Tunnelling in soils – ground movements, and damage tobuildings in Workington, UK
A.R. SELBY*School of Engineering, Durham University, DH1 3LE, UK
(Received 14 January 1999; accepted 20 April 1999)
Abstract. Tunnelling through soils results in ground loss, causing surface settlements and transversemovements. Where the tunnel drive passes below an existing structure, it is important to estimate theeffects upon the structure. However, the free ground deformations should not simply be imposed upon astructure, because the structure contributes to stiffening of the ground. A computational soil-structureinteraction analysis is required, to otain detailed stress–deformation response. First, linear finite elementand Lagrangian finite difference methods are used to estimate ground movements due to a tunnel in freeground, and the results are compared with values based on empirical equations. The two linear methodsand an additional hybrid FE method are then used to assess with soil-structure interaction; two cases ofa typical short wall and a long wall lying across the route of tunnels of different depths. The resultssupport the validity of the hybrid method which is used to estimate interactive ground settlements forcomparison with a reported case of tunnelling below a building in central London. A more detailed casestudy is then undertaken to assess building damage caused by gross settlements during tunnelling inmixed soils, at a site in Workington, west Cumbria. A survey allowed estimation of free groundmovements. Analysis by the hybrid method on the soils plus uncracked structures indicated intolerablehorizontal stresses. Re-analysis with major cracks introduced into the structures resulted in close agree-ment between measured and computed settlements.
Tunnelling in soils generally results in ground losses due to face relaxation, radialtake as the soil tightens around the permanent liner behind the shield, and ovalling ofthe excavation due to steering manoeuvres. Free ground surface settlements aredirectly proportional to ground losses, which are a function of soil type and oftunnelling method.
Ground losses
When tunnelling is undertaken in clay soils by the traditional open face shieldmethod, the in situ soil stresses normal to the excavation face reduce to zero. The soil
* To whom correspondence should be addressed at: Tel. 144–191–374 3919; fax: 144–191–374 2550;e-mail: [email protected]
face relaxes into the free space, and the basic face take is proportional to the facearea. These movements are time-dependent because of the pore water drainageelement of plastic strain, and so the face take is a function of the clay soil stiffnessand permeability, and is also inversely related to rate of advance. Cording et al.(1976) have developed empirical expressions for the face loss, which they claim tobe applicable to most soils.
A second source of ground loss arises when the shield is oversize to the permanentliner and especially when the shield has a partial or full circle bead to reduce dragduring shield advance. Ground losses from radial relaxation may be of the sameorder as the face loss (Attewell et al., 1986). Finally, other ground losses may occurresulting from steerage of the shield or due to soil drainage allowing consolidation.Typical losses in cohesive soils are 0.5%–2% of face area. Excavation of granularsoils by shield generally requires some face control by breasting doors. A free facein loose sands would collapse, with consequential large losses. Radial movementstowards the permanent liner tend to occur immediately. Ground take in granular soilsis typically larger, poorly controlled, and unpredictable. Examples range from 1% to5% or more.
Earth pressure balance machines have been developed specifically to minimizeface take in mixed soils, by using pressurized drilling muds to provide pressure onthe excavation face which matches the in situ stress. Excavation is achieved by arotating full face cutter. When working effectively, these machines allow negligibleface loss, usually less than 0.5% of face area. However, some ground disturbance isinevitable.
The new Austrian tunnelling method (NATM) was originally designed as a rapidsupport system for tunnels in rock. The method has been adapted for tunnels in claysoils, and even in cemented sands. Large excavations are made before any support isinstalled, causing ground disturbance and relaxation around the roof, floor and face.A number of schemes have been completed successfully, but there have also beenseveral catastrophic failures, notably the Heathrow Express concourse tunnel (Oliver,1994). When the method is used successfully, the ground loss may be relativelylarge, although the empirical database is still rather limited. A valuable exampleof the trial tunnel for the Heathrow Express link was reported by New andBowers (1994), in which total ground losses were measured to be 1–1.5% of tunnelface area. Additional data are given for the Lisbon Metro scheme by Malato et al.(1998).
