Tunneling: A Practical Treatise.

by Charles Prelini

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 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.

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[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 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 A f B, [Fig. 1]. The instrument is set up at V, 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 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 in [Fig. 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, ¹⁄₄ in. thick and 10 ins. long, having a hole near one end and a 1 in. slot at the other, is screwed tightly into the 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, since the 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 by [Fig. 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 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 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 by [Fig. 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 which a 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 by [Fig. 5]. 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 along the line BW until it intersects the line of the main tunnel, whose center line is determined by measuring off underground a distance equal to the distance BO on the surface. By setting the instrument over the underground point O, 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 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 as may be to the line of the curve, and as soon as it has progressed far enough the tangent AT, [Fig. 6], is ranged out. At B a point is located over which to set the instrument, and the distance AB is measured for the purpose of finding the ordinate of the right angle triangle OAB. Now OA = r, AB = d, and φ = angle ABO. Then: Tang. φ = rd.

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

Doubling the value of φ and making the angle ABC = 2 φ, the line BC will be fixed and the point C located by taking AB = BC. On BC the ordinates are laid off to locate the curve. Prolong CB so that CD = CB. Then the portion of the curve CF is symmetrical with CE, and the ordinates used to locate EC may be employed to locate CF, 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 these inconveniences, 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 to first 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.