the bone specimen subjected to four point bending. The microscopic modulus of the same area were measured at different degrees of damage including fracture. So microscopic damage can be divided into three stages: first, the modulus decreased rapidly and then They fell slowly, before fracture the decline became fast again. After fracture, the average modulus decreased by 20%. The results of inner and outer planes explained the influence of compressive and tensile loads on modulus. Both the compressive and tensile moduli decreased with the accumulation of damage. They reached the minimum at ending and increased after fracture. The modulus evolution under different strains were revealed by the side. They all fell slowly and then fast with the accumulation of damage. The fractured results indicated that the elastic modulus decreased obviously at the high strain while decreased less at the low strain. During the fatigue progress, there was a significant difference in modulus at low degree of damage. However, the dispersed modulus tended to be similar at high degree of damage, but they became different again after the failure.

Keywords: fatigue damage, fracture, microscopic modulus, bone, nano-identation

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4453 Selected Technological Factors Influencing the Modulus of Elasticity of Concrete

Authors: Klara Krizova, Rudolf Hela


The topic of the article focuses on the evaluation of selected technological factors and their influence on resulting elasticity modulus of concrete. A series of various factors enter into the manufacturing process which, more or less, influences the elasticity modulus. This paper presents the results of concrete in which the influence of water coefficient and the size of maximum fraction of the aggregate on the static elasticity modulus were monitored. Part of selected results of the long-term programme was discussed in which a wide scope of various variants of proposals for the composition of concretes was evaluated.

Keywords: mix design, water-cement ratio, aggregate, modulus of elasticity

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4452 Assessment of Analytical Equations for the Derivation of Young’s Modulus of Bonded Rubber Materials

Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell


The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: bonded rubber, quasi-static test, shape factor, apparent Young’s modulus

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4451 Ground Deformation Module for the New Laboratory Methods

Authors: O. Giorgishvili


For calculation of foundations one of the important characteristics is the module of deformation (E0). As we all know, the main goal of calculation of the foundations of buildings on deformation is to arrange the base settling and difference in settlings in such limits that do not cause origination of cracks and changes in design levels that will be dangerous to standard operation in the buildings and their individual structures. As is known from the literature and the practical application, the modulus of deformation is determined by two basic methods: laboratory method, soil test on compression (without the side widening) and soil test in field conditions. As we know, the deformation modulus of soil determined by field method is closer to the actual modulus deformation of soil, but the complexity of the tests to be carried out and the financial concerns did not allow determination of ground deformation modulus by field method. Therefore, we determine the ground modulus of deformation by compression method without side widening. Concerning this, we introduce a new way for determination of ground modulus of deformation by laboratory order that occurs by side widening and more accurately reflects the ground modulus of deformation and more accurately reflects the actual modulus of deformation and closer to the modulus of deformation determined by the field method. In this regard, we bring a new approach on the ground deformation detection laboratory module, which is done by widening sides. The tests and the results showed that the proposed method of ground deformation modulus is closer to the results that are obtained in the field, which reflects the foundation's work in real terms more accurately than the compression of the ground deformation module.

Keywords: build, deformation modulus, foundations, ground, laboratory research

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4450 Impact of the Quality of Aggregate on the Elasticity Modulus of Concrete

Authors: K. Krizova


This objective of this article is to present concrete that differs by the size of the aggregate used. The set of concrete contained six concrete recipes manufactured as traditional vibrated concrete containing identical basic components of concrete. The experiment focused on monitoring the resulting properties of hardened concrete, specifically the primary strength and modulus of the concrete elasticity and the developing parameters from 7 to 180 days were assessed.

