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Dams

DAMS Any well-made earthen embankment of moderate height, and of such thickness and uniformity of construction as to ensure freedom from excessive percolation at any point, will in the course of time become almost impermeable to surface water standing against it; and when permeable rocks are covered with many feet of soil, the leakage through such soil from standing water newly placed above it generally diminishes rapidly, and in process of time often ceases entirely. Even the beds of sluggish rivers flowing over porous strata generally become so impermeable that excavations made in their neighbourhood, though freely collecting the subsoil water, receive no FIG. 6. Section of Typical Low Earth Embankment in Flat Plain.

clay can never become dry, plasticity and ductility are, for reasons to be explained below, the first consideration, and there the proportion of grit should be lower. The resistance of clay to percolation by water depends chiefly upon the density of the clay, while that density is rapidly reduced if the clay is permitted to absorb water. Thus, if dry clay is prevented from expanding, and one side be subjected to water pressure while the other side is held up by a completely porous medium, the percolation will be exceedingly small; but if the pressure preventing the expansion is reduced the clay will swell, and the percolation will increase. On the restoration of the pressure, the density will be again increased by the reduction of the water-filled interstices, and the percolation will be correspondingly checked. Hence the extreme importance in high dams with clay cores of loading the clay well for some time before water pressure is brought against it. If this is done, the largest possible quantity of clay will be slowly but surely forced into any space, and, being prevented from expanding, it will be unable subsequently to absorb more water. The percolation will then be very small, and the risk of disintegration will be reduced to a minimum. The embankments on either side of the puddle wall are merely to support the puddle and to keep it moist above the ground level when the reservoir is low. They may be quite permeable, but to prevent undue settlement and distortion they must, like the puddle, be well consolidated. In order to prevent a tendency to slip, due to sudden and partial changes of saturation, the outer embankment should always be permeable, and well drained at the base except close to the puddle. The less permeable materials should be confined to the inner parts of the embankments; this is especially important in the case of the inner embankment in order that, when the water level falls, they may remain moist without becoming liable to slip. The inner slope should be protected from the action of waves by so-called " hand-pitching," consisting of roughlysquared stonework, bedded upon a layer of broken stone to prevent local disturbance of the embankment by action of the water between the joints of the larger stones.

In mountain valleys, rock or shale, commonly the most impermeable materials met with in such positions, are sometimes not reached till considerable depths are attained. There are several cases in Great Britain where it has been necessary to carry down the puddle trench to about 200 ft. below the surface of the ground vertically above those parts. The highest dams of this class in the British islands impound water to a level of about no ft. above the bottom of the valley. Such great works have generally been well constructed, and there are many which after fifty years of use are perfectly sound and water-tight, and afford no evidence of deterioration. On the other hand, the partial or total failure of smaller dams of this description, to retain the reservoir water, has been much more common in the past than is generally supposed. Throughout Great Britain there are still many reservoirs, with earthen dams, which cannot safely be filled; and others which, after remaining for years in this condition, have been repaired. From such cases and their successful repair valuable experience of the causes of failure may be derived.

Most of these causes are perfectly well understood by experienced engineers, but instances of Era Ion bv ma ' construct ion of recent date are still met with., A fl " few such cases will now be mentioned. The base of a puddle trench is often found to have been placed upon rock, perfectly sound in itself, but having joints which are not impermeable. The loss of water by leakage through such joints or fissures below the puddle wall may or may not be a serious matter in itself; but if at any point there is sufficient movement of water across the base of the trench to produce the slightest erosion of the clay above it, that movement almost invariably increases. The finer particles of clay in the line of the joint are washed away, while the sandy particles, which nearly all natural clays contain, remain behind and form a constantly deepening porous vein of sand crossing the base of the puddle. Percolation the sand. Thus the permeable vein grows vertically rather than horizontally, and ultimately assumes the form of a thin vertical sheet traversing the puddle wall, often diagonally in plan, and having a thickness which has varied in different cases from a few inches to a couple of feet or more, of almost clean sand rising to an observed height of 30 or 40 ft., and only arrested in its upward growth by the necessary lowering of the reservoir water to avoid serious danger. The settlement of the plastic clay above the eroded portion soon produces a surface depression at the top of the embankment over or FIG. 7. Earth Embankment, with stone toe and concrete trench.

through this sand is thus added to the original leakage. Having passed through the puddle core the leaking water sometimes rises to the _surface of the ground, producing a visibly turbid spring. As erosion proceeds, the contraction of the space from which the clay is washed continues, chiefly by the sinking down of the clay above FIG. 8. Leakage due to improperly formed discharge culvert through puddle wall of reservoir.

nearly over the leakage, and thus sometimes gives the first warning of impending danger. It is not always possible to prevent any leakage whatever through the strata below the bottom or beyond the ends of the trench, but it is always possible to render such leakage entirely harmless to the work above it, and to carry the water by relief-pipes to visible points at the lower toe of the dam. Wherever the base of a puddle wall cannot be worked into a continuous bed of clay or shale, or tied into a groove cut in sound rock free from water-bearing fissures, the safest course is to base it on an artificial material at once impermeable and incapable of erosion, interposed between the rock and the puddled clay. Water-tight concrete is a suitable material for the purpose; it need not be made so thick as the puddle core, and is therefore sometimes used with considerable advantage in lieu of the puddle for the whole depth below ground. In fig. 7 a case is shown to be so treated. Obviously, the junction between the puddle and the concrete might have been made at any lower level.

