RESERVOIRS AND DAMS
1. =Reservoirs.=--The object of a reservoir is to store water for
town supply or for irrigation or other purposes. Reservoirs for the
water supply of towns are divided into “impounding reservoirs” and
“service reservoirs,” the latter being of comparatively small size,
and their object being to store, near to the town, a supply sufficient
for a short period. Instead of one impounding reservoir there may be
several, formed by various dams and one discharging into another. When
a reservoir is mentioned without qualification, an impounding reservoir
is meant. A reservoir is generally made by blocking up a valley by
means of a dam of earth or masonry. The site of the dam should be
selected at a place where the valley is narrow. The lowest portion or
“bottom water” of a reservoir is usually not drawn upon, because it is
less pure than the rest, and it has to be left, in dry weather, for the
fish. It is not included in calculating the capacity of the reservoir.
In Great Britain, when the water of a stream is impounded,
“compensation water” has to be given back to the stream lower down.
This compensation water is generally given in the form of a constant
supply, and amounts to perhaps a quarter of the available supply. It
has to be included in calculating the daily supply taken out of the
reservoir. The advantage to the stream in having this addition to it
during dry weather is very great.
It has already been seen (CHAP. IX., _Art. 1_) that in an earthen bank
which has to retain water the leakage generally decreases rapidly and
the bank becomes almost impermeable. The same is true of the surface of
a valley, in the case of most ordinary soils, provided that it is kept
submerged. Any portions which become exposed to the sun and weather are
likely to crack and give rise to percolation. Thus a reservoir formed
by the construction of a dam resting on the surface of the ground may
be more or less water-tight according to circumstances. There are many
which are sufficiently water-tight. But in most cases the dam--or an
impervious core-wall--is carried down to an impervious stratum. A
masonry dam is carried down to rock.
In the case of dams of considerable height the soil should be examined
by borings. If there is an inclined stratum not well connected with
that below it, unequal settlement of the dam may occur; and this
may also happen if there is a thick stratum of clay, owing to its
compressibility.
Except for very high dams--those, for instance, more than 110 or
120 feet in height measured from the ground to the water-level--an
earthen dam is cheaper than a masonry dam. It is also more easily
raised and strengthened--though this operation has also been effected
on masonry dams--in case, for instance, of the silting up of the
reservoir, a process which is slow in England, but not so slow when
water containing much silt is dealt with, as in the case of irrigation
reservoirs in India. Sometimes a dam consists of a wall of masonry
or concrete with earth behind it as a support. Whatever kind of dam
is used, its construction always demands very great care. Serious
disasters, with much loss of life, have occurred owing to failures of
dams.
A reservoir with an earthen dam is provided with a waste weir for the
purpose of passing off flood water, which might otherwise overtop the
dam and destroy it. Generally the waste weir is a continuation of the
line of the dam. Its crest has to be below the high-water level of
the reservoir, but not lower than can be helped, and its length has
therefore to be considerable. Sometimes it is provided with grooved
piers between which planks are placed in the season when floods are not
likely to occur.
In connection with irrigation reservoirs in Western India, it has been
pointed out by Strange (_Min. Proc. Inst. C.E._, vol. cxxxii.) that
a long high-level waste weir is best suited to cases in which the
replenishment of the reservoir is uncertain, and that in cases where
it is nearly certain, the high-level weir prevents the water-level in
the reservoir being quickly lowered in the case of an accident or for
the purpose of effecting repairs, impounds the earliest floods, which
are most charged with silt, and causes the water area to be a maximum,
and therefore gives all floods the maximum time in which to deposit
silt. He accordingly suggests that the crests of waste weirs in these
reservoirs should be shortened and lowered and provided with falling
shutters (this had been done in one reservoir and has since been done
in another), and that sluices be added with sills at a still lower
level than the lowered crest. These proposals seem to be entirely
reasonable, though of course it would be necessary to have skilled
supervision over the working of the sluices. Sometimes the waste weir
is made in a separate place, being separated from the dam by a saddle.
A masonry dam may act as its own waste weir, the flood water flowing
over the crest and down the rear slope; but in cases where heavy floods
are liable to occur it is usual to provide a separate waste weir by
cutting away the side of the gorge either close to the dam or at some
other place.
While a dam is in course of construction arrangements must be made to
deal with flood water. Generally the construction of some part of the
dam has to be deferred to let the water pass. In the case of a masonry
dam it does not much matter what part is thus deferred provided the
usual procedure of stepping the work back is followed. In the case
of an earthen dam it is best to defer a portion, not in the lowest
ground where the dam is highest, but to one side of it, thus allowing
the highest part of the dam to be brought up continuously. Temporary
embankments and weirs can be constructed to cause the water to traverse
the desired route without doing damage. Stepping of the earthwork
should be avoided as far as possible. If it has to be adopted, the
steps should be small. Sometimes the flood water is conveyed away by
means of a “by-wash,” by an entirely different route.