Keywords: aggregate, cement, concrete, elasticity modulus

Procedia PDF Downloads 190
4449 First-Principles Calculations and Thermo-Calc Study of the Elastic and Thermodynamic Properties of Ti-Nb-ZR-Ta Alloy for Biomedical Applications

Authors: M. Madigoe, R. Modiba


High alloyed beta (β) phase-stabilized titanium alloys are known to have a low elastic modulus comparable to that of the human bone (≈30 GPa). The β phase in titanium alloys exhibits an elastic Young’s modulus of about 60-80 GPa, which is nearly half that of α-phase (100-120 GPa). In this work, a theoretical investigation of structural stability and thermodynamic stability, as well as the elastic properties of a quaternary Ti-Nb-Ta-Zr alloy, will be presented with an attempt to lower Young’s modulus. The structural stability and elastic properties of the alloy were evaluated using the first-principles approach within the density functional theory (DFT) framework implemented in the CASTEP code. The elastic properties include bulk modulus B, elastic Young’s modulus E, shear modulus cʹ and Poisson’s ratio v. Thermodynamic stability, as well as the fraction of β phase in the alloy, was evaluated using the Thermo-Calc software package. Thermodynamic properties such as Gibbs free energy (Δ?⁰?) and enthalpy of formation will be presented in addition to phase proportion diagrams. The stoichiometric compositions of the alloy is Ti-Nbx-Ta5-Zr5 (x = 5, 10, 20, 30, 40 at.%). An optimum alloy composition must satisfy the Born stability criteria and also possess low elastic Young’s modulus. In addition, the alloy must be thermodynamically stable, i.e., Δ?⁰? < 0.

Keywords: elastic modulus, phase proportion diagram, thermo-calc, titanium alloys

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4448 Preparation of Carbon Nanofiber Reinforced HDPE Using Dialkylimidazolium as a Dispersing Agent: Effect on Thermal and Rheological Properties

Authors: J. Samuel, S. Al-Enezi, A. Al-Banna


High-density polyethylene reinforced with carbon nanofibers (HDPE/CNF) have been prepared via melt processing using dialkylimidazolium tetrafluoroborate (ionic liquid) as a dispersion agent. The prepared samples were characterized by thermogravimetric (TGA) and differential scanning calorimetric (DSC) analyses. The samples blended with imidazolium ionic liquid exhibit higher thermal stability. DSC analysis showed clear miscibility of ionic liquid in the HDPE matrix and showed single endothermic peak. The melt rheological analysis of HDPE/CNF composites was performed using an oscillatory rheometer. The influence of CNF and ionic liquid concentration (ranging from 0, 0.5, and 1 wt%) on the viscoelastic parameters was investigated at 200 °C with an angular frequency range of 0.1 to 100 rad/s. The rheological analysis shows the shear-thinning behavior for the composites. An improvement in the viscoelastic properties was observed as the nanofiber concentration increases. The progress in the modulus values was attributed to the structural rigidity imparted by the high aspect ratio CNF. The modulus values and complex viscosity of the composites increased significantly at low frequencies. Composites blended with ionic liquid exhibit slightly lower values of complex viscosity and modulus over the corresponding HDPE/CNF compositions. Therefore, reduction in melt viscosity is an additional benefit for polymer composite processing as a result of wetting effect by polymer-ionic liquid combinations.

Keywords: high-density polyethylene, carbon nanofibers, ionic liquid, complex viscosity

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4447 Climate Change Effect on the Dynamic Modulus Property of Asphalt Concrete in Southern England Using UKCP09

Authors: David Idiata


This paper is directed at using the UKCP09 climate change projection tool to predict the effect of climate change on the dynamic modulus of asphalt concrete is Southern England knowing that there is a pressing challenge directly facing infrastructure in the urban cities in the world today due to climate change. Climate change causes change in the environment which in turn impacts on the long-term structural performance of structures. From the projection values obtained, it was discovered that as the temperature increases, the dynamic modulus reduces and this effect was more on the South West which have temperature range of 36.8 oC to 48.3 oC and dynamic modulus range of 2,212 MPa to 1256 MPa.

