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.