CHAPTER I.PRELIMINARY CONSIDERATIONS. CHOICE BETWEEN A TUNNEL AND OPEN CUT. GEOLOGICAL SURVEYS.

[1]“Tunneling,” Encly. Brit., 1889, vol. xxiii., p. 623.

The Roman tunnels were designed for public utility. Among those which are most notable in this respect, as well as for being fine examples of tunnel work, may be mentioned the numerous conduits driven through the calcareous rock between Subiaco and Tivoli to carry to Rome the pure water from the mountains above Subiaco. This work was done under the Consul Marcius. The longest of the Roman tunnels is the one built to drain Lake Fucino, as mentioned above. This tunnel was designed to have a section of 6 ft. × 10 ft.; but its actual dimensions are not uniform. It was driven through calcareous rock, and it is stated that 30,000 men were employed for eleven years in its construction. The tunnels which have been mentioned, being designed for conduits, were of small section; but the Romans also built tunnels of larger sections at numerous points along their magnificent roads. One of the most notable of these is that which gives the road between Naples and Pozzuoli passage through the Posilipo hills. It is excavated through volcanic tufa, and is about 3000 ft. long and 25 ft. wide, with a section of the form of a pointed arch. In orderto facilitate the illumination of this tunnel, its floor and roof were made gradually converging from the ends toward the middle; at the entrances the section was 75 ft. high, while at the center it was only 22 ft. high. This double funnel-like construction caused the rays of light entering the tunnel to concentrate as they approached the center, and thus to improve the natural illumination. The tunnel is on a grade. It was probably excavated during the time of Augustus, although some authorities place its construction at an earlier date.

During the Middle Ages the art of tunnel building was practiced for military purposes, but seldom for the public need and comfort. Mention is made of the fact that in 1450 Anne of Lusignan commenced the construction of a road tunnel under the Col di Tenda in the Piedmontese Alps to afford better communication between Nice and Genoa; but on account of its many difficulties the work was never completed, although it was several times abandoned and resumed. For the most part, therefore, the tunnel work of the Middle Ages was intended for the purposes and necessities of war. Every castle had its private underground passage from the central tower or keep to some distant concealed place to permit the escape of the family and its retainers in case of the victory of the enemy, and, during the defense, to allow of sorties and the entrance of supplies.

The tunnel builders of the Middle Ages added little to the knowledge of their art. Indeed, until the 17th century and the invention of gunpowder no practical improvement was made in the tunneling methods of the Romans. Engravings of mining operations in that century show that underground excavation was accomplished by the pick or the hammer and chisel, and that wood fires were lighted at the ends of the headings to split and soften the rocks in advance. Although gunpowder had been previously employed in mining, the first important use of it in tunnel work was at Malpas, France, in 1679-81, in the tunnel for the Languedoc Canal. Thistunnel was 510 ft. long, 22 ft. wide, and 29 ft. high, and was excavated through tufa. It was left unlined for seven years, and then was lined with masonry.

With the advent of gunpowder and canal building the first strong impetus was given to tunnel building, in its modern sense, as a commercial and public utilitarian construction, since the days of the Roman Empire. Canal tunnels of notable size were excavated in France and England during the last half of the 17th century. These were all rock or hard-ground tunnels. Indeed, previous to 1800 the soft-ground tunnel was beyond the courage of engineer except in sections of such small size that the work better deserves to be called a drift or heading than a tunnel. In 1803, however, a tunnel 24 ft. wide was excavated through soft soil for the St. Quentin Canal in France. Timbering or strutting was employed to support the walls and roof of the excavation as fast as the earth was removed, and the masonry lining was built closely following it. From the experience gained in this tunnel were developed the various systems of soft-ground subterranean tunneling since employed.

It was by the development of the steam railway, however, that the art of tunneling was to be brought into its present prominence. In 1820-26 two tunnels were built on the Liverpool & Manchester Ry. in England. This was the beginning of the rapid development which has made the tunnel one of the most familiar of engineering structures. The first railway tunnel in the United States was built on the Alleghany & Portage R. R. in Pennsylvania in 1831-33; and the first canal tunnel had been completed about 13 years previously (1818-21) by the Schuylkill Navigation Co., near Auburn, Pa. It would be interesting and instructive in many respects to follow the rise and progress of tunnel construction in detail since the construction of these earlier examples, but all that may be said here is that it was identical with that of the railway.

