Tunneling: a practical treatise

Front matter

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Chapter I

PRELIMINARY CONSIDERATIONS. CHOICE BE-

TWEEN A TUNNEL AND OPEN CUT.

GEOLOGICAL SURVEYS

CHOICE BETWEEN A TUNNEL AND AN OPEN CUT

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 detour 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 cost

■of maintenance, owing to the pi-otection 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 detour 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 l)etween 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 sliould extend into the mountain- or hill-sides only to tlie points where the surface is 60 ft. above

CHOICE BETWEEN A TUNNEL AND AN OPEN CUT 3

grade, 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.

THE METHOD AND PURPOSE OF GEOLOGICAL SURVEYS

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.

Character of Material. — The character of the material through which the proposed tunnel will penetrate is best ascertained by means of diamond rock-drills. Tliese machines bore an annular 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 may

CHOICE BETWEEN A TUNNEL AND AN OPEN CUT 5

divide hard rocks into two sub-classes ; viz., hard rocks unaffected by tlid 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 whicli 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 laminae of lenticular form separated by smooth surfaces and easily detached from each other. Laminated clays generally have a dark color, red, ocher or greenish blue, 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.

Inclination of Strata 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 excavatioUo 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 soil

CHOICE BbyrWEEX A TUNNEL x\ND AN OPEN CUT T

whose 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 Avdiile the earth tends to fall and settle on both sides at an angle depending upon the friction and cohesion of thematerial, 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 theother, and consequently the pressures are different, or in other words, they are unsymmetrical. These unsym metrical 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.

Presence of Water. — An idea of the likelihood of findingwater 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 bearingthese 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 tlirough 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, winch comes from the melted ice and snow percolating thiough the rock crevices.

Some detrital soils, like gravel and sand, are pervious, and others, 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.

Chapter II. Methods Of Determining The Center

LINE AND FORMS AND DIMENSIONS OF

CROSS-SECTION.

DETERMINING THE CENTER LINE.

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 Ime 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.

Rectilinear Tunnels. — 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 * 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 ranj^e 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,

* " Practical Tunneling," by F. W. Simms.

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 vs^ill be no fear but that a perfectly straight line has been obtained.

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 let A and B be the entrances and a and b be the two distinct fixed points which have been ranged in with the center line located on the ground surface over the hill AfB, Fig. 1. The instrument is set up at F", any point on the line A a produced, 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

B"' A

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

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.

In very long tunnels excavated under high mountains more elaborate methods have to be adopted for locating the center line. The theodolites employed must be of large size ; in ranging the center line of the St. Gothard tunnel, the theodolite used had an object glass eight inches in diameter.* Instead of

* See also Simplon Tunnel, Chapter IX.

DETEKMLSIXG THE CENTEK LINE the ordinary mounting a masonry pedestal witli 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 sucii a way as to reduce the errors to a minimum, since the final meeting of the headings depends upon their elimination.

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

V.Boreh m.Stabbielh mfibbla Fig. 2. — Triangulation System for Establishing the Center Line of the St. Gothard Tunnel.

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 by Fig. 2 ; 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 coinpen-

Wire sated 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 the headings 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 accom.plished 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 by Fig. 3.

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. Compass readings are employed to check the transit lines ranged on the plumb bobs. Where there are rocks containing iron ore a miner's transit should be employed for making the compass reading.

When the shaft is placed at one side of the tunnel the

Fig. 3.— Method of Transferring the Center Line down Center Shafts.

Fig. 4 m

i

■Y

|W

Method of Transferring the Center Line down Side Shafts.

pillars or bench marks are placed normal to the center line on

the edges of the shaft as shown by Fig. 4. Between the points

A and B a 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 alono- the

line ^TF until it intersects the

line of the main tunnel, whose

center line is determined by center' -o ~I//7^

measurinor off undero-round a

distance equal to the distance

BO on the surface. By setting

the instrument over the under-ground point 0, and turning off

a right angle from the line BO^ the center line of the tunnel is

extended into the headings.

Curvilinear Tunnels. — There are various methods of locating

the center line of curvilinear tunnels, but the method of tangent offsets is the one most commonly employed. It consists in finding the length of an ordinate DC^ Fig. 5^ perpendicular to the tangent JLX, at a point D taken at a known distance AD = d from tlie point of tangent A, being the center of the arc AB and OA being the radius. Pig. 5. — Diagram From draw OZ parallel to the tangent AX^ Showing Method ^^^ producc the perpendicular DC until it in-

of Determining ^ r l

Tangent Offsets tcrsccts tlic line OZ at E. Joiu and C,

for Arcs of 90*^

or Less. From the right^angle triangle OCE^

OE = AD = d

CO = r

ED = OA = r

DC = r - EC = ij .

(1) (2)

Substituting these values in equations (1) and (2) we have, y = r — Vr' — (T.

When the arc AB is greater than a quadrant, as in Fig. 6, the projection AF of the arc becomes equal to its radius, and

for any value of d between this projection and that of the chord AK there are thus two values of ^, viz.,

Vi and both deduced from the

Fig. 6. — Diagram Showing Method of Determining Tangent Oifsets for Arcs of over 90°.

formula, y = r ± \lr^ — d?.

Assuming the value of d = AG^ to locate the point H^ GrH = y^ = r — 'slr^ — (i^ and to locate the point iai=y^=r+ \l7^ - d\ By giving to d the values between and AF^ the various values for the tangent offsets are obtained.

In staking out the center line of a curvilinear tunnel the greatest accuracy is required, since a very small error will throw the work out and cause serious trouble. At the beginning the excavation is conducted as closely as may be to the line of the curve, and as soon as it has progressed far enough the tangent AT, Fig. 7, is ranged out. At ^ a point is located over wliich to set the instrument, and the distance AB is measured for the purpose of finding the ordinate of the right angle triangle GAB. Now OA = r, AB = d, and <^ = angle AB 0. Then : Tang. r

* = 5-

Frcr. 7.

Method of Laying Out the Center Line of Curvilinear Tunnels.

Doubling the value of ^ and making the angle ABC = 2cf>, the line BC will be fixed and the point C located by taking AB = BC. On 56^ the ordinates are laid off to locate the curve. Prolong CB so that CD = CB. Then the portion of the curve CE is symmetrical with CE^ and the ordinates used to locate EC may be employed to locate (7F, by laying them off in the reverse order.

FORM AND DIMENSIONS OF CROSS-SECTION.

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.

Form of 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 hwse earth which slides along a plane whose inclination is diiectly 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 ])e designed to offer thfe greatest resistance at its highest point, and the curve must, therefore, be sharper there, and may decrease toward the ])ase. In (piicksand, 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 underground city rapid-transit railways built 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.

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. 8 shows such a profile, in which DH is the vertical axis. The section is unsymmetrical in respect to the horizontal axis GrE, The

Fio. 8. — Diagram of Polycentric Sectional Profile.

upper part forming the roof arch is usually a semi-circle or semi-oval, while the lower part, comprising the side walls and invert or floor, varies greatly in outline. Sometimes the side walls are vertical and the invert is omitted, as shown by Fig. 9 ; and sometimes the side walls are inclined, with their bottoms braced apart by the invert, as shown by Fig. 10. In more treacherous soils the side walls are curved, and are connected by small curved sections to the invert, as shown by Fig.