Search results for: modulus of subgrade reaction

Authors: M. Guler, E. Guler

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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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Authors: Reza Ziaie Moayed, Javad Shamsi Soosahab

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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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Authors: Muhammad Swilam

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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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Authors: E. Güler, M. Güler

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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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Authors: E. Güler, M. Güler

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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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Authors: Faramarz Ashenai Ghasemi, Ismail Ghasemi, Sajad Daneshpayeh

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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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Authors: Alireza Motamadnia, Roohollah Zohdi Oliayi, Hümeyra Bolakar, Ahmet Tortum

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Dynamic compression as a method of soil improvement in recent decades has been considered by engineers and experts. Three methods mainly, deep dynamic compaction, soil density, dynamic and rapid change have been proposed and implemented to improve subgrade conditions of highway road. Northern highway route in Tabriz (Pasdaran), Iran that was placed on the manual soil was the main concern. Engineering properties of soil have been investigated experimentally and theoretically. Among the three methods rapid dynamic compaction for highway has been suggested to improve the soil subgrade conditions.

Keywords: manual soil, subsidence, improvement, dynamic compression

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

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

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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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Authors: Jiri Brozovsky

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

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

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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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Authors: Jae Hong Kim, Sang Cheol Um, Jong Kook Lee

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Strong and biocompatible wollastonite (CaSiO3) was fabricated by pressureless sintering at temperature range of 1250~ 1300 ℃ and phase transition of to β-wollastonite with an addition of MgSiO3. Starting pure α-wollastonite powder were prepared by solid state reaction, and MgSiO3 powder was added to α-wollastonite powder to induce the phase transition α to β-wollastonite over 1250℃. Sintered wollastonite samples at 1250℃ with 5 and 10 wt% MgSiO3 were α+β phase and β phase respectively, and showed higher densification rate than that of α or β-wollastonite, which are almost the same as the theoretical density. Hardness and Young’s modulus of sintered wollastonite were dependent on the apparent density and the amount of β-wollastonite. Young’s modulus (78GPa) of β-wollastonite added 10 wt% MgSiO3 was almost double time of sintered α-wollastonite. From the in-vitro test, biphasic (α+β) wollastonite with 5wt% MgSiO3 addition had good bioactivity in simulated body fluid solution.

Keywords: β-wollastonite, high density, MgSiO3, phase transition

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Authors: Sirada Sripinun

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This work studied the isomerization of 1-butene over hydrotalcite catalyst. The experiments were conducted at various gas hourly space velocity (GHSV), reaction temperature, and feed concentration. No catalyst deactivation was observed over the reaction time of 16 hours. Two major reaction products were trans-2-butene and cis-2-butene. The reaction temperature played an important role on the reaction selectivity. At high operating temperatures, the selectivity of trans-2-butene was higher than the selectivity of cis-2-butene while it was opposite at a lower reaction temperature. In the range of operating conditions, the maximum conversion of 1-butene was found at 74% when T = 673 K and GHSV = 4 m3/h/kg-cat with trans- and cis-2-butene selectivities of 54% and 46% respectively. Finally, the kinetic parameters of the reaction were determined.

Keywords: hydrotalcite, isomerization, kinetic, 1-butene

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

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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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Authors: Ehsan Mehryaar, Reza Bushehri

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One of the principal parameters defining the clay soil dynamic response is the strain-shear modulus relation. Predicting the strain and, subsequently, shear modulus reduction of the soil is essential for performance analysis of structures exposed to earthquake and dynamic loadings. Many soil properties affect soil’s dynamic behavior. In order to capture those effects, in this study, a database containing 1193 data points consists of maximum shear modulus, strain, moisture content, initial void ratio, plastic limit, liquid limit, initial confining pressure resulting from dynamic laboratory testing of 21 clays is collected for predicting the shear modulus vs. strain curve of soil. A model based on an extreme gradient boosting technique is proposed. A tree-structured parzan estimator hyper-parameter tuning algorithm is utilized simultaneously to find the best hyper-parameters for the model. The performance of the model is compared to the existing empirical equations using the coefficient of correlation and root mean square error.