Regardless of the tunnelling method or ground loss source, the resulting surfacesettlements and inward movements are normally of the form shown in Figure 1. Atsome distance behind the advancing face, in uniform soils in green field conditions,the fully developed settlement trough has a transverse profile in the form of a normaldistribution curve centred above the tunnel axis, described by the empirical expres-sion for settlement, w, (Attewell, 1978) as:
352 SELBY
w 5Vs
Î2p
exp(2y2 / 2i2)
i(1)
where, Vs is the ground loss at the ground surface, ‘i’ is a trough dimensionparameter, and y is the transverse distance from the tunnel axis. Vs is very much afunction of the method of tunnel excavation and rate of progress, but is typicallybetween 0.5% and 2% for tunnels in cohesive soils. Tunnels through loose granularsoils may cause much larger values of ground loss. Rankin (1987) proposed that ‘i’for tunnels in clay soils in the UK is typically 0.5 z0. According to O’Reilly and New(1982), the trough width parameter ‘i’ may be taken at the ground surface, for atunnel of depth zo, as
i 5 0.43.z0 1 1.1 m for cohesive soils, where 3 # z0 # 34 m (2a)
or
i 5 0.28.z0 2 0.1 m for granular soils, where 6 # z0 # 10 m (2b)
Additionally, the ground surface moves transversely, showing inward movementstowards the centreline. These ground movements should not be overlooked, sincethey cause a significant proportion of the distress to existing structures located within
Figure 1. Typical ground movements normal to a tunnel drive.
353TUNNELLING IN SOILS
the zone of influence. An empirical expression is given by Attewell et al. (1986) forinward movement at depth z, for a tunnel of depth z0,
v 52n
zo 2 zyw (3)
where n is generally close to 1.0, and y and w are as in equation 1. A typical set ofground surface movements is shown in Figure 2.
Figure 2. Surface movements across a transverse section normal to the drive.
354 SELBY
made for 4 m diameter tunnels at depths of 10 m, 20 m and 30 m, in uniform claysoils. They are then used to exemplify the form of interactive behaviour whentunnelling beneath either a short (16 m) wall or a very long wall of masonry locatedtransverse to the line of the drive. Another approach developed by Selby (1985) forsoil-structure behaviour, described here as a ‘hybrid FE’ method, is used which isshown to give similar interaction capability but with considerable flexibility concern-ing the modelling of narrow, deep, surface settlement troughs. The procedure usingPAFEC is in three parts:
(1) Calculate both vertical and horizontal green field ground surface movements dueto the tunnel using equations 1 and 3 with empirical values for V and i, atsufficient node points on a transverse section.
(2) Enforce these calculated nodal movements onto a plane strain FE model of theground alone. The results of this computation are the forces required at the nodesto achieve the prescribed displacement set.
(3) Construct a FE model of both ground and structure. Apply the previouslycomputed set of forces (vertical and horizontal) to this new model, to computemovements and building strains due to the tunnelling-induced movements.
The primary objective in assessing the effects of tunnelling is to make realisticestimates of stresses induced into existing structures which lie above the line of thetunnel drive.
Computation of free ground movements
Linear analyses of ground movements due to a 4 m tunnel at an axis depth of 10 mwere made using PAFEC and FLAC with the half-symmetric mesh or grid as shownin Figure 3. Uniform isotropic parameters of elastic modulus of 50 MPa and
Figure 3. FLAC finite difference grid and PAFEC Finite Element mesh.
355TUNNELLING IN SOILS
Poisson’s ratio 0.49 were chosen, which are appropriate for undrained analysis ofstiff clay. The base and the distant vertical boundary were totally restrained.
The disturbance of the mesh to represent tunnelling ground loss was achieved byapplying a uniform radial tensile stress over the tunnel surface of 200 kPa, which wassufficient to cause inward movements equivalent to a volume of 0.15 m3 m21 or 1.2%of the tunnel face area. This is characteristic of a well controlled drive in clay soils,where the total ground take is a combination of face relaxation (depending uponsupport, if any, and rate of progress), and of radial movement from the shielddiameter as excavated inwards as far as the smaller diameter final liner.
The surface settlements and inward movements from these computations areplotted in Figure 4a. Also shown are curves for hand calculations, denoted ‘NPC’,based on equations 1, 2 and 3, with values of 0.15 m3 m21 for Vs, and of 5.4 m forthe ‘i’ parameter, following the recommendation of O’Reilly and New. The exercisewas repeated for tunnel depths of 20 m and 30 m, using a similar ground loss valuebut with ‘i’ values of 9.7 m and 14 m respectively. The results for the 30 m deeptunnel are shown in Figure 4b.
