Drainage Engineering (Hydraulic boundary conditions)

1. BOUNDARY CONDITIONS

2. In steady-state flow of groundwater through homogeneous
soils, four types of boundaries are encountered.
1. Impervious boundary
2. Boundaries of the reservoirs
3. Surface of seepage
4. Line of seepage (free surface, depression curve)
Groundwater divides are hydraulic boundaries and can shift
position as conditions change in the field.

3. 1. Impervious boundary
At impervious boundaries the fluid can neither penetrate the boundary
nor leave gaps; thus the velocity component normal to the boundary
at any point must vanish.
Defining n and t as the normal and tangential directions, respectively,
at a point on the boundary, we have:
ψ represent Streamlines and
 represent Equipotential lines
Streamlines ψ are parallel to
no flow boundaries.
ttanconsisHence
tn


,,0






4. In Figure 1
Boundary AB defines the lowest streamline/flow line
Bottom contour of the impervious structure defines upper flow line
Figure 1

5. 2. Boundaries of the reservoirs
Along the boundaries of the reservoir the pressure distribution may be
taken as hydrostatic.
At point M along the boundary AD of Figure 2, the pressure in the water
is
 = - kh1 + C
Since k, C, and h1 are all constants,  = Constant
And thus all reservoir boundaries, such as O1 and 8G of Figure 1 and
AD and EB of Figure 2, are equipotential lines.
 yhp w  1
Figure 2
Figure 1

6. 3. Surface of seepage
The surface of seepage (GE of Figure 2) represents a boundary where
the seepage leaving the flow region enters a zone free of both liquid
and soil.
As the pressure on this surface is both constant and atmospheric, and
since the surface is neither an equipotential line nor a streamline,
along this boundary
Hence, we obtain the linear relationship
 + k y = constant
Cyk
pk
w



Figure 2

7. 4. Line of seepage (free surface, depression curve)
The line of seepage is the upper streamline in the flow domain.
It separates the saturated region of flow from that part of the soil body
through which no flow occurs, such as DG of Figure 2.
In addition to the requirement that the line of seepage be a streamline (ψ
= constant) it is evident that the pressure at every point along its surface
is constant and equal to atmospheric pressure. Thus, along this line
 + k y = constant
Figure 2
This requires constant vertical
intercepts (Δy = constant) at the
points of intersection of the line of
seepage with successive equi-
potential lines of equal drops (Δ of
Figure 3).
which demonstrate that the velocity potential (and total head) along the
line of seepage varies linearly with elevation head.

8. Figure 3

9. Figure 4: Various entrance and emergence for the line of seepage

10. Effluent or Gaining Stream
Low water flow of streams is derived from groundwater
Low flow in stream
Before storm - Flow from groundwater to the stream

11. High flow in stream
After storm - Flow from the stream to the groundwater
Flood level in the stream recedes
Groundwater again starts contributing to the stream
Influent or Losing Stream