plot an enetiol common set of axes) for the soil/water column BeD. TO l the inle
ID: 1845098 • Letter: P
Question
plot an enetiol common set of axes) for the soil/water column BeD. TO l the inlet side head for the effective stress at D to become zero (the "quicksand" condition 5. A cross-section of a dam is shown on the attached sheet. The flow lines, determined from a complete flow net solution by Dr. Wolf, are given (previous students would say you are lucky) 5a. Determine the number and location of equipotential lines which form "squares" (There may be one line of partial squares). Calculate the shape factor $ Nf/ Ne, and the total flow, in gallons per minute, under a dam running 300 feet across a river. 5b. Determine the uplift pressure on the base at points A, B, and C in lb/ft2. Estimate the total uplift force on a dam 300 ft long across the river. 5c. Determine the exit gradient, ie, by calculating the local gradient across the "exit square.Explanation / Answer
On Fig. each interval between two equipotentials corresponds to a head loss h equal to 1/Nd
of the total head loss h through the soil :
h = h / Nd
Where Nd = Total number of equipotentials.
Consider a pair of flow lines, clearly the flow through this flow tube must be constant and so as the
tube narrows the velocity must increase.
Let us consider the flow through abcd delimited by two flow lines and two equipotentials.
The hydraulic gradient is :
i = h/l1 = h / (Nd. l1)
Where l1 is the distance between the two equipotentials.
The flow passing into abcd, per m width of soil, is :
qabcd = Area x velocity = l2.1. k .h / (Nd. l1)
If we draw the flow net taking l2 = l1 (a "squared" mesh net is more convenient to draw : it is
possible to draw an inscribed circle, see Fig.4), qabcd = k .h / Nd (the flow through any
quadrilateral of the flow net is thus the same as the one through abcd ).
The total flow will then be equal to :
Q = Nf
. q = k .h . Nf
/ Nd
Where Nf
= Number of flow tubes.
From that equation, one can see that the flow is function of the ratio Nf
/ Nd and thus if the flow net
is refined by dividing each cell in four smaller cells, the ratio will remain unchanged. That means
that Q is independent of the refinement of the flow net! It is thus easy to determine quickly an
estimate of the flow of water passing under a dam or wall.
To calculate quantities of interest, that is the flow and pore water pressures, a flow net must be
drawn.
The flow net must consist of two families of orthogonal lines that ideally define a square mesh, and
that also satisfy the boundary conditions.
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