School of the Built Environment
Setting Out Underground Works 1.
Introduction
Positional control of tunnel operations is an area in Civil Engineering where accuracy is paramount – a mistake of only a few minutes of arc in setting the heading of a tunnel can lead to a considerable discrepancy in position at the other end if the tunnel is long. Mistakes in position are very difficult to rectify and, unlike straights and curves set out on the surface, the alignment of a tunnel cannot be checked by eye or other means before it is dug. Furthermore, by their nature, tunnels present surveying problems that are usually deliberately avoided on the surface; initial control along a short sight (typically 4 to 5 metres) is extended to a tunnel hundreds of metres in length and a theodolite traverse in a tunnel is long and very thin, a poor shape by “surface” standards. Tunnel design data will specify the co-ordinates of shafts or inspection chambers (i.c.); most sewer tunnels are driven straight between each i.c., though this is less the case with large diameter main sewers, and road or rail tunnels must clearly contain curves where changes of direction are required. Construction methods will dictate what access is available for setting out, and a ground survey on the surface will have established control points along the length of the proposed tunnel. The problem for the setting-out engineer is the transfer of the surface control to the tunnel, and it is with this that these notes are concerned. 2.
Types of tunnel entry for control transfer
There are basically two types of entry to a tunnel through which control can be transferred. Road or rail tunnels must meet the surface at some point, and if tunneling is to commence at this point, then a portal entry can be utilized, as illustrated in figure 1. Here, direct transfer of control is possible by positioning the theodolite on a control point in front of the tunnel portal, sighting other control points and then turning the telescope to sight directly along the tunnel.
Theodolite
Tunnel
Surface Control Points Figure 1: Control transfer via portal entry to tunnel. Problems arise, however, when entry to the tunnel is via a shaft, the diameter of which will usually be strictly limited by considerations of space availability and cost. In this case, the baseline for the transfer is limited to the diameter of the shaft, and must be extended along the length of the tunnel. Surface Control Points
Shaft Tunnel Control
Figure 2: Control transfer via shaft entry to tunnel. Errors in tunnel heading are far more important than imprecise positioning (co-ordinates) of the shaft(s), since an error of only 1’ of arc will result in a lateral shift of the tunnel of 300mm over each kilometer driven. Such errors are difficult and expensive to rectify. 3.
Positioning of shafts
Before tunneling work commences, shafts must be driven to provide access for the equipment and personnel. These are positioned from the control survey points, usually by EDM. Control points may be some distance from the actual line of the tunnel, though they should obviously be sited as close as practical, within the constraints put upon them (inter-visibility, security, accessibility etc.). The following example shows the positioning of a shaft by offset from one of the control lines: Data will be available as follows: • bearings of proposed tunnels • bearings of control lines • co-ordinates of shaft positions • co-ordinates of control points Control survey
to D to P
T
Proposed tunnels N
C
to M
Figure 3: Setting out a shaft position by offset from a control line. The following data will be used: Line C-D N-M N-P
Bearing 39° 41′ 27″ 224° 03′ 12″ 36° 10′ 15″
Point C N
Co-ordinates 311.73 mE, 214.76 mN 394.83 mE, 280.65 mN
In order to measure the offset, point T must be located along the control line C-D. Distance C-T can be calculated with reference to Figure 4, and established using EDM set up at station C. Bearing C-N from co-ordinate differences T North = 51° 35′ 09″ Bearing C-T = Bearing C-D = 39° 41′ 27″ N Angle TCN = 51° 35′ 09″ - 39° 41′ 27″ = 11° 53′ 42″ C
Distances: CT = 103.767 m TN = 21.858 m
Figure 4: Positioning of offset from control line. The theodolite is transferred to point T, a right angle set off and distance T-N measured out. A peg can now be positioned at point N and checked carefully by another method than that used for setting out, e.g. by sighting to or from other control points and using intersection/resection. Because an excavation will soon take place at N, for the shaft, position marks must immediately be established in safe places either side of the proposed shaft, usually on the line of one of the tunnel bearings, and made sufficiently robust (e.g. cast in concrete). Accurate alignment of these marks is critical, and should be done from long sights onto control points, with several rounds of angles taken on both faces of the instrument, and the work checked thoroughly by another engineer.
to P
Orienting sighting Long sight to A
N
Surface Control Points
to M Figure 5: Establishment of alignment points across shaft position. It can be seen that it is considerably easier to establish surface alignment points before work on the shaft commences, since the theodolite can be set up directly over point N. 4.
