MSeep



In delta areas the land is protected from floods and high tides by dikes. In general these are constructed of impervious clays and built on a sandy aquifer as subsoil. Such structures are vulnerable to an erosion effect called piping. The actual word 'piping' refers to the development of shallow channels in the sand below the dike, which begins at the downstream side of the structure. Here often a ditch is situated with a burst bottom due to excess water pressures. The subsequent erosion process develops backwards to the high head side. The natural nonhomogeneity in the soil causes the shallow channels to be irregularly shaped. Below a critical value of the hydraulic head over the structure the erosion process eases down until water only is transported through the channels. It is common to observe sand boils behind the dike, which produce water alone. However, if a critical head difference is reached, the erosion process continues and the structure may in the end collapse.

MSeep simulates two dimensional stationary groundwater flow in a cross section of layered soil structures or in one phreatic aquifer, composed of different material areas. All kinds of boundary conditions can be defined. In MSeep a module has been implemented to determine Piping and Heave.

 

Problem definition
Cross Section
The soil structure in the vertical x-y plane can be composed of several soil layers divided by layer boundaries. Permeability in x- and y-direction has to be specified for each layer. Sheetpiles can also be defined.

Phreatic aquifer
The soil structure in the horizontal x-z plane consists of one vertical layer with different material areas. Permeability in x- and z-direction has to be specified for each area.

On the geometry border the available boundary conditions are:

  • closed boundary
  • constant discharge boundary
  • constant potential boundary

And only for a cross section:

  • freatic or seepage boundary (with rain)
  • freatic or closed boundary
  • overtopping boundary.

Within the geometry constant discharges or fixed potential can be specified in certain points.

 

A built-in mesh generator creates an element mesh of iso-parametric triangles for the geometry. The element mesh can be refined locally by specifying rectangular refinement boxes.

Calculation method
The finite element method is used to solve the differential equation of Laplace, which represents the stationary groundwater flow. A direct solution technique solves the set of equations. The final position of the freatic surface(s) is found using an iterative process, in which each step the finite element mesh is adapted (cross section) or the transmissivity is recalculated (aquifer).
If no internal nodes were specified with a constant discharge or a fixed potential, an extra calculation can be performed to determine the streamlines.

Output
The results of the calculations are presented in two ways. First of all there is the output file with an echo of the input and the potentials and discharges of all the mesh nodes.

A second option is to view the results graphically in the form of a number of drawings:

  • the geometry with the soil layers and sheetpiles
  • boundary conditions
  • (numbered) element mesh
  • distorted element mesh
  • potential and/or stream iso-lines.