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DESIGN or A' SMALL‘CONCBETE DAM

THESIS 110B THE DEERE! OF B. S.
Clyde H Coster
‘ 1931_._

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DESIGN OF A SMALL CONCRETE DAM

A Thesis Submitted to

The Faculty of
MICHIGAN STATE COLLEGE
of
AGRICULTURE AND APPLIED SCIENCE

3?

Clyde H. Coeter

Candidate for the Degree of

Bachelor of Science

June, 1931

 

 

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DESIGN OF A SMALL COHCRETE DAM
(GRAVITY TYPE)

Object:

The object of this thesis is to locate and
design a small dan. In order to properly proceed with
this work the following field operations were carried
out and a copy of the field notes taken is submitted as
a portion of this thesis.

Notes were taken for the topography of the
reservoir and dam site,.end levels were run for the profile
of the stream.

The following are a few of the factors which
Taste the project desirable and worthwhile.

There are, all over the country, countless small
streams which are unsuited for even small water power
develOpment. If they cannot be considered from a utilitarian
standpoint perhaps they can be deve10ped from some other
angle. Consider this one case in particular. About two
miles north of Montague, Michigan, on the prOperty of
Charles Larson there is a small spring fed stream. It
originates near one edge of the property and flows across
the farm for about one-eighth of a mile. There is only a
negible amount of water flowing near the source but the
flow is increased by the contributions of numerous other

springs downstream. The stream flows along the botto-

Qé934

of e gully considerably below the level of the surround-
ing land. Near the source, the gully is quite wide
asking an ideal site for a pond.

In its present state, the stream.instead of
adding to the attractiveness of the property, detracts
from.it for the following reasons:

The sides of the gully are made up of clean
sand which is very unstable, and although the stream
naturally serves only as a drainage for the springs, its
flow is increased in the spring when.nelting ice and
snow fronxthe lands above find their way to it. This
large proportional increase in flow washes the loose sand
from the side of the gully and carries it downstream.

The sand has practically no binder and is absolutehy
unstable. lt‘is'estimated that in the last five years
hundreds of tons of sand have been washed downstream, filling
up the stream bed and asking the site near the head of the
stream very unsightly.

Two ways of preventing this disfiguration of the
land present themselves. The first is by protecting the
sides of the gully by planting or rip-rap; the second is
by regulating the stream flow. Planting, however, is
extremely difficult on account of the nature of the soil
and rip-rap complete enough to offer protection would be
very expensive and of questionable value. The most

satisfactory method would be to regulate the stream flow

by means of a smell den.

7 i concrete dam was designed because of the
eecessibility_of a good grade of coarse aggregate about
600 feet from the dam site, and because of the permanence
and unquestioned stability of a correctly designed
concrete den. in earthen dam with a concrete epillway
would be an alternative choice for this type of dam.

The only reason it was not used here was because of the
factors mentioned above.

The spillway section does not extend across
the entire length of the dam. It is 8 feet long and is
placed at the center line of the stream. In times of
high water the velocity of the stream will be greatest
in the center and practically neglible along the sides
of the resertoir thus preventing scouring and erosion
of the reservoir. If at any time the flow should be so
great that the spillway section could not handle it,
the water could overflow the crest of the dam without
any permanent hams.

The den site was selected where the sides of
the gully are close together at a point about 500 feet
from the source. The left bank.has a slope of about
3 on 6 and the right bank about 2 on 7. Both banks are
quite solid at this point. The right bank is more
stable here than at most other places. It is well

sedded and has several good-sired trees in it.

The top of the dam will be at an elevation
of 605.0 feet, and the top of the spillway at an
elevation of 605.5 feet. This will give about 7 feet
of water back of the dam and about 5 feet of water at
the source when the reservoir is full. At this stage the
reservoir will have a capacity of 26 acre feet. no
provision has been.made for flashboards but if it is so
desired the dam may be equipped with them.to raise the
level of the pond and increase its capacity. Due to the
natural tapography of the land, none of the adjoining
preperty will be flooded.

