Fig. 62.
Fig. 62.
Fig. 63.
Fig. 63.
Calculations of the above kind do not, of course, enable all the stresses in a solid mass of masonry to be found. Great stresses are caused by expansion and contraction owing to changes in temperature. Others are caused by the connections of the dam with the rock on which it rests and with the sides of the gorge. The method of calculation described above indicates a suitable form for the profile of a dam. The large factor of safety adopted allows for other stresses. The sections of the oldest dams, made in Spain, were somewhat as shown infig. 64, and contained about twice as much material as was necessary. The object of the calculations is to save this needless expenditure.
Masonry dams designed on the above principles have been constructed for heights ranging up to nearly 300 feet, measured from the foundation to the top. The foundation is always on hard rock free from fissures. Generally a foundation trench is cut. The ends of the dam are carried into the rock on the sides of the gorge. They should not, however, if the sides of the gorge are steep, be built in with mortar, but be allowed to expand and contract vertically, a water-tight joint being made by means of asphalt (Ency. Brit., Tenth Edition, vol. 33, “Water Supply”). This obviously reduces the straining. A dam should be built in cool weather, so that any stresses to which it will eventually be subjected owing to changes in temperature will be chiefly compressive. The upstream face should be as water-tight as possible. There should not, however, be too sudden a change in the character of the masonry from the face work to the inside work. If there are any springs, they must be carefully connected to pipes and carried outside the dam. No water must be permitted to get under or inside the dam, either from springs in the sides of the gorge or from the water in the reservoir. Many existing dams leak slightly where they join the sides of the valley,and most have developed some vertical cracks normal to the face.
Fig. 64.
Fig. 64.
Out of some hundred high masonry dams which have been erected, only three are known to have failed. Of these, the Puentes dam was partly founded on piles; and in two, the Habra and Bouzey dams, the rule of the middle third was not attended to. Another dam, not so high, the Austin dam, in Texas, U.S.A., failed seven years after construction. It was 65 feet high and founded on limestone, the width of the base being 66 feet. Springs in the bed and sides of the gorge had, during the construction of the dam, given much trouble, and had, after its completion, forced their way through the underlying rock. At the time of failure 11 feet of water was passing over the dam, which sheared in two places, a length of 440 feet of it being pushed forward for 40 or 50 feet without overturning, but subsequently breaking up. The dam was founded in a trench cut in the rock. The rock on the downstream side of the foundation trench appears to have been worn away by the water, so that there was no longer a trench (Scientific American, 28th April 1900). The above, however, does not seem to be sufficient to account for failure. The horizontal water-pressure on a 1-foot length of the dam would be 180,000 lbs. and the weight of masonry to be moved perhaps 320,000 lbs. It seems probable that water from upstream found its way under the dam and exercised a lifting force on it and so caused it to slide.
If a masonry dam, instead of being straight, is made curved on plan, with its convexity upstream, it acts as an arch, and its thickness can, in the case of a fairly narrow gorge, be greatly reduced. This type of dam isa suitable one to use when the sides of the gorge are of firm and solid rock and there is no doubt about their being able to stand the thrust without yielding. Several dams of very considerable size have recently been built in this way. The thickness of the upper part of the dam and the ratio of the versed-sine of the arch to the span can be decided on by the methods used for arches in general. The lower part of the dam is made thicker. The lowest part cannot act as an arch, because it is attached to the foundation. It is, however, assisted by the portion above it, which acts as an arch, and thus need not be so thick as in a “gravity” section. The Bear Valley dam, which is 64 feet high, is only 3 feet thick at the top. The thickness increases gradually to 8½ feet at 48 feet from the top. The chord of the curve is 250 feet and the radius of curvature 335 feet. If the gorge is wide, the thickness of the arch comes out so great that nothing is saved by adopting the curved form. But in such a case, and in any case, a dam can be made slightly curved so as to offer a greatly increased resistance to overturning. It need not act as an arch, and can be prevented from so acting, in order that excessive stresses may be avoided, by letting the ends of the dam, after they have entered the grooves cut in the sides of the gorge, stop short of the ends of the grooves.
Fig. 65.
Fig. 65.
