World Academy of Science, Engineering and Technology

Authors: M. Si-Ahmed, A. Belakrouf, S. Kenai

Abstract:

The use of additions in cement in manufacturing, mortar and concrete offers economic and ecological advantages. Cements with additions such as limestone, slag and natural pouzzolana are produced in cement factories in Algeria. Several studies analyzed the effect of these additions on the physical and mechanical properties as well as the durability of concrete. However, few studies were conducted on the effect of local metakaolin on mechanical properties and durability of concrete. The main purpose of this paper is to analyze the performance of mortar and concrete with local metakaolin. The preparation of the metakaolin was carried out by calcination of kaolin at a temperature of 850 °C for a period of 3 hours. The experimental results have shown that the rates of substitutions of 10 and 15% metakaolin increases the compressive strength and flexural strength at both early age and long term. The durability and the permeability were also improved by reducing the coefficient of sorptivity.

Keywords: Metakaolin, calcination, compressive strength, durability.

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Authors: Y. Si Youcef, M. Chemrouk

Abstract:

The present work presents a method of calculating the ductility of rectangular sections of beams considering nonlinear behavior of concrete and steel. This calculation procedure allows us to trace the curvature of the section according to the bending moment, and consequently deduce ductility. It also allowed us to study the various parameters that affect the value of the ductility. A comparison of the effect of maximum rates of tension steel, adopted by the codes, ACI [1], EC8 [2] and RPA [3] on the value of the ductility was made. It was concluded that the maximum rate of steels permitted by the ACI [1] codes and RPA [3] are almost similar in their effect on the ductility and too high. Therefore, the ductility mobilized in case of an earthquake is low, the inverse of code EC8 [2]. Recommendations have been made in this direction.

Keywords: Ductility, beam, reinforced concrete, seismic code, relationship, time bending, resistance, non-linear behavior.

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Authors: Surendran M, Palani G. S, Nagesh R. Iyer

Abstract:

Multi-site damage (MSD) has been a challenge to aircraft, civil and power plant structures. In real life components are subjected to cracking at many vulnerable locations such as the bolt holes. However, we do not consider for the presence of multiple cracks. Unlike components with a single crack, these components are difficult to predict. When two cracks approach one another, their stress fields influence each other and produce enhancing or shielding effect depending on the position of the cracks. In the present study, numerical studies on fracture analysis have been conducted by using the developed code based on the modified virtual crack closure integral (MVCCI) technique and finite element analysis (FEA) software ABAQUS for computing SIF of plates with multiple cracks. Various parametric studies have been carried out and the results have been compared with literature where ever available and also with the solution, obtained by using ABAQUS. By conducting extensive numerical studies expressions for SIF have been obtained for collinear cracks and non-aligned cracks.

Keywords: Crack interaction, Fracture mechanics, Multiple site damage, stress intensity factor, collinear cracks, non-aligned cracks.

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Authors: V. Salajka, J. Kala, P. Hradil

Abstract:

The presented article deals with the description of a numerical model of a corridor at a Central Interim Spent Fuel Storage Facility (hereinafter CISFSF). The model takes into account the effect of air flows on the temperature of stored waste. The computational model was implemented in the ANSYS/CFX programming environment in the form of a CFD task solution, which was compared with an approximate analytical calculation. The article includes a categorization of the individual alternatives for the ventilation of such underground systems. The aim was to evaluate a ventilation system for a CISFSF with regard to its stability and capacity to provide sufficient ventilation for the removal of heat produced by stored casks with spent nuclear fuel.

Keywords: Temperature fields, Spent Fuel, Interim storage facility, CFD.

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Authors: Amir Ayazi, Hamde Ahmadi, Soheil Shafaei

Abstract:

Composite steel shear wall is a lateral load resisting system which consists of a steel plate with concrete wall attached to one or both sides to prevent it from elastic buckling. The composite behavior is ensured by utilizing high-strength bolts. This paper investigates the effect of distance between bolts, and for this purpose 14 one-story one-bay specimens with various bolts spacing were modeled by finite element code which is developed by the authors. To verify the model, numerical results were compared with a valid experiment which illustrate proper agreement. Results depict increasing the distance between bolts would improve the seismic ever, this increase must be limited, because of large distances will cause widespread buckling of the steel plate in free subpanels between bolts and would result in no improvement. By comparing the results in elastic region, it was observed initial stiffness is not affected by changing the distance.