[Illustration: FIG. 57.]
In Indian reservoirs the discharge over the waste weir may at times
be great. The waste weir is sometimes in the position shown in fig.
57, _a e_ being the weir. In such a case a special hydraulic problem
arises. In a case where a stream whose velocity is V issues from a
reservoir or takes off at right angles from a larger stream there is
(_Hydraulics_, CHAP. II., _Arts. 19_ and _20_) a fall in the water of
about V^2/2_g_. The same thing occurs downstream of a weir, at least
when there is a clear fall which is vertical or nearly so, so that the
water after falling has no horizontal velocity. The water has to be
started afresh on its course. In the case represented by the figure,
the width of the channel is often restricted because of high ground
beyond _f_, and the velocity in the channel may be very high. Suppose
the channel below _e f_ to be of brickwork with vertical sides, and
to have a 20-foot bed, a slope of 1 in 500, and a depth of water of
10 feet. The velocity may be 15 feet per second, and V^2/2_g_ is 3·49
feet. If the water has a clear fall over the weir at _e_, allowance
must be made for a depth of water of 13·49 feet, not 10 feet, in the
channel at _e_. Ordinarily the length _a e_ will be much greater,
relatively to _e f_, than shown in the figure. Suppose that _a e_ is
300 feet and that the slope of the floor of the channel is carried on
at 1 in 500 from _e f_ up to _a_, _b_, _c_, and _d_, following in each
case the lines marked on the figure which represent the directions of
flow. The length _f a_ will be about 310 feet, and the floor level
at _a_ will be about ·62 feet higher than at _e f_. The water-levels
below the weir will be in each case 13·49 feet above the floor. This
should be allowed for in the design. It is true that the stream on
first starting into horizontal motion below the weir moves more or
less at right angles to it, and has thus a large sectional area and a
low velocity; but it very soon has to turn parallel to the weir and
acquire the full velocity of 15 feet per second, and there must be the
requisite extra head to give this velocity. If the weir is drowned, the
water on passing over it may have a high horizontal velocity, but it
will be at right angles to the axis of the channel, and its effect will
be wasted in eddies.
2. =Capacity of Reservoirs.=--A reservoir depends for its supply on
the yield of a particular valley or valleys which form its catchment
area, and the capacity of the reservoir or reservoirs can be altered
by altering the height or number of the dams. The need for a reservoir
is entirely owing to the inequality in the distribution of the
rainfall. If the rain fell in equal quantities week by week, the daily
fluctuations could probably be equalised by the service reservoirs. The
impounding reservoir could be quite small. Actually, a reservoir is
needed to “equalise” the flow--that is, to give a steady flow for an
intermittent one. The smaller the reservoir, the sooner it will go dry
in a drought and the sooner it will overflow in wet weather and cause
waste of the water. In other words, the larger the reservoir the better
it will fulfil its function of equalising the flow and the greater the
degree to which the catchment area will be utilised.
[Illustration: FIG. 58.]
In the British Isles the distribution of the rainfall which is most
trying for a reservoir, occurs when the rain is heavy during the winter
and very light in summer. Fig. 58 shows a diagram for a reservoir
in the driest year, when the rainfall is (CHAP. II., _Art. 1_) ·63
of the mean annual fall. The distribution of the fall is supposed
to be unfavourable as just described. The lower part of the figure
shows the water-level at the end of each month, the reservoir being
supposed to have vertical sides so that the quantity of water in it is
proportional to the depth of water. The upper part of the figure shows
the water impounded (available fall multiplied by area of catchment)
in full lines, and the consumption in a dotted line. The distance
between the two lines in any month is the same as the rise or fall of
the reservoir in that month. There is supposed to be no overflow, and
the total consumption of water in the year is equal to the quantity
impounded in the year, so that the levels of the reservoir water
surface on 1st January and 31st December, as shown by the horizontal
lines A, B at the left and right of the figure, are the same. Deacon,
who has investigated the subject, has found (_Ency. Brit._, Tenth
Edition, vol. 33, “Water Supply”) that, in order to satisfy the above
conditions, the capacity of the reservoir must be 30 per cent. of the
water impounded during the year, or about 110 days’ consumption. On
1st January the reservoir must be about two-thirds full. At the end
of February it is ready to overflow. At the end of August it is just
becoming dry. The daily consumption is supposed to be steady throughout
the year.