The art of tunneling entered its last and greatest phasewith the construction of the Mont Cenis tunnel in Europe and the Hoosac tunnel in America, which works established the utility of machine rock-drills and high explosives. The Mont Cenis tunnel was built to facilitate railway communication between Italy and France, or more properly between Piedmont and Savoy, the two parts of the kingdom of Victor Emmanuel II., separated by the Alps. It is 7.6 miles long, and passes under the Col di Fréjus near Mont Cenis. Sommeiller, Grattoni, and Grandis were the engineers of this great undertaking, which was begun in 1857, and finished in 1872. It was from the close study of the various difficulties, the great length of the tunnel, and the desire of the engineers to finish it quickly, that all the different improvements were developed which marked this work as a notable step in the advance of the art of tunneling. Thus the first power-drill ever used in tunnel work was devised by Sommeiller. In addition, compressed air as a motive power for drills, aspirators to suck the foul air from the excavation, air compressors, turbines, etc., found at Mont Cenis their first application to tunnel construction. This important rôle played by the Mont Cenis tunnel in Europe in introducing modern methods had its counterpart in America in the Hoosac tunnel completed in 1875. In this work there were used for the first time in America power rock-drills, air compressors, nitro-glycerine, electricity for firing blasts, etc.

There remains now to be noted only the final development in the art of soft-ground submarine tunneling, namely, the use of the shield and metal lining. The shield was invented and first used by Sir Isambard Brunel in excavating the tunnel under the River Thames at London, which was begun in 1825, and finished in 1841. In 1869 Peter William Barlow used an iron lining in connection with a shield in driving the second tunnel under the Thames at London. From these inventions has grown up one of the most notable systems of tunneling now practiced, which is commonly known as the shield system.

In closing this brief review of the development of modern methods of tunneling, to the presentation of which the remainder of this book is devoted, mention should be made of a form of motive power which promises many opportunities for development in tunnel construction. Electricity has long been employed for blasting and illuminating purposes in tunnel work. It remains to be extended to other uses. For hauling and for operating certain classes of hoisting and excavating machinery it is one of the most convenient forms of power available to the engineer. Its successful application to rock-drills is another promising field. For operating ventilating fans it promises unusual usefulness.

TUNNELING

When a railway line is to be carried across a range of mountains or hills, the first question which arises is whether it is better to construct a tunnel or to make such a détour as will enable the obstruction to be passed with ordinary surface construction. The answer to this question depends upon the comparative cost of construction and maintenance, and upon the relative commercial and structural advantages and disadvantages of the two methods. In favor of the open road there are its smaller cost and the decreased time required in its construction. These mean that less capital will be required, and that the road will sooner be able to earn something for its builders. Against the open road there are: its greater length and consequently its heavier running expenses; the greater amount of rolling-stock required to operate it; the heavy expense of maintaining a mountain road; and the necessity of employing larger locomotives, with the increased expenses which they entail. In favor of the tunnel there are: the shortening of the road, with the consequent decrease in the operating expenses and amount of rolling-stock required; the smaller costof maintenance, owing to the protection of the track from snow and rain and other natural influences causing deterioration; and the decreased cost of hauling due to the lighter grades. Against the tunnel, there are its enormous cost as compared with an open road and the great length of time required to construct it.

To determine in any particular case whether a tunnel or an open road is best, requires a careful integration of all the factors mentioned. It may be asserted in a general way, however, that the enormous advance made in the art of tunnel building has done much to lessen the strength of the principal objections to tunnels, namely, their great cost and the length of time required for their construction. Where the choice lies between a tunnel or a long détour with heavy grades it is sooner or later almost always decided in favor of a tunnel. When, however, the conditions are such that the choice lies between a tunnel or a heavy open cut with the same grades the problem of deciding between the two solutions is a more difficult one.