Keywords: Composite steel shear wall, bolt, buckling, finite element.

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Authors: J. Maděra, M. Jerman, R. Černý

Abstract:

Temperature, relative humidity and overhygroscopic moisture fields in a sandstone wall provided with interior thermal insulation were calculated in order to assess the hygric performance of the retrofitted wall. Computational simulations showed that during the time period of 10 years which was subject of investigation no overhygroscopic moisture appeared in the analyzed building envelope so that it performed in a satisfactory way from the hygric point of view.

Keywords: Sandstone wall, interior thermal insulation, moisture, computational modeling.

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Authors: Z. Pavlík, J. Žumár, M. Pavlíková, J. Kočí, R. Černý

Abstract:

Water vapour transport properties of gypsum block are studied in dependence on relative humidity using inverse analysis based on genetic algorithm. The computational inverse analysis is performed for the relative humidity profiles measured along the longitudinal axis of a rod sample. Within the performed transient experiment, the studied sample is exposed to two environments with different relative humidity, whereas the temperature is kept constant. For the basic gypsum characterisation and for the assessment of input material parameters necessary for computational application of genetic algorithm, the basic material properties of gypsum are measured as well as its thermal and water vapour storage parameters. On the basis of application of genetic algorithm, the relative humidity dependent water vapour diffusion coefficient and water vapour diffusion resistance factor are calculated.

Keywords: Water vapour transport, gypsum block, transient experiment, genetic algorithm.

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Authors: J. Kala, P. Hradil, V. Salajka

Abstract:

Reinforced concrete crash barriers used in road traffic must meet a number of criteria. Crash barriers are laid lengthwise, one behind another, and joined using specially designed steel locks. While developing BSV reinforced concrete crash barriers (type ŽPSV), experiments and calculations aimed to optimize the shape of a newly designed lock and the reinforcement quantity and distribution in a crash barrier were carried out. The tension carrying capacity of two parallelly joined locks was solved experimentally. Based on the performed experiments, adjustments of nonlinear properties of steel were performed in the calculations. The obtained results served as a basis to optimize the lock design using a computational model that takes into account the plastic behaviour of steel and the influence of the surrounding concrete [6]. The response to the vehicle impact has been analyzed using a specially elaborated complex computational model, comprising both the nonlinear model of the damping wall or crash barrier and the detailed model of the vehicle [7].

Keywords: Crash Barrier, impact, static analysis, concrete nonlinear model.

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Authors: S. Guettala, B. Mezghiche

Abstract:

In this paper, the effect of addition the dune sand powder (DSP) on development of compressive strength and hydration of cement pastes was investigated as a function of water/binder ratio, was varied, on the one hand, the percentage of DSP and on the other, the fineness of DSP. In order to understand better the pozzolanic effect of dune sand powder in cement pastes, we followed the mixtures hydration (50% Pure Lime + 50% DSP) by X-ray diffraction. These mixtures the pastes present a hydraulic setting which is due to the formation of a C-S-H phase (calcium silicate hydrate). The latter is semi-crystallized. This study is a simplified approach to that of the mixtures (80% ordinary Portland cement + 20% DSP), in which the main reaction is the fixing of the lime coming from the cement hydration in the presence of DSP, to form calcium silicate hydrate semi-crystallized of second generation. The results proved that up to (20% DSP) as Portland cement replacement could be used with a fineness of 4000 cm²/g without affecting adversely the compressive strength. After 28 days, the compressive strength at 5, 10 and 15% DSP is superior to Portland cement, with an optimum effect for a percentage of the order of 5% to 10% irrespective of the w/b ratio and fineness of DSP.

Keywords: Ordinary Portland Cement, Pure Lime, Dune Sand Powder, Compressive Strength, Hydration.

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Authors: Mohamed M. El-Gendy, Ibrahim A. El-Arabi, Rafik W. Abdel-Missih, Omar A. Kandil

Abstract:

In the present research, a finite element model is presented to study the geometrical and material nonlinear behavior of reinforced concrete plane frames considering soil-structure interaction. The nonlinear behaviors of concrete and reinforcing steel are considered both in compression and tension up to failure. The model takes account also for the number, diameter, and distribution of rebar along every cross section. Soil behavior is taken into consideration using four different models; namely: linear-, nonlinear Winkler's model, and linear-, nonlinear continuum model. A computer program (NARC) is specially developed in order to perform the analysis. The results achieved by the present model show good agreement with both theoretical and experimental published literature. The nonlinear behavior of a rectangular frame resting on soft soil up to failure using the proposed model is introduced for demonstration.

