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The text ONLY of the Paper is given below; but it will probably be more useful to read the .pdf file that includes illustrations and can be found in the Library.  The text is given below simply so that Google and other "crawl engines" can find the text.

This Paper was presented at "Underground Construction 2005" on 17 June 2005.

Examples of the use of Wriggle

Surveys of Tunnels

by  Robin B. Clay


When a tunnel is driven, particularly using a TBM, alignment problems can arise, and, with high-speed tunnelling, can get worse very quickly, and so need swift resolution. Changes to the alignment, where possible, are always cheaper and quicker than breaking out newly-built lining. A wriggle survey of the out-of-tolerance lining is the first step, followed by processing and analysis, followed in turn by judicious re-design of the alignment. The wriggle survey data then needs to be processed again using the new alignment, in an iterative process. This Paper presents some incidents, one from the 1960s, one from the 1980s and some more recent, so that others may learn from the experience.


Computer-aided design, Design methods and aids, Land surveying, Mathematical modelling, Rail track design, Rehabilitation reclamation and renovation, Roads and highways, Tunnels and tunnelling, Wriggle survey

Examples of the use of Wriggle Surveys of Tunnels

by Robin B. Clay,  M.SC., C.ENG., M.I.C.E.



Railways generally are quite tolerant of mis-alignments, which is just as well, because tracks historically are laid on ballast that moves under the influence of the loading imposed by trains.

One of the traditional items of maintenance has been checking and adjusting “top and line”, and for “top”, this is done by inserting (or occasionally abstracting) ballast under the tracks as necessary. For “line”, the tracks are nudged over as necessary. In the last fifty years, these tasks have been mechanised. But the first task is to establish where the rails are in relation to where they should be.

This whole procedure is fairly straight forward out in the open, but when the line is in tunnel, the situation is completely changed. This is because the cost of driving a tunnel is a function of both the perimeter of the excavation (i.e. the quantity of lining), and also a function of the cross-sectional area (i.e. the volume to be dug out). Consequently, the cost is roughly proportional to the square of the diameter, and so tunnels are usually built with as small a clearance as practicable(1). The consequence of this is that any error in alignment encroaches on the clearance, and if the tolerance is exceeded, then, strictly, the lining needs to be broken out to accommodate the alignment. This is as true for roads as it is for railways (water tunnels and sewerage tunnels are generally immune to these problems). Any experienced tunneller knows that, for all the modern aids we have to control tunnel driving, every Tunnel Boring Machine (TBM) has a mind of its own regarding alignment, and if the driving tolerances are exceeded, there is the real possibility that extra work will be required. However, it is often possible to avoid this extra work, which is both expensive and timeconsuming, by carrying out a wriggle survey, to establish the precise location of the tunnel, and follow that with detailed inspection and processing, that can lead to the development of a new design for the alignment that complies with the relevant standards and will also allow the as-built lining to be accepted. Below are given some examples, at twenty-year intervals, that indicate how some aspects have changed enormously, while the principles remain unchanged.

