Settlements above tunnels in the United Kingdom – their magnitude and prediction

Settlements can be a problem with soft ground tunnelling in urban areas where buildings, both modern and ancient, can be put at risk, services, too, can be endangered and at times it has been deemed necessary to divert services before tunnelling is begun. These environmental considerations have led to a considerable research effort being devoted to the study of settlements caused by tunnelling through soft ground; much of the research work has been undertaken either directly by or under contract for the Transport and Road Research Laboratory. Measurements of settlement and ground movement made on tunnelling projects located, in the main, in built-up areas are reviewed. The ground conditions studied included stiff-fissured clays, glacial deposits and recently deposited silty clays, as well as cohesionless soils of low density, weak rocks and made ground.

Many of the tunnels were driven in free air by use of shields, but compressed air was used in the weaker soils to maintain stability; the bentonite shield and chemical treatment of the ground were also used in loose sands. The data from these case studies are used to provide simple analytical tools that enable better prediction of the magnitude of settlements and ground movements caused by tunnelling through soft ground to be made.

One of the three basic requirements for the design of a satisfactory tunnel [1] [2] is that its construction should cause as little damage as possible to overlying or adjacent existing structures and services. With soft-ground tunnelling settlement is often a problem in built-up areas, where buildings, old and new, important or otherwise, can be put at mains and sewers can be endangered and it has occasionally been deemed prudent to carry out considerable service diversion and relocation works as a prelude to tunnelling.

To minimise overall project costs and the risk of damage or accident as a result of tunnel construction the engineer who designs the tunnel needs to be able to make reliable predictions of the extent and amount of settlement that are likely to arise from tunnelling in various conditions. Given reliable forecasts of ground deformations he would be in a position to choose between a number of options, that, depending on the particular location, might include:

1. Relocation of the tunnel well clear of sensitive structures

2. A longer tunnel in better ground

3. Chemical stabilisation or freezing of weak ground on the more direct route

4. Underpinning of existing buildings and relocation of water and gas mains

Such considerations and a growing emphasis on environmental problems led to a considerable research effort being devoted

during the 1970s, both in the United Kingdom ad abroad, to the study of the settlements and ground deformations caused by driving tunnels in soft ground. Much of this research in the United Kingdom was undertaken either directly by, or under contract for, the Transport and Road Research Laboratory, and the results obtained on some individual schemes and groups of schemes have already been reported [3-13]. At the same time a programme of centrifuge and static model tests was being carried out at Cambridge University to obtain a better understanding of the response of the ground to tunnelling [14-17]. In this paper summarised data from all the tunnel sites studied have been assembled and analysed so that the designers and constructor of tunnels are better equipped to make predictions of the settlements and ground deformations that result from tunnelling.

Pattern of ground

Movement

Ground movements above tunnels may conveniently be considered under two headings. The first, surface settlement, may adequately be described by assigning a particular geometrical form to the settlement profile and using case history data to predict its magnitude. Secondly, the horizontal component of surface ground movement and generalised subsurface ground displacements are less easily dealt with, as further assumptions are required to define the nature of the deformations. The lack of reliable case history data – as exist for surface settlements – and the different behaviour of cohesive and cohesionless soils make prediction of these movements somewhat speculative. As surface horizontal and subsurface ground movement will, however, often be of considerable interest, an attempt is made to determine the form of these displacements, particularly in the vicinity of the ground surface.

Surface settlement

Considering only vertical ground displacement at the surface, it is now well established an accepted that the shape of the settlement trough above a tunnel may be reasonably represented by an error function curve of the form:

Where S is the surface settlement at a transverse distance y from the tunnel centre line Smax is the maximum settlement (at y = 0) and i is the standard deviation of the curve. The value of i provides a means of defining the width of the trough and corresponds to the value of y at the point of inflexion of the curve; for practical purposes the width of the trough can be taken as 6i. This formulation was put forward by Martos [18] and was based on statistical evaluation of field observations of settlements above tabular mine openings. Other authors, notably Schmidt [19] and Peck [1], have shown that this approach adequately models the shape of the settlement trough caused by tunnelling in soft ground. On site it is usually more convenient to measure settlement, although it is the angular distortions that result from differential settlement that are of greatest interest with regard to potential damage to overlying structures and installations.

