• 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 Geotechnical Society
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• v.24 no.8
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• pp.5-12
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• 2008

Biot proposed the frequency dependent formulation for the propagation of elastic waves in saturated media based on the coupled theory mixtures. Based on Biot theory, a special frequency called 'the characteristic frequency' contains unique information of the permeability of soils. The characteristic frequency is measured from I/Q (inverse quality factor) versus frequency curve by an acoustic sweep test, and the permeability of soils is computed from Biot equation. In this paper, laboratory tests are performed at The University of Mississippi using a large test box. The measured characteristic frequency is consistently obtained at 3500 Hz for mortar sands. The computed permeability of mortar sands based on Biot equation turned out 2.01 $10^{-4}m/sec$, while the permeability from the laboratory constant head test turned out 1.49 $10^{-4}m/sec$. This paper addresses the theoretical background and experimental procedure of this technique.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.934-937
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• 2006

This investigation presents a topology formulation to design optimal poroelastic acoustic foams to maximize absorbing ability. For successful formulation, a single set of equations based on Biot's theory is adopted and an appropriate material interpolation strategy is newly developed. Because there was no earlier attempt to solve poroelastic acoustic foam design problems in topology optimization setting, many challenging issues including modeling and interpolation must be addressed. First, the simulation accuracy by a proposed unified model encompassing acoustic air and poroelastic material was checked against analytical and numerical results. Then a material interpolation scheme yielding a distinct acoustic air-poroelastic material distribution was developed. Using the proposed model and interpolation scheme, the topology optimization of a two-dimensional poroelastic acoustic foam for maximizing its absorption coefficient was carried out. Numerical results show that the absorption capacity of an optimized foam layout considerably increases in comparison with a nominal foam layout.

• Proceedings of the Korean Society for Rock Mechanics Conference
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• 2000.09a
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• pp.105-115
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• 2000

As large underground projects such as radioactive waste disposal, hot water and heat storage, and geothermal energy become influential, the study, which consider all aspects of thermics, hydraulics and mechanics would be needed. Thermo Hydro-Mechanical coupling analysis is one of the most complex numerical technique because it should be implemented with the combined three governing equations to analyze the behavior of rock mass. In this study, finite element code, which is based on Biot's consolidation theory, was developed to analyze the thermo-hydro-mechanical coupling in continuum rock mass. To verify the implemented program, one-dimensional consolidation model under the isothermal and non-isothermal conditions was analyzed and was compared with the analytic solution. The parametric study on two-dimensional consolidation was also performed and the effects of several factors such as poisson's ratio and hydraulic anisotropy on rock mass behavior were investigated. In the future, this program would be revised to be used for analysis of general discontinuous media with incorporating discrete joint model.

• Tunnel and Underground Space
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• v.10 no.3
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• pp.355-365
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• 2000

As large underground projects such as radioactive waste disposal, hot water and heat storage, and geothermal energy become influential, the study, which consider all aspects of thermics, hydraulics and mechanics would be needed. Thermo-Hydro-Mechanical coupling analysis is one of the most complex numerical technique because it should be implemented with the combined three governing equations to analyze the behavior of rock mass. In this study, finite element code, which is based on Biot's consolidation theory, was developed to analyze the thermo-hydro-mechanical coupling in continuum rock mass. To verify the implemented program, one-dimensional consolidation model under the isothermal and non-isothermal conditions was analyzed and was compared with the analytic solution. The parametric study on two-dimensional consolidation was also performed and the effects of several factors such as poisson's ratio and hydraulic anisotropy on rock mass behavior were investigated. In the future, this program would be revised to be used for analysis of general discontinuous media with incorporating discrete joint model.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1992.10a
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• pp.168-173
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• 1992

In the design and construction of underground structures, it is essential to accurately predict the structural behavior of the fluid-saturated ground during and after excavation. Terzaghi and Biot established the theory for the behavior of such two phase material. For the purpose of analysing the saturated porous solid system, finite element procedure provides a powerful tool. In this paper, a finite element analysis procedure based upon Biot's theory is presented to evaluate the deformation of solid skeleton and pore pressure of entraped fluid. Teraghi's onf-dimensional and Gibson's two-dimensional problems are solved using Q4 and Q8 element to verify the program validity.

• Journal of the Korean Geotechnical Society
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• v.36 no.12
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• pp.7-16
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• 2020

This study presents an acoustic technique to estimate the hydraulic conductivity of soils. Acoustic attenuation and propagation velocity spectra were measured for dry and saturated sandy specimens to confirm that the relationship between Biot's characteristic frequency and its associated hydraulic conductivity exists only for saturated soils. From the experiments presented in this paper, both attenuation-based and propagation-velocity-based techniques resulted in almost identical characteristic frequencies for saturated soils. The propagation velocity based measurements, however, show a a a slightly clearer trend compared to the attenuation based measurements. The results also show that the acoustically estimated hydraulic conductivities of soils agree well with constant head laboratory test results, demonstrating that this acoustic technique can be a useful nondestructive tool to estimate the hydraulic conductivity of sandy or silty soils.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.11a
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• pp.938-941
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• 2006

We present a new design method of one-dimensional multi-layered acoustic foams for transmission loss maximization by topology optimization. Multi-layered acoustic foam sequences consisting of acoustic air layers and poroelastic material layers are designed for target frequency values. For successful topology optimization design of multi-layered acoustic foams, the material interpolation concept of topology optimization is adopted. In doing so, an acoustic air layer is modeled as a limiting poroelastic material layer; acoustic air and poroelastic material are handled by a single set of governing equations based on Biot's theory. For efficient analysis of a specific multi-layered foam appearing during optimization, we do not solve the differential equations directly, but we use an efficient transfer matrix approach which can be derived from Biot's theory. Through some numerical case studies, the proposed design method for finding optimal multi-layer sequencing is validated.

• Coupled systems mechanics
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• v.11 no.2
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• pp.93-106
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• 2022

The total embankment settlement consists of three stages: the initial settlement, the primary consolidation settlement, and the secondary consolidation settlement. The total embankment settlement is largely controlled by the primary consolidation settlement, which is usually computed with numerical models that implement Biot's theory of consolidation. The key parameter that affects the primary consolidation time is the coefficient of permeability. Due to the complex stress and strain states in the foundation soil under the embankment, to be able to predict the consolidation time more precisely, aside from porosity-dependency, the strain-dependency of the coefficient of permeability should be also taken into account in numerical analyses. In this paper, we propose a two-dimensional plane strain numerical model of embankment primary consolidation, which implements Biot's theory of consolidation with both porosity-dependent and strain-dependent coefficient of permeability. We perform several numerical simulations. First, we demonstrate the influence of the strain-dependent coefficient of permeability on the computed results. Next, we validate our numerical model by comparing computed results against in-situ measurements for two road embankments: one near the city of Saga, and the other near the city of Boston. Finally, we give our concluding remarks.