A Characteristic Finite Element Model for Solute Transport in Saturated-Unsaturated Soil

Author(s):  
Jin-Zhong Yang ◽  
Wei-Zhen Zhang
1997 ◽  
Vol 05 (04) ◽  
pp. 383-402
Author(s):  
Tony W. H. Sheu ◽  
C. C. Fang

A hyperbolic equation is considered for the propagation of pressure disturbance waves in layered fluids having different fluid properties. For acoustic problems of this sort, the characteristic finite element model alone does not suffice to ensure prediction of the monotonic wave profile across fluids having different properties. A flux corrected transport solution algorithm is intended for incorporation into the underlying Taylor–Galerkin finite element framework. The advantage of this finite element approach, in addition to permitting oscillation-free solutions, is that it avoids the necessity of dealing with medium discontinuity. As an analysis tool, the proposed monotonic finite element model has been intensively verified through problems which are amenable to analytic solutions. In modeling wave propagation in layered fluids, we have investigated the influence of the degree of medium change on the finite element solutions. Also, different finite element solutions are considered to show the superiority of using the flux corrected transport Taylor–Galerkin finite element model.


Author(s):  
Yongren Wu ◽  
John Glaser ◽  
Hai Yao

The intervertebral disc (IVD) is the largest cartilaginous structure in human body that contributes to flexibility and load support in the spine. To accomplish these functions, the disc has a unique architecture consisting of a centrally-located nucleus pulposus (NP) surrounded superiorly and inferiorly by cartilage endplates (CEP) and peripherally by the annulus fibrosus (AF). Disc degeneration is strongly linked to low back pain. Poor nutrient supply has been suggested as a potential mechanism for disc degeneration. Previous theoretical studies have shown that the distributions of nutrients and metabolites (e.g., oxygen, glucose, and lactate) within the IVD depended on tissue diffusivities, nutrient supply, and cellular metabolic rates [1, 2]. Based on a multiphasic mechano-electrochemical finite element model of human IVD [3], our recent theoretical study suggested that the mechanical loading has little effect on small solute transport (e.g., glucose), but significantly affects large solute transport (e.g., growth factor). The objective of this study was to further develop the multiphasic finite element model of IVD by including the cartilage endplate and considering the nutrient consumption of disc cells. Using this model, the effects of endplate and mechanical loading on solute transport in IVD were examined.


1987 ◽  
Vol 24 (4) ◽  
pp. 565-580 ◽  
Author(s):  
L. Lam ◽  
D. G. Fredlund ◽  
S. L. Barbour

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.


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