Search results for: concrete nonlinear model.

Authors: M. Nassereddine, J. Rizk, A. Hellany, M. Nagrial

Abstract:

The prologue of new High Voltage (HV) transmission mains into the community necessitates earthing design to ensure safety compliance of the system. Concrete poles are widely used within HV transmission mains; many retired transmission mains with timber poles are being replaced with concrete ones, green transmission mains are deploying concrete poles. The earthing arrangement of the concrete poles could have an impact on the earth grid impedance also on the input impedance of the system from the fault point of view. This paper endeavors to provide information on the soil resistivity of the area and the deployments of concrete poles. It introduce the cut off soil resistivity value ρ_SC, this value aid in determine the impact of deploying the concrete poles on the earthing system. Multiple cases were discussed in this paper.

Keywords: Soil Resistivity, HV Transmission Mains, Earthing, Safety.

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Authors: Zhifeng Xu, Zhongfan Chen

Abstract:

A series of tests on cold-formed steel foamed concrete (CSFC) composite walls subjected to axial load were proposed. The primary purpose of the experiments was to study the mechanical behavior and identify the failure modes of CSFC composite walls. Two main factors were considered in this study: 1) specimen with pouring foamed concrete or without and 2) different foamed concrete density ranks (corresponding to different foamed concrete strength). The interior space between two pieces of straw board of the specimen W-2 and W-3 were poured foamed concrete, and the specimen W-1 does not have foamed concrete core. The foamed concrete density rank of the specimen W-2 was A05 grade, and that of the specimen W-3 was A07 grade. Results showed that the failure mode of CSFC composite wall without foamed concrete was distortional buckling of cold-formed steel (CFS) column, and that poured foamed concrete includes the local crushing of foamed concrete and local buckling of CFS column, but the former prior to the later. Compared with CSFC composite wall without foamed concrete, the ultimate bearing capacity of spec imens poured A05 grade and A07 grade foamed concrete increased 1.6 times and 2.2 times respectively, and specimen poured foamed concrete had a low vertical deformation. According to these results, the simplified calculation formula for the CSFC wall subjected to axial load was proposed, and the calculated results from this formula are in very good agreement with the test results.

Keywords: Cold-formed steel, composite wall, foamed concrete, axial behavior test.

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Authors: Swarniv Chandra, Basudev Ghosh

Abstract:

Using the quantum hydrodynamic (QHD) model for quantum plasma at finite temperature the modulational instability of electron plasma waves is investigated by deriving a nonlinear Schrodinger equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of electron plasma waves in quantum plasma.

Keywords: Amplitude Modulation, Electron Plasma Waves, Finite Temperature Model, Modulational Instability, Quantum Plasma.

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Authors: Qiaozhen Song

Abstract:

Based on the feature of model disturbances and uncertainty being compensated dynamically in auto – disturbances-rejection-controller (ADRC), a new method using ADRC is proposed for the decoupling control of dispenser longitudinal movement in big flight envelope. Developed from nonlinear model directly, ADRC is especially suitable for dynamic model that has big disturbances. Furthermore, without changing the structure and parameters of the controller in big flight envelope, this scheme can simplify the design of flight control system. The simulation results in big flight envelope show that the system achieves high dynamic performance, steady state performance and the controller has strong robustness.

Keywords: ADRC, ESO, nonlinear system

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Authors: Hanizam Awang, Muhammad Hafiz Ahmad

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An experimental study was conducted on foamed concrete with synthetic and natural fibres consisting of AR-glas, polypropylene, steel, kenaf and oil palm fibre. The foamed concrete mixtures produced had a target density of 1000kg/m³ and a mix ratio of (1:1.5:0.45). The fibres were used as additives. The inclusion of fibre was maintained at a volumetric fraction of 0.25 and 0.4%. The water absorption, thermal and shrinkage were determined to study the effect of the fibre on the durability properties of foamed concrete. The results showed that AR-glass fibre has the lowest percentage value of drying shrinkage compared to others.

Keywords: Foamed concrete, Fibres, Durability.