Keywords: XGBoost, hyper-parameter tuning, soil shear modulus, dynamic response

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Authors: A. Khodabakhshi, A. Mortazavi

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Accurate determination of rock mass deformation modulus, as an important design parameter, is one of the most controversial issues in most engineering projects. A 3D numerical model of standard plate load test (PLT) using the FLAC3D code was carried to investigate the mechanism governing the test process. Five objectives were the focus of this study. The first goal was to employ 3D modeling in the interpretation of PLT conducted at the Bazoft dam site, Iran. The second objective was to investigate the effect of displacements measuring depth from the loading plates on the calculated moduli. The magnitude of rock mass deformation modulus calculated from PLT depends on anchor depth, and in practice, this may be a cause of error in the selection of realistic deformation modulus for the rock mass. The third goal of the study was to investigate the effect of testing plate diameter on the calculated modulus. Moreover, a comparison of the calculated modulus from ISRM formula, numerical modeling and calculated modulus from the actual PLT carried out at right abutment of the Bazoft dam site was another objective of the study. Finally, the effect of plastic strains on the calculated moduli in each of the loading-unloading cycles for three loading plates was investigated. The geometry, material properties, and boundary conditions on the constructed 3D model were selected based on the in-situ conditions of PLT at Bazoft dam site. A good agreement was achieved between numerical model results and the field tests results.

Keywords: deformation modulus, numerical model, plate loading test, rock mass

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Authors: Natalie M. Wride, Xueyu Geng

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Subgrade soils of railway infrastructure are subjected to a significant number of load applications over their design life. The use of slab track on existing and future proposed rail links requires a reduced maintenance and repair regime for the embankment subgrade, due to restricted access to the subgrade soils for remediation caused by cyclic deformation. It is, therefore, important to study the deformation behaviour of soft cohesive subsoils induced as a result of long term cyclic loading. In this study, a series of oedometer tests and cyclic triaxial tests (10,000 cycles) have been undertaken to investigate the undrained deformation behaviour of soft kaolin. X-ray Computer Tomography (CT) scanning of the samples has been performed to determine the change in porosity and soil structure density from the sample microstructure as a result of the laboratory testing regime undertaken. Combined with the examination of excess pore pressures and strains obtained from the cyclic triaxial tests, the results are compared with an existing analytical solution for long term settlement considering repeated low amplitude loading. Modifications to the analytical solution are presented based on the laboratory analysis that shows good agreement with further test data.

Keywords: creep, cyclic loading, deformation, long term settlement, train loading

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Authors: Kumator Taku, Bilkisu Amartey

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This research used Grid indentation technique to investigate the effect of the addition of Coconut Shell Ash (CSA) on the nanomechanical properties of the main phases of the hydrated cement paste. Portland cement was partially replaced with 15% CSA at a water-binder ratio of 0.5 and cubes casted and cured for 28 days after which they were polished to reduce surface roughness to the barest minimum. The result of nanoindentation shows that addition of 15% CSA to cement paste transforms portlandite to C-S-H by the pozzolanic reaction. More so, there is reduced porosity and a reduction in the volume of CH by the addition of the CSA. Even though the addition of 15% CSA does not drastically change the average values of the hardness and elastic modulus of the two phases of the C-S-H, it greatly modifies their relative proportions, leading to the production of more HD C-S-H. Overall, incorporating 15%CSA to cement mortar improves the Nanomechanical properties of the four main phases of the hydrated cement paste.