Equations for the ground slope and curvature may be readily derived by differentiation of equation one, and the settlement volume, Vs, per unit advance is obtained by integration:

Horizontal and subsurface

Displacements

The above description of the shape of the surface settlement trough gives no indication of horizontal ground movement or of the changing width of the subsurface settlement profile as the soil particles migrate toward the area of ground loss in the vicinity of the tunnel. As differing mechanisms are likely to apply, the problem is best considered separately for cohesive or clay soils and for cohesionless sands and gravels.

Cohesive soils

In addition to the assumption that the settlement trough takes the form of an error function curve, the following analysis assumes that all particulate movements in the soil occur along radial paths toward the tunnel axis and that conditions of plane strain constant volume deformation apply.

Support from field measurements for the radial flow postulate is limited by lack of below ground deformation measurements, but the data that do exist do not conflict with such an assumption. The most convincing evidence in support is provided by the results of the centrifuge tests on model tunnels in soft clay reported by Mair [20] (see Figure 2). The information available tends to suggest that the flow is directed towards a ‘sink’, which is located at a point somewhat below axis level of the tunnel perhaps close to invert level. Such variation in location of the sink is not, however, of significance in consideration of deformations towards the surface well away from the tunnel.

The adoption of radial flow assumption means that the width of the zone of deformed ground decreases linearly with depth below the ground surface. This results in the magnitude of the ground movements increasing linearly with depth below the surface to conform with the plane strain constant volume postulate:

where iz is the standard deviation (trough width parameter) at height z above tunnel axis and K is an empirical constant of proportionality. It also follows that

where H(y,z) and S(y,z) are, respectively, the horizontal and vertical components of soil displacement at a transverse distance y and a vertical distance z from the tunnel axis. Glossop’s [21] stochastic analysis of subsurface movements around tunnels gives a result identical to equation seven, as does Martos [18] for horizontal surface displacements above tubular openings.

From equations one, three, six and seven, the generalised displacements are given by

(note that ( v = - H, which satisfies the conditions of plane strain constant volume deformation). These equations are not applicable in the region close to the tunnel – say, within about a diameter of the periphery – because of the simplifying assumptions in their derivation.

Granular soils

The analysis given above for cohesive soils is unlikely to be applicable to granular soils as the assumption that particle displacements away from the tunnel are directed toward the tunnel axis is not supported by laboratory studies. Further, the assumption of deformation at constant volume is untenable as some dilation or compaction of granular soils is almost inevitable during deformation. Again, data from the field are limited and inconclusive. Independent model studies reported by Potts [22] and Cording et al [23] indicate a rapid narrowing with large inward displacements of the settlement trough near the ground surface with the sand soils funneling down into the void created by the excavation (see Figure 3). This settlement mode was discussed by Atkinson and coworkers [24] in terms of a dilating wedge over the tunnel crown, which develops until collapse occurs on surfaces that propagate vertically upwards from the tunnel haunches.

This type of ground movement has been noted in the field and, when associated with vertical ground strains in excess of 0.5 per cent, leads to a deep and narrow settlement trough with high horizontal surface strains that may not always be accurately approximated by an error function curve [25].

Field measurements

Both the strength of the ground and the method of tunnel construction can affect the distribution and amount of settlement that result from the driving of a tunnel. And, although the grosser effects of soil resistance to deformation at the tunnel collapse condition can be dealt with quantitatively, the construction method adopted and in particular, the rate of advance of the tunnel opening and the application of support can clearly influence the amount of settlement.

