A. E. Krzhizhanovsky.

Dams

and

the Use of Water Energy

to Power an Engine

Tomsk.

Steam Typo-Lithography of P. I. Makushin. Blagoveshchensky Lane, own house.

1904.

ERRATA

Page	Line	Printed	Should read
1	9	most	most
5	13	Neelov	Neelov
14	29 (eq. b)	$h+y_2=y+i$	$h+y_2=y_1+i$
14	20	$cb$	$cd$
15	12 (eq. g)	$-dy-i\,dx=\dfrac{V\,dv}{g}-\beta\,\dfrac{dx}{y}$	$-dy-i\,dx=\dfrac{V\,dv}{g}-\beta\,\dfrac{dx}{y}\,\dfrac{V^2}{2g}$
15	15 (eq. h)	$y\,dv=v\,dy$	$y\,dV-V\,dy$
15	17	$dy+i\,dx=\dfrac{V^2\,dy}{gy}+\dfrac{3}{2}\dfrac{dx}{y}\dfrac{V^2}{2g}$	$dy+i\,dx=\dfrac{V^2\,dy}{gy}\dfrac{3}{2}-\dfrac{dx}{y}\dfrac{V^2}{g}$
16	1 and following	$i=\dfrac{3}{2}$	$i=\dfrac{3}{2}$
16	11	in
16	22	$d\,\dfrac{V^2}{2g}=\dfrac{V\,dV}{y}=\dfrac{V_1^2-V^2}{2y}$	$d\,\dfrac{V^2}{2g}=\dfrac{V\,dV}{g}=\dfrac{V_1^2-V^2}{2g}$
16	28	$\Theta=bcu=byv$	$\Theta=bcU=b\cdot V$
16	28	$v^2=\dfrac{u^2 l^2}{y^2}$	$V^2=\dfrac{U^2 e^2}{y^2}$
16	30	$dy=-i\,dx+\dfrac{1}{k^2}\dfrac{U^2 l^3}{y^3}\,dx$	$dy=i\,dx+\dfrac{1}{k^2}\dfrac{U^2 e^2}{y^3}\,dx$
18	7 (eq. 2)	$\dfrac{ix}{e}=\Phi\!\left(\dfrac{z}{e}\right)-\Phi\!\left(\dfrac{z}{e}\right)$	$\dfrac{ix}{e}=\Phi\!\left(\dfrac{Z}{e}\right)-\Phi\!\left(\dfrac{z}{e}\right)$
22	note	Evlevich	Evnevich,
30	last	$eas$ and $dbt$	$eaf$ and $dbg$
31	1	$dk$ and $fh=gh$	$dK$ and $fh=gK$
31	2	$heasutbdk$	$heasutbdK$
31	3	$hea$ and $kdb$	$hea$ and $Kdb$
31	21--22	$cd$	$ed$
31	23	$kh$	$Kh$
32	20	Gausman	Gausman
35	2nd from bottom	this	this
58	20	semi-circular	semi-circular

ERRATA IN THE DRAWINGS

Page / Table	Printed	Should read
19	the letter $K$ is omitted on the continuation of the line $hkfeg$
Table VI	bullock	bullock
Table VII	heavy	harnessed,

ERRATA IN THE TABLE OF CONTENTS

Location	Printed	Should read
Last line	66 pp.	56 pp.

Preface.

Our technical literature is very poor in works dealing with the exploitation of water as motive power for factories. This subject in itself falls into two independent divisions: the study of methods for collecting and preserving the energy of natural waters, and the study of water engines. Leaving aside the latter division, which has been more fully investigated in our literature, it may be noted that on questions of the first division we have, it seems, only one printed book devoted to it as an independent subject. This is Mr. Neyelov’s book, Dams, published in 1884 and now completely out of print. The courses that are read in our higher technical schools, appearing in the form of lithographed lectures, do not circulate among the public. Meanwhile, interest in this subject among us is increasing with every year.

The latest improvements in turbine construction, the improvement of the transmission of energy by electricity, and the incessant rise in the cost of fuel compel ever more frequent recourse to the exploitation of nature’s free power—the force of falling water. Foreign experience and the magnificent results achieved there further encourage our industry along this path. Whereas formerly the work of exploiting water was carried out almost exclusively, so to speak, by artisanal methods, in the hands of home-grown technicians, now on these questions people repeatedly turn to the educated specialist, and sometimes do not hesitate to expend considerable capital without certainty, even without a guarantee of success. But since there are still very few such specialists among us in Russia, it seems to me that every manual on this subject should be of benefit.

In compiling my book, I had in view presenting, in as concise a form as possible, everything that, in my opinion, is necessary for a correct understanding of

II

and the calculation of the use of water, and since this use almost never takes place without the construction of dams, I have gathered empirical and theoretical data for the design of dams and have given descriptions of various structures. Further, knowing from experience how important examples are in design, I have taken care that, in the appended atlas, every type of dam should have at least one actually existing example.

Intending my little book only for those who are more or less technically prepared, and wishing to reduce the size of the book, I omit everything that, having only an incidental relation to the exposition, should be known from elementary preparatory courses in physics, geodesy, hydraulics, and civil engineering.

Available Work

Every artificial barrier that obstructs the flow of a river with the aim of raising the water level in it constitutes a water-retaining dam. If such a rise is effected for the purpose of setting a water motor in motion, then the dam is often called, depending on the enterprise that is driven by the water, a mill dam, a factory dam, or an industrial-plant dam. Since, for the operation of plants, in most cases small rivers and streams are exploited, in which there is often too little water to produce the full required reserve of motive power, the study both of the rivers themselves and of dams from the point of view of the most proper use of the energy of water is a very important question, one that should be addressed before studying the construction of dams themselves.

As is known from hydraulics, when a certain volume of water \(\Theta\) cubic meters is moved from one level to another lying \(H\) meters lower, irrespective of the path by which this movement is accomplished, the water, by virtue of its weight, performs work which, for the volume \(\Theta\), is expressed as

\[ L = \Theta H \cdot \gamma\ \mathrm{klg.\ mtr.} \]

Here \(\gamma\) is the weight of a cubic meter of water \(= 1000\ \mathrm{klg}\). If \(\Theta\) is the volume per second, otherwise the discharge, then the work per second, expressed in horsepower, will be

\[ N = \frac{\Theta \gamma H}{75}; \ldots (1). \]

This work \(N\) (the available work of the water) can be received by the motor with certain losses, depending on the perfection of the design. A dam, by producing at a given place on the river a considerable difference between the levels of the upper and lower water, makes it possible to transfer water from the upper to the lower level, passing it along this path through the motor machine, and thus to utilize the work for the plant.

Equality (1) shows that the available work is directly proportional to $\Theta$—the per-second discharge—and to $H$—the head of water ($H$ is often also called the fall). To obtain the greatest work, one should strive to obtain, as far as possible, larger $\Theta$ and $H$. Let us consider each of these factors of work separately.

Variability of discharge in rivers and regulation by ponds.

The discharge of a given river at a definite moment is a quantity which, in most cases, depends exclusively on natural conditions that vary over the course of the entire year; for this reason the discharge fluctuates continuously. It is impossible to establish a relation, common to all rivers, between the discharges of water at different times of the year: depending on the geographical latitude of the locality, the fall of the river itself, the soil of the basin, and so forth, these relations may be extremely different, and in this respect each river must be studied separately. Most Russian rivers in spring, during the melting of the snows, carry for several weeks—and sometimes even days—enormous quantities of water; their discharge at this time exceeds by 100–200 times and more the discharge in the driest period, while their normal discharge, lasting for the greater part of the year, is 3–10 times greater than the minimum. However, even these broad limits are by no means a general rule.

Such an enormous fluctuation of discharge can, to some extent, be equalized by the proper construction of a dam. The point is that a dam, by backing up the water of a river, can cause it to leave its banks and flood the adjacent low-lying surroundings; in this way a lake or pond may be formed, which will be filled during the flood. Then the reserve of water thus obtained can be used to make up the deficiency in the dry period.

To obtain the plan of such a lake, one must first compile a topographic map of the river and the adjacent locality in horizontal contours; then, having set the rise of the water and knowing that the surface of the lake will be horizontal, it is no longer difficult to determine both the entire surface of the lake and its entire volume.

However, the entire volume of water in the pond cannot be taken into account. In addition to various losses, which will be discussed below, in most cases it proves impossible to draw the water down below a certain level. Thus, if such a lake is situated immediately at the dam or not far from it, and right there on the downstream side of the dam is the lower water level, then the fluctuation of the water in the lake must

will be strongly reflected in the whole head. An engine is ordinarily installed to work at a definite head and, without considerable losses, does not admit of any special lowering of it; this is one point. Secondly, according to expression (1), the work of one and the same quantity of water is proportional to the head; if this head is lowered, then, consequently, operation proceeds less successfully. If, therefore, a pond has some constant, or at times limited, inflow of water, then the head should not be lowered too much, because then, when water again flows into the pond, the water may no longer rise to its former height, and work will have to be lost all the time. These considerations also compel one to use only a certain layer of water, the thickness of which constitutes only a part of the total head.

Here one may see ponds in which, in dry weather, the lowering of the water level reaches 50% of the head; but after such a lowering, the operation of the engine on it ceases entirely until spring, when it fills again. Obviously, such a lowering is not always rational, and it is hardly ever advisable, with a continuous inflow of water, to lower the head by more than 10–20%.

All the quantity of water below the discharge layer, of course, cannot be included in the calculation, and therefore deepening the bottom in ponds by digging pits, as I have happened to see, is an entirely senseless and costly undertaking.

In calculating storage ponds for a small head, if prolonged regulating action is required from the pond, its surface area turns out to be very considerable, and it is sometimes unprofitable to construct such ponds.

I shall explain this best by an example. Let us find the surface area of a pond needed to form a reserve of water providing one horsepower over the course of 2 months, if it is known that during this time the head is reduced from 3 to 2.5 metr. For simplicity, let us suppose the banks of the pond to be vertical to a depth of 0.5 metr., and let us assume that an estimated work of 100 kg. metr. per sec. is capable of giving one horsepower on the engine shaft.

Then, taking the head throughout to remain equal to the average \(= 2.75\) metr., we obtain the quantity of water necessary for work over the course of 60 twenty-four-hour days as equal to

\[ \frac{60.24.60.60.100}{2.75} = \infty 190 \text{ mil. kil. i.e. } 190{,}000 \text{ cub. metr.,} \]

and since a layer of 0.5 metr. is drawn off from the pond, the required surface area is

\[ = \infty 380{,}000 \text{ sq. metr.} = \infty 35 \text{ desyatins.} \]

Even assuming that one horsepower is capable of yielding an income of 1 kopeck per hour, the total income over 60 days will be 14 rubles 40 kopecks, which, per desyatina of land covered with water, gives only 40 kopecks. But land can yield such an insignificant income only in exceptional cases.

If the head were 30 meters, then, allowing the same fluctuation of level as a percentage of the total head, we would obtain from a desyatina already 40 rubles; and with a head of 300 meters, with the possibility of lowering the level by 50 meters, the income from a desyatina of flooded land would already amount to 4000 rubles.

There are, however, cases when even with a small fall a pond is very advantageous. This is so, for example, when over the course of a day, or of several days, the machines operate with variable power.

Many rural mills operate only by day; then the pond must store all the water flowing in during the night.

Keeping to the same magnitude of head and fluctuation of level as in the preceding example, we find that for one horsepower over 12 hours of daytime operation about 0.35 desyatina of pond will be required, and owing to this surface 12,360 working hours can be saved during the year, which, according to the preceding valuation of a horsepower-hour, will give us 43 rubles, while a desyatina will give 125 rubles.

Such a small storage pond is not only useful but, in part, even necessary; otherwise, with considerable fluctuation in the discharge of water to the engine, the head would begin to fall very rapidly, which would cause stoppages and, in general, irregularities in the operation of the engine; whereas the storage in the pond, by making the fluctuations of level slower, makes it possible to reduce the work of the machine in good time without changing the speed of the engine. Where the engine operates with the full discharge, the absence of even a small pond has a very harmful effect on the entire course of work, and this should always be borne in mind.

The surface of the entire dammed-up river must, of course, also be included in the surface of the pond, but only in part, since by lowering the level at the dam by some height \(h\), upstream we obtain smaller and smaller lowerings; in other words, the depth of the layer that can be taken from the river diminishes as the distance from the dam increases. I shall return to this phenomenon in the further exposition.

It is clear that the location of the pond does not play an essential role. Most often it is built immediately behind the dam, but there are cases when it is located somewhere far from the dam upstream. Sometimes, to form a pond, a separate dam is built and

the loss of water in the river is made up by releasing water into the channel as needed.

Besides constructing a pond on a river, it may sometimes prove advantageous to arrange a pond for the runoff of snow and rain waters and to make use of the reserve of water thus formed. Whatever the pond may be, however, there is always a loss of water in it from drying out (evaporation), seepage into the ground, and absorption. Evaporation depends on the size of the pond, the season of the year, the climate, and the locality. Observations show that, generally speaking, from the surface of water protected from the wind (in a forest, in the mountains), evaporation is three times less than from the surface of water in an open place, all other conditions being equal.

Mr. Nebelov, in his book, points to one pond in Smolensk Province, well protected, as he writes, by vegetation, which, during a summer drought with a strong north-easterly wind, gave, over the course of a week, a loss of water of 6″. According to Volkov, in navigable canals the greatest evaporation in twenty-four hours amounts to 1/2″. He gives a formula determining the average daily loss of water during the navigation season (250 days) from evaporation, seepage and absorption into the ground, and through the sluice; this loss, according to his formula, is

\[ =\left(\frac{1}{84}S+60\right)\ \text{cubic sazhens}, \]

where \(S\) is the area of the pond in square sazhens, and 60 is the loss, in cubic sazhens, through the sluice.

Mr. Nebelov proposes using this formula also for ponds, applying it to the whole year, i.e., 360 days, by which, in his opinion, only greater reliability is introduced, since in winter the losses are generally smaller. I believe, however, that this formula has significance only for soils that are completely or only slightly permeable, and only for the north-western region of Russia, where Volkov’s observations were actually made. It is risky to rely on this formula in general; it is far more reliable to make a direct observation for at least one year, by first digging several large pits at the site of the proposed pond and filling them with water.

If the ground proves to be highly permeable, then it is better to seek another site for the pond.

Impermeability can be reduced by concreting the bottom and walls of the reservoir. Lean concrete is laid in a layer 4 to 8″ thick and firmly rammed, after which it is covered with earth in a layer of 12–20″. Instead of concrete, rich soft clay mixed with fine—

sand, laying this mixture in layers 4″ thick and tamping it down firmly. For 1 volume of fat clay, take 1½ volumes of fine sand; it is also useful to add lime milk in the amount of 5–10 liters per 1 cubic meter of earth. The total thickness of the packing is made from 8–20″; this layer, like concrete, is covered with earth for protection. Both of these methods, especially the first, are very expensive and therefore almost inapplicable for large ponds; moreover, both of these means require the pond to be drained in order to carry them out.

A much cheaper method is to introduce into the reservoir a slurry formed by stirring clay or silt with water; it is useful to add lime milk to this slurry, chiefly because lime kills the worms which, making passages in the bottom of the basin, promote its seepage. The slurry, settling, tightens all the more permeable places toward which it is directed by the current of the seeping water. This method is very cheap and, when repeated, gives good results in still waters, as indicated by experiments in Bavaria and France. Separate places of intensified seepage, the so-called washouts, which are easily noticed by the resulting deepening of the bottom, are well repaired by filling the formed pits, as far as possible, with the finest sand. Finally, it should be noted that over time the pond silts up by itself and seepage decreases.

Ponds for Collecting Rain and Snow Waters

If a pond is constructed on a river and the calculation of its filling is made on the basis of measuring the water discharges in the river at different times, then obviously this already includes, of itself, the atmospheric precipitation that affects changes in the river discharge. If, however, a pond is built to be filled exclusively by atmospheric precipitation, then determining the inflow of water into it becomes more complicated. As is known, only part of the atmospheric precipitation reaches a river: some of the water that has fallen on the ground evaporates, some is absorbed by plants, some seeps into the ground, and some runs off along the surface into a body of water; to this latter portion, over time, is added part of the water from that which has seeped into the soil. It is rather difficult to determine the quantity of water that will enter a basin from atmospheric precipitation. According to the observations of many scientists, this quantity, depending on many circumstances, for soils that are poorly permeable or themselves saturated with water, amounts to from ½ to ¼ of the precipitation that has fallen in the basin during the course of a year. But if the soil of the basin is dry

and absorbs water, or is permeable to a considerable depth, then nothing may get into the pond. Thus, for example, chernozem, while greedily absorbing water, is capable of retaining it in almost twice the quantity of its own weight; this water evaporates over time, and if this evaporation proceeds more vigorously than the inflow of fresh atmospheric precipitation, then, of course, not a single drop of the water that has fallen on the chernozem will reach the catchment. There are also known examples of the disappearance of entire rivers when they enter regions of sands or chalk formations.

Determining the actual basin of a pond in permeable soils is likewise very difficult, since the watersheds must then, of course, lie on the underlying impermeable strata, and consequently can be discovered only by geological investigations. Therefore, in view of all the complexity of this question, if there are not, for a given locality, sufficiently precise data obtained by direct experience, the most prudent course is to proceed as was done in the “Expedition for Irrigation in the South of Russia and the Caucasus.” The expedition was engaged in constructing ponds for irrigating lands. The head of this expedition, General Zhilinsky, writes in his report, among other things, the following: “Precipitation falling in spring, summer, and autumn is of only secondary importance. Observations made by the expedition showed that only in exceptional cases did rainwater noticeably increase the quantity of water in reservoirs. Of the remaining winter precipitation, not all the water can be collected in a pond, since part of it is absorbed by the soil at the place where the snow melts, and part evaporates. The quantity of absorbed water depends on the composition of the soil, on the degree of its looseness, on the depth of freezing, on its slope, and on the conditions under which the snow melts: with a simultaneous and rapid thaw, less water penetrates into the soil than with a slow and gradual one; finally, after a dry autumn the soil absorbs much more spring water than after a rainy autumn. Snow falling on frozen soil yields twice as much water as on thawed soil. The quantity of evaporating water depends on the air temperature, on the length of time the water remains on the soil, and on the degree of saturation of the latter.