It is generally assumed that when the cut required will have a vertical depth exceeding 60 ft. it is less expensive to build a tunnel unless the excavated material is needed for a nearby embankment or fill. This rule is not absolute, but varies according to local conditions. For instance, in materials of rigid and unyielding character, such as rock, the practical limit to the depth of a cut goes far beyond that point at which a tunnel would be more economical according to the above rule. In soils of a yielding character, on the other hand, the very flat slope required for stability adds greatly to the cost of making a cut.

It may be noted in closing that the same rule may be employed in determining the location of the ends of the tunnel, for assuming that it is more convenient to excavate a tunnel than an open cut when the depth exceeds 60 ft., then the open cut approaches should extend into the mountain- or hill-sides only to the points where the surface is 60 ft. abovegrade, and there the tunnel should begin. If, therefore, we draw on the longitudinal profile of the tunnel a line parallel to the plane of the tracks, and 60 ft. above it, this line will cut the surface at the points where the open-cut approaches should cease and the tunnel begin. This is a rule-of-thumb determination at the best, and requires judgment in its use. Should the ground surface, for example, rise only a few feet above the 60 ft. line for any distance, it is obviously better to continue the open cut than to tunnel.

When it has been decided to build a tunnel, the first duty of the engineer is to make an accurate geological survey of the locality. From this survey the material penetrated, the form of section and kind of strutting to be used, the best form of lining to be adopted, the cost of excavation, and various other facts, are to be deduced. In small tunnels the geological knowledge of the engineer should enable him to construct a geological map of the locality, or this knowledge may be had in many cases by consulting the geological maps issued by the State or general government surveys. When, however, the tunnel is to be of great length, it may be necessary to call in the assistance of a professional geologist in order to reconstruct accurately the interior of the mountain and thereby to ascertain beforehand the different strata and materials to be excavated, thus obtaining the data for calculating both the time and cost of excavating the tunnel.

The geological survey should enable the engineer to determine, (1) the character of the material and its force of cohesion, (2) the inclination of the different strata, and (3) the presence of water.

—The character of the material through which the proposed tunnel will penetrate is best ascertained by means of diamond rock-drills. These machines bore anannular hole, and take away a core for the whole depth of the boring, thus giving a perfect geological section showing the character, succession, and exact thickness of the strata. By making such borings at different points along the center line of the projected tunnel, and comparing the relative sequence and thickness of the different strata shown by the cores, the geological formation of the mountain may be determined quite exactly. Where it is difficult or impracticable to make diamond drill borings on account of the depth of the mountain above the tunnel, or because of its inaccessibility, the engineer must resort to other methods of observation.

The present forms of mountains or hills are due to weathering, or the action of the destructive atmospheric influences upon the original material. From the manner in which the mountain or hill has resisted weathering, therefore, may be deduced in a general way both the nature and consistency of the materials of which it is composed. Thus we shall generally find mountains or hills of rounded outlines to consist of soft rocks or loose soils, while under very steep and crested mountains hard rock usually exists. To the general knowledge of the nature of its interior thus afforded by the exterior form of the mountain, the engineer must add such information as the surface outcroppings and other local evidences permit.

For the purposes of the tunnel builder we may first classify all materials as either, (1) hard rock, (2) soft rock, or (3) soft soil.

Hard rocks are those having sufficient cohesion to stand vertically when cut to any depth. Many of the primary rocks, like granite, gneiss, feldspar, and basalt, belong to this class, but others of the same group are affected by the atmosphere, moisture, and frost, which gradually disintegrate them. They are also often found interspersed with pyrites, whose well-known tendency to disintegrate upon exposure to air introduces another destructive agency. For these reasons we maydivide hard rocks into two sub-classes; viz., hard rocks unaffected by the atmosphere, and those affected by it. This distinction is chiefly important in tunneling as determining whether or not a lining will be required.

Soft rocks, as the term implies, are those in which the force of cohesion is less than in hard rocks, and which in consequence offer less resistance to attacks tending to break down their original structure. They are always affected by the atmosphere. Sandstones, laminated clay shales, mica-schists, and all schistose stones, chalk and some volcanic rocks, can be classified in this group. Soft rocks require to be supported by timbering during excavation, and need to be protected by a strong lining to exclude the air, and to support the vertical pressures, and prevent the fall of fragments.