Keywords: dynamic modulus, asphalt concrete, UKCP09, Southern England

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4446 Comparison for Some Elastic and Mechanical Properties of Plutonium Dioxide

Authors: M. Guler, E. Guler


We report some elastic parameters of cubic fluorite type neptunium dioxide (NpO2) with a recent EAM type interatomic potential through geometry optimization calculations. Typical cubic elastic constants, bulk modulus, shear modulus, young modulus and other relevant elastic parameters were also calculated during research. After calculations, we have compared our results with the available theoretical data. Our results agree well with the previous theoretical findings of the considered quantities of NpO2.

Keywords: NpO2, elastic properties, bulk modulus, mechanical properties

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4445 Effect of Elastic Modulus Anisotropy on Helical Piles Behavior in Sandy Soil

Authors: Reza Ziaie Moayed, Javad Shamsi Soosahab


Helical piles are being used extensively in engineering applications all over the world. There are insufficient studies on the helical piles' behavior in anisotropic soils. In this paper, numerical modeling was adopted to investigate the effect of elastic modulus anisotropy on helical pile behavior resting on anisotropic sand by using a finite element limit analysis. The load-displacement behavior of helical piles under compression and tension loads is investigated in different relative densities of soils, and the effect of the ratio of horizontal elastic modulus with respect to vertical elastic modulus (EH/EV) is evaluated. The obtained results illustrate that in sandy soils, the anisotropic ratio of elastic modulus (EH/EV) has notable effect on bearing capacity of helical piles in different relative density. Therefore, it may be recommended that the effect of anisotropic condition of soil elastic modulus should be considered in helical piles behavior.

Keywords: helical piles, bearing capacity, numerical modeling, soil anisotropy

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4444 Extended Multi-Modulus Divider for Open Loop Fractional Dividers and Fractional Multiplying Delay Locked Loops

Authors: Muhammad Swilam


Solutions for the wrong division problem of the Extended Multi-Modulus Divider (EMMD) that occurs during modulus extension (i.e. switching the modulus value between two different ranges of division ratios), in open loop fractional dividers and fractional multiplying delay locked loop, is proposed. A detailed study for the MMD with Sigma-Delta is also presented. Moreover, extensive simulations for the divider are presented to ensure and verify its functionality and compared with the conventional dividers.

Keywords: extended multi-modulus divider (EMMD), fractional multiplying delay locked loop, open loop fractional divider, sigma delta modulator

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4443 A Benchmark for Some Elastic and Mechanical Properties of Uranium Dioxide

Authors: E. Güler, M. Güler


We present some elastic parameters of cubic fluorite type uranium dioxide (UO2) with a recent EAM type interatomic potential through geometry optimization calculations. Typical cubic elastic constants, bulk modulus, shear modulus, young modulus and other related elastic parameters were calculated during research. After calculations, we compared our results not only with the available theoretical data but also with previous experimental results. Our results are consistent with experiments and compare well the former theoretical results of the considered parameters of UO2.

Keywords: UO2, elastic constants, bulk modulus, mechanical properties

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4442 A Comparison for Some Elastic and Mechanical Properties of Neptunium Dioxide

Authors: E. Güler, M. Güler


We report some elastic quantities of cubic fluorite type plutonium dioxide (PuO2) with a recent EAM type interatomic potential through geometry optimization calculations. Typical cubic elastic constants, bulk modulus, shear modulus, young modulus and other related elastic quantities were calculated during present research. After present calculations, we have compared our results with the existing theoretical data of literature. Our results are consistent with previous theoretical findings of the considered parameters of PuO2.

Keywords: PuO2, elastic properties, bulk modulus, mechanical properties

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4441 Tensile strength and Elastic Modulus of Nanocomposites Based on Polypropylene/Linear Low Density Polyethylene/Titanium Dioxide Nanoparticles

Authors: Faramarz Ashenai Ghasemi, Ismail Ghasemi, Sajad Daneshpayeh


In this study, tensile strength and elastic modulus of nanocomposites based on polypropylene/ linear low density polyethylene/ nano titanium dioxide (PP/LLDPE/TiO2) were studied. The samples were produced using a co-rotating twin screw extruder including 0, 2, 4 Wt .% of nano particles, and 20, 40, 60 Wt.% of LLDPE. The styrene-ethylene-butylene-styrene (SEBS) was used as comptabiliser. Tensile strength and elastic modulus were evaluated. The results showed that modulus was increased by 7% with addition of nano particles in comparison to PP/LLDPE. In addition, tensile strength was decreased.

