1846.} 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



100 



PRESSURE ON RETAINING WALLS. 



In the first volume of llie Transactions of the Institution of Civil En- 

 gineers, Ireland, is published a paper by IVIr. Neville, on the horizontal 

 resistance required to sustain banks of earth. The formula; arrived at in 

 this paper were printe<l at p. 242 of the last volume of our journal; and 

 a letter liaving appeared at p. 359 of the same volume, subscribed '' A 

 Youn;; Engineer," asking for a demonstration of the results given, Mr. 

 Neville has been good enough to send us in reply a copy of his printed 

 paper. Hefore, however, making any extracts from if, we wish to stale an 

 objection which appears lo us to apply generally to the mechanical consi- 

 derations on wliich the mathematical investigalions are based. If, how- 

 ever, we mistake Mr. Neville's views, he will, of course, have the oppor- 

 tunity of replying. 



The earih behind a revetement wall of a railway cutting pressing on 

 every part of the masonry, tlie equations given by Mr. Neville determine 

 the resultant of all the horizontal pressures, but the moment of this result- 

 and the application are left undetermined. Now, the determination 

 of the value of the resultant pressure, is not sufficient of itself for ascer- 

 taining the necessary strength of the retaining walls, or rather, that value, 

 if it alone be determined, does not afford the slightest assistance whatever 

 in examining the conditions of equilibrium. The case contemplated by 

 . JMr. Neville appears to be one which seldom if ever occurs in practice — 

 namely, the moving of the revetement wall bodily forward without over- 

 turning. Whereas, in reality, the real points to be ascertained are the 

 necessary thicknesses of masonry, to prevent, 1st, the slipping of the 

 courses of bricks on each other ; 2nd, the overturning the structure about 

 . its base. 



In order to the ascertaining these two points, two sets of equations are 

 required. The first set of equations must exhibit the variations in Ihe de- 

 gree of pressure on the revetement at dill'crent heights from the ground. 

 It is manifest that the pressure will not be uniform, that it will generally 

 be greater near the base than the top of the wall. Consequently, lo pre- 

 vent the courses of masonry slipping on each other, the " wall of equal 

 strength" (that is, the wall in which the strength is everywhere propor- 

 tionate to the pressure) will be of the greatest thickness at the base and 

 diminish upwards. To ascertain tlie varying form of the wall the law of 

 Tariation of thediflercnt pressures must be ascertained. Mr. Neville has, 

 however, considered only one single pressure to be acting on the wall- 

 namely, the resultant of all the pressures, which, in reality, exist. 



The next point to be ascertained is the tendency to overthrow the wall 

 by turning it about ils base, to lliis end we must have equations exhibiting 

 not the value of the pressures merely, but their moment or leverage. For 

 it is clear that of two equal pressures acting on a wall, that which is ap- 

 plied at the greatest distance frum the base will have the greatest jiwrc/wsc 

 or effect to throw down the structure. To find therefore how strong the 

 wall must be built to prevent its being overturned, it will be necessary 

 either to ascertain the resultant force and also its point of application ; or 

 (if it be possible) we may determine the sum of ihe moments of the 

 pressures on every point of the wall. In analytical language if;) be the 

 pressure on a unit of the area of the wall at a height x from the base, the 



quantity to be determined is 



i I p X dr. 



The calculations of the paper before us would be perfectly satisfactory, 

 if it were possible so to build the relaining wall that by means of it a 

 pressure equal, and exactly opposite to the resultant of the pressures from 

 the earth could act at the same point of application. This, however, is 

 obviously impossible, for the horizontal resisting force exerted by the mall 

 is applied at the base, since all the strength of the structure is derived 

 ultimately from ils connection or cohesion wilh ils foundations. The re- 

 Bultant pressure of the earthwork is however applied at some point above 

 the base ; ihe two forces, that which sustains Ihe wall, and that tending to 

 overthrow it, cannot therefoi-e besupposed t.j be applied at the same point. 