Soft soils are composed of detrital materials, having so little cohesion that they may be excavated without the use of explosives. Tunnels excavated through these soils must be strongly timbered during excavation to support the vertical pressure and prevent caving; and they also always require a strong lining. Gravel, sand, shale, clay, quicksand, and peat are the soft soils generally encountered in the excavation of tunnels. Gravels and dry sand are the strongest and firmest; shales are very firm, but they possess the great defect of being liable to swell in the presence of water or merely by exposure to the air, to such an extent that they have been known to crush the timbering built to support them. Quicksand and peat are proverbially treacherous materials. Clays are sometimes firm and tenacious, but when laminated and in the presence of water are among the most treacherous soils. Laminated clays may be described as ordinary clays altered by chemical and mechanical agencies, and several modifications of the same structure are often found in the same locality. They are composed of laminæ of lenticular form separated by smooth surfaces and easily detached from each other. Laminated clays generally have a dark color, red, ocher or greenishblue, and are very often found alternating with strata of stiatites or calcareous material. For purposes of construction they have been divided into three varieties.

Laminated clays of the first variety are those which alternate with calcareous strata and are not so greatly altered as to lose their original stratification. Laminated clays of the second variety are those in which the calcareous strata are broken and reduced to small pieces, but in which the former structure is not completely destroyed; the clay is not reduced to a humid state. Laminated clays of the third variety are those in which the clay by the force of continued disturbance, and in the presence of water, has become plastic. Laminated clays are very treacherous soils; quicksand and peat may be classed, as regards their treacherous nature, among the laminated clays of the third variety.

—Knowing the inclination of the strata, or the angle which they make with the horizon, it is easy to determine where they intersect the vertical plane of the tunnel passing through the center line, thus giving to a certain extent a knowledge of the different strata which will be met in the excavation. On the inclination of the strata depend: (1) The cost of the excavation; the blasting, for instance, will be more efficient if the rocks are attacked perpendicular to the stratification; (2) The character of the timbering or strutting; the tendency of the rock to fall is greater if the strata are horizontal than if they are vertical; (3) The character and thickness of the lining; horizontal strata are in the weakest position to resist the vertical pressure from the load above when deprived of the supporting rock below, while vertical strata, when penetrated, act as a sort of arch to support the pressure of the load above. The foregoing remarks apply only to hard or soft rock materials.

In detrital formations the inclination of the strata is an important consideration, because of the unsymmetrical pressures developed. In excavating a tunnel through soft soilwhose strata are inclined at 30° to the horizon, for instance, the tunnel will cut these strata at an angle of 30°. By the excavation the natural equilibrium of the soil is disturbed, and while the earth tends to fall and settle on both sides at an angle depending upon the friction and cohesion of the material, this angle will be much greater on one side than on the other because of the inclination of the strata; and hence the prism of falling earth on one side is greater than on the other, and consequently the pressures are different, or in other words, they are unsymmetrical. These unsymmetrical pressures are usually easily taken care of as far as the lining is concerned, but they may cause serious cave-ins and badly distort the strutting. Caving-in during excavation may be prevented by cutting the materials according to their natural slope; but the distortion of the strutting is a more serious problem to handle, and one which oftentimes requires the utmost vigilance and care to prevent serious trouble.

—An idea of the likelihood of finding water in the tunnel may be obtained by studying the hydrographic basin of the locality. From it the source and direction of the springs, creeks, ravines, etc., can be traced, and from the geological map it can be seen where the strata bearing these waters meet the center line. Not only ought the surface water to be attentively studied, but underground springs, which are frequently encountered in the excavation of tunnels, require careful attention. Both the surface and underground waters follow the pervious strata, and are diverted by impervious strata. Rocks generally may be classed as impervious; but they contain crevices and faults, which often allow water to pass through them; and it is, therefore, not uncommon to encounter large quantities of water in excavating tunnels through rock. As a rule, water will be found under high mountains, which comes from the melted ice and snow percolating through the rock crevices.