Keywords: Coconut Shell Ash, Elastic Modulus, Hardness, Nanoindentation, Porosity

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Authors: Yang Zhong, Mei-Jie Xu

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To study the dynamic mechanics response of asphalt pavement under the temperature load and vehicle loading, asphalt pavement was regarded as multilayered elastic half-space system, and theory analysis was conducted by regarding dynamic modulus of asphalt mixture as the parameter. Firstly, based on the dynamic modulus test of asphalt mixture, function relationship between the dynamic modulus of representative asphalt mixture and temperature was obtained. In addition, the analytical solution for thermal stress in the single layer was derived by using Laplace integral transformation and Hankel integral transformation respectively by using thermal equations of equilibrium. The analytical solution of calculation model of thermal stress in asphalt pavement was derived by transfer matrix of thermal stress in multilayer elastic system. Finally, the variation of thermal stress in pavement structure was analyzed. The result shows that there is an obvious difference between the thermal stress based on dynamic modulus and the solution based on static modulus. Therefore, the dynamic change of parameter in asphalt mixture should be taken into consideration when the theoretical analysis is taken out.

Keywords: asphalt pavement, dynamic modulus, integral transformation, transfer matrix, thermal stress

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Authors: Rishikesh Yadav, Ramakanta Meher, Vishnu Narayan Mishra

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The main aim of this article is to investigate the statistical convergence of the summation of integral type operators and to obtain the weighted statistical convergence. The rate of statistical convergence by means of modulus of continuity and function belonging to the Lipschitz class are also studied. We discuss the convergence of the defined operators by graphical representation and put a better rate of convergence than the Szasz-Mirakjan-Kantorovich operators. In the last section, we extend said operators into bivariate operators to study about the rate of convergence in sense of modulus of continuity and by means of Lipschitz class by using function of two variables.

Keywords: The Szasz-Mirakjan-Kantorovich operators, statistical convergence, modulus of continuity, Peeters K-functional, weighted modulus of continuity

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Authors: Niaz Gharavi, Hexin Zhang

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The shear modulus of a timber beam can be determined using torsion test or shear field test method. The shear field test method is based on shear distortion measurement of the beam at the zone with the constant transverse load in the standardized four-point bending test. The current code of practice advises using two metallic arms act as an instrument to measure the diagonal displacement of the constructing square. The size and the position of the constructing square might influence the shear modulus determination. This study aimed to investigate the size and the position effect of the square in the shear field test method. A binocular stereo vision system has been employed to determine the 3D displacement of a grid of target points. Six glue laminated beams were produced and tested. Analysis of Variance (ANOVA) was performed on the acquired data to evaluate the significance of the size effect and the position effect of the square. The results have shown that the size of the square has a noticeable influence on the value of shear modulus, while, the position of the square within the area with the constant shear force does not affect the measured mean shear modulus.

Keywords: shear field test method, structural-sized test, shear modulus of Glulam beam, photogrammetry approach

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Authors: Adewoyin O. Olusegun, Akinwumi I. Isaac

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In some part of the world where legislations related to site investigations before constructions are not strictly enforced, the expenses and time required for carrying out a comprehensive geotechnical investigation to characterize a site can discourage prospective private residential building developers. Another factor that can discourage a developer is the fact that most of the geotechnical tests procedures utilized during site investigations, to a certain extent, alter the existing environment of the site. This study suggests a quick, non-destructive and non-intrusive method of obtaining key subsoil geotechnical properties necessary for foundation design for proposed engineering facilities. Seismic wave velocities generated from near surface refraction method was used to determine the bulk density of soil, Young’s modulus, bulk modulus, shear modulus and allowable bearing capacity of a competent layer that can bear structural load at the particular study site. Also, regression equations were developed in order to directly obtain the bulk density of soil, Young’s modulus, bulk modulus, shear modulus and allowable bearing capacity from the compressional wave velocities. The results obtained correlated with the results of standard geotechnical investigations carried out.

Keywords: characterize, environment, geophysical, geotechnical, regression

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Authors: A. Vinod Kumar, G. Sunny Deol, Rakesh Kumar, B. Chandra

