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1.
Semi-analytical method for solving Fokker-Planck's equations
Majeed Ahmed Al-Jawary, Ghassan Hasan Radhi, Jure Ravnik, 2017, original scientific article

Abstract: In this paper, the linear and nonlinear Fokker-Planck equations (FPE) are solved by a semi-analytical iterative technique. This technique was proposed by Temimi and Ansari (TAM) in 2011. It is used to obtain the exact solutions for the 1D, 2D and 3D FPE. We solve several linear and nonlinear examples to show that the method is efficient and applicable. The results demonstrate that the presented method is very effective and reliable and does not require any restrictive assumptions for nonlinear terms. A symbolic manipulator Mathematica®10 was used to evaluate terms in the iterative process.
Keywords: Fokker-Planck's equation, semi-analytical method, analytic solution, Brownian motion, Kolmogorov's equation
Published: 03.11.2017; Views: 352; Downloads: 241
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2.
The anchored pile wall optimization using NLP approach
Helena Vrecl-Kojc, 2005, original scientific article

Abstract: The type of a retaining structure as well as the structure configuration mainly depends on geological conditions. If geological, urban and other data allow an alternative, the costs should also be considered as an important factor. In geotechnical practise, pile walls are especially used in excavations, in the erection of traffic facilities and in the sanitation of landslides. This paper is aimed at presenting economical differences between cantilever and anchoring pile walls and the impact of different parameters on costs. The optimization method, which uses mathematical programming, gives an optimal solution to geometry, self-manufacturing costs, and other characteristics of the structure in a uniform optimization process. This paper presents the optimization process using the nonlinear programming (NLP) approach for the anchored pile wall. The application presented only serves to confirm the effectiveness of the proposed optimization method. Therefore, the retaining structure is situated in homogeneous non-cohesive soil at three different soil friction angles of 35°, 30° and 25°. The generalized analytical method, the USA method, which was first introduced by Bowles [3], isused in the application. The analysis of the results shows the impact of parameters, the main controlling factors, configuration geometry and savings. The optimal results allowed from 18 up to 47 per cent savings compared to the cantilever pile wall depending on ground and structure input data and the excavation depth.
Keywords: civil engineering, optimum design, retaining structures, USA analytical method, nonlinear programming
Published: 16.05.2018; Views: 301; Downloads: 26
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3.
Analytical solutions for one-dimensional consolidation in unsaturated soils considering the non-Darcy law of water flow
Jiwei Li, Huabin Wang, 2014, original scientific article

Abstract: Analytical solutions were derived for the non-linear, one-dimensional consolidation equations for unsaturated soils. The governing equations with a non-homogeneous mixed-boundary condition were presented, in which the water flow was assumed to be governed by a non-Darcy law, whereas the air flow followed the Darcy law. The non-Darcy law was actually the non-linear, flux-gradients relationship. The consolidation equations were thus present in a strong, non-linear way. In order to analytically solve the equation, a homotopy analysis method (HAM) was introduced in the study, which is an analytical technique for nonlinear problems. Firstly, a governing equation in a dimensionless form was derived for a one-dimensional consolidation under unsaturated soils. The method was then used for a mapping technique to transfer the original nonlinear differential equations to a number of linear differential equations. These differential equations were independent with respect to any small parameters, and were convenient for controlling the convergence region. After this transferring, a series solution to the equations was then obtained using the HAM by selecting the linear operator and the auxiliary parameters. Meanwhile, comparisons between the analytical solutions and the results of the finite-difference method indicate that the analytical solution is more efficient. Furthermore, our solutions indicate that the dissipation of air pressure is much faster than that of water pressure, and the values for the threshold gradient I have obvious effects on the dissipation values of the excess pore-water pressure, but no significant effect on that of the excess pore-air pressure.
Keywords: unsaturated soil, homotopy analysis method, analytical solutions, non-Darcy law, initial and boundary conditions
Published: 14.06.2018; Views: 140; Downloads: 50
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4.
Reinforced piled embankment for a high-speed railway over soft soil
Yan Zhuang, Xiaoyan Cui, 2015, original scientific article

Abstract: A geosynthetic, reinforced, piled embankment is an effective and economic method to solve the problems of possible bearing failure, unacceptable settlement and slope instability for an embankment built over soft soil; this has led to its widespread use, especially for high-speed railway embankments. Some design methods have been developed to assess the performance of these reinforced structures, which are mainly based on the results from small-scale models and numerical simulations. However, the reliability of these methods needs to be validated under full-scale field tests. This paper presents a numerical and analytical study for a full-scale field test of the Fengyang high-speed railway embankment. The results were analyzed and discussed in terms of the settlement of subsoil, the stressconcentration ratio (SCR), the axial force and the frictional stress of the pile. They showed that the settlement of the subsoil, from both the finite-element method (FEM) and the analytical method, were in good agreement with the measurement, and thus was a reliable parameter to assess the performance of the piled embankment with reasonable accuracy. The SCR was overestimated by the modified Terzaghi method, with a difference of 25%, while it was underestimated by the FEM, with a difference of approximately 20%. It was also shown that the tensile force in the reinforcement could be effectively assessed using the proposed analytical method, while it was overestimated by the FEM with a difference of 44%.
Keywords: reinforced piled embankment, high-speed railway, numerical simulation, analytical method
Published: 15.06.2018; Views: 349; Downloads: 22
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