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Authors: Zongqing Lu

Abstract:

It has proved that nonlinear diffusion and bilateral filtering (BF) have a closed connection. Early effort and contribution are to find a generalized representation to link them by using adaptive filtering. In this paper a new further relationship between nonlinear diffusion and bilateral filtering is explored which pays more attention to numerical calculus. We give a fresh idea that bilateral filtering can be accelerated by multigrid (MG) scheme which likes the nonlinear diffusion, and show that a bilateral filtering process with large kernel size can be approximated by a nonlinear diffusion process based on full multigrid (FMG) scheme.

Keywords: Bilateral filter, multigrid

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Authors: Rama Shanker, Anil Kumar Sachan

Abstract:

Basic ingredients of concrete are cement, fine aggregate, coarse aggregate and water. To produce a concrete of certain specific properties, optimum proportion of these ingredients are mixed. The important factors which govern the mix design are grade of concrete, type of cement and size, shape and grading of aggregates. Concrete mix design method is based on experimentally evolved empirical relationship between the factors in the choice of mix design. Basic draw backs of this method are that it does not produce desired strength, calculations are cumbersome and a number of tables are to be referred for arriving at trial mix proportion moreover, the variation in attainment of desired strength is uncertain below the target strength and may even fail. To solve this problem, a lot of cubes of standard grades were prepared and attained 28 days strength determined for different combination of cement, fine aggregate, coarse aggregate and water. An artificial neural network (ANN) was prepared using these data. The input of ANN were grade of concrete, type of cement, size, shape and grading of aggregates and output were proportions of various ingredients. With the help of these inputs and outputs, ANN was trained using feed forward back proportion model. Finally trained ANN was validated, it was seen that it gave the result with/ error of maximum 4 to 5%. Hence, specific type of concrete can be prepared from given material properties and proportions of these materials can be quickly evaluated using the proposed ANN.

Keywords: Aggregate Proportions, Artificial Neural Network, Concrete Grade, Concrete Mix Design.

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Authors: M. A. Ghorbani, M. Pasbani Khiavi

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The seismic response of steel shear wall system considering nonlinearity effects using finite element method is investigated in this paper. The non-linear finite element analysis has potential as usable and reliable means for analyzing of civil structures with the availability of computer technology. In this research the large displacements and materially nonlinear behavior of shear wall is presented with developing of finite element code. A numerical model based on the finite element method for the seismic analysis of shear wall is presented with developing of finite element code in this research. To develop the finite element code, the standard Galerkin weighted residual formulation is used. Two-dimensional plane stress model and total Lagrangian formulation was carried out to present the shear wall response and the Newton-Raphson method is applied for the solution of nonlinear transient equations. The presented model in this paper can be developed for analysis of civil engineering structures with different material behavior and complicated geometry.

Keywords: Finite element, steel shear wall, nonlinear, earthquake

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Authors: S. M. Gupta, Vanita Aggarwal, Som Nath Sachdeva

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The work reported through this paper is an experimental work conducted on High Performance Concrete (HPC) with super plasticizer with the aim to develop some models suitable for prediction of compressive strength of HPC mixes. In this study, the effect of varying proportions of fly ash (0% to 50% @ 10% increment) on compressive strength of high performance concrete has been evaluated. The mix designs studied were M30, M40 and M50 to compare the effect of fly ash addition on the properties of these concrete mixes. In all eighteen concrete mixes that have been designed, three were conventional concretes for three grades under discussion and fifteen were HPC with fly ash with varying percentages of fly ash. The concrete mix designing has been done in accordance with Indian standard recommended guidelines. All the concrete mixes have been studied in terms of compressive strength at 7 days, 28 days, 90 days, and 365 days. All the materials used have been kept same throughout the study to get a perfect comparison of values of results. The models for compressive strength prediction have been developed using Linear Regression method (LR), Artificial Neural Network (ANN) and Leave-One-Out Validation (LOOV) methods.

Keywords: ANN, concrete mixes, compressive strength, fly ash, high performance concrete, linear regression, strength prediction models.