The Victoria Line


The Victoria Line(2) was built in the early 1960s, before the days of computers or even handheld calculators, and survey calculations were carried out using seven figure log tables, writing down every step of the calculations. Distances were measured in feet and decimal feet, but sometimes in feet, inches and fractions of an inch; angles were measured in degrees, minutes and seconds. During the construction of the first TBM drive on one Contract was from Highbury to King’s Cross, through stiff London Clay. The tunnel was 12’-2½” ID and lined with two-foot long mass-concrete segments with knuckle joints. Tunnel-driving tolerance laid down in the Specification was the usual “within an inch”, but at Tender time, the Tenderers offered to build a 14’ ID tunnel for the same price, to increase their construction tolerance. This proposal was rejected by the Client, as a close fit was required for ventilation purposes (see below). After the straight section through Highbury Station, the alignment started on a 56 chains radius clockwise curve. The Setting-out process Survey stations were established at one hundred foot centres in the crown of the tunnel at the intersection point (IP) of two tangents to the curve. Each IP comprised a screw-eye fixed into the concrete lining, with a small hole drilled vertically through the bottom part of the eye. A piece of string was threaded through this hole, with a knot above to retain it, and a weight on the other end – usually a lump of tunnel spoil – to form a plumb-line. The theodolite was placed beneath this (the weight being replaced by a plumb-bob), and a back-sight taken to the previous station. Plumb-lines were then established at twenty-foot centres, fixed on the tangent to the curve, with three in use at a time, checked against each other. The location of the TBM in plan was established by lining up two plumb-lines onto a target plate fixed to the TBM, and measuring the offset. The direction in which the TBM was facing was checked by comparing the lead at axis level of the left hand side of the TBM against the right hand side, measured from square marks inscribed on the tunnel walls perpendicular to the alignment. For level, inverted T adjustable boning rods were suspended from the tunnel roof in threes at ten-feet centres, and adjusted so that the top of the horizontal arm was in the design location. Readings were taken by sighting across the boning rods onto the target fixed to the TBM, and measuring the vertical distance from the target centre, and this was then compared with the design offset. Overhang or look-up was measured with a plumb-bob. The incident The calculations of the offsets were all carefully checked, as were the setting-out points and the measurements of the offsets to the TBM, but the HIPs (Horizontal Intersection Points) were checked only every three hundred feet, as a follow-up survey – and as luck would have it, the follw-up survey had fallen behind schedule. Thus the TBM had travelled over seven hundred feet along the curve before it was discovered that it was in the wrong place – some 7’-6” off line. It is easy to imagine the consternation that ensued. The TBM was stopped, and the length of tunnel very carefully surveyed to establish where it actually was. This survey and subsequent investigation showed that the deflection angles had been set out ten minutes less than they should have been. The error had arisen because the Contractor’s setting-out Engineer started using a new theodolite with which he was not familiar.

Figure 1: Victoria Line - As-built errors from design alignment

The wriggle survey

The tunnel cross-section was circular. The first step was to check and re-check the HIPs that had been established at 300-ft spacing. From these, the lining was surveyed at five-ring (ten foot) intervals, by setting up the theodolite under one HIP and sighting the next. Using a levelling staff held horizontally, the offset of each tunnel wall at axis level was measured, at the leading edge of the ring. Processing the wriggle survey From these offsets, the versines at each surveyed ring were calculated on a twenty-foot chord, and these versines were plotted on squared paper against chainage. The design line of these versines would have been along the zero intercept along the straight, then an inclined straight line along the transition (radius, and hence versine, proportional to distance), and a straight horizontal line (constant versine) along the circular curve (constant radius). The as-built versines formed a series of arcs (created by the offsets that were correct for a 56 chain curve) along a straight line lower than intended (created by deflection angles being too small, i.e. a larger radius curve). A best-fit line was drawn on the squared paper, and the radius of this was deduced. The process was then repeated using this radius as the design radius, to check the clearances. The results Having established the alignment of the as-built tunnel, a new curve was designed to join this new curve to the original alignment. Fortunately, the radius was very large, and the new alignment lay within the limits of deviation, and the as-built tunnel was within tolerance, so no remedial work was necessary.

Figure 2: Victoria Line - Design, As-built and New Alignments (feet)

An intermediate curve was then introduced to get the TBM back to the original alignment before the next obstacle, a chamber at Gibson Square that had already been built to accommodate the TBM for servicing before it completed the drive to King’s Cross.

Figure 4: Victoria Line - As-built errors from new alignment (compare with Figure 1)

From the above graph, Figure 4, it can be seen that the maximum error was changed from some 11½ feet (at the eventual worst point) to some 0.035 feet, less than half an inch, and so within tolerance. No lining needed to be modified, the only penalty was a lot of extra work for the site engineers and the design engineers.

The Hong Kong Mass Transit Railway


The Hong Kong Mass Transit Railway was constructed in phases, starting in 1975. By this time, hand-held calculators were commonplace, although still quite large. Desktop computers were just starting to become available – the first IBM PC was introduced in 1980, with provision for recording onto cassette tape. Theodolites, too, had progressed, and “total stations” were available, with electronic distance measurement (EDM).


The wriggle was processed by computer, which accepted wriggle data over the telephone from surveyors on site, in the form of horizontal and vertical angles and distance, from the instrument to each of about six points disposed around the periphery of the tunnel, and checked at five-metre centres. The measuring was done by holding up to each point a wand with a 35mm dia. reflector at the end; the instrument then measured to the centre of the reflector. The computer then compared this data with the alignment, and the calculations produced profiles showing the error at each surveyed point from the design position. Later, this program was further developed by the Author to show the errors longitudinally.


