This paper presents observations of the response of long structures when exposed to tunnelling activities in London Clay. The type of structures varied from a 100 years old masonry arch tunnel to a more modern reinforced concrete frame structure. The common property shared by these structures is that they are long in comparison to the depth beneath them of the tunnels being constructed. Numerical analyses have also been carried out to back analyse the observed data using the London Clay soil parameters. The model was then extended to include a depth and a structural stiffness variable and demonstrate sensitivity to those factors

Bloodworth, A.G.

Gleig, F.D.

Yu, Y.C.

English

Southampton (e-Prints Soton)

Lu, Bloodworth & Gleig 1 of 9 Behaviour of long structures in response to tunnelling.  Lu Y C Brown & Root Services, Leatherhead, UK.  Bloodworth A G Dept. of Civil & Environmental Engineering, University of Southampton, formerly Brown & Root Services, Leatherhead, UK.  Gleig F D Brown & Root Services, Leatherhead, UK.         Abstract  This  paper  presents  observations  of  the  response  of  long  structures  when  exposed  to  tunnelling activities in London Clay. The type of structures varied from a 100 years old masonry arch tunnel to a more modern reinforced concrete frame structure. The common property shared by these structures is that  they  are  long  in  comparison  to  the  depth  beneath  them  of  the  tunnels  being  constructed. Numerical analyses have also been carried out to back analyse the observed data using the London Clay  soil  parameters.  The  model  was  then  extended  to  include  a  depth  and a  structural  stiffness variable and demonstrate sensitivity to those factors.  Keywords Tunnelling, structures, risk, prediction, settlement, trough, modification  Conference Theme The effect of building stiffness   Lu, Bloodworth & Gleig 2 of 9  1  Introduction  The current increase in tunnelling activity in built-up areas results in an increased exposure of existing services  and  structures  to  ground  movements.  To  assess  the  associated  risks  requires  either  the application of an over-simplified and conservative methodor complex numerical analysis, which can be time consuming. When only the risks to the structure are of interest, the important parameter is the half-width  of  the  settlement  trough  between  the  points  of  inflexion,  i.  That  value  is  used,  in conjunction with the anticipated volume loss, to produce a deflected shape for which the structure can be assessed. This paper provides a method of obtaining this parameter for long structures within a range of stiffness (EI) values.   2  Euston Square Station  In November 1996, London Electricity plc (LE) constructed a 3m diameter tunnel under the existing Metropolitan Line at Euston Square station (Lu et. al., 1999, Samuel et. al., 1999). This tunnel was driven within London Clay to achieve a clearance of approximately 7m between the two structures.  The Metropolitan Line was built in 1863 (Baker, 1885), and the section under Euston Road was a brick arch constructed using the cut and cover method. The foundations of the arch were just into London Clay and the arch was covered with about 8m of Terrace Gravel and made ground. A  site investigation  was  conducted  and  brick  cores were  taken  from  the  masonry  to  obtain  both strength and stiffness parameters. The unconfined compressive tests produced a range of strengths between 6.9 and 22 N/mm2 and the average Young’s modulus was 8500 N/mm2.  During the LE tunnel construction, precise levelling was carried out to measure the displacements along the walls and the crown (see plan Figure 1 for instrumentation sections). This surveying method was accurate to 1mm and the measured data at the axis and foundation (P6 and P7 respectively) is shown in Figure 2. The predicted greenfield settlement curve, based on a value of i calculated as half the depth between the LE tunnel axis and the arch foundations, is also shown. The back analysis of the settlement data showed a ‘best fit’ Gaussian curve with the point of inflexion, i, equal to 1.5 times the depth between the LE tunnel axis and the arch foundation. The actual settlement curve was 3 times wider than the greenfield condition and the volume loss was 2.5% one week after construction. Lu, Bloodworth & Gleig 3 of 9  Figure 1.  Plan at Euston Square Station.  Distance from station headwall,  mSettlement, mm0-4-8 P6     P7    - Gaussian Curve20 10 30 0   Figure 2.  Observed and predicted settlements at tunnel axis and foundation levels, Euston Square Station.  Lu, Bloodworth & Gleig 4 of 9  3  Longford Street Spur Tunnel  A spur tunnel was excavated from an electricity substation to intersect the main tunnel drive, described in Section 2 above, at a point approximately 400m to the east of Euston Square. The spur tunnel was 77m long and 2.9m in diameter and was hand excavated in London clay on a decline at shallow depth, ranging from 4m to 15m beneath an existing structure (Bloodworth and Macklin, 1999).   