 The determination of the value of the latter force, therefore, is not of itself 

 of any value, for it may happen for instance to be applied at a distance of 

 two feet from the base, or at a distance of four feel, and in the latter case its 

 effect will be twice as great as in the former. It is not Ihe pressure, but 

 the momentum of it which is to be sought for, and wilhout this be de- 

 termined, no useful result can be deduced from the mathematical investi- 

 gations. 



Mr. Neville quotes in a note the concluding remarks of a paper on the 



resistance to banks of earth, by Tredgold, in the 5Ist volume of the 

 " Philosophical Magazine,'' anri adds " It is, however, evident that Tred- 

 gold was mistaken in this conclusion." If Mr. Neville will again refer 

 to the original, he will, perhaps, see that the mistake is hisown, and arises 

 from a misapprehension of the sense intended to be conveyed. He might, 

 by-the-bye, have laken a hint for his own investigation from Tredgold, who 

 is careful to determine not the pressure only, but the moment of it. 



OCEAN WAVES. 



(We liave slightly abridged this interesting paper from the " Nautical Magazine.") 

 Oceanic waves, from whatever source they may arise, have always been 

 regarded as objects of interest to command our attention, yet very little 

 is known of the laws whereby they are raised, augmented, or transferred. 

 Landsmen, when actually embarked in stormy weather, are generally so 

 deranged by sea-sickness and the ship's motion, as to be rendered unlit 

 for observation or philosophical research. On the other hand, practical 

 seamen, accustomed to the sea from an early age, although not altogether 

 disqualified, become so familiar with all kinds of waves, that the subject 

 is a matter of indifference to them. 



It is, however, very certain that erroneous notions are entertained about 

 waves, for we read in works of acknowledged merit, that the height of 

 waves above the mean sea level, seldom exceeds six or eight feet, yet the 

 language of poetry and metaphor raises them into aqueous mountains. 



Some sense, and a good deal of nonsense about waves, was published 

 by a section of the British Association for the advancement of Science. 

 Being smitten wilh the mania of making observations on waves, and leav- 

 ing Daddy Neptune to make the actual experiments, I seriously set to 

 work at my ofticial residence, which is within thirty feet of the Atlantic, 

 and 3,800 miles from the nearest land on the north-east coast of South 

 America ; the waves, therefore, coming from the south-west have " a pretty 

 considerable fetch." I had, perhaps, the best opportunity, and much in- 

 clination to collect as many fjcts as possible about the waves, that are 

 almost constantly commanding my attention. 1 now send those I made at 

 Plymouth, believing ihey may be useful ; as nothing of the kind has ever 

 been published, Ihey afford data for mathematical research. The obser- 

 vations are arranged in a tabular form, willi very brief remarks of my own, 

 extracted from a paper of mine, where the subject is more fully discussed . 



Obscrvalions made on Waves reaching Bovisand, east-end of Plijmouth 

 Breakwater. 



Remarks on the Observations^ 



No. 1.— San Carlos to Bovisand Rocks. 



2. — This evening only ten waves over space. 



3.— Distance traversed from San Carlos Huoy to Pi.t. 



4. — Waves become crowded near tlie Pier. 



5. — The east wind has probably diminished the vtlocity of the waves. 



6. 



* On this day, the height of the waves, unbrokm. was measured, by means of many 

 obseivalioiis. The mean level of smoo'.h water on the tide gauge was noted, and the eye 

 ot tlie ol)6erver being 3-' feet above the sea level, his visible horizon was li^JyJO feet. The 

 buoy on the Tinker Shoal was distant '»,l8il feet, and as the waves resiched this buoy and 

 raised it, the summit of the wave was in u line with the observer's eya and his visible 

 horizon. Since the distance of the visible hoiizon ana height of t!ie eye are given, ani 

 the distance of the Tinker Buoy also Kiven, the height of the waves at the buoy may be 

 fonnd, because, 3'J,.'J20 : ;i2 feet ; I 3y..'')20— G,180 : 27 feet, the height of the wave above 

 the mean level, and as the sea wns brciiking in a di.'pth of five futiioms, the depressioM 

 were equal to the elevations . * , the faeitjLt beUveeii the two extremities, or rather hollow, 

 would be bl ftel. 



