One-dimensional consolidation theory: unsaturated soils

1979 ◽  
Vol 16 (3) ◽  
pp. 521-531 ◽  
Author(s):  
Delwyn G. Fredlund ◽  
Jamshed U. Hasan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Pore Water ◽  
Unsaturated Soils ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Partial Differential ◽  
Total Load ◽  
One Dimensional ◽  
Consolidation Theory

A one-dimensional consolidation theory is presented for unsaturated soils. The assumptions made are in keeping with those used in the conventional theory of consolidation for saturated soils, with the additional assumption that the air phase is continuous. Two partial differential equations are derived to describe the transient processes taking place as a result of the application of a total load to an unsaturated soil.After a load has been applied to the soil, air and water flow simultaneously from the soil until equilibrium conditions are achieved. The simultaneous solution of the two partial differential equations gives the pore-air and pore-water pressures at any time and any depth throughout the soil. Two families of dimensionless curves are generated to show the pore-air and pore-water dissipation curves for various soil properties.For the case of an applied total load, two equations are also derived to predict the initial pore-air and pore-water pressure boundary conditions. An example problem demonstrates the nature of the results.

scholarly journals Analytical Solution and Application for One-Dimensional Consolidation of Tailings Dam

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Hai-ming Liu ◽  
Gan Nan ◽  
Wei Guo ◽  
Chun-he Yang ◽  
Chao Zhang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Pore Water ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Great Influence ◽  
Tailings Dam ◽  
Partial Differential ◽  
One Dimensional ◽  
The Stability

The pore water pressure of tailings dam has a very great influence on the stability of tailings dam. Based on the assumption of one-dimensional consolidation and small strain, the partial differential equation of pore water pressure is deduced. The obtained differential equation can be simplified based on the parameters which are constants. According to the characteristics of the tailings dam, the pore water pressure of the tailings dam can be divided into the slope dam segment, dry beach segment, and artificial lake segment. The pore water pressure is obtained through solving the partial differential equation by separation variable method. On this basis, the dissipation and accumulation of pore water pressure of the upstream tailings dam are analyzed. The example of typical tailings is introduced to elaborate the applicability of the analytic solution. What is more, the application of pore water pressure in tailings dam is discussed. The research results have important scientific and engineering application value for the stability of tailings dam.

Analysis of One-Dimensional Thermal Consolidation for Saturated Soil Considering Different Permeabilities

2014 ◽  
Vol 919-921 ◽  
pp. 641-644
Author(s):  
Cai Xia Guo ◽  
Rui Qian Wu
Keyword(s):  
Pore Water ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Saturated Soil ◽  
Excess Pore Water Pressure ◽  
One Dimensional ◽  
Consolidation Theory ◽  
Thermal Consolidation ◽  
The One ◽  
Excess Pore

Based on the analytical solutions of pore-water pressure and settlement. Problems of the one-dimensional thermal consolidation of saturated soil considering three different permeabilities were analyzed. Aiming at each permeability of thermal consolidation theory, compared with the corresponding Terzaghis consolidation theory, the one-dimensional thermal consolidation behaviour of saturated soil was analyzed in terms of excess pore-water pressure, the settlement. The results show that the permeability plays an important role in the thermal consolidation. The more permeability, the quicker pore-water pressure dissipation and the rate of settlement. Settlement of ground is more sensitive to temperature condition than the excess pore-water pressure. The behaviour of excess pore-water pressure in the process of thermal consolidation is very similar to the corresponding Terzaghis theory.

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

Consolidation Theory for Composite Ground with Granular Columns Based on Different Calculation Models

2011 ◽  
Vol 261-263 ◽  
pp. 1534-1538
Author(s):  
Yu Guo Zhang ◽  
Ya Dong Bian ◽  
Kang He Xie
Keyword(s):  
Pore Water ◽  
Analytical Solutions ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Vertical Flow ◽  
Excess Pore Water Pressure ◽  
Consolidation Theory ◽  
Composite Ground ◽  
Granular Column ◽  
Excess Pore

The consolidation of the composite ground under non-uniformly distributed initial excess pore water pressure along depth was studied in two models which respectively considering both the radial and vertical flows in granular column and the vertical flow only in granular column, and the corresponding analytical solutions of the two models were presented and compared with each other. It shows that the distribution of initial excess pore water pressure has obvious influence on the consolidation of the composite ground with single drainage boundary, and the rate of consolidation considering the radial-vertical flow in granular column is faster than that considering the vertical flow only in granular column.

scholarly journals GROUP PROPERTIES OF A ONE-DIMENSIONAL NONLINEAR POROELASTICITY EQUATION

2019 ◽  
Vol 4 (1) ◽  
pp. 149-155
Author(s):  
Kholmatzhon Imomnazarov ◽  
Ravshanbek Yusupov ◽  
Ilham Iskandarov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Lie Algebra ◽  
Three Dimensional ◽  
Group Classification ◽  
Second Order ◽  
Partial Differential ◽  
One Dimensional ◽  
Preliminary Group

This paper studies a class of partial differential equations of second order , with arbitrary functions and , with the help of the group classification. The main Lie algebra of infinitely infinitesimal symmetries is three-dimensional. We use the method of preliminary group classification for obtaining the classifications of these equations for a one-dimensional extension of the main Lie algebra.

Aspects of the behaviour of compacted clayey soils on drying and wetting paths

2002 ◽  
Vol 39 (6) ◽  
pp. 1341-1357 ◽  
Author(s):  
Jean-Marie Fleureau ◽  
Jean-Claude Verbrugge ◽  
Pedro J Huergo ◽  
António Gomes Correia ◽  
Siba Kheirbek-Saoud
Keyword(s):  
Water Content ◽  
Pore Water ◽  
Unsaturated Soils ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Dry Density ◽  
Clayey Soils ◽  
Maximum Dry Density ◽  
Optimum Water Content ◽  
Optimum Water

A relatively large number of drying and wetting tests have been performed on clayey soils compacted at the standard or modified Proctor optimum water content and maximum density and compared with tests on normally consolidated or overconsolidated soils. The results show that drying and wetting paths on compacted soils are fairly linear and reversible in the void ratio or water content versus negative pore-water pressure planes. On the wet side of the optimum, the wetting paths are independent of the compaction water content and can be approached by compaction tests with measurement of the negative pore-water pressure. Correlations have been established between the liquid limit of the soils and such properties as the optimum water content and negative pore-water pressure, the maximum dry density, and the swelling or drying index. Although based on a limited number of tests, these correlations provide a fairly good basis to model the drying–wetting paths when all the necessary data are not available.Key words: compaction, unsaturated soils, clays, drying, wetting, Proctor conditions.

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