As an instance, suppose the catchment area to be 1000 acres, the mean
annual fall 60 inches, with a loss from evaporation and absorption
of 14 inches. The available rainfall of the year is (see last column
of table below) 23·8 inches, or 1·983̇ feet. The water impounded and
consumed during the year is 1000 × 43,560 × 1·983̇ × 6·25 = 539,962,000
gallons. The reservoir capacity must be 3/10ths of this, or 161,988,600
gallons. This is represented by the height C E. If the mean available
rainfall in January and February is 6·3 inches, or ·525 feet, the
water impounded during those months is 1000 × 43,560 × ·525 × 6·25 =
143,931,000 gallons, and the consumption is 539,962,000/6 = 89,993,667
gallons. The difference, 53,937,333 gallons, represents the addition
A C, to the reservoir. Similarly, the light summer rainfall causes
the depletion A E, and the heavy rainfall in the last four months of
the year the addition E B. If the height of the reservoir above A B
were less than A C, there would be overflow at the end of February;
and if the depth below A B were less than A E, the reservoir would go
dry before the drought ended. If the capacity of the reservoir were
increased either at the top or bottom, the cost would be increased and
nothing would be gained. It is not meant that the highest and lowest
levels of any reservoir designed as above would always, in the driest
year, exactly correspond with the points of overflow and going dry, but
they would do so nearly. Deacon states that such a reservoir would fail
only once in fifty years, and then only for a short time.
The reservoir considered above does not, as already remarked, fully
utilise the yield of the catchment area. In a wetter year there
would be overflow and the yield from the reservoir would not be much
increased. In order to equalise the flow of the two driest years
the capacity of the reservoir must be increased, its yield being
also increased, and so on for larger groups of years. By collecting
information for large numbers of places in the British Isles, Deacon
has prepared diagrams and tables which show the capacities and yields
of reservoirs. The following table gives the figures for the case where
the rainfall is 60 inches and the loss by evaporation and absorption 14
inches:--
+-----------+-------------+-----------+----------+--------+---------+
| Number of | | |Column 2 ÷| | |
| Driest | Net Capacity| | Column 3 | | |
|Consecutive| of Reservoir| | or Number|Ratio of| |
| Years the | for a | Daily | of Days’ |Rainfall|Available|
| Flow of | Catchment | Yield of | Supply |to Mean |Rainfall.|
| which | Area of 100 |Reservoir. | contained| Annual | |
| is to be | acres. | | in the | Fall. | |
| Equalised.| | |Reservoir.| | |
+-----------+-------------+-----------+----------+--------+---------+
| | Gallons. | Gallons. | | | Inches. |
| 1 | 166,000,000 | 1,475,000 | 113 | ·63 | 23·8 |
| 2 | 258,000,000 | 1,815,000 | 142 | ·72 | 29·2 |
| 3 | 329,000,000 | 1,987,000 | 165 | ·77 | 32·2 |
| 4 | 390,000,000 | 2,103,000 | 190 | ·80 | 34·0 |
| 5 | 441,000,000 | 2,187,000 | 201 | ·82 | 35·2 |
| 6 | 487,000,000 | 2,255,000 | 216 | ·835 | 36·1 |
+-----------+-------------+-----------+----------+--------+---------+
The figures in the fifth column are those given in CHAP. II., _Art.
1_. The figures in the last column show the corresponding available
falls, after deducting the loss of 14 inches. It will be seen that,
owing to this deduction, the available falls for the shorter periods
are reduced in a greater ratio than the figures in the fifth column.
In arranging for the supply of towns in the British Isles it is usual
to design the reservoirs so as to equalise the flow of the three driest
consecutive years. Existing reservoirs, old and new, usually contain
from 140 to 170 days’ supply, but some contain less. The above table
shows that for the assumed fall of 60 inches and loss of 14 inches, the
capacity of a reservoir, to allow for a six-year dry period, has to be
49 per cent. more than for a three-year dry period, while the daily
supply from it is only 13 per cent. greater.
The following statement gives Deacon’s figures for mean annual
rainfalls ranging from 30 to 100 inches. The columns marked R show the
reservoir capacities in millions of gallons, and those marked S the
daily yields of the reservoirs in thousands of gallons. The figures
for other falls can be interpolated. For a fall of, for instance, 50
inches, the figures, whether of R or S, are practically a mean between
those for falls of 40 and 60 inches.
