One-dimensional Consolidation of Thawing Soils

1971 ◽  
Vol 8 (4) ◽  
pp. 558-565 ◽  
Author(s):  
N. R. Morgenstern ◽  
J. F. Nixon
Keyword(s):  
Moving Boundary ◽  
Practical Interest ◽  
Moving Boundary Problem ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Pressure Distributions ◽  
Thaw Consolidation ◽  
Degree Of Consolidation ◽  
Compressible Soil ◽  
Excess Pore Pressures

The physics of consolidation of a thawing soil is formulated in terms of the well-known theories of heat conduction and of linear consolidation of a compressible soil. A moving boundary problem results, and closed form solutions have been obtained for several cases of practical interest. The results are presented in terms of normalized pore pressure distributions. It is shown that the excess pore pressures and the degree of consolidation in thawing soils depend primarily on the thaw consolidation ratio.

Thaw–Consolidation Tests on Remoulded Clays

1973 ◽  
Vol 10 (1) ◽  
pp. 25-40 ◽  
Author(s):  
Norbert R. Morgenstern ◽  
Laurence B. Smith
Keyword(s):  
General Solution ◽  
Soil Behavior ◽  
One Dimensional ◽  
Pore Pressures ◽  
Thaw Consolidation ◽  
Degree Of Consolidation ◽  
Stress Boundary Conditions ◽  
Excess Pore Pressures ◽  
Stress Boundary ◽  
Excess Pore

A general solution to the problem of one-dimensional thaw–consolidation has been formulated by Morgenstern and Nixon (Can. Geotech. J. 8, p. 558, 1971). In order to assess the validity of the theory it was necessary to develop a special oedometer (permode) which could impose the necessary thermal and stress boundary conditions for one-dimensional thaw–consolidation.The permode permits the measurement of settlements, temperatures at various depths on the side of the sample, and excess pore pressures at the base of the sample during thaw–consolidation.Controlled thaw–consolidation tests were carried out on three types of remoulded clays. The resulting data showed that the excess pore pressures and the degree of consolidation in a thawing soil depend primarily on the thaw–consolidation ratio. The results obtained demonstrate that the theory adequately represents the soil behavior. Applications of the theory in practice are indicated.

scholarly journals One-dimensional large-strain thaw consolidation using nonlinear effective stress – void ratio – hydraulic conductivity relationships

2018 ◽  
Vol 55 (3) ◽  
pp. 414-426 ◽  
Author(s):  
Simon Dumais ◽  
Jean-Marie Konrad
Keyword(s):  
Heat Transfer ◽  
Hydraulic Conductivity ◽  
Effective Stress ◽  
Void Ratio ◽  
Moving Boundary ◽  
Initial Conditions ◽  
Large Strain ◽  
One Dimensional ◽  
Consolidation Theory ◽  
Thaw Consolidation

A one-dimensional model for the consolidation of thawing soils is formulated in terms of large-strain consolidation and heat-transfer equations. The model integrates heat transfer due to conduction, phase change, and advection. The hydromechanical behaviour is modelled by large-strain consolidation theory. The equations are coupled in a moving boundary scheme developed in Lagrangian coordinates. Finite strains are allowed and nonlinear effective stress – void ratio – hydraulic conductivity relationships are proposed to characterize the thawing soil properties. Initial conditions and boundary conditions are presented with special consideration for the moving boundary condition at the thaw front developed in terms of large-strain consolidation. The proposed model is applied and compared with small-strain thaw consolidation theory in a theoretical working example of a thawing fine-grained soil sample. The modelling results are presented in terms of temperature, thaw penetration, settlements, void ratio, and excess pore-water pressures.

scholarly journals COMPUTATION OF ONE DIMENSIONAL ONE PHASE STEFAN PROBLEMS

2020 ◽  
Author(s):  
V.G. Naidu ◽  
P. Kanakadurga Devi
Keyword(s):  
Single Phase ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Initial Time ◽  
Neumann Condition ◽  
Type Problem ◽  
Governing Equations ◽  
Accurate Analysis ◽  
One Dimensional ◽  
Stefan Problems

To design an efficient device or to calculate the performance of existing device requires an accurate analysis of parameters involved in the system. In this work, an efficient front tracking finite difference method is developed to solve one dimensional single phase moving boundary problem with Neumann condition. The basic difficulty apart from the need to find the moving boundary presented, that there is no domain for the first phase at initial time. This difficulty is handled by the age old principle of basic mathematics. Naturally, giving symbolic names to the unknowns by modelling the problem, governing equations are developed with the conditions of the Stefan type problem, solved it and compared the obtained solutions with existing results wherever possible.

Consolidation of a soil layer subsequent to cessation of deposition

2005 ◽  
Vol 42 (2) ◽  
pp. 678-682
Author(s):  
Guofu Zhu ◽  
Jian-Hua Yin
Keyword(s):  
Pore Pressure ◽  
Soil Layer ◽  
Average Degree ◽  
Excess Pore Pressure ◽  
Triangular Distribution ◽  
Pressure Distributions ◽  
Pore Pressures ◽  
Degree Of Consolidation ◽  
Excess Pore Pressures ◽  
Excess Pore

It is necessary in certain cases to estimate the progress of consolidation in a soil layer that has ceased increasing in thickness over time. In this paper, the existing excess pore pressures for two time–thickness relations are used as the "initial" pore pressures for analysing the consolidation of soil subsequent to the cessation of deposition. Average degrees of consolidation of the soil layer are presented for one-way drainage and two-way drainage boundary conditions. The average degrees of consolidation are compared with those for uniform and triangular initial excess pore pressure distributions. It is found that the average degree of consolidation for one-way drainage boundaries can be estimated using the value for the triangular distribution. The average degree of consolidation for two-way drainage boundaries is bound by the averages for both the uniform and the triangular initial excess pore pressure distributions.Key words: consolidation, deposition, drainage, settlement, soil.

MODELLING SCAFFOLD OCCUPATION BY A GROWING, NUTRIENT-RICH TISSUE

2007 ◽  
Vol 17 (supp01) ◽  
pp. 1721-1750 ◽  
Author(s):  
DUNCAN J. WILSON ◽  
JOHN R. KING ◽  
HELEN M. BYRNE
Keyword(s):  
Cell Growth ◽  
Potential Problem ◽  
Moving Boundary ◽  
Deterministic Model ◽  
Porous Scaffold ◽  
Linear Complementarity ◽  
Moving Boundary Problem ◽  
Two Dimensional ◽  
One Dimensional ◽  
Nutrient Limitations

In this paper we present a simple deterministic model of a biological tissue growing within a porous scaffold. By neglecting the effects of nutrient limitations and intercellular pressure on cell growth, and by using Darcy's law to model the cells' movement through the scaffold, our model is formulated as a moving boundary problem. Due to the difficulty in solving the resulting system, we reformulate it as a linear complementarity problem using the Baiocchi transformation, and give both one-dimensional analytical solutions and two-dimensional numerical ones. We then focus on the behaviour of the moving boundary as the colony approaches confluence, using asymptotic analysis to derive the time of confluence and the shape of the moving boundary; we show in particular that the moving boundary evolves to an ellipse. We also show that pressures increase considerably in the tissue shortly before the scaffold is filled, and identify the potential problem for tissue engineers of a "slit" being left devoid of cells.

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