Figure 4a. Surface movements transverse to 4 m diameter tunnel, 10 m deep.
356 SELBY
Observations on the sets of results in Figures 4a and 4b include the following. Thesettlements and movements are all very small, being only several millimetres. Thegeneral form of the computed surface settlements and inward movements is inagreement with the accepted pattern as shown in Figure 2. Computations of settle-ments and inward movements using FLAC and PAFEC are in fairly close agreementwith each other in all cases; the results from PAFEC are slightly larger throughout,probably because of a more compliant and concentrated mesh local to the tunnel.
While the computations are broadly in agreement with the hand calculations,identified as ‘NPC’, at a tunnel depth of 30 m, the disagreement becomes larger forthe shallow tunnel. In effect, the FE and FD computations estimate a wider, shal-lower settlement trough than is reasonable in the light of considerable recorded site
Figure 4b. Surface movements transverse to a 4 m diameter tunnel, 30 m deep.
357TUNNELLING IN SOILS
data; the inward movements are underestimated similarly. This behaviour is charac-teristic of FE analysis of tunnelling settlements (Lee and Rowe, 1989; Addenbrooke,1996; Potts and Addenbrooke, 1997). Realistic computation of movements due to ashallow tunnel is problematic, requiring the use of complex orthotropic, yielding soilmodels. The approach by Lee and Rowe (1989) achieved promising results, but therequisite soils information is rarely available in practice.
Computations of soil-structure interaction
The capabilities of the linear FLAC and PAFEC models for interactive assessmentsof the soil together with a 5 m-high masonry wall are next evaluated. The wall waslocated transversely to the tunnel drive, and was either 16 m long or 60 m long. Thewall had an effective thickness of 0.4 m compared with the 1 m-thick soil slice, andhad a modulus of 10 3 109 Pa and Poisson’s ratio of 0.2. Results for the ‘hybrid FE’approach are also included based upon the ‘green field’ results of the PAFEC runs ofthe previous section. A simple graded mesh of 8 3 7 elements of 8-noded planestrain rectangles was used.
Results of interactive computations for soil plus a 16 m long by 5 m high masonrywall transverse to the tunnel drive, are shown in Figure 5. The free ground settle-ments are shown for comparison. All three computations show a major distortion ofthe smooth ‘green field’ settlement trough, with a width of 8 m each side of thetunnel axis being enforced by the wall stiffness into an almost flat profile. Outsidethis area, the settlements return rapidly towards the free NPC. The results from thedirect PAFEC computation and from the ‘hybrid FE’ method are nearly identical,which verifies the hybrid approach. The FLAC results are rather more shallow, whichmay be due to a less refined grid around the tunnel, and to a poorer capability forcomputation of a model with two materials of strongly different moduli. Thedisplacements are very small, and interactive inward movements were smaller again,particularly within the 8 m either side of the centre-line; however, their effects uponstresses should not be overlooked.
Computed settlement curves including a transverse wall 60 m long are shown inFigure 6, for the three methods. In this situation, the wall flattens out the free soiltrough into a wide shallow smooth curve, with the three computed curves in closeagreement. Similar results were obtained for the cases of a 20 m and 30 m deeptunnel, although the settlements and curvatures reduced with tunnel depth. Althoughthese induced wall deformations (and strains) are small, the stresses induced arerelatively large. The longitudinal stresses induced in the top level, sxxt, and basecourse, sxxb, of the short and long walls, are listed in Table 1, for positions directlyabove the tunnel axis.
The stresses tabulated are longitudinal stresses, in preference to principal stresses,because the cracking of masonry or brickwork is dominated by the stresses in the
358 SELBY
mortar perpends. In this case longitudinal tensile stresses act to open the perpends,while compressive stresses act to stabilize the perpend mortar. The stresses inducedin the long wall are significantly higher than those in the 16 m long wall, and wouldprobably cause some opening of joints. This emphasizes the recommendations byMorton (1986) that brickwork should be designed with movement joints at spacingsof the order of 12 m.