During the last few years much attention has been given to the investigation of the stresses to which a masonry dam is subjected. Some investigations have been theoretical and others practical, models of india-rubber and other substances having been used for experiment. The investigations show that generally the stresses in a model of a dam are very much thesame as would be expected, but that there is a tensile stress, previously overlooked, near the point M (fig. 65), where the dam rests on its foundation. The tension is on the foundation, on the line M N, and is due to the horizontal thrust of the water. It is natural that in an elastic model this stress should manifest itself by deformation. In the case of an actual dam resting on rock, matters are different; but this tensile stress deserves consideration. For the present let it be supposed that there is no trench, the dam merely standing on the rock. Suppose that the rock has only the thickness M R. There is tension in M N, and probably compression in N R. It is assumed that, along the base M P, there is perfect union between the dam and the rock. The tension to which the rock is occasionally subjected owing to changes of temperature may exceed any tension due to the water-pressure, but it is conceivable that the tension occurring from both causes might cause a crack at M N, and that this might extend to R. This implies a minute sliding of the dam and of the rockbelow it, movement taking place on the plane R Q. The thrust of the water is now resisted by the rock downstream of P Q. The dam, with the rock M R Q P adhering to it, tends to rotate about the point P. The tendency to rotate will be enhanced if water enters M R, and still more if it enters R Q. No rotation can, however, take place unless the rock at M R is splintered away. The rock would also have to fracture at P Q. It has been suggested that the upstream face of the dam be made curved as shown by the dotted line. This would shift the chief tension tom n, and the dam, with the rock beneath it and the weight of the water above the curved portion, would obviously offer an increased resistance to rotation about P. The cost of the dam would of course be increased. The danger of a crack forming at M N seems to exist only when there is a thin upper stratum of rock not firmly connected to rock below. When this condition is believed to exist, a masonry dam, if built at all, should have the upstream face curved as above described. In the case of any existing dam of great height, when the above condition is suspected to exist, the reservoir might be laid dry, and if any crack at M N is discovered a curved portion could be added; but in this case the union between the new and the old work would be imperfect, and the curve should start from high up on the upstream face of the dam. It has been suggested that asphalt or some impervious material be laid on the rock to prevent water from entering any crack. It would, however, not only have to be laid upstream of the dam, but to extend under part of the dam, and thus weaken it to some extent.
In the case (fig. 63) in which the dam is founded in a deep trench, the building up of the upstreamtriangular space and uniting the material both to the dam and to the side of the trench, might be of some use, but a crack might form in it. It would be desirable to add a curved portion, as above described, on the top of the rock if sound, or to remove the unsound rock and widen the trench and then add the curved portion. Adding material to the downstream triangular space, and uniting it well, would also increase the resistance of the dam to overturning, not so much because of the additional weight, as because of the raising of the point about which the dam would have to revolve in overturning.
Several recent dams have been built of cyclopean concrete, blocks of rock as heavy as 10 tons being sometimes used in the work. Such blocks are laid on one of their flat faces. In the U.S.A. some reservoirs have been made with walls of reinforced concrete, backed by earth embankments (Min. Proc. Inst. C.E., vol. clxxxix.), and also of cyclopean masonry reinforced with steel rods. Another kind of dam which has been used in the U.S.A. is the rock-fill dam with a core—corresponding to the puddle wall in an earthen dam—of steel plates riveted together and made water-tight and inserted into the rock at each side. In the case of the East Canyon Creek Reservoir, Morgan, Utah, the dam is 110 feet high. The steel plates vary in thickness from 3/8-inch at the bottom to ¼-inch at the top, and are embedded in asphaltum concrete and rest on a concrete base. The dry-stone work of the dam is hand-packed on both faces, and also on both sides of the core. The rest is thrown in. The upstream face is 1 to 1, and the downstream face 2 to 1. The waste weir is at one end of the dam and is continued by a flume, so that the water falls clear of the dam. The outlet is a tunnel in the rock.
In a funnel-shaped estuary, especially if it faces the direction of the tidal wave in the sea, the tide in going up the channel increases in velocity, and the momentum of the water causes it to rise higher and higher as the width decreases. At the upper end of the Bristol Channel the range of the tide is double the range in the sea outside the channel. The Bay of Fundy is another place where a similar phenomenon occurs. When a river or estuary is shallow and the range of the tide is great, so that its rise is rapid, the flood tide in some cases advances in the form of a wave or “bore,” causing a sudden rise in the water-level and a sudden reversal of the flow of the stream. A bore is most pronounced at spring tides. That of the Severn is well known.
In the case of a tide running along a coast or up an estuary, the water of the flood tide, after it has ceased to rise, continues for a short time, owing to its momentum, to flow in the same direction as before. The same thing happens when the ebb tide ceases to fall. The tide also acquires special velocity, just as a river does, round any projecting headland.