One incident in particular is worthy of mention. Here, the tunnel had been constructed to form a slight trough compared with the design, i.e. the TBM had gone low, but had then been pulled up again to the correct alignment, and this trough extended over a distance of about fifty metres. The railway is operated by overhead line equipment (OLE), with electricity carried along wires suspended from the tunnel soffit, and picked up by pantographs mounted on the trains. In this incident, the trough exceeded the construction tolerance, in that the tunnel soffit encroached further into the tunnel than it should have done. Under the terms of the contract, the Contractor could have been required to dig out the tunnel lining in the crown and re-build it to the correct alignment. This would have been an expensive exercise, but more significantly would have delayed the opening of the railway. Result From inspection of the longitudinal plot, it was possible to put to the Contractor the alternative, that if he was prepared to pay for the extra cost of installing a few extra OLE support brackets (at about $6,000 each), then the tunnel could be accepted as-built. Silly question, really!

Channel Tunnel Rail Link

Phase Two of the Channel Tunnel Rail Link is mostly in tunnel. However, the trains travel at considerably higher speeds than they do in the London Underground. In a normal Tube tunnel, the train is a close fit in the tunnel, as described above. This means that the train tends to push the air ahead of it, what is called the piston effect. This shows itself in the draughts experienced by passengers waiting on the platform as the train approaches. With the CTRL high speed trains, this is not a practicable option, so the tunnels are much bigger, to allow the trains to pass through the air, the air being squeezed into the gap between the train and the tunnel walls. This means that there is much greater clearance between tunnel and train, and this allows the tunnel alignment to wander away from its designed position to a much greater extent, i.e. the construction tolerances are greatly increased. In these particular circumstances, and if nothing goes wrong, a wriggle survey may not be necessary.

Adana-Gaziantep Motorway tunnels

The motorway between Adana and Gaziantep in Southern Turkey was constructed in the 1990s. The route passes through several tunnels that were driven by drill-and-blast through rock, and supported by a structural primary lining of sprayed shotcrete, followed by a secondary lining of insitu concrete. Although the tunnel drives were not without incident(2), there were no significant alignment problems. The equipment used to check the tunnel included the latest “total stations”, and this took sightings onto reflecting studs fixed around the periphery of the tunnel to form profiles. The instrument was set up in a suitable location on a tripod at ground level, and a series of readings were taken on previous studs (to locate the instrument) and on new ones. There were no “survey stations” in the previous conventional method. For checking over/underbreak, a specialist “profiler” was used, that used a laser beam that swept a full circle around the periphery of the tunnel, recording the distance of the tunnel wall from the instrument. This machine was fully automatic; once one profile was complete, the machine moved itself on to the next location. All readings were logged and fed into a computer for detailed processing and the results could be seen on screen or printed out, in whatever format was required. A far cry from the methods used on the Victoria Line thirty years before.


Another motorway tunnel


During the construction of a recently-completed pair of two-lane motorway tunnels, some alignment problems arose despite the use of the most up-to-date equipment. The TBM had been erected inside an adit, resting on rails cast into concrete. The machine was built to cut rock that constituted most of the drive, but the shaft had been sunk in the only suitable surface location, through soft ground down to tunnel level. The first short stretch of tunnel was therefore through soft ground. The TBM was set slightly low, in anticipation of a tendency to float in the soft ground, the weight of the TBM being less than that of the removed spoil. Unfortunately, shortly after the TBM left the adit, an unexpected pocket of sand was encountered at crown level. With the tail firmly supported by the rails, with the TBM being nose-heavy, and with little resistance at the top of the cutter-head, the TBM started to tilt downwards. The alignment here, at the start of the drive, was on a 4% down gradient, a relaxation from the normal 3% maximum gradient, allowed only for the first 100 metres. As the drive progressed, the tilt became worse, and eventually reached about 7%. Finally, at the suggestion of the Author, cables were attached to the top of the TBM and anchored back to the shaft. This provided the necessary resistance, and thereafter the TBM was under control. However, the final maximum error was some 800mm low, compared with the tolerance of 75mm. Fortunately, there was sufficient clearance within the tunnel to adjust the alignment such that a 4% gradient could be wriggled through the as-built tunnel without any need to modify the primary lining. Special measures were needed, however, for the secondary lining, whose thickness was reduced in places from a nominal 225mm to only 150mm. The changes to the alignment affected not just to the vertical alignment, but to the horizontal alignment as well. In addition, due to a cross-over between the two bores, the horizontal and vertical alignments of the other tunnel also had to be re-designed to suit. Here follow three pairs of figures, in each pair, one figure “before” to the design alignment, and one figure “after” to the re-designed alignment. The figures are firstly a cross-section at the worst pinch-point in the invert, secondly a cross-section at the worst pinch-point in the crown, and thirdly longitudinal sections showing (a) Line & Level; (b) Shoulder clearances, and (c) knee clearances.