From the computational considerations, the FLAC stress estimates are lowestthroughout. The matching of two dissimilar materials is handled less well by FLAC.The PAFEC and hybrid methods show close correlation, with minor differences forthe 10 m deep tunnel due to small differences in mesh stiffnesses. However, thislevel of agreement and its lack of conservatism gives support for the conceptualaspects of the hybrid FE method. Significantly, this method has the advantage ofbeing highly flexible in application towards green field settlement troughs whetherdeep and narrow or shallow and wide.
Figure 5. Interactive soil/wall settlements, 16 m long wall, tunnel 10 m deep.
359TUNNELLING IN SOILS
Inspection of the stresses in Table 1 shows the importance of the inwardmovements to structural distress, an effect which is particularly strong at shallowtunnel depths. Consider first the results for the long wall. If induced bending hadbeen the sole effect then the compressive stress sxxt and the tensile stress sxxb would
Figure 6. Interactive soil/wall settlements, 60 m long wall, 10 m deep tunnel.
Table 1. Longitudinal stresses in short and long walls due to tunnelling movements
be equal in magnitude. However, the effects of imposed compressive strain along thebase of the wall above the tunnel axis are to reduce sxxb substantially, and to reducesxxt by a small amount (the line of action being outside the ‘middle third’ of the wallheight). For the short 16 m wall, the induced compressive strain dominates overbending effects, with the resultant of both sxxt and sxxb being compressive in sense.Fortunately, this effect is strongly beneficial to the integrity of the wall.
It is highly conservative to apply the free ground curvature to the structure. Forexample, if the long wall had been subjected to the free curvature due to the 10 mdeep tunnel, the induced longitudinal stresses would be estimated to be 61500 kPa.This value is some six times greater than the stresses computed from interactiveanalyses.
To conclude, all three methods, FLAC, PAFEC and hybrid, show the dominanteffects of soil-structure interaction, particularly with respect to the gross conservatismof design based upon imposed free ground curvature, and to the very significanteffect of the horizontal strains. The close correlation of displacements and stressesfrom the PAFEC and hybrid methods validates the computational procedure of thehybrid approach. Only the hybrid method is capable of following a narrow and deepfree ground profile.
A case study in London
Published examples of building deformations caused by tunnelling are rare. Anoteworthy example was recently presented by Frischmann et al. (1994), describingsettlements of the Mansion House in central London during driving of tunnels forunderground trains. In particular, the measured deformations of the west wall arereported, in response to a 3.05 m diameter tunnel driven at a depth of 15 m below thewall. The Mansion House is a substantial building in the City of London, containingseveral large open rooms on four stories above ground plus a basement under part ofthe building. The walls comprise brickwork with a stone cladding.
For the purpose of this simple exercise (and lacking architectural details of thewall, roof and foundations) the west wall was assumed to comprise a plain solid wall10 m high and 50 m long, and of equivalent thickness of 0.4 m compared with acontributing soil thickness of 1.0 m in plane strain. The modulus of the brickworkwas quoted by the authors as 1 GPa. The soil parameters were chosen arbitrarily asuniform elastic modulus of 50 MPa and Poisson’s ratio of 0.49, although soilstiffness generally increases with depth and is often orthotropic. The predicted greenfield settlements from the above paper show a deep narrow trough, with a maximumof 11.5 mm and a parameter ‘i’ of some 5 m. This latter value is unusually small fora tunnel at a depth of 15 m in cohesive soils, and indicates the contribution of the 8 mdeep gravels overlying the London clay. Because of the configuration of thissettlement trough only the ‘hybrid FE’ method was suitable, the linear FLAC and
361TUNNELLING IN SOILS
PAFEC models being unable to model the ground movements. The line of the tunnelwas offset from the mid-length of the wall, so symmetry could not be employed inthis case. Figure 7 shows the green field curve presented by Frischmann et al. (1994),and their measured deformation of the west wall. The green field settlements plusdeduced inward horizontal movements were then used as phase 1 data for the hybridmethod. The settlements estimated by the hybrid method are also plotted in Figure 7.The computed settlements could be made to correspond more closely with themeasured values by stiffening the wall to include foundations, roof and wall ends,but the reported values are those estimated at the first attempt. Generally, thecorrelation in displacements is close. The characteristic shallow curve along thestructure, here located between 210 m to 140 m, is far less severe than the greenfield profile. The measured deflection ratio, D/L (maximum deflection from a baselength L), was 0.12 3 1023, while the value from the hybrid computations was0.15 3 1023. This may be compared with the value indicated by Burland and Wroth(1975) of 0.5 3 1023 for the onset of cracking.