However well the work may be done, the lower part of a mass of puddled clay invariably settles into a denser mass when weighted with the clay ( above. If, theretore, one part is held up, fett ] ement . by unyielding rock for example, while an adjoining part has no support but the clay beneath it, a fracture ^-not unlike a geological fault must result. Fig. 8 is a part longitudinal section through the puddle wall of an earthen embankment. The puddle wall is crossed by a pedestal of concrete carrying the brick discharge culvert. The puddle at a was originally held up by the flat head of this pedestal; not so the puddle at 6, which under the superinweight settled down and produced the fault be, cumbent _____ - . - accompanied with a shearing or tangential strain or, less probably, with actual fracture in the direction bd. Serious leakage at once began between c and 6 and washed out the clay, particle by particle, but did not wash out the sand associated with it, which remained behind in the crevice. The clay roof, rather than the walls of this crevice of sand, gave way and pressed down to fill the vacancy, and the leakage worked up along the weakened plane of tangential strain bd. On the appearance of serious leakage the overflow level of the water originally at ef was lowered for safety to gh; and for many years the reservoir was worked with its general level much below gh. The sand-filled vein, several inches in width, was found, on taking out the puddle, to have terminated near the highest level to which the water was allowed to rise, but not to have worked downwards. There can be little doubt that the puddle at the right-hand angle j w.is also strained, but not to the point of rupture, as owing to the rise of the sandstone base there was comparatively little room for settlement on that side. In repairing this work the perfectly safe form shown by the dotted lines ka, kj was substituted for the flat surface aj, and this alone, if originally adopted, would have prevented dangerous shearing strains. As an additional precaution, however, deep tongues of concrete like those in fig. 7 were built in the rock throughout the length of the trench, and carried up the sides and over the top of the pedestal. The puddle was then replaced, and remains sensibly watertight. The FIG. 9. Overhanging Rock Leakage.

lesson taught by fig. 8 applies also to the ends of puddle walls where they abut against steep faces of rock. Unless such faces are so far below the surface of the puddle, and so related to the lower parts of the trench, that no tension, and consequent tendency to separation of the puddle from the rock, can possibly take place, and unless abundant time is given, before the reservoir is charged, for the settlement and compression of the puddle to be completed, leakage with disastrous results may occur. In other cases leakage and failure have arisen from allowing a part of the rock bottom or end of a puddle trench to overhang, as in fig. 9. Here the straining of the original horizontal puddle in settling down is indicated in a purposely exaggerated way by the curved lines. There is considerable distortion of the clay, resulting from combined shearing and tensile stress, above each of the steps of rock, and reaching its maximum at and above the highest rise ab, where it has proved sufficient to produce a dangerous line of weakness ac, the tension at a either causing actual rupture, or such increased porosity as to permit of percolation capable of keeping open the wound. In such cases as are shown in figs. 8 and 9 the growth of the sand vein is not vertical, but inclined towards the plane of maximum shearing strain. Fig. 9 also illustrates a weak place at b where the clay either never pressed hard against the overhanging rock or has actually drawn away therefrom in the process of settling towards the lower part to the left. When it is considered that a parting of the clay, sufficient to allow the thinnest film of water to pass, may start the formation of a vein of porous sand in the manner above explained, it will be readily seen how great must be the attention to details, in unpleasant places below ground, and below the water level of the surrounding area, if safety is to be secured. In cases like fig. 9 the rock should always be cut away to a slope, such as that shown in fig. 10.

If no considerable difference of water-pressure had been allowed between the two sides of the puddle trench in figs. 8 or 9 until the clay had ceased to settle down, !* ' s P r bable that the interstices, at first formed between the puddle and the concrete or rock, would have been sufficiently filled to prevent injurious percolation at any future time. Hence it is always a safe precaution to afford plenty of time for such settlement before FIG. 10. Proper Figure for Rock Slope. a reservoir is charged with water. But to all such precautions should be added the use of concrete or brickwork tongues running longitudinally at the bottom of the trench, such as those shown at a higher level in fig. 7.

In addition to defects arising out of the condition or figure of the rock or of artificial work upon which the puddle clay rests, the puddle Defect* la wa " itself is " en def ective. The original material may have been perfectly satisfactory, but if, for example, in wall. *" e P r g res ? of the work a stream of water is allowed to flow across it, fine clay is sometimes washed away, and the gravel or sand associated with it left to a sufficient extent to permit f future percolation. Unless such places are carefully dug out or re-puddled before the work of filling is resumed, the percolation may increase along the vertical plane where it is greatest, by the erosion and falling in of the clay roof, as in the other cases cited. Two instances probably originating in some such cause are shown in fig. 1 1 in the relative positions in which they were found, and carefully measured, as the puddle was removed from a crippled reservoir dam. These fissures are in vertical planes stretching entirely across the puddle trench, and reaching in one case, oa, nearly to the highest level at which the reservoir had been worked for seventeen years after the leakage had been discovered. The larger and older of these veins was 44$ ft. high, of which 14 ft. was above the original ground level, and it is interesting to note that this portion, owing probably to easier access for the water from the reservoir and reduced compression of the puddle, was much wider than below. The little vein to the left marked bb, about 3! ft. deep, is curious. It looks like the beginning of success of an effort made by a slight percolation during the whole life of the reservoir to increase itself materially by erosion.

EmbarJ&nent, malty intended top water level - Highest working level allowed FIG. n. Vertical Vein of Leakage.

There is no reason to believe that the initial cause of such a leakage could be developed except during construction, and it is certain that once begun it must increase. Only a knowledge of the great loss of capital that has resulted from abortive reservoir construction justifies this notice of defects which can always be avoided, and are too often the direct result, not of design, but of parsimony in providing during the execution of such works, and especially below ground, a sufficiency of intelligent, experienced and conscientious supervision.

In some cases, as, for example, when a high earthen embankment crosses a gorge, and there is plenty of stone to be had, it is desirable to place the outer bank upon a toe or platform of rubble stonework, as in fig. 7, by which means the height of the earthen portion is reduced and complete drainage secured. But here again great care must be exercised in the packing and consolidation of the stones, which will otherwise crack and settle.

f As with many other engineering works, the tendency to slipping either of the sides of the valley or of the reservoir embankment itself has often given trouble, and has sometimes led to serious disaster.