+----------+-----------+------------+------------+------------+
| Number | F = 30. | F = 40. | F = 60. | F = 100. |
| of Years | | | | |
| whose | | | | |
| Supply | | | | |
|is to be +-----+-----+-----+------+-----+------+-----+------+
|Equalised.| R. | S. | R. | S. | R. | S. | R. | S. |
+----------+-----+-----+-----+------+-----+------+-----+------+
| 1 | 35 | 300 | 79 | 695 | 166 | 1475 | 345 | 3040 |
| 2 | 85 | 470 | 140 | 900 | 258 | 1815 | 495 | 3600 |
| 3 | 120 | 560 | 190 | 1050 | 329 | 1987 | 610 | 3900 |
| 4 | 150 | 620 | 230 | 1110 | 390 | 2103 | 710 | 4100 |
| 5 | 175 | 650 | 260 | 1170 | 441 | 2187 | 800 | 4230 |
| 6 | 195 | 680 | 290 | 1220 | 487 | 2255 | 887 | 4320 |
+----------+-----+-----+-----+------+-----+------+-----+------+
In all cases the loss is supposed to be 14 inches annually. If it is
15 or 13 inches, the reservoir capacity is less or more by about five,
ten, or fifteen million gallons, according as the number of years in
column 1 is 1, 3, or 6. And the daily yield is less or more by about
50,000 gallons.
With a low rainfall the advantage of a large reservoir is somewhat
increased. The capacity of the six-year reservoir for a fall of 30
inches is 63 per cent. more than that of the three-year reservoir, but
the supply is 22 per cent. greater.
The figures given above for reservoir capacities are suitable for the
British Isles. They assume that the distribution of the rainfall is the
least favourable that is at all likely to occur. Deacon states that
the figures do not relieve the engineer of the exercise of judgment.
As regards the British Isles, the chief questions on which judgment
has to be exercised are whether to equalise the flow of three years or
of another number, and how much to allow for loss. As already stated,
three years is the period usually taken. The figures are suitable for
most places in Europe, but in some places, _e.g._ on the Mediterranean
coast, the distribution of the rainfall is somewhat less favourable
than in the British Isles. In other parts of the world, and notably in
or near the tropics, the distribution of the rainfall must be specially
studied, and a diagram be prepared on the same principle as in the case
of fig. 58. The diagram should be extended to cover the desired number
of years. In hot countries loss by evaporation from the surface of the
reservoir should be allowed for. In India during the hot dry months
this loss may be half an inch in twenty-four hours.
In the article above quoted it is shown that if, as commonly happens,
the consumption of water is, in summer, greater than the mean, and in
winter less, the conditions are still more trying for the reservoir;
and that in the case where the summer consumption is 13 per cent.
greater than the mean, the capacity of the reservoir which impounds the
water of the driest year must be 33 per cent., instead of 30 per cent.,
of the total supply impounded during the year. It would then contain
121 days’ instead of 110 days’ mean supply. In the table on page 170
the number of days’ supply is 113. From this it appears that the tables
from which extracts have been given are calculated on the basis of a
constant consumption. This, however, in the case where the number of
years whose supply is equalised is greater than one, makes, owing to
the increased size of the reservoir, no practical difference.
The calculations for the great reservoirs in Radnorshire for the supply
of the city of Birmingham are as follows (_Min. Proc. Inst. C.E._,
vol. clxxx.). The ratio of the mean fall in the three driest years to
the mean annual fall was taken as ·80 instead of ·77. There is some
difference of opinion as to the best figure:--
Mean annual fall determined from readings
of various gauges 65 inches
Mean fall of three driest years 52 ”
Deduct loss from evaporation and absorption
and losses during floods 15 ”
Available rainfall 37 ”
This multiplied by 44,000 acres, the area of the catchment, gives 102
million gallons per day. Of this, 27,000,000 gallons is compensation
water, leaving 75,000,000 gallons for Birmingham. Capacity of
reservoirs, 17,250,000,000 gallons, or 169 days’ supply.
[Illustration: FIG. 59.]
3. =Earthen Dams.=--Before an earthen dam is made, any soft soil on the
site should be removed and the ground downstream of the site should
be drained. A few trenches, running parallel to the axis of the dam,
can be dug so as to give the dam a hold, though there is never any
danger of its being moved horizontally by the thrust of the water.
If the ground has a side-long slope it should be benched as shown in
fig. 59. The front slope of an earthen dam is generally about 3 to 1,
and the rear slope about 2 to 1. The top has a width of ⅓ to ½ the
greatest depth of water held up, and is 5 to 10 feet above the highest
water-level. The borrow pits from which the earth for the dam is got
should not be near enough to it to in any way affect its stability.
[Illustration: FIG. 60.]