Longitudinal stresses were computed in the wall in the top and bottom courses. Inthe top of the wall the compressive stress above the tunnel axis was 59 kPa, while thelargest tensile stress of 52 kPa occurred some 20 m north of the tunnel axis. In thebottom course a peak tensile stress of 53 kPa occurred just south of the tunnel axis,
Figure 7. Reported and computed settlements, west wall, Mansion House.
362 SELBY
while a compressive stress of 36 kPa was indicated at 20 m north of the axis. Thepattern of stresses indicates that in this case the induced curvatures were moresignificant than the effects of the inward horizontal movements because of thenarrow deep settlement profile. The level of stress is sufficiently small to give littlerisk of cracking due to tunnelling alone. However, a building of this age and locationwill have endured previous differential movement, and so additional effects due totunnelling may initiate damage.
Severe settlements at Workington Town Rugby League Club
Workington is a light-industrial market town in Cumbria in the north-west of England.It has a harbour for local fishing boats. The town is also home to Workington TownRugby League Club, one of the professional teams playing in the North of England.The club grounds are located on the northern edge of the town, and club propertycomprises the main playing pitch, stands with seating facilities, changing rooms, barsand meeting rooms, a large gymnasium and office facilities. The club has existed inits present form for some 55 years, and some of the buildings and parts of theperimeter wall are of similar age.
During the summer of 1998 a tunnel was driven, at some 18 m depth, below a carpark area and near to a functions building and to the gymnasium and offices com-plex. The tunnel, for waste water collection and disposal, is some 2.8 m in diameter,and was constructed using an earth pressure balance tunnelling machine. Groundconditions comprise a series of saturated sands, silts and gravels overlying clay,which form the lower portion of the tunnel excavation. Good progress was made, andsurface levelling and monitoring had generally shown good control of ground loss.
On September 3, 1998, a localized but severe surface settlement occurred over anarea of roughly 5 m 3 3 m and close to some buildings forming part of the clubfacilities. The popular press hypothesized that a pocket of loose soils located abovethe centre line of the tunnel drive had been disturbed and collapsed. However, it isconsidered to be more likely that the mole had run into conditions comprising alower horizon to the tunnel face of stiff clays, while the upper half of the faceconsisted of loose sands, silts and gravels. The consequence was that the mole drewin the loose granular soils from the upper levels, while failing to match this earth‘take’ with forward progress because of the stiff clays in the lower part of the face.
The ground disturbance caused a single-storey office block to tilt and crackseverely, while a two-storey functions building cracked from ground to roof, break-ing its back, so that part of the structure tilted towards the area of ground settlement.The buildings were evacuated, and have not been used since. The local Councilapplied an order prohibiting access to the two-storey building, for public safety, andbarriers were erected to exclude the public from the area.
363TUNNELLING IN SOILS
Officers of the club kindly allowed the author access to the area to undertakelevelling surveys of the damaged buildings. Internal access was available to theoffices and gymnasium, but not to the functions building. Before-and-after surveyswere not possible, nor were time-related changes measurable. However, the interiorfloors were assumed to have been reasonably level before the incident. Externally,levelling was conducted by reference to the damp proof courses (dpc) which againwere considered to be have been level prior to the settlement. A plan of the affectedbuildings, and of the survey lines is shown in Figure 8. The surveys were simply ofrelative levels, and were not tied into OS bench marks.
At the time of the major settlement the tunnel was passing under a space betweentwo groups of buildings, including on one side: a gymnasium, an office, a corridorand additional offices; and on the other side: a two-storey building housing functionrooms and bars (Figures 8 and 9). The construction of the damaged buildings com-prised reinforced concrete ground-bearing slabs of unknown thickness. The walls
Figure 8. Outline plan of buildings affected by settlements, Workington.
364 SELBY
were of cavity brickwork with conventional ties; the inner leaves of the walls wereeither plastered blockwork or unplastered facing bricks. Lightweight steel sheetedroofs were supported by joists and purlins. Window and door openings had concretelintels.