This, however, is^ kind of failure not always attributable to want of proper supervision during construction, but rather to improper choice of the site, or treatment of the case, by those primarily responsible.

In .countries where good clay or retentive earth cannot be obtained, numerous alternative expedients have been adopted with more or less success. In the mining districts wMi'aht- f America, for example^ where timber is cheap, rough phragms stone embankments have been lined on the water face efwood, w j t jj timber to form the water-tight septum. In such cre<e C etc' a position, even if the timber can be made sufficiently water-tight to begin with, the alternate immersion and exposure to air and sunshine promotes expansion and contraction, and induces rapid disintegration, leakage and decay. Such an expedient may be justified by the doubtful future of mining centres, but would be out of the question for permanent water supply. Riveted sheets of steel have been occasionally used, and, where bedded in a sufficient thickness of concrete, with success. At the East Canon Creek dam, Utah, the height of which is about 61 ft. above the stream, the trench below ground was filled with concrete much in the usual way, while above ground the water-tight diaphragm consists of a riveted steel plate varying in thickness from & in. to ^ in. This steel septum was protected on either side by a thin wall of asphaltic concrete supported by rubble stone embankments, and owing to irregular settling of the embankments became greatly distorted, apparently, however, without causing leakage. Asphalt, whether a natural product or artificially obtained, as, for example, in some chemical manufactures, is a most useful material if properly employed in connexion with reservoir dams. Under sudden impact it is brittle, and has a conchoidal fracture like glass; but under continued pressure it has the properties of a viscous fluid. The rate of flow is largely dependent upon the proportion of bitumen it contains, and is of course retarded by mixing it with sand and stone to form what is commonly called asphalt concrete. But given time, all such compounds, if they contain enough bitumen to render them water-tight, appear to settle down even at ordinary temperatures as heavy viscous fluids, retaining their fluidity permanently if not exposed to the air. Thus they not only penetrate all cavities in an exceedingly intrusive manner, but exert pressures in all directions, which, owing to the density of the asphalt, are more than 40 % greater than would be produced by a corresponding depth of water. From the neglect of these considerations numerous failures have occurred.

Elsewhere, a simple concrete or masonry wall or core has been used above as well as below ground, being carried up between embankments either of earth or rubble stone. This construction has received its highest development in America. On the Titicus, a tributary of the Croton river, an earthen dam was completed in 1895, with a concrete core wall 100 ft. high almost wholly above the original ground level, which is said to be impermeable; but other dams of the same system, with core walls of less than too ft. in height, are apparently in their present condition not impermeable. Reservoir No. 4 of the Boston waterworks, completed in 1885, has a concrete core wall. The embankment is 1800 ft. long and 60 ft. high. The core wall is about 8 ft. thick at the bottom and 4 ft. thick at the top, and in the middle of the valley nearly 100 ft. in height. At irregular intervals of 150 ft. or more buttresses 3 ft. wide and i ft. thick break the continuity on the water side. That this work has been regarded as successful is shown by the fact that Reservoir No. 6 of the same waterworks was subsequently constructed and completed in 1894 with a similar core wall. There is no serious difficulty in so constructing walls of this kind as to be practically water-tight while they remain unbroken; but owing to the settlement of the earthen embankments and the changing level of saturation they are undoubtedly subject to irregular stresses which cannot be calculated, and under which, speaking generally, plastic materials are much safer. In Great Britain masonry or concrete core walls have been generally confined to positions below ground. Thus placed, no serious strains are caused either by changes of temperature or of moisture or by movements of the lateral supports, and with proper ingredients and care a very thin wall wholly below ground may be made watertight.

The next class of dam to be considered is that in which the structure as a whole is so bound together that, with certain reservations, it may be considered as a monolith subject chiefly to the overturning tendency of waterpressure resisted by the weight of the structure itself and the supporting pressure of the foundation. Masonry dams are, for the most part, merely retaining walls of exceptional size, in which the overturning pressure is water. If such a dam is sufficiently strong, and is built upon sound and moderately rough rock, it will always be incapable of sliding. Assuming also that it is incapable of crushing under its own weight and the pressure of the water, it must, in order to fail entirely, turn over on its outer toe, or upon the outer face at some higher level. It may do this in virtue of horizontal water-pressure alone, or of such pressure combined with upward pressure from intrusive water at its base or in any higher horizontal plane. Assume first, however, that there is no uplift from intrusive water. As the pressure of water is nil at the surface and increases in direct proportion to the depth, the overturning moment is as the cube of the depth; and the only figure which has a moment of resistance due to gravity, varying also as the cube of its depth, is a triangle. The form of stability having the least sectional area is therefore a triangle. It is obvious that the angles at the base of such a hypothetical dam must depend upon the relation between its density and that of the water. It can be shown, for example, that for masonry having a density of 3, water being i, the figure of minimum section is a right-angled triangle, with the water against its vertical face; while for a greater density the water face must lean towards the water, and for a less density away from the water, so that the water may lie upon it. For the sections of masonry dams actually used in practice, if designed on the condition that the centre of all vertical pressures when the reservoir is full shall be, as hereafter provided, at two-thirds the width of the base from the inner toe, the least sectional area for a, density of 2 also has a vertical water face. As the density of the heaviest rocks is only 3, that of a masonry dam must be below 3, and in practice such works if well constructed vary from 2-2 to 2-6. For these densities, the deviation of the water face from the vertical in the figure of least sectional area is, however, so trifling that, so far as this consideration is concerned, it may be neglected.