In England, and generally in other countries, an earthen dam has a
core-wall (fig. 60) which is carried down to an impervious stratum,
and is keyed into it to a depth of a foot or more in the case of
hard rock and several feet in the case of clay. On this core-wall
the impermeability of the dam chiefly depends. The core-wall may be
of clay puddle, concrete, or masonry. In England it is generally of
clay puddle. The core-wall sometimes extends down to a depth of 100
or 200 feet. Its top is horizontal and about level with the highest
water-level. It is desirable not to make the foundation stepped,
but to let it follow the profile of the impervious stratum. The
wall is keyed at its ends into the sides of the valley or gorge. A
core-wall of concrete or masonry is, in a high dam, necessarily a
comparatively thin structure, and it may be subjected to great strains
by unequal pressures of the earth which surrounds it. It is therefore
to some extent liable to crack. A core-wall of concrete used for the
water-works of Boston, U.S.A., is 100 feet high, 8 feet thick at the
base, and 4 feet thick at the top. A clay-puddle wall, being plastic
and moist, at least during the period immediately succeeding the
construction of the work, is not very liable to crack. The top width
of a puddle wall may be 4 to 10 feet, and the batter of the sides from
1 in 20 to 1 in 8. The clay used for the wall above the ground-level
should contain about 33 per cent. of sand and stones. This diminishes
its shrinkage if it dries. It should not be given too much water in
mixing. It should be thoroughly mixed and worked up and trodden down.
The clay puddle and the earth of the dam should be carried up
uniformly. The allowance for settlement may be 1/30 to 1/50. The earth
should be deposited in thin layers, moistened and rammed, and all clods
broken. In India and some other countries, instead of the earth being
rammed, cattle or sheep are driven over it repeatedly. This makes
earthwork of most excellent quality, and the settlement, if any, is
very small.
In cases where, owing to a fissure in the rock below the bottom of the
puddle trench, water comes through under the puddle, it is usual to
carry it away in a pipe running vertically in a groove up the side of
the trench and then horizontally till it emerges from the dam. Such
water, and any other leakage, can often in Great Britain be used as
part of the compensation water. There is, however, a certain chance,
when there are water-bearing fissures in the rock below the bottom of
the trench, that some percolating stream of water may wash away the
puddle, and it is preferable to use a concrete core-wall in such cases,
carrying it up to about ground-level and keying it into a much thicker
wall of puddle which is carried up to the water-level.
It has been suggested that the clay puddle or other impervious layer
should be placed, not vertically and in the middle of the dam, but
lying on the upstream face of the dam, so as to keep out water from
the whole dam instead of from only half of it. Objections to this, if
clay puddle is used, are that vermin may bore holes in it, and that,
with some clays, it would slip. These objections might be overcome to
some extent by laying a pitching of concrete blocks over the puddle.
Other objections, applying also when masonry or concrete is used, are
that the superficial area and cost are increased, and that cracks would
occur from settlement of the earth and from changes of temperature when
the water in the reservoir was low. A good many cases have occurred in
which an impervious layer laid on the slopes has failed from one cause
or another. In France it is usual to rely on such a layer--concrete
is used--and to dispense with a core-wall. The practice of having a
vertical wall appears to be the best, and is the most widely adopted.
When puddle is used the weight of the mass above it forces it to
completely fill the trench, and when once it is in position and covered
up it is not at all likely to be damaged.
[Illustration: FIG. 61.]
The outer portion of a high embankment sometimes slips (fig. 61), and
precautions should be taken against this. A slip may occur if the site
of the dam has not been carefully selected as to geological formation,
or if there is unequal settlement owing to the work having been done at
different times. One cause of slips is sudden and partial changes in
the degree of saturation, and another cause is excessive saturation.
Some clays when wet require extremely flat side slopes, and will
not stand even at 5 to 1. The outer parts of the embankment are not
required for stopping percolation (this will be further considered in
the following paragraph), and, though they must be carefully laid and
consolidated, they should be of porous material, and the part on the
downstream side of the dam must be well drained. A series of surface
drains may be arranged and filled with loose stone and gravel. There is
also a distinct advantage in using heavy material such as small stone
for the lowest portion of the outer parts on both sides of the dam.
When good material cannot be obtained, the side slope on the downstream
side of the dam may be flattened. A side slope starting at the top
with 3 to 1 and becoming 4 to 1 lower down, and finally 5 to 1 at the
base, is a very good form for prevention of slipping and generally
for the safety of a dam. The part on the side next the reservoir is
not likely to slip. It becomes soaked, but it has the pressure of the
water against it and is pitched. In Madras, where reservoirs are very
numerous, the slope on the side next the water is generally only 1½ to
1.
The different parts of an earthen dam fulfil two distinct functions.
