Civil Engineering Reference
In-Depth Information
New dynamic real arrays:
angs
angles to horizontal made by sloping mesh lines
bottom width
x
-coordinates of nodes at base of mesh
oldpot
nodal total head values from previous iteration
current total head values of free surface
surf
x
-coordinates of initial nodes at top of mesh
top width
In this program we consider a boundary condition frequently met in geomechanics
in relation to the flow of water through dams. Free-surface problems involve an upper
boundary, the location of which is not known
a priori
, so an iterative procedure is required
to find it. This iteration can be done in several ways; for example, a fixed mesh can be used
and nodes separated into “active” and “inactive” ones depending upon whether fluid exists
at that point. An alternative strategy is to use the present program, whereby the mesh is
deformed so that its upper surface ultimately coincides with the free surface. A summary
of the boundary conditions is given in Figure 7.11
The analysis starts by assuming an initial position for the free surface. Solution of
Laplace's equation gives values of the total head along the free-surface nodes which will
not in general equal the elevation of the upper surface of the mesh. The elevations of the
nodes along the upper surface are therefore adjusted to equal the total head values just
calculated at those locations. In order to avoid distorted elements, the library geometry
subroutine
geom freesurf
ensures that the nodes beneath the top surface are evenly
distributed. The geometry subroutine is designed for solving free surface problems with
initially trapezoidal meshes and counts nodes and elements in the
x
-direction. The anal-
ysis is then repeated with the new mesh. Since many of the coordinates have changed,
the conductivity matrices of all the elements must be re-computed and assembled into
the global system. In order to avoid the need for numerical integration of the element
conductivity matrices at each iteration, library subroutine
seep4
computes the element
No flow boundary
potential = elevation
Potential = elevation
Constant
upstream
potential
Constant
downstream
potential
No flow boundary
Figure 7.11 Boundary conditions for free surface flow