Estimate of Cost:

Land:
Acquisition of property .................$ 0.00

Damages to property ..................... 0.00
Dam and Cement work:

Concrete, 37 cusyds. at $1.80 ........... 99.90
Excavating, 206 cu.yds. at .40 62.40
Piling, 28 - 10 ft. piles at 15¢ ft. .... 4.20

Total ...........$1se.oo

This estimate has been based on the following;

Six sacks of cement per cu. yd. of concrete cement at

*0e ‘5 ”1' out.
Aggregates to be secured from gravel pit 500 feet away

at no cost.

This assumes that all labor will be done by
the owner, as is his intention.

In case the Job should be let by contract (a
more general case) the cost estimate would be revised

as follows:

Concrete, 37 cu.yds at $6.00 .........$222.00
Excavating, 205 cu.yds. at .40 ....... 82.40
Piling, 28 - 10 ft. piles at .15 ..... 4.20

Total ............$308.60

DESIGN or DA!
(recs CREAGER a JUSTIN)

For economy, a trapezoidal dam with vertical
face upstream was chosen. The top width which may be
assumed was taken as six inches and the base figured as

follows:

 

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Height

top width

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specific gravity of masonry

 

b - 64 " E I}. - 2: - 2607 ‘- e51 - 025
2.4 4 4 4
. 5e1 " 025 . 4e85 U8. 5'

This fonnula gives a bass of sufficient width so
that the resultant of the forces acting on the dam falls
within the middle one-third of the base. This is

absolutely essential for a correctly designed dam.

The common.methods of failure of a grawity
dam are three; lst, by sliding along a horizontal Joint,
2nd, by overturning about the toe, 3rd, by crushing.

In investigating these methods of failure we need only
consider the first two as the dam is of insufficient
height to cause failure by crushing. ‘ I

Computations for factor of safety in sliding:

 

Pu _ W,f ‘ . S
r in?

P3 - Resisting force

- Effective wt. of section of dam 1 ft. long

f - Friction factor (gravel foundation with piles)
- .6

P - Pressure in lbs. of water against section of

dam 1 ft. wide and h ft. high
W - Unit weight of water
S - Factor of safety I

The effective weight of the dam is obtained by
subtracting from the weight of the masonry in a section

1 ft. long, the upward pressure on this section. The
upward pressure is due to the weight of a column of
water h ft. high times 62.5 lbs. This pressure varies
from the toe to the heel of the dam. The average up-
ward pressure is taken and multiplied by the width of
the base giving the total upward pressure.

The effective weight of the dam when multiplied
by its friction factor and divided by the water pressure
gives the factor of safety.

Downward pressure . 6000.0#
Upward pressure - 2187.§fi
W, ' Effectiv. "to . 3812.“

Effective head - 7'

W. I
i th

3812.5 x .5 , 1955.25 _ 1.35
2 52.4 x 49 1450

 

This factor of safety is not very large but it
may be considered sufficient when it is realised that
this is an extreme case. It is figured in the above
computations that the reservoir is full and that there is

10

no tail water, which would be an unusual case. If there
is any tail water at all, it of course will decrease the
effective head and than give a larger-factor of safety.
For instance, with 2 ft. of tail water the effective
head is only 5 ft. and the factor of safety is:

 

5812.5 x .5 _ 1955.25 _2J5
% x 62.4 x 25 780~

Computations of factor of safety to resist

overturning.
Take moments about the too.

There are three forces which tend to overturn
the dam. They are:

1. Ice pressure which may be disregarded in this case
due to the very short length of the dam, the
gentle slepes, and soft soil of the sides of the
gully.

2. Pressure of the impounded water in a horizontal

‘ direction, and,

5. Pressure of the underground water in a vertical up-

- ward direction.