If the right-angled triangle abc, fig. 12, be a profile i ft. thick of a monolithic dam, subject to the pressure of water against its vertical side to the full depth ab = d in feet, the horizontal Vatr level- Q- pressure of water against the section of the dam, increasing uniformly with the depth, is properly represented by the isosceles right-angled triangle abe, in which be is the maximum / water-pressure due to the tetfrtar-iraKr pressure n>- full depth d, while the area <P abe = is the total hori- zontal pressure against the dam, generally stated in cubic feet of water, acting at one-third its depth above FIG. 12. Diagram of Right-Angled Triangle Dam.

the base. Then is the resultant horizontal pressure with an over- turning moment of If x be the width of the base, and p the density of the masonry, the weight of the masonry in terms of a cubic foot of water will be -j- acting at its centre of gravity g, situated at fx from the outer toe, and the moment of resistance to overturning on the outer toe, ^ '-" Equating the moment of resistance (2) to the overturning moment (i), we have and -4- (3)

V2p That is to say, for such a monolith to be on the point of overturning under the horizontal pressure due to the full depth of water, its base must be equal to that depth divided by the square root of twice the density of the monolith. For a density of 2-5 the base would therefore be 44-7 % of the height.

We have now to consider what are the necessary factors of safety, and the modes of their application. In the first place, it is out of . the question to allow the water to rise to the vertex o * of such a masonry triangle. A minimum thickness must ** be adopted to give substance to the upper part ; and where th dam is not used as a weir it must necessarily rise several feet above the water, and may in either event have to carry a roadway. Moreover, considerable mass is required to reduce the internal strains caused by changes of temperature. In the next place, it is necessary to confine the pressure, at every point of the masonry, to an intensity which will give a sufficient factor of safety against crushing. The upper part of the dam having been designed in the light of these conditions, the whole process of completing the design is simple enough when certain hypotheses have been adopted, though somewhat laborious in its more obvious form. It_is clear that the greatest crushing pressure must occur, either, with the reservoir empty, near the lower part of the water face ab, or with the reservoir full, near the lower part of the outer face ac. The principles hitherto adopted in designing masonry dams, in which the moment of resistance depends upon the figure and weight of the masonry, involve certain assumptions, which, although not quite true, have proved useful and harmless, and are so convenient that they may be continued with due regard to the modifications which recent investigations have suggested. One such assumption is that, if the dam is well built, the intensity of vertical pressure will (neglecting local irregularities) vary nearly uniformly from face to face along any horizontal plane. Thus, to take the simplest case, if abce (fig. 13) represents a rectangular mass already designed for the superstructure Centre of *is-6fer pressure FIG. 13. Factor of Safety Diagram.

of the dam, and g its centre of gravity, the centre of pressure upon the base will be vertically under g, that is, at the centre of the base, and the load will be properly represented by the rectangle bfgc, of which the area represents the total load and the uniform depth of its uniform intensity. At this high part of the structure the intensity of pressure will of course be much less than its permissible intensity. If now we assume the water to have a depth d above the base, the total water pressure represented by the triangle kbh will have its centre at <f/3 from the base, and by the parallelogram of forces, assuming the density of the masonry to be 2-5, we find that the centre of pressure upon the base be is shifted from the centre of the base to a point i nearer to the outer toe c, and adopting our assumption of uniformly varying intensity of stress, the rectangular diagram of pressures will thus be distorted from the figure bftc to the figure of equal area bjlc, having its centre o vertically under the point at which FIG. 14. Diagram showing lines of pressure in Masonry Dam.

the resultant of all the forces cuts the base be. For any lower level the same treatment may, step by step, be adopted, until the maximum intensity of pressure cl exceeds the assumed permissible maximum, or the centre of pressure reaches an assigned distance from the outer toe c, when the base must be widened until the maximum intensity of pressure or the centre of pressure, as the case may be, is brought within the prescribed limit. The resultant profile is of the kind shown in fig. 14.

Having thus determined the outer profile under the conditions hitherto assumed, it must be similarly ascertained that the water face is everywhere canable of resisting the vertical pressure of the masonry when the reservoir is empty, and the base of each compartment must be widened if necessary in that direction also. Hence in dams above 100 ft. in height, further adjustment of the outer profile may be required by reason of the deviation of the inner profile from the vertical. The effect of this process is to give a series of points in the horizontal planes at which the resultants of all forces above those planes respectively cut the planes. Curved lines, as dotted in fig. 14, drawn through these points give the centre of pressure, for the reservoir full and empty respectively, at any horizontal plane. These general principles were recognized by Messrs Graen and Delocre of the Fonts et Chaussees, and about the year 1866 were put into practice in the Furens dam near St Etienne. In 1871 the late Professor Rankine, F.R.S., whose remarkable perception of the practical fitness or unfitness of purely theoretical deductions gives his writings exceptional value, received from Major Tulloch, R.E., on behalf of the municipality of Bombay, a request to consider the subject generally, and with special reference to very high dams, such as have since been constructed in India. Rankine pointed out that before the vertical pressure reached the maximum pressure permissible, the pressure tangential to the slope might do so. Thus conditions of stress are conceivable in which the maximum would be tangential to the slope or nearly so, and would therefore increase the vertical stress in proportion to the cosecant squared of the slope. It is very doubtful whether this pressure is ever reached, but such a limit rather than that of the vertical stress must be considered when the height of a dam demands it. Next, Rankine pointed out that, in a structure exposed to the overturning action of forces which fluctuate in amount and direction, there should be no appreciable tension at any point of the masonry. But there is a still more important reason why this condition should be strictly adhered to as regards the inner face. We have hitherto considered only the horizontal overturning pressure of the water; but if from originally defective construction, or from the absence of vertical pressure due to weight of masonry towards the water edge of any horizontal bed, as at ab in fig. 14, water intrudes beneath that part of the masonry more readily than it can obtain egress along be, or in any other direction towards the outer face, we shall have the uplifting and overturning pressure due to the full depth of water in the reservoir over the width i added to the horizontal pressure, in which case all our previous calculations would be futile. The condition, therefore, that there shall be no tension is important as an element of design; but when we come to construction, we must be careful also that no part of the wall shall be less permeable than the water face. In fig. 13 we have seen that the varying depth of the area bjlc approximately represents the varying distribution of the vertical stress. If, therefore, the centre of that became so far removed to the right as to make ;' coincident with b, the diagram of stresses would become the triangle j'l'c', and the vertical pressure at the inner face would be nil. This will evidently happen when the centre sf pressure *' is two-thirds from the inner toe 6' and one-third from the outer toe c' ; and if we displace the centre of pressure still further to the right, the condition that the centre of figure of the diagram shall be vertically under that centre of pressure can only be fulfilled by allowing the point j' to cross the base to j* thus giving a negative pressure or tension at the inner toe. Hence it follows that on the assumption of uniformly varying stress the line of pressures, when the reservoir is full, should not at any horizontal plane fall outside the middle third of the width of that plane.

