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senting the base of the dam at a point 2 160 ft. above the drain, or
1 040 ft. up stream from the upper toe of the actual dam. All the pres-
sure observations taken by the author mvist have been affected by the
drain. Under these conditions, the water could not rise to the base
of the dam near the lower toe. In the model, the author has imjwsed
conditions which would not be reproduced in actual practice. If the
dam is to operate under the same conditions as the model, then 360
ft. below the lower toe of the dam a trench, 240 ft. deep and 40 ft.



DISCUSSION ON DESIGNING AN EARTH DAM 45

wide, must be constructed across the canyon. This trench must be Mr.
filled with large stone, in order to provide a perfect drain. In the
bottom of the trench, or at the 240-ft. level, there must be openings
with sufficient capacity to carry off the water as it arrives. The water
must then be conveyed to a reservoir of infinite capacity. In the
model, the drain should be 216 in. from the lower toe, instead of
36 in., or it will affect the water pressure imder the base of the dam.
If the writer's contentions are correct, the results of the author's ex-
periments are of little practical value.

That the drain referred to has affected seriously the results of the
experiments is indicated by the excessive seepage through the founda-
tion of the model. In Test No. 17, Table 3, the seepage, per linear foot
of the model, was 0.00222 cu. ft. per sec. The slope of the line of
saturation in the model is assumed to be the same as that of the actual
dam. The length of travel in the model is proportional to that of the
actual dam. The head and all other dimensions in the model being
proportional to those of the actual dam, the seepage through the latter,
per linear foot, will be 120 times that through the model per linear
foot. The length of the actual dam is to be 2 000 ft., and its left end
will extend into a bank of gravel similar to that which is to compose
the foundation. Considerable excavation will be necessary in order
that the water-tight section of the dam can be carried well into this
bank. It is assumed that the area exposed to water pressure will be
equivalent to the area of 1 200 ft. of maximum section. The seepage
through the actual dam, therefore, would be 120X1200X0.00222,
which equals 320 cu. ft. per sec.

Mr. Hays has not disproved the "line of creep" theory. In the
first test, with the two rows of sheet-piling, he found a small loss of
head at the upper row of piling. This, no doubt, was due to water
passing through the upper section of the dam and entering the founda-
tion both above and below the upper row of sheet-piling.

The pressure at D, Fig. 8, below the lower row of sheet-piling, was
no doubt due to the water from the upper section of the dam entering
the foundation between the piling and the cut-off wall. In fact, the
drain would prevent the water from rising to D after passing below
the lower row of sheet-piling. If Mr. Hays wiU place the drain 216 in.
below the lower toe of the model dam, separate the upper section of
the dam from the foundation, with a sheet of tin, and connect the tin
with the cut-off wall and the two rows of sheet-piling with water-tight
joints, then the hydraulic gradient will begin at the upper toe. Under
these conditions, the effect of the two rows of sheet-piling can be de-
termined, and undoubtedly the ''line of creep" theory, somewhat
modified, will prove to be correct. That is, instead of following down
one side of the sheet-piling and up the other, thence along the base of



46 DISCUSSION ON DESIGNING AN EAKTH DAM

Mr. the dam to the second row of sheet-piling, etc., the water will follow
^^ "^" down the upper side of the first row of sheet-piling and thence in the
general direction of the lower end of the second row of sheet-piling.

Assiiming that there were no other defects in the model, the writer
believes the results of the tests to be imreliable for the following
reasons :

1. — The model dam, being only 11 in. high, and subjected to a head
of 10 in. of water, the entrance head and capillary action would, no
doubt, affect the hydraulic gradient to such an extent that the pres-
sure observations in the model would not indicate the action of the
water in the final structure, where similar material will be subjected
to a head 120 times greater than that on the model.

2. — The model dam was constructed of the same material as that
to be used in the actual structure. It would seem that the material
for the former should have been coarser than that to be used in the
latter. The ratio between the coarseness of the materials in the two
structures, which would result in the action of the water on the model
being comparable to that on the actual dam, could perhaps be de-
termined by extensive experiments.