Some parts, which may be called the staunches, have to stop the
percolation of water from the reservoirs. Other parts, which may
be called the supports, have merely to hold up the staunches. In
the British type of dam the portion nearest the core-wall on either
side (fig. 60) is generally made of earth specially selected for
impermeability. The distance to which it extends from the wall depends
partly on the quantity of such earth available. In any case it has to
be very carefully made and consolidated, to avoid unequal pressures
on the core-wall, or unequal settlement which might cause it to part
from the wall. One of its functions is to keep the core-wall moist
when the water-level in the reservoir falls. Whether it is also to
be considered as a staunch or a support might at first appear to be
of no consequence, but it is of importance as affecting the question
of drainage. The support on the downstream side of the dam must, as
has just been seen, be made of porous material and be well drained;
but obviously a staunch must not be porous, nor can it be penetrated
by drains. The question must be decided in each case according to
judgment. In a discussion which took place on the above-mentioned paper
by Strange, at the Institution of Civil Engineers, much diversity of
opinion was expressed among eminent engineers as to the desirability
of draining the downstream half of the dam, _i.e._ the part downstream
of the core-wall. By some it was urged that drainage is necessary to
lessen the chance of the earthwork slipping. Others contended that any
drain which penetrates the dam must facilitate the percolation of water
from the reservoir. It is clear that some of the speakers regarded
the dam downstream of the core-wall as being partly staunch, and some
as being wholly support. If for any reason there seems a chance of
water leaking through the core-wall, it is desirable to regard the
earth-filling next to it as staunch.
In Western India a kind of puddle is made by mixing three parts of
“black cotton soil” with two of sand. The object of the puddle wall is
only to prevent water from finding its way along the surface of the
ground. It is carried down only to a fairly water-tight stratum and
is carried up only to 1 foot above the ground. Above that the mass of
the dam is made of black cotton soil as a staunch, with more porous
material on both sides of it.
In order to afford full protection against waves and their splashes,
the pitching on the upstream face of a dam should extend up to a height
of 5 feet, measured vertically, above the highest water-level. In the
case of a dam in which the “fetch” or distance over which the waves
have been in process of formation exceeds two miles, the above height
should be slightly increased.[21] The pitching is usually of stones
roughly squared at their outer ends and laid on a layer of broken
stones.
The water from a reservoir is usually drawn off by means of pipes which
are laid inside a masonry culvert built under the dam. The pipes can
thus be inspected. The culvert is blocked at its upstream end by a
thick masonry wall through which the pipes pass. Accidents which have
happened in the past have been due to weakness of the culvert or to
water finding its way along the outside of the masonry. The culvert can
be made of proper strength, and it should have a thick coating of clay
puddle which is worked into the clay-puddle core-wall of the dam. If
the core-wall is of masonry or concrete, the masonry of the culvert is
properly joined to it. In many cases the culvert and pipes are taken
through a cutting or tunnel and not under the dam.
At the upstream end of the culvert there is a masonry tower--access to
it is obtained from the top of the dam by a foot-bridge,--and from it
valves for opening and closing the pipes are worked. If the reservoir
is for the water supply of a town, it is arranged, by means of a
vertical pipe, that the draw-off can be at various levels so that the
surface-water can always be used. In the case of some of the towers at
the reservoirs whence Birmingham is now supplied, the vertical pipe
consists of a number of steel cylinders with gun-metal faces which are
so accurately made that the joint is water-tight when one cylinder
merely stands on another. The draw-off is obtained from a given level
by lifting a particular number of cylinders. Sometimes the tower is
made of reinforced concrete. When it is lofty it should be strong
enough to resist a strong wind, blowing when the reservoir is empty.
4. =Masonry Dams.=--For heights much exceeding 110 or 120 feet a
masonry dam may be cheaper than an earthen dam; and in case a flood
occurs while work is in progress the masonry might suffer little
injury, while earthwork might be swept away completely. Masonry dams
are usually built of random rubble masonry with faces of dressed stone.
Such masonry weighs about 140 lbs. per cubic foot, and is ordinarily
quite safe when subjected to pressures of 20 tons per square foot, but
in a masonry dam a high factor of safety is necessary, and 15 tons per
square foot may be allowed. In a wall of such masonry with both faces
vertical, the pressure, owing to the weight of the wall, will reach the
above limit when the wall has attained a height of about 220 feet.
In a masonry dam, although the masonry is always of the best quality,
it is a rule to calculate the dimensions so as to give no tension on
any part of the masonry. Any crack or opening of a joint, occurring
perhaps before the masonry had hardened, would let in water, and its
pressure would tend to gradually extend the crack and eventually to
overturn the portion above the crack.