The approach adopted in the field investigations was to identify and monitor a number of tunnel construction projects that were located in a range of soft ground formations representative of conditions in the more populous built-up areas of the United Kingdom. Such a collection of case history data would provide, in the first instance, the quantitative information from which estimates might be made on the basis of experience of the likely extent and amount of settlement that result from new tunnelling in similar ground conditions. It would subsequently provide the basic field data on which more rational – less empirical – approaches could be tried and tested.

Stiff fissured clays

The construction of the Victoria Line of the London Underground provided a great deal of data on vertical settlement over tunnels in London Clay during the late 1960s [26]. Further, more detailed studies were carried out at Green Park [3] and Regents Park [5] during the construction of the Jubilee Line, on an access tunnel near Kings Cross Station [13] and on a sewer at Sutton. A comprehensive study of the settlements caused to Grand Buildings during the construction of Strand Station has also been undertaken [27] and, quite recently, measurements have been made over a tunnel driven through Oxford Clay.

Cohesive glacial deposits

Settlement studies have been made at Tyneside on sewer tunnels driven in free air at Hebburn and Howden [25] and at Eldon Square Newcastle on a tunnel that is being driven for the metro.

Recent silty clay deposits

Of considerably more concern are the settlements caused when tunnelling, usually in compressed air, through recent silty clay deposits, which occur widely in coastal areas; their undrained shear strengths are typically in the 10-50kN/ m2 range. Studies in such deposits were first made at Grangemouth, where considerable further settlement was recorded subsequent to the release of compressed air [29]. Further studies have been carried out at Willington Quay [9], at Belfast [10], on the M5 near Bristol [12] and at Grimsby on tunnels driven in compressed air; a small-diameter tunnel driven in free air at Stockton-on-Tees [8] has also been studied.

Cohesionless soils

Traditionally, either compressed air or chemical treatment had been used where required in these conditions to stabilise the tunnel face and control ground movements [30].

The bentonite tunnelling process [31] has recently been developed as an alternative to these and was shown to be effective in controlling ground movements at trials at New Cross [4]. The construction of three lengths of sewer tunnel at Warrington in loose granular soils enabled ground settlements to be monitored where the above three methods have been used as well as on sections of tunnel driven in free air [11]; a hand-excavated tunnel shield driven below the water-table in sand has been monitored at Irvine [32].

Weak rock formations

Settlements have been measured over sections of tunnel driven in chalk at Chinnor [6], in Keuper Marl at Cardiff and in sandstone at Warrington [11].

Loose filled or made ground

Measurements have been made in Newcastle on a sewer tunnel driven across a valley infilled with municipal rubbish; a section of tunnel overlain by fill has also been monitored at Sutton.

Analysis of results

Data from the sites where the settlement profile normal to the direction of tunnelling was established are summarised in Tables One and Two, the former dealing with predominantly cohesive soils and the latter with granular soils; information on the excavation method and ground conditions is also included. It was found that the majority of settlement profiles could, as expected, be represented by an error function curve and values of the trough width parameter, i, and ground loss, Vs, are given for each settlement profile. The simple analysis that follows is designed to provide empirical predictions of i and Vs that together uniquely define the settlement profile.

As had been found previously [19] [33], no well-defined relations were apparent between ground losses and stability ratio [34]. This also proved to be the case when attempts were made to relate ground losses to load factor [17], which, conceptually, has the ability to make allowance for differing ground support conditions at and behind the tunnel face [16] [20] [35].

Difficulties of determining the appropriate value of the undrained shear strength of the ground mass, particularly in stiff fissured clays [36], and uncertainties in the operative P/D ratio (P is the distance from tunnel face to lining and D is excavated diameter of tunnel) values in the field were two reasons for this.

In addition, ground losses are related to the rate of tunnel advance, so in many cases equilibrium will not have been reached by the time that lining is completed.

Settlement trough width

The transverse distance from the tunnel centre line to the point of inflexion (y = i) is used to describe the width of the settlement trough and has been considered to be related both to the depth from ground surface to axis, Z, and to a lesser extent the diameter of the tunnel. Multiple linear regression analyses performed on the field data presented here, however, revealed no significant correlation between the trough width parameter, i, and tunnel diameter, although the expected strong correlation of i with tunnel depth, Z, was found. This was true for both cohesive and granular data groupings.

