Robin B. Clay

 

 

LIST OF CONTENTS

1.... INTRODUCTION.......................................................................4

Scope of Services...........................................................................4

2.... Alignment Principles.................................................................4

3.... Primary Lining – Segmental Rings............................................ 6

Theory............................................................................................ 6

Deviation of the As-Built tunnel from its design position................ 7

Wriggle Survey............................................................................... 7

Wriggle Assessment....................................................................... 8

4.... Secondary lining - in-situ concrete........................................... 8

Theory............................................................................................. 8

Shutter Alignment............................................................................ 9

Design Procedure for shutter alignment......................................... 10

Final Wriggle Survey of the Secondary Lining................................. 11

5.... Re-alignment in practice........................................................................................... 12

6.... Implications of the REVISED ROUTE and Shutter alignments.... 12

7.... Tables and Longitudinal Charts................................................ 12

8.... Special Measures...................................................................... 17

9.... Departures from the Specification............................................. 17

10... Conclusions.............................................................................. 17

acknowledgements.......................................................................... 17

References........................................................................................ 17

 

 

 

Re-alignment after Wriggle can save time and money

Robin B. Clay

 

 

 

SYNOPSIS

 

When driving a tunnel, particularly using a TBM, alignment problems can arise. Changes to the alignment, where possible, are always cheaper and quicker than digging out existing lining.

 

Fine-tuning the alignment following a wriggle survey can result in small but significant changes to the alignment, sufficient to bring the As-Built lining within tolerance, and yet comply with the standards, thus resolving an otherwise very serious problem.  Computer technology now provides a very sophisticated weapon for the tunneller’s armoury.

 

This Paper discusses the challenge in general theoretical terms. Re-alignment techniques can permit a smaller (cheaper) tunnel to be built to tighter tolerances, as results obtained can usually allow construction to continue without any need to break out any primary lining, thus saving a considerable amount of time and money.

KEYWORDS

Design methods and aids, Land surveying, Mathematical modelling, Rail track design, Rehabilitation reclamation and renovation, Roads and highways, Tunnels and tunnelling

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Re-alignment after Wriggle can save time and money

Robin B. Clay

 

1       INTRODUCTION

One of the very first decisions to be made when planning a road or railway tunnel is the diameter^{1, 2}.  Driving a tunnel is expensive, and the cost is a function principally of the size of the tunnel, so anything that helps to reduce the size of the tunnel can have significant financial benefit.  Wriggle is one such factor^3.

For all the modern aids we have to control tunnel driving, every Tunnel Boring Machine (TBM) has a mind of its own regarding alignment, particularly at the very start of tunnel driving.  If the tunnel is as small as possible, to reduce the cost, then the tolerances will need to be tight.  Providing extra tolerance as "insurance" can prove to have an exorbitantly expensive "premium”.

Where a tunnel does deviate by more than the tolerance, then, in conjunction with the results of a wriggle survey of the As-Built tunnel, very careful and precise calculations can usually produce a new alignment that, possibly together with some "special measures", will comply with the requirements of the Specification but yet remain within the defined Standards, and in most cases, no digging out will be required, there will be no attributable delay to the Works, and the extra cost will be relatively low.

Scope of Services

The work involved will be :-

1.To examine the wriggle survey data received from site

2.To process it to produce a table and graphical plots showing, both cross-sectional and in plan and elevation, the clearances between the lining and critical points of the Clearance Envelope related to the design alignment (the “before” situation)

3.To define construction re-work required by the original alignment and by the provisional alignment

4.From studying the graphical plots mentioned in Step 2 above, to prepare a new alignment that will enable the Clearance Envelope to pass through the As-Built lining with sufficient clearance

5.To repeat Step 2 related to the new alignment; iterate as necessary to produce the “after” situation.

6.To define any “special measures” (required where there remains a conflict between the As-built tunnel and the Clearance Envelope) that will provide clearance to the Clearance Envelope and define the extents between which these measures must be used, defined by the new alignment.