Keywords: Nonlinear analysis, Geometric nonlinearity, Material nonlinearity, Reinforced concrete, Finite element method, Soilstructure interaction, Winkler's soil model, Continuum soil model

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Authors: O. Kratochvíl, J. Križan

Abstract:

The paper deals with the analysis of the dynamic response of footbridges under human - induced dynamic loads. This is a frequently occurring and often dominant load for footbridges as it stems from the very purpose of a footbridge - to convey pedestrian. Due to the emergence of new materials and advanced engineering technology, slender footbridges are increasingly becoming popular to satisfy the modern transportation needs and the aesthetical requirements of the society. These structures however are always lively with low stiffness, low mass, low damping and low natural frequencies. As a consequence, they are prone to vibration induced by human activities and can suffer severe vibration serviceability problems, particularly in the lateral direction. Pedestrian bridges are designed according to first and second limit states, these are the criteria involved in response to static design load. However, it is necessary to assess the dynamic response of bridge design load on pedestrians and assess it impact on the comfort of the user movement. Usually the load is considered a person or a small group which can be assumed in perfect motion synchronization. Already one person or small group can excite significant vibration of the deck. In order to calculate the dynamic response to the movement of people, designer needs available and suitable computational model and criteria. For the calculation program ANSYS based on finite element method was used.

Keywords: Footbridge, dynamic analysis, vibration serviceability of footbridges, lateral vibration, stiffness, dynamic force, walking force, slender suspension footbridges, natural frequencies and vibration modes, rhythm jumping, normal walking.

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Authors: A. Rouili

Abstract:

In the present paper the results of a numerical study are presented, numerical models were developed to simulate the behaviour of vertical massive dikes. The proposed models were developed according to the geometry, boundary conditions, loading conditions and initial conditions of a physical model taken as reference. The results obtained were compared to the experimental data. As far as the overall behaviour, the displacements and the failure mechanisms of the dikes is concerned, the numerical results were in good agreement with the experimental results, which clearly indicates a good quality of numerical modelling. The validated numerical models were used in a parametric study were the displacements and failure mechanisms were fully investigated. Out of the results obtained, some conclusions and recommendations related to the design of massive dikes are proposed.

Keywords: Water conservation, dikes, risk assessment and numerical modelling.

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Authors: Douangmala Kounsana, Toru Takahashi

Abstract:

In recent years, the number of natural disasters in Laos has a trend to increase, especially the disaster of flood. To make a flood plan risk management in the future, it is necessary to understand and analyze the characteristics of the rainfall and Mekong River level data. To reduce the damage, this paper presents the flood risk analysis in Luangprabang and Vientiane, the prefecture of Laos. In detail, the relationship between the rainfall and the Mekong River level has evaluated and appropriate countermeasure for flood was discussed.

Keywords: Lao flood, Mekong river, rainfall, risk management.

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Authors: Douangmala Kousnana, Toru Takahashi

Abstract:

In recent years, the number of natural disasters in the world has occurred frequently. After a strong earthquake occurs, multiple disasters due to tsunami, strong aftershocks or heavy snow can possible to occur. To prevent a secondary disaster and to save a life, the quick inspection of the damaged building is necessary. This paper investigated on a possibility of post earthquake quick inspection of damaged building by ordinary people which used the European Macro- Seismic Scale 1998 (EMS-98).

Keywords: Quick Assessment, EMS-98, Ordinary People, Post-Earthquake

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Authors: N. Zaki Alamdari, M. Banihashemi, A. Mirghasemi

Abstract:

To estimate the risks of dam failure phenomenon, it is necessary to understand this phenomenon and the involved governing factors. Overtopping and piping are the two main reasons of earthdam failures. In the piping context, the piping is determined as a phenomenon which is occurred between two phases, the water liquid and the solid soil. In this investigation, the onset of piping and its development, as well as the movement of water in soil, are numerically approached. In this regard, a one-dimensional numerical model based on the mass-conserving finite-volume method is developed and applied in order to simulate the piping phenomenon in a continuous circular tunnel of given initial length and radius, located between upstream and downstream. The simulation result includes the time-variations of radius along the tunnel until the radius value reaches its critical and the piping phenomenon converts to overtopping.