The  existing  structure  comprises  a  single-storey  reinforced  concrete  frame  which  is  the  former basement of a substantial office development, demolished in 1996 to ground level (Figure 3). The basement extends over a wide area either side of the tunnel axis. The frame consists of columns at 7m centres in both directions and a ground level slab. At basement level, a reinforced concrete slab is cast against the columns but is not structurally connected to them. The vertical separation of ground and basement level slabs is 4m. The columns are founded on pad footings 2m below basement slab level, approximately at the top of the London clay. Precise level monitoring of the columns above the tunnel axis (points A – C), the basement slab over a wide area each side of the tunnel (points 1 –29) and for subsurface settlements 4m below basement slab level at a point where the tunnel axis was 8m below basement slab level (points 101 – 103) was carried out.  The settlement results at the chainage of the subsurface monitoring points are shown in Figure 4. The back analysis of the settlement data showed a volume loss of 0.8%, which was consistent with the depth of the tunnel below basement slab level and the stability number of the heading (Macklin, 1999). The  trough  width  parameter  i  at  the  level  of  the  subsurface  monitoring  points  was  found  to  be approximately 5.5m, twice the width predicted by methods based on subsurface settlement trough width in London clay (Mair et al, 1993). This widening of the trough was also observed at basement slab level.    Lu, Bloodworth & Gleig 5 of 9 2.59 I.D.CABLETUNNELX XX XX XXXX XXXXXX X X XXX XXXXXXX12345678910111213141516171819202122232425262729 XXX28A B C101102103Notes(1)  POINTS 1 TO 29 ARE HILTINAILS IN BASEMENT SLAB(2)  POINTS A B & C ARE SOCKETSIN COLUMNS AT BASEMENT SLABLEVEL(3)  101 102 & 103 ARE SUBSURFACE LEVELLINGPOINTS 4m BELOW BASEMENT SLAB LEVELEXIT TO RESTOF CAR PARKENTRY FROMREST OF CARPARKAA2.44m ID BOLTEDLINING TO SPURTUNNEL101-103BHMade groundStiff to VeryStiff FissuredLondon ClayOriginal Building Demolished toground floor levelLONGFORDSTREETJUNCTIONCHAMBERWeathered London clayC B A+25m+20m+25mVerticalScalem AOD10m 5m 0mHorizontalScale24.0720.0SECTION A-APLANBasement Slab level Figure 3.  Plan and Section of Longford Street Spur Tunnel.  012345678-10 -5 0 5 10Transverse Distance from Spur Tunnel Centreline, y (m)Settlement (mm) Predicted greenfield subsurface Observed subsurfaceObserved column C Observed basement slab Figure 4.  Predicted and observed settlement above spur tunnel, Longford St. Lu, Bloodworth & Gleig 6 of 9   4  Analysis Considerations  The simplest method to assess the level of risk, due to tunnelling beneath a structure, was to assume a flexible structure with the greenfield ground displacements superimposed. From this deflected shape, the gradients along the structure were calculated and compared with published data of settlement damage to buildings (eg. Boscardin and Cording, 1989). This method yielded conservative results.  Potts and Addenbrooke (1997), proposed an alternative method, modelling the building as an elastic beam  and  defining  relative  bending  and  axial  stiffnesses  as    =  EI/EsH4  and  *=  EA/EsH respectively, where Es is the representative soil stiffness. When H, the half width of the beam, became infinitely long, both stiffnesses would reduce to very small values. In their Figure 6, the i/Z value then became 0.5 for all values of relative axial stiffness ratios and Z is the depth between the structure foundation to the axis of the tunnel.  Based on the two cases presented, the contribution from the structure appeared to become significant when the clearance between the structure and the tunnel was reduced. This could be attributed to the reduced  trough  width  and  the  ability  of  the  structure  to  ‘bridge’  across the  trough.  In  a  limiting situation, when the stiff structure could span across a sufficiently narrow trough, very little structural deflections would be anticipated which implied a large i/Z ratio. This assumes that the ground was capable of carrying the increased pressure at the foundation.  A  series  of  FLAC  (Fast  Lagrangian  Analysis  of  Continua)  models  were  developed  to  study  the behaviour  of  long  structures  subjected  to  underground  construction,  with  reference  to  the  Euston Square Station case study (Lu et al., 1999). The structure was idealised as a long beam glued to the top of the grid. A surcharge was also included to model the material above the arch tunnel. The soil was modelled as a non-linear elastic, undrained London Clay of stiffness parameters stated in Jardine et. al.