From inspection of the damage to the buildings and from evaluation of thededuced changes in level (Table 2), it appeared that hinge lines had developed inthe concrete ground-bearing slabs, parallel to the tunnel line, and approximately asindicated by lines L1, L2 and L3 in Figures 8 and 9. Line L3 ran right through thebuilding but was more severe at the south end. Lines L1 and L2 were most severetowards the south end, but were less easily identified towards the north edge of the
Figure 9. Schematic elevation of damaged buildings, Workington.
Table 2. Relative levels (m) on the independent level surveys conducted at Workington RugbyLeague Club, on September 29, 1998
Survey 1, stations: A B G H99.900 99.985 99.985 99.910
Survey 2, stations: B' C D E F99.985 100.000 100.005 100.000 99.955
buildings. The lack of continuity of the crosswalls between the offices and the corridor,and between office and gymnasium, undoubtedly contributed to the formation of thehinge lines L1 and L2.
Rotation of hinge line L1 caused separation of the office and corridor away fromthe gymnasium, although the gymnasium wall appeared to be undamaged. A crackhad opened in the south elevation of the office/corridor unit, running from the hingeline vertically up the corner (near X1) and then diagonally to the lower corner of thewindow; it ran up the side of the window and to eaves level. The crack was perhaps2–3 mm at ground level, widening to 5 mm at the top. Diagonal cracking wasapparent inside the office on the north wall. The rotational of line L2 was moresevere than that of L1, but the damage to the brickwork was less easily described.The entrance door opening (around X3–X4) was badly warped. The external southelevation of the office had tilted with some diagonal cracking near the top left corner.Internally, lintels and brickwork showed relative movements of some 10 mm, anddoor frames were so badly deformed that doors would not close. Diagonal crackingwas observed both in the cross walls and in the east wall (the latter caused by moresevere settlement at X5 than at X9). The slope to the floor in this end office wassevere, being some 0.021, or 1:45. The steel sheet roofing had been restrained by itsconnection to the gymnasium wall, and the tilting brickwork had pushed outwards,deforming the roof edge detail.
Turning now to the two-storey functions building, the pattern of damage wasclearer. The location of the hinge line L3 was determined by the combination of thehog curvature of the ground and of the presence of a doorway and window above, onthe south elevation. A single major crack ran from ground to roof level, up the dooredge, almost vertically to the widow opening (through bricks as well as up theperpends) and then diagonally to the roof. The crack was 2 mm wide at dpc level,some 5 mm at the doorway head, and was about 25 mm wide at the top. A similarbut less severe crack was apparent on the north end wall, starting on the hinge lineand running more diagonally to pick up an upper storey doorway (which hadprobably been a fire exit). Internal inspection of the building was not permitted.
Computational analysis of the response of the damaged buildings
The hybrid approach was used to model the response of the soil plus uncrackedstructures, then the soil plus cracked structures due to the severe ground movements.The first task was to estimate the free ground settlement profile from the site levellingsurveys. By plotting the probable settlements and then fitting a curve of the form ofequation 1, the estimated ground surface volume loss was taken to be 1.02 m3 m21
of advance. This was equivalent to 16% of the tunnel face diameter, which maybe considered as a fairly extreme value, by reference to Attewell et al. (1984).Additionally, the maximum settlement was estimated to be 120 mm, and hence fromequation 1, the trough width parameter ‘i’ was estimated as 3.35 m. Estimation of a
366 SELBY
typical surface width parameter from the expression by O’Reilly and New (1982) of(0.28z 2 0.1) m yields a value for ‘i’ of 4.9 m, so this settlement trough was narrowand deep (see Figure 10). However, it should be recognized that estimates of both thevolume loss and the width parameter for tunnels in granular soils are much morevariable and less predictable than are equivalent values for tunnelling in clay soils.
