magnetic meredian makes with the direction of the tunnel must be carefully observed at the top of each shaft, with a miner's compass, (a kind of circumferentor,) that the proper direction of the work may be set out with the same instrument at the bottom of the shaft: but, if the tunnel be curved, the direction of the tangent to the curve at the top of each shaft must be observed, that the same direction may be given to it at the bottom of the shaft, and that from thence the curve may be laid out in the tunnel, in the same direction as it was on the surface of the ground; it would be also advisable to bore from the surface to the tunnel, before the works thereof have proceeded far, to test their accuracy, as ferruginous matter in the earth might cause the magnetic needle to deviate, and thus give a wrong direction to the works, if this precaution be not taken. 6. The excavations of a tunnel on the narrow gauge should be about 30 feet in depth and width, the depth extending 5 or 6 feet below the intended line of the rails, to give room for the inverted arch and the ballasting: but when the tunnel is made through rock sufficiently hard to form the side walls, its height need not exceed 22 or 25 feet, and its width 26 feet, the excavation in this case extending only to the formation level. For the railways on the broad guage the excavations of the tunnel must be proportionably larger. The cross-section of the masonry of tunnel is shown in the annexed figure, with the ballasting on which the rails are laid. This cross-section is such as is required where the excavation of the tunnel is made through loose earth, the arch above being only requisite when made through hard rock.-The following notes on the construction of tunnels, are chiefly extracted from Dempsey's Practical Railway Engineering. NOTE 1. Like mining and all other subterranean operations, the construction of a tunnel can be but little aided by mechanical appliances; it chiefly requires hard manual labour, exercised under circumstances which do not admit of that thorough superintendance which promotes economy, and, moreover, liable to unforeseen interruptions, of surmounting which neither the manner nor the expense can be predetermined. Thus the Kilsby tunnel, on the North Western Railway, was estimated to cost £40. per yard lineal; whereas the actual cost was £130 per yard, owing to its intersecting a quicksand that had escaped the trial borings. Thus a vast expense was incurred in setting up and working pumping machinery to dry the sand. The Box tunnel on the Great and lined with masonry only Western Railway, excavated through oolite rock, through a portion of its length, cost upwards of £100. per lineal yard. The length of this tunnel is 3123 yards, or upwards of 14 miles, it has eleven principal shafts, and four intermediate ones. The Bletchingly and Saltwood tunnels in the South Eastern Railway, cost respectively £72. and £118. per ineal yard, the greater cost of the latter work arising from the great body of water in the sand which it intersects. The method of proceeding with tunnelling depends mainly upon the kind of material to be excavated. This having been generally ascertained by boring and trial shafts, which must be sufficiently capacious to admit readily of lowering men and materials, raising materials excavated, fixing pumps, and also for starting the headway of the intended tunnel, when the required depth is reached. NOTE 2. The working shafts are made from 8 to 10 feet internal diameter. They are of brick work, usually 9 inches thick, and carried up 8 or 10 feet above the surface of the ground. These, and all other shafts, rest upon curbs of cast iron, fitted into the crown of the tunnel, and forming a level base for the shaft. The air shafts are of a smaller thickness and diameter, the latter of which is usually about 3 feet.-The number of working shafts will depend chiefly on the rate of speed with which the work is required to be accomplished. With plenty of men, horses, material, and plant, the work is much facilitated by sinking extra shafts, which will usually repay their cost. NOTE 3. The Watford tunnel, 75 chains in length, on the North Western Railway, was worked with six shafts, about 8 feet internal diameter; the brick work was moulded to fit the circumference of the shafts, and laid in two halfbrick rings. Air shafts were sunk at about 2 chains distance on each side of each working shaft. The arch and side of the tunnel were chiefly made two bricks thick, and the invert one and a half brick, except where the stratum, passed through, seemed to suggest an increased or diminished thickness. The form of the top of the tunnel is nearly semi circular, supported by curved side walls standing on stone footings, or skew backs, which rest on the invert. NOTE 4. In commencing the work of the Saltwood tunnel, referred to in Note 1., great difficulty was encountered from the great quantity of water in the green sand, which the tunnel intersects. The course adopted was to make a headway 5 feet high and 4 wide quite through the hill, on a level with the bottom of the tunnel, in which the water was collected and drained off before the tunnel was begun. The size of this, and also the Bletchingley tunnel, is 24 feet wide at the broadest part, 30 feet including the side walls; 25 feet high in the clear, 30 feet including the invert and top arch, and 21 feet above the level of the rails. The brick work of the top arch and walls varies from 2 to 4 bricks in thickness; and the invert is 3 bricks in thickness. NOTE 5. The section of the Box tunnel, already referred to, was designed to be 27 feet wide at the springing of the invert, and 30 feet wide at a height of 7 feet above this, and the clear height above the rails 25 feet. As a great portion of the tunnel is constructed by mere excavation, and without masonry, these dimensions are, in some cases, departed from, in order to clear away loose portions of the stone, and secure solid surfaces. Where brick work is used, the sides are seven half brick rings in thickness, the arch six, and the invert four. During the construction, the constant flow of water into the works, from the numerous fissures of the rock, compelled pumping on a most expensive scale to be adopted. NOTE 6. When much water issues from the earth, in sinking shafts cr building tunnels, the back of the wall should be well lined with puddle, and Roman cement should be used instead of mortar. The entire tunnel at Kilsby was built with Roman cement, the thickness of the brick-work being mostly 27 inches. This tunnel is 2423 yards long: it has two ventilating shafts 60 feet in diameter; the brick-work of which is 3 feet thick, and laid in Roman cement throughout these shafts intersect the line of the tunnel, and form curved recesses, by part of their width extending beyond the tunnel on both sides. CHAPTER V. THE METHODS OF FINDING THE CONTENTS OF RAILWAY CUTTINGS, &c. In making