The rise and fall of the tide are least rapid near the turns of the tide. If the time from the beginning to the end of the flow be divided into six equal parts, the proportional rise of the water will be approximately as follows. And similarly with the fall during the ebb.
Tidal waters are frequently charged, more or less, with silt, obtained from the shore or from shallows near it, either by currents or tidal waves sweeping along it, or by the action of ordinary waves. Tidal waters flowingup and down the lower portions of rivers render them to an enormous degree more capable of carrying navigation and, especially if they become enlarged and form estuaries, more capable of being altered by training works.
A tide-gauge is constructed on the same principle as a self-registering stream-gauge. The rise and fall of the water are reduced, by mechanism, to a convenient range, and are recorded on a band carried on a drum, which is caused to revolve by clockwork. Another kind, which depends on the use of an inverted syphon filled with air and a syphon of mercury, is described inMin. Proc. Inst. C.E., vol. clxiv.
Fig. 66.
Fig. 66.
Thus the time of high tide at M is later than at H. It is later for each point passed in going up the river from H towards A. Eventually a point A is reached where there is no tide, that is, no rise or fall. Far below this point, between A and B, there is a point above which there is no upward current but only a slackening of the downstream flow. At H a diagram showing the rise and fall of the tide is symmetrical, at N the rises and falls are less than at H, and the periods of their occurrence later. In going up the river the duration of the flood tide decreases and that of the ebb tide increases. The flood tide attains its greatest velocity soon after its commencement, the ebb tide towards its close. The distances to which the tidal influence extend are of course greater the greater the range of the tide and the flatter the slope of the river. The discharge of the river of course varies. The greater the discharge the more the rise of the river tends to keep pace with that of the tide and the less the distance to which the tidal influence extends. On a longitudinal section of the river, the high-water line will be shown asA N H. This is merely done for convenience. It is never high water at all points simultaneously. To show the actual state of affairs at various stages of the tide, series of lines must be drawn as infig. 67, where the firm lines show the flood, and the dotted lines the ebb tide.
The flow in the tidal reach of a river is the same as if the water was alternately headed up by a movable weir and then allowed to flow freely and be drawn down. If the water carries silt, the tendency for deposit to occur is (Chap. V.,Art. 2) no greater than if there was no heading up or drawing down. The tendency depends chiefly on whether there is, on the average, any reduction in velocity or increase in depth as compared with the non-tidal upstream reach, and whether the water in that reach is fully charged with silt. If both the answers are in the negative, no deposit due to river silt is likely to occur in the tidal reach.
Fig. 67.
Fig. 67.
If the sea water is charged with silt, it will of course carry silt into the river as it flows up, but the whole volume of water which enters has to flow out again. On the whole, the tendency for silt to be deposited in the river is due only to the period of “slack tide” near the time when the flow ceases. The tendency is seldom marked.
If the sea water carries silt and the river water is clear, the latter assists of course in removing any deposit—that is, it tends to keep the channel clear.
If the river channel is soft and if the sea water carries no silt, it may, in passing up and down the river, become charged with silt and return to sea still carrying it. It thus has a scouring effect on the channel, and may deepen or widen it. If, owing, for instance, to the flattening of the bed slope in its lower reaches, the river tends to deposit its own silt in its tidal reach, the sea water may prevent this deposit. Thus, as regards silting in the tidal reach of the river, the tidal water of the sea has little prejudicial effect if it is silt-laden, and a beneficial effect if it is not. Silt is likely to deposit in the tidal reach of a river of uniform width, only in a case in which the river water carries much silt, and the slope is flat or cross-section great compared to that of the upper reach.
Sea water is heavier than fresh water by about 2·4 per cent., and this, to some extent, prevents their mixing. At all stages of the flood tide the tendency at the point where the fresh water meets the salt water is for the fresh water to accumulate towards the surface and the sea water towards the bottom. When the tide begins to flow up the river there may be a low-level salt water current moving landward and a high-level fresh water current moving seaward, but this is quite a temporary state of affairs. The surface slope is landward, and the water moving seaward is not moving in obedience to the surface slope. It is only moving as a result of momentum previously acquired. The low-level current may have some extra velocity and extra scouring power, but this cannot be much, because the mean landwardvelocity of the whole stream must, owing to the internal resistances caused by the two currents, be less than it would be if there were not two currents. Moreover, the state of affairs is temporary. The two kinds of water mix eventually, and their temporary separation has no considerable effect on the general tendency of the river in the tidal reach to scour or to silt.
