Changing impermeability boundary conditions to obtain free surfaces in unconfined seepage problems

2011 ◽  
Vol 48 (5) ◽  
pp. 841-845 ◽  
Author(s):  
S. López-Querol ◽  
P. Navas ◽  
J. Peco ◽  
J. Arias-Trujillo
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Free Boundaries ◽  
Flow Through Porous Media ◽  
Free Surfaces ◽  
Coupled Numerical Model ◽  
Flow Through

A coupled numerical model of flow through porous media, formulated in terms of the fluid displacements and changing the impermeability boundary conditions, is applied to calculate the free surface in unconfined, steady-seepage problems. In this new methodology, the domain of computation is kept constant, and the free surface is iteratively obtained by imposing impermeability conditions at the free boundaries, which are updated at the end of each iteration, aiming to simulate the physics of the problem. By doing so, a line of pore-water pressure equal to zero (free surface) is obtained in a few iterations, usually two or three. The results obtained with the proposed method have been successfully compared to analytical and numerical solutions in several examples to show the usefulness of the method in practical seepage problems.

One-dimensional consolidation of multilayered aquifer systems with viscoelastic properties induced by time-dependent groundwater drawdown

2021 ◽  
pp. qjegh2021-073
Author(s):  
Weitao Yang ◽  
Jin Xu
Keyword(s):  
Viscoelastic Properties ◽  
Numerical Solutions ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Time Dependent ◽  
Analytical Models ◽  
Consolidation Process ◽  
One Dimensional ◽  
Groundwater Drawdown ◽  
Aquifer Systems

Most analytical and semi-analytical models for pumping-induced land subsidence invoke the simplifying assumptions regarding characteristics of geomaterials, as well as the pattern of drawdown response to pumping. This paper presents an analytical solution for one-dimensional consolidation of the multilayered soil due to groundwater drawdown, in which viscoelastic property and time-dependent drawdown are taken into account. The presented solution is developed by using the boundary transformation techniques. The validity of the proposed solution is verified by comparing with a degenerated case for a single layer, as well as with the numerical solutions and experimental results for a two-layer system. The difference between the average consolidation degree Up defined by hydraulic head and that Us defined by total settlement is discussed. The detailed parametric studies are conducted to reveal the effects of viscoelastic properties and drawdown patterns on the consolidation process. It is revealed that while the effect of different drawdown response patterns is significant during the early-intermediate stages of consolidation, the viscoelastic properties may have a more dominant influence on long-term consolidation behavior, depending on the values of the material parameters, which are reflected in both the deformation process of soil layers and the dissipation of excess pore-water pressure.

A Continuous Desingularized Source Distribution Method Describing Wave–Body Interactions of a Large Amplitude Oscillatory Body

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Aichun Feng ◽  
Zhi-Min Chen ◽  
W. G. Price
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Water Surface ◽  
Numerical Solutions ◽  
Free Water ◽  
Source Distribution ◽  
Surface Boundary ◽  
Distribution Method ◽  
Collocation Points ◽  
Calm Water

A Rankine source method with a continuous desingularized free surface source panel distribution is developed to solve numerically a wave–body interaction problem with nonlinear boundary conditions. A body undergoes forced oscillatory motion in a free water surface and the variation of wetted body surface is captured by a regridding process. Free surface sources are placed in continuous panels, rather than points in isolation, over the calm water surface, with free surface collocation points placed on the calm water surface. Nonlinear kinematic and dynamic free surface boundary conditions along the collocation points on the calm water surface are solved in a time domain simulation based on a Lagrange time dependent formulation. Compared with isolated desingularized source points distribution methods, a significantly reduced number of free surface collocation points with sparse distribution are utilized in the present numerical computation. The numerical scheme of study is shown to be computationally efficient and the accuracy of numerical solutions is compared with traditional numerical methods as well as measurements.

Long-wave-induced flows in an unsaturated permeable seabed

2007 ◽  
Vol 586 ◽  
pp. 323-345 ◽  
Author(s):  
PHILIP L.-F. LIU ◽  
YONG SUNG PARK ◽  
JAVIER L. LARA
Keyword(s):  
Diffusion Equation ◽  
Pore Water ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Soil Column ◽  
Seepage Flows ◽  
Dimensional Diffusion ◽  
Special Cases

We present both analytical and numerical solutions describing seepage flows in an unsaturated permeable seabed induced by transient long waves. The effects of compressibility of pore water in the seabed due to a small degree of unsaturation are considered in the investigation. To make the problem tractable analytically, we first focus our attention on situations where the horizontal scale of the seepage flow is much larger than the vertical scale. With this simplification the pore-water pressure in the soil column is governed by a one-dimensional diffusion equation with a specified pressure at the water–seabed interface and the no-flux condition at the bottom of the seabed. Analytical solutions for pore-water pressure and velocity are obtained for arbitrary transient waves. Special cases are studied for periodic waves, cnoidal waves, solitary waves and bores. Numerical solutions are also obtained by simultaneously solving the Navier–Stokes equations for water wave motions and the exact two-dimensional diffusion equation for seepage flows in the seabed. The analytical solutions are used to check the accuracy of the numerical methods. On the other hand, numerical solutions extend the applicability of the analytical solutions. The liquefaction potential in a permeable bed as well as the energy dissipation under various wave conditions are then discussed.

scholarly journals A note on withdrawal through a point sink in fluid of finite depth

1996 ◽  
Vol 37 (3) ◽  
pp. 406-416 ◽  
Author(s):  
Lawrence K. Forbes ◽  
Graeme C. Hocking ◽  
Graeme A. Chandler
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Finite Depth ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Flow Through

AbstractWithdrawal flow through a point sink on the bottom of a fluid of finite depth is considered. The fluid is at rest at infinity, and a stagnation point is present at the free surface, directly above the point sink. Numerical solutions are computed by means of the method of fundamental solutions, and it is observed that flows of this type are apparently possible for Froude number less than about 1.5. Relationships to previous work are discussed.

Sign in / Sign up

Export Citation Format

Share Document