Next, a 2D mesh was constructed to represent the ground alone. The free groundsettlement profile, as defined by equation 1 and with the values outlined in thepreceding paragraph, was calculated manually for each ground surface node. Surfaceinward movements were also estimated. These settlements and inward movementswere then imposed upon the surface nodes in an FE analysis to compute the reactionforces required. The ground was modelled as a 1 m thick slice of uniform homo-geneous material, with modulus, E, of 50 MPa and Poisson’s ratio of 0.3. Theseproperties are typical of a medium dense sand. Finally, the 2D mesh was extended toinclude representations of the single-storey offices and gymnasium to the left-handside of the tunnel axis, and of the two-storey functions building to the right. Theground-bearing concrete slab was assumed to be 600 mm deep and of unit thickness.Uncracked elastic modulus of concrete was taken as 30 GPa. Brickwork wasmodelled simply as a uniform isotropic plate of thickness 200 mm and elasticmodulus of 20 GPa.
The computation was conducted firstly with the structures in their uncracked state.The results showed horizontal tensile stresses of up to 10 MPa in the top levels ofbrickwork, which are considerably in excess of those likely to cause major cracking(Hendry, 1981). A further model was then analysed which incorporated hinges in thebase slab and vertical cracks through the full height of the brickwork walls. Thedeflected form of the latter mesh is shown in Figure 11. The results of thecomputation for the deflected forms of the buildings are plotted to exaggerated scalein Figure 12, for comparison with the settlements estimated from the results of thelevels survey. Very close agreement can be observed. Residual longitudinal stressesin the cracked model nowhere exceeded 1.0 MPa, and were mostly compressive.
Crack widths observed in the two-storey function rooms building were some25 mm at eaves level. Computed crack width at the same point was some 45 mm.This discrepancy may be due to the compliance of the uncracked segments of thebuilding, or to partial restraint by the roof structure (which was not included in themodel). No other cracks could be detected on the main façade. The computed crackwidth at the wall top, above line L1 was 44 mm. No single element of crackingshowed more than about 10 mm width, but in this location there was a combinationof cracking, wall distortion and pull-out. Cracking between the second office unit andthe gymnasium was estimated to be 14 mm, but the diagonal cracks running from thewindow corners did not exceed 5 mm. This general lack of agreement indicates thatprediction of crack widths is problematic.
Figure 11. Computed displacements of fully cracked buildings.
368 SELBY
Discussion
The computed building response was conducted by the ‘hybrid’ method, but withforeknowledge of the ground volume loss and of an estimate of the free groundsettlement profile. Thus it was in no sense a ‘Category A’ prediction. Additionally,full height cracks in the brickwork and hinges in the base slabs were introduced intothe model at the locations where they were observed in the buildings; these locationswere predictable, however, because they occurred where walls were discontinuous,or where a doorway plus window acted as major stress-raisers.
Notwithstanding these input parameter values, the hybrid analysis has achieved anaccurate prediction of the settlements of the damaged buildings in the zone of influenceof the tunnel. It is unlikely that any computational model of ground movements intoa tunnel would produce a sensible result, because the settlement trough was sodeep and narrow. The above computation included the surface tractions caused byhorizontal inward movements of the soil, although there were no field data availablefor comparison. If detailed stresses were required then these horizontal surfacemovements might be significant despite the stiff ground floor slab.
Figure 12. Measured and computed settlements of offices and of functions building, Workington.
369TUNNELLING IN SOILS
The achievement of a close estimate of settlements by the hybrid method is notunexpected given the foreknowledge of the settlement trough, that the buildingstructures were founded on stiff rafts and that the building articulations were sopredictable. A more testing scenario for the hybrid method would be for much lessstiff building elements with ill-defined hinges. This close agreement does, however,give strong evidence of the effectiveness of the hybrid method, provided that thefree ground settlement trough can be defined, either by direct measurement or byreference to the very considerable empirical database.
Conclusions
When considering the effects of settlements caused by tunnelling in soils, the primaryconsideration is the effect upon existing structures or buried services. Computationalestimates must incorporate soil-structure interaction. Estimation of ground settle-ments and inward movements by linear elastic finite elements or finite differencespredicts wider shallower troughs than are commonly observed in practice. Differ-ences are greater for shallow tunnels.
Computations incorporating soil-structure interaction clearly show modificationsto the green field soil movements. Computed structural stresses are much smallerthan those estimated simply by applying green field curves to a structure; the latterdesign approach is grossly over-conservative. Stresses induced into structures abovea tunnel line are strongly influenced by the horizontal inward ground movements,effects which may dominate over bending stresses.