Some detrital soils, like gravel and sand, are pervious, andothers, like clay and shale, are impervious. Detrital soils lying above clay are almost certain to carry water just above the clay stratum. In tunnel work, therefore, when the excavation keeps well within the clay stratum, little trouble is likely to be had from water; should, however, the excavation cut the clay surface and enter the pervious material above, water is quite certain to be encountered. The quantity of water encountered in any case depends upon the presence of high mountains near by, and upon other circumstances which will attract the attention of the engineer.

A knowledge of the pressure of the water is desirable. This may be obtained by observing closely its source and the character of the strata through which it passes. Water coming to the excavation through rock crevices will lose little of its pressure by friction, while that which has passed some distance through sand will have lost a great deal of its pressure by friction. Water bearing sand, and, in fact, any water bearing detrital material, has its fluidity increased by water pressure; and when this reaches the point where flow results, trouble ensues. The streams of water met in the construction of the St. Gothard tunnel had sufficient pressure to carry away timber and materials.

Tunnels may be either curvilinear or rectilinear, but the latter form is the more common. In either case the first task of the engineer, after the ends of the tunnel have been definitely fixed, is to locate the center line exactly. This is done on the surface of the ground; and its purpose is to find the exact length of the tunnel, and to furnish a reference line by which the excavation is directed.

—In short tunnels the center line may be accurately enough located for all practical purposes by means of a common theodolite. The work is performed on a calm, clear day, so as to have the instrument and observations subjected to as little atmospheric disturbance as possible. Wooden stakes are employed to mark the various located points of the center line temporarily. The observations are usually repeated once at least to check the errors, and the stakes are altered as the corrections dictate; and after the line is finally decided to be correctly fixed, they are replaced by permanent monuments of stone accurately marked. The method of checking the observations is described by Mr. W. D. Haskoll[2]as follows:

“Let the theodolite be carefully set up over one of the stakes, with the nail driven into it, selecting one that will command the best position so as to range backwards and forwards over the whole length of line, and also obtain a view of the two distant points that range with the center line; this being done,let the centers of every stake ... be carefully verified. If this be carefully done, and the centers be found correct, and thoroughly in one visual line as seen through the telescope, there will be no fear but that a perfectly straight line has been obtained.”

[2]“Practical Tunneling,” by F. W. Simms.

Fig. 1.—Diagram Showing Manner of Lining in Rectilinear Tunnels.

The center line which has thus been located on the ground surface has to be transposed to the inside of the tunnel to direct the excavation. To do this letAandBbe the entrances andaandbbe the two distinct fixed points which have been ranged in with the center line located on the ground surface over the hillA f B,Fig. 1. The instrument is set up atV, any point on the lineA aproduced, and a bearing secured by observation on the center line marked on the surface. This bearing is then carried into the tunnel by plunging the telescope, and setting pegs in the roof of the heading. Lamps hung from these pegs furnish the necessary sighting points. This same operation is repeated on the opposite side of the hill to direct the excavation from that end of the tunnel. These operations serve to locate only the first few points inside the tunnel. As the excavation penetrates farther into the hill, it becomes impossible to continue to locate the line from the outside point, and the line has to be run from the points marked on the roof of the heading. Great accuracy is required in all these observations, since a very small error at the beginning becomes greater and greater as the excavation advances. To facilitate the accurate location of points on the roof of the tunnel, a simple device was designed by Mr. Beverley R. Value, shown inFig. 2. Two iron spikes, each having a small hole in the flat end, are driven into the rock about 9 ins. apart. A brass bar, 1 in. high,1⁄4in. thick and 10 ins. long, having a hole near one end and a 1 in. slot at the other, is screwed tightly intothe head of the spikes. The middle part of the bar is divided into inches and tenths of an inch. A separate brass hanger is fitted to the bar, having a vernier with its zero at the middle of the hanger and corresponding to a plumb line attached below. The hanger is moved back and forth until it coincides with the line of sight of the transit, and then the readings of the vernier are recorded. Any time that the hanger is placed on the bar and the vernier marks the same reading, the plumb line will indicate the center line of the tunnel. When, instead of one bar, two are inserted at a distance of 20 or 30 ft. apart, the plumb lines suspended from the hangers will represent the vertical plane passing through the axis of the tunnel in coincidence with the one staked out on the surface ground.