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Authors: Andre A. Keller

Abstract:

The optimal control is one of the possible controllers for a dynamic system, having a linear quadratic regulator and using the Pontryagin-s principle or the dynamic programming method . Stochastic disturbances may affect the coefficients (multiplicative disturbances) or the equations (additive disturbances), provided that the shocks are not too great . Nevertheless, this approach encounters difficulties when uncertainties are very important or when the probability calculus is of no help with very imprecise data. The fuzzy logic contributes to a pragmatic solution of such a problem since it operates on fuzzy numbers. A fuzzy controller acts as an artificial decision maker that operates in a closed-loop system in real time. This contribution seeks to explore the tracking problem and control of dynamic macroeconomic models using a fuzzy learning algorithm. A two inputs - single output (TISO) fuzzy model is applied to the linear fluctuation model of Phillips and to the nonlinear growth model of Goodwin.

Keywords: fuzzy control, macroeconomic model, multiplier - accelerator, nonlinear accelerator, stabilization policy.

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Authors: Mantai Chen, Johnny Ching Ming Ho

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The stress-strain relationship of concrete under flexure is one of the essential parameters in assessing ultimate flexural strength capacity of RC beams. Currently, the concrete stress-strain curve in flexure is obtained by incorporating a constant scale-down factor of 0.85 in the uniaxial stress-strain curve. However, it was revealed that strain gradient would improve the maximum concrete stress under flexure and concrete stress-strain curve is strain gradient dependent. Based on the strain-gradient-dependent concrete stress-strain curve, the investigation of the combined effects of strain gradient and concrete strength on flexural strength of RC beams was extended to high strength concrete up to 100 MPa by theoretical analysis. As an extension and application of the authors’ previous study, a new flexural strength design method incorporating the combined effects of strain gradient and concrete strength is developed. A set of equivalent rectangular concrete stress block parameters is proposed and applied to produce a series of design charts showing that the flexural strength of RC beams are improved with strain gradient effect considered.

Keywords: Beams, Equivalent concrete stress block, Flexural strength, Strain gradient.

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Authors: C. Pislaru, A. Shebani

Abstract:

This paper uses the radial basis function neural network (RBFNN) for system identification of nonlinear systems. Five nonlinear systems are used to examine the activity of RBFNN in system modeling of nonlinear systems; the five nonlinear systems are dual tank system, single tank system, DC motor system, and two academic models. The feed forward method is considered in this work for modelling the non-linear dynamic models, where the KMeans clustering algorithm used in this paper to select the centers of radial basis function network, because it is reliable, offers fast convergence and can handle large data sets. The least mean square method is used to adjust the weights to the output layer, and Euclidean distance method used to measure the width of the Gaussian function.

Keywords: System identification, Nonlinear system, Neural networks, RBF neural network.

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Authors: Klara Krizova, Rudolf Hela

Abstract:

The paper reflects current state of popularization of static elasticity modulus of concrete. This parameter is undoubtedly very important for designing of concrete structures, and very often neglected and rarely determined before designing concrete technology itself. The paper describes assessment and comparison of four mix designs with almost constant dosage of individual components. The only difference is area of origin of small size fraction of aggregate 0/4. Development of compressive strength and static elasticity modulus at the age of 7, 28 and 180 days were observed. As the experiment showed, designing of individual components and their quality are the basic factor influencing elasticity modulus of current concrete.

Keywords: Concrete, Aggregate, Strength, Elasticity Modulus, Quality

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Authors: M. Cortés, E. Vera, O. Rojas

Abstract:

The research studies of the kinetics of the corrosion process that attacks concrete and occurs within sewerage systems agree on the amount of variables that interfere in the process. This study aims to check the impact of the pH levels of the corrosive environment and the concrete surface, the concentrations of chemical sulfuric acid, and in turn, measure the resistance of concrete to this attack under controlled laboratory conditions; it also aims to contribute to the development of further research related to the topic, in order to compare the impact of biogenic sulfuric acid and chemical sulfuric acid involvement on concrete structures, especially in scenarios such as sewerage systems.

Keywords: Acid Sulfuric, concrete, corrosion.

