• Journal of the Korean GEO-environmental Society
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• v.4 no.2
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• pp.93-104
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• 2003

Porous media consist of physically and chemically different materials and have an extremely complicated behavior due to the different material properties of each of its constituents. In addition, the internal structure of porous materials has generally a complex geometry that makes the description of its mechanical behavior quite complex. Thus, classical continuum mechanics cannot explain the behavior of materials with pore spaces, such as concrete, soils and organic materials in waste landfill. For these reasons, porous media theory has been developed in the nineteenth century. Biot had the greatest influence on the development of porous media theory. Biot's work has been referred by many authors in the literature. Development of numerous fundamental equations in porous media theory were made possible due to Biot's work. His contributions made the greatest influence on porous media theory. Therefore, it is highly advantageous to review Biot's publications. This work presents a review of Biot's work. It shows how porous media theory has been developing so far and provides a chance to discuss the contribution of his work to the modern porous media theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.153-163
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• 2000

The non-dimensional convective heat losses from each surface are investigated as a function of the non-dimensional fin length, width and the ratio of upper surface Biot number to bottom surface Biot number (Bi2/Bi1) using the three-dimensional separation of variables method. Heat loss ratio in view of each surface with the variation of Bi2/Bi1 is presented. The variation of the non-dimensioal temperare profile along the fin center line for a thermally asymmetric conditions is also presented.

• East Asian mathematical journal
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• v.36 no.4
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• pp.455-474
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• 2020

In this study, we investigate the latus rectum, one of the geometric measures of the conics, as one of the ways in which learners harmonize the geometric and algebraic approaches to conics from a pedagogical point of view. We also introduce the conical curve of Biot as presented in 'The Discourse on the Latus Rectum in conics(2013)' by Takeshi Sugimoto and reinterpret it for visualization and use as teaching material. Therefore, we expect that the importance of mathematical concepts will be recognized in conics and students can experience geometry learning that is explored in the school field and have a positive effect in developing the power to apply even in the context of applied problems.

• Journal of KSNVE
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• v.9 no.6
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• pp.1218-1226
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• 1999

In this paper, the extended Biot's semilinear model was developed. Combining the extended Biot model with the dynamic equation yields the nonlinear wave equation in poproelastic sound absorbing materials. Both perturbation and matching techniques are used to find solutions for nonlinear wave equations. By comparing results between linear and nonlinear wave solutions, characteristics of nonlinear waves in poroelastic sound abosrbing materials have been studied. Nonlinear waves were found to be attenuated faster than the linear ones. A maximum amplitude of the nonlinear wave occurred near its surface boundaries and decay quickly with distance from the surface. It has also been found that, if the amplitudes of linear waves are known at the surface boundaries, those of nonlinear ones can be determined. This will be the basis of finding effects of nonlinearity on the absorption coefficient and the transmission loss.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.109-120
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• 2002

The dimensionless heat loss from a modified asymmetric rectangular fin is investigated as a function of the fin top and tip Biot numbers using the two-dimensional separation of variables method. A rectangular fin is modified by attaching the wing on the top side of the fin. Fin effectiveness and efficiency with the variation of the location of the wing and the width of the wing are presented. The relationship between top surface Biot number and bottom surface Biot number as well as the relationship between the dimensionless wing height and the location of the wing for equal amount of heat loss is also discussed.

• Journal of the Korean Society for Nondestructive Testing
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• v.28 no.2
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• pp.112-118
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• 2008

In the present study, the dependence of ultrasonic phase velocity on porosity and frequency in cancellous bone was predicted using the Biot model and the modified Biot-Attenborough (MBA) model for propagation in fluid-saturated porous media. It was also compared with previously published measurements in human and bovine cancellous bones in vitro. It was shown that the phase velocity in cancellous bone decreased with increasing porosity and frequency The dependence of phase velocity on propagation angle in cancellous bone as predicted using the Schoenberg model together with the Biot model and tile MBA model which were modified to include the effect of angle. The theoretical models used in the present study advance our understanding of the interaction between ultrasound and cancellous bone and can be expected to be usefully employed for the diagnosis of osteoporosis.

