Transient seepage model for saturated–unsaturated soil systems: a geotechnical engineering approach

1987 ◽  
Vol 24 (4) ◽  
pp. 565-580 ◽  
Author(s):  
L. Lam ◽  
D. G. Fredlund ◽  
S. L. Barbour
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Finite Element Model ◽  
Unsaturated Soil ◽  
Unsaturated Zone ◽  
Element Model ◽  
Element Formulation ◽  
Soil System ◽  
Governing Differential Equation ◽  
Transient Seepage

A two-dimensional finite element model is proposed to simulate transient seepage for complex groundwater flow systems. The complete soil system is treated as a continuum encompassing flow in both saturated and unsaturated zones. In the unsaturated zone, the air phase is assumed to be continuous and open to atmospheric pressure. The coefficient of permeability of the unsaturated soil is assumed to be a function of pore-water pressure.The governing differential equation is derived within a framework familiar to geotechnical engineers. The stress state variables and the constitutive relationships for an unsaturated soil are used in the derivation. The finite element solution to the governing differential equation is based on the Galerkin weighted-residual method. The nonlinearity of the equation is solved by iterative procedures.The finite element formulation is implemented into a computer model named TRASEE. The model can be applied to a wide variety of problems involving complex boundary conditions and geometries with arbitrary degrees of heterogeneity and anisotropy. Example problems are presented to demonstrate the capabilities of the model. The results indicate that the quantity of water flow in the unsaturated zone may be substantial, and that the phreatic line is not a flow line. It has been found that the traditional "saturated-only" flow-net technique can be approximated as a special case to the proposed saturated–unsaturated model. Key words: unsaturated flow, finite element model, phreatic line, permeability function, transient seepage.

Finite Element Analysis of Beams With Constrained Damping Treatment Modeled Via Fractional Derivatives

1997 ◽  
Vol 50 (11S) ◽  
pp. S216-S224 ◽  
Author(s):  
Luis E. Sua´rez ◽  
Arsalan Shokooh ◽  
Jose´ Arroyo
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Single Layer ◽  
Element Model ◽  
Beam Element ◽  
Element Formulation ◽  
Beam Model ◽  
Element Analysis ◽  
Damping Material ◽  
Derivatives Of

This paper presents a finite element formulation for the modeling of beams and frames with artificial damping provided by means of a constrained single layer of damping material. The behavior of the damping material is described using the fractional derivative model of viscoelasticity. In this model, the first order derivatives of the strains in the constitutive equations of the viscoelastic materials are replaced by derivatives of order α < 1. The finite element model developed is a one-dimensional beam element with three degrees of freedom per node. The dynamic response is calculated with a procedure involving a transformation of the original equations of motion to the state space and its decoupling with the eigenvectors of a special eigenvalue problem. The accuracy of the modal properties obtained with the beam model is compared with those calculated from a more elaborate plane stress finite element model. It was found that the proposed beam element provides very accurate results and with much lower computational costs than the 2-D model.

An Efficient Three Nodded Finite Element Formulation for Free Vibration Analysis of Sandwich Arches with Graded Metallic Cellular Core

2020 ◽  
Vol 12 (06) ◽  
pp. 2050069
Author(s):  
Mohammad Amir ◽  
Mohammad Talha
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Finite Element Model ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Core Layer ◽  
Element Model ◽  
Element Formulation ◽  
Present Formulation ◽  
Porosity Coefficient

An efficient finite element model based on three nodded element has been developed for the vibration analysis of sandwich arches with graded metallic cellular (GMC) core. The present formulation is based on the higher-order shear deformation theory and orthogonal curvilinear coordinate axes. The arch consists of two isotropic face sheets and a GMC core layer. The internal pores in the core layer follow the different types of distributions. The material properties of the GMC core layer of the sandwich arches vary in the thickness direction as a function in terms of porosity coefficient and mass density. Three types of porosity distributions have been considered to accomplish the vibration responses of sandwich arches. The present formulation is validated with limited results available in the literature. Few new results are computed and the effects of different influencing parameters such as porosity coefficient [Formula: see text], porosity distribution type, the thickness-to-length ratio [Formula: see text], boundary conditions and opening angle [Formula: see text] on the free vibration characteristics of sandwich arches with the GMC core are observed. The present finite element model gives better convergence and more accurate results than a conventional two nodded element-based finite element model.

scholarly journals Study on the Trajectory of Free-End Fiber in Jet Vortex Spinning Based on the Elastic Thin-Rod Finite Element Model of Flexible Fiber

2020 ◽  
Vol 20 (1) ◽  
pp. 43-48
Author(s):  
Chenchen Han ◽  
Weidong Gao ◽  
Lifen Chen
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Finite Element ◽  
Finite Element Model ◽  
Mass Conservation ◽  
Element Model ◽  
Momentum Conservation ◽  
Mechanical Equilibrium ◽  
Flexible Fiber ◽  
The Finite Element Model

AbstractDuring the air flow twisting process of jet vortex spinning, the moving characteristics of flexible free-end fiber are complex. In this paper, the finite element model of the fiber is established based on elastic thin rod element. According to the air pressure and velocity distribution in the airflow twisting chamber of jet vortex spinning, this paper analyzes the undetermined coefficients of the finite element kinetic differential equation of the free-end fiber following the principle of mechanical equilibrium, energy conservation, mass conservation and momentum conservation. Based on numerical simulation, this paper gets the trajectory of the free-end fiber. Finally, the theoretical result of the free-end fiber trajectory by finite element simulating is tested by an experimental method. This paper has proposed a new method to study the movement of the fiber and learn about the process and principle of jet vortex spinning.