Figure 6: Ring 1 to Option 104 alignment

Figure 7: Ring 38 to Option 104 alignment

Figure 8: Ring 38 to DESIGN alignment

Figure 9: Line & Level to DESIGN alignment

Figure 10: Line and Level to Option 104 alignment

Crown Thickness is shown by a solid green line with round black blobs; this line SHOULD always be above the dotted green line at 225, and below the solid green line at 400, and MUST always be above the dotted black line at 200 (Right hand axis) Tunnel Level is shown by a Solid red line with square blobs; this line should be close to the red Zero line (Right hand axis) Shutter Level is shown by a dotted red line with round blobs; this line should be between the red Tunnel Level line and the red Zero line (Right hand axis) Tunnel Line is shown by a solid blue line with diamond blobs; this line should be close to the blue Zero line (Left hand axis) Shutter Line is shown by a dotted blue line with round blobs; this line should be between the blue Tunnel Line line and the blue Zero line (Left hand axis)

Figure 11: Shoulder clearances to DESIGN alignment

Figure 12: Shoulder clearances to Option 104 alignment Left Shoulder Clearance is shown by a dotted blue line with square blobs; this line MUST always be above the blue Zero line Left Shoulder Thickness is shown by a solid blue line with triangular blobs; this line SHOULD always be above the blue line at 225, and MUST always be above the blue line at 200. Right Shoulder Clearance is shown by a dotted red line with diamond blobs; this line MUST always be below the red Zero line Right Shoulder Thickness is shown by a solid red line with round blobs; this line SHOULD always be below the red line at 225, and MUST always be below the red line at 200.

Figure 13: Knee clearances to DESIGN alignment

Figure 14: Knee clearances to Option 104 alignment Left Knee Clearance is shown by a dotted blue line with square blobs; this line MUST always be above the blue Zero line Left Knee Thickness is shown by a solid blue line with triangular blobs; this line SHOULD always be above the blue line at 225, and MUST always be above the blue line at 200. Right Knee Clearance is shown by a dotted red line with diamond blobs; this line MUST always be below the red Zero line Right Knee Thickness is shown by a solid red line with round blobs; this line SHOULD always be below the red line at 225, and MUST always be below the red line at 200.

Incident No 2

In another incident, the TBM wandered 240mm off-line. Following a wriggle survey, a new horizontal alignment was produced that enabled tunnel-driving to continue, and the secondary lining to be completed without modification, maintaining both the minimum thickness of the secondary lining and the specified clearances.

Incident No 3

In a third incident, the TBM wandered 80mm off-line and 100mm off-level. Unfortunately, matters were exacerbated by the operator bringing the TBM back on line as rapidly as he could. This produced a kink in the as-built alignment. However, following the wriggle survey a new alignment was produced that enabled the as-built tunnel to be accepted, but the secondary lining shutter alignment had to be adjusted significantly relative to the primary lining in order to maintain clearance and concrete thickness.


The results obtained in all three incidents allowed the secondary lining to be placed without any need to break out any primary lining, thus saving a considerable amount of time and money. This was achieved by the use of wriggle survey and bespoke VBA routines written by the Author and running in MicroSoft’s Excel.


For both road and railway tunnels, where alignment and clearances are important, wriggle survey is an essential tool in the tunneller’s armoury. Equally important is the facility to process the results not just in cross-section, but longitudinally as well, and to appreciate that a re-design of the alignment should be regarded as the first option to solve any problem with clearances. It is important, too, to realise that things can always go wrong.


The Author acknowledges his debt to those organisations that have enabled him to gather the experiences outlined above. These include Sir William Halcrow & Partners, Mott, Hay & Anderson, Charles Haswell & Partners, Rail Link Engineering and the HK MTRC.


(1) Morgan and Bartlett “The Victoria Line: planning and design“ ICE Proceedings Paper 7270S Suppl. 1969 pp.377-395

(2) Clay and Takacs “Tunnel collapses - case study” Tunnelling ‘97, The Institution of Mining and Metallurgy, ISBN 1 870706 34 X 1997 

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