Transfer of Horizontal Control (Bearing)
There are two methods of control transfer down a shaft; it may be performed either optically or mechanically. In addition to these methods, an independent means of orientation underground is by means of the “Gyro-theodolite”, an instrument which, as the name suggests, combines a theodolite alidade with a gyroscope which oscillates about an axis parallel to the axis of rotation of the earth, i.e. it can be made to point to True North. These are highly sophisticated and very expensive instruments, used in mining engineering but rarely in civil engineering – an example of their use in the latter was in the construction of the Channel Tunnel during which two gyro-theodolites were used to check the alignment control performed by conventional theodolites. 4.1. Optical control transfer Direct transfer of control by sighting through a theodolite can be performed if the shaft is wide and relatively shallow. Permanent control points are sited some distance from the shaft and used to transfer marks on the same alignment to stations immediately adjacent to the shaft. A theodolite is set up on one of the marks near the shaft, aligned onto the distant control point and the telescope pointed down into the shaft, allowing a new mark to be made on the base of the excavation, as shown in the diagram below: shaft
B
A
B tunnel
Plan view: Control Point
theodolite position
Section: Transfer of control from B to B′
B′
Figure 6: Optical transfer of control via a shallow shaft.
The process is then repeated with the theodolite on the other side of the shaft to transfer A down to A′. Once this has been repeated several times, on both faces of the theodolite, and checked carefully, then line A′-B′ will be on the same bearing as line A-B, and can be extended along the tunnel as required. Great care is required in the accurate control of steep sightings such as these, which are very susceptible to errors in level of the theodolite base. For further advice on how to minimize this problem, see Schofield1 chapter 4. 4.2. Mechanical transfer of control The principal method of transfer of control down shafts is by suspension of wires, usually from brackets attached to the top of the shaft lining. The diagram below shows the general arrangement: Pulley Drum Coloured wires
Surface base
Tunnel base
Tunnel base Oil/water damping
Section through shaft
Coloured wires
Surface base
Shaft
Plan view
Figure 7: Transfer of control via suspended wires. All mechanical methods of control transfer share this basic arrangement. There are different suspension methods, depending upon the mechanism and method chosen, but in general the following guidelines should be used: •
Wires should be as fine as possible and handled with extreme care to avoid kinking.
•
Weights hung on the wires should load them to about 50% of ultimate strength.
•
The weights should be suspended in drums of water or, preferably, light oil to minimize oscillation.
•
It is useful to have the wires colour coded either by using coloured wires or by tying coloured paper to them.
4.2.1. Co-planing
1
W. Schofield “Engineering Surveying” 5th Ed Butterworth 2001
Co-planing is the most straightforward method in terms of theory, though it is fiddly to perform in practice and is not suited to all wire hanging systems. It derives its name from the fact that the two wires form a perfectly vertical flat plane, whose bearing is the same at the top and the bottom. Alignment marks are made at the surface and wires hung to these marks. For this method it is therefore essential that safe access can be obtained to the top of the shaft lining and that appropriate fittings (e.g. metal plates or dogs) can be fitted to it. The method proceeds as follows: On the surface: • A station (C1 in the diagram below) is positioned on the desired alignment and the theodolite set up over it. • Angles are transferred from the surface control stations (i.e. baseline) so that the theodolite telescope is aligned along the desired bearing. Marks are made on metal plates attached to the shaft lining at either side, or metal dogs driven directly into it, precisely on the alignment. Several rounds of angles are taken, on both faces of the theodolite. • Wires are suspended from the marked plates/dogs down the shaft into damping drums. A Control B base C1 w1 w2 Angles transferred as for a Shaft Figure 8: Surface alignment of wires for co-planing Underground: • • •
The theodolite is set up at C2, usually outside the baseline along the initial drive of the tunnel, as close as possible to the line marked by the two wires, paying particular attention to the careful leveling of the tripod head. The theodolite is moved sideways across the theodolite head until both wires are in exact alignment when viewed trough the telescope. The distance through which the theodolite must be moved sideways can be estimated by sighting onto the distant wire and reading the measurement on a ruler or tape with its end held to the near wire, as in the following diagram:
Theodolite at C2 Far wire (w1)
Near wire (w2)
Required position
e1
e2
d1
Initial position
d2
Figure 9: Underground alignment of the theodolite during co-planing. From similar triangles, the distance e2 through which the theodolite has to be moved sideways can be calculated: e1 d1 •
=
e2 d2
i.e.
e2
=
e 1 d2 d1
The position of the theodolite is checked by focusing on one of the wires, aligning the cross-hairs with the wire and then re-focusing onto the other wire, at which point the second wire must also be exactly coincident with the cross-hairs.