Observations in the south of Russia do not yet provide a sufficient basis for determining the quantity of water lost through absorption by the soil and through evaporation. In calculating the quantity of water that may accumulate in a reservoir, the expedition took into account the entire quantity of winter precipitation, since in winter evaporation is negligible and there is no filtration at all.”

He further advises that ponds intended exclusively for filling with snow water should be made, at the dam, no less than 2 sazhens deep, since shallower ones soon dry up and become choked with silt. From the calculations given in the outline it is evident that in winter the expedition counted not astronomical time, but meteorological time, i.e. 4 months for the south of Russia.

To determine the area of the basin, watersheds were taken according to the outer surface of the ground, since frozen ground is impermeable to water flowing over it. Despite all this prudence, however, there were indeed exceptional years when the expedition’s ponds did not fill with water; this always occurred after a very dry autumn, when snow fell on dry ground.

From all that has been said one may conclude that, by collecting atmospheric precipitation in ponds, it is not always possible to obtain unchanging results from year to year; nevertheless they can serve as a good auxiliary supply, provided there is some permanent source of water.

Here I give a small table of atmospheric precipitation for various cities of Russia. The precipitation is distributed by the seasons of the year (astronomical).

	Average precipitation in millimeters	Average precipitation in millimeters	Average precipitation in millimeters	Average precipitation in millimeters	Average precipitation in millimeters
	Winter	Spring	Summer	Autumn	Year
Petersburg	74	87	180	129	470
Vilna	88	131	207	137	563
Pinsk	77	119	256	145	597
Warsaw	96	119	223	131	569
Kiev	89	112	206	121	528
Astrakhan	36	41	44	35	156
Moscow	94	116	195	133	538
Tomsk	41	56	189	82	368

The distribution of evaporation from a free water surface by months, according to observations of the Main Physical Observatory in Petersburg, is as follows:

Months	January	February	March	April	May	June	July	August	September	October	November	December	Year
Evap. in m/m	4	4	10	19	33	60	63	44	29	18	9	5	298

Note. These data are borrowed from the book by Academician Wild, On Precipitation in the Russian Empire, and also from the observations of the Physical Observatory.

For the initial filling of a pond, observations show that from \(1 \tfrac{1}{2}\) to 3 times more water than its capacity is required.

Collecting Water from Marshes

Sometimes nature itself forms natural ponds or lakes through which a river flows; the importance of such natural formations, in the sense of regulating the discharge of water, is the same as that of artificial ones. Marshes, which very often occur in river basins, have the same significance.

But here, in detail, the action is already somewhat different: first, since a marsh is a surface covered with vegetation, evaporation from its surface will be different than from a water surface; further, the very vegetation of the marsh—mosses—and the soil—peat—absorb water and retain it within themselves, whereby the peat swells, which also explains the sometimes observed swelling of peat marshes. In my opinion, however, there is no reason to suppose that less water enters the marsh than is supplied by precipitation over the whole basin during the winter months. If, moreover, one takes into account that peat marshes lie on impermeable strata, that evaporation from them is less than from open reservoirs, and finally that, as is asserted, peat has the property of absorbing moisture from the air, then I think that, in calculating the amount of water received from the surface of a marsh as equal to the winter atmospheric precipitation of its basin, we shall have made a large allowance for reliability.

The matter ordinarily occurs in nature as follows. In spring the marshes are flooded, and part of the water, draining from the flooded surface, goes into the rivers and is carried away without any benefit, since at that time there is always an excess of water. When the spring waters have subsided, the slow feeding of the rivers by marsh water begins, so that by the next spring the marsh still remains saturated with water and can absorb only a small part of the fresh inflow. The greater part of the snow water will again be lost for nothing. But if, with the aid of ditches, the water is continually diverted in such a way that by the following spring the marsh can dry out completely, then the marsh is in a condition to absorb a large part, or all, of the snow water and then, throughout the entire following year, can feed the river uniformly by means of the ditches. The advantage here is obvious.

If in autumn, during the rains, the marshes have time to fill with water for a second time in the year, then obviously the ditches should be calculated in such a way that they have time to drain the water by autumn.

In order to collect water from the entire surface of a marsh, the following procedure is usually adopted.

Along the principal slope of the marsh, if there is one, or, if there is none, then along the middle, a main trunk canal is laid out, whose purpose is to receive the inflow of all the water from the marsh. Into this trunk canal, at an acute angle (approximately \(40\text{–}60^\circ\)), a series of parallel canals is brought in from the right and from the left; these canals in this way divide the whole area of the marsh into parallel strips. These secondary canals, collecting water from the surface of the marsh, deliver it into the main canal. The approach at an acute angle is made so that the water, when flowing into the main canal, should not have a velocity directed against the motion in it. It is obvious that the deeper these secondary canals are, the greater the layer of water that can be utilized; the closer they are to one another, the more rapidly the drainage of the whole area of the marsh will proceed. On the other hand, the depth of the secondary canals must be coordinated with the depth of the trunk canal, in the sense that they cannot be deeper than the trunk canal. The distance between the canals depends on the speed with which we wish to drain the marsh and on the nature of the marsh itself. For lack of a sufficient quantity of materials on which one might base the layout of secondary canals, I can cite only the indications of how these canals were built by the “Commission for the Drainage of the Pinsk Marshes,” which worked under the direction of the above-mentioned General Zhilinsky. The canals were dug trapezoidal, with a side slope of \(45^\circ\); their width at the top was from 1 to \(1\frac{1}{2}\) sazhen, their depth from 2.3 to 3.28 feet; they were dug in peat; the length of such a canal is sometimes 5 versts and even more. The distance between parallel canals was from one verst to \(1\frac{1}{2}\) versts. The bottom slope was made such that, when the entire cross-section of the canal was filled with water, the velocity in it was about 0.3 meters; this is necessary to avoid clogging the canals with sand and silt.

It should be noted that, in draining the Pinsk marshes, agricultural aims were pursued, for which reason the canals had to drain the surface of the hayfields within approximately 3 months, counting from the spring flood; on the other hand, it was useless and even harmful to drain the marsh deeper than one arshin, because then the roots of the grasses are deprived of moisture and the hayfield is poor. This explains both the comparative frequency of the canals and their small depth. For our purposes it is useful to make them deeper and to increase the distance between them; and the best and most correct procedure is to make, for each canal, at its entrance into the trunk canal, a sluice by which, as desired, the water may be released, regulating the inflow.

Assuming that the secondary ditches fulfill their purpose, i.e., deliver to the main canal the quantity of water per second for which we have calculated, it is no longer difficult to compute the dimensions of the main canal.

If we denote by \(V\) the mean velocity of the water in the canal, in meters; \(P\) the perimeter of the wetted part of the canal, in meters; \(F\) the area, in square meters, of the cross-section; \(i\) the fall of the bed; \(g\) the acceleration of gravity \(= 9.81\) meters; and \(\chi\) a coefficient from certain experiments, then, according to Weisbach’s formula,

\[ i=\chi \cdot \frac{1}{2g}\cdot V^2\frac{P}{F}; \]

in addition, the discharge of the canal in cubic meters is \(\theta = F \cdot V\).

In these expressions the velocity must be such that, first, scouring of the soil does not occur and, secondly, that the canal is not filled with sand, silt, and the like. The first of these requirements reduces the velocity, while the second increases it. From the canals existing among us, excavated in earth and peat, and also from existing canals in France, one may conclude that this velocity should lie within the limits from 0.3 meters to 0.5 meters. A higher velocity may be allowed only in rocky and stony soils. The coefficient \(\chi\) varies depending on the velocity: at a velocity \(V = 0.3\), \(\chi = 0.009\), and at \(V = 0.5\) to \(1\) meter, \(\chi = 0.008\).

Note: Although in hydraulics, in order to avoid scouring, the velocity \(V\) is allowed to be somewhat less than the indicated limits, nevertheless this is impracticable in practice. I base the reference to French canals on the table given in Dingelshtedt’s book (Agricultural Hydraulics, 1904).

At the velocities indicated above, the slope of the canal bed is usually expressed in ten-thousandths. For Polesian canals this slope is less than 0.0003, since the outermost drained marshy areas are 150 versts from the Pripyat River, while at the same time lying 24 sazhens above the level of this river, precisely where the water of the marsh is diverted.

Connecting a river of another basin and locks.

It is clear that a means of increasing the discharge of a river may be the connection to the given river of another basin. In mountainous localities it often happens that a mountain ridge, serving as a watershed for rivers flowing down opposite slopes, at the same time, owing to its winding form, makes it possible, without significant expense, by means of a canal or sometimes a short tunnel, to divert

water flowing down one slope of a mountain to the opposite one, where they too can be included in the common basin. Devices of this kind may very often be seen in mountainous countries with a developed exploitation of water power, for example in Switzerland, Austria, and Italy. In comparatively level terrain, this kind of joining of basins, though possible, is rarely repaid by the advantages.

In concluding the discussion of means for increasing discharge, I consider it appropriate to say a few words about springs.

Springs owe their formation to the water which, having penetrated into the soil, moves there along the slopes of impermeable strata; in the course of time, passages are formed under the soil, along which motion is established already in whole streams. These streams, in the form of springs, break through in the lower parts of the earth’s surface. Springs are especially abundant in ravines and along river banks. Some of them yield an enormous quantity of water. One cannot but cite as examples several springs whose water, immediately after emerging from the ground, sets in motion entire mills and then, already in the form of a small river, flows onward. Springs serve as a major support in feeding small rivers, and therefore they should not be ignored. Among the peculiarities of springs one may note their tendency to become clogged, and the decrease in a spring’s output under increased pressure on its outlet.

The first can easily be remedied by clearing the spring’s outlet, which should be carried out rather deep into the ground, by means of an earth auger or, in the extreme case, a spade.

The second depends on the fact that the outflow of water from the spring’s outlet takes place under pressure on the water of the underground layers of liquid. If the pressure on the outlet is increased, let us say owing to its being covered by a layer of water, then, understandably, the expelling pressure decreases, and therefore the velocity of outflow also decreases. The spring may cease giving water altogether, or may break through somewhere else, where this additional pressure does not exist. To avoid such a case, the channel of the canal along which the water from the spring flows should be kept as clean as possible of all clogging, and, when constructing a dam, care should be taken that the spring not end up beneath the surface of the pond. Springs often flow periodically, appearing only in spring and disappearing in summer. Such springs are of little use, because in spring there is usually plenty of water anyway. Clearing such springs is likewise useless, since it will only hasten their drying up. If, however, a spring flows throughout the entire year with almost constant strength, then one may hope that clearing it will give good results.

Reasons Limiting the Height of the Head.

Turning now to the consideration of another factor of the available work, namely the head, it is necessary to note the following circumstances that hinder the unrestricted increase of this factor:

1) An excessively high raising of the water will also require a very high dam, but the materials from which the dam is built, as well as the foundation soil, do not always permit such an increase.

2) The quantity of material, and consequently the cost of the dam per unit of its length, increases almost in proportion to the square of the height of the dam; moreover, in most cases the cross profiles of rivers are such that, after a certain height has been exceeded, the dam becomes disproportionately long. Thus, for example (Fig. 1), the line AB shows the top, or crest, of the dam; when the head is increased by a small height \(h\), the length of the dam increases to MN, i.e., almost doubles. Therefore the cost of the dam generally increases faster than the square of the height; and since the benefit from the increased head, according to equation (1), increases only in proportion to the head, it is evident from this that it is not always advantageous to increase the head, since the expenditure may not pay for itself.

3) The formation of a head is always accompanied by a rise of the water in the channel far upstream. This rise may cause undesirable flooding of certain bank areas or create backwater at dams already existing on the river. These circumstances are extremely important and must always be taken into account before determining the height of the dam.

Determination of the Profile of the Backed-Up River.

We shall show how, when building a dam, one can determine the outline in longitudinal section of the surface that the dammed river will present to us. Several hydraulic engineers have dealt with the solution of this question, and on the basis of a theoretical study of the nonuniform motion of water in a river they derived formulas that give almost identical results. These formulas are usually used in solving the question. In addition to them, there also exist empirical data for determining this profile; however, all of them give results that are too unreliable, and therefore one may strongly advise against using them—which is precisely what so authoritative a person as the hydraulic engineer “Dupuit” does.

Let us now proceed to the derivation of the so-called equation of the backwater line.

Let, in drawing (2), \(AB\) represent the longitudinal profile of the river bed; let the line \(LM\), parallel to \(AB\), be the surface profile of the unimpounded river.

After a dam has been constructed at point \((B)\), the longitudinal profile of the backwater will be expressed by the line \(PR\). We shall denote the angle of fall \(ABT\) by \(\varphi\), the depth of the unimpounded river by \(e\), and the width of the river—which we shall always assume constant—by \(b\). Take two infinitely close vertical sections \(ab\) and \(cd\), and let \(o\) and \(o_1\) be their centers of gravity.

We note that, since the angle \(\varphi\) is always very small, it is entirely immaterial whether we measure the length of the reach in the horizontal direction or along the bed, since, by taking the length of the line’s projection instead of the length of the line itself at a very small \(\varphi\), we make an error of an infinitely small quantity of higher order. For the same reason it is immaterial whether we measure the depth of the river vertically or perpendicular to the bed.

Denoting the length of the reach by \(l\), the velocity in section \(ab\) by \(V_1\), and in section \(cb\) by \(V_2\), the depths of these sections by \(y_1\) and \(y_2\), and observing that the pressure at the center of gravity of a section is equal to one half of the depth, it is easy, on the basis of D. Bernoulli’s equation, to write the following relation:

\[ h = \frac{V_2^2 - V_1^2}{2g} + \eta \ldots (a), \]

where \(h\) is the lowering of the water surface, and \(\eta\) is the work of the resistances along the path considered.

On the other hand, from the drawing it is seen that \(h + y_2 = y_1 + l \operatorname{tg}\varphi\), or, by the smallness of \(\varphi\), putting \(\operatorname{tg}\varphi = i\), we have

\[ h + y_2 = y + l \cdot i \ldots (b). \]

Combining equations \((a)\) and \((b)\), we have

\[ -(y_2 - y_1) + l i = \frac{V_2^2 - V_1^2}{2g} + \eta \ldots (c) \]

According to Weisbach, the resistance \(\eta\) may be expressed as follows:

\[ \eta = \zeta \frac{P}{A} \cdot l \cdot \frac{V^2}{2g}. \]

where \(\zeta\) is a coefficient, \(P\) is the wetted perimeter of the section, and \(A\) is the area;

we have

\[ \frac{P}{A}=\frac{2y+b}{by}=\frac{2\frac{y}{b}+1}{y}; \]

we shall assume that \((y)\) is very small in comparison with \(b\), then approximately

\[ \frac{P}{A}=\frac{1}{y}; \]

and, for our case:

\[ \eta=\zeta\,\frac{1}{y_1}\cdot\frac{V_1^{\,2}}{2g}\ .\ .\ .\ .\ (d). \]

Combining \((c)\) and \((d)\) into one, we have:

\[ -(y_2-y_1)+li=\frac{V_2^{\,2}-V_1^{\,2}}{2g} +\zeta\,\frac{1}{y_1}\cdot\frac{V_1^{\,2}}{2g}\ .\ .\ .\ .\ (f) \]

Let us now choose the coordinate axes so that the \(X\)-axis is \(BA\), and the \(y\)-axis is \(By\); then \(l=-dx,\ y_1=y;\ V_1=V\)

the equation \(f\) will be

\[ -dy-i\,dx=d\left(\frac{V^2}{2g}\right)-\zeta\,\frac{dx}{y}\cdot\frac{V^2}{2g} \quad \text{or} \]

\[ -dy-i\,dx=\frac{V\,dv}{g}-\zeta\,\frac{dx}{y}\ .\ .\ .\ .\ (g) \]

Since the discharge \(\Theta\) of the dammed and undammed river is one and the same, denoting the velocity of the undammed river by \(u\), we have

\[ \Theta=beu=byv, \]

whence

\[ ydv=-vdy\ .\ .\ .\ (h) \]

combining \(g\) and \(h\), we have:

\[ dy+i\,dx=\frac{V^2\,dy}{gy} +\frac{\zeta}{2}\,\frac{dx}{y}\,\frac{V^2}{2g} \]

whence:

\[ \frac{dy}{dx} = -\frac{ i\left(1-\frac{\zeta}{2i}\cdot\frac{V^2}{gy}\right) }{ 1-\frac{V^2}{gy} } \ .\ .\ .\ (k) \]

Expression \((k)\) represents the differential equation of the curve.

Since \(\frac{dy}{dx}\) is the tangent of the angle which the tangent to the curve makes with the axis of abscissas, it follows from this:

1) If \(i = \zeta/2\), then \(\dfrac{dy}{dx} = -i = -\tg \varphi = \tg(180-\varphi)\), and the backwater profile turns into the horizontal straight line \(AB\) (Fig. 3).

2) If \(i > \zeta/2\), then \(\dfrac{dy}{dx} < -i\), and the curve, proceeding all the time from the dam, will lie below the horizon \(AB\), so that it will have the direction \(AC\). It is obvious that in this case the backwater cannot extend beyond the horizon \(AB\).

Since \(\zeta\) is, for a river, approximately \(0.008\), in practice it is assumed that, for a river fall \(i > 0.004\), the backwater line is horizontal and does not extend beyond the point \(B\).

3) If \(i < \zeta/2\), then \(\dfrac{dy}{dx} > -i\), and the curve will go along \(AD\); to resolve the question in this case it is necessary to integrate the expression (g) derived by us.