Keywords: PP/LLDPE/TiO2, nanocomposites, elastic modulus, tensile strength

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4440 Estimation of Subgrade Resilient Modulus from Soil Index Properties

Authors: Magdi M. E. Zumrawi, Mohamed Awad


Determination of Resilient Modulus (MR) is quite important for characterizing materials in pavement design and evaluation. The main focus of this study is to develop a correlation that predict the resilient modulus of subgrade soils from simple and easy measured soil index properties. To achieve this objective, three subgrade soils representing typical Khartoum soils were selected and tested in the laboratory for measuring resilient modulus. Other basic laboratory tests were conducted on the soils to determine their physical properties. Several soil samples were prepared and compacted at different moisture contents and dry densities and then tested using resilient modulus testing machine. Based on experimental results, linear relationship of MR with the consistency factor ‘Fc’ which is a combination of dry density, void ratio and consistency index had been developed. The results revealed that very good linear relationship found between the MR and the consistency factor with a coefficient of linearity (R2) more than 0.9. The consistency factor could be used for the prediction of the MR of compacted subgrade soils with precise and reliable results.

Keywords: Consistency factor, resilient modulus, subgrade soil, properties

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4439 Experimental Investigations on Nanoclay (Cloisite-15A) Modified Bitumen

Authors: Ashish Kumar, Sanjeev Kumar Suman


This study investigated the influence of Cloisite-15A nanoclay on the physical, performance, and mechanical properties of bitumen binder. Cloisite-15A was blended in the bitumen in variegated percentages from 1% to 9% with increment of 2%. The blended bitumen was characterized using penetration, softening point, and dynamic viscosity using rotational viscometer, and compared with unmodified bitumen equally penetration grade 60/70. The rheological parameters were investigated using Dynamic Shear Rheometer (DSR), and mechanical properties were investigated by using Marshall Stability test. The results indicated an increase in softening point, dynamic viscosity and decrease in binder penetration. Rheological properties of bitumen increase complex modulus, decrease phase angle and improve rutting resistances as well. There was significant improvement in Marshall Stability, rather marginal improvement in flow value. The best improvement in the modified binder was obtained with 5% Cloisite-15A nanoclay.

Keywords: Cloisite-15A, complex shear modulus, phase angle, rutting resistance

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4438 Determination of Small Shear Modulus of Clayey Sand Using Bender Element Test

Authors: R. Sadeghzadegan, S. A. Naeini, A. Mirzaii


In this article, the results of a series of carefully conducted laboratory test program were represented to determine the small strain shear modulus of sand mixed with a range of kaolinite including zero to 30%. This was experimentally achieved using a triaxial cell equipped with bender element. Results indicate that small shear modulus tends to increase, while clay content decreases and effective confining pressure increases. The exponent of stress in the power model regression analysis was not sensitive to the amount of clay content for all sand clay mixtures, while coefficient A was directly affected by change in clay content.

Keywords: small shear modulus, bender element test, plastic fines, sand

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4437 Estimation of Elastic Modulus of Soil Surrounding Buried Pipeline Using Multi-Response Surface Methodology