Keywords: Earth dam, dam break, piping, internal erosion

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Authors: Lenka Ševelová, Aleš Florian

Abstract:

To improve the efficiency of parametric studies or tests planning the method is proposed, that takes into account all input parameters, but only a few simulation runs are performed to assess the relative importance of each input parameter. For K input parameters with N input values the total number of possible combinations of input values equals NK. To limit the number of runs, only some (totally N) of possible combinations are taken into account. The sampling procedure Updated Latin Hypercube Sampling is used to choose the optimal combinations. To measure the relative importance of each input parameter, the Spearman rank correlation coefficient is proposed. The sensitivity and the influence of all parameters are analyzed within one procedure and the key parameters with the largest influence are immediately identified.

Keywords: Concrete, pavement, simulation, reliability, Latin Hypercube Sampling, parametric studies.

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Authors: Hyun-Woo Cho, Jae-Heum Moon, Jang-Hwa Lee

Abstract:

In order to supplement the brittle property of concrete, fibers are added into concrete mixtures. Compared to general concrete, various characteristics such as tensile strength, bending strength, bending toughness, and resistance to crack are superior, and even when cracks occur, improvements on toughness as well as resistance to shock are excellent due to the growth of fracture energy. Increased function of steel fiber reinforced concrete can be differentiated depending on the fiber dispersion, and sand percentage can be an important influence on the fiber dispersion. Therefore, in this research, experiments were planned on sand percentage in order to apprehend the influence of sand percentage on the bending properties and direct tension of SFRC and basic experiments were conducted on bending and direct tension in order to recognize the properties of bending properties and direct tension following the size of the aggregates and sand percentage.

Keywords: Steel Fiber Reinforced Concrete, Bending Toughness, Direct tension.

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Authors: L. Menaa, A. Cherifi, K. Tigouirat, M. Choura

Abstract:

Analyse of locally manufactured Low Density Polyethylene (LDPE) durability, used within lining systems at bottom of Municipal Solid Waste (landfill), is done in the present work. For this end, short and middle time creep behavior under tension of the analyzed material is carried out. The locally manufactured material is tested and compared to the European one (LDPE-CE). Both materials was tested in 03 various mediums: ambient and two aggressive (salty water and foam water), using three specimens in each case. A testing campaign is carried out using an especially designed and achieved testing bench. Moreover, characterisation tests were carried out to evaluate the medium effect on the mechanical properties of the tested material (LDPE). Furthermore, experimental results have been used to establish a law regression which can be used to predict creep behaviour of the analyzed material. As a result, the analyzed LDPE material has showed a good stability in different ambient and aggressive mediums; as well, locally manufactured LDPE seems more flexible, compared with the European one. This makes it more useful to the desired application.

Keywords: LDPE membrane, solid waste, aggressive mediums, durability

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Authors: Si-Hwan Kim, Gum-Sung Ryu, Kyung-Taek Koh, Jang-Hwa Lee

Abstract:

Despite of the preponderant role played by cement among the construction materials, it is today considered as a material destructing the environment due to the large quantities of carbon dioxide exhausted during its manufacture. Besides, global warming is now recognized worldwide as the new threat to the humankind against which advanced countries are investigating measures to reduce the current amount of exhausted gases to the half by 2050. Accordingly, efforts to reduce green gases are exerted in all industrial fields. Especially, the cement industry strives to reduce the consumption of cement through the development of alkali-activated geopolymer mortars using industrial byproducts like bottom ash. This study intends to gather basic data on the flowability and strength development characteristics of alkali-activated geopolymer mortar by examining its FT-IT features with respect to the effects and strength of the alkali-activator in order to develop bottom ash-based alkali-activated geopolymer mortar. The results show that the 35:65 mass ratio of sodium hydroxide to sodium silicate is appropriate and that a molarity of 9M for sodium hydroxide is advantageous. The ratio of the alkali-activators to bottom ash is seen to have poor effect on the strength. Moreover, the FT-IR analysis reveals that larger improvement of the strength shifts the peak from 1060 cm–1 (T-O, T=Si or Al) toward shorter wavenumber.