We shall do this following Rühlmann. Let us write expression (g) as

\[ dy=-\frac{V\,dv}{g}-i\,dx+\zeta\frac{1}{y}\cdot\frac{V^{2}}{2g}\ldots(h) \]

Since, for small falls and velocities in a river, the term \(-\dfrac{V\,dv}{g}\) is small, Rühlmann discards it, as in general a quantity very small compared with \(dy\). Indeed, let us take two sections of a river; let in the first the depth \(=1\) metr. and \(V=0.5\), and in the second the depth be \(2\) metr.; then \(V_{1}=0.25\) metr. In passing from one section to the other, the change in \(y\), or \(dy=1\) metr.; while the change in live force

\[ d\frac{V^{2}}{2g}=\frac{V\,dv}{g}=\frac{V_{1}^{2}-V^{2}}{2g}=\infty\,0.01\ \text{metr.} \]

Moreover, it is clear that by discarding this term only the safety is increased, because, proceeding upstream from the dam, we obtain for the lowering of the depth, by the discarded amount, less than in reality. And so we are entitled to write

\[ dy=-i\,dx+\zeta\frac{dx}{y}\cdot\frac{V^{2}}{2g};\ldots(1) \]

from the expression \(\Theta=beu=byv\), we have \(V^{2}=\dfrac{U^{2}l^{2}}{y^{2}}\), and therefore, denoting \(\dfrac{\zeta}{2g}\) by \(\dfrac{1}{k^{2}}\), we shall write equation (1) thus:

\[ dy=-i\,dx+\frac{1}{k^{2}}\cdot\frac{U^{2}l^{2}}{y^{3}}\,dx\ldots(g) \]

On the other hand, applying equation (d) to the uniform motion of the unimpounded river and noting that then \(\tilde{\zeta}=h\), equal to the lowering of the river bed, since the entire motive force of gravity goes into overcoming resistance, we shall write:

\[ h=\frac{\zeta}{2g}\cdot\frac{1}{e}\cdot U^2,\quad \text{whence} \]

\[ \frac{h}{1}=i=\frac{U^2}{e k^2}\quad \text{or}\quad \frac{U^2}{k^2}=ie, \]

substituting this expression into (g), we obtain

\[ dy=-i\,dx+dx\,\frac{i e^3}{y^3}=dx\cdot i\left(\frac{e^3}{y^3}-1\right)\quad \text{or} \]

\[ i\cdot dx=\frac{y^3\,dy}{e^3-y^3}\ .\ .\ .\ .\ (m) \]

By integrating this expression one can find the relation between the distance \(x\) from the dam and the depth of the river \(y\) at that same distance, which will make it possible to determine the whole profile point by point.

In deriving equation (m), the following assumptions were made: 1) equality of the width of the river before and after the dam, 2) a very large width of the river in comparison with its depth.

These two conditions do not always occur in practice. Nevertheless, everyday experience convinces us that the results given by equation (m) are quite sufficient and reliable for practice, which is why the use of this formula has become generally accepted.

To facilitate the calculations, Rühlmann somewhat transformed expression (m), putting in it \(y=e+z\), where \(z\) is evidently the rise of the water in the impounded river above the surface of the unimpounded one in the corresponding section. Then equation (m) will be

\[ i\cdot dx=\frac{(e+z)^3}{e^3-(e+z)^3} =-\left[1+\frac{e^3}{(e+z)^3-e^3}\right]dz. \]

By direct division we find:

\[ i\,dx=-e\left[\frac{1}{3}\frac{dz}{z}+\frac{2}{3}\frac{dz}{e} +\frac{2}{9}\frac{z\cdot dz}{e^2} -\frac{1}{9}\frac{z^2\cdot dz}{e^3} +\frac{1}{27}\frac{z^3\,dz}{e^4}\ .\ .\ \right]. \]

Restricting himself to a sufficient number of terms and integrating within the limits from the dam, where \(z=Z\), to an arbitrary section, Rühlmann obtained a result which he presented in the following form:

\[ i\cdot\frac{X}{e} =\Phi\left(\frac{Z}{e}\right)-\Phi\left(\frac{z}{e}\right) \]

The right-hand side of this expression evidently represents the integral of the quantity enclosed in brackets in the preceding equation. To facilitate the calculation of \(\Phi \left(\dfrac{z}{e}\right)\), for various ratios \(\dfrac{z}{e}\), Rühlmann compiled the table which we give below.

Thus, in the case when the slope \(i < 0.004\), one should use the equation

\[ \frac{ix}{e} = \Phi\left(\frac{Z}{e}\right) - \Phi\left(\frac{z}{e}\right) \ldots \tag{2} \]

and the following table.

\(\dfrac{z}{e}\)	\(\left(\Phi \dfrac{z}{e}\right)\)	\(\dfrac{z}{e}\)	\(\left(\Phi \dfrac{z}{e}\right)\)	\(\dfrac{z}{e}\)	\(\left(\Phi \dfrac{z}{e}\right)\)	\(\dfrac{z}{e}\)	\(\left(\Phi \dfrac{z}{e}\right)\)	\(\dfrac{z}{e}\)	\(\left(\Phi \dfrac{z}{e}\right)\)
0.01	0.0067	0.1	0.835	1	2.2841	1.9	3.2553	10.0	11.4117
0.02	0.2444	0.2	1.1361	1.1	2.3971	2.0	3.3595	15.0	16.4117
0.03	0.3863	0.3	1.3428	1.2	2.5084	2.5	3.8754	20.0	21.4147
0.04	0.4889	0.4	1.5119	1.3	2.6179	3.0	4.3844	30.0	31.4153
0.05	0.5702	0.5	1.6611	1.4	2.7264	3.5	4.8911	50.0	51.4157
0.06	0.6376	0.6	1.7980	1.5	2.8337	4.0	5.3958	100	101.4158
0.07	0.6958	0.7	1.9266	1.6	2.9401	5.0	6.4019
0.08	0.7482	0.8	2.0495	1.7	3.0458	6.0	7.4056
0.09	0.7933	0.9	2.1683	1.8	3.1508	8.0	9.4097

The meaning of the letters is as follows: \(i\) is the slope, \(x\) the length of the river reach, \(e\) the depth of the undammed river, \(Z\) and \(z\) the rise of the water, measured from the surface of the undammed river; \(Z\) is in the lower section of the section under consideration, and \(z\) in the upper one along the current.

In order to show how to use this table, let us give an example:

A river with a natural slope of \(\dfrac{1}{5000}\) and an average depth of 2 feet is dammed by a weir so that at the weir the rise amounts to 3 feet, i.e. the depth is 5 feet. Find at what distance from the weir the rise will amount to 2 feet.

At the dam, \(\Phi\left(\dfrac{Z}{e}\right) = \Phi\left(\dfrac{3}{2}\right) = \Phi(1.5) =\), according to the table, \(2.8337\); at the section where the rise is 2 feet,

\[ \dfrac{z}{e} = 1;\quad \Phi\left(\dfrac{z}{e}\right)=\Phi(1)=2.2841, \]

after substituting these values into equation (2) we obtain

\[ \dfrac{X}{5000.2}=0.5496, \]

whence \(X = 5496\) ft.; at such a distance from the dam the water rises by 2 feet.

If the depth and rise of the river had been given to us not in feet, but in meters or sazhen, then, without any change in the course of the solution, we would have obtained for \(X\) an expression in meters or sazhen.

Considering the table given above, we note that it begins with the ratio \(\dfrac{z}{e}=0.01\). In practice, under such conditions, \(z\) usually turns out to be so small that such a rise may safely be neglected. Rollmann, too, assumes the existence of backwater over the distance from the dam to the point where \(\dfrac{z}{e}=0.01\); beyond this point the backwater does not extend, and consequently the rise is equal to zero.

Method of Removing the Excess Impounded Water

Water impounded by a dam, having risen to the height of the crest, if it does not find some special path for itself, will begin to overflow over the crest, forming a waterfall; the dam itself is then called an overflow dam. Sometimes, for the discharge of water, special openings are arranged in the dam, called sluices; these sluices are furnished with openings that can be closed and opened at will, through which water may be released. Sometimes the discharge of water is arranged by means of simple and siphon pipes. The calculation of the discharge capacity of spillways, large openings, and pipes is considered in hydraulics; formulas for such calculations are available in all handbooks; therefore, omitting this question, I pass directly to the description of dams.

Selection of Soil for the Foundation of a Dam

According to the kind of material, dams may be divided into earth, wooden, and stone dams. In order that a dam may fulfill its purpose, it must be not only strong, but also impermeable. Obviously, the soil on which the dam is erected must possess this same property. Pure sandy soil, although not compressible, nevertheless has great permeability, and besides is easily washed away by water. Therefore sand cannot be considered a favorable foundation for a dam; in any case such a foundation will require enclosures made of sheet piles, which is expensive. Far more reliable is dense clayey soil, with a thickness of about 2 arshins or more. Pure clay is impermeable to water with a much smaller thickness, but it is easily washed away by water, and besides, during frosts it heaves (increases in volume), whereby, of course, the strength of the dam suffers. To prevent this from happening, the clay must be well protected both from the action of running water (standing water is not harmful to it) and from the action of frost, for which purpose the clay must be covered with a thick layer of earth. Under such conditions, pure, compacted dense clay may be regarded as the best soil for a foundation.

Excellent in its qualities as a soil is loam, which is a mixture of clay with sand. With a content of 50 to 60% by volume of more or less coarse sand, such loam is only slightly compressible, not washed away, does not heave from frost, and is almost as impermeable as clay. If the sand is very fine, then the loam is easily washed away; if there is very much clay, it begins to heave from frost; however, whatever the loam may be in sand content, still, provided it lies sufficiently deep and has sufficient thickness, it should be considered a good foundation.

Rock also, with sufficient thickness, presents a very good foundation for a dam, but cracks are often found in rock. To ensure impermeability, all cracks under the foundation of the dam must be located and carefully packed with clay or filled with concrete. When an earth dam is erected on rock, impermeability between the sole of the dam foundation and the rock is difficult to achieve, which is why stone dams are most often erected on rock.

The remaining soils are of little suitability for the foundation of a dam, either because of their great permeability or great compressibility, and before the dam is erected they must be removed down to a reliable layer or properly strengthened.

Earthen Dams

Turning now to the body itself of an earthen dam, it should be noted that not all those earths which are good as soil beneath a foundation are suitable for constructing the embankment itself. Here first place belongs to loam containing 50–60% coarse sand. The same kind of material as loam is loess. Being of aeolian origin, loess in nature is often found in a rather loose state; but when carefully laid into the body of the dam in thin layers, with tamping and watering, this looseness disappears, and then loess is in no way different from loam. In the absence of loam of the proper composition, it may be prepared artificially by kneading clay with sand or gravel. Coarse silty sand, or sand mixed with chernozem, may also be used to advantage for building a dam.

For want of anything better, sand of medium coarseness may also be used in the dam, as well as fine sand, though not dust-like. Chernozem, or vegetable soil without admixture of sand and clay, is used only for very low dams. Chernozem in itself belongs to the impermeable earths and therefore can partly replace clay, but it is very compressible, light in weight, and heaves under frost.

The body of a dam is never built exclusively of the following materials:

1) Of pure clay, although vertical walls for impermeability are often erected from it inside the body of the dam.
2) Of very fine dust-like sand, because of its erodibility.
3) Of gravel and pebbles, because of their permeability.
4) Of weak peaty soil, because of its compressibility, lightness, and permeability.

If, in building a dam, several kinds of earth are used, care should be taken that the more impermeable ones be placed on the upstream (impounded-water) side of the dam.

Since in practice, in most cases, the earth used is that which is available nearby, in order to determine the greater or lesser suitability of the material, practitioners employ simple methods of comparison. The composition of loam is easily determined by kneading. Permeability is determined by digging small pits, pouring water into them, and observing the time of absorption. Erodibility is determined by throwing lumps of earth into running water and observing the formation of turbidity. All

these methods, although they give results that are very inexact, are sufficient for a comparative estimate.

Sometimes, when constructing a dam of permeable material, it is useful to know its absolute permeability, in order to determine the loss that may occur from this.

Experience teaches us that the velocity of seepage of water may be expressed by the following formula

\[ U = \varphi \frac{h}{l},\ ^{*}) \]

where \(u\) is the velocity, \(\varphi\) a certain numerical coefficient depending on the material, \(h\)—the head under which the flow takes place, and \(l\) the thickness of the permeable layer.

For sand, \(\varphi\) depends on the size of the grains of sand.

\[ \begin{aligned} \text{With grain diameter } \delta &= 0.54 \ —\ \varphi = 0.0032\\ \delta &= 0.7 \ —\ \varphi = 0.0053\\ \delta &= 0.8 \ —\ \varphi = 0.0098\\ \delta &= 0.9 \ —\ \varphi = 0.0159 \end{aligned} \]

This little table, however, can in practice be used only very rarely, since in nature soils are a mixture of particles of very different sizes.

To determine impermeability by direct experiment, I used the following simple apparatus.

I took two bottles with their bottoms knocked out, connected to one another by a rubber tube one inch in diameter (Fig. 4). In the lower vessel two frames \(mm\) and \(nn\), covered with fine mesh, were inserted; the space between the meshes was filled with the soil being tested. In order that no leakage should form along the walls of the bottle, before the soil was poured in the bottle was smeared with tallow. A fine brass mesh can easily tear when the soil is poured in and tamped; therefore directly beneath it a mesh of thick wire and with large openings was stretched; this latter mesh supported the former, which lay directly against the soil. The openings of the fine mesh must be so small that the soil under test cannot pass through them and be carried away by the water. If the vessels are arranged as in the drawing and water is poured into the upper vessel, maintaining it at a constant level, then after some time water will begin to pour out of the lower vessel. I found the quantity of water flowing out in \(1''\) by direct measurement; from this it was possible to determine

Note. This formula has also been derived theoretically. See Eylevich’s Course of Hydraulics.

and the seepage velocity \(U\). The motion of water through the layer \(e\) took place under the head \(h\) (Fig. 4), after subtracting the losses, of which the most important in passing through the screen (in the tube the velocity was small) is this loss: \(\zeta \dfrac{U^2}{2g}\); therefore

\[ U=\varphi\,\frac{h-\zeta\frac{u^2}{2g}}{e}; \]

whence it is easy to find \(\varphi\).

The quantity \(\zeta\) is determined by the following experiment. The earth is removed, only two screens remain, and water is made to flow through them under the head \(h'\); let the velocity in the cross-section of the lower bottle be \(V\), then \(\dfrac{V^2}{2g}+\zeta\dfrac{V^2}{2g}=h'\); \(h'\) and \(V\) can be found by direct measurements.

Knowing the coefficient \(\varphi\), it is possible to determine approximately the loss due to the seepage of water through the dam. Suppose that we have a trapezoidal dam in section, the dimensions of which are indicated in drawing (5). Taking a meter of the dam’s length in the direction perpendicular to the drawing, and assuming, for simplicity, that the motion of the seeping water is horizontal, we may, for some element \(mn\) to the right, write the seepage velocity as:

\[ u=\varphi\,\frac{y}{h+3y} \]

(the meaning of the letters is as in the drawing). The elementary discharge through the infinitely narrow element \(mn\),

\[ dq=\varphi\cdot 1\,dy\,\frac{y}{h+3y}; \]

the total discharge over the whole height of the dam,

\[ \Theta=\varphi\int_0^h \frac{dy\cdot y}{h+3y} =\varphi h\left(\frac{1}{3}-\frac{\ln 4}{9}\right) \]

\[ =\Theta=0.18\,\varphi h \]

if \(\varphi\) is \(0.005\), then the discharge per square meter of the vertical projection of the dam will be \(0.0009\), i.e. \(0.9\) liter. With a great length of the dam this discharge may be so considerable that the entire inflow of water will be lost by seepage.

The seepage velocity in individual parts must in no case be greater than that at which the earth is carried away, since in that case the dam will inevitably be destroyed.

Stable Dimensions of an Earthen Dam and Methods of Construction

We shall now undertake the determination of the stable dimensions of the dam. An earthen dam has, in cross section, the form of a trapezoid (Fig. 6); \(BE = CF = h\) is called the height of the dam, the angle \(CDI\) is the angle of the natural slope in air, and the angle \(BAE\) in water.

The destruction of the dam under the head of water consists in its displacement along the plane \(AD\). The forces acting will be as follows: on the plane \(AB\) there acts a certain normal force \(P\), as the resultant of the water pressure. The force \(P\) may be resolved into the horizontal \(p_1\) and the vertical \(p_2\). The force \(p_1\) tends to move the dam, while \(p_2\) presses the dam against the plane \(AD\), increasing the friction in this plane. In the same way, the force \(p_2\) is affected also by the weight of the entire dam. For greater reliability we shall assume that the whole dam is saturated with water; then its weight will be the weight of a body submerged in water.

For example, let us suppose that the dam is built of loam, that the upstream slope is double, and the downstream slope ordinary, and let us consider a part of the dam of length equal to one unit.

Then the pressure is

\[ P = AB \cdot \frac{h}{2} \cdot 1 \cdot \gamma \quad (\gamma \text{ is the weight of a cubic meter of water}); \]

\[ p_1 = \frac{h^2}{2}\gamma; \qquad p_2 = h^2\gamma \]

The weight of the whole dam in water will be

\[ G = \frac{b + b + 3h}{2}\cdot h\,(\varphi - \gamma), \]

where \(\varphi\) is the weight of a cubic meter of earth; for loam \(\varphi = 2\gamma\).

Taking the coefficient of friction of earth on earth as approximately equal to \(1/3\), we shall write the equality of the projections of the forces on the horizontal axis. We shall have:

\[ p_1 = (p_2 + G)\cdot f; \]

and if we adopt a twofold factor of safety, then

\[ 2p_1 = (p_2 + G)f \ldots (3). \]

Substituting their values for the letters, we finally find \(b = \frac{1}{2}h\).

Thus the thickness of the dam at the crest must be not less than \(1/2\) of its height. However, this theoretical conclusion has only secondary significance for practice.

First, it does not take into account the dynamic action that may manifest itself during wave motion in reservoirs, from

the impact of ice floes, etc.; and, secondly, the climate of the locality, especially freezing, has a very substantial influence on the destruction of a dam.

In France, where freezing is extremely slight, for dams built of selected material, with very careful workmanship, they take:

\[ b = 3 + \frac{5}{17}(h - 3). \]

\(h\) and \(b\) are expressed in meters.