11

These may be computed as follows:

20 PIEEE; ‘ h

w - unit weight of water
head of water

P . 62e‘ I 64
2

 

8
'5 - 5, 530#

3, P. . Ihb

 

b - base of dam

 

p, a 62.4 x 8 x 5 x 3.2 _ 4,160#
2 3 “——
Total overturning force - 9,490#

The force resisting these overturning forces is
the weight of the dam acting thru the center of gravity

of the dam.
Solving for the center, of gravity of the dam.

18

d . .5 x 8 x 2 + 4 x 4.5Lx (.5 x .33 x 5.5) _
8xe5*4x4e5

1011 ft. fr“ “patron” edge.

PR . VI 2 5e89

w - wt. of 1 ft. section of dam
Pa - 4500 x 3.89 - 17,505#

The resisting moment divided by the over-
turning moment given the factor of safety against over-

 

turning.
PB 17,505
'- - - 1.85
P 9,490

In designing a dam which impounds a large
body of water above a village or city, a factor of
safety of 1.85 would be too small. However, in this
case where economy is a major factor and no home would
be done in case the dam failed, a factor of safety
approaching 2 may be considered sufficient. ‘

The dam.as designed provides for double sheet

piling near the upstream edge of the dam. This is

13

primarily to shut off the flow of underground water
which appears to be quite large. The sheet piling

acts also as support for the dam. As an alternative,
corrugated sheet metal may be driven or Jetted to

hard pan and used as a cut-off wall. In this case, it
would be well to re-space the piles or use an additional
row in order to distribute the weight of the dam evenly.

The base of the dam proper is 5 feet as cal-
culated from the design formula. The base at the spill—
way section has been extended an additional five feet
making a total of ten feet. The tap of the section has
been rounded off and the lower third is concayely
curved in order that the water leaving the apron has
only a horizontal force. In this way the impact of the
falling water has been practically done away with. it
the outside edge of the apron there is a cut-off wall
extending downward two feet. This will prevent the
spillway flow from eroding or washing away the earth from
beneath the apron.

In case it is desired to construct a walk across
the top of the dam 2 inch pipe may be imbedded in the top
of the dam at five feet intervals. These should be
threaded on the top and a "tee" screwed on. One foot
sections of pipe may be threaded into each side of the
"tee” perpendiculary to the dam. A 2 ft. plank walk may

be laid on these as suppprts.

14

Large field stones may be imbedded in the dam
during construction for the sake of economy. They should
be surrounded by at least six inches of mortar. This is
known as "cyclopean' concrete and.may be used without
harmful results. A desirable effect may be secured on the
spillway by placing small stones of not more than 4 inches
diameter in the surface of the concrete.

It is recommended that a four inch steel pipe
be put thru the spillway section about 1 feet above
stream bed. This will provide for draining the reservoir
in case it should ever be desirable or necessary. A
hand Operated valve on the upstream end of the pipe will
serve as a gate. This pipe could be used as a regulator
on the height of the water in the pond.

No loss of water need be expected thru
saturation as the water table is very close to the surface
of the ground at all points. The only loss will be thru
underground flow. It is therefore important that the sheet
piling in the cut-off well be driven as deep as possible
and fitted together carefully in order to prevent this
loss.

There is no provision made for retaining walls
along the sides of the reservoir. The banks near the
ends of the dam should be carefully filled in and protected

so as to prevent washing out around the ends of the dam

 

in case of exceptional high water. They should be well
sodded and planted with shrubbery or trees.

15

 

j '* . -. .,r - 3-. - * ~‘~-'"L{$T

SHIRLEY

is shown by the cost estimate, the dam can
be constructed for approximately $175.00. The owner
will then have a fresh spring water reservoir of 26
acre-feet capacity. The water will have an average
depth of 6 feet.

The usefulness of the dam will be confined
mainly to improvement of the surrounding land, although
the reservoir may be planted with trout with very
successful results as demonstrated by a property owner
about one mile downstream.

Another phase which might be-developed in the
near future is the possibility of using the reservoir
for irrigation purposes. During the winter ice may be
removed from the pond and stored for summer utilisation.
Thus the dam will have an economic value in addition to

the intangible values for which it is designed.

 

 

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