Rankine in his report adopted the prudent course of taking as the safe limits certain pressures to which, at that time, such structures were known to be subject. Thus for the inner face he took, as the limiting vertical pressure, 320 ft. of water, or nearly 9 tons per sq. ftand for the outer face 250 ft. of water, or about 7 tons per sq. ft.

For simplicity of calculation Rankine chose logarithmic curves for both the inner and outer faces, and they fit very well with the conditions. With one exception, however the Beetaloo dam in Australia 1 10 ft. high there are no practical examples of dams with logarithmically curved faces.

After Rankine, a French engineer, Bouvier, gave the ratio of the maximum stress in a dam to the maximum vertical stress as I to the cosine squared of the angle between the vertical and the resultant which, in dams of the usual form, is about as 13 is to 9.

During the last few years attention has been directed to the stresses including shearing stresses on planes other than ' horizontal. M. Levy contributed various papers on the subject which will be found in the Comptes rendus de I Academic des Sciences (1895 and 1898) and in the Annales des Fonts et Chaussees (1897). He investigated the problem by means of the general differential equations of static equilibrium for dams of triangular and rectangular form considered as isotropic elastic solids. In one of these papers Levy formulated the requirement now generally adopted in France that the vertical pressure at the upstream end of any joint, calcu- lated by the law of uniformly varying stress, should not be less than that of the water pressure at the level of that joint in order to prevent intrusive water getting into the structure.

These researches were followed by those of Messrs L. W. Atcherley and Karl Pearson, F.R.S., 1 and by an approximate graphical treatment by Dr W. C. Unwin, F.R.S. 2 Dr Unwin took two horizontal planes, one close above the other, and calculated the vertical stresses on each by the law of uniformly varying stresses. Then the difference between the normal pressure on a rectangular RESERVOIR element in the lower plane and that on the upper "^ plane is the weight of the element and the difference between the shears on the vertical faces of that element. The weights being known, the principal stresses may be determined. These researches led to a wide discussion of the sufficiency of the law of uniformly varying stress when applied to horizontal joints as a test of the stability of dams. Professor Karl Pearson showed that the results are dependent upon the assumption that the distribution of the vertical stresses on the base of the structure also followed the law of uniformly varying stress. In view of the irregular forms and the uncertainties of the nature of the materials at the foundation, the law of uniformly varying stress was not applicable to the base of the dam. He stated that it was practically impossible to determine the stresses by purely mathematical means. The late Sir Benjamin Baker, F.R.S., suggested that the stresses might be measured by experiments with elastic models, and among others, experiments were carried out by Messrs Wilson and Gore * with indiarubber models of plane sections of dams (including the foundations) who applied forces to represent the gravity and water pressures in such a manner that the virtual density of the rubber was increased many times without interfering with the proper ratio between gravity and water pressure, and by this means the strains produced were of sufficient magnitude to be easily measured.

The more important of their results are shown graphically in figs. 15 and 1 6, and prove that the law of uniformly varying stress is generally applicable to the upper two-thirds of a dam, but that at parts in or near the foundations that law is departed from in a way which will be best understood from the diagrams.

Fig. 15 shows a section of the model dam. The maximum principal stresses are represented by the directions and thicknesses of the two systems of intersecting lines mutually at right angles.

Tensile stresses (indicated by broken Jines on the diagram) are shown at the upstream toe notwithstanding that the Une of resistance is well within the middle third of the section. It is important to notice that the maximum value of the tension at the toe lies in a direction approximately at 45 to the vertical, but at points lower down in the foundation this tension, while less in magnitude, becomes much more horizontal. This feature indicates that in the event of a crack occurring at the upstream toe, its extension would tend to turn downwards and follow a direction nearly parallel with the maximum pressure lines, in which direction it would not materially affect the stability of the structure.

As a matter of fact, the foundations of most dams are carried down in vertical trenches, the lower part only being in sound materials so that actual separation almost corresponding with the hypothetical 1 On Some Disregarded Points in the Stability of Masonry Dams, Drapers' Company Research Memoir (London, 1904).

* Engineering (May mh, 1905).

3 Proceedings of the Institution of Civil Engineers, vol. 172, p. 107.

crack is allowed in the first instance with no harmful effects. Similar experiments upon models with rounded toes but otherwise of the same form showed a considerable reduction in the magnitude of the tensile stresses.

On examining the diagram it will be observed that the maximum compressive stresses are parallel to and near to the down stream face of the section, which values are approximately equal to the maximum value of the vertical stress determined by the law of uniformly varying stress divided by the cosine squared of the angle between the vertical and the resultant.

The distributions of stress on the base line of the model for " reservoir empty " and " reservoir full " are shown in fig. 16 by ellipses of stress and by diagrams of stress on vertical and horizontal sections.

Arrow heads at the ends of an axis of an ellipse indicate tension as distinct from compression, and the semi-axes in magnitude and direction represent the principal stresses.

FIG. 15. Diagrams illustrating results of Wilson and Core's experiments with an Indiarubber model dam. Reservoir full.