2       Alignment Principles

The several different longitudinal “alignments” for the tunnel, all based upon the alignment of the centreline of the Route, at least originally, are –

• The Route alignment – the mathematically-defined centre-line of the top surface of the roadway, which forms the basis for the others;
• The Tunnel alignment – the centre-line of the tunnel, mathematically-derived  from the Route alignment, and makes allowance for super-elevation;

Wherever there is super-elevation, one side of the carriageway is raised higher than the other; the Clearance Envelope may or may not be symmetrical about the vertical through the centreline of the Route. In order to maintain the correct clearances between the Clearance Envelope and the internal profile of the tunnel, the centre of the tunnel has to move with the centre of the Clearance Envelope, and so the centre of the tunnel moves down and across to suit, and often the primary lining must also be rotated about its centre, see Figure 1 below :

 

Tunnel without Super-elevation

 

 

Tunnel with Super-elevation

Tunnel Centre

Height

v

Super-elevation %

h

 

						Road width

 

Route Level

Route     ¢

Route Centre

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1 - The Tunnel centre is offset from the Route centre.

 

< >The As-Built primary lining alignment, which is totally independent, and is not derived from mathematical formulae, but consists of surveyed data;The Shutter alignment, which is based upon the Route alignment, but judiciously adjusted to improve the clearances between the shutter skin and the Primary Lining on the outside and the Clearance Envelope on the inside; andThe As-Built secondary lining alignment, which is similar to the As-Built primary lining alignment, and also totally independent.Chainage, the distance along the route; Eastings, Northings and Level, the location in three dimensions (line and level);Whole Circle Bearing, the direction in plan (square);Gradient, the direction in elevation (plumb); andSuper-elevation (or Cant), the cross-fall or rotation of the road surface about the longitudinal axis (roll).Type of element to the next point – straight, circular curve or spiral, and the parameters of the curve.The Clearance Envelope, the principal profile that must not be encroached upon by any fixed structure. The Clearance Envelope is mathematically derived from the Route alignment and may change shape with super-elevation.  The theoretical Primary Lining profile, which is mathematically derived from the Tunnel alignment;The actual Primary Lining profile, which is “a fact”, and thus is totally independent. The position of the lining is established after construction by means of a Wriggle Survey, which is then processed to compare the actual position with its theoretical position and provide a schedule of errors.  This may show places where the primary lining has to be modified in order to meet the clearance criteria, or else may form a basis for a re-design of the Route alignment;In cases where there is to be a Secondary Lining, its theoretical profile, which is mathematically derived from the Shutter alignment. Run against the theoretical and the actual Primary Lining alignment and profile, this will indicate concrete thicknesses, etc.;The actual Secondary Lining profile, which also is “a fact”, and thus totally independent.  As with the primary lining, a Wriggle Survey is carried out and processed to establish the construction errors.3       Primary Lining – Segmental Rings

Theory

Generally, the primary lining installed behind a TBM consists of segments bolted together with circumferential bolts to form rings, and generally each ring is bolted to its predecessor by longitudinal bolts. Normally, the rings are not rolled relative to each other except by a complete bolt-hole position.  Theoretically, a straight tunnel could be driven using straight segments, that is, rings whose width in the longitudinal direction is the same on each side of the tunnel, and at top and bottom. 

A tunnel could be driven on a circular curve by providing tapered rings to suit the horizontal radius. However, in practice, there are transitions between straight and circular sections, and curves are of different radii.  It is therefore usual to provide tapered segments designed to suit the tightest radius, and to install them intermittently with straight rings to achieve the required horizontal radius at any location along the tunnel – a radius that varies along the transitions.  Tapered rings are cylindrical, with one of both faces at an angle to the longitudinal axis,

Deviation of the As-Built tunnel from its design position

Because the rings are straight and the tunnel is curved, the rings generally will be offset slightly from their theoretical positions.  This is exacerbated where curved rings are alternated with straight rings (see Figure 2 below), and where the rings are placed to a different radius from that being followed by the TBM.  In addition, it is rare for any TBM to follow the alignment precisely.  The rings as built will therefore rarely be in the precise theoretical position.

Figure 2 - Taper and straight Rings in curved tunnel

Wriggle Survey

As discussed above, the final as-built position of the internal face of the primary lining differs from its designed position, but it should nevertheless always fall inside the tolerance envelope.  It is essential therefore, after the ring is complete, to carry out a precise survey to establish exactly where the tunnel is, and this is called a Wriggle Survey. Wriggle data from this survey is provided as 3-D co-ordinates “in space” of discrete points around the periphery of the tunnel. The results are then compared with the design position. The result of this process is a schedule of the horizontal, vertical and radial errors of discrete points (usually at least seven or eight) around the internal profile of the tunnel, at intervals (usually five metres or less) along the tunnel. 