The writer makes the following suggestions:

1. — That the author construct a model which will represent ex-
actly the original dam as it was to have been built. It is probable
that the results of tests on this model would show the structure to be
safe, provided the model were constructed with the drain 36 in. below
the lower toe. As a matter of fact, with a head of 24 ft. on the actual
dam, the water passed freely through the partly completed structure.

2. — That the author could obtain more reliable information from a
series of tests on models 1, 2, 4, 8, and 12 ft. in height, provided the
drain shown in Fig. 8 were placed at a section 216 in. down stream
from the lower toes of the respective dams. From the results of the
experiments with each of these models, it is possible that some sort
of a curve could be prepared which might be extended to show ap-
proximately the action of the water on the final structure under a
head of 100 ft.

Conclusions. —

1. — The author has not stated clearly how each experiment was
carried on. In some places it is necessary for the reader to assume
that the experiment was conducted under certain imposed conditions.

2. — The model dam used by the author was too small to give reliable
results.

3. — The pressure, at all points observed in the tests, was affected
by the drain; therefore, the results of the experiments are of little
practical value.



DISCUSSION ON DESIGNING AN EARTH DAJI 47

4. — The drain in the model should have been placed 216 in. below Mr.
the lower toe, instead of 36 in.

5. — The author has not disproved the "line of creep" theory.

6. — It would appear that too much dependence was placed on the
impermeability of the material in the upper section of the dam.

7. — If the dam, as designed, were constructed to operate under the
conditions imposed in the model, the flow under it would be about
320 cu. ft. per sec.

8. — It is the writer's opinion that the sheet-piling should be placed
beneath the core-wall. If the core-wall in the partly completed dam is
to be used, then the sheet-piling should be placed near the core-wall
on the up-stream side. A water-tight connection shovild be made
between the core-wall and the sheet-piling. The writer, being some-
what familiar with the conditions at the dam site, feels that, at best,
there will be considerable seepage under the dam, and for this
reason he would suggest that the slope of the down-stream face, below
the 30-ft. berm, be made as flat as 3i : 1 or 4 : 1. The proper slope for
the down-stream face could no doubt be determined by extensive tests
on a series of properly designed models of various heights.

George M. Bacon,* M. Am. Soc. C. E. (by letter). — The main ob- xMr.
jection to drawing conclusions from these experiments seems to be the
assumption that the foundation as composed for the model represents
sub-surface conditions at the dam site, an assumption hardly correct.
What part of the foundation in the model corresponds to the actual
condition on the ground, which allowed sheet-piling to sink "as deep
as 32 ft. with one or two blows from a 1 700-lb. hammer" ? The
mountain streams formed "great cones, or fans, of very porous mate-
rial". Was this material duplicated in the model, and, if so, where?
In an experiment of this kind, it is vital to duplicate the actual condi-
tions which are the subject of investigation. No ingenuity of observa-
tion and recording can minimize the importance of this. There is prac-
tically nothing in the paper showing how the foundation in the model
was formed, or indicating its similarity to actual conditions.

The author's theoretical analyses are interesting, but, should they
serve as a basis for' the solution of the problem actually presented?
If the premises are not correct, any deductions from experiment are
not only of no value, but can easily be harmful as well as misleading.

H. A. PETTERSON,t Assoc. M. Am. Soc. C. E. (by letter). — The Mr.

. Petterson.
writer is a great believer in experimental engineering, and realizes

that much of the advance made in engineering knowledge is due to

the researches of careful and ingenious experimenters. He cannot

believe, however, that experiments made on models with a depth of

* Salt Lake City, Utah.

t Tientsin, China.



48 DISCUSSION ON DESIGNING AN EARTH DAM

Mr. water of only 10 in., will bring forth results of any great practical
et erson. ^^^^^ ^j^ designing a dam to impound water 100 ft. and more in
depth. Our knowledge of the underground flow of water is not as
complete as it ought to be. This is true especially of \m.derground
flow as affected by cut-off walls penetrating only part way into the
porous stratum.