Fig. 62 shows the upper part of a masonry dam. The lines with arrows
show the vertical force due to the weight of the masonry above A B, the
horizontal force due to the water-pressure on it--acting at two-thirds
of the depth,--and the resultant of these two. In order that there may
be no tension on the masonry, the resultant must always fall within
the middle third of the thickness of the dam. In order to prevent its
falling outside the middle third, the downstream face must be splayed
out, and the splay will go on increasing somewhat. Suppose, now, that
the reservoir is laid dry. It will be found that in the case of a dam
more than 100 feet high the pressure due to the weight of the wall
alone will fall outside the middle third--to the upstream side of it,
of course--of the thickness of the wall, and a slight splay must be
given to the upstream side. The vertical pressure of the water on this
splayed part must be taken into consideration. The limit of pressure,
15 tons per square foot, may eventually be reached owing to the height
of the dam, and additional splay may have to be given for this. When
the outside splay becomes considerable a further allowance is made
for it, because the stress at the edge of a horizontal section is
tangential to the face. In order that the tangential stress may not
exceed 15 tons per square foot, the vertical stress at the outer edge
of a horizontal section of the dam must not exceed about 12 tons. By
following the above rules the section of the dam can be calculated,
beginning from the top and working downwards. The resulting profile of
the dam is somewhat as shown in fig. 63. If a masonry dam is designed
on the principles given above--that is, so as to be safe as regards
crushing and overturning--it will be safe as regards shearing or
sliding horizontally, but a test calculation can easily be made for
this.
[Illustration: FIG. 62.]
[Illustration: FIG. 63.]
Calculations of the above kind do not, of course, enable all the
stresses in a solid mass of masonry to be found. Great stresses are
caused by expansion and contraction owing to changes in temperature.
Others are caused by the connections of the dam with the rock on which
it rests and with the sides of the gorge. The method of calculation
described above indicates a suitable form for the profile of a dam. The
large factor of safety adopted allows for other stresses. The sections
of the oldest dams, made in Spain, were somewhat as shown in fig. 64,
and contained about twice as much material as was necessary. The object
of the calculations is to save this needless expenditure.
Masonry dams designed on the above principles have been constructed for
heights ranging up to nearly 300 feet, measured from the foundation
to the top. The foundation is always on hard rock free from fissures.
Generally a foundation trench is cut. The ends of the dam are carried
into the rock on the sides of the gorge. They should not, however,
if the sides of the gorge are steep, be built in with mortar, but be
allowed to expand and contract vertically, a water-tight joint being
made by means of asphalt (_Ency. Brit._, Tenth Edition, vol. 33, “Water
Supply”). This obviously reduces the straining. A dam should be built
in cool weather, so that any stresses to which it will eventually be
subjected owing to changes in temperature will be chiefly compressive.
The upstream face should be as water-tight as possible. There should
not, however, be too sudden a change in the character of the masonry
from the face work to the inside work. If there are any springs, they
must be carefully connected to pipes and carried outside the dam. No
water must be permitted to get under or inside the dam, either from
springs in the sides of the gorge or from the water in the reservoir.
Many existing dams leak slightly where they join the sides of the
valley, and most have developed some vertical cracks normal to the
face.
[Illustration: FIG. 64.]
Out of some hundred high masonry dams which have been erected, only
three are known to have failed. Of these, the Puentes dam was partly
founded on piles; and in two, the Habra and Bouzey dams, the rule of
the middle third was not attended to. Another dam, not so high, the
Austin dam, in Texas, U.S.A., failed seven years after construction.
It was 65 feet high and founded on limestone, the width of the base
being 66 feet. Springs in the bed and sides of the gorge had, during
the construction of the dam, given much trouble, and had, after its
completion, forced their way through the underlying rock. At the time
of failure 11 feet of water was passing over the dam, which sheared in
two places, a length of 440 feet of it being pushed forward for 40 or
50 feet without overturning, but subsequently breaking up. The dam was
founded in a trench cut in the rock. The rock on the downstream side of
the foundation trench appears to have been worn away by the water, so
that there was no longer a trench (_Scientific American_, 28th April
1900). The above, however, does not seem to be sufficient to account
for failure. The horizontal water-pressure on a 1-foot length of the
dam would be 180,000 lbs. and the weight of masonry to be moved perhaps
320,000 lbs. It seems probable that water from upstream found its way
under the dam and exercised a lifting force on it and so caused it to
slide.
If a masonry dam, instead of being straight, is made curved on plan,
with its convexity upstream, it acts as an arch, and its thickness
can, in the case of a fairly narrow gorge, be greatly reduced. This
type of dam is a suitable one to use when the sides of the gorge are
of firm and solid rock and there is no doubt about their being able to
stand the thrust without yielding. Several dams of very considerable
size have recently been built in this way. The thickness of the upper
part of the dam and the ratio of the versed-sine of the arch to the
span can be decided on by the methods used for arches in general. The
lower part of the dam is made thicker. The lowest part cannot act as
an arch, because it is attached to the foundation. It is, however,
assisted by the portion above it, which acts as an arch, and thus
need not be so thick as in a “gravity” section. The Bear Valley dam,
which is 64 feet high, is only 3 feet thick at the top. The thickness
increases gradually to 8½ feet at 48 feet from the top. The chord
of the curve is 250 feet and the radius of curvature 335 feet. If
the gorge is wide, the thickness of the arch comes out so great that
nothing is saved by adopting the curved form. But in such a case, and
in any case, a dam can be made slightly curved so as to offer a greatly
increased resistance to overturning. It need not act as an arch, and
can be prevented from so acting, in order that excessive stresses may
be avoided, by letting the ends of the dam, after they have entered the
grooves cut in the sides of the gorge, stop short of the ends of the
grooves.
