' behind in the crevice. The clay roof, rather than the walls of this precaution, however, deepla to tongues of concrete like those in fig. 7 were built in the rock throughout the helength of the trench, and ob carried up the sides and slidw over the top of the ped-bat The puddle was miso sestal. then replaced, and remains FIG. 9.-Overhanging Rock Leakage.no sensibly watertight. The lesson taught by fig. 8 applies also to the ends of puddle walls where they abut against steep faces of rock. Unless such faces amad 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 use reservoir is charged, for the settlement and compression of the ama 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 an is indicated in a purposely exaggerated way by the curved lines.d There is considerable distortion of the clay, resulting from combined bolle 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 euo as to permit of percolation capable of keeping open the wound. In o such cases as are shown in figs. 8 and 9 the growth of the sand vein is -bood not vertical, but inclined towards the plane of maximum shearing strain. Fig. 9 also illustrates a weak place at b where the clay either ro never pressed hard against the overhanging rock or has actually or drawn away therefrom in the process of settling towards the lower to d part to the left. When it is considered that a parting of the clay, o 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 550 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 would have been sufficisently filled to prevent injurious percolation at any future time. Hence it is always a safe precaution ato 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 Defects la wall itself is often defective. The original material may have been perfectly satisfactory, but if, for example, in puddle Hiv wall. the progress 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 of 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 XXVII 7* Haw 9105 T FIG. 11. Vertical Vein of Leakage. mamedo d 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. 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 a kind of failure not always attributable to want | by changes of temperature or of moisture or by movements of of proper supervision during construction, but rather to improper the lateral supports, and with proper ingredients and care choice of the site, or treatment of the case, by those primarily responsible. a very thin wall wholly below ground may be made watertight. Dams phragms 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 with dia of America, for example, where timber is cheap, rough stone embankments have been lined on the water face of wood, with timber to form the water-tight septum. In such steel, concrete, &c. 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 Cañon 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. dams. 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 water- Masonry pressure 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 suffisiently 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 1 ft. thick of a monolithic dam, subject to the pressure of water against its vertical side to the full depth ab= in feet, the horizontal Water lost 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 Centre of water pressure w. full depth d, while the area abe 2 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 thed 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 100 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 1 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 = is the total hori. zontal pressure against the dam, generally stated in cubic feet of water, acting at one-third its depth above d the base. Then turning moment of e FIG. 12.-Diagram of Right-Angled Triangle Dam. is the resultant horizontal pressure with an over If x be the width of the base, and p the density of the masonry, the pxd weight of the masonry in terms of a cubic foot of water will be acting at its centre of gravity g, situated at 3x from the outer toe, and the moment of resistance to overturning on the outer toe, px'd (2) WATER SUPPLY 399 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 Factors of the question to allow the water to rise to the vertex a safety. of such a masonry triangle. A minimum thickness must the dam is not used as a weir it must necessarily rise several feet be adopted to give substance to the upper part; and where above the water, and may in either event have to carry a roadway; Morcover, 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 Equating the moment of resistance (2) to the overturning moment the resultant of all the forces cuts the base bc. For any lower level (1), we have 300 290 misqze the same treatment may, step by step, be adopted, until the maximum intensity of pressure d exceeds the assumed permissible maximum intensity of pressure or the centre of pressure, as the maximum, or the centre of pressure reaches an assigned distance from the outer toe c, when the base must be widened until the profile is of the kind shown in fig. 14.ad olan od) to boratipa agizoo hitherto assumed, it must be similarly ascertained that the water case may be, is brought within the prescribed limit. The resultant face is everywhere cap- Overflow able of resisting the Level Having thus determined the outer profile under the conditions masonry when the reser- is al voir is empty, and they pressure of the direction also. Hence in od srit if necessary in that upon od base of each compart-sluyash lo dams above 100 ft. in not you ment must be widened l height, further adjust- aniyy abilo ment of the outer profile araw ar reason of the deviation of the inner profile from dvd bo the vertical. The effect,non may be required by ving of this process is to give my l a series of points in the oos niwto which the resultants of yd t all forces above those t planes respectively cut stag horizontal planesonatedio ad s the planes. FIG. 13.-Factor of Safety Diagram.sif of the dam, and g its centre of gravity, the centre of pressure upon judars and 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 & above the base, the total water pressure represented by the triangle kbh will have its centre at d/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 bc is shifted from the centre of the base to a point i nearer to the outer toe c, and adopting our assump-safe limits certain pressures to which, at that time, such structures tion of uniformly varying intensity of stress, the rectangular diagram were known to be subject. Thus for the inner face he took, as the of pressures will thus be distorted from the figure bfgc to the figure of limiting vertical pressure, 320 ft. of water, or nearly 9 tons per sq. ft.. Rankine in his report adopted the prudent course of taking as the in equal area bjlc, having its centre o vertically under the point at which and for the outer face 250 ft. of water, or about 7 tons per sq. ft..yo 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 110 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 l'Académie des Sciences (1895 and 1898) and in the Annales des Ponts et Chaussées (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 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 in. trusive water getting into the structure. RESERVOIR These researches were followed by those of Messrs L. W. Atcherley and Karl Pearson, F.R.S., and by an approximate graphical treatment by Dr W. C. Unwin, F.R.S. 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 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 16, 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 lines on the diagram) are shown at the upstream toe notwithstanding that the line 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 12th, 1905). 107. Proceedings of the Institution of Civil Engineers, vol. 172, p. 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 "reser voir 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 Gore'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 de 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 abcd 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, &c., 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 reser voir 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 ad hesion. 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-wr.1-sin 2 1+sin |