Authors: Won Mog Choi, Seong Kyeong Hong, Seok Young Jeong


The stress on the buried pipeline under pavement is significantly affected by vehicle loads and elastic modulus of the soil surrounding the pipeline. The correct elastic modulus of soil has to be applied to the finite element model to investigate the effect of the vehicle loads on the buried pipeline using finite element analysis. The purpose of this study is to establish the approach to calculating the correct elastic modulus of soil using the optimization process. The optimal elastic modulus of soil, which minimizes the difference between the strain measured from vehicle driving test at the velocity of 35km/h and the strain calculated from finite element analyses, was calculated through the optimization process using multi-response surface methodology. Three elastic moduli of soil (road layer, original soil, dense sand) surrounding the pipeline were defined as the variables for the optimization. Further analyses with the optimal elastic modulus at the velocities of 4.27km/h, 15.47km/h, 24.18km/h were performed and compared to the test results to verify the applicability of multi-response surface methodology. The results indicated that the strain of the buried pipeline was mostly affected by the elastic modulus of original soil, followed by the dense sand and the load layer, as well as the results of further analyses with optimal elastic modulus of soil show good agreement with the test.

Keywords: pipeline, optimization, elastic modulus of soil, response surface methodology

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4436 Stress Variation around a Circular Hole in Functionally Graded Plate under Bending

Authors: Parveen K. Saini, Mayank Kushwaha


The influence of material property variation on stress concentration factor (SCF) due to the presence of a circular hole in a functionally graded material (FGM) plate is studied in this paper. A numerical method based on complex variable theory of elasticity is used to investigate the problem. To achieve the material property, variation plate is decomposed into a number of rings. In this research work, Young's modulus is assumed to be varying exponentially and it is found that stress concentration factor can be reduced by increasing Young’s modulus progressively away from the hole.

Keywords: stress concentration, circular hole, FGM plate, bending

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4435 Study of Interaction between Recycled Asphalt Pavement (RAP) Material and Virgin Material

Authors: G. Bharath, K. S. Reddy, Vivek Tandon, M. Amaranatha Reddy


This paper presents the details of a study conducted to evaluate the interaction between recycled binder and fresh binder in Recycled Asphalt Pavement (RAP) mixes. When RAP is mixed with virgin aggregates in the presence of fresh binder there will be partial blending in a hot mix asphalt mixture. A recent approach used by some researchers for studying the degree of blending of RAP binder with virgin binder has been adopted in this study. Dense Bituminous Macadam mix of Ministry of Road Transport of India with a nominal maximum aggregate size of 19 mm was studied. Two proportions of RAP-20% and 35% and two types of virgin binders – viscosity grade VG10 and VG30 were considered. Design binder contents were determined for all the four types of mixes (two RAP contents and two virgin binders) as per Marshall mix design procedure. The degree of blending of RAP and virgin binders was evaluated in terms of the complex modulus of the binder. Laboratory test results showed that with an increase in RAP content, the degree of blending decreases. Better blending was observed for softer grade binder (VG10).

Keywords: blending, complex modulus, recycled asphalt pavement, virgin binder

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4434 Calcium Silicate Bricks – Ultrasonic Pulse Method: Effects of Natural Frequency of Transducers on Measurement Results

Authors: Jiri Brozovsky


Modulus of elasticity is one of the important parameters of construction materials, which considerably influence their deformation properties and which can also be determined by means of non-destructive test methods like ultrasonic pulse method. However, measurement results of ultrasonic pulse methods are influenced by various factors, one of which is the natural frequency of the transducers. The paper states knowledge about influence of natural frequency of the transducers (54; 82 and 150kHz) on ultrasonic pulse velocity and dynamic modulus of elasticity (Young's Dynamic modulus of elasticity). Differences between ultrasonic pulse velocity and dynamic modulus of elasticity were found with the same smallest dimension of test specimen in the direction of sounding and density their value decreases as the natural frequency of transducers grew.