The two systems of lines mutually at right angles show the directions of the maximum and minimum stresses respectively. Such stresses are termed principal stresses. Tension is indicated by broken lines and compression by full lines.

The shearing stresses are zero along the lines of principal stress and reach a maximum on lines at 45 thereto. The magnitudes of the maximum shearing stresses are indicated by the algebraic differences of the thicknesses of the lines of principal stress.

Line ab is in such a position that the stresses along and above it are not materially affected by the more irregular stresses below that line produced by the sudden change in section at the base of the dam. The vertical distance above the line ab of any point in the dotted line dc is proportional to the vertical component of the compressive stress on the line ab assumed to vary uniformly from face to face, and similarly the vertical distance of any point in the 3-dot-and-dash line ae above the line ab is proportional to the vertical component of the stress determined experimentally. The vertical component diagrams abed and abea are drawn to a larger scale than the lines indicating the principal stresses.

It is obvious that experiments of the kind referred to cannot take into account all the conditions of the problem met with in actual practice, such as the effect of the rock at the sides of the valley and variations of temperature, etc., but deviations in practice from the conditions which mathematical analyses or experiments assume are nearly always present. Such analyses and experiments are not on that account the less important and useful.

So far we have only considered water-pressure against the reservoir side of the dam ; but it sometimes happens that the water and earth pressure against the outer face is considerable enough to modify the lower part of the section. In dams of moderate height above ground and considerable depth below ground there is, moreover, no reason why advantage should not be taken of the earth resistance due either to the downstream face of the trench against which the foundations are built, or to the materials excavated and properly embanked against that face above the ground level or to both. We do not always know the least resistance which it is safe to give to a retaining wall subject to the pressure of earth, or conversely, the maximum resistance to side-thrust which natural or embanked earth will afford, because we wisely neglect the important but very variable element of adhesion between the particles. It is notorious among engineers that retaining walls designed in accordance with the well-known theory of conjugate pressures in earth are unnecessarily strong, and this arises mainly from the assumption that the earth is merely a loose granular mass without any such adhesion. As a result of this theory, in the case of a retaining wall supporting a vertical face of earth beneath an extended horizontal plane level with the top of the wall, we get p_iV3? I sin d> ~ 2 ' I +sin <t>

where P is the horizontal pressure of the earth against the wall exerted at one-third its height, w the weight of unit volume of the material, x the height of the wall, and the angle of repose of the material. That the pressure so given exceeds the maximum possible pressure we do not doubt; and, conversely, iT we put p,_w**.i +sin <t> 2 I sin <f>' we may have equal confidence that P' will be less than the maximum pressure which, if exerted by the wall against the earth, will be borne without disturbance. But like every pure theory the principles of conjugate pressures in earth may lead to danger if not applied with due consideration for the angle of repose of the material, the modifications brought about by the limited width of artificial embankments, the possible contraction away from the masonry, of clayey materials during dry weather for some feet in depth and the tendency of surface waters to produce scour between the wall and the embankment. Both the Neuadd and the Fisher Tarn dams are largely dependent upon the support of earthen embankments with much economy and with perfectly satisfactory results.

In the construction of the Vyrnwy masonry dam Portland cement concrete was used in the joints. When more than six months old, 9 in. cubes of this material never failed under compression below in tons per sq. ft. with an average of 167 tons; and the mean resistance of all the blocks tested between two and three years after moulding exceeded 215 tons per sq. ft., while blocks cut from the concrete of the dam gave from 181 to 329 tons per sq. ft. It has been shown that the best hydraulic lime, or volcanic puzzuolana and lime, if properly ground while slaking, and otherwise treated in the best-known manner, as well as some of the so-called natural (calcareous) cements, will yield results certainly not inferior to those obtained from Portland cement. The only objection that can in any case be urged against most of the natural products is that a longer time is required for induration; but in the case of masonry dams sufficient time necessarily passes before any load, beyond that of the very gradually increasing masonry, is brought upon the structure. The result of using properly treated natural limes is not to be judged from the careless manner in which such limes have often been used in the past. Any stone of which it is desirable to build a masonry dam would certainly possess an average strength at least as great as the above figures for concrete; the clay slate of the Lower Silurian formation, used in the case of the Vyrnwy dam, had an ultimate crushing strength of from 700 to 1000 tons per sq. ft. If, therefore, with such materials the work is well done, and is not subsequently liable to be wasted or disintegrated by expansion or contraction or other actions which in the process of time affect all exposed surfaces, it is clear that 1 5 to 20 tons per sq. ft. must be a perfectly safe load. There are many structures at present in existence bearing considerably greater loads than this, and the granite ashlar masonry of at least one, the Bear Valley dam in California, is subject to compressive stresses, reaching, when the reservoir is full, at least 40 to 50 tons per sq. ft., while certain brickwork linings in mining shafts are subject to very high circumferential stresses, due to known water-pressures. In one case which has been investigated this circumferential pressure exceeds 26 tons per sq. ft., and the brickwork, which is 18 in. thick and 20 ft. internal diameter, is perfectly sound and water-tight. In portions of the structure liable to important changes of pressure from the rise and fall of the water and subject to the additional stresses which expansion and contraction by changes of temperature and of moisture induce, and in view of the great difficulty of securing that the average modulus of elasticity in all parts of the structure shall be approximately the same, it is probably desirable to limit the calculated load upon any external work, even of the best kind, to 15 or 20 tons per sq. ft. It is clear that the material upon which any high masonry dam is founded must also have a large factor of safety against crushing under the greatest load that the dam can impose upon it, and this consideration unfits any site for the construction of a masonry dam where sound rock, or at least a material equal in strength to the strongest shale, cannot be had; even in the case of such a material as shale the foundation must be well below the ground.