Fig. 2.—B. R. Value’s Device for Locating the Center Line Inside of a Tunnel.

The location of the center line of a long tunnel, which is to be excavated under high mountains, is a very difficult operation, and the engineers usually leave this part of the work to astronomers, who fix the stations from which the engineers direct the work of construction. The center lines of all the great Alpine tunnels were located by astronomers who used instruments of large size. Thus, in ranging the center line of the St. Gothard tunnel, the theodolite used had an object glass eight inches in diameter.[3]Instead of the ordinary mounting a masonry pedestal with a perfectly level top is employed to support the instrument during the observations. The location is made by means of triangulation. The various operations must be performed with the greatest accuracy, and repeated several times in such a way as to reduce the errors to a minimum, sincethe final meeting of the headings depends upon their elimination.

[3]See also the Simplon Tunnel,Chapter X.

Fig. 3.—Triangulation System for Establishing the Center Line of the St. Gothard Tunnel.

The St. Gothard tunnel furnishes perhaps the best illustration of careful work in locating the center line of long rectilinear tunnels of any tunnel ever built. The length of this tunnel is 9.25 miles, and the height of the mountain above it is very great. The center line was located by triangulation by two different astronomers using different sets of triangles, and working at different times. The set or system of triangles used by Dr. Koppe, one of the observers, is shown byFig. 3; it consists of very large and quite small triangles combined, the latter being required because the entrances both at Airolo and Goeschenen were so low as to permit only of a short sight being taken. The apices of the triangles were located by means of the contour maps of the Swiss Alpine Club. Each angle was read ten times, the instrument was collimated four times for each reading, and was afterwards turned off 5° or 10° to avoid errors of graduation. The average of the errors in reading was about one second of arc. The triangulation was compensated according to the method of least squares. The probable error in the fixed direction was calculated to be 0.8″ of arc at Goeschenen and 0.7″ of arc at Airolo. From this it was assumed that the probable deviation from the true center would be about two inches at the middle of the tunnel, but when theheadings finally met this deviation was found to reach eleven inches.

Comparatively few tunnels are driven by working from the entrances alone, the excavation being usually prosecuted at several points at once by means of shafts. In these cases, in order to direct the excavation correctly, it is necessary to fix the center line on the bottom of the shaft. This is accomplished in two ways,—one being employed when the shaft is located directly over the center line, and the other when the shaft is located to one side of the center line.

When the shaft is located on the center line two small pillars are placed on opposite edges of the shaft and collimating with the center line as shown byFig. 4. On these two pillars the points corresponding to the center line are correctly marked, and connected by a wire stretched between them. To this wire two plumb bobs are fastened as far apart as possible. These plumb bobs mark two points on the center line at the bottom of the shaft, and from them the line is extended into the headings as the work advances. In these operations, heavy plumb bobs are used. In the New York subway plumb bobs of steel, weighing 25 lbs. each, were used, and to prevent rotation they were made with cross-sections, in the shape of a Greek cross, and were sunk in buckets filled with water. Owing to the difference between the temperature at the top and that at the bottom of the shaft, strong currents of air are produced, which keep in constant oscillation the wires to which the bobs are suspended.

Fig. 4.—Method of Transferring the Center Line down Center Shafts.

To determine the center line at the bottom of the shaft, the headings are first driven from both sides of the shaft, after whicha transit is set up on the same alignment with the two wires, and this will indicate the vertical plane passing through the axis of construction. Two points are then fixed on the roof of the tunnel in continuation of this vertical plane. When the plumb bobs are removed from the shaft and two small plumb bobs are suspended to the two points mentioned, they will always give the same vertical plane passing through the axis of construction transferred from the surface.

Because of the continuous moving of the wires, the fixing of the points on the roof of the tunnel is very troublesome, and the operation should be repeated by different men at different times before the points are permanently fixed.

Fig. 5.—Method of Transferring the Center Line down Side Shafts.