Keywords: Bottom Ash, Geopolymer mortar, Flowability, Strength Properties.

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Authors: J. Kala, V. Salajka, P. Hradil

Abstract:

The main focus of this paper is on the human induced forces. Almost all existing force models for this type of load (defined either in the time or frequency domain) are developed from the assumption of perfect periodicity of the force and are based on force measurements conducted on rigid (i.e. high frequency) surfaces. To verify the different authors conclusions the vertical pressure measurements invoked during the walking was performed, using pressure gauges in various configurations. The obtained forces are analyzed using Fourier transformation. This load is often decisive in the design of footbridges. Design criteria and load models proposed by widely used standards and other researchers were introduced and a comparison was made.

Keywords: Pedestrian action, Experimental analysis, Fourier series, serviceability, cycle loading.

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Authors: Behnam Shirkhanghah, Vahid Shahbaznejhad-Fard, Houshyar Eimani-Kalesar, Babak Pahlevan

Abstract:

Flat double-layer grid is from category of space structures that are formed from two flat layers connected together with diagonal members. Increased stiffness and better seismic resistance in relation to other space structures are advantages of flat double layer space structures. The objective of this study is assessment and calculation of Behavior factor of flat double layer space structures. With regarding that these structures are used widely but Behavior factor used to design these structures against seismic force is not determined and exact, the necessity of study is obvious. This study is theoretical. In this study we used structures with span length of 16m and 20 m. All connections are pivotal. ANSYS software is used to non-linear analysis of structures.

Keywords: Behavior factor, Double-layer, Intensified resistance, Non-linear analysis

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Authors: Rado Flajs, Miran Saje

Abstract:

We present a simple nonconforming approximation of the linear two–point boundary value problem which violates patch test requirements. Nevertheless the solutions, obtained from these type of approximations, converge to the exact solution.

Keywords: Generalized patch test, Irons' patch test, nonconforming finite element, convergence.

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Authors: Mudjiastuti Handajani

Abstract:

The national economy development affects the vehicle ownership which ultimately increases fuel consumption. The rise of the vehicle ownership is dominated by the increasing number of motorcycles. This research aims to analyze and identify the characteristics of fuel consumption, the city transportation system, and to analyze the relationship and the effect of the city transportation system on the fuel consumption. A multivariable analysis is used in this study. The data analysis techniques include: a Multivariate Multivariable Analysis by using the R software. More than 84% of fuel on Java is consumed in metropolitan and large cities. The city transportation system variables that strongly effect the fuel consumption are population, public vehicles, private vehicles and private bus. This method can be developed to control the fuel consumption by considering the urban transport system and city tipology. The effect can reducing subsidy on the fuel consumption, increasing state economic.

Keywords: city, consumption, fuel, transportation

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Authors: V. Precupas, A. Ivan, M. Ivan

Abstract:

The dome with ribs and rings, which covers the ROMEXPO pavilion from Bucharest, was designed after the collapse of the single layer reticulated dome. In this paper, it was made the checking of the structure, under the dynamic loads with three recorded accelerograms calibrated according to Romanian seismic design code P100-1/2006. Under the action the dynamic loadings, it was made a time-history analysis to determine the zones where the plastic hinges appear, at what accelerations and their position on the structure. The studied dome is formed by 32 spatial semi arches and three rings: one circular ring located at the top of the dome and another two rings, design as trusses, the first near the supports and the second as an intermediate rings above the skylights. Above the skylights up to the top, the dome is tight together with purlins and bracings.

Keywords: dome, dynamic analysis, plastic hinges, time-history

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Authors: Abdussamad Ismail, Dong-Sheng Jeng

Abstract:

A self-evolution algorithm for optimizing neural networks using a combination of PSO and JPSO is proposed. The algorithm optimizes both the network topology and parameters simultaneously with the aim of achieving desired accuracy with less complicated networks. The performance of the proposed approach is compared with conventional back-propagation networks using several synthetic functions, with better results in the case of the former. The proposed algorithm is also implemented on slope stability problem to estimate the critical factor of safety. Based on the results obtained, the proposed self evolving network produced a better estimate of critical safety factor in comparison to conventional BPN network.

Keywords: Neural networks, Topology evolution, Particle swarm optimization.