The actual construction of successful masonry dams has varied from the roughest rubble masonry to ashlar work. It Materials. ls P r bable, however, that, all things considered, random rubble in which the flattest side of each block of stone is dressed to a fairly uniform surface, so that it may be bedded as it were in a tray of mortar, secures the nearest approach to uniform elasticity. Such stones may be of any size subject to each of them covering only a small proportion of the width of the structure (in the Vyrnwy dam they reached 8 or 10 tons each), and the spaces between them, where large enough, must be similarly built in with smaller, but always the largest possible, stones; spaces too small for this treatment must be filled and rammed with concrete. All stones must be beaten down into their beds until the mortar squeezes up into the joints around them. The faces of the work may be of squared masonry, thoroughly tied into the hearting; but, in view of the expansion and contraction mentioned below, it is better that the face masonry should not be coursed. Generally speaking, in the excavations for the foundations springs are met with; these may be only sufficient to indicate a continuous dampness at certain beds or joints of the rock, but all such places should be connected by relief drains carried to visible points at the back of the dam. It should be impossible, in short, for any part of the rock beneath the dam to become charged with water under pressure, either directly from the water in the reservoir or from higher places in the mountain sides. For similar reasons care must be taken to ensure that the structure of the water face of the dam shall be the least permeable of any part. In the best examples this has been secured by bedding the stones near to the water face in somewhat finer mortar than the rest, and sometimes also by placing pads to fill the joints for several inches from the water face, so that the mortar was kept away from the face and was well held up to its work. On the removal of the pads, or the cutting out of the face of the mortar where pads were not used, the vacant joint was gradually filled with almost dry mortar, a hammer and caulking tool being used to consolidate it. By these means practical impermeability was obtained. If the pores of the water face are thus rendered extremely fine, the surface water, carrying more or less fine detritus and organic matter, will soon close them entirely and assist in making that face the least permeable portion of the structure.

But no care in construction can prevent the compression of the mass as the superincumbent weight comes upon it. Any given yard of height measured during construction, or at any time after construction, will be less than a yard when additional weight has been placed upon it; hence the ends of such dams placed against rock surfaces must move with respect to those surfaces when the superincumbent load conies upon them. This action is obviously much reduced where the rock sides of the valley rise slowly; but in cases where the rock is very steep, the safest course is to face the facts, and not to depend for water-tightness upon the cementing of the masonry to the rock, but rather to provide a vertical key, or dowel joint, of some material like asphalt, which will always remain water-tight. So far as the writer has been able to observe or ascertain, there are very few masonry dams in Europe or America which have not been cracked transversely in their higher parts. They generally leak a little near the junction with the rock, and at some other joints in intermediate positions. In the case of the Neuadd dam this difficulty was met by deliberately omitting the mortar in transverse joints at regular intervals near the top of the dam, except just at their faces, where it of course cracks harmlessly, and by filling the rest with asphalt. Serious movement from expansion and contraction does not usually extend to levels which are kept moderately damp, or to the greater mass of the dam, many feet below high-water level.

The first masonry dam of importance constructed in Great Britain was that upon the river Vyrnwy, a tributary of the Severn, in connexion with the Liverpool water-supply (Plate I.). Its height, subject to water-pressure, is about 134 ft., and a carriage-way is carried on arches at an elevation of about 1 8 ft. higher. As this dam is about 1 180 ft. in length from rock to rock, it receives practic- ally no support from the sides of the valley. Its construction drew much attention to the subject of masonry dams in England where the earthwork dam, with a wall of puddled clay, had hitherto been almost universal and since its completion nine more masonry dams of smaller size have been completed. In connexion with the Elan and Claerwen works, in Mid-Wales, for the supply of Birmingham, six masonry dams were projected, three of which are completed, including the Caban Gocn dam, 590 ft. long at the water level, and subject to a water-pressure of 152 ft. above the rock foundations and of 122 ft. above the river bed, and the Craig-yr-allt Goch dam, subject to a head of 133 ft. The latter dam is curved in plan, the radius being 740 ft. and the chord of the arc 515 ft. In the Derwent Valley scheme, in connexion with the water supplies of Derby, Leicester, Nottingham and Sheffield, six more masonry dams have received parliamentary sanction. Of these the highest is the Hagglee, on the Ashop, a tributary of the Derwent, which will impound water to about 136 ft. above the river bed, the length from rock to rock being 980 ft. Two of these dams are now in course of construction, one of which, the Howden, will be 1080 ft. in length and will impound water to a depth of 114 ft. above the river bed. In 1892 the excavation was begun for the foundations of a masonry dam across the Croton river, in connexion with the supply of New York. The length of this dam from rock to rock at the overflow level is about 1500 ft. The water face, over the maximum depth at which that face cuts the rock foundations, is subject to a water-pressure of about 260 ft., while the height of the dam above the river bed is 163 ft. The section, shown in fig. 17, has been well considered. The hearting is of rubble masonry, and the faces are coursed ashlar.

bnresttfqrtof '. foiuulation,. vvv voc FIG. 17. Section of Croton Dam.

So-called " natural cement " has been used, except during frosty weather, when Portland cement was substituted on account of its more rapid setting. An important feature in connexion with this dam is the nature of the foundation upon which it stands. Part of the rock is schist, but the greater portion limestone, similar in physical qualities to the Carboniferous limestone of Great Britain. The lowest part of the surface of this rock was reached after excavating through alluvial deposits to a depth of about 70 ft., but owing to its fissured and cavernous nature it became necessary to excavate to much greater depths, reaching in places more than I2O ft. below the original bottom of the valley. Great pains appear to have been taken to ascertain that the cavernous portions of the rock had been cut out and built up before the building was begun.