In Russia, with ordinary material and ordinary methods of constructing embankments, it is considered necessary to have the width of the dam at the crest \(b = h\)—the height of the dam.

In the Urals, where freezing reaches 4–5 arshins, \(b\) is taken to be not less than \(1.5h\) to \(2h\), these dimensions being considered necessary.

In these expressions \(h\) is the dimension measured to the height of the upper water level.

The slopes of the embankment are made, on the upstream side, three-to-one and four-to-one; on the downstream side, three-to-one, down to one-to-one, depending on the quality of the soil. Experience shows that a slope is better preserved if it is made in benches. The benches are separated by horizontal or slightly inclined berms. It is likewise useful to make the slopes gentler toward the base of the dam.

For protection against erosion, the upstream slope is often paved or covered with a layer of stone on hydraulic mortar; the downstream slope is strengthened with turf and by planting willow, osier, etc. The berms on the downstream slope, if there are any, are provided with ditches to carry off rainwater.

The actual work of constructing the dam proceeds in the following order: at the selected place, on the surface of the ground, the outline of the dam’s base is staked out, marking the points of the perimeter with small stakes. The entire upper vegetative, weak and permeable layer within this outline is removed. For better bonding of the base with the soil, the soil is either loosened with a heavy iron harrow, or several ditches are dug along the base, for the whole length of the dam; the largest of these is located exactly under the future crest and is called the key. In the case of a very high dam, ditches are usually not made, since the weight of such a dam is sufficient to ensure good adhesion of the base to the soil.

If the impermeable soil lies too deep to be reached by excavation, then impermeability is achieved by driving rows of sheet piles.

Opposite the crest of the dam, at an equal distance from the center line of the crest, equal to approximately about 0.5 meter, two rows are driven in.

parallel sheet-pile stakes, into a previously dug trench. The length of the piles must be such that their ends enter the impermeable layer by 2–3 feet (Drawing 7). If, moreover, the soil of the embankment is permeable, then the height of the sheet-pile row reaches the upper water level. The space between the piles is packed with clay.

The construction of the embankment itself is carried out gradually, in layers. When the earth has been brought in and leveled to a layer thickness of about one foot, it is lightly sprinkled with water and tamped by hand or with rollers; then the upper layer is loosened with a harrow or heavy iron rakes, and the next layer is again poured on, and so forth.

If the dam is built of sand, then neither tamping nor sprinkling with water is required; but then, in order to eliminate seepage, a core of clay is often arranged. This core (Drawing 8) is a vertical clay wall erected through the entire height of the dam. Its dimensions are shown in the drawing.

The wall is built up in layers simultaneously with the whole embankment; the clay is tamped with sprinkling of water, to which it is useful to add lime milk, or ashes to the clay itself, as a remedy against moles, mice, and worms, which impair the impermeability of the wall by their passages.

The height of the dam must be such that not only does the water at high stage not reach the crest, but even waves cannot splash over the crest, since overflowing water can very easily destroy the dam. The crest of the dam must therefore be at least one arshin above the very highest level of the headwater.

In view of the settlement produced by an earthen embankment, the height of the dam must be 10 percent greater than the calculated height.

According to Neelov, the maximum height of earthen dams in our country is not more than 7 sazhen. However, with selected material and good execution they can be much higher.

Zborzhek gives an example of a very ancient dam built of loess in India, many centuries before the Nativity of Christ, which to this day excellently fulfills its purpose without the slightest repair, holding back water to 13 sazhen. French engineers even now build earthen dams for similar heads, but for this they use only selected material and the methods of construction themselves are rather expensive, so that the cost of such a dam is often comparable with that of a masonry one.

For the body of such a dam, exclusively natural or artificially prepared loam is used, with a content of not less than 50% coarse sand. The embankment is erected in dry, sunny—

in dry weather, for the quickest drying. Each layer, no thicker than 20 cm, is moistened by sprinkling with a solution of cement or hydraulic lime and is rolled with smooth road rollers weighing eight poods—70 to 150 (per linear inch of the roller—2 to 3 poods). Then, to form an uneven surface, it is rolled with similar but already corrugated rollers. The depth and width of the corrugations is about 10 cm. If much moisture appears in the process, dry cement or lime powder is poured over the surface. Onto the surface prepared in this way the next layer is placed, and so on. As a result one obtains a mass which, after some time, is difficult to break through with a crowbar. The upstream slope in such dams is usually faced with stone masonry in hydraulic mortar.

According to Zbrożek’s data, for 1 cubic sazhen of earth in such a dam about 7 poods of hydraulic lime or cement are required.

In drawings 9–10 are shown cross sections of three dams built by General Zhilinsky in the south of Russia. Two of them have the upstream slope paved with rubble stone on straw; all have cut-offs at the base, the significance of which has been discussed. One has, for impermeability, a single longitudinal sheet-pile wall.

Drawings 11–12–13–14 show a section of one of the French dams, equipped with siphon and ordinary tubular outlets arranged in a special stone tower. The siphon operates automatically, lowering the level to a definite mark. The lower opening, closed by a shield (Figs. 11–13), serves for complete emptying of the reservoir.

In drawing 12 one can see a section of the earthen body itself. The upstream slope is stepwise and is faced with stone masonry in cement mortar. Along the crest of the dam a road has been laid. The rainwater that collects is carried off by a special channel (dotted line) into a ditch at the toe of the dam.

When choosing a site for a dam, care should be taken that springs do not fall within the limits of the base, since they are very difficult to deal with. In addition, it is desirable to protect the dam from the dynamic action of water upon it; therefore it is very good if above the dam there are projections of soil that could absorb the blows of waves, ice floes, and so forth. Thus, if (drawing 15) A and B are projecting hills, the dam should be placed behind the hills, for example at C. It is likewise useful if, in front of the dam on its upstream side, there is a natural rise of the ground; in this case the water, moving toward the dam and running up the inclined plane, will lose its living force and therefore act less destructively.

The Simplest Methods of Strengthening the Surface of an Earthen Dam.

Earthen dams can withstand very well the pressure and even the impact action of water, but only until a more or less strong seepage through the dam is formed, or water begins to spill over its crest; then the particles of earth are quickly carried away by the current and the dam is destroyed. In view of this, it appears extremely dangerous to arrange, directly in the earthen body of the dam, any canals for the passage of water without strengthening the walls of this opening with more reliable materials. The simplest means of protecting the walls of an earthen water outlet, used, however, only for spillways, is fascine work.

A fascine consists of bundles of brushwood, made from thin flexible branches. These branches are tied in such a way that the thick butt ends are laid in one direction and the tops in the other; the length of such a bundle is about 10 feet, the diameter about one foot, and the tying is done in two or three places with the same flexible branches. Such a fascine is called single-ended (Fig. 16); a double-ended fascine is tied somewhat differently: the butt ends are placed at the ends of the bundle, while the tops of the branches meet in the middle; the length of such a fascine is almost twice that of a single-ended one. The best binding material is young shoots of vine, willow, and poplar. For the fascine itself all soft deciduous species are good, and only in the most extreme case are coniferous species used. On the upstream side of the dam, the fascine is usually laid so that the butt end lies at the embankment and the top points against the movement of the water; it is laid tightly one beside another, in rows slightly inclined to the horizontal, sprinkling each row with earth (best of all with gristle), tamping it into the gaps between the brushwood until the whole row is completely covered. Then the next row is laid, and so on. Sometimes each row is strengthened in place not only by a covering of earth, but also with stakes. For this purpose, over each layer of fascine a rope 1.5 to 2 vershoks thick, twisted from branches, is stretched; this rope is fastened to the ground with knotty stakes (Fig. 16). Water, moving against the branches, encounters great resistance; the branches are forced open, which assists the packing of earth and leaves into the comparatively small angles between the branch and its side shoots; the fascine is quickly drawn tight with silt and becomes impermeable. Therefore this kind of laying is very suitable for stopping scours in the earthen body of a dam, quickly putting an end to seepage. In these cases, to hasten the action, manure, straw, and pieces of turf are often thrown into the water upstream in front of the fascine, besides earth,

which are carried by the current of water between the branches and very quickly stop any flow. On the crest of the dam the fascine is usually laid in two layers, placing each fascine along the crest. On the downstream side, however, a single-layer fascine is laid, again with its butt ends toward the embankment. With such laying, the water quickly runs off, sliding over the branches, and does not penetrate into the body of the dam, which might first cause the destruction of the earth and then a collapse. Everywhere the fascine must be laid tightly against one another and well covered with gravel, or, in the last resort, with ordinary earth. Fig. (17–18) shows the strengthening of the spillway in an earthen dam by means of fascines.

Sometimes, instead of fascines, sacks or mat bags filled with sand (three quarters of the sack’s volume) are used, laying them in exactly the same way as fascines.

Sometimes the surface of the earth is also protected from washout by covering it with wickerwork made of willow, poplar, or osier branches, fastening the wickerwork to the ground with stakes.

The surface of the earth can also be strengthened by paving it with large stones.

However, all these methods, of which fascines are the strongest, can be applied only when the overflowing stream is only a few inches thick; moreover, they are not durable. Alternating exposure to air and water is especially harmful to the surface reinforcements described: fascines and sacks rot very quickly under these conditions; frost also acts very harmfully, breaking up the swollen branches.

If it is necessary to deal with the discharge of a large quantity of water at high velocity, and if it is desirable to have a spillway that could serve for a long time, then usually, at the place where the release of water is proposed, the earthen dam is interrupted, or, as they say, a gap is made in the dam. In place of the gap a wooden or stone dam is erected, which is provided with a spillway. I now turn to the description of these dams.

Wooden Dams

Wooden dams are in most cases built with the intention that they may serve, either constantly or at times, for passing a definite quantity of water. Blind wooden dams are constructed only in exceptional cases. Since the riverbed presents the most convenient place for passing large quantities of water, spillways are very often built in the riverbed itself.

In any timber dam one may distinguish three parts: 1) the foundation; 2) the side walls or shoulders, by which the timber dam abuts against the embankment or the bank; 3) the superstructure erected on the foundation.

The foundation of a timber dam, in turn, may be divided into three types: 1) pile; 2) cribwork; 3) made of fascines.

Pile foundation.

The pile foundation is the most widespread. It consists of several rows of sheet piles, whose purpose is chiefly to eliminate seepage, and several rows of round piles supporting the superstructure. The sheet-pile rows are driven from timbers whose thickness varies from 4 to 12 inches, depending on the hardness of the soil; moreover, in very hard ground an iron pointed shoe is fitted onto the end of the pile. Round piles are from 5 to 8 vershoks thick.

The setting out on the site of the sheet-pile lines is carried out in the following manner. Let Fig. 19 represent, in plan, the river on which it is intended to build the dam. Let it further be known to what height the water will be backed up, and also what width of opening must be made in the dam for the passage of water. Then along the middle of the riverbed the straight line \(MM'\), parallel to the banks, is drawn; then the straight line \(P\Theta\), perpendicular to it, is drawn, and from the point of intersection \(o\) there are set off to the right and to the left \(ob = oa =\) half the width of the waterway. The straight line \(ab\) is taken as the line of the principal sheet-pile row, above which the shields will stand. This row is the most important and must be made of the thickest and longest piles; it is also continued for several sazhens into the banks, to the points \(P\) and \(\Theta\). Besides this row, several more sheet-pile rows are usually driven: upstream one or two rows are driven, the first \(cd\) at a distance \(ok\), equal to from 4 to 7 feet, the second \(lK\), at a distance from the first \(ek = 3\) to 6 sazhens. Often the row \(cd\) is not made.

Downstream from the line \(P\Theta\) several rows of sheet piles are also driven; the last of them, \(st\), lies at a distance \(ov\), equal to from 4 to 7 times the head attained by the dam. The number of all the transverse (with respect to the flow of the river) sheet-pile rows in the whole dam is determined as the quotient obtained by dividing the head of water, expressed in feet, by 4. All transverse sheet-pile rows are continued for several sazhens into the banks. For the final outline of the entire outlet area, the straight lines \(eas\) and \(dbt\) are drawn parallel—

parallel to \(MM'\), and the straight lines \(he\) and \(dk\), so that \(fh = qh =\) from \(1/6\) to \(1/4\) \(ab\). Then the figure \(heasutbdk\) will represent the outline, in plan, of the sluiceway; the lines \(hea\) and \(kdb\) are likewise the lines of sheet-pile rows driven between the transverse sheet-pile rows, but not cutting across them.

Sometimes sheet piles are driven also along the lines \(as\) and \(bt\). In addition to the sheet-pile rows, rows of round piles are also driven; the distance between the piles and the rows is taken from 3 to 5 feet. Rows of round piles are driven only within the limits of the outline of the sluiceway; they are never continued into the banks.

All the rows of piles are covered with caps, upon which the floors are then laid and the upper structure is erected. A longitudinal section (along the river) is shown in Fig. 20. To construct it, proceed as follows: let the vertical \(zo\) be the line of the principal sheet-pile row; let, further, \(f'g'\) be the level of the backed-up water.

From point \(z\), along the vertical, we set off \(zo\), equal to the depth of the sluiceway; point \(o\) will be the upper point of the cap on the principal sheet-pile row. The position of the caps on the other sheet-pile rows is determined from the following data. The floor covering the piles above point \(o\), called the upstream floor, is usually made as consisting of a horizontal platform \(ok\), as far as the first sheet-pile row \(cd\) (see the plan), and of an inclined part \(ek\), running from the cap of row \(cd\) to the cap of row \(kh\), with a slope of from \(1/5\) to \(1/10\) to the horizon. If above the main row only one outer sheet-pile row is driven, then the floor has the inclined position \(eo\) (dotted in the drawing). Below the main row the floor is called the downstream floor; it may be made either entirely horizontal \(ov\), or slightly inclined \(om\), or, finally, in the form of several horizontal platforms descending in steps. In this last case the first platform, called the stilling-basin floor, begins at the height of the cap of the main row; the steps are made from 3 to 5 feet high. The cap on the main row is called the dead or red timber; for it the largest and best-selected material is used, not less than 8 vershoks square. It forms the sill on which the gates for releasing water are installed. The space under the floors is filled with heavy and impermeable materials. Each horizontal platform of the stepped floor is bounded by sheet-pile rows, i.e., it begins at the upper sheet-pile row and ends at the cap of the lower one. The purpose of the upstream floors is to ensure the impermeability of the dam; the purpose of the downstream floors is to protect the river bed below the dam from scour.

To explain the causes of scour of the bottom, we shall present drawings (21 and 22), which constitute a summary of observations made on one of the French rivers.

On the river there was the stone dam shown in the drawing, backing up the water by 2 metr.; the thickness of the overflowing sheet varied from 0.5 to 2 metr. From the drawing it is evident that the water in the spaces B and C was carried by the overflowing stream into a circular motion. This circular motion in space C is what causes scour of the bottom. It is obvious that if the apron floor is given the outline of the lower edge of the jet, then neither a whirlpool nor scour can occur in space C.

The arrangement of apron floors in the form of steps is preferable to others, since in this case the water, falling from a height, each time on striking the floor loses a considerable part of its live force, as a result of which its scouring force is also reduced. Whatever the apron floor may be, it is considered a rule that the last discharge element of it, during the release of water, should be submerged at least 2 feet below the lower water level in the river. In this way scour of the bottom is prevented.

All the empirical data cited thus far have been borrowed by me from the course of Prof. Gausman.

He also considers it necessary that immediately beyond the sill there should be a horizontal stilling floor, the length of which is 5 to 7 times the head taken over the sill; if this platform is absent and the entire apron floor is made sloping, then he says that, in order to avoid scour, the length of the floor, reckoning from the sill, must be at least equal to 20 heads above the sill. It is self-evident that part of such a long floor may be replaced by some other protection of the bottom against scour.

According to data from other authors, the length of the sloping floors is made from $h$ to $2h$, where $h$ is the whole head of water, reckoned from the upper to the lower level; the length of the stilling portion is $3h$ to $5h$, and of the apron $6h$—$7h$; if, in addition, the soil of the bottom is weak, then, to avoid scour, a stone riprap is made beyond the floors, a pavement of heavy stones with fascines inside, etc.; sometimes a fascine mattress is sunk.

A fascine mattress is prepared in the following manner: on a level place a net is prepared from twig ropes, with square meshes about 3 feet on a side (Draw. 23). For this purpose, first a row of parallel ropes is laid along the length of the mattress; upon it is laid a row of perpendicular ropes; at all points of intersection the ropes are tied with thin twig ropes of the same kind (withes). Upon the net thus formed, layers of uniform—

a root fascine. The laying of the first layer is done so that the fascine lies perpendicular to the lower ropes of the net, with its brush ends directed downstream; the second layer is laid perpendicular to the first, the third perpendicular to the second, and so on. In laying, care is taken: 1) that fascine lies against fascine as tightly as possible; 2) that in each layer the butts of the fascines are covered by the brush ends of the following row; 3) that the brush ends of the fascines in the odd-numbered layers project 3–4 feet beyond the downstream rope of the net, thereby covering the entrance of water under the net; 4) that the thickness of each transverse and longitudinal layer, taken together, be approximately constant at all points.

Each layer of fascine should be sprinkled with coarse sand or earth. The former is preferable.

When the required number of layers has thus been laid, the same kind of wattle net is placed on the upper layer as below, and both nets are tied together with ropes through the entire thickness of the mattress. These ropes are tied to the knots of the lower net before the laying of the fascine begins. In order to make it easier to pass them through the entire thickness of the mattress to the knots of the upper net, the usual procedure is as follows: at all the knots where the ropes are tied, vertical pegs are driven into the lower net, to which the ends of the ropes are tied; these pegs remain in place for the whole time during which the fascine is being laid, and are pulled out only after the upper net has been laid and tied. The tightening of the mattress with ropes is done at all the knots around the perimeter of the nets; in the middle part it may be tightened through every other knot.