(1982).An initial analysis was conducted which excluded the structure and good agreement between the numerical and theoretical curves can be seen in the Figure 7 of Lu et. al., 1999.  Three Z values were included in the analyses, namely 4.5m, 9.5m and 15m respectively. Figure 5 and Figure 6 shows the deflected shape of the structure compared with the greenfield settlement trough of i/Z=0.5 for tunnels at depth, Z, of 4.5m and 15m respectively. Lu, Bloodworth & Gleig 7 of 9 Tunnel at z=4.5m-1.2-1.0-0.8-0.6-0.4-0.20.00 5 10 15 20 25Horizontal Distance From Tunnel Axis, mS/SmaxGreenfield Conditioni/Z=2.0 Figure 5.  Deflected shape of structure for tunnel at Z=4.5m.  Tunnel at z=15m-1.2-1-0.8-0.6-0.4-0.200 5 10 15 20 25Horizontal Distance From Tunnel Axis, mS/Smax Greenfield Conditioni/Z=0.75 Figure 6.  Deflected shape of structure for tunnel at Z=15m.  These  analyses  demonstrated  that  a  reduced  clearance  between  the  tunnel  and  the  structure  would increase the trough width parame ter. The effect of the long structure would no longer be significant when the 3m diameter tunnel was more than 20m beneath it.   5  Proposed Design Chart and Analysis Method  A  sensitivity  study  has  been  conducted  to  investigate  the  influence  of  the  structu ral  stiffness,  EI, towards its deflected shape, where I is the gross section modulus. It was found that changing the EI from brick masonry to reinforced concrete would not have increased the trough width. The range of EI used in this work was between 1x107 and 1x108 kNm2/m. Figure 7 shows the semi-log plot for the i/Z Lu, Bloodworth & Gleig 8 of 9 to C/D ratios, where C is the clear space between the tunnel and structure. Data points in the figure also include the two case studies, Euston Square station and Longford Street. 1100 0.5 1 1.5 2 2.5i/ZC/DEuston Square Station,EI=4.25x107 kNm2/m.log10(C/D)=-0.56(i/Z)+1.06Longford Street,Approx. EI= 5x107 kNm2/m.* Numerical Analysis* Z=15m*Z=9.5m*Z=4.5m Figure 7.  Proposed design chart.  The equation derived from the plot is log10(C/D) = -0.56 (i/Z) + 1.06, where the i/Z ratio should not be greater than 2 or less than 0.5. This range was perceived as the upper bound based on current work and the lower bound from observed greenfield data in stiff clay. From the plot, the limiting C/D ratio, for i/Z = 0.5, was 6.  The recommended procedure to assess the risk on a long structure due to tunnelling would be applying the known C/D ratio to the above equation to obtain the i/Z value. This point of inflexion, i, is then combined with the anticipated volume loss to produce a deflected shape of the structure, which is compared with published structure performance charts or tables to obtain the risk levels.   6  Conclusion  Using greenfield condition to predict structure response due to tunnelling, without accounting for the structural  stiffness,  will  provide  a  conservative  result.  However,  the  relative  depth  of  the  tunnel beneath the structure will also influence its deflected shape. The ability of a long structure to bridge across a settlement trough will need to be taken into consideration in order to provide a realistic prediction of the structural deflections. Lu, Bloodworth & Gleig 9 of 9  ACKNOWLEDGEMENTS  The authors would like to thank the technical skill group leaders in Brown & Root Services, Mr G Wilkinson and Mr I Brough, for their support in the preparation of this paper.   REFERENCES  Baker, B. 1885. The Metropolitan and Metropolitan District Railways. Proceedings of the Institution of Civil Engineers. Vol. LXXXI, 1-33.  Bloodworth, A.G. and Macklin, S.R. (1999). Ground and structure response to a hand driven decline in  London  clay.  Proc.  International  Symposium  on  Geotechnical  Aspects  of  Underground Construction in Soft Ground, Tokyo, 75-80.  Boscardin,  M  D  and  Cording  E  J.  (1989).  Building  Response  to  Excavation  Induced  Settlement. Journal of Geotechnical Engineering, ASCE, Vol. 115, No.1.  Jardine R J, Potts D M, Fourie A B and Burland J B (1982). Studies of the influence of non-linear stress-strain characteristics in soil-structure interaction. Geotechnique 36, No.3, 377-396.  Lu Y C, Samuel H R and Chudleigh I (1999). Response of a masonry arch tunnel to underground tunnelling. Proceedings of the 5th International Symposium on Field Measurements in Geomechanics, Singapore,.  Macklin, S.R. (1999). The prediction of volume loss due to tunnelling in overconsolidated clay based on heading geometry and stability number. Ground Engineering, Vol. 32, No. 4.  Mair, R.J., Taylor, R.N. and Bracegirdle, A. (1993). Subsurface settlement profiles above tunnels in clays. Geotechnique, Vol. 43, No. 2, 315-320.  Samuel H R, Mair R J, Lu Y C, Chudleigh I, Addenbrooke T I and Readings P(1999). The effects of boring  a  new  tunnel  under  an  existing  masonry  tunnel.  Proc.  International  Symposium  on Geotechnical Aspects of Underground Construction in Soft Ground, Tokyo, 293-298.  