The final alignment underground, and any transfer of bearing necessary to reach the underground base, should look like the following: Y
Underground base X
C1
Shaft Figure 10: Underground transfer of bearing using co-planing. For accurate transfer of alignment using this method, it is vital to use a carefully adjusted instrument; sideways movement of the theodolite across the flat head of the tripod must be done without upsetting the leveling of the base-plate (special attachments are available to make this easier) and the sighting (i.e. cross-hair) and focusing lenses must be in precise alignment. 4.2.2. Weisbach Triangle A more common method of control transfer, which does not require such precise alignment of the theodolite, is based upon the Weisbach triangle. Another advantage of this method is than precise alignment of the wires is not essential, so that they can be suspended from cantilever brackets or pulleys without having to ensure their precise positioning.
The Weisbach triangle consists of two very small angles and one angle close to 180º. In order to form such a triangle, the theodolite is positioned slightly off the line formed by the two wires, as below: wire w2
wire w1 β α
Figure 11. The Weisbach Triangle.
Theodolite position (S)
If the distances between the theodolite and the nearest wire, Sw1, and between the wires, w1w2, are known then the sine rule can be applied using the angles α and β:
i.e.
Sw1 sin β
=
w1w2 sin α
sin β
=
Sw1 sin α w1w2
Because α and β are small angles (i.e. sin α ≈ α in radians), we may write β
≈
Sw1 α w1w2
where α and β are in radians
and, because both α and β can be converted to seconds by multiplying by the same constant (180/π x 60 x 60), we can also write β(″)
≈
Sw1 α (″) w1w2
This is applied to a typical problem as follows: A w1
w2 β
α
S Angle ASw2
Shaft Figure 12: Use of the Weisbach triangle to calculate the bearing of the wires.
The work proceeds as follows: On the surface: • The theodolite is set up close to the line of the two wires. Angle readings are taken to the control station and the two wires, so that angles α and ASw2 can be measured. Several rounds are taken, on both faces of the theodolite. • Distances between the wires and between the theodolite station and the nearest wire are measured accurately. For highest accuracy, a steel tape is stretched in catenary. • To maximize accuracy, the following criteria should be met: o For 7-figure accuracy, α must be less than 17′. o For 6-figure accuracy, α must be less than 45′. o The distance Sw1 should be less than distance w1w2. • The whole-circle bearing of the line is calculated from the orienting sighting to the control base and the Weisbach triangle: β(″)
≈
Sw1 α(″) w1w2
WCBSw2
=
WCBSA + angle ASw2
i.e.
WCBw2S
=
WCBSw2 + 180°
and
WCBw2w1
=
WCBw2S + β
Underground: • The theodolite is set up close to the wire alignment, using the same criteria as above, and the same procedure repeated, the aim this time being to find the bearing of the sight line from the theodolite (line Tw1 in the diagram below): X w2
T γ
δ
w1
angle w1TX Shaft Figure 13: Weisbach triangle used to transfer bearing from wires to underground base. •
Angle δ is calculated from the Weisbach triangle: δ(″)
≈
Sw1 γ(″) w1w2
•
The whole-circle bearing of the sight line Tw1, and hence the line TX is calculated: WCBw1T
=
WCB w1w2 - δ
i.e.
WCBTw1
=
WCBw1T + 180°
and
WCBTX
=
WCB Tw1 + angle w1TX
Note: Extreme care should be taken when calculating angles to ensure that the correct signs for the angles β and δ are used. Always draw a diagram. 4.2.3. Transfer of centreline The methods above allow the transfer of bearing from the surface down a shaft to a tunnel. It should be clear that the process of co-planing does this directly on the centreline of the tunnel, and its position is therefore transferred directly. The Weisbach triangle, however, positions the theodolite slightly off the centreline, and the offset can be calculated simply as (Sw1 + w1w2) x β where β is expressed in radians (see figure 11) 5.
Transfer of Vertical Control (Levels)
A TBM must be established in the tunnel, and vertical distance measurements must be taken down the shaft from a TBM at the surface. This is most easily accomplished using a suspended steel tape, though it is also possible to use EDM to sight down the shaft using a mirror mounted at the top of the shaft. Taping proceeds as follows, with intermediate measuring marks being made if the shaft depth is greater than the length of the tape.
Surface datum
Steel tape: csa = A modulus = E Std. Tension = Ts
Measuring mark/datum
l
L
Weight, M Gravity, g
Figure 14: Taping down a shaft to transfer vertical control.
The properties of the tape (cross-sectional area, elastic modulus and standard tension) will be known from the manufacturer’s data. The elongation of the tape over the measuring length l can be calculated: Elongation s =
g l M + 0.5M(2L – l) – Ts AE g
Since the effect of elongation is to make the reading on the tape smaller than the true distance between the marks, the elongation is therefore added to the measured value: True distance =
l + s
Taping continues down the shaft until the tunnel TBM is reached.