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Authors: Behnam Shirkhanghah, Ali Darabadi-Zare, Houshyar Eimani-Kalesar, Babak Pahlevan

Abstract:

Prestressing in structure increases ratio of load-bearing capacity to weight. Suspendomes are single-layer braced domes reinforced with cable and strut. Prestressing of cables alter value and distribution of stress in structure. In this study two configuration, diamatic and lamella domes is selected. Investigated domes have span of 100m with rise-to-span ratios of 0.1, 0.2, and 0.3. Single layer domes loaded under service load combinations according to ISO code. After geometric nonlinear analysis, models are designed with tubular and I-shaped sections then reinforced with cable and strut and converted to suspendomes. Displacements and stresses of some groups of nodes and elements in all of single-layer domes and suspendomes for three load combinations, symmetric snow, asymmetric snow and wind are compared. Variation due to suspending system is investigated. Suspendomes are redesigned and minimum possible weight after addition of cable and strut is obtained.

Keywords: Braced dome, Prestressing, Single-layer, Suspendome.

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Authors: Rohit, S. Vishnuvardhan, P. Gandhi, Nagesh R. Iyer

Abstract:

The evaluation of energy release rate and centre Crack Opening Displacement (COD) for circumferential Through-Wall Cracked (TWC) pipes is an important issue in the assessment of critical crack length for unstable fracture. The ability to predict crack growth continues to be an important component of research for several structural materials. Crack growth predictions can aid the understanding of the useful life of a structural component and the determination of inspection intervals and criteria. In this context, studies were carried out at CSIR-SERC on Nuclear Power Plant (NPP) piping components subjected to monotonic as well as cyclic loading to assess the damage for crack growth due to low-cycle fatigue in circumferentially TWC pipes.

Keywords: 304LN stainless steel, cyclic J-integral, Elastic- Plastic Fracture Mechanics, J-integral, Through-wall crack

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Authors: M. Jayakumar, Lau Chee Sing

Abstract:

The pavement constructions on soft and expansive soils are not durable and unable to sustain heavy traffic loading. As a result, pavement failures and settlement problems will occur very often even under light traffic loading due to cyclic and rolling effects. Geotechnical engineers have dwelled deeply into this matter, and adopt various methods to improve the engineering characteristics of soft fine-grained soils and expansive soils. The problematic soils are either replaced by good and better quality material or treated by using chemical stabilization with various binding materials. Increased the strength and durability are also the part of the sustainability drive to reduce the environment footprint of the built environment by the efficient use of resources and waste recycle materials. This paper presents a series of laboratory tests and evaluates the effect of cement and fly ash on the strength and drainage characteristics of soil in Miri. The tests were performed at different percentages of cement and fly ash by dry weight of soil. Additional tests were also performed on soils treated with the combinations of fly ash with cement and lime. The results of this study indicate an increase in unconfined compression strength and a decrease in hydraulic conductivity of the treated soil.

Keywords: Pavement failure, soft soil, sustainability, stabilization, fly ash, strength and permeability.

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Authors: Li Hao, Yan Zhang, Jingan Cui

Abstract:

The Eulerian numerical method is proposed to analyze the explosion in tunnel. Based on this method, an original software M-MMIC2D is developed by Cµ program language. With this software, the explosion problem in the tunnel with three expansion-chambers is numerically simulated, and the results are found to be in full agreement with the observed experimental data.

Keywords: Eulerian method, numerical simulation, shock wave, tunnel

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Authors: B. Singh, K. K. Agrawal, B. K. Nanda

Abstract:

In built-up structures, one of the effective ways of dissipating unwanted vibration is to exploit the occurrence of slip at the interfaces of structural laminates. The present work focuses on the dynamic analysis of welded structures. A mathematical formulation has been developed for the mechanism of slip damping in layered and welded mild steel beams with unequal thickness subjected to both periodic and non-periodic forces. It is observed that a number of vital parameters such as; thickness ratio, pressure distribution characteristics, relative slip and kinematic co-efficient of friction at the interfaces, nature of exciting forces, length and thickness of the beam specimen govern the damping characteristics of these structures. Experimental verification has been carried out to validate the analysis and study the effect of these parameters. The developed damping model for the structure is found to be in fairly good agreement with the measured data. Finally, the results of the analysis are discussed and rationalized.

Keywords: Slip damping, tack welded joint, thickness ratio, inplane bending stress

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