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Application of fiber reinforcement in road construction is gaining some interest in enhancing soil strength. In this paper, the natural geotextile material obtained from gunny bags was used due to its vast local availability. Construction of flexible pavement on weaker soil such as clay soils is a significant problem in construction as well as in design due to its expansive characteristics. Jute geotextile (JGT) was used on a foundation layer of flexible pavement on rural roads. This problem will be conquered by increasing the subgrade strength by decreasing sub-base layer thickness by improving their overall pavement strength characteristics which ultimately reduces the cost of construction and leads to an economical design. California Bearing Ratio (CBR), unconfined compressive strength (UCS) and triaxial laboratory tests were conducted on two different soil samples, CI and MI. Weaker soil is reinforced with JGT, JGT+Bitumen. JGT+polythene sheet was varied with heights while performing the laboratory tests. Subgrade strength evaluation was investigated by conducting soak CBR test in the laboratory for clayey and silt soils. Laboratory results reveal that reinforced soak CBR value of clayey soil (CI) observed was 10.35%, and silty soil (MI) was 15.6%. This study intends to develop new technique for reinforcing weaker soil with JGT varying parameters for the need of low volume flexible pavements. It was observed that the performance of JGT is inferior when used with bitumen and polyethylene sheets.

Keywords: CBR, jute geotextile, low volume road, weaker soil

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Authors: A. Vinod Kumar, G. Sunny Deol, Rakesh Kumar, B. Chandra

Abstract:

Application of fiber reinforcement in road construction is gaining some interest in enhancing soil strength. In this paper, the natural Geotextile material obtained from gunny bags was used due to vast local availability material. Construction of flexible pavement on weaker soil such as clay soils are a significant problem in construction as well as in design due to its expansive characteristics. Jute Geotextile (JGT) was used on a foundation layer of flexible pavement on rural roads. This problem will be conquered by increasing the subgrade strength by decreasing sub-base layer thickness by improving their overall pavement strength characteristics which ultimately reduces the cost of construction and leads to economically design. The California Bearing Ratio (CBR), unconfined compressive strength (UCS) and triaxial laboratory tests were conducted on two different soil samples CI and MI. Weaker soil is reinforced with JGT, JGT+Bitumen; JGT+polythene sheet was varied with heights while performing the laboratory tests. Subgrade strength evaluation was investigated by conducting soak CBR test in the laboratory for clayey and silt soils. Laboratory results reveal that reinforced soak CBR value of clayey soil (CI) observed was 10.35%, and silty soil (MI) was 15.6%. This study intends to develop new technique for reinforcing weaker soil with JGT varying parameters for the need of low volume flexible pavements. It was observed that the performance of JGT is inferior when used with bitumen and polyethylene sheets.

Keywords: CBR, Jute geotextile, low volume road, weaker soil

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Authors: Magdi M. E. Zumrawi, Nehla Mansour

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This paper aims to assess the efficiency of using geogrid reinforcement for subgrade stabilization. The literature of applying geogrid reinforcement technique for pavements built on soft subgrades and the previous experiences were reviewed. Laboratory tests were conducted on soil reinforced with geogrids in one or several layers. The soil specimens were compacted in four layers with or without geogrid sheets. The California Bearing Ratio (CBR) test, in soaking condition, was performed on natural soil and soil-geogrid specimens. The test results revealed that the CBR value is much affected by the geogrid sheet location and the number of sheets used in the soil specimen. When a geogrid sheet was placed at the 1^st layer of the soil, there was an increment of 26% in the CBR value. Moreover, the CBR value was significantly increased by 62% when geogrid sheets were placed at all four layers. The high CBR value is attributed to interface friction and interlock involved in the geogrid/ soil interactions. It could be concluded that geogrid reinforcement is successful and more economical technique.

Keywords: geogrid, reinforcement, stabilization, subgrade

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Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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Authors: Yonosuke Murayama