Towards Dynamic Tolerance Analysis Using a Finite Element Formulation

2000 ◽  
Author(s):  
Otto Salomons ◽  
Elmer Arentsen ◽  
Ronald Aarts ◽  
Fred van Houten
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Dynamic Behavior ◽  
Geometric Model ◽  
Tolerance Analysis ◽  
Element Model ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Large Numbers ◽  
Physical Effects

Abstract A theoretical framework is proposed by which the effect of tolerances can be analyzed. Especially it focuses on the influence of clearances on the dynamic behavior of mechanisms. As opposed to previous publications, where a bondgraph formulation was used, this paper uses a finite element formulation in order to simulate the dynamic behavior under the influence of tolerances and other physical effects. The finite element formulation that has been selected for this work has two major advantages when compared to a bondgraph formulation. The first important advantage is that the method is analytical to a great extent. As a result, no numerically derived derivatives will exist, hence not leading to numeric inaccuracies. The second advantage is that small numbers can be separated from large numbers allowing to separate tolerances from the nominal path, resulting in faster simulations. The paper describes how a geometric model, including its tolerances, can be transformed into a corresponding finite element model that on its part consists of submodels. Based on this model, simulations can be performed which can provide insight in the dynamic behavior of the mechanism. The paper details on how geometric tolerances (such as form, orientation, position as well as size and clearances), with the focus on clearances, can be accounted for in a finite element model.

Numerical and model studies of strip footing supported by a reinforced granular fill - soft soil system

1999 ◽  
Vol 36 (5) ◽  
pp. 793-806 ◽  
Author(s):  
K M Lee ◽  
V R Manjunath ◽  
D M Dewaikar
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Bearing Capacity ◽  
Soft Soil ◽  
Element Model ◽  
Model Tests ◽  
Laboratory Model ◽  
Soil System ◽  
Granular Fill ◽  
The Finite Element Model

Laboratory model tests have been carried out using a rigid strip footing supported on dense sand overlying soft clay with and without a layer of geotextile reinforcement at the interface. The study aimed at determining the effect of geotextile reinforcement and the thickness of a sand layer on the ultimate bearing capacity and settlement characteristics of the footing resting on a granular fill - soft soil system. It was found that the bearing capacity increases with an increase in the ratio of sand thickness to footing width until it reaches a critical value, which can be considered as the optimum limit of improvement of the bearing capacity of the layered soil. The installation of a geotextile reinforcement at the interface resulted in an appreciable increase in bearing capacity and decrease in settlement of the footing. The optimum thickness of the sand layer for a geotextile-reinforced foundation was found to be 0.8 times the width of the footing, which was significantly lower than that of an unreinforced foundation. The results of the laboratory model tests were validated by a comparison with the results of a finite element analysis. The results obtained using the finite element model compared well with data obtained from the laboratory tests. Additional parametric study was carried out by the finite element model to supplement the results of the laboratory model tests. Design recommendations are given based on the results of the finite element model and laboratory model studies for a rigid footing supported on a reinforced granular fill - soft soil system. Key words: model tests, footing, bearing capacity, granular fill, clays, finite elements, geotextiles.

scholarly journals Building Spectral Element Dynamic Matrices Using Finite Element Models of Waveguide Slices and Elastodynamic Equations

2013 ◽  
Vol 20 (3) ◽  
pp. 439-458 ◽  
Author(s):  
P.B. Silva ◽  
A.L. Goldstein ◽  
J.R.F. Arruda
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Transfer Matrix ◽  
Cross Section ◽  
Element Model ◽  
Spectral Element ◽  
Forced Response ◽  
Spectral Elements ◽  
Element Formulation ◽  
Element Mesh

Structural spectral elements are formulated using the analytical solution of the applicable elastodynamic equations and, therefore, mesh refinement is not needed to analyze high frequency behavior provided the elastodynamic equations used remain valid. However, for modeling complex structures, standard spectral elements require long and cumbersome analytical formulation. In this work, a method to build spectral finite elements from a finite element model of a slice of a structural waveguide (a structure with one dimension much larger than the other two) is proposed. First, the transfer matrix of the structural waveguide is obtained from the finite element model of a thin slice. Then, the wavenumbers and wave propagation modes are obtained from the transfer matrix and used to build the spectral element matrix. These spectral elements can be used to model homogeneous waveguides with constant cross section over long spans without the need of refining the finite element mesh along the waveguide. As an illustrating example, spectral elements are derived for straight uniform rods and beams and used to calculate the forced response in the longitudinal and transverse directions. Results obtained with the spectral element formulation are shown to agree well with results obtained with a finite element model of the whole beam. The proposed approach can be used to generate spectral elements of waveguides of arbitrary cross section and, potentially, of arbitrary order.

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