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Authors: Taher Lotfi , Parisa Bakhtiari , Katayoun Mahdiani , Mehdi Salimi

Abstract:

In this paper, verified extension of the Ostrowski method which calculates the enclosure solutions of a given nonlinear equation is introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the scheme.

Keywords: Iinterval analysis, nonlinear equations, Ostrowski method.

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Authors: Ana Clara Santos, Maria Manuela Portela, Bettina Schaefli

Abstract:

This work assesses the performance of an analytical model framework to generate daily flow duration curves, FDCs, based on climatic characteristics of the catchments and on their streamflow recession coefficients. According to the analytical model framework, precipitation is considered to be a stochastic process, modeled as a marked Poisson process, and recession is considered to be deterministic, with parameters that can be computed based on different models. The analytical model framework was tested for three case studies with different hydrological regimes located in Switzerland: pluvial, snow-dominated and glacier. For that purpose, five time intervals were analyzed (the four meteorological seasons and the civil year) and two developments of the model were tested: one considering a linear recession model and the other adopting a nonlinear recession model. Those developments were combined with recession coefficients obtained from two different approaches: forward and inverse estimation. The performance of the analytical framework when considering forward parameter estimation is poor in comparison with the inverse estimation for both, linear and nonlinear models. For the pluvial catchment, the inverse estimation shows exceptional good results, especially for the nonlinear model, clearing suggesting that the model has the ability to describe FDCs. For the snow-dominated and glacier catchments the seasonal results are better than the annual ones suggesting that the model can describe streamflows in those conditions and that future efforts should focus on improving and combining seasonal curves instead of considering single annual ones.

Keywords: Analytical streamflow distribution, stochastic process, linear and non-linear recession, hydrological modelling, daily discharges.

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Authors: Leo Laine, Morgan Johansson

Abstract:

To meet the civilizations future needs for safe living and low environmental footprint, the engineers designing the complex systems of tomorrow will need efficient ways to model and optimize these systems for their intended purpose. For example, a civil defence shelter and its subsystem components needs to withstand, e.g. airblast and ground shock from decided design level explosion which detonates with a certain distance from the structure. In addition, the complex civil defence shelter needs to have functioning air filter systems to protect from toxic gases and provide clean air, clean water, heat, and electricity needs to also be available through shock and vibration safe fixtures and connections. Similar complex building systems can be found in any concentrated living or office area. In this paper, the authors use a multidomain modelling language called Modelica to model a concrete wall as a single degree of freedom (SDOF) system with elastoplastic properties with the implemented option of plastic hardening. The elastoplastic model was developed and implemented in the open source tool OpenModelica. The simulation model was tested on the case with a transient equivalent reflected pressure time history representing an airblast from 100 kg TNT detonating 15 meters from the wall. The concrete wall is approximately regarded as a concrete strip of 1.0 m width. This load represents a realistic threat on any building in a city like area. The OpenModelica model results were compared with an Excel implementation of a SDOF model with an elastic-plastic spring using simple fixed timestep central difference solver. The structural displacement results agreed very well with each other when it comes to plastic displacement magnitude, elastic oscillation displacement, and response times.

Keywords: Airblast from explosives, elastoplastic spring model, Modelica modelling language, SDOF, structural response of concrete structure.

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Authors: Muqdad Al-Juboori, Bithin Datta

Abstract:

Hydraulic structures such as gravity dams are classified as essential structures, and have the vital role in providing strong and safe water resource management. Three major aspects must be considered to achieve an effective design of such a structure: 1) The building cost, 2) safety, and 3) accurate analysis of seepage characteristics. Due to the complexity and non-linearity relationships of the seepage process, many approximation theories have been developed; however, the application of these theories results in noticeable errors. The analytical solution, which includes the difficult conformal mapping procedure, could be applied for a simple and symmetrical problem only. Therefore, the objectives of this paper are to: 1) develop a surrogate model based on numerical simulated data using SEEPW software to approximately simulate seepage process related to a hydraulic structure, 2) develop and solve a linked simulation-optimization model based on the developed surrogate model to describe the seepage occurring under a concrete gravity dam, in order to obtain optimum and safe design at minimum cost. The result shows that the linked simulation-optimization model provides an efficient and optimum design of concrete gravity dams.