A body of water included at any moment between any two cross-sections of the tidal portion of a river may not reach the sea during the next ebb tide. In this case it will flow back up the channel with the next flood tide, and so be kept moving up and down, getting nearer, however, to the sea at each tide.
De Franchimont has shown (Min. Proc. Inst. C.E., vol. clx.) how a diagrammatic route-guide can be prepared for any tidal river to show pilots or captains of vessels the best times for starting on voyages up or down the river, and for passing each point on it.
Any weir or similar structure which abruptly stops the flow of the tide up a river checks it of course for a long distance back, perhaps to the mouth. Old London Bridge used to obstruct the tide, and its removal increased the range of the tide, and was beneficial.
Tidal rivers generally widen out to some extent near their mouths, and are thus rather estuaries than rivers. The works in such rivers are more fully discussed inArt. 5.
The ebb tide in an estuary does not always follow exactly the same course as the flood tide. Of course the lowest parts of the estuary are filled first and emptied last, but the channels are not all continuous. A channel open at its lower end may have a dead end at its upper termination, andvice versa. Also, at sharp bends in the channels, the momentum of the water may cause differences in the paths traversed by the flowing and ebbing currents. Wherever there is a deep channel the water from the adjacent sandbanks tends, towards the close of the ebb, to flow cross-wise into the channel, and in doing this it to some extent washes down the banks into the channel.
If an estuary is not funnel-shaped, if, for instance, it widens out very rapidly, the tidal flow is much less effective in keeping the channel open. In this case, training works, which would give the necessary funnel shape, are indicated rather than dredging. If an estuary is narrow at the entrance, the flow is much less powerful, unless the narrow part is of greater depth, but even then the force of the tide is reduced owing to the change in the shape of the channel.
The bed of an estuary may be of such soft or sandy material that a dredged channel would be likely to be quickly filled up again by the slipping in of material at the sides (Art. 4). In such a case an untrainedchannel can only be kept open to its full depth by constant dredging, and probably the best course is to construct a trained channel, although it may be more expensive than in the case of a harder channel, because of the depth to which the foundations of the walls must be sunk into the soft bed. Also, if the bed of the estuary is constantly shifting, a dredged channel alone will not succeed, and training must be resorted to. Again, the bed may be of such hard material that training walls would not cause it to scour. In this case a channel should be dredged and need not be trained. For the great body of intermediate cases in which the deep channel can be formed either by dredging or training, both methods can be adopted. A common plan is to train the upper part and to dredge the lower part where the estuary is wider and the training walls would be more exposed to the waves.
Fig. 68.
Fig. 68.
When an estuary is thus partly trained, the deepening due to the training does not extend far beyond the point where the walls terminate. The deposit of material along the sides of the estuary may, however, extend some distance further down in places where the tide can no longer have free play. This occurred in the Seine estuary (fig. 68). The authorities of Havre,which lies at one side of the estuary not far from its mouth, feared that if the training walls were brought further down, the deposits might extend to their neighbourhood. The reduction in the capacity of the estuary, due to the deposits, caused it to become filled up more quickly, and the time of high water at Havre was advanced. The dotted lines show a good arrangement of training walls proposed by Harcourt.
There is no doubt that it is always feasible to carry training walls right through an estuary, or at least down to a point where deep water is reached, and if a proper funnel shape is given to the channel the reduction of the tidal flow and silting up of the spaces behind the walls need not cause any trouble. Training the complete estuary was carried out in the case of the Tees, where, however, the estuary was not of great length, and was not of a good shape for keeping itself open. Any affluents entering the estuary can be provided with separate trained channels. Difficulty may, however, arise if there are towns which would be shut off from the estuary by the silt banks.
Generally the line selected for the trained or dredged channel should, though it must be as short and direct as possible, coincide as nearly as possible with that which the water naturally tends to keep open. This may be toward one side of the estuary or the other, according to the direction from which the tidal wave approaches. In the case of the Dee, the best line was not adopted, attention having been chiefly given to the question of silting up the spaces outside the walls and so reclaiming land, a matter which should always be treated as of quite secondary importance. Training walls in estuaries are generally built only up to half-tidelevel. Were it not for the expense they might be built up to high-water level. In the Seine estuary the walls were made of blocks of chalk.
Whether a trained channel will keep itself open or will need periodical dredging depends, of course, on the amount of silt in the water and on its velocity and depth. The question must be worked out and calculated as in the case of a non-tidal river.
