TARLAC STATE UNIVERSITY

COLLEGE OF ENGINEERING AND TECHNOLOGY

TARLAC CITY

SEEPAGE TANK MODEL

Instructions Manual
 TABLE OF CONTENTS

I. General Overview …………………………………….. 1

II. Routine Maintenance …………………………………….. 3

III. General Comments …………………………………….. 3

IV. Basic Theories ………………………………………………… 3-10

a. Darcy’s Law ………………………………………………… 3-5

b. Flow Nets ………………………………………………… 6-8

c. Rate Of Seepage ……………………………………. 9-10

V. Experimentation Procedure For Flow

Nets Demonstration …………………………………… 11-13

a. Flow Net Visualization……………………….. 11-12

b. Flow Net Construction ……………………….. 12-13

c. Seepage Rate ………………………………………………. 13

VI. Cleaning ………………………………………………………….. 13

General Overview usually deal only with the flow pattern and quantity of the water traversing
the strata. The forces exerted by seepage remain of secondary importance.
The class of problems involving flow of water through permeable Mining is an area where both seepage and ground water flow is
media has a wide range and is of considerable importance to engineers and fundamentally important. The design of an effective drainage system for a
scientists. The Seepage Tank facilitates a detailed study of the movement of mine must be based on profound knowledge of permeability, of the degree
water through permeable media. of water saturation of the various geological layers, of seepage rates and of
the effect of pumping or draining the water on the balance of forces.
The engineer is probably the one who faces such problems most
frequently and whose success or failure will often depend on his knowledge Ground water hydrology and hydrogeology are the main non-
and understanding of phenomena related to the movement of the water in engineering fields dealing with flow of water through permeable media and
soils. This is one of the most important aspects in the design of almost all require the study of problems such as salt-water intrusion into fresh water
hydraulic structures. Consider an earth or rock fill dam, for instance. Water basins, underground movement of water towards inner channels, discharge
flows directly through the engineering structure itself. Obviously, it is of ground water into surface run-offs, recharge of water from rivers to
important to know how much water we can expect to lose from the underground storage, artificial recharge of ground water. Generally
reservoir by seepage through the dam. speaking, the movement of water through soil under natural conditions is
very complex and cannot be reproduced in full in the laboratory. This
We also need to know whether a certain kind of soil can be used to
complexity is caused by the non-uniformity of natural soils over large areas,
construct the dam without running the risk that the reservoir will run dry
the stratified and the tectonic structures of geological layers, and by the fact
after filling. The safety and the very existence of the dam depends on the
that water movement in nature is generally three-dimensional.
flow pattern of the penetrating water and on the balance of the hydraulic
and static forces. Many earth dams have collapsed because of improper Such movement is not easy to handle mathematically. In the
design with respect to the movement of water through their bodies. In fact, laboratory, we have the advantage of being able to use homogeneous
the conditions of seepage are vital, not only for earth dams, but for any materials of known properties. This simplifies the problem and makes it
dams having permeable materials in the foundations. possible to reduce the number of components involved. By this means
significant relationships between the physical properties of the medium and
A dam can collapse or be badly damaged as a result of seepage
characteristics of flow are found.
underneath its bottom, or because of hydrostatic forces exerted by the
penetrating waters. These forces cannot be determined without prior To further simplify the problem, we usually restrict ourselves to a
determination of the flow pattern underneath the structure. Once known, two-dimensional flow, investigating conditions in a vertical cross section*
they can be altered using drains, cut-offs, sheet pile walls and other means along the horizontal direction of the moving water mass. The Seepage Tank
to change the flow pattern. Similar problems arise in other engineering Model, is specifically designed to permit the simulation in the laboratory of
structures built from, or on, soil. As examples, we can mention levees, road such vertical cross sections.
and railway embankments, canals, navigation locks, foundations of
buildings, bridges, harbor walls and similar structures. * For obvious practical reasons the cross sections are not planar across
sections. But their thicknesses are small in relation to the height.
Another engineering field where good understanding of water
movement in soil is essential is water supply and drainage. In both we are
concerned with extracting water from saturated strata by using wells,
horizontal galleries, tile lines, or trenches. In this type of problem, we
Routine Maintenance Responsibility Darcy's Law can be expressed mathematically as:

To preserve the life and efficient operation of the equipment it is

important that the equipment is properly maintained. Regular maintenance …. (1)
of the equipment is the responsibility of the end user and must be
performed by qualified personnel who understand the operation of the where Q = flow rate
equipment. General In addition to regular maintenance the following notes
A = cross-sectional area of flow
should be observed:
K = a proportionality constant, called the "coefficient of permeability"
1. When not in use, the equipment should be disconnected from the
electrical supply.
= head loss
2. The equipment should be kept clean.
= length of the flow path.
3. After use the drain should be washed thoroughly to remove any particles
that may be blocking the filter material. A more usual statement of Darcy's Law, however, in terms of velocity of
flow.

General Comments
The following set of experiments has been designed to demonstrate
the most typical situations that arise in dealing with water as it moves Since velocity is given as …. (2)
through a permeable medium. The situations described are mostly
"engineering" situations. In addition to the water and the medium through
which it moves, they usually involve some artificial, or "engineering"
element like a wall, a dam, a tile line etc. There are fourteen basic division of equation (1) by A leads to the familiar statement of
experiments and two variants described. However, any number of other
practical investigations can be made which will add to general knowledge
and enrich the experience of the experimenter. Darcy's Law:

Basic Theory …. (3)

a. Darcy's Law
The flow of water through porous media is governed by what is known Since the ratio , which is called "hydraulic gradient:
as Darcy's Law: "The flow rate through porous media is proportional to and is analogous to slope, is dimensionless, the
head loss and inversely proportional to the length of the flow path". coefficient of permeability K must have the
dimensions of velocity for equation (3) to be valid. The coefficient K is
 different for different materials and is determined in the laboratory by b. Flow Nets
using equation (1) in the form: Flow Lines and Equipotential Lines

Note that all the right-hand side terms can be directly measured. A A flow net is a graphical representation of flow through soil (or any
method of doing so is shown in Figure i below. other porous medium). From the flow net, information may be obtained
on such features as the amount of seepage or leakage below a dam or
through an earth dam, the uplift pressure caused by the water on the
base of a concrete dam (or, say a harbor wall); and the danger of a
"quick" or liquefaction condition at points where seepage water comes
to the ground surface.

The path which a particle of water follows in its course of seepage

through a saturated soil mass is called a flow line. In isotropic soil, flow
follows paths of greatest hydraulic gradient, much as bodies rolling or
sliding downhill tend to pick paths having the steepest slope.

It follows from Darcy's Law, and from common sense that water can
flow through soil only if some head difference h exists between the
places between which the flow might occur. This head difference (which
may be made up of several components, see Figure iii) represents a
certain amount of potential energy which is transformed into the kinetic
For the purpose of classifying various types of soil with respect to energy of the moving water. The soil through which the water is pushed
permeability it has been found convenient to make use of a so-called, by the pressure head resists its movement in much the same manner, as
"laboratory (ie. 'standard') coefficient of permeability" designated as K. K a rough surface resists, or brakes, the movement of a sliding body.
is defined as the flow of water at 60 deg F in gallons per day through a
The soil resistance to moving water is called viscous friction since it
one-square-foot cross sectional area of the soil in question under a
causes a gradual dissipation of the kinetic energy in the moving water.
hydraulic gradient of one foot per foot.
Within limitations it can be treated as a negative head.

Classification of soils with respect to K

 lines. Examples of such pairs are represented by points a s, bs and at, bt.
The connecting lines asbs and atbt represent the equipotential lines
between the pairs.

Such a system of flow lines and equipotential lines is what is called

the flow net. In each flow net, the flow lines and the equipotential lines
intersect at right angles.

This important feature of a flow net can be explained as follows.