Keywords: Artificial neural network, concrete gravity dam, genetic algorithm, seepage analysis.

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Authors: Maruful H. Mazumder, Raymond I. Gilbert

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The design specifications for calculating development and lapped splice lengths of reinforcement in concrete are derived from a conventional empirical modelling approach that correlates experimental test data using a single mathematical equation. This paper describes part of a recently completed experimental research program to assess the effects of different structural parameters on the development length requirements of modern high strength steel reinforcing bars, including the case of lapped splices in large-scale reinforced concrete members. The normalized average bond stresses for the different variations of anchorage lengths are assessed according to the general form of a typical empirical analytical model of bond and anchorage. Improved analytical modelling equations are developed in the paper that better correlate the normalized bond strength parameters with the structural parameters of an empirical model of bond and anchorage.

Keywords: Bond stress, Development length, Lapped splice length, Reinforced concrete.

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Authors: Jongho Park, Taekyun Kim, Jungbhin You, Sungnam Hong, Sun-Kyu Park

Abstract:

Due to the aging of bridges, increasing of maintenance costs and decreasing of structural safety is occurred. The steel corrosion of reinforced concrete bridge is the most common problem and this phenomenon is accelerating due to abnormal weather and increasing CO₂ concentration due to climate change. To solve these problems, composite members using textile have been studied. A textile reinforced concrete can reduce carbon emissions by reduced concrete and without steel bars, so a lot of structural behavior studies are needed. Therefore, in this study, textile reinforced concrete beam was made and flexural test was performed. Also, the change of flexural strength according to the prestressing was conducted. As a result, flexural strength of TRC with prestressing was increased compared and flexural behavior was shown as reinforced concrete.

Keywords: AR-glass, flexural strength, prestressing, textile reinforced concrete.

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Authors: Mohammed Farag, Mina Attari, S. Andrew Gadsden, Saeid R. Habibi

Abstract:

Battery state of charge (SOC) estimation is an important parameter as it measures the total amount of electrical energy stored at a current time. The SOC percentage acts as a fuel gauge if it is compared with a conventional vehicle. Estimating the SOC is, therefore, essential for monitoring the amount of useful life remaining in the battery system. This paper looks at the implementation of three nonlinear estimation strategies for Li-Ion battery SOC estimation. One of the most common behavioral battery models is the one state hysteresis (OSH) model. The extended Kalman filter (EKF), the smooth variable structure filter (SVSF), and the time-varying smoothing boundary layer SVSF are applied on this model, and the results are compared.

Keywords: State of charge estimation, battery modeling, one-state hysteresis, filtering and estimation.

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Authors: L. Wong, H. Asrah, M.E. Rahman, M.A. Mannan

Abstract:

The storage of chemical fertilizers in concrete building often leads to durability problems due to chemical attack. The damage of concrete is mostly caused by certain ammonium salts. The main purpose of the research is to investigate the durability properties of concrete being exposed to ammonium nitrate solution. In this investigation, experiments are conducted on concrete type G50 and G60. The leaching process is achieved by the use of 20% concentration solution of ammonium nitrate. The durability properties investigated are water absorption, volume of permeable voids, and sorptivity. Compressive strength, pH value, and degradation depth are measured after a certain period of leaching. A decrease in compressive strength and an increase in porosity are found through the conducted experiments. Apart from that, the experimental data shows that pH value decreases with increased leaching time while the degradation depth of concrete increases with leaching time. By comparing concrete type G50 and G60, concrete type G60 is more resistant to ammonium nitrate attack.

Keywords: Normal weight concrete durability, Aggressive Ammonium Nitrate Solution, G50 & G60 concretes, Chemical attack.