• The Journal of the Acoustical Society of Korea
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• v.27 no.2E
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• pp.45-50
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• 2008

In recent years, quantitative ultrasound (QUS) technologies have played a growing role in the diagnosis of osteoporosis. Most of the commercial bone somometers measure speed of sound (SOS) and/or broadband ultrasonic attenuation (EUA) at peripheral skeletal sites. However, the QUS parameters are purely empirical measures that have not yet been firmly linked to physical parameters such as bone strength or porosity. In the present study, the theoretical models for wave propagation in cancellous bone, such as the Biot model, the stratified model, and the modified Biot-Attenborough (MBA) model, were applied to predict the dependence of phase velocity on porosity in cancellous bone. The optimum values for the input parameters of the three models in cancellous bone were determined by comparing the predictions with the previously published measurements in human cancellous bone in vitro. This modeling effort is relevant to the use of QUS in the diagnosis of osteoporosis because SOS is negatively correlated to the fracture risk of bone, and also advances our understanding of the relationship between phase velocity and porosity in cancellous bone.

• Proceedings of the Acoustical Society of Korea Conference
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• autumn
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• pp.183-186
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• 2004

Biot's theory and a modified Biot-Attenborough (MBA) model are applied to predict the dependences of acoustic characteristics on frequency and porosity in cancellous bone. The phase velocity and the attenuation coefficient predicted by both theories are compared with previous in vitro experimental measurements in terms of the mixed, the fast, and the slow waves. Biot's theory successfully predicts the dependences of phase velocity on frequency and porosity in cancellous bone, whereas a significant discrepancy is observed between predicted and measured attenuation coefficients. The MBA model is consistent with reported measurements for both dependences of phase velocity and attenuation coefficient on frequency and porosity. Based on the theoretical predictions from the MBA model, it is suggested that the attenuation coefficient of the mixed wave is dominated by the fast wave in the low-porosity region while it is dominated by the slow wave in the high-porosity region. This provides a qualitative explanation for the nonlinear relationship of attenuation of the mixed wave with porosity in cancellous bone.

• Geomechanics and Engineering
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• v.22 no.6
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• pp.553-564
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• 2020

In this study, a simple numerical approach for a circular tunnel opening in strain-softening surrounding rock is proposed considering out-of-plane stress and seepage force based on Biot's effective stress principle. The plastic region of strain-softening surrounding rock was divided into a finite number of concentric rings, of which the thickness was determined by the internal equilibrium equation. The increments of stress and strain for each ring, starting from the elastic-plastic interface, were obtained by successively incorporating the effect of out-of-plane stress and Biot's effective stress principle. The initial value of the outmost ring was determined using equilibrium and compatibility equations. Based on the Mohr-Coulomb (M-C) and generalized Hoek-Brown (H-B) failure criteria, the stress-increment approach for solving stress, displacement, and plastic radius was improved by considering the effects of Biot's effective stress principle and the nonlinear degradation of strength and deformation parameters in plastic zone incorporating out-of-plane stress. The correctness of the proposed approach is validated by numerical simulation.

• Journal of Mechanical Science and Technology
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• v.20 no.12
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• pp.2203-2208
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• 2006

Both 1-D and 2-D analytic methods are used for a rectangular fin optimization. Optimum heat loss is taken as 98% of the maximum heat loss. Temperature profile using 2-D analytic method and relative error of temperature along the fin length between 1-D and 2-D analytic methods are presented. Increasing rate of the optimum heat loss with the variation of Biot number and decreasing rate of that with the variation of the fin base length are listed. Optimum fin tip length using 2-D analytic method and relative error of that between 1-D and 2-D analytic methods are presented as a function of Biot numbers ratio.