Just as water flowing downhill naturally follows the steepest path, so
does water flowing between equipotential lines follow the path of
maximum gradient. By definition, gradient is the difference in potential
between two equipotential lines divided by the distance between the
lines. If the lines are parallel the maximum gradient will occur where the
distance between the lines is least, (i.e. along any line which is
perpendicular to the equipotential lines). This is true even if the
Let us imagine a situation where water penetrates under a sheet equipotential lines are infinitely close to one another.
pile wall from basin I to basin II as shown above and let the pressure
head between the two basins be h. Water will enter the soil along the Now imagine two adjacent equipotential lines which are infinitely
whole bottom of basin I, and according to the location of its point of close to one another but not parallel. The shortest distance between the
entry, each elemental volume will follow a different path on its way to two lines at any point along one of them can be established as follows.
basin II. However, all the elemental volumes, whatever paths they follow, Using the intersection of the two equipotential lines as a center, describe
will have the same potential at the points of entry and, similarly, they will an imaginary arc that passes through the point in question and also
have the same potential when eventually reaching the bottom of basin II. intersects the second equipotential line. The chord of that arc which is
This follows from the fact that the water tables in both basins I and II are contained between the two equipotential lines can be shown to be the
horizontal as well as their bottoms. So, the pressure is constant along the shortest distance between the two lines at the point in question. Hence,
whole bottom of each basin. the gradient will be maximum along that chord. However, by definition,
the two lines are infinitely close together at that point.
Now we pick two of the unlimited number of possible flow lines and
denote them by A and B as shown in Figure above. So, the difference in length between the arc and the chord is
infinitely small. Hence, at that point, the gradient along the arc is equal
The lines connecting points with equal potentials on different flow lines to the gradient along the chord. By construction, the arc is perpendicular
are called equipotential lines. Thus, we see that the contours of the two to each equipotential line at its intersection with that line. It follows,
bottoms represent two equipotential lines since they connect, then, that all lines representing the paths of maximum gradient intersect
respectively, points a1 and b1 having equal potentials, and points a n and all lines of equipotential at right angles.
bn also having equal potentials.
Since flow follows the path of maximum gradient, it, too is perpendicular
Naturally, pairs of points having equal potentials must also exist to all equipotential lines.
between the two pairs located at the beginning and the end of the flow
c. Rate of Seepage If a pair of flow lines is given, there is only one way to divide the strip
between them into a sequence of "squares" (i.e. tetragonal) whose four
Now consider that same portion of the water that seeps out of corners form right angles and whose mean distances between opposite
basin I and into basin II (see diagram above) in a given time will pass faces are alike. Therefore, if we succeed in dividing the strip between the
through an area dF bounded by the two flow lines (a sat and bsbt) shown. two flow lines into a sequence of such "squares", we can use their
This seepage, Q, will be measured in gallons per unit of time per running number n for calculating the potential drop dh between two successive
foot (ie. per foot normal to the plane of the section). If we designate that equipotential lines. Since all the values of dh must be the same according
portion of the seepage passing through dF as dq we get from Darcy's to equation (8) we have:
Law:

......... (9)
…. (4)
Knowing dh, we can finally determine from equation (5) the discharge
where dh is the potential drop between the two equipotential lines, the (per unit length) through the area between two flow lines.
only unknown in equation (4).
Although it is advantageous to have a "square" flow net, it is also
If we choose equipotential lines such that the area dF resembles a possible to determine dh from a rectangular net if all the rectangles
square, then the distance dm is approximately equal to ds, and equation between two flow lines
(4) reduces to:

dq = kdh …. (5) have the same ratio . Denoting this ratio by c, equations (5) and
For the subsequent "square" area dF' the discharge is (6) become respectively.

dq' = Kdh' …. (6) dq = K c dh .........