The benefit of movement joints in masonry and brickwork walls has been shownby reference to detailed analysis of stresses in short and long walls within the zoneof influence of a typical tunnelling activity.
A hybrid method based upon realistic green field movements is verified, which isversatile with respect to trough shape. The advantage of the approach is that it avoidsthe need for modelling very large strains close to the tunnel drive. The method wasapplied to a reported case study and estimated settlements of a brick structureshowed reasonable agreement with measured values.
A more detailed example of severe damage to buildings was analysed by thehybrid approach using estimates of volume loss and trough width from estimatesbased on a levels survey. A severe settlement trough was observed close to existingbrick buildings in Workington Rugby Club. The buildings were observed to havecracked along well-defined hinge lines. Close agreement of settlements was observedwhen an appropriate hybrid FE model was used which contained cracks at similarlocations. However, crack widths were not predicted accurately.
While there are numerous reports of tunnelling settlements in open sites, there arevery few detailed reports of the response of buildings, or of damage caused. Thismay be due in part to a reluctance to publicize what might be considered as a failure
370 SELBY
in ground loss control. However, the industry as a whole would benefit from pub-lished records of this type, and such publication must be strongly recommended.
Acknowledgements
Access to Workington Town Rugby Football Club grounds was kindly permitted bythe Club Directors. Club Secretary Mrs Kennedy was most helpful in describing theevent, and in displaying the area of damage.
References
Addenbrooke, T. (1996) Numerical analysis of tunnelling in stiff clay. Ph.D Thesis, Imperial College ofScience, Technology and Medicine, London.
Attewell, P.B. (1978) Ground movements caused by tunnelling in soil. In Large ground movements andstructures, J.D. Geddes (ed.), Pentech Press, London, pp. 812–948.
Attewell, P.B., Yeates, J. and Selby, A.R. (1986) Soil movements induced by tunnelling and their effectson pipelines and structures. Blackie, Glasgow.
Burland, J.B. and Wroth, C.P. (1975) Settlement of buildings and associated damage. Building ResearchEstablishment CP33/75, Garston.
Cording, E.H., Hansmire, W.H., MacPherson, H.H., Lenzini, P.A. and Vonderohe, A.D. (1976)Displacements around tunnels in soil. Final report, Contract DOT FR 30022 Dept. of Transportation,Washington, DC.
against damage caused by ground movements due to the Docklands Light Railway extension. Proc.Inst. Civ. Engrs., Geotech. Engg. 107, 65–76.
Lee, K.M. and Rowe, R.K. (1989) Deformations caused by surface loading and tunnelling: the role ofelastic anisotropy. Geotechnique 39, 125–140.
Malato, P., Torrado da Silva, J., Marques, F. and Almeida e Sousa (1998) Lisbon Metro – Behaviour ofa shallow tunnel in stiff clays. World Tunnel Congress ’98 Sao-Paulo, Brazil.
Morton, J. (1986) Designing for movement in brickwork. Brick Development Association Design note 10Brick Development Association, Windsor, Berks.
New, B.M. and Bowers, K.H. (1994) Ground movement model validation at the Heathrow Express trialtunnel. Tunnelling 94, I.M.M. & Br. Tunnelling Soc. Chapman & Hall, London.
Oliver, A. (1994) Tunnel collapse followed midnight repairs. New Civil Engineer, 10th Nov.O’Reilly, M.P. and New, B.M. (1982) Settlements above tunnels in the United Kingdom – their
Selby, A.R. (1985) Tolerance of highway bridges to ground movements induced by tunnelling in soil.Ground Movements and Structures, Geddes, J.D. (ed.), Pentech Press, London, pp. 630–642.
Selby, A.R. (1987) Some variables in the calculation of the effects upon floor slabs of tunnelling-inducedsettlements. Proc. Int. Conf. on Foundations & Tunnels. ETP. pp. 15–19.
![Studies in East European Thought Volume 54 Issue 3 2002 [Doi 10.1023%2Fa%3A1015993401680] James F. Pontuso -- Transformation Politics- The Debate Between Václav Havel and Václav](https://static.documents.pub/doc/80x56/577cc0581a28aba7118fc2d7/studies-in-east-european-thought-volume-54-issue-3-2002-doi-1010232fa3a1015993401680.jpg)