The length of the mattress may be made equal to the width of the river, but its width is not made more than 5.5 sazhens. If a greater width is required, it is more convenient to sink several mattresses side by side. Where the bottom is uneven, it is useful to make the mattress as thin as possible, so that, deforming more easily, it will fit well to the bottom. The maximum thickness of the mattress is no more than 6 feet. For the final sinking of the mattress to the bottom, it is loaded with stone. To prevent this stone from rolling off the surface, several rows of pegs are driven into the mattress, so that the pointed ends of these pegs terminate in the lower layer of fascine but do not pass through that layer. The upper projecting ends of the pegs are interwoven with willow, so that several rows of little fences are formed on the surface of the mattress, between which the stone is poured. After the mattress has been lowered to the bottom, sometimes, for its final fixing, several rows of round piles are driven through it.

Considering the dams that exist among us in Russia, one may observe that the majority of them have a far smaller number of transverse sheet-pile rows across the river than would follow from calculation according to the data given above.

The sheet-pile row is the most expensive part of any dam; hence the understandable desire, wherever possible, to reduce the number of sheet-pile rows. On the other hand, under more or less favorable soil conditions, a single sheet-pile row is sometimes sufficient for impermeability. Still more reliable in the sense of impermeability is the arrangement of two sheet-pile rows—the main one and the outer one—beneath the apron floor, with the space between these rows filled with impermeable material and with the construction of the apron floor. Of the remaining rows, only the last row, beneath the horizontal water-cushion platform, has some importance; for, by maintaining the water beneath the water cushion at the height of the sill, it prevents rotting of the main row, increasing the durability of the entire dam and the impermeability of the main row. The remaining rows have only secondary importance for impermeability; they are more important for strength, and the last row beneath the spillway floor, moreover, often serves as protection against the undermining of the dam.

Round piles, as was said earlier, are intended only to receive vertical load. If the number of sheet-pile rows is insufficient, the latter are no longer able safely to take the entire component of the horizontal pressure of the water; it is then necessary, in support of them, to transmit this pressure also to the round piles. Dams constructed in this manner may nevertheless be sufficiently strong and serve for a sufficiently long time. As an example of such a dam, I may point to the dam that existed on the Isa River, in Grodno Province, at the factories of the Słonim-Albertin estate. With a spillway length of 15 sazhen and a head of more than 2 sazhen, the dam had only 2 sheet-pile rows in all, of which one was the main row and the other was at the beginning of the apron floor; nevertheless, the dam served in fully satisfactory condition for more than fifteen years. By that time, leakage through the main row, owing to the rotting of the piles, had increased to such an extent that it became necessary to undertake a thorough repair. The sill in this dam had been laid at a height of one sazhen above the lower level; under the water-cushion and spillway floors no backfill had been made; it is therefore clear that, along the whole sazhen of height, the wall of the sheet-pile row presented conditions most favorable to rotting. If there had been one more sheet-pile row beneath the water-cushion floor, then the main ...

the row would be better preserved, and the repair would consist only in correcting this last row, which would be much cheaper.

The impermeability of each sheet-pile row is achieved, as far as possible, by the accurate fitting of the tenons and the tight fitting of the caps over the sheet-pile row. In drawings (24–25) are shown a sheet pile prepared for driving, an identical round pile, and iron shoes, the first for the sheet pile, the second for the round pile.

The methods used in driving piles also play a rather important role.

First of all, it is necessary to investigate the line of the bottom along which it is proposed to drive the piles. This is done with the aid of an iron rod with a sharp end, called a probe. With this rod the whole line is sounded, noting whether there are any large stones, stumps, etc., on it; all these objects must be removed, or, if this is impossible, another line should be chosen.

For proper driving it is necessary to set up, along the entire line, guiding frames for the piles; for this purpose round piles must first be driven on both sides of the sheet-pile line, and the guide beams are then fitted onto them. Drawings 26, 27, and 28 show the arrangement of such frames. The longitudinal distance between the piles is taken as from 5 to 7 feet. If sheet piles have to be driven in the interval between previously driven ones, then they usually proceed gradually from one edge of the opening to the other, and the last pile is hewn slightly into a wedge so as to press all the piles tightly together (drawing 29). In order that the beams of the frames may not bend sideways, tightening bolts are passed through both cheek beams, m, drawing 26, at approximately one sazhen from one another. During the driving of a pile, at the place where bolt m was, it is removed and passed alongside, through an already driven pile.

The cap on the crest of the sheet piling is made with a groove, but every 3 to 6 feet one or two piles from the sheet-pile row are passed through with a tenon, through the whole thickness of the cap; this tenon is wedged and holds the cap beam in place. In addition, iron clamps also serve to hold the beam (drawing 30).

Special care is taken when fitting the dead beam to the main sheet-pile row. Here, before the final fitting of the cap in place, a strip of felt or peasant cloth soaked in boiling tar is laid in the groove of the beam, for greater impermeability. They try to give the beam itself the greatest possible strength, since the destruction of this row is especially dangerous, and it is subject to the greatest pressure. Drawings 30–31 show the constructions of such

beams and the methods of fastening them. Sheet-pile rows, together with their caps, withstand the horizontal pressure from the water, which is not difficult to calculate, knowing the difference in the water levels and the entire arrangement of the upper structure. This force tends to bend the sheet-pile line and to break or split it along the caps. The existing designs of dead timbers, created by practitioners, are quite primitive and do not always fulfill their purpose; cases of their destruction are very frequent. This must be borne in mind and, when constructing a dam, all the caps of the sheet-pile rows must be connected with the dead timber by longitudinal timbers running along the river, so that the pressure can be distributed over all the sheet-pile rows. Only with such an arrangement can one hope that the pressure will be transmitted both to all the sheet piles and to the loading that will be placed under the floor upstream and downstream.

It is desirable, as far as possible, for the dead timber to be integral along its entire length, but this cannot be considered an indispensable condition. If there are not enough sheet-pile rows, or if they are poorly connected with one another, it often happens that the pressure on the dead timber is transmitted to the round piles. One of the methods of straightening a bent row consists precisely in trying to move the dead timber with wedges, driving them into the gap from (Fig. 32), between the tenon of the round pile and the cap bearing against the dead timber. For freedom of movement, the mortise in the cap behind the tenon must be lengthened. In the above-mentioned dam on the Is’ River, the dead timber, with a span of 15 sazhen, consisted of three parts joined end to end; opposite each end of a separate part, a longitudinal row of round piles was driven along the river, so that the transverse distance between the rows of piles opposite the joints was no more than a foot, whereas in other places it was about 4 feet. That all the round piles facilitated the work of the dead timber could be clearly judged from the appearance of the tenons, which were pressed only by their front part against their mortises, and also from the somewhat inclined position of some individual piles.

The length of the sheet piles, for impermeability, must be such that the ends of the piles enter 2–3 feet into the impermeable layer. But if this layer lies very deep, then of course the piles must be made shorter. In this case, increasing the distance between the sheet-pile rows is useful, since this increases the path for seepage around the lower ends of the piles.

Since there is seepage of water beneath the sheet-pile rows, the water, entering from below into the space under the downstream floors, can produce such strong pressure that the flooring of the floors may be torn off. To prevent this, a sufficiently heavy and impermeable...

impermeable load, such as, for example, a thick layer of clay, concrete, regular masonry in hydraulic mortar, and so forth. This same load, beneath apron and spillway floors, also plays the role of ballast, preventing the dam from moving in the horizontal direction. The length of round piles, if they serve only to support the upper structure, is usually taken to be no greater than the length of the sheet piles; but if the round piles also participate in resisting horizontal forces, then the depth to which the pile is driven is connected with the condition of its firm embedment in the soil. Knowing the bending force of the pile and the distance of the point of application of this force from the bottom, one can also calculate the driving depth.

The timber species used for pile work are oak, larch, pine, black alder, and spruce. The durability of oak and larch in parts situated alternately in water and air is considered to be up to 40 years; under the same conditions pine and alder last 20 to 25 years, and spruce no more than 15. Provided that they remain constantly under water, the durability of each species increases by more than \(2^{1/2}\) times, while alder is not inferior to oak.

Raft Foundation.

If the soil is such that it is impossible to drive piles into it, then each sheet-pile row is replaced by a timber crib or row of cribs. For this purpose, across the river, along the bottom and for several sazhens into the banks, ditches are excavated from 1 to 2 sazhens wide, down to the hard subsoil or even somewhat deeper. In each such trench a longitudinal crib is installed, made of carefully fitted logs. Each crib is divided by transverse walls into cells. The crib is usually cut in advance on the bank; only the final assembly is carried out in the trench. After assembly, all refuse and chips are removed, and the whole space of the cells and around the crib in the trench is filled with an impermeable material, for example, rich loam. A crib constructed in this way represents, as it were, a separate sheet-pile wall. For strength, all the cribs must be connected with one another along the river, for which purpose connecting walls are used, erected at distances of 1 to 2 sazhens from one another; these walls, joined by lap joints or by half-lap notching to the principal walls of the cribs, firmly connect the whole foundation into a single whole. To support the connecting walls, stools are sometimes dug in beneath them. Beams are rolled over the walls parallel to the cribs, and the floors are then laid on them; in drawing 33 is shown—

a foundation is arranged in longitudinal section, consisting of three log frames replacing sheet-pile rows. At the present time, instead of round logs for the longitudinal rows, hewn and grooved timbers are more often used; in this case the impermeability of the wall increases both because of the more accurate fitting of the timbers and because the earth adheres much more tightly to the smooth timber walls, without, during settlement, forming empty spaces along the entire length of the timbers, as always occurs with round logs along the line of their contact.

It is useful to connect the upper crowns of the log frame with the lower ones by iron clamps. If the crib foundation is set on rock, then the lower log frame is drawn to the rock by foundation bolts, and, for close contact, the irregularities of the bottom are leveled with concrete. The working dimensions of the main log frames are usually taken as follows: the distance between the axes of the longitudinal walls is about one sazhen, and the distance between the transverse connecting walls is also about one sazhen. The disadvantages of this foundation include: 1) the difficulty of execution, since the installation of such a foundation requires diversion and pumping out of the water, and 2) the large quantity of construction material, compared with a sheet-pile foundation. In strength it is not inferior to, and even surpasses, a sheet-pile foundation. In view of the latter circumstance, with very great heads and depths of water, a sheet-pile pile foundation is built up with cribwork. According to Zbrożek, such an addition is always made when the head is less than one sazhen and the sill rises more than one sazhen above the bottom, and when the head is greater than a sazhen, when the height of the sill is more than \(1/2\) sazhen above the bottom. Fig. 34 shows a longitudinal section of a sheet-pile foundation with a cribwork addition.

Foundation of Slan.

Slan is the name given to perfectly straight spruce pole timber, 2 to 3 vershoks thick at the butt and 15 to 20 arshins long.

Slan is put into use in a freshly felled state; the bark is not removed from it, \(2/3\) of the length of the entire tree, counting from the butt, is completely cleared of branches, and on the remaining part the branches are removed only from two diametrically opposite sides. Prepared in this way, the tree can lie well against a plane, touching it along the entire length of the trunk.

Slan is laid in rows on the bottom, in the water, with the length of the trunk along the current and with the top against the current. In laying it, one must bear in mind the attainment of greater impermeability and the elimination of the possibility

scouring of the bottom beneath the fascine mattress. For this purpose it is considered a rule to lay each row of the fascine mattress so that the small tree lies tightly against the small tree, and so that the broom end lies 4–6 vershoks lower than the butt end. For the latter purpose either a suitable place in the river is selected, or a depression is dug in the bottom, or, finally, a log is placed under the butts, sometimes fastened to round piles driven in or dug in. Under each row of the fascine mattress, moreover, spruce boughs are placed beneath the butts; each row is sprinkled with brushwood, and the branches are kneaded down with the feet, so that they become compacted and form a bond for the whole layer of fascine mattress. The next layer of fascine mattress is begun somewhat farther upstream, so that the brush ends of the new row completely cover the brush ends already laid. The number of rows for proper protection of the bottom against scouring must be no fewer than four. The last upper layer is leveled in the direction transverse to the current by adding fascine mattress according to a water level, and, finally, the entire foundation is pressed down to the bottom by the upper structure erected upon it.

For impermeability, in the middle of the broom-like part of the fascine mattress, a filling is made of alternating thin layers of brushwood, strawy manure, and clay. These materials, carried along by the current of water seeping through the fascine mattress, are drawn in and, in time, clog all the passages through which water has filtered.

The construction of this foundation is usually carried out directly in the channel of the river without diverting the water to the side, but good results require considerable experience.

Of all types of foundation this is the most expensive in terms of the quantity of required material; moreover, with it it is impossible to eliminate seepage under the fascine mattress, unless the river bottom itself is an impermeable soil.

In view of what has been said, this foundation may be used only for comparatively small heads, and where the cost of building timber is insignificant. At present a dam foundation of this kind is rather difficult to encounter, but, on the other hand, small blind dams are often built here entirely of fascine mattress. For this purpose, to be sure, selected material is not used, but any small material at hand, such as, for example, young birches, pine and spruce branches, any shrubbery, and the like; it is laid in the same way as fascine mattress. After the last layer has been laid, a thick layer of earth is placed upon it for final fastening of the branches against floating up, and on the upstream side a thick layer of earth is added. A dam built in this way

can be classified rather as an earthen one with reinforcement by fascines. Fascines are also often used in the embankment of openings in an earthen dam, when work has to be done in running water.

Side walls.

The side walls of a dam, or abutments, are intended to prevent the washing away of the earthen body adjoining the dam.

With a sheet-pile foundation, the role of these walls may be performed by sheet-pile rows driven along the side outline of the waterway. The height of these walls must be equal to the height of the earth embankment. In this case the wall will be subjected to the pressure of the earth, under whose action it may be bent. To strengthen the wall, the arrangement shown in Figs. 35–36 is used. Figs. 37–38 show a simpler arrangement of side walls. When the pressure of the earth is more than 1.5 sazhen, the indicated constructions, because of their low strength, are unsuitable, and then cribwork reinforcement is used (Figs. 39–40).

In this case the cribs are usually set on round piles. If, in addition, a sheet-pile row has already been driven along the outline of the waterway, then the face of the crib is set on the crest of the sheet-pile row, as shown in Fig. 41. The cells of the cribs are filled with stone and clay. If the cribs are placed directly on the ground, or only on round piles, then care must be taken that the lower crown of the crib lies at least 2 feet below the low-water level, since otherwise the crib can easily be undermined.

Sometimes stone walls, Figs. 41–42, are also used to strengthen the sides of the waterway—the strongest, but at the same time the most expensive, reinforcement. During the release of water, side walls may be subjected to blows from floating bodies, such as ice floes, tree trunks, and the like; in order that these striking bodies should not damage the walls, the surface of the latter must be smooth, so that the striking body slides along it. If the walls are erected from round logs, then the face must be smoothed sufficiently with axes. Formerly, for smoothness, the front wall of the crib was often sheathed with thick planks; however, it is much cheaper and more reliable to build this wall of grooved beams, whereby, of course, impermeability will also be improved. At the present time this is usually done.

Upper Structure

The upper structure of a dam may be of the post-and-board or the cribwork system. The first consists in this: along the sill timber there is installed a row of vertical posts, or sometimes posts slightly inclined toward the spillway floor. Each pair of posts forms a frame, into the grooves of which board shields are lowered. The latter, resting with their lower edge on the sill timber, obstruct the movement of the water over the spillway floors and raise its level above the sill. To release water from the impoundment, the shields are lifted upward or removed entirely. For strength, the posts are made, depending on the head, of one, two, or three timbers; on the downstream side they must be supported by braces. To prevent swaying in a direction perpendicular to the current, the posts are tied at the top by horizontal timbers to the side walls of the dam. Often a bridge is made above the dam; in that case the bridge structure serves as an excellent tie for the posts in the direction perpendicular to the axis of the river. In front of the post, an inclined timber is sometimes installed, protecting the post, during the movement of the water, from blows by ice floes, by which the post may be damaged. Board sheathing of the post with its braces also serves this same purpose.

In Figs. 43–44 two such posts are shown; in Fig. 45 a post of extremely strong construction is shown, installed on a pile-and-crib foundation.

Simpler types of posts will be given below in the drawings of dams. In some cases, as for example during a heavy ice run, when there is fear that the posts may be broken by blows from ice floes, the posts are made removable, so that for the passage of water not only the shields but also the posts are removed, and then the water can freely rush through the entire opening between the side walls. Fig. (46) gives an idea of the arrangement of such a post: here the post is set with its lower end in a cast-iron box bolted to the sill timber, while the brace to it is made on hinges. Posts of this kind, however, are installed very rarely, since mill dams are generally built on small rivers, where ice runs are insignificant. To eliminate the danger from ice, it is usually sufficient, a few sazhen above the dam, to drive opposite it one or several rows, in a staggered arrangement, of large piles and to connect them together with caps; large ice floes will be stopped by these piles, while small ones are not dangerous.

A cribwork superstructure consists of an elongated crib of three long walls across the river and several transverse ones along it. The crib is set several sazhen into the banks, and its cells are loaded with stone and clay. This superstructure is installed either on a cribwork foundation of the same kind, or on a fascine foundation. In the latter case it presses the fascine mattress to the bottom.

Sometimes the lower crib of the dam is placed on tenons of piles driven through the fascine mattress; but in doing so one must bear in mind the necessity of allowing the dam to settle freely as the fascine mattress begins to settle. For this purpose, clearance is provided in the tenons and mortises.

At a certain height, openings are made in the long walls of the dam, closed by stop-logs, through which water can be let through at will.

For strength it is considered necessary that all the long walls, up to the sill of the sluice openings, consist of whole logs; likewise it is necessary to make two or three courses above the openings of whole logs. The height of the openings is no more than 1.5 arshins; the distances between the transverse walls are about 1 sazhen. At the level of the sill of the opening, a spillway floor is sometimes arranged, the space beneath which is filled with clay loam. On the upstream side of the crib an embankment is made of alternating layers of gravel, manure, clay, and spruce branches, called the otmel.

A cribwork superstructure offers no special advantages; on the contrary, it is costly in terms of the quantity of material. Owing to the small height of the openings, it always comes out longer than the post system. It very often requires repair of the embankment above the sill. In spring, if ice floes block the sluice openings—which can happen because of their small height—the dam may be destroyed or the banks may be breached around the dam. At present this system of superstructure is used rarely, and then only for small heads. In the appended atlas we have drawings, and at the end of the booklet descriptions, of two such dams.