Keywords: calcium silicate brick, ultrasonic pulse method, ultrasonic pulse velocity, dynamic modulus of elasticity

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4433 Formulating the Stochastic Finite Elements for Free Vibration Analysis of Plates with Variable Elastic Modulus

Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara


In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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4432 The Elastic Field of a Nano-Pore, and the Effective Modulus of Composites with Nano-Pores

Authors: Xin Chen, Moxiao Li, Xuechao Sun, Fei Ti, Shaobao Liu, Feng Xu, Tian Jian Lu


The composite materials with pores have the characteristics of light weight, sound insulation, and heat insulation, and have broad prospects in many fields, including aerospace. In general, the stiffness of such composite is less than the stiffness of the matrix material, limiting their applications. In this paper, we establish a theoretical model to analyze the deformation mechanism of a nano-pore. The interface between the pores and matrix material is described by the Gurtin-Murdoch model. By considering scale effect related with current deformation, we estimate the effective mechanical properties (e.g., effective shear modulus and bulk modulus) of a composite with nano-pores. Due to the scale effect, the elastic field in the composite was changed and local hardening was observed around the nano-pore, and the effective shear modulus and effective bulk modulus were found to be a function of the surface energy. The effective shear modulus increase with the surface energy and decrease with the size of the nano-pores, and the effective bulk modulus decrease with the surface energy and increase with the size of the nano-pores. These results have potential applications in the nanocomposite mechanics and aerospace field.

Keywords: composite mechanics, nano-inhomogeneity, nano-pores, scale effect

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4431 Temperature Susceptibility of Multigrade Bitumen Asphalt and an Approach to Account for Temperature Variation through Deep Pavements

Authors: Brody R. Clark, Chaminda Gallage, John Yeaman


Multigrade bitumen asphalt is a quality asphalt product that is not utilised in many places globally. Multigrade bitumen is believed to be less sensitive to temperature, which gives it an advantage over conventional binders. Previous testing has shown that asphalt temperature changes greatly with depth, but currently the industry standard is to nominate a single temperature for design. For detailed design of asphalt roads, perhaps asphalt layers should be divided into nominal layer depths and different modulus and fatigue equations/values should be used to reflect the temperatures of each respective layer. A collaboration of previous laboratory testing conducted on multigrade bitumen asphalt beams under a range of temperatures and loading conditions was analysed. The samples tested included 0% or 15% recycled asphalt pavement (RAP) to determine what impact the recycled material has on the fatigue life and stiffness of the pavement. This paper investigated the temperature susceptibility of multigrade bitumen asphalt pavements compared to conventional binders by combining previous testing that included conducting a sweep of fatigue tests, developing complex modulus master curves for each mix and a study on how pavement temperature changes through pavement depth. This investigation found that the final design of the pavement is greatly affected by the nominated pavement temperature and respective material properties. This paper has outlined a potential revision to the current design approach for asphalt pavements and proposes that further investigation is needed into pavement temperature and its incorporation into design.

Keywords: asphalt, complex modulus, fatigue life, flexural stiffness, four point bending, multigrade bitumen, recycled asphalt pavement

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4430 Young’s Modulus Variability: Influence on Masonry Vault Behavior

Authors: Abdelmounaim Zanaz, Sylvie Yotte, Fazia Fouchal, Alaa Chateauneuf


This paper presents a methodology for probabilistic assessment of bearing capacity and prediction of failure mechanism of masonry vaults at the ultimate state with consideration of the natural variability of Young’s modulus of stones. First, the computation model is explained. The failure mode is the most reported mode, i.e. the four-hinge mechanism. Based on this assumption, the study of a vault composed of 16 segments is presented. The Young’s modulus of the segments is considered as random variable defined by a mean value and a coefficient of variation CV. A relationship linking the vault bearing capacity to the modulus variation of voussoirs is proposed. The failure mechanisms, in addition to that observed in the deterministic case, are identified for each CV value as well as their probability of occurrence. The results show that the mechanism observed in the deterministic case has decreasing probability of occurrence in terms of CV, while the number of other mechanisms and their probability of occurrence increase with the coefficient of variation of Young’s modulus. This means that if a significant change in the Young modulus of the segments is proven, taken it into account in computations becomes mandatory, both for determining the vault bearing capacity and for predicting its failure mechanism.

Keywords: masonry, mechanism, probability, variability, vault

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