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Authors: Pedro Gutemberg de Alcântara Segundinho, José Antonio Matthiesen, Marcelo Rodrigo Carreira

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Timber-concrete structures were recently introduced in Brazil as a viable option for bridge construction on side roads. Binding between timber and concrete is fundamentally important to assure the rigidity and performance of this structural system. The objective of this study was to assess the structural performance of a timber-concrete bridge prototype with width of 170cm and span of 400cm, whose binding among timber beams and concrete slabs was made with metal pins, obtained from CA 50 construction steel bars of 12.5mm diameter. It was possible to conclude, from the results obtained experimentally in laboratory, that the timber-concrete bridge prototype showed a good structural performance. This structural system provides an economical, rapid implementation solution, which may be used on side roads, favoring regional integration and agricultural production flow.

Keywords: Binding, bridge prototype, timber and concrete

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Authors: A. Zerkane, K. El Bikri, R. Benamar

Abstract:

The purpose of the present paper is to show that the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) with immovable ends can be reduced to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters by using an homogenization procedure. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results. The non-dimensional curvatures associated to the nonlinear fundamental mode are also given for various vibration amplitudes in the case of clamped-clamped FGB.

Keywords: Nonlinear vibrations, functionally graded materials, homogenization procedure.

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Authors: Javad Abdalkhani

Abstract:

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very large intervals..

Keywords: Nonlinear transformation, Abel Volterra Equations, Mathematica

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Authors: Paratibha Aggarwal, Yogesh Aggarwal

Abstract:

The paper presents the potential of fuzzy logic (FL-I) and neural network techniques (ANN-I) for predicting the compressive strength, for SCC mixtures. Six input parameters that is contents of cement, sand, coarse aggregate, fly ash, superplasticizer percentage and water-to-binder ratio and an output parameter i.e. 28- day compressive strength for ANN-I and FL-I are used for modeling. The fuzzy logic model showed better performance than neural network model.

Keywords: Self compacting concrete, compressive strength, prediction, neural network, Fuzzy logic.

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Authors: Jafar Biazar, Behzad Ghanbari

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In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

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Authors: Nizami Mustafa, C. Ardil

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In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

Keywords: Approximate solution, Fixed-point principle, Nonlinear singular integral equations, Vekua integral operator

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Authors: V. Spaeth, A. Djerbi-Tegguer

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The recycling of concrete, bricks and masonry rubble as concrete aggregates is an important way to contribute to a sustainable material flow. However, there are still various uncertainties limiting the widespread use of Recycled Concrete Aggregates (RCA). The fluctuations in the composition of grade recycled aggregates and their influence on the properties of fresh and hardened concrete are of particular concern regarding the use of RCA. Most of problems occurring while using recycled concrete aggregates as aggregates are due to higher porosity and hence higher water absorption, lower mechanical strengths, residual impurities on the surface of the RCA forming weaker bond between cement paste and aggregate. So, the reuse of RCA is still limited. Efficient polymer based treatment is proposed in order to reuse RCA easier. The silicon-based polymer treatments of RCA were carried out and were compared. This kind of treatment can improve the properties of RCA such as the rate of water absorption on treated RCA is significantly reduced.

Keywords: Recycled concrete aggregates, water absorption, silicon-based agent and polymer.

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Authors: Y. Mohammadi, H. M. Ghasemzadeh, T. B. Talari, M. A. Ghorbani

Abstract:

Concrete pavement has superior durability and longer structural life than asphalt pavement. Concrete pavement requires less maintenance compared to asphalt pavement which requires maintenance and major rehabilitation. Use of the concrete pavement has been grown over the past decade in developing countries. Fibre reinforced concrete (FRC) has been successfully used in design of concrete pavement in past decade. In this research, the effect of fibre volume fraction in modulus of rupture, load-deflection, equivalent flexural strength (fe,3) and the equivalent flexural strength ratio (Re,3) has been used in different fibre volume fraction. Crimped-type flat steel fibre of size 50 x 2.0 x 0.6 mm was used with 1.0%, 1.5% and 2.0% volume fraction. Beam specimens of size 500 x 100 x 100 mm were used for flexural as well as with JCI method for analysis flexural toughness, equivalent flexural strength. It was obtained as the 2% fibre volume fractions; reduce 45% of the concrete pavement thickness.

Keywords: Concrete pavement, Equivalent flexural strength, Fibre, Load-deflection curves.

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