As has already been said, to close the bay between the posts and the openings in the cribwork walls, shields made of boards are used. Their construction is shown in drawings 47–48. The shields shown in these drawings are usually raised upward with the aid of a stake, bringing its end under crossbeam C and acting as with a lever. For large openings, composite shields are sometimes used, consisting of two or three separate shields; in this case the boards are joined by iron strips, drawings 49–50. Drawing 50 shows the use of the simplest windlass for lifting such shields. Each of the composite shields is raised separately. In order to catch the eye with the hook, on the hook ...

the stick is put on. The construction of the hook and stick is shown in Drawing 51; after the hook has been put onto the eye of the shield, the stick is easily unscrewed.

If the distance between the posts is very great, then sometimes, instead of shields, stoplogs are used, i.e. fitted beams, each laid in separately. Stoplogs may be vertical or horizontal; the construction of the latter is shown in Drawing 52. (Vertical stoplogs are not used for factory dams, since with them leakage is difficult to avoid.) The area of a separate shield is rarely more than \(1/2\) square sazhen, since at larger dimensions it is difficult to handle it. It is, of course, not difficult to calculate the thickness of the boards of a shield, knowing the pressure of the water upon it. In a composite shield, the lower component parts may be made of thicker boards. When calculating the force for raising the shield, one must bear in mind that, owing to freezing, swelling, etc., the coefficient of friction of the shield against the groove will be very considerable. It is usually quite sufficient to take this coefficient as equal to 1.

In order to ensure freedom for raising the shields at any moment, the entire space above the apron is covered with a plank flooring, supported by special posts set on the apron, so that the boards lie a few inches above the surface of the water. This flooring is in turn covered with a thick layer of manure and straw. Under such conditions the water beneath it, even in the Urals, does not freeze, which makes it possible, at the first signs of the coming flood, to throw out all the shields easily.

Bulls.

I have already said that they usually try to make the sill beam continuous. In crib construction the long walls must also contain continuous logs; therefore, if the water-passage opening turns out to be very large, then, taking into account the available building material, it is divided into several separate openings, separated by bulls. Bulls may be of cribwork or of stone.

Cribwork bulls are erected on round piles. Sometimes all or part of the outer walls of the bull, for impermeability, are erected on a sheet-pile row. If the bull does not have such a sheet-pile enclosure, then its first lower course must be laid sufficiently deep, so that undermining from below cannot occur. A cribwork bull consists of 3 or 4 long walls (along the river) and several transverse...

external. Since the outer walls must be smooth and impermeable, they are most often built not of round logs, but of hewn and tongued beams. On the upstream side, to cut the water, the pier should have a pointed form; the sharp angle is reinforced with a special corner beam, fastened to the walls with iron clamps. The distance between the longitudinal and transverse walls is from 0.75 to 1 sazhen; the total width of the pier is from 1.5 to 3 sazhens, i.e., two or three boxes. The boxes are loaded with stone and loam. According to Gausman, the weight of the pier should amount to 5 to 7 times the horizontal pressure of the water acting upon it. Stone piers do not differ in their form from cribwork piers. They are placed either directly on the bedrock, or on a foundation of round piles; in the latter case they are enclosed around the perimeter by a row of sheet piling. The thickness of a stone pier is not less than 5–8 feet. The details of the construction of piers are clearly visible in the drawings of individual dams placed in the atlas.

Stone Dams

Stone dams may be divided into two types. The first, for comparatively small heads, replace wooden spillways; the second are blind dams, replacing earthen ones, for all possible heads. In terms of durability, stone offers great advantages in comparison with wood. But in order that a dam built of stone should be impermeable, it must reach the bedrock. If the bedrock lies deep and the soil is weak, then, with a small height, the dam may be erected on a pile foundation, and to ensure impermeability it is enclosed all around its entire perimeter by a row of sheet piling. It is self-evident that the masonry must be laid on hydraulic mortar. Such dams are made as overflow dams, but often also have an upper structure of the sluice system; the posts may be wooden or iron. The dam must have sufficient length and a suitable profile to eliminate the scouring action of the water.

While in a wooden dam resistance to sliding under the head of water is achieved chiefly only thanks to the strength of the wood, in stone dams this sliding is opposed almost exclusively by weight, which is why the dam itself is more reliable. All parts of the dam are calculated so that only compressive forces can arise in the stone; and for this, as is known, the resultant of the weight and of the water pressure on the dam must pass ...

through the middle third of the base. One of the appended plates shows several such dams; at the end of the booklet there is a brief description of them.

Solid masonry dams are ordinarily built for greater heads. In such heads it is found more convenient to discharge the water by means of iron or cast-iron pipes, since masonry sluices at great heads are very expensive; moreover, owing to the very high velocity of the water in them, one cannot always be sure of their strength. An iron pipe may be inserted into the lower part of the dam and, if of sufficient length, is capable of carrying the water away to a place safe from undermining. The pipe is closed on the upstream side by a valve.

The rational profile of such dams, with the use of the smallest quantity of material, has been developed comparatively recently, which is why these dams have only recently begun to spread. I shall briefly set out the principles that served for finding this profile.

As is known from elementary geometrical figures, a triangle placed on its base has the greatest stability under the action of forces in its plane; this is the profile that ought to be given to a masonry dam.

But the triangle on the base \(BC\) (Fig. 53) may have its vertex at \(A_1\), \(A\), or \(A''\); the question is which of these profiles is preferable.

An obtuse angle \(B\) cannot be used, since in that case the wall \(A'B\) would overhang and separate stones might break away and fall. There remain two profiles: with a right angle at \(B\), and with an acute angle. In order to determine which of these profiles is more advantageous, we shall proceed as follows.

Knowing that the overturning force in both the first and the second case will be one and the same horizontal force of the water pressure, applied at a height of \(1/3\) of the head, we shall determine the moments of resistance to overturning about the edge \(C\) for the first and the second case, taking the length of the dam along the crest to be \(1\). Let \(BC=b\), \(AB=h\), \(AA''=e\), and the weight of the dam be \(G\).

With angle \(B\) right, the resisting moment will be \(G \cdot \frac{2}{3} b\).

For the profile \(BA''C\), in addition to the weight, the vertical pressure of the water on the wall \(A''B\), equal to the weight of a water prism with base \(AA''B\) and height equal to unity, will also resist overturning. The point of application of this force lies at a height of \(\frac{1}{3}h\).

It is not difficult to derive that, if \(\delta\) is the weight of a cubic unit of water, then the moment of the resisting force for the triangle \(BA'C\)

\[ \text{will be} = G\left(\frac{2}{3}h-\frac{e}{3}\right)+\frac{eh\delta}{2}\left(h-\frac{e}{3}\right); \]

if the first profile is advantageous, then

\[ G \cdot \frac{2}{3}h > G\left(\frac{2}{3}h-\frac{e}{3}\right)+\frac{eh\delta}{2}\left(h-\frac{e}{3}\right); \]

if \(\gamma\) is the weight of a cubic unit of masonry, then

\[ G=\frac{bh}{2}\cdot \gamma \]

and therefore:

\[ \frac{e h . h . \gamma}{6} > \frac{e h . \delta . h}{2} - \frac{1}{6}e^2 h \delta, \]

an inequality possible when

\[ \frac{\gamma}{\delta} > 3-\frac{e}{h} \]

The hard kinds of stone from which masonry dams are built usually have a specific weight of about 3; therefore, for them the profile in the form of a right triangle is the most rational, but this profile, in view of certain considerations, must be somewhat modified.

The crest of the dam must always rise somewhat above the water level. The thickness of the crest must be sufficient both to resist the action of waves that may arise in the reservoir, and also to resist properly the action of atmospheric influences. These considerations require that the apex of the triangle be built up with a rectangular part (Fig. 54).

A further modification of the triangular form is obtained from calculation. For the stability of a masonry wall in general, as is known, it is considered necessary, first, that the maximum compressive stress should not exceed a certain norm, and, second, that tensile forces should nowhere be able to appear in the masonry. These same requirements are imposed in the calculation of a masonry dam. In the calculation one must have in mind two cases. The first case is when the reservoir is filled with water; in this case the greatest compression appears on the downstream edge, and the second, when the reservoir is empty—the greatest compression on the upstream edge. The calculation can be carried out graphically; its basis is as follows.

Let the drawing (54) show the profile of the dam. Let \(R\) be the resultant of the weight \(G\) of the entire part of the dam above the section \(MN\), and of the horizontal pressure of the water \(S\). We transfer the point of application of the force \(R\) to the point \(C\), and here resolve it into \(S\) and \(G\).

The force \(S\) tends to move the dam along the plane \(MN\). To prevent this, it is necessary that \(S \leq Gf\), where \(f\) is the coefficient of friction, taken as \(0.76\) for masonry.

To increase the friction in the plane \(MN\), in laying the masonry one should provide bonding of the stones along the height of the walls; at the very least, each horizontal layer should have stones projecting from its upper surface, preventing the sliding of the next layer. Sometimes, for the same purpose, the joints of the masonry are made not horizontal but slightly inclined, so that the angle of the joint and of the resultant \(R\) approaches a right angle.

When by such means the force \(S\) has been balanced, the remaining force \(G\) will produce uniform compression of the section and its bending, as the result of the moment \(Ge\), where \(e\) is the distance of the center of gravity of the section from the point \(C\). If we assume that we are considering a unit length of the dam and denote the length \(MN\) by \(b\), then it is easy to see that the stress in the section \(MN\) due to compression will be

\[ Z = \frac{G}{b}; \]

and due to bending at the edges \(M\) and \(N\)

\[ S = \pm \frac{6Ge}{b^2}; \]

the compound stress at the edge \(N\) cannot be greater than the allowable \(Kz\), and at the edge \(M\) cannot be less than zero, since then the masonry would be in tension; therefore, for the point \(M\) we have

\[ \frac{G}{b}\left(1 + \frac{6e}{b}\right) \leq Kz \ . . . . . A. \]

and for the point \(N_1\)

\[ \frac{G}{b}\left(1 - \frac{6e}{b}\right) > 0 \ . . . . . (A_1) \]

The latter inequality is satisfied when \(e \leq \frac{b}{6}\); hence one may make the general conclusion that, in general, tensile stresses do not appear in the masonry if the resultant passes through the middle third of the section under consideration.

In the case when the reservoir is empty, it is not difficult to derive that the compound compressive stress at the edge \(M\) will be

\[ \frac{G}{b}\left(1 + \frac{6e'}{6}\right); \]

(here \(e\)

the distance from the point of intersection of the force \(G\) with the straight line \(MN\) to the middle of this straight line, i.e., to the center of gravity).

By the condition

\[ \frac{G}{b}\left(1+\frac{6e'}{b}\right)=Kz\ldots (A_2). \]

We have no need to determine the stress on the rib \(M\); it is required only that the direction of the force \(G\) should not pass outside the middle third of the base. On the basis of what was noted earlier, this is quite sufficient to prevent the appearance of a tensile force.

It is now not difficult to make clear how the graphical calculation should be carried out. Having first selected the form of a right-angled triangle with a rectangular addition corresponding to the crest of the dam, one passes gradually from one horizontal section to another, lying lower. It is most convenient to divide the entire height of the dam into several horizontal layers. For every horizontal section it is necessary that the direction of the weight of the entire part lying above, and the direction of the resultant of the weight and of the water pressure on the whole overlying part, should not pass outside the middle third of the section; it is also necessary that inequalities \((A)\) and \((A_2)\) be satisfied.

Usually, on the downstream slope, one tries to observe the equality

\[ \frac{G}{b}\left(1+\frac{6e'}{b}\right)=Kz, \]

while on the upstream side, owing to the verticality of the wall, it is sufficient that inequality \((A_2)\) be fulfilled; if \(Kz\) proves too large, then the section must be widened, moving the excessively loaded rib farther away from the middle of the section.

Using this method of calculation, we arrive at a profile similar to that of the masonry solid dam built in France on the river Furens (see the atlas). On its profile are also shown the lines of pressures, i.e., the geometric locus of the points of intersection of each horizontal section with the resultant forces acting on the part of the dam above that section. It is easy to find that these lines do not go outside the middle third.

The dam is erected on rock, the surface of which is deliberately made uneven for better bonding and connection with the cement.

From observation of existing dams of the described type, it may be concluded that, when the height of the dam is more than 30 meters, the only reliable foundation for it is rock. At heights of less than 30 meters, it may also be erected on ordinary dense subsoil, but on a special stone foundation laid sufficiently deep. In designing the foundation, one must take into consideration the possibility of water penetrating under the sole of the foundation and exerting upward pressure on it.

With weak soil, the construction of an earthen dam is far more reliable. The compressive stress in existing dams is, for limestone and sandstone, from 6 to 7.5 kilograms, and for granite from 8 to 12 kilograms per square centimeter.

When large reservoirs are formed, the dimensions of the dam crests should be according to Krantz.

Head (meters)	5	10	15	20	25	30	50
Height of the crest above the water	0.5	1	1.5	2	2.5	3	3.5
Thickness of the crest	1	2.5	3	3.5	4	4.5	5

For small reservoirs, when wave action is not dangerous, the thickness of the crest may be reduced, but in general this thickness is not taken as less than one meter.

A completely special type of masonry dam is represented by the dam erected in 1902 by the English across the Nile River for purposes of irrigation. This most colossal structure in the world, which cost, in our money, about 24 million rubles, is a gigantic granite wall about 2 versts long, 7 meters wide at the crest, with a downstream batter of \(2/3\). On the upstream side there is an enormous stone embankment with an inclination to the horizon of only 0.056; the height of the dam in places reaches up to 110 meters, measured from the base. The head of water may reach up to 30 meters. In the middle part, over a length of 759 sazhens, the dam has 180 discharge openings in the form of narrow but long windows in the vertical direction. Each window is closed on the upstream side by a special shield, set in motion by a hand winch. For better regulation of the level, the windows are arranged in groups at different heights. The granite bottom of the riverbed served as the foundation for the dam.

In drawing (54a) a perspective view of this dam from the downstream side is shown.

Temporary Dams

The construction of dams, like hydraulic-engineering works in general, does not present any particular difficulty when conditions permit them to be carried out in a dry place—in the air; but when they have to be carried out in water, then the matter becomes more complicated. Of the works described by us earlier, in standing water the following may be carried out: raising an earthen embankment, driving a sheet-pile row, and, in general, driving piles.

On flowing water these works are already difficult; but if it is required to lay the foundation of a masonry dam, to make a deep excavation in the bottom, then the removal of the water is already absolutely necessary. The methods used for this purpose may vary, depending on local conditions. Sometimes the entire riverbed is diverted to the side by digging a bypass canal; then, at the site of the dam being erected, there remains only standing water, in which it is already easier to work. After the work is completed, the canal is filled in with fascines, earth, brushwood, stone, and the like, and the river is directed into its old channel, onto the dam that has been erected.

If for some reason the river cannot be diverted, then often the width of the river is divided into several sections; one of them is enclosed by a special temporary dam, and the river is then directed through the remaining unenclosed part. In the enclosed space standing water is formed, which, if necessary, can be pumped out, and the work carried out in the dry. When in this way part of the dam has been constructed, the temporary dam is removed and the next section is enclosed; meanwhile the water can be directed to the unenclosed part, including onto the already constructed part of the spillway, etc.

These temporary enclosures are, in themselves, dams from which no particular strength, nor even absolute impermeability, is required; but it is important that their cost be minimal, that they can be erected quickly and just as quickly destroyed.

In their construction, the experience and ingenuity of the supervisor come to the fore. Here it is important not only to choose the appropriate type of dam in accordance with the whole sum of existing local conditions, but also the very method of erecting the dam must be modified depending on these conditions, which are extremely varied in each individual case. If methods are used unskillfully or inappropriately, there is always a risk that the dam will be carried away by the current during the work. I shall describe several of the most commonly encountered types of temporary dams.

For an enclosure in standing water, and also in moving water when the velocity of flow is small, a sheet-pile row may serve. Of particular interest is the construction of such a row in moving water.

Driving is usually carried out from the two ends of the row, narrowing the opening until the water in the remaining gap rushes with such force that it begins to scour the bottom at this place; then the driving is stopped.

Into the remaining open span, in the guide frame, as many tongue-and-groove piles are inserted, fitted close to one another, as are needed to fill the entire span. These piles, with their pointed ends, touch the surface of the water, and are kept from falling by small wedges placed between the piles and the cheek of the guide frame. Sometimes the piles are tied together in pairs with iron staples.

On special platforms arranged on both sides of the hanging wall thus formed, workers with hand pile-drivers are placed opposite one another, with the arrangement that there should be no more than four piles for every two workers.

At a given signal the workers strike the cheeks of the frame; from the shaking, the wedges spring out, the entire wall falls, and the pointed ends of the piles are driven into the bottom with momentum. Now begins the continuous driving of the piles with hand pile-drivers. At this time, at the base of the piles on the upstream side, bags of sand are lowered, in order to prevent the water from scouring out the bottom around the pointed end of the pile, which may occur because the stopped water, rising, will begin to press upon the bottom. When the piles have thus been secured in the evening, their further driving is carried out the next morning to a sufficient depth.

A tongue-and-groove enclosure made of timbers, because of its expense, is used rarely; more often a board enclosure made of tongue-and-groove boards is used, in connection with earth embankments. Such enclosures are known under the name of cofferdams. In Fig. 55 is shown a cofferdam of two rows of tongue-and-groove boards, driven by hand to a depth of 2–3 feet, with clay fill between them. It is easy to see that, by adding earth slopes to it, it can easily be transformed into a true earth dam. The distance between the walls is taken equal to the depth of the water.

In Fig. 56 is shown a cofferdam of one row of inclined boards and an earth bank. Cofferdams of this kind are often installed on the apron floor of wooden dams when repairing shield posts and the dead timber; in order that the ends of the boards should not slip along the floor, it is useful to drive into them nails pointed at both ends; with one end the nail is driven into the end of the board, and the other pointed end enters the floor.

Sometimes, however, for this same purpose cofferdams are arranged from horizontal boards (Fig. 32).