When the shaft is placed at one side of the tunnel the pillars or bench marks are placed normal to the center line on the edges of the shaft as shown byFig. 5. Between the pointsAandBa wire is stretched, and from it two plumb bobs are suspended, as described in the preceding case; these plumb bobs establish a vertical plane normal to the axis of the tunnel. The excavation of the side tunnel is carried along the lineBWuntil it intersects the line of the main tunnel, whose center line is determined by measuring off underground a distance equal to the distanceBOon the surface. By setting the instrument over the underground pointO, and turning off a right angle from the lineBO, the center line of the tunnel is extended into the headings.

—There are various methods of locating the center lines of curvilinear tunnels, but the method of tangent offsets is the one most commonly employed.

At the beginning the excavation is conducted as closely asmay be to the line of the curve, and as soon as it has progressed far enough the tangentAT,Fig. 6, is ranged out. AtBa point is located over which to set the instrument, and the distanceABis measured for the purpose of finding the ordinate of the right angle triangleOAB. NowOA=r,AB=d, and φ = angleABO. Then: Tang. φ =rd.

Fig. 6.—Method of Laying Out the Center Line of Curvilinear Tunnels.

Doubling the value of φ and making the angleABC= 2 φ, the lineBCwill be fixed and the pointClocated by takingAB=BC. OnBCthe ordinates are laid off to locate the curve. ProlongCBso thatCD=CB. Then the portion of the curveCFis symmetrical withCE, and the ordinates used to locateECmay be employed to locateCF, by laying them off in the reverse order.

In curvilinear tunnels several cases may be considered.

(1) When the tunnel for almost its entire length is driven on a tangent with a curve at each end.

(2) When the tunnel begins with a curve and ends with a straight line.

(3) When the whole tunnel is in curve from portal to portal.

(4) The helicoidal or corkscrew tunnel.

(1) The axis of every one of the great Alpine tunnels is a straight line, with a curve at each end. To range out the center line of one of these long tunnels from a curve, no matter how accurately laid out, will certainly cause an error, which, magnified with the distance, may produce serious results. To avoid theseinconveniences, the determination of the axis of the tunnel should be made from a straight line. This means that the tunnel is at first excavated on a straight line for its entire length and after the headings driven from both portals have met, the two portions of the tunnel or curve are excavated and constructed. The portions of the tunnel excavated on straight lines for conveniences of construction may then be abandoned or used in cases of accidents or repairs.

When the axis of a short tunnel has a curve at each end and a straight line in the middle, it is driven directly from the entrances; first, however, excavating the curvilinear portions of the tunnel. In such a case it would be advisable to proceed in the following manner. Drive the headings on the curvilinear portions of the tunnel, staking out the center line by means of the offsets from the tangents. At the ends of the curves lay out from both fronts the rectilineal portion of the tunnel. Only very narrow headings should be excavated at first while the whole section could be enlarged near the entrances. The excavation of the headings at the front should advance very rapidly, in order that the headings may meet in the shortest possible time. When communication is established, it is comparatively easy to correct an error resulting from driving the tunnel from the curves.

(2) When a tunnel begins with a curve and ends with a straight line, the work of excavation should proceed from both ends. From the straight end of the tunnel only the heading should be driven, while from the curvilinear end the whole section could be opened at once. By this arrangement the excavation progresses slowly from the curvilinear end and rapidly from the straight end of the tunnel. Once communication has been established and any error corrected, the work of enlarging the profile of the tunnel may be pushed with the same activity from both ends.

(3) When the center line of the entire tunnel is a curve, there is more probability of slight deviations from the true axis of the proposed work. In such a case it would be advisable tofirst excavate a narrow heading and to concentrate all the efforts in driving the headings as rapidly as possible in order that they may meet in the shortest time. The center line of these headings is staked out by the usual method of the offsets from the tangent. The enlarging of the section of the tunnel could be commenced at both portals and be driven slowly until the headings have met and any errors corrected, when the work could be pushed with the greatest activity all along the line.