the estimates for a projected railway, the contents of the several cuttings, embankments, &c., are in most cases found by tables, calculated for the purpose, the surface of the ground being considered as on the same level as the centre of the line. But when the projectors of the line have been empowered to construct it, cross sections of the cuttings are carefully taken, at every variation of the surface of the ground, especially if the surface be sidelaying, or inclined laterally with respect to the direction of the line, as in the cross sections in Problems II., III., and IV., Chap. III. The distance of these cross sections may vary from 10 or 12 chains to less than 1 chain, according to the regularity or irregularity of the slopes of the surface. These cross sections must next be plotted on a large scale, as in the problems just referred to, and their areas found by any of the methods given in Chap. III., preparatory to finding the contents of the cuttings by tables; but if the surface lines of any of the cross sections be level, or so nearly so as to be readily reduceable to a level surface line by casting, their areas need not be found, their depth only being required for finding the contents by the tables. NOTE. Some take a mean of the areas of every two consecutive cross sections, and others a mean of the depths, where the surface line is level, as a basis for calculating the contents of the cuttings, which methods are both erroneous, especially where the consecutive areas or depths of the cross section differ considerably. TABLES FOR FINDING THE CONTENTS OF RAILWAY CUTTINGS, &c. Numerous tables exist for this purpose, some of which are voluminous; those by M'Neill, Bidder, Huntingdon, Hughes, Bashforth, Sibley, and Rutherford, Law and Lowe, are well adapted for the purpose, assuming the surface line of the cross sections to be level, or to be reduced to that position; but none of these tables will properly apply to sectional areas, which is the most important part of their use, excepting Bashforth's; but his method of using them is erroneous, the error approximating to 50 per cent, as a maximum. I would therefore recommend for this purpose, the General Earthwork Table,* in conjunction with Two Auxiliary Tables, on the same sheet in Baker's Engineering, as being applicable to all varieties of ratio of slopes and widths of formation level in common use; and with the help of Barlow's Tables of Square Roots, these tables will apply to sectional areas, with all the mathematical accuracy that can be attained, with very little more calculation than adding the contents between every two cross sections, as given by the General Table. -The contents in the General Table are calculated to the nearest unit, as are also those in the Auxiliary Table, No. 2, which is for the decimals of feet in the depths. The Auxiliary Table, No. 1, shows the depths of the meeting of the side slopes below the formation level, with the number of cubic yards to be subtracted from the contents of the General Table for each chain in length, for eight of the most common varieties of ratio of slope. NOTE 1. These Tables, with very little additional calculation, may be extended to every variety of formation level and ratio of slopes that can occur, and even to cases where that ratio differs in the two sides of the same cutting, as shall be shewn in the following Problems. NOTE. 2. The investigations of the method of forming these tables and using them are given in Baker's Railway Engineering, also further investigations are given at the end of the following Problems, respecting Mr. Bashforth's Erroneous Methods of Calculating Earthwork. The following diagrams and explanations will further illustrate the method of taking the dimensions of railway cuttings, preparatory to using the above named tables. m a C A M 3 Let A B D C cab d, be a railway cutting, of which A B D C, abdc are the cross sections, A B=ab= width of formation level, M M', mm' the middle depths of the two crosssections; the side-slopes A C, B D, a c, bd, when prolonged two and two, will intersect at N and n, at which points the prolongations of M M', m m' will also meet, thus constituting a prism A B Nna b, the content of which is to be deducted from the whole content, given by the General table, by means of the table No 1.; in which the depth M'N=m'n is also given, as already stated, to several varieties of slope and bottom width. N The numbers for the side slopes, forming the alternate lines in Bidder's Table, will supply the place of the General Table, and the formula Prob. III., page 199 gives the cubic yards to be deducted for each chain in length, the quantities for the decimals in the depths, as shown by Table No. 2, may be omitted by taking the nearest whole numbers in the depths. b a To place this subject in a more practical point of view, let the annexed figure represent a longitudinal and vertical section of a cutting, passing through the middle A E of the formation level. H I, the line of the rails, and a h, the line in which the slopes if prolonged, would meet. It will be seen that the cutting Abcd E commences and runs out on the formation level A E, and that the depth A a = Be =Cƒ= &c. is to be added to the several depths Bb Cc, D d of the cutting, the first and last depth at A and E being each=0; or, what amounts to the same thing H Ai a B C D E 9 h the several depths must be measured from the line ah: thus, Aa, be, c f, &c. are the depths to be used. And since the depth A a is given in Table No. 1, for all the most common cases, or it may be readily found by calculation for all cases, as shall hereafter be shown, the line corresponding to a h must, therefore, be ruled on the railway-section, at the proper distance below A E, from which the several depths must be measured; or the vertical scale may be marked with Indian ink (which may be readily rubbed off) at the same distance, and this mark may then be applied to the formation level A E, for the purpose of measuring the several depths. In the case of an embankment, the line for the several depths must be placed at a like distance above the formation level. PROBLEM I. The several depths of a railway cutting to the meeting of the side slopes, its width of formation level, and the ratio of the slopes being given, to find the content of the cutting in cubic yards, from the Tables referred to, the distances of the depths being one chain each. RULE. Take the several quantities corresponding to every two succeeding depths of a cutting or embankment, measured to the meeting of the side slopes, at the distance of 1 chain each. from the General Table in Baker's Railway Engineering and multiply their sum by the ratio of the slopes; from the product subtract the cubic yards corresponding to the given bottom width and ratio of slopes from Table No. 1., multiplied by the whole length of the cutting, and the remainder will be the content of the cutting in cubic yards. |