[Illustration: FIG. 65.]
During the last few years much attention has been given to the
investigation of the stresses to which a masonry dam is subjected. Some
investigations have been theoretical and others practical, models of
india-rubber and other substances having been used for experiment. The
investigations show that generally the stresses in a model of a dam are
very much the same as would be expected, but that there is a tensile
stress, previously overlooked, near the point M (fig. 65), where the
dam rests on its foundation. The tension is on the foundation, on the
line M N, and is due to the horizontal thrust of the water. It is
natural that in an elastic model this stress should manifest itself
by deformation. In the case of an actual dam resting on rock, matters
are different; but this tensile stress deserves consideration. For the
present let it be supposed that there is no trench, the dam merely
standing on the rock. Suppose that the rock has only the thickness
M R. There is tension in M N, and probably compression in N R. It
is assumed that, along the base M P, there is perfect union between
the dam and the rock. The tension to which the rock is occasionally
subjected owing to changes of temperature may exceed any tension due to
the water-pressure, but it is conceivable that the tension occurring
from both causes might cause a crack at M N, and that this might extend
to R. This implies a minute sliding of the dam and of the rock below
it, movement taking place on the plane R Q. The thrust of the water is
now resisted by the rock downstream of P Q. The dam, with the rock M
R Q P adhering to it, tends to rotate about the point P. The tendency
to rotate will be enhanced if water enters M R, and still more if it
enters R Q. No rotation can, however, take place unless the rock at M
R is splintered away. The rock would also have to fracture at P Q. It
has been suggested that the upstream face of the dam be made curved
as shown by the dotted line. This would shift the chief tension to _m
n_, and the dam, with the rock beneath it and the weight of the water
above the curved portion, would obviously offer an increased resistance
to rotation about P. The cost of the dam would of course be increased.
The danger of a crack forming at M N seems to exist only when there is
a thin upper stratum of rock not firmly connected to rock below. When
this condition is believed to exist, a masonry dam, if built at all,
should have the upstream face curved as above described. In the case of
any existing dam of great height, when the above condition is suspected
to exist, the reservoir might be laid dry, and if any crack at M N is
discovered a curved portion could be added; but in this case the union
between the new and the old work would be imperfect, and the curve
should start from high up on the upstream face of the dam. It has been
suggested that asphalt or some impervious material be laid on the rock
to prevent water from entering any crack. It would, however, not only
have to be laid upstream of the dam, but to extend under part of the
dam, and thus weaken it to some extent.
In the case (fig. 63) in which the dam is founded in a deep trench,
the building up of the upstream triangular space and uniting the
material both to the dam and to the side of the trench, might be of
some use, but a crack might form in it. It would be desirable to add a
curved portion, as above described, on the top of the rock if sound,
or to remove the unsound rock and widen the trench and then add the
curved portion. Adding material to the downstream triangular space,
and uniting it well, would also increase the resistance of the dam to
overturning, not so much because of the additional weight, as because
of the raising of the point about which the dam would have to revolve
in overturning.
Several recent dams have been built of cyclopean concrete, blocks
of rock as heavy as 10 tons being sometimes used in the work. Such
blocks are laid on one of their flat faces. In the U.S.A. some
reservoirs have been made with walls of reinforced concrete, backed
by earth embankments (_Min. Proc. Inst. C.E._, vol. clxxxix.), and
also of cyclopean masonry reinforced with steel rods. Another kind
of dam which has been used in the U.S.A. is the rock-fill dam with a
core--corresponding to the puddle wall in an earthen dam--of steel
plates riveted together and made water-tight and inserted into the rock
at each side. In the case of the East Canyon Creek Reservoir, Morgan,
Utah, the dam is 110 feet high. The steel plates vary in thickness
from 3/8-inch at the bottom to ¼-inch at the top, and are embedded in
asphaltum concrete and rest on a concrete base. The dry-stone work
of the dam is hand-packed on both faces, and also on both sides of
the core. The rest is thrown in. The upstream face is 1 to 1, and the
downstream face 2 to 1. The waste weir is at one end of the dam and is
continued by a flume, so that the water falls clear of the dam. The
outlet is a tunnel in the rock.