However, we can get only as much water into dF' as has passed (10) dq' = K c
through dF. There is simply no other place from which the water could
dh ..........(11)
come. Nor is there any other place where the water from dF could go.
Therefore we have: which again means that equation (8) holds and we can obtain dh from
dq = dq' ........(7) equation (9) where n is the number of rectangles between the two flow
lines. Discharge dq is then obtained from equation (10).
which, from equations (5) and (6) gives:
If, for some reason, we do not have a flow net consisting of squares
dh = dh' ........(8) or geometrically similar rectangles, we would have to measure the
This is a very important result. It implies that the potential drop actual heads at all equipotential lines in order to obtain the potential
between two adjacent pairs of equipotential lines is the same if they drops between each.
share the same pair of adjacent flow lines and enclose an area similar to
a square.
 7. To stop the experiment, shut off the dye input by lowering dye
container until dye surface is about 50mm below water level in
Seepage Underneath a Sheet Pile Wall pool. Let the flow lines wash away. Do not take out the needles
before the dye input has been shut off as indicated. Otherwise
dye will get into water in the pool while needles are being
Seepage underneath a sheet pile wall is one of the seepage problems removed.
that are most common in practice. Sheet pile walls are used to reduce
seepage under all types of dams, sea walls, dividing walls, lock walls, coffer-
dams and similar structures. They are also used to reduce leakage from II. Flow Net Construction
canals, rivers and the sub soils surrounding an excavation and the like. It is
also this type of seepage which most clearly illustrates the concept of a flow 1. Trace the flow line pattern and the boundary conditions (the
net where the flow net has a simple and intuitively clear pattern and fully perimeter of the cross section of the body of sand in the tank)
defined boundary conditions. on tracing paper taped to the transparent wall of the tank. Use
I. Flow Line Visualisation a felt marker to prevent erasing the contours which are to serve
as a firm skeleton of the net when sketching in the completed
1. Prepare about 50 ml of light-colored dye (preferably a dye net with a pencil later on.
which is in contrast with the color of the sand mixture being 2. To obtain a square flow net, try first to fit the squares between
used). one pair of the experimentally obtained flow lines. Proceed
2. Fill the tank with pure sand to a level of about 350mm above with the sketching of the equipotential lines from the upstream
the bottom of the tank. to the downstream boundary (ie. upstream sand surface to
3. Adjust the upstream overflow so that its top is about 600 mm downstream sand surface) using care to obtain right angle
above the bottom of the tank and the downstream overflow so intersections.
that its top is about 90 mm above the surface of the sand bed. 3. On the first trial, a narrow residual rectangle will probably occur
4. Pour water slowly into the tank. Start with the downstream at the end. The correction can be made in two ways. The width
pool and transfer the input into the upstream after the lower of the "channel" formed by the two experimental flow lines can
pool is full. After overflow occurs both upstream and be either increased or reduced by drawing a parallel trial line
downstream reduce water input to the minimum needed to close to one of the original lines.
maintain constant water level in the upstream pool (in this case 4. Using this corrected flow line instead of one of the
there will be a small continuous overflow from the upper pool). experimental ones, a new set of squares is fitted into the
Smooth out any sharp irregularities of the sand bed which may "channel". If the new "channel" is wider than the original, the
have formed while filling the pool. length of the residual rectangle will reduce eventually to zero. If
5. Inject then the dye with the syringe containing of about 10 mL if it is narrower, the residual rectangle will eventually be
dye. The suggested needle distances from the screen for 4 flow lengthened until it approximates a square.
lines, are approximately 60, 120, 180, 240mm. 5. Once the square net between one pair of flow lines has been
6. The formation of flow lines may require several minutes to an established, the equipotential lines can be extended across the
hour or two, depending on the permeability of the sand used. whole flow field so that they intersect all the experimental flow
lines at right angles. Then flow lines are interpolated between
 the experimental ones so as to form, with the equipotential
lines, a square network.
6. Since the "channels" near the boundary flow lines need not be
square at the first trial, the whole flow net may be adjusted. A
way to avoid this is to set up a separate rectangular flow net in
each of the two boundary "channels". This can be done by
appropriately changing the position of some equipotential lines.

III. Seepage Rate

First, the pressure drop dh is determined from equation (9).

Then the seepage rate in each flow "channel" is determined using
equation (5) in case of a square network, or equation (10) in case of
a rectangular network. The total seepage flow rate per running foot
underneath the steel pile is the sum of all the rates through the
individual flow "channels".

Cleaning
After conducting the experiment, unplug any electrical devices used
then thoroughly open the clean out valve located at the bottom part of
the Seepage Tank Model and use water to flush the sand into the basin
provided. Use water to remove excess sand on the walls of the tank.
Wipe with dry rag afterwards.