If a tunnel deviates from its design position by more than the tolerance, there are usually two options :–

< >the expensive and slow option is to excavate and re-build the lining to within the tolerance of the original design alignment;the cheaper and quicker option (if it is possible) is to re-design the alignment to fit the tunnel.Wriggle Assessment

The traditional method of assessing wriggle is by using versines, hand plotting and the “method of Slews”, and was used on the Victoria Line in the 1960s, but the advent of computers since then has allowed a quicker and more precise approach. An Excel spreadsheet has been developed which uses routines from a bespoke add-in library.  Together, these enable the wriggle data to be processed against any one or two selected alignments, and the results compared, and automatically plotted on charts to give a pictorial representation of the construction errors -

< >cross-sections showing the Clearance Envelope and the as-built profile at any required wriggled location, i.e. at the Leading or at the Trailing edge of any Ring; and a longitudinal “profile” showing clearances between the Clearance Envelope and the Primary Lining for defined pairs of points (e.g. for left and right Shoulders), for each ring along the tunnel.4       Secondary lining - in-situ concrete

Theory

Many tunnels – particularly water and sewerage tunnels - are provided with a secondary lining of in-situ concrete to be cast behind a straight shutter. On the tightest curve, if the front and back of the shutter are in the theoretically correct centre of the tunnel (see Figure 3 below), then the middle of the shutter will be offset towards the centre of curvature by some 25 mm (“centre throw”), so the concrete at the middle of the shutter on the outside of the curve will be that much thicker than the design thickness, while at the ends on the inside of the curve the concrete will also be the same amount thicker than the design.  On the opposite side of the tunnel, the concrete will be at its thinnest, thinner than the design by the same amount ("End Throw").  When the primary lining is off-line (which it almost always will be, as explained above), then these figures will vary.

Figure 3 - Straight shutter in curved tunnel

Shutter Alignment

In order to optimise the concrete thickness, it is necessary to consider the relative positions of the as-built segments and the Clearance Envelope, and to vary the direction and gradient of the shutter to suit.  Again, this may be complicated by niches for services, cross-passages etc., and it may even prove desirable in practice occasionally to adjust the length of the shutter. 

In order to set out the shutter, the surveyors will need an alignment schedule, giving the required position of the front (leading face) of the shutter – the back (trailing face) is either selected similarly, for the first shutter, or taken as the leading face of the previous shutter.

The optimum shutter position with reference to the Clearance Envelope should be such that the error from the design position at the middle of the shutter (“centre throw”) is the same as the error from the design position at the end of the shutter (“end throw”). However, the thickness of concrete should be checked at the leading face of each ring of primary lining, by comparing the position of the centre of the leading face of each ring (either calculated or derived from the As-Built survey) with the position of the centre of the shutter at that chainage.  This may prompt a small adjustment to the shutter position to increase the minimum concrete thickness. In particular, a small adjustment of one shutter may have a significant effect on the next shutter – a “leverage” effect – and this may be more important than adjustment to suit the present shutter.

Put very simply, the intention is that the alignment of the shutter should cross the road alignment roughly at the quarter-points along each shutter length. As the shutter lengths and the curve radii vary, then “manual” adjustment is necessary to get the optimum solution.  These complex calculations can be done using Excel and the add-in library.

Design Procedure for shutter alignment

The actions to produce the Shutter Alignment are as follows: –

< >Select a minimum acceptable concrete thickness;Assume that the centre of the face of the shutter is offset towards the outside of the curve by half the versine of the radius at the Chainage of the mid-point of the next shutter, for a chord of the length of that shutter – this balances the error, with the same amount of “throw” at the ends of the shutter and at halfway along its length – the centreline of the shutter should then be on line at about the quarter points of its length;Start from some known position and orientation of the trailing face of the current shutter – at the start of concreting, the trailing face of the first shutter, or thereafter, the leading face of the last shutter;Establish (by survey if appropriate) the position of the centre of the trailing face of the current shutter;Calculate the position of the centre of the trailing face of the next shutter, i.e. offset from the alignment centreline by the “end throw” to suit the radius at the mid-point of the next shutter;Refer to the Wriggle Survey, and for each Ring calculate the offsets between the centre of the leading face of the ring and the centre of the shutter at that Chainage – from this can be deduced the minimum concrete thickness;Shift the centre of the leading face of the shutter sideways or vertically (rotate the shutter about the centre of its trailing face) as indicated by the deductions;Check that the minimum thickness is still retained at all points (i.e. repeat from the previous step);Allowing for niches, etc., deduce the 3D co-ordinates (i.e. convert the shifts to co-ordinates) and deduce also the horizontal and vertical offsets (from the tunnel alignment) of the centre of the leading face of the shutter;Progress to the next shutter by using the position of the leading face of this new shutter as the trailing face of the next shutter, and repeat from Step 3 above. Table 1 - Shutter Alignment Schedule

