ANALYTICAL AND NUMERICAL SOLUTIONS OF ONE-DIMENSIONAL NONLINEAR CONSOLIDATION CONSIDERING LOADING RATES AND DOUBLE-LAYERED SOILS

2017 ◽  
Author(s):  
Marcos Antonio Gonçalves da Silva Filho ◽  
Roberto Quevedo Quispe ◽  
Deane Roehl
Keyword(s):  
Numerical Solutions ◽  
Layered Soils ◽  
One Dimensional ◽  
Loading Rates ◽  
Analytical And Numerical Solutions ◽  
Nonlinear Consolidation

scholarly journals Analytical and Numerical Solutions of Pollution Concentration with Uniformly and Exponentially Increasing Forms of Sources

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
N. Manitcharoen ◽  
B. Pimpunchat
Keyword(s):  
Source Term ◽  
Numerical Solutions ◽  
Pollution Source ◽  
Suitable Model ◽  
One Dimensional ◽  
Analytical And Numerical Solutions ◽  
Advection Dispersion ◽  
Pollutant Sources ◽  
Important Basis ◽  
Incremental Concentration

The study of pollution movement is an important basis for solving water quality problems, which is of vital importance in almost every country. This research proposes the motion of flowing pollution by using a mathematical model in one-dimensional advection-dispersion equation which includes terms of decay and enlargement process. We are assuming an added pollutant sources along the river in two cases: uniformly and exponentially increasing terms. The unsteady state analytical solutions are obtained by using the Laplace transformation, and the finite difference technique is utilized for numerical solutions. Solutions are compared by relative error values. The result appears acceptable between the analytical and numerical solutions. Varying the value of the rate of pollutant addition along the river (q) and the arbitrary constant of exponential pollution source term (λ) is displayed to explain the behavior of the incremental concentration. It is shown that the concentration increases as q and λ increase, and the exponentially increasing pollution source is a suitable model for the behavior of incremental pollution along the river. The results are presented and discussed graphically. This work can be applied to other physical situations described by advection-dispersion phenomena which are affected by the increase of those source concentrations.

Analytical and Numerical Solutions of One-Dimensional Cold Plasma Equations

2021 ◽  
Vol 61 (9) ◽  
pp. 1485-1503
Author(s):  
O. S. Rozanova ◽  
E. V. Chizhonkov
Keyword(s):  
Cold Plasma ◽  
Numerical Solutions ◽  
One Dimensional ◽  
Analytical And Numerical Solutions

scholarly journals Time dependent monochromatic scattering of radiation in one dimensional media: Analytical and numerical solutions

Astrophysics ◽  
2008 ◽  
Vol 51 (1) ◽  
pp. 85-98
Author(s):  
D. I. Nagirner ◽  
S. L. Kirusheva
Keyword(s):  
Numerical Solutions ◽  
Time Dependent ◽  
One Dimensional ◽  
Analytical And Numerical Solutions

scholarly journals Finite Analytic Method for One-Dimensional Nonlinear Consolidation under Time-Dependent Loading

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Dawei Cheng ◽  
Wenke Wang ◽  
Xi Chen ◽  
Zaiyong Zhang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Time Dependent ◽  
Analytic Method ◽  
Partial Differential ◽  
One Dimensional ◽  
Finite Analytic Method ◽  
Nonlinear Consolidation

For one-dimensional (1D) nonlinear consolidation, the governing partial differential equation is nonlinear. This paper develops the finite analytic method (FAM) to simulate 1D nonlinear consolidation under different time-dependent loading and initial conditions. To achieve this, the assumption of constant initial effective stress is not considered and the governing partial differential equation is transformed into the diffusion equation. Then, the finite analytic implicit scheme is established. The convergence and stability of finite analytic numerical scheme are proven by a rigorous mathematical analysis. In addition, the paper obtains three corrected semianalytical solutions undergoing suddenly imposed constant loading, single ramp loading, and trapezoidal cyclic loading, respectively. Comparisons of the results of FAM with the three semianalytical solutions and the result of FDM, respectively, show that the FAM can obtain stable and accurate numerical solutions and ensure the convergence of spatial discretization for 1D nonlinear consolidation.

scholarly journals Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model

2012 ◽  
Vol 25 (2-4) ◽  
pp. 243-268 ◽  
Author(s):  
Andrés Alessandro León Baldelli ◽  
Blaise Bourdin ◽  
Jean-Jacques Marigo ◽  
Corrado Maurini
Keyword(s):  
Thin Film ◽  
Numerical Solutions ◽  
Variational Model ◽  
One Dimensional ◽  
Analytical And Numerical Solutions

Nonlinear consolidation of thin layers subjected to time-dependent loading

2007 ◽  
Vol 44 (6) ◽  
pp. 717-725 ◽  
Author(s):  
Enrico Conte ◽  
Antonello Troncone
Keyword(s):  
Numerical Solutions ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Solution Procedure ◽  
Thin Layers ◽  
Time Dependent ◽  
One Dimensional ◽  
Clay Layers ◽  
Analytical Expressions ◽  
Nonlinear Consolidation

The paper deals with one-dimensional consolidation of saturated clays with variable compressibility and permeability. A formulation is developed to analyse the consolidation of thin clay layers subjected to time-dependent loading. Moreover, a simple solution procedure is presented, which makes use of some analytical expressions derived in this study in conjunction with the Fourier series. Comparisons with other analytical and numerical solutions are shown, and some aspects of the nonlinear consolidation caused by time-dependent loading are highlighted.Key words: one-dimensional consolidation, nonlinear theory, time-dependent loading, excess pore-water pressure, settlement rate.

Analytical and Numerical Solutions of Generalized Dispersion Equations for One-Dimensional Damped Plasma Oscillation

2005 ◽  
Vol 43 (4) ◽  
pp. 479-485 ◽  
Author(s):  
B. V. Alekseev ◽  
A. E. Dubinov ◽  
I. D. Dubinova
Keyword(s):  
Numerical Solutions ◽  
Plasma Oscillation ◽  
One Dimensional ◽  
Dispersion Equations ◽  
Analytical And Numerical Solutions
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