This finding is to some extent explained by Glossop, who carried out an analysis based on stochastic/ numerical modelling techniques [21]. The analysis showed that at distances of more than about one tunnel diameter from the periphery of the tunnel the shape of the settlement trough is not significantly dependent on the tunnel diameter and the loss of ground may be considered to occur at a point ‘sink’ located at the tunnel axis.

The two-variable regression analyses carried out on the data in Table One and Two gave the relationships:

where i and Z are in metres. Figure 4 shows the trough width parameter plotted against tunnel axis depth for both ground types. The linear relationship for cohesive soils is well defined.

The fewer data for granular soils are more scattered and reflect the often unpredictable consequences of tunnelling in such ground. The data do not suggest that any relationship between i and Z, other than linear, would be more appropriate for either ground conditions.

The linear regression lines pass close to the origin and may for most practical purposes be simplified to the form

where K = 0.5 for cohesive or 0.25 for granular soils. Further review of field data suggests that for clays K varies between 0.4 (stiff clays) and 0.7 (soft, silty clay). For granular materials above the water-table K ranges between 0.2 and 0.3.

Volume of lost ground

As has already been discussed, both ground conditions and construction method determine the ground losses that result from tunnelling. To normalise the volume of lost ground with respect to tunnel size the volume of the settlement trough at the surface, Vs, is expressed as a percentage of the tunnel volume excavated, Vexc.

Examination of Tables One and Two shows that the volume of lost ground is well related to ground conditions. In the stiff fissured London Clay ground losses for the 4m-diameter underground railway tunnels fall in the 1-2 per cent range.

Ground losses can be somewhat larger on the smaller tunnels, where the overcut annulus around the shield represents a larger proportion of the excavated cross-section; on the other hand, losses may well double over a station complex with large multiple openings [27]. Ground losses were 0.4 per cent over a 2.8m-diameter sewer tunnel in Oxford Clay.

Although there are only two examples, the volume of lost ground for tunnels driven in free air in cohesive glacial deposits appears to be marginally higher, up to 2.5 per cent, than is found in London Clay. The application of compressed air has reduced total ground losses to 1.25 per cent, of which 1 per cent had occurred by the time the compressed air was released.

Settlement occurs at tunnels driven through soft recent silty clay deposits in two distinct parts: (1) an initial portion that, as for tunnels driven in free air, commences as the tunnel approaches the measurement point and, finally, stabilises sometime after the tunnel has gone past and (2) a second phase that commences with the release of air pressure and continues often for considerable periods thereafter. The amount and extent of the settlement during the second phase may well exceed that in the initial phase and has on occasion caused considerable damage to overlying buildings, e.g. at Willington Quay the volume of ground lost was 2.6 per cent and 10.5 per cent of the tunnel volume in the initial and second phase, respectively. Ground losses of 32-42 per cent were recorded during the driving of the small-diameter tunnel at Stockton-on-Tees in such soils. In the cohesionless soils at Warrington ground loss was about 7 per cent in the tunnel driven below the water table in loose sand with Standard Penetration Test (SPT) values of 2-8, and in a tunnel driven nearby in loose gravels, following groundwater lowering, losses were 4.5 per cent. Where the bentonite tunnelling process was used ground losses were usually less than 2 per cent. On the sections of tunnel where chemical treatment was used, ground losses did not, in general, exceed 0.5 per cent, although quite damaging ground movements were caused when the chemicals were being injected from the ground surface.

Ground losses above a tunnel driven through municipal rubbish were 16 per cent, and at Sutton the volume of the settlement trough was more than doubled where the in-situ London Clay was overlain by backfilled ground. In weak sandstone [11] and in chalk [6] the volume of lost ground was similar to that found on chemically treated sands, and no movements were detected at the ground surface over a tunnel driven at depth in Keuper Marl in Cardiff.