 

In practice, each calculated shutter position has to be inspected “manually” and judiciously adjusted by trial-and-error, see  Table 1 above.  The cross-sections generated by the spreadsheet show the primary lining and the Clearance Envelope as before, but also show the shutter profile, and a Table is provided that gives the minimum clearance between shutter and Clearance Envelope, and the minimum thickness of secondary concrete (clearance between shutter and primary lining).

After the shutter is stripped, the exact position of the leading face should be surveyed, and this data used to establish the optimum position of the front of the next shutter.  The orientation is not important, for the orientation of that shutter is adjustable – but the position of the trailing face (which should be established) is fixed by the recently-cast concrete.

Final Wriggle Survey of the Secondary Lining

By the very fact of using a straight shutter in a curved tunnel, the final position of the shutter will constitute an encroachment into the tolerance, which must also take into account the errors in the position of the primary lining discussed in 3 above, and must also allow neither the secondary lining nor any of the services and fittings to encroach into the Clearance Envelope.  To ensure that this is the case, a final wriggle survey of the secondary lining is needed, with measurements taken at the end and centre (the locations of maximum deviation) of each bay of secondary lining, and these then need to be compared with the Clearance Envelope, to establish (a) that the clearances between them are sufficient, and (b) that there is room for each of the various fittings in their intended locations.  It may be found that at some point the combination of encroachments is such that a small re-alignment of the road is required, and it may even be the case that, even after re-alignment, it may be necessary to move a fitting rather than breaking out the lining. 

5       Re-alignment in practice

The processed wriggle will generate a Table giving the errors in Line and Level, and in the clearances at Crown, Shoulders and Knees.  From these, it is possible to decide where the worst points lie, and by how much the alignment should be nudged.  If the shoulders converge, then the alignment is descending relative to design; if the shoulders shift sideways, but parallel to each other, then the tunnel is drifting off-line. If the knees converge, then the alignment is ascending relative to design; if the knees shift sideways, but parallel to each other, then the tunnel is drifting off-line.

6       Implications of the REVISED ROUTE and Shutter alignments

Charts are generated automatically to show graphically the differences between any two alignments.

Having generated the differences between the old and new alignments, it is essential to investigate what the effects (and the extents of those effects along the tunnel) of the changes will be on the primary lining, on the secondary lining (if any), and upon the various services, walkways, drainage and fixings, as well as on any cross-passages.

7       Tables and Longitudinal Charts

Normal output shows in tabular and graphical form the results of the wriggle and the alignment of the shutters, both plotted against of the Clearance Envelope that follows the relevant alignment of the Route –

1.Cross-section at any given surveyed profile, showing, relative to the design position of the centre of the tunnel, the Clearance Envelope and the surveyed points.  Also the design position of the inner and outer faces of the secondary lining, with clearances tabulated.

Figure 4 - Cross-section

 

2.Table of clearances and concrete thicknesses, for the crown, for both knees and for both knees, at the surveyed edges of the rings. Also gives horizontal and vertical offsets of as-built tunnel and of shutter relative to the alignment.  Cells are shaded where the thickness is less than the minimum or greater than the maximum, or where the clearance is less than the tolerance. 

Table 2- Clearances and concrete thicknesses

 

3.Chart (against Chainage) of the thickness of the concrete in the crown of the tunnel, and two pairs of lines on this first Chart to represent the offsets from the alignment of the centre of the as-built tunnel and of the centre of the shutter – these lines are almost of academic interest only.

 

 

 

Figure 5- Line, Level and thickness of concrete in the crown vs. Chainage

4.Chart (against Chainage) of the clearances and concrete thicknesses obtained at the shoulders of the Clearance Envelope.

 

 

 

Figure 6 - Clearances and thickness of concrete at the shoulders vs. Chainage

 

5.Chart (against Chainage) of the clearances and concrete thicknesses obtained at the knees of the Clearance Envelope.

 

 

Figure 7 - Clearances and thickness of concrete at the knees vs. Chainage