The estuary of the Mersey differs from most others. Towards the mouth, near Liverpool, it is narrow and it widens out further inland. The tides, running through the narrow portion, to fill up the large inland basin and to empty it again, keep the narrow part scoured to a great depth. It was proposed to train the wide portion for the Manchester Ship Canal. The training would, no doubt, have succeeded, but, owing to the silting up of the greater part of the estuary, the scouring near Liverpool would have been very greatly reduced and serious damage done to that port.
The bars at the mouths of deltaic rivers cannot usually be kept down by dredging except at great expense.The usual method of dealing with them is to run out two parallel jetties, in continuation of the river banks, so as to bring the mouth of the river out to the bar. The river then scours a channel through the bar and, if the walls are not too far apart, the depth will probably become as great as in the river and sufficient for navigation. The river, however, tends to at once form a new bar further out. The rapidity with which the new bar forms will be greater or less as the specific gravity of the materials carried by the river is greater or less, and as the strength of any littoral current is less or greater. Clay is spread far out while sand quickly sinks. All deposits are, however, swept away if there is a strong littoral current. The steeper the slope of the bed of the sea away from the bar the longer the new deposit will take in forming a fresh bar. Also the less the discharge of the river the less the deposit will be. The branch of a deltaic river selected for improvement by having the bar at its mouth removed, should be one which has a small discharge and whose mouth is in a position where there is a strong littoral current. In the case of the Rhone, the branch selected was the eastern one, whose mouth was not exposed to any littoral current. Moreover, the other branches of the river were closed, and this increased the discharge of the branch which was left open. The work did not succeed. In other cases, the parallel jetty method has succeeded, and notably in the case of the Mississippi. In this case willow mattresses weighted with stones were used. The question of keeping down the discharge does not, however, appear to have always received sufficient attention. In the case of the Mississippi the “South pass” was selected for improvement. In order to remove a shoal its upper endwas narrowed and its discharge reduced. The upper ends of the other “passes” were then obstructed so as to restore the discharges of all the passes to their former amounts. The wisdom of this step is questionable. It is desirable to keep down the discharge of the branch which is to be improved to the lowest limit consistent with free navigation.
If the width of the river near its mouth is greater than is desirable for the width between the jetties, the latter are sometimes made to converge though their outer ends are made parallel.
In the case of the Mississippi the jetties were made with a slight curve to the right. It would seem desirable always to make the jetties with quite a considerable curve. The jetty which was convex to the channel could then probably be shortened. In a case where there is a littoral current, say to the right, the curve of the jetties could be to the right, so that the stream on issuing would tend to merge into the current and assist it.
Most rivers have bars at their mouths. In the case of deltaic rivers the bar, as already stated, is caused by the heavy silt carried by the river, though it may be assisted by littoral drift. In the case of non-deltaic rivers flowing into tideless seas, the quantity of silt isnot enough to form a bar, and the same is generally true in the case of tidal rivers where the volume of tidal water is usually much greater than that of the upland water. In both these classes of rivers the formation of the bars is due chiefly to littoral drift or to sediment brought in by the sea water. The bar, as in the case of deltaic rivers, may be partly scoured away by a flood in the river, and the scoured material may deposit on the seaward slope of the bar. Generally, the navigation channel across a bar of this kind can be kept sufficiently deep by dredging, but sometimes jetties, like those mentioned in the preceding article, have been constructed, and in this case there is the great advantage that the bar is not liable to form further out. If littoral drift tends to accumulate, the jetties, or at least the one on the side whence the drift comes, can be lengthened. This was done, as mentioned by Harcourt (Rivers and Canals,Chap. IX.), in the case of the rivers Chicago, Buffalo, and Oswego, which flow into the Great Lakes of America. The same writer states that the jetties at the Swine mouth of the tideless river Oder were made to curve to the left, the convex or left-hand jetty being the shorter, but that this exposed the mouth to littoral drift coming from the left. The river, upstream of the jetties, had a slight curve towards the left, but this could have been corrected or, at all events, the jetties made to curve to the right.
A case (fig. 69) where parallel jetties were recently constructed in a tidal sea is that of the mouth of the Richmond River, New South Wales (Min. Proc. Inst. C.E., vol. clx.).
Fig. 69.
Fig. 69.
In the case of a bar at the mouth of an estuary, parallel jetties would be too far apart. In such casesconverging breakwaters (fig. 70) are sometimes made, especially if the tidal capacity of the estuary is small. The entrance is generally 1000 to 2500 feet wide. If made narrow, it would reduce the tidal flow too much. The space inside the breakwaters adds to the tidal capacity, and thus induces scour at the bar. The case is similar to that of the Mersey estuary (Chap. XIV.,Art. 5), the breakwaters assisting scour at the bar,though perhaps slightly interfering with the tidal flow in the estuary.