The most reliable experiments, however, would be those made on
existing dams and weirs built on porous foundations. There are many
structures in different parts of the world on which experiments could
be made, and these could follow essentially the methods developed by
Mr. C. S. Slichter.* Until such experiments are made, the writer, for
one, would advocate following present methods, a brief presentation
of the underlying principles of which will be given.

The principles governing the design of an earth dam with imper-
vious core-wall to impervious foundation need not be reviewed, as they
are treated in any number of good textbooks. The problem of securing
water-tightness in earth dams is essentially one of securing the maxi-
mum density of the material; and the laws governing this are known
by the Engineering Profession, even though not universally applied.
Strict adherence to these principles in earth dam construction involves
extra cost, which is not always warranted by the results obtained.

This discussion, therefore, will be confined to the principles involved
in the design of an earth dam on a porous foundation of such great
depth that an impervious cut-off wall to an impervious stratum is
financially impracticable. It will be assumed that the dam will be
made relatively impervious, and safe against ordinary methods of
failure. The principles to be elucidated are the securing of stability
against the possible destructive effect of water flowing under the dam
(not through it) ; also, as it is assumed that the dam is to impound
water in a reservoir, the investigation of the quantity of water lost
by percolation is important from an economic standpoint, though it
may in no way affect the stability of the dam.

A rational design cannot be made without a comprehensive grasp
of the laws governing the flow of underground water. A very brief
summary of present knowledge on these laws will be given, for the
purpose of calling attention to the incompleteness of that knowledge
and to make clearer the writer's comments on certain of the author's
statements.

Laws of Underground Flow,

Hazen's formula, reduced to English units.f is
,, h A (t-\- 10)

* Described in Water Supply Papers, Nos. 67 and 140.

t Report, Mass. State Board of Health, 1892, p. 553 ; also, Turneaure and Russel,
"Public Water Supplies", p. 96.



DISCUSSION ON DESIGNING AN EAKTH DAM 49

.Slicbter's formula* is Mr.

Petterson.

16 272 d^ h A

Q = 1 r- [1 + 0.0187 {t — 32)] (2)

k 1j



Baldwin- Wiseman's formulaf is
h



(3)



In these formulas, c, c^, c^, and h, are coefficients. The values
of c in Hazen's formula vary from 400 to 1 000. The values of A;
are tabulated by Slichter, and vary only with porosity, c^, in Equa-
tion (3), is proportional to cxX^ and — in Equations (1) and (2).
c^ corresponds to the temperature correction of Equations (1) and (2).

Q = discharge, in cubic feet per day, through the area, A ;

A = area of cross-section, in square feet, normal to the line of

flow;
li = difference of water surface, in feet, for two points distant

L feet apart;
L = distance, in feet, measured in direction of line of flow ;
d = effective size of sand grains, in millimeters, determined by

mechanical analysis with sieves in Hazen's formula, and

by the use of King's aspirator:}: in Slichter's formula ;
V = velocity of percolation ;
t = temperature of the water, in degrees, Fahrenheit.

These three equations all agree in several respects:
First. — The rate of flow increases with temperature.

Second. — The rate of tiow increases with the first power of - ,

-L/

or, if h is constant, varies inversely with L.
Third. — The rate of flow varies with some power of the effective
size of the sand grains.

By platting on logarithmic paper, a straight-line relation will be
found to exist between Slichter's values of k and the porosity of the
material. The same relation holds between porosity and the
tabulated values of the transmission coefficient in Water Supply Paper

* U. S. Geological Survey, Water Supply Papers, Nos. 67 and 140 ; also, 19th
Annual Report, U. S. Geol. Survey, Part II, 1899, p. 295.

t Mimttes of Proceedinns, Inst. G. E., Vol. CLXXXI, p. 15 ; also, Technical
Paper No. 97, Govt, of India, 1902.

% For description of King's aspirator, see 15th Annual Report, Agricultural
Experiment Station, Univ. of Wisconsin, 1898.



50 DISCUSSION ON DESIGNING AN EARTH DAM

Mr. No. 140. It may be shown that Slichter's tabulated results may be

Petterson. j • .i j- n •



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