CHAPTER XIII

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.

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.

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.

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.

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.

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.

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.

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.

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.