The Furens dam, already referred to as the earliest type of a scientifically designed structure of the kind, is subject to a pressure of about 166 ft. of water; the valley it crosses is only about 300 ft. wide at the water level, and the dam is curved in plan to a radius of 828 ft. Much discussion has taken place as to the utility of such curvature. The recent investigations already referred to indicate the desirability of curving dams in plan in order to reduce the possibility of tension and infiltration of water at the upstream face. In narrow rock gorges extremely interesting and complex problems relating to the combined action of horizontal and vertical stresses arise, and in some such cases it is evident that much may be done by means of horizontal curvature to reduce the quantity of masonry without reduction of strength. The Bear Valley dam, California, is the most THE VYRNWY VALLEY, MONTGOMERYSHIRE, June 1888.

daring example in existence of the employment of the arch principle. Its height from the rock bed is 64 ft., and it is subject during floods to a head of water not much less. The length of the chord of the arc is the valley is about 250 ft. and the radius 335 ft. The dam was begun in 1883, with a base 20 ft. thick, narrowing to 13 ft. at a height of 16 ft. The cost of this thickness being regarded as too great, it abruptly reduced to 8 ft. 6 in., and for the remaining 48 ft. it was tapered up to a final width of about 3 ft. The masonry is described by Mr Schuyler as " a rough uncut granite ashlar, with a hearting of rough rubble all laid in cement mortar and gravel." This dam has been in satisfactory use since 1885, and the slight filtration through the masonry which occurred at first is said to have almost entirely ceased.

In New South Wales thirteen thin concrete dams, dependent upon horizontal curvature for their resistance to water pressure, have been constructed in narrow gorges at comparatively small cost to impound water for the use of villages. The depth of water varies from 1 8 ft. to 76 ft. and five of them have cracked vertically, owing apparently to the impossibility of the base of the dam partaking of the changes of curvature induced by changes of temperature and of moisture in the upper parts. It is stated, however, that these cracks close up and become practically water-tight as the water rises.

Something has been said of the failures of earthen dams. Many masonry dams have also failed, but, speaking generally, we know less of the causes which have led to such failures. The Failures, examination of one case, however, namely, the bursting in 1895 of the Bouzey dam, near Epinal, in France, by which many lives were lost, has brought out several points of great interest. It is probably the only instance in which a masonry dam has slipped upon its foundations, and also the only case in which a masonry dam has actually overturned, while curiously enough there is every probability that the two circumstances had no connexion with each other. A short time after the occurrence of the catastrophe the dam was visited by Dr W. C. Unwin, F.R.S., and the writer, and a very careful examination of the work was made by them. Some of the blocks of rubble masonry carried down the stream weighed several hundred tons. The original section of the dam is shown by the continuous thick line in fig. 18, from which it appears that the work was subject to a pressure of only about 65 ft. of water. In the year 1884 a length V. 450-0 1 FIG. 19. Elevation and Plan of Bouzey Dam.

FIG. 1 8. Section of Bouzey Dam.

of 450 ft. of the dam, out of a total length of 1706 ft., slipped upon its foundation of soft sandstone, and became slightly curved in plan as shown at a, b, fig. 19, the maximum movement from the original straight line being about I ft. Further sliding on the base was prevented by the construction of the cross-lined portions in the section (fig. 18). These precautions were perfectly effective in securing the safety of the dam up to the height to which the counterfort was carried. As a consequence of this horizontal bending of the dam the vertical cracks shown in fig. 19 appeared and were repaired. Eleven 1 See Proc. Inst. C.E. vol. cxxvi. pp. 91-95.

years after this, and about fifteen years after the dam was first brought into use, it overturned on its outer edge, at about the level indicated by the dotted line just above the counterfort; and there is no good reason to attribute to the movement of 1884, or to the vertical cracks it caused, any influence in the overturning of 1895. Some of the worst cracks were, indeed, entirely beyond the portion overturned, which consisted of the mass 570 ft. long by 37 ft. in depth, and weighing about 20,000 tons, shown in elevation in fig. 19. The line of pressures as generally given for this dam with the reservoir full, on the hypothesis that the density of the masonry was a little over 2, is shown by , long and short Water Fate " dots in fig. 1 8. Materials actually collected from the dam indicate that the mean density did not exceed 1-85 when dry and 2-07 when saturated, which would bring the line of pressures even closer to the outer face at the top of the counterfort. In any event it must have approached well within si ft. of the outer face, and was more nearly five-sixths than two-thirds of the width of the darn distant from the water face; there must, therefore, have been considerable vertical tension at the water face, variously computed according to the density assumed at from ij to 1} ton per square foot. This, if the dam had been thoroughly well constructed, either with hydraulic lime or Portland cement mortar, would have been easily borne. The materials, however, were poor, and it is probable that rupture by tension in a roughly horizontal plane took place. Directly this occurred, the front part of the wall was subject to an additional overturning pressure of about 35 ft. of water acting upwards, equivalent to about a ton per square foot, which would certainly, if it occurred throughout any considerable length of the dam, have immediately overturned it. But, as a matter of fact, the dam actually stood for about fifteen years. Of this circumstance there are two possible explanations. It is known that more or less leakage took place through the dam, and to moderate this the water face was from time to time coated and repaired with cement. Any cracks were thus, no doubt, temporarily closed ; and as the structure of the rest of the dam was porous, no opportunity was given for the percolating water to accumulate in the horizontal fissures to anything like the head in the reservoir. But in reservoir work such coatings are not to be trusted, and a single horizontal crack might admit sufficient water to cause an uplift. Then, again, it must be remembered that although the full consequences of the facts described might arise in a section of the dam I ft. thick (if that section were entirely isolated), they could not arise throughout the length unless the adjoining sections were subject to like conditions. Any horizontal fissure in a weak place would, in the nature of things, strike somewhere a stronger place, and the final failure would be deferred. Time would then become an element. By reason of the constantly changing temperatures and the frequent filling and emptying of the reservoir, expansion and contraction, which are always at work tending to produce relative movements wherever one portion of a structure is weaker than another, must have assisted the water-pressure in the extension of the horizontal cracks, which, growing slowly during the fifteen years, provided at last the area required to enable the intrusive water to overbalance the little remaining stability of the dam.

Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)

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