Instead of boards, stakes are sometimes taken directly, driven in as a loose palisade; the gaps between them are then filled with straw, manure, and turf, throwing these materials upstream; then the current of the water itself directs these materials into the gaps of the palisade, after which an embankment of earth is made.

A brushwood dam, remarkable for its cheapness, is built in the following way: across the river one or several rows of round piles are driven, each pile at a distance of from 1 to 2 arshins from the next. The piles are tied together above the water level by caps, on which a temporary plank platform is laid. On the platform the material for building the dam is prepared, and from it the construction itself is also carried out. Bundles of bound brushwood are thrown into the water so that each bundle, lying with its length across the current, would bear against the piles and could not be carried away by the current; these bundles are pressed down to the bottom with poles and are covered with rubble, gravel, pebbles, and even stone; if, in doing this, it is noticed that the water begins to scour the bottom, sand-filled sacks are lowered from the upstream side of the laid layer, pressing them to the bottom. When in this way the first layer has been laid so that neither floating up nor scouring of it occurs, a second layer is placed, and so on, until the whole required height has finally been laid. A permeable wall is obtained, but one which nevertheless holds back water. Then, by throwing manure, straw mixed with earth, pieces of turf, and the like from the upstream side, the large openings in the brushwood are gradually clogged, and sufficient watertightness of the dam is attained. Such dams are successful where the bed has firm and non-erodible soil, such as, for example, compact clay.

Where the bottom is stony and rocky, temporary dams are made of dumped stones. From stones dumped into the water, an embankment is raised thick enough that the pressure of the water cannot destroy it. When the stone wall has been erected, its watertightness is achieved by covering it with alternating layers of manure, earth, turf, sand, and the like; to clog the openings it is useful to throw in straw, lowering it to the bottom, and pieces of turf.

A saving in the quantity of stone, as well as greater strength, is achieved when the stones are not thrown directly into the river, but into a previously installed log crib. For economy, and also for ease of lowering into the water, these cribs may be made with large gaps between the logs (fig. 58); in this case the water will not press especially strongly, finding a free passage through the gaps. The purpose of the crib is only to hold the stone; watertightness is achieved by an earth backfill on the upstream side. The dams described, in their strength, often serve as permanent dams, but they almost always leak heavily.

In the construction of the Nile dam mentioned earlier, for the temporary enclosures they first of all built an embankment of dumped gro—

small granite blocks, whose weight reached as much as several hundred poods.

Despite this, the current was so strong that in some places these stones were displaced. For reinforcement, entire wagons filled with stones had to be thrown into these places. The weight of such a wagon with its contents reached up to 2,000 poods. When, finally, the stone bank was erected, perfectly calm water formed in front of it upstream. In it a dam was built of bags filled with sand, which, adjoining the stone wall with its ends, enclosed the space for carrying out the work; after this, for impermeability, an enormous quantity of sand was poured on the headwater side, and then the water was pumped out by steam pumps. This pumping continued without interruption throughout the whole time of the work, so as not to allow the seeping water to collect.

From this description we have also seen that a good enclosure is provided by a dam made of bags. For cheapness, the bags are often made of matting; it is best to load them with grus, or, if possible, with coarse sand, to which pebbles are also added. A bag should never be packed tight, since this prevents it from fitting closely. Usually it is filled to no more than \(3/4\) of its volume. In Fig. (59) a dam of bags is shown schematically.

French Dams.

These dams make it possible very quickly to free the entire opening of a sluice from any obstructions whatever, for example, posts, gates, and so on, thereby providing a completely free passage for water and floating bodies. As factory dams, these are used rarely; their principal application is in navigation. I therefore give only the briefest description of the three most widespread types *).

Poirée Dam is shown in Fig. 60 \(a, b, c, d\). As is evident from these drawings, the supports of this dam are iron frames rotating about the axis of the lower horizontal edge of the frame. The foundation of the dam has, along the whole length of the opening, a recess into which the frames can be laid by rotation (Figs. \(a\) and \(b\)). Both lowering and raising of these frames must be done in succession, moving from one

*) Details of the calculation of these dams may be found in the booklet: “Materials for the Design of French Submersible Dams.” K. A. Akulov. Kiev, 1902.

bank to the other. Before the frame is lowered, the vertical shutters and the plank flooring are first removed from each bay between two uprights. Then the workers, standing on the flooring of the next bay, remove the connecting strip with a handle and two forks (c), and with this same strip push away the frame, which, rotating, falls to the bottom and enters the niche. The frame is raised by the workers moving in the opposite direction, with the aid of chains. After it has been brought into the vertical position, the frame is fixed in place by the connecting strip C and by the floor decking.

The dismantling and assembly of such dams is carried out very quickly. Sometimes panels are used instead of shutters.

In the city of Moscow, on the same river, there is a dam of a similar kind. Simultaneously with navigation locks, the head is also used here for putting turbines into operation.

Chanoine Dam consists of a row of inclined plank panels installed in a single line along the sill beam. One of the panels is shown in Fig. 61. Here we see that the panel has a horizontal axis of rotation somewhat below its center of gravity. This axis is at the same time the upper edge of an iron frame, which can in turn rotate about the axis of its lower horizontal edge, secured by the panels in bearings on the sill beam. The iron frame is supported by a prop (Fig. 61), connected at one end to the frame by means of a hinge, and at the other end resting against a projection of a special cast-iron box embedded in the foundation. Above the projection this box has a planed track. It is sufficient to push the end of the prop off the projection for it, sliding along the track, to come into motion, whereupon the panel together with the frame falls to the bottom. The props are pushed off from the bank by means of a special trolley (Fig. 61) running on a guiding beam embedded in the foundation. The panels are set in place from a boat. This system also makes it possible to regulate the head of water automatically; for this purpose the position of the panel’s axis of rotation is calculated so that, when the water rises above the normal level, the moment of pressure on the upper part of the panel would exceed the moment of pressure on the lower part; then, obviously, the panel will turn into a horizontal position and let the water pass.

Desfontaines Dam. Fig. 62 shows a transverse section of this dam. The upper plane of the foundation here rises approximately by \(1/2\) of the normal head above the lower horizon. Along the entire bay a channel is arranged, as shown in the drawing. This channel is divided every 1.5 meters along its length by cast-iron diaphragms (boards), having

two openings, one horizontal, A, the other vertical, B; above, along the diaphragms, it is covered with cast-iron plates and at its ends connects with conduits located in the bull and in the abutments. In each of the supports one conduit communicates with opening A, and the other with opening B. Along the axis of the canal, between the diaphragms and the plates covering them, cast-iron pipes are inserted (see the drawing), with internal annular and external flat flanges. The external flanges of these pipes are connected by bolts to the cast-iron plates, while the internal ones serve as bearings for the axes of rotation. In each interval between the diaphragms a shield is placed, consisting of two parts almost equal in height: the upper, or shield proper, located outside the foundation, and the lower, or counter-shield, located in the canal (Fig. 62). The counter-shield has a curvilinear shape. The counter-shield and the shield have two solid ribs, passed into the slot of the pipe and mounted therein on the axis of rotation; iron sheathing is fastened to the ribs.

The shields stand upright and maintain the head, as shown in Fig. 62, when opening A, by means of the corresponding conduits in the supports, is connected with the upper water; the shields are lowered and laid down, as shown by the dotted line, when by means of the conduits opening A is connected with the lower water and opening B with the upper; the lying shields are raised if opening A is connected with the upper water and B with the lower water. Thus all manipulations with the shields here are performed very quickly and from the bank abutment.

Brief Explanation of the Appended Drawings.

Cross section of the dam on the River Furens in France. Plate V.

The dam was built in 1866 from local stone of granite rock; in designing it, the considerations set forth above in the text were adopted for the first time. The dam closes the entrance to a mountain gorge, forming a water reservoir with a capacity of 1,600 thousand cubic meters. This enormous reservoir is filled with water at a time when the River Furens is abundant in it, and serves to make up the shortage in dry periods, when previously the water supply of the nearby city of St. Étienne, as well as of the factories situated downstream, suffered from insufficiency. The dam is built on solid rock and with its ends also rests against the bank rocks.

The greatest head is 50 meters; the axis of the dam in plan has an arc-shaped form, with its convexity turned upstream; the radius of this arc is about 250 meters, the chord, i.e. the span closed by the dam, 100

m. The arc-shaped form, making the body of the dam resemble a vault, of course increases its resistance to pressure, although this circumstance was not taken into account in the calculation.

There are no openings in the body of the dam. Two cast-iron pipes, each 0.4 meter in diameter, and one of 0.216 meter, serve to empty the reservoir. To lay these pipes it was necessary to pierce a tunnel connecting the reservoir with the neighboring valley, into which the discharge is made. The tunnel is laid at a height of 8 meters from the lowest point of the bottom of the reservoir. For strength, the pipe is embedded in masonry occupying 11 meters of the tunnel length from the reservoir.

For regulating the water level there is another tunnel, situated at a height of 44.5 meters from the bottom; in addition, in the upper reaches of the dam a wide bypass spillway channel has been cut. Water from the river can also be directed into this channel when it is rich in silt, in order to avoid filling the reservoir.

This dam, without the water conduits, cost 900 thousand francs. The construction of the lower tunnel, 2 meters high, 1.8 m wide, and 200 long, together with the cast-iron pipes and gates, cost 102 thousand fr.; the upper tunnel, 1.95 m high, 1.5 wide, and 65 meters long, cost 18 thousand francs.

Frame spillway dam. Table IV.

The drawing of the dam was made from an existing structure in Kovno Province, on a small river flowing into the Oknista estate. In view of the excellent construction soil (compact, greasy clay), this dam is completely impermeable. The special feature of this dam is the leaning wall C, made of rammed, inclined boards, whose purpose is to increase impermeability. The space beneath the boards is rammed with clay, and on the outer side a gentle embankment of manure and earth is made. In order that, when the crib settles, the boards might slide with their upper leaning ends, the supporting log on the outer side of the crib is hewn. The crib boxes are filled with clay mixed with stone and covered with floors made of a single row of boards.

Frame dam on a slate foundation. Table VI.

The dam is situated on one of the tributaries of the Pripyat River in Minsk Province. The dam is divided by a frame abutment into two openings. The boxes of the abutment and of the bank mouths are loaded with loam mixed with stone, and also with a large quantity of iron slag, which prov—

depending on proximity. The space beneath the submerged floor is tamped with layers of loam and manure. Upstream, a sloping backfill (apron) is arranged. This apron consists of alternating thin layers of fir brush, manure, brushwood, and clay. The upper layer is covered with a thicker (2 vershoks) flooring of fir laths with brushwood, and is well sprinkled with sand and pebbles. The apron also covers the crest of the slope, reducing seepage. The stilling and overflow floors shown in the drawing are in fact absent, and the space beneath them is filled with large stone and slag. The sluice openings are closed by board gates sliding in the grooves of timber frames inserted into the openings of the crib walls (not shown in the drawing). A carriage bridge is built over the dam.

Wooden sluices (water outlets) on the irrigation canals of the Valuisky district of Samara Province. Table VII.

These sluices were built by the expedition for irrigation of the south of Russia and may serve as an example of small water outlets where the flow of water is calm. As is evident from the drawings, the water outlet has neither overflow floors nor lateral reinforcements. Such a construction can be allowed only under very favorable soil conditions, since when the gates are opened the water rushes with force into the canal and can easily form a scour hole below the sill. Usually, below the sill, part of the canal bed is lined with boards, or at the very least the bottom and side slopes are paved with large stone, in order to eliminate the possibility of undermining.

Tinguta Dam. Tables VII and VIII.

This dam was built by the same irrigation expedition, on the Little Tinguta River, Astrakhan Province, to form an irrigation pond. The site plan shows part of the dam and the main irrigation canal. At first the entire dam was made solid and had no wooden water outlet; the surplus water was diverted by a special spillway channel dug in the upper reaches of the dammed area. After the dam was washed out in the spring of 1882, repairs were begun. The earthen body was strengthened by two rows of sheet piles driven parallel at a distance of 4 sazhen, between which all the alluvial soil was removed down to the clay subsoil; the space between the piles was filled with clay with careful tamping, and the body of the dam itself was thickened; at the same time

they decided to make a wooden water outlet and to keep the water lower than it had been before. This precisely explains the considerable elevation of the old, uneroded part of the dam above the bridge decking of the water outlet (Plate VIII, elevation and section).

The wooden cribwork part of the dam, with crib abutments, is built in the middle of the ravine. The opening of the dam, 7 sazhens wide, is divided in the middle by a pier into two spans, each span in turn being divided by posts into three openings closed by stop-logs. In addition, for regulating a less considerable inflow of water, in each span, below the stop-logs, two outlet windows are placed, closed by gates set in motion by means of iron lifting rods.

The crib abutments are 1.9 sazhens high, the boxes being filled with clay, sand, and an admixture of stone. In front of the spillway floor a stone riprap has been made; the slopes of the earthen embankment are protected from washout by wooden side walls consisting of a row of piles driven along the direction of each of the side walls and sheathed with boards. The walls are supported by anchor piles. For crossing the water outlet a wooden beam bridge has been arranged, and, for protection from ice during spring floods, in front of the apron an ice-retaining grating has been built, consisting of four-sazhen seven-vershok pine piles driven at a distance of 0.75 sazhen from one another, braced on the dam side with struts and tied at the top with a longitudinal beam. The wooden grating is 25 linear sazhens long, and the upper beam is situated 1.5 sazhens above the sill of the dam.

For admitting water from the reservoir into the irrigation canal, on the left bank, across the body of the dam, three cast-iron pipes are laid in the natural ground, each 12″ in diameter and 18 sazhens long. On the reservoir side these pipes adjoin a masonry well, whose cast-iron cover is provided with gates for admitting water. The ends of the pipes on the outlet side likewise adjoin a masonry well, and to the end of each of them a cast-iron box is attached, closed by a slide gate.

The water-conveying irrigation canal passes across the river bed in the form of a wooden aqueduct on piles, the drawings of which are given in Plate VII.

Dam on the Trukhanovka River, Vitebsk Province. Table IX.

This dam was built several years ago to set a mill in motion. The choice of a site at a bend in the river, strange at first glance, is explained both by the properties of the river and by the character of the soil. The very high banks of the river, up to 2 sazhen at low water and more, reveal the following stratification: the first layer from the surface of the soil is a thin layer of vegetable earth; below it follows a layer of fine sand 2–3 arshins thick; farther on the sand passes into loam, increasingly enriched with clay the deeper it goes; still deeper, beneath the river bed, lies pure compacted clay. In some places the clay forms hills projecting onto the surface of the soil of the banks. The entire basin of the river is hilly and at the same time consists chiefly of clayey soils, as a result of which this small river, after every rain, rises very quickly and very strongly, filling its channel to the brim. After several hours the level has already fallen to normal. In spring, during the melting of the snows, the river overflows its banks, and the flood sometimes lasts up to two weeks.

The site for the dam was chosen on the following grounds: 1) At the site of the building the water never came, even in spring. 2) The whole left bank appeared at this place sufficiently firm, since, a few sazhen back from it, there lay a thick layer of fatty clay, coming out onto the surface of the soil; a separate vein of this clay pierced the bank in some places through its entire height. 3) The right bank, forming a peninsula, had no layer of sand, which probably had over time been washed away by the water. Directly beneath the vegetable layer lay loam. The height of this bank was 2 arshins lower than the left one, so that during a flood the water overflowing from the banks was directed, as indicated by the arrow (see the situation drawing), to where the lowering of the soil was greatest. Thus, during high water, a natural spillway was formed here, owing to which the pressure on the proposed dam should have been considerably reduced. 4) The chosen site lay almost at the very boundary of the property, which made it possible to use almost the entire fall on the proprietor’s section.

After the choice of the site, the determination of the available work was undertaken.

Leveling showed that the fall over a section 3.5 versts long amounts on average to about

\[ \frac{1}{2100}, \]

and the average width of the river was about

7 sazhens, with an average depth of about 0.2 sazhen. The normal discharge is 1.2 cubic meters. With these data it is easy to calculate, by Rühlmann’s formula (see the definition of a backed-up river profile), that if a head of 0.75 sazhen is made at the dam, then at the upper end of the reach (the boundary of ownership) the rise of the water will be extremely insignificant, namely about 0.02 sazhen. This rise did not exceed the usual fluctuation of the level, so that it was not even noticed by the peasants whose village was situated precisely at the boundary. Subsequently it was intended to increase the head somewhat, after reaching agreement with the peasants.

In view of the considerable height of the banks, the sluiceway was built without diverting the river water. Since, as regards impermeability, the soil was sufficiently favorable—although it was washed out rather easily owing to the very fine sand contained in the loam—nevertheless, in order to make the dam cheaper, it was decided to drive only one main sheet-pile row, while the apron and spillway rows were replaced by walls made of horizontal planks set on edge. These walls, made of grooved planks with inserted tongues, were joined together and nailed to rows of round piles (see the drawing).

The entire opening of the sluiceway was divided into two parts, of 3 and 5 sazhens; these openings were separated by a wall of sheet-pile planks driven along the channel. This wall included three very large and long square piles, which served to secure the guiding frames when driving the planks. In addition, these piles greatly increased the resistance of the wall to the action of forces directed along the channel, which was highly desirable, since the dead timbers of both openings abutted against this wall with their ends. The main sheet-pile row was driven 4 sazhens into the bank; moreover, adjoining it are wings of sheet-pile planks driven into each bank for 4 sazhens.

The left opening of the sluiceway is a flash-board dam, the sill of which was laid at the very low-water level. The right opening was made as a spillway, and its sill was laid at the level of the proposed pond horizon. Construction of the right opening was begun only when the left part had been completely finished. As the sheet piles were being driven in the right opening, the water began to rise and soon flowed over the sill of the left opening, without interfering with work on the right.

When both openings of the dam were thus ready, the left part was closed with flashboards and construction of the water conduit to the engine was begun.

The side walls were made as cribwork. The apron and spillway floors were made of a single row of 2-inch planks, joined together...

in a groove with an inserted tenon. The space under the apron was filled with rich clay; under the stilling basin, with alternating layers of clay, sand, fascines, and manure. The cribwork boxes were filled with loam, with manure and brushwood added at the bottom. Stone was not used in the work, since none was available nearby.