Prediction of ground

displacements

Predictions of ground displacements may be made by substituting the appropriate values of i and Vs by use of the information discussed earlier into the appropriate equations given in the section ‘Pattern of ground movement’. The value of i may be taken from equation 14 or, where possible, related more specifically to ground conditions on site. The estimate of settlement trough volume may be based on values given in the section ‘Volume of lost ground’ and should, where possible, include an engineering appraisal that takes account of the proposed tunnelling methods and site conditions and peculiarities.

The data obtained on cohesive soils can be summarised as shown in Table 3; the values of the trough width parameter constant, K, for the recent silty clay soils allows for a considerable amount of long-term settlement, but some further movement may still take place. The results for granular soils are fewer and more variable and, as yet, there are no marked trends.

Given the uncertainty involved, calculations for design purposes should check the sensitivity of the situation to the likely range of conditions to be encountered. Estimates of the ‘best’ and ‘worst’ cases should be made to bracket the extent and depth of ground deformation – this provides a useful starting point in any assessment. It is important to realise that this predictive model can only give a general indication of the form and magnitude of the prospective settlement. In practice, unexpected ground conditions on site or difficulties of construction or poor tunnelling technique or a combination of all three could lead to significantly different ground displacements. The values suggested for i and Vs are derived from data limited as follows:

A. Tunnels with a cover of at least one diameter

B. Tunnel diameters 1-5m approximately C. Maximum depth to axis, Z of 10m for granular materials

D. Maximum depth to axis, Z of 30m for cohesive materials

Strictly, therefore, they are only applicable within these limits, but the indications are that the values would not be appreciably different for reasonable extrapolation beyond the limits of ‘B’, ‘C’ and ‘D’ above, but the limitation on cover must not be contravened. Further, the analysis given is two-dimensional and, although this may be satisfactory in the prediction of conditions subsequent to the tunnel construction, other signi_ cant ground deformations of a three-dimensional character may occur during the passing of the tunnel face [16] [20] [35]. Considerable monitoring of ground and building settlement is now routinely carried out on most tunnelling projects in urban areas. Where the extent and/or magnitude of the predicted settlement are important, consideration should be given to arranging the construction programme so that the settlement pro_ le is determined in a ‘safe’ location, e.g. under parkland, as early as possible in the project.

Such data interpreted within the framework given here enable the predictions made during the design stages to be revised so that decisions on costly underpinning or ground treatment can be made on the best available information.

CONCLUSION

The researches of the past decade have greatly improved the understanding of the settlement of the ground that results from tunnelling, and the designers and constructors of tunnels are today in a much better position to estimate and to some extent control such ground movements.

Considerable gaps in knowledge remain, however, and the amount of usable _ eld data is still quite limited; this is particularly so for subsurface deformations, especially close to the tunnel periphery, where any non-uniformity or asymmetry in the situation can be magni_ ed and exaggerated.

Clients, consulting engineers and contractors could do much to add to the store of knowledge; in many cases this would only involve marginal extensions to settlement monitoring programmes that are already undertaken. In the past data collected on ground settlements has often been less than comprehensive.

In many instances settlements above the tunnel centre line only were obtained, so the lateral extent of the disturbance and the distortions in the ground cannot be determined. The minimum requirements for settlement data to be suitable for analysis are:

1. Complete de_ nition of the settlement trough – this requires measurements of settlement to be made to a distance of 1.5 to 2.5 times the depth of the tunnel from centre line

2. Information on ground conditions, including water table levels and some indication of soil consistency, such as undrained shear strength or SPT

3. Details of tunnel size, depth, method of construction and lining

The ground deformations due to tunnelling having been estimated, their effect on nearby structures and services has to be assessed. The interactions between ground and structures can be extremely complex and only broad-brush treatments are currently available to tackle the problem [37] [38]. The problem is inherently less dif_ cult for services and the situation is further improved by research into the effects of nearby excavations on them [28] [39] [40