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We have developed and studied a metastable beta Ti alloy, which shows super-elasticity and low Young’s modulus according to the phase stability of its beta phase. The super-elasticity and low Young’s modulus are required in a wide range of applications in various industrial fields. For example, the metallic implant with low Young’s modulus and non-toxicity is desirable because the large difference of Young’s modulus between the human bone and the implant material may cause a stress-shielding phenomenon. We have investigated the role of Sn and Al in metastable beta Ti-Cr-Sn, Ti-Cr-Al, Ti-V-Sn, and Ti-V-Al alloys. The metastable beta Ti-Cr-Sn, Ti-Cr-Al, Ti-V-Sn, and Ti-V-Al alloys form during quenching from the beta field at high temperature. While Cr and V act as beta stabilizers, Sn and Al are considered as elements to suppress the athermal omega phase produced during quenching. The athermal omega phase degrades the properties of super-elasticity and Young’s modulus. Although Al and Sn as single elements are considered as an alpha stabilizer and neutral, respectively, Sn and Al acted also as beta stabilizers when added simultaneously with beta stabilized element of Cr or V in this experiment. The quenched microstructure of Ti-Cr-Sn, Ti-Cr-Al, Ti-V-Sn, and Ti-V-Al alloys shifts from martensitic structure to beta single-phase structure with increasing Cr or V. The Young’s modulus of Ti-Cr-Sn, Ti-Cr-Al, Ti-V-Sn, and Ti-V-Al alloys decreased and then increased with increasing Cr or V, each showing its own minimum value of Young's modulus respectively. The composition of the alloy with the minimum Young’s modulus is a near border composition where the quenched microstructure shifts from martensite to beta. The border composition of Ti-Cr-Sn and Ti-V-Sn alloys required only less amount of each beta stabilizer, Cr or V, than Ti-Cr-Al and Ti-V-Al alloys. This indicates that the effect of Sn as a beta stabilizer is stronger than Al. Sn and Al influenced the competitive relation between stress-induced martensitic transformation and slip deformation. Thus, super-elastic properties of metastable beta Ti-Cr-Sn, Ti-Cr-Al, Ti-V-Sn, and Ti-V-Al alloys varied depending on the alloyed element, Sn or Al.

Keywords: metastable beta Ti alloy, super-elasticity, low Young’s modulus, stress-induced martensitic transformation, beta stabilized element

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Authors: Mark T. Hanson, Alan T. Varughese

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Osteoporosis is a disease affecting bone quality which in turn can increase the risk of low energy fractures. Treatment of osteoporosis using Bisphosphonates has the beneficial effect of increasing bone mass while at the same time has been linked to the formation of atypical femoral fractures. This has led to the increased study of micro-fractures in bones of patients using Bisphosphonate treatment. One of the mechanics related issues which have been identified in this regard is the loss in stiffness of bones containing one or many micro-fractures. Different theories have been put forth using fracture mechanics to determine the effect of crack presence on elastic properties such as modulus. However, validation of these results in a deterministic way has not been forthcoming. The present analysis seeks to provide this deterministic evaluation of fracture’s effect on the elastic modulus. In particular, the effect of crack size, crack orientation and crack number on elastic modulus is investigated. In particular, the Finite Element method is used to explicitly determine the elastic modulus reduction caused by the presence of cracks in a representative volume element. Single cracks of various lengths and orientations are examined as well as cases of multiple cracks. Cracks in tension as well as under shear stress are considered. Although the focus is predominantly two-dimensional, some three-dimensional results are also presented. The results obtained show the explicit reduction in modulus caused by the parameters of crack size, orientation and number noted above. The present results allow the interpretation of the various theories which currently exist in the literature.

Keywords: cracks, elastic, fracture, modulus

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Authors: Abdul Halim Abdul, Wan Ismail Wan Yusoff

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The geological formation at Limau Manis Besar area, are consist of low grade metamorphic rock and undulating mountaineers, rugged terrain and the quite steeply 45 degree slope gradient. The objectives of this paper are present the methods and devices used in measurement of P-wave velocity to estimate the initial Shear Modulus (Go) in steady state and critical state soil consolidation. The relationship between SPT-N values and the Shear Modulus (Go) at very small strain is widely considered to be evaluated. Based on the seismic reflection survey, the constant (K) poroelastic theory, mean effectives stress and primer wave velocity (Vs) increase as the soil depth increase. The steady state and critical state, Degree of Soil Consolidation(U) concept is used to interpret the behavior of Shear Modulus (Go). The relationship between Consolidation Test and Seismic Reflection Survey is also discussed.

Keywords: geological setting, shear modulus, poroelastic theory, steady state and none steady state degree of soil consolidation, consolidation test

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