Fig. 70.
Fig. 70.
Converging breakwaters also tend to stop littoral drift, and the space inside them acts as a harbour of refuge in storms and as a sheltered place where dredgers can work (Rivers and Canals,Chap. XI.). They have to be heavily built and are very expensive, and they are generally adopted only when there is an important seaport, and when they can be put to all the uses above indicated.
Fallacies in the Hydraulics of Streams(Chap. I.,Art. 4, andChap. VI.,Art 2).—In an inundation canal in India the supply during floods was excessive. Orders were given that a flume be made at the head, as shown infig. 71. The sides were to be revetted, as shown infig. 19(Chap. VI.,Art. 3); the length, excluding the splayed parts, was to be 200 feet, and the floor was to be a mattress well staked or pegged down. The order stated that “by this means we cannot get into the canal much more than its true capacity.” With 9 feet of water, a surface fall of 4 inches in 300 feet would give a velocity of some 6·5 feet per second, and a further fall of about 8 inches would be required at the head of the flume to impress this velocity on the water. The flume would reduce the depth of water in the canal by 1 foot,i.e.from 9 feet to 8 feet. This would not be in anything like the proportion desired. Moreover the flume, unless the bed was extremely well protected,would be destroyed. The above is a case of exaggerating the effect of an “obstruction.”
Fig. 71.
Fig. 71.
Again, on a branch canal it was observed that “wherever cattle crossings exist there is a deep silt deposit which practically blocks the branch.” The deposit exists because the sides of the channel are worn down. A wide place always tends to shoal (Chap. IV.,Art. 9). If the deposit obstructed the flow of water there would be a rush of water past it, and it could not exist.
The Gagera branch of the Lower Chenab Canal—the left-hand branch infig. 72—was found to silt. It was proposed to make a divide wall (fig. 72) extending up to full supply level. The idea is unintelligible. The silt does not travel by itself but is carried or rolled by the water. As long as water entered the Gagera branch, silt would go with it. The authorities, who had apparently accepted the proposal, altered the estimate when they received it, and ordered the wall to be made as shown dotted and of only half the height. This was done. The idea seems to have been that the wall would act as a sill and stop rolling silt. This is intelligible, but seeChap. IV.,Art. 2, last paragraph. Moreover, there was a large gap, A B, in the wall. The work is said to have proved useless, and proposals have been made to continue the wall from A to B. In this form it is conceivable that it may be of use.
Fig. 72.
Fig. 72.
In a river, the rises and falls at different places are not, ofcoarse, the same, even when they are long continued. In the river Chenab, at the railway bridge at Shershah, the rise from low water to high flood is generally a foot or two more than the rise at a point 25 miles upstream. It has been suggested that the railway embankments, which run across the flooded area, cause a heading up of the stream. If this were the case, to any appreciable extent, there would be a “rapid” through the bridge, which, if it did not destroy the bridge, would at least be visible and audible.
The exaggerated ideas which often prevail regarding the tendency of a river, when in flood, to scour out a new channel, have been mentioned inChap. IV.,Art. 8. Spring, in his paper on river control, admits, when mentioning Dera Ghazi Khan, that there was little danger, but in mentioning the Chenab Bridge at Shershah he quotes, without disputing it, an opinion of the opposite kind (Government of India Technical Paper, No. 153, “River Training and Control on the Guide Bank System”).
For some other fallacies, seeHydraulics,Chap. VII.,Arts. 9and15.
Pitching and Bed Protection(Chap. VI.,Art. 3, andChap. X.,Art. 2).—Any scour upstream of a weir is merely due to the eddies formed upstream of the crest (Hydraulics,Chap. II.,Art. 7), and is not serious. And, similarly, as to scour upstream of a pier. A hole formed alongside a pier or obstruction, if there is no floor, may work upstream. The chief use of a floor extending far upstream is to flatten the hydraulic gradient (Chap. X.,Art. 3).
For pitching of the sides, monolithic concrete is not very suitable, because it may settle unequally and crack. For heavy pitching, concrete blocks can be used. They can rest on a layer of 3 to 6 inches of rammed ballast or gravel. The toe wall, as shown infig. 13, page 65, is sometimes dispensed with, the pitching being merely continued to a suitable depth below the bed, and the bottom edge being at right angles to the slope instead of horizontal. The portion below the bed may be of concrete.