(4) In corkscrew or helicoidal tunnels the entire center line is on a curve. In these tunnels, as a rule, there is a great difference of level between the two portals, one being much higher than the other, so careful attention should be paid to the tunnel grade. Working in the limited spaces afforded by narrow headings it is very probable that errors may be made in fixing both the alignment and the grade of the tunnel. To prevent these almost unavoidable errors, it would be well to excavate at first only the headings, to stake the center line in the roof of these headings and then to lay the grade of the tunnel as accurately as possible. The work on the headings should be pushed as rapidly as possible in order that they may meet quickly, so that the center line, as temporarily laid out, may be corrected and permanently fixed for the direction of successive operations. In these tunnels the headings should be excavated near the center of the tunnel cross-section so that the sides and roof of the heading would be at some distance from the sides and roof of the proposed tunnel. This arrangement will easily permit corrections to be made in case any slight difference from the true line was erroneously made during the excavation of the headings.

In deciding upon the sectional profile of a tunnel two factors have to be taken into consideration: (1) The form of section best suited to the conditions, and (2) the interior dimensions of this section.

—The form of the sectional profile of a tunnel should be such that the lining is of the best form to resist the pressures exerted by the unsupported walls of the tunnel excavation, and these vary with the character of the material penetrated. These pressures are both vertical and lateral in direction; the roof, deprived of support by the excavation, tends to fall, and the opposite sides for the same reason tend to slide inward along a plane more or less inclined, depending upon the friction and cohesion of the material. In some rocks the cohesion is so great that they will stand vertically, while it may be very small in loose earth which slides along a plane whose inclination is directly proportional to the cohesion.

From the theory of resistance of profiles we know that the resistance of a line to exterior normal forces is directly proportional to its degree of curvature, and consequently inversely proportional to the radius of the curve. Hence the sectional profile of a tunnel excavated through hard rock, where there are no lateral pressures owing to the great cohesion of the material, and having to resist only the vertical pressure, should be designed to offer the greatest resistance at its highest point, and the curve must, therefore, be sharper there, and may decrease toward the base. In quicksand, mud, or other material practically without cohesion, the pressures will all be normal to the line of the profile, and a circular section is the one best suited to resist them. These theoretical considerations have been proved correct by actual experience, and they may be employed to determine in a general way the form of section to be adopted. Applying them to very hard rock, they give us a section with an arched roof and vertical side walls. In softer materials they give us an elliptical section with its major axis vertical, and in very soft quicksands and mud they give us the circular section. These three forms of cross-section and their modifications are the ones commonly employed for tunnels. An important exception to this general practice, however, is met with in some of the city underground rapid-transit railwaysbuilt of late years, where a rectangular or box section is employed. These tunnels are usually of small depth, so that the vertical pressures are comparatively light, and the bending strains, which they exert upon the flat roof, are provided for by employing steel girders to form the roof lining.

Fig. 7.—Diagram of Polycentric Sectional Profile.

From what has been said it will be seen that it is impossible to establish a standard sectional profile to suit all conditions. The best one for the majority of conditions, and the one most commonly employed, is a polycentric figure in which the number of centers and the length of the radii are fixed by the engineer to meet the particular conditions which exist. In a general way this form of center may be considered as composed of two parts symmetrical in respect to the vertical axis.Fig. 7shows such a profile, in whichDHis the vertical axis. The section is unsymmetrical in respect to the horizontal axisGE. The upper part forming the roof arch is usually a semi-circle or semi-oval, while the lower part, comprising the side walls and invert of floor, varies greatly in outline. Sometimes the side walls are vertical and the invert is omitted, as shown byFig. 8; and sometimes the side walls are inclined, with their bottoms braced apart by the invert, as shown byFig. 9. In more treacherous soils the side walls are curved, and are connected by small curved sections to the invert, as shown byFig. 10. In the last example the side walls are commonly called skewbacks, and the lower part of the section is a polycentric figure like the upper part, but dissimilar in form.

In a tunnel section whose profile is composed entirely of arcs the following conditions are essential: The centers of thespringer arcsGaandEa′,Fig. 7, must be located on the lineGE; the center of the roof arcbDb′must be located on the axisHD; the total number of centers must be an odd number; the radii of the succeeding arcs fromGtowardDandEtowardDmust decrease in length, and finally the sum of the angles subtended by the several arcs must equal 180°.

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