Wooden spillway of the Mariinskaya water system. Table VII.

After what has already been said in the description of the preceding dams, little remains to be said here. Examination of the drawing will best clarify the details. The filling of the space under the aprons and stilling-basin floors here is made of lean concrete.

Wooden spillway of the Vyshnevolotskaya system. Table VIII.

This spillway has certain special features. The backwater above the mudsill is very considerable, up to 2.5 sazhens. To reduce the pressure on the gates, the posts are placed very close to one another. They do not have braces in the vertical plane, but rest on several horizontal beams, whose ends are embedded in the bullnoses and abutments. These beams in turn have braces in the horizontal plane. The span between each two posts is closed by several plank gates, raised upward by means of a capstan. The spillway has a double row of posts and gates, which is very convenient for repairs. The second row downstream is always closed, while the first is a reserve row. During ice drift, not only the gates but also the posts are removed, which is easy to do, since the post here is a vertical beam freely entering shallow guide recesses in the horizontal beams and, at its lower end, inserted into a cast-iron box screwed to the mudsill. The installation of the posts in place is likewise not difficult. The space under the floors is filled with concrete and a layer of regular stone masonry on cement, in order to prevent the pressure of the seeping water from acting on the floors from below upward. The plank sheathing of the upper horizontal plane of the bullnoses has special little doors; by opening them, one can observe the condition of the filling of the bullnose.

The Sestroretsk Dam (Tables XII and XIII).

It was built by Prof. Hausman in 1862 and cost 240 thousand rubles. In material, this dam represents something intermediate between stone and wooden. The soil on which the dam was erected was very poor. Dense, reliable clay lay...

only at a depth of 37 ft. from the upper water horizon; above this clay there lay a layer several feet thick of silty, very heterogeneous alluvial deposit, with a large quantity of stones, pebbles, sand, and so forth. This layer was permeable to water and was easily liquefied under its pressure. Above this layer lay fine-grained, readily washed-out sand (quick-sand). In view of such properties of the soil, great caution was permitted by the builder. The number of transverse sheet-pile walls was brought up to 8; rows 1, 3, 4, and 8, reckoning downstream, were extended far into the banks, so that the length of each was 70 sazhens, whereas the span of the spillway was only about 15 sazhens, including the thickness of the abutments. The sheet piles, of sufficient length for their ends to enter the clay by about 2 ft., were provided with heavy iron shoes; but nevertheless not all of them could penetrate through the silt layer, striking stones in it, and therefore seepage of water could not be avoided. To reduce this seepage, between rows 2 and 3—4 and 5—7 and 8, within the limits of the spillway opening, the sand was excavated to a certain depth and the space was filled with concrete. Only between rows 7 and 8 was the concrete laid to a proper depth, down to the firm ground.

To carry out a very deep excavation between rows 2 and 3—4 and 5 proved very difficult, both because of the increase in pressure from the external sides on the sheet-pile walls, whereby the walls might bend, and, chiefly, because as the depth increased the seepage of water also increased, and it became ever harder to pump it out.

Thus only the last concrete wall fully impeded the movement of the seeping water; the water that seeped under the front concrete walls could rise upward and exert great pressure on the spillway floors, and even tear them away. To eliminate this, two floors were made, a lower and an upper one; the space between them was filled with regular stone masonry on cement mortar. Each wooden floor consists of two courses of 2-inch boards, the joints of the edges of the lower boards being covered by the upper. The space beneath the lower floor is filled with lean concrete. The weight of the stone masonry counteracts the upward pressure, and its impermeability prevents the water from penetrating beneath the upper floor. The dead timber sill is made of hewn granite blocks, joined with iron dowels and cement. The bank walls and abutments are built of rough-dressed stone blocks. All projecting corners of the masonry are faced with hewn granite stone. The spillway has three spans of 25 ft. each; these 25 ft. are in turn divided by two cast-iron posts into

into three openings, closed by plank gates. The stone riprap at the spillway is reinforced with rows of round piles connected by caps, since at a considerable velocity of the water the stone is easily carried away.

In Table XIII there is also shown a section of the old Sestroretsk dam. This dam existed on another branch of the river, now completely filled in.

Dam on the Rhine near Schaffhausen. (Table XIII).

The dam is built on the Rhine rapids that precede the waterfall; it runs along the bottom of the channel parallel to the bank. Since the river here has an enormous fall, and the portion of the channel separated off at the lower end of the dam is closed by sluices, the water level between the bank and the dam is maintained at the level of the water in the river at the upper end of the dam. Thus, at the lower end of the dam, a head is obtained equal to the lowering of the level in the Rhine over the entire length of the dam. Owing to the peculiarities of the riverbed at this place, it was necessary to use a somewhat unusual construction. The dam consists of a solid wooden wall made of large logs. In plan this wall has the form of a broken line, corresponding to the bends of the bank. The ends of the logs forming the wall are set into special cast-iron frames A, capable of rotating on a vertical iron round rod E, rigidly fastened into the rocky bottom of the channel. To fasten these rods, cylindrical holes with a conical widening downward were drilled in the rock; into this widening an iron wedge b was lowered, the rod was placed over the wedge by its split end, and by blows of a hammer on the upper end it was driven into place, the lower end, wedging itself apart tightly, fitting against the conical opening. Part A is fastened in the required position by screws c. For greater strength, the upright E is supported by a cast-iron strut D, fitted with a sleeve at its lower end onto a round iron rod standing next to upright E and fastened by its lower end in the rock. Since the bed of the river here has deep cracks in many places, through which water could rush under the wooden wall, rods G were lowered into the cracks to eliminate this; they were attached to the upper log of the wooden wall and served as supports for stone slabs and concrete, with which the gaps were sealed.

Stone Kamyshlaty Spillway, Samara Province (Plate XIV).

The spillway was built at an earthen dam erected by an irrigation expedition in southern Russia, to form an artificial irrigation pond. A section of the earthen body of the dam, together with a section of the wooden discharge pipe fixed in it, is shown in the drawing. This pipe conveys water into the irrigation canal. For the passage of spring waters, a stone spillway was built in the earthen dam, consisting of two openings, each 0.67 sazhen in clear width, closed by two rows of wooden shields, each 0.65 sazhen high, while the head above the sill of the sluice is 1.25 sazhen. The abutments and the foundation of the spillway are of stone. Since a place was chosen for the spillway where dense clay soil was found beneath its foundation, the latter was laid only 0.7 sazhen below the bottom, i.e. below the freezing depth of the ground. Along the line of the gates, beneath the sill and beneath the walls of the abutments, a stone wall was built 1.2 sazhen deep and 0.6 sazhen thick. The thickness of the stonework replacing the apron floor and overflow floor (flotbet) is 0.2 sazhen. The cones of the inner slope adjoining the watercourse are paved with stone. In spring the spillway is opened even before the snow melts, and only when, after the spring flood, the depth of the water flowing through the spillway is no more than 0.25 sazhen are the shields put back in place.

Diagrammatic drawing of the installation for utilizing power at Kubele near St. Gallen in Switzerland. (Plate XV).

This installation may serve as an example of the utilization of a large fall of water. The energy obtained here by hydraulic motors is immediately converted into electric current, which supplies the cities of St. Gallen and Herisau, where it is used for lighting streets and houses and for running tramways. The head here reaches up to 93.8 meters, and the discharge up to 4 cubic meters per second. The capacity of the hydroelectric station now in operation, put into service only in 1900, can be brought up to 3,500 horsepower. The voltage of the electric current is 10,000 volts. The water feeding the motors is obtained from the small river Urnäsch; it is later intended to connect another river, the Sitter, to this river by driving a connecting adit 500 meters long. At present, near the town of Herisau, a small diversion dam has been built across the bed of the Urnäsch. Somewhat above this dam begins a long tunnel (4,626 meters), diverting the impounded water into a neighboring, high-lying valley. The outlet of this valley

to dam up with a blind stone dam, and in this way a lake was formed, the purpose of which is to collect a reserve of water when there is much of it in the rivers and to make up for the shortage in times of scant water. The surface of the lake (part of which is visible in plan in the drawing) occupies 17 hectares. The reservoir represents a reserve of water of about 2,000,000 cubic meters. The stone dam that backs up this lake has an arc-like shape, with its convexity turned toward the lake; the length of its chord is 105 meters, its height 23.5 meters, its thickness at the base 15 meters, and at the crest 3 meters. The tunnel bringing water into the lake has clear dimensions of 1.8 meters in width and 1.9 meters in height, and a bottom slope of \(0.75^{0}/_{00}\) (0.75 m per 1000 m). The tunnel is provided at its upper end with a grating and at its upper and lower ends with sluice gates. When the whole cross-section is filled, it is capable of delivering 4.16 cubic meters of water per second. The conveyance of water to the engines is made by a steel pipe 1.6 meters in diameter. The pipe is embedded in the stone dam and passes partly along the length of the valley, and partly descends down the cliff to the river, where the hydroelectric station is situated. The total length of the pipe is 293 meters; at its upper end it is provided with a grating and a gate. In addition, in a special booth by the dam there is placed a regulating throttle valve. In two places in the pipe, sleeve couplings have been made so that it can freely lengthen. The pipe rests on specially erected foundation stone piers. By an iron bridge it passes to the other bank of the river and here, branching, supplies water to six hydraulic engines (Pelton wheels), located inside the building. The cost of this structure amounts to about 4 million francs. The filling of the reservoir with water took place over almost an entire year; it was filled not at once to its full depth, but in layers. After each raising of the water level, a pause of several weeks was made. In this way time was allowed for the bottom to compact well under the pressure; in addition, all weak places and cracks in the bottom were discovered in good time and sealed. Such precaution was necessary because of the very high position of the lake and, consequently, the great danger to the whole surrounding area in the event of its bursting. To maintain the water level at a constant height in the lake, an overflow in the form of a box was made in the left part of the dam. The overflowing water is led along a channel to the cliff and there, spreading out in a broad but thin stream, flows down into the river bed. The channel has several drops with wells in which water remains (a layer of about 1 meter); by taking the impact of the falling jet, it protects the channel from destruction.

Types of frequently encountered spillway dams. (Tables VIII and XIII).

The first of them is a wooden pile-and-crib dam, with abutments made of grooved logs. The second is a stone dam, on a pile foundation, with the profile of the outline of the discharging jet, which should prevent scouring of the bottom. The third has a form that is not rational, both in terms of the quantity of material used and because water, falling freely from the height of the crest to the bottom, must possess great destructive force, and therefore strong protection of the bottom will be required. This form, however, is used quite often on small rivers, especially where beauty is a concern, since the waterfall formed by such a dam has its own merits in this respect.

Table of Contents

	p.
Available work of water	1
Variability of discharge in rivers and regulation by ponds	2
A pond for collecting rainwater	6
Collecting water from marshes	9
Joining rivers of another basin and springs	11
Causes limiting the height of the head	13
Determination of the profile of the backed-up water	13
Method of removing the excess of backed-up water	19
Choice of soil for the foundation of a dam	30
Earthen dams	28
Stable dimensions of an earthen dam	24
The simplest methods of strengthening the surface of an earthen dam	28
Wooden dam	29
Pile foundation	30
Crib foundation	37
Foundation of slate	38
Side walls	40
Upper structure	41
Abutments	43
Stone dams	44
Temporary dams	49
French dams	53
Brief description of the appended drawings, namely: 1) of the stone dam on the River Florence; 2) of a crib spillway; 3) of a crib dam on a slate foundation; 4) of wooden sluices on irrigation canals; 5) of the Tingut dam; 6) of the dam on the River Trukhanovka; 7) of the water outlet of the Mariinsky system; 8) of the water outlet of the Vyshnevolotsk system; 9) of the Sestroretsk dam; 10) of the dam on the Rhine near Schaffhausen; 11) of a stone Kammlach water outlet; 12) of the utilization of water power at Kubel in Switzerland; 13) of frequently encountered types of spillway dams	66

Plate I

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Visible labels: \(P\), \(P_1\), \(a\), \(b\), \(c\), \(e\), \(f\), \(h\), \(n_1\), \(n_2\).

Fig. 7

Visible labels: sand; clay.

Fig. 8

Visible labels: \(h\), \(10\ \text{m}\).

Fig. 9

Fig. 10

Visible labels: [[unclear: word before “level”]] level.

Fig. 11 (plan, to scale)

Fig. 12

Fig. 13

Fig. 14

Table II.

Fig. 16.

Fig. 16. (Stakes for fastening fascines and brushwood flooring.)

Fig. 17.

Fig. 18.

Fig. 19.

Fig. 20.

Fig. 21.

Fig. 22.

Fig. 23.

Fig. 23. (Laying fascines on the frame.)

Fig. 23a.

Fig. 24.

Fig. 24a.

Fig. 25a.

Fig. 25b.

Fig. 30.

Fig. 31.

Fig. 32. ([[unclear: caption in parentheses]])

Plate III

Fig. 34.

Upstream apron.
Cribwork.
Spillway.

Fig. 41.

Fig. 42.

Fig. 43.

Fig. 40 and below Fig. 39.

Fig. 33.

[[unclear: handwritten annotation along the figure]]

Fig. 36.

[[unclear: handwritten label inside the figure, apparently referring to a “cribwork foundation”]]

Visible dimensions: 0,55–1/2; 0,95–3/4.

Fig. 35.

Fig. 37.

Fig. 38.

Plate IV

Fig. 44.

Fig. 45.

Elevation.

Section along \(ab\).

Fig. 46.

Fig. 47a.

Fig. 47b.

Fig. 48.

Fig. 49.

Fig. 50.

Fig. 51.

Fig. 52.

Fig. 53.

Fig. 54.

Fig. 55.

Fig. 56.

Fig. 57.

Fig. 58.

Fig. 59 \((ab = h;\ cd = 2\text{–}3h.)\)

Plate V

Fig. 60. Aswan Dam on the River Nile (downstream view).

Cross-section of the dam on the River Furance.

Fig. 61a (sill).

Fig. 61b.

Fig. 61c (plan).

Fig. 61d.

Fig. 62.

Fig. 63.

Plate VI.

Rzhev Overflow Dam.

Rzhev Dam on a Shale Foundation, with a Tank in the Middle.

Visible annotations in the drawings:

• Section along \(AB\). View of the upstream side of the tank.
• Section along \(mn\). View of the downstream side of the tank.
• View from downstream.
• View from upstream.
• Dam.
• Scale.
• New structures.
• Old structures.
• Water.

Plate VII

Wooden sluice on a small canal (dimensions in sazhen).

Facade.

Plan.

Section.

Scale.

No. 3. Cross-section and part of the plan of the [[unclear: Tyazhkevo/Tyazhkov]] spillway dam.

Cross-section along A–B.

Plan.

Scale.

Aqueduct over the middle channel of the [[unclear: Tinut/Tinuta]].

Facade.

Plan.

Scale.

WOODEN LOCK

On the water-power canal of the Valuyki section

Plan.

Section.

Facade.

AQUEDUCT OVER THE BED OF THE TINGUTA RIVER

Facade.

Plan.

PLAN

of the dam of the Tinguta reservoir

Scale.

Plan.

Scale
Sazhens: 0, 1, 2, 3, 4, 5

Visible labels in the drawing:

• Plan.
• Scale.
• Sazhens.
• Water.
• Wood.
• [[unclear: handwritten label near the water conduit]].

Plate IX

Dam on the Trusanovka River near the village of [[unclear: village name]].
View from the pond.

Plan

• Upper maximum water level
• Former channel
• Direction of current
• Scale
• Water discharge along AB

Legend:

• A — dam
• B — lower sluice/gate [[unclear]]
• C — water conduit into the wheel flume [[unclear]]
• D — [[unclear: handwritten label]]

Elevations and sections

• Facade along AB
• Facade along CD
• Protection along CD
• Sluice [[unclear]]
• Wheel along AB
• Water-gate along [[unclear]]
• Scale
• Plan
• Section [[unclear]]

Table X.

Water outlet on one of the canals of the Mariinsky system.

Plan

A — B — C — D — E — F

Facade and section along A.B.

Longitudinal section along C.D.

Horizon [[unclear: water]]

Section along line E.F.

Horizon [[unclear: water]]

Water Outlet on One of the Canals of the Vyshny Volochyok System

Plate XI

Elevation.

Scale for drawings 1–2.

Drawing 2. P I and II.

Section along A.

Visible labels in the drawings:

• Spillway level
• Low-water level

Scale for drawing B.

Plate XII

Plans of the stone water-release dam designed by K. Baumgarten in 1859–1862.

Detail of the curved wall and sill.

Visible labels on the drawing:

• Highway
• Scale in sazhens
• Scale in feet
• Feet
• Sazh.
• [[unclear: small handwritten construction labels within the plan]]

Plate XIII

Dam on the River near Champloiseau (waterfall)

Plan, elevation, and [[unclear: scale/measure note]].

Stone Dam for Small Heads

[[unclear: handwritten annotations and scale marks in the drawings]]

Longitudinal Sections of the Sestroretsk Dams

[[unclear: handwritten annotation referring to a spillway/water outlet, 1862]]

[[unclear: scale annotations and small explanatory labels in the drawings]]

Plate XIV.

Water outlet at the dam on the Bolsh. Kamyshlak River

Façade

Plan

Section of the opening [[unclear: handwritten label]]

Longitudinal profile

Lifting gates

Wooden pipe for conveying water

Lowered horizon [[unclear: handwritten label]]

Transverse section

Materials for the water outlet and regulator

For the wooden pipe

Plate XV

Schematic drawing with preservation of head; the fall of the water power in the pipe is more than 6 m; installation in Switzerland.

Section along A B (C)

• Section along A B (C)
• Scale
• 0, 10, 20, 30, 40, 50 fathoms

Plan

• Plan
• Spillway
• Branch channel
• A - B
• C
• Dam
• Artificial lake
• Water outlet
• Entrance to the lock
• Pipeline
• Pipe for pumping
• \(H = 80\) fathoms

Section along M N

• Section along M N
• Rails
• Movable building
• Turbine
• Building
• M
• N