Concept Of Equivalent Time Research Articles

Cellular Automata Approach to Hydration Heat of Concrete Based on Equivalent Time

Cellular automata can be used to analyze a physical system which is satisfying differential equations. A cellular automata program for a thermal analysis of hydration heat was developed. Based on the fundamental theory of cellular automata, the heat conduction equation was deduced for validating the cellular automata approach. By introduction of the concept of equivalent time, the variation of the chemical reaction rate of hydration heat with temperature was studied by use of the Arrhenius function. The relationship between the adiabatic temperature rise and equivalent time was determined by analyzing testing data．A parametric analysis of ambient temperature and concrete slab thickness was also conducted. The temperature rise of concrete increases with increasing ambient temperature and thickness of the slab.

초고성능 콘크리트의 수화발열 및 역학적 특성 모델

Structural Engineering & Bridges Research Division, Korea Institute of Construction Technology, Goyang 411-714, KoreaABSTRACT Concrete has excellent mechanical properties, high durability, and economical advantages over other constructionmaterials. Nevertheless, it is not an easy task to apply concrete to long span bridges. That's because concrete has a low strengthto weight ratio. Ultra high performance concrete (UHPC) has a very high strength and hence it allows use of relatively small sectionfor the same design load. Thus UHPC is a promising material to be utilized in the construction of long span bridges. However,there is a possibility of crack generation during the curing process due to the high binder ratio of UHPC and a consequent largeamount of hydration heat. In this study, adiabatic temperature rise and mechanical properties were modeled for the stress analysisdue to hydration heat. Adiabatic temperature rise curve of UHPC was modeled superposing 2-parameter model and S-shaped func-tion, and the Arrhenius constant was determined using the concept of equivalent time. The results are verified by the mock-up testmeasuring the temperature development due to the hydration of UHPC. In addition, models for mechanical properties such as elas-tic modulus, tensile strength and compressive strength were developed based on the test results from conventional load test andultrasonic pulse velocity measurement.Keywords : UHPC, heat of hydration heat, adiabatic temperature rise curve, equivalent time

Equivalent times and one-dimensional elastic viscoplastic modelling of time-dependent stress–strain behaviour of clays

This paper describes the recent concept of equivalent time and how it can be used in a revised version of an earlier elastic viscoplastic model for one-dimensional straining of clays. It clarifies how parameters in the model can be determined using data from single-stage or multistage creep tests. The model can describe one-dimensional stress or strain responses under general conditions that include multistage loading with creep straining, continuous loading, and unloading or reloading. It also describes modelling for constant rate of straining tests, constant rate of stressing tests, and relaxation tests. Preconsolidation pressures are shown to depend on unloading–reloading, aging, and other loading processes. Key words : clay, compression, creep, equivalent time, elastic viscoplastic, preconsolidation pressure.

Modeling fission track annealing in apatite: An assessment of uncertainties

Abstract If a model is to be used as the basis of an interpretive scheme then it is essential to have some idea of the uncertainties associated with the model predictions. Equations describing the annealing of induced fission tracks in Durango apatite can be applied to variable temperature thermal histories over geologic time scales, but the calculation of confidence limits on the predicted value is not straightforward. The basis of the modeling method is the concept of equivalent time, t 0 , which allows a pair of variable temperature annealing steps, each of time Δ t and temperatures T 1 and T 2 respectively, to be expressed as a single isothermal annealing step of length (Δ t + t 0 ) at temperature T 2 . The numerical approximation is very stable, roundoff errors being insignificant if the time step is less than ≈ 2% of the model time. Error in the predicted value due to uncertainties in the regression coefficients of the model equations is difficult to ascertain analytically and we adopt a Monte Carlo technique to obtain an estimate of this error. Two cases are considered: a comparison with variable temperature annealing experiments in the laboratory and prediction of fission track parameters for simple thermal histories over geologic time scales. Monte Carlo simulations suggest that for variable temperature annealing over an eight hour period, the 2σ error in the predicted value of mean track length is 1-1.5 μm; for thermal histories of 100 Ma (cooling from 100 to 0°C, heating from 0 to 100°C and isothermal heating at 50°C), the 2σ errors for the predicted model ages range from 8 to 26 Ma. A comparison between three different models that have been used to describe the annealing of fission tracks in apatite reveals that there is close agreement between the results from the fanning Arrhenius model and the first order model for thermal histories at > 95°C. This coincidence of results could explain the apparent success of the first order model as an interpretive tool in the past.

Role of Debris Cover in the Thermal Physics of Glaciers

AbstractA mathematical model is presented of non-stationary melting processes of ice including particles of morainic material. The problem is treated as a Stephen-type one with the phase boundary of ice melting being located under the debris cover. The main terms of the heat-balance equation for a glacier surface are solar radiation and convective heat transfer. The quantitative relationships characterizing the effect of glacier run-off augmentation from under a thin layer of debris cover are obtained for different bulk moraine concentrations inside the ice. The concept of equivalent time is introduced. It is defined as the time elapsed until the moment the sub-moraine ice-ablation rate becomes equal to the ablation rate of clean ice. This moment signifies the beginning of the shielding stage. Thus, a glacier can be considered as a self-controlling system with respect to its summer run-off. A series of numerical tests for Djankuat glacier, Central Caucasus, has been carried out. The dynamics of moraine-cover growth and alterations of seasonal ablation rate under debris show perfect agreement between the computed data and the results of 14 years of direct observations. Some practical recommendations concerning artificial blackening of a glacier surface for augmentation of liquid run-off are presented. Conditions promoting increase of run-off are: relatively high albedo, relatively low summer air temperature, and relatively small convective heat transfer between the air and the ice surface. The method of artificially blackening a glacier surface is by means of a durable thin dark polymer film. In conclusion, some further aspects of the problem are discussed.

Role of Debris Cover in the Thermal Physics of Glaciers

AbstractA mathematical model is presented of non-stationary melting processes of ice including particles of morainic material. The problem is treated as a Stephen-type one with the phase boundary of ice melting being located under the debris cover. The main terms of the heat-balance equation for a glacier surface are solar radiation and convective heat transfer. The quantitative relationships characterizing the effect of glacier run-off augmentation from under a thin layer of debris cover are obtained for different bulk moraine concentrations inside the ice. The concept of equivalent time is introduced. It is defined as the time elapsed until the moment the sub-moraine ice-ablation rate becomes equal to the ablation rate of clean ice. This moment signifies the beginning of the shielding stage. Thus, a glacier can be considered as a self-controlling system with respect to its summer run-off. A series of numerical tests for Djankuat glacier, Central Caucasus, has been carried out. The dynamics of moraine-cover growth and alterations of seasonal ablation rate under debris show perfect agreement between the computed data and the results of 14 years of direct observations. Some practical recommendations concerning artificial blackening of a glacier surface for augmentation of liquid run-off are presented. Conditions promoting increase of run-off are: relatively high albedo, relatively low summer air temperature, and relatively small convective heat transfer between the air and the ice surface. The method of artificially blackening a glacier surface is by means of a durable thin dark polymer film. In conclusion, some further aspects of the problem are discussed.

A Reliability Model for Dependent Failures in Parallel Redundant Systems

The concept of Equivalent time is introduced to find the hazard rates of elements in a parallel redundant systems which is subject to dependent failures. True acceleration is defined as an adjunct to this concept.