Addenbrooke T I and Readings P(1999). The effects of boring a new tunnel under an existing masonry tunnel.

Building Response to Excavation Induced Settlement.

Ground and structure response to a hand driven decline in London clay.

Response of a masonry arch tunnel to underground tunnelling.

Studies of the influence of non-linear stress-strain characteristics in soil-structure interaction.

Subsurface settlement profiles above tunnels in clays.

The Metropolitan and Metropolitan District Railways.

The prediction of volume loss due to tunnelling in overconsolidated clay based on heading geometry and stability number.

Behaviour of long structures in response to tunnelling

Yu, Y. C.

Bloodworth, Alan G.

Gleig, F. D.

Warwick Research Archives Portal Repository

     warwick.ac.uk/lib-publications      Original citation: Yu, Y. C., Bloodworth, Alan G. and Gleig, F. D. (2001) Behaviour of long structures in response to tunnelling. In: International Conference on the response of buildings to excavation-induced ground movements, 17-18 Jul 2001. Published in: Proceedings of the International Conference on the response of buildings to excavation-induced ground movements  Permanent WRAP URL: http://wrap.warwick.ac.uk/80787      Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.  Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way.  A note on versions: The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher’s version. Please see the ‘permanent WRAP URL’ above for details on accessing the published version and note that access may require a subscription.  For more information, please contact the WRAP Team at: wrap@warwick.ac.uk  Lu, Bloodworth & Gleig 1 of 9 Behaviour of long structures in response to tunnelling.  Lu Y C Brown & Root Services, Leatherhead, UK.  Bloodworth A G Dept. of Civil & Environmental Engineering, University of Southampton, formerly Brown & Root Services, Leatherhead, UK.  Gleig F D Brown & Root Services, Leatherhead, UK.         Abstract  This paper presents observations of the response of long structures when exposed to tunnelling activities in London Clay. The type of structures varied from a 100 years old masonry arch tunnel to a more modern reinforced concrete frame structure. The common property shared by these structures was that they were long in comparison to the depth beneath them of the tunnels being constructed. Numerical analyses have also been carried out to back analyse the observed data using the London Clay soil parameters. The model was then extended to include a depth and a structural stiffness variable and demonstrate sensitivity to those factors.  Keywords Tunnelling, structures, risk, prediction, settlement, trough, modification  Conference Theme The effect of building stiffness   Lu, Bloodworth & Gleig 2 of 9  1 Introduction  The current increase in tunnelling activity in built-up areas results in an increase exposure of existing services and structures to ground movements. To assess the associated risks requires either the application of an over-simplified and conservative method or complex numerical analysis, which can be time consuming. When only the risks to the structure are of interest, the important parameter is the half-width of the settlement trough between the points of inflexion, i. That value is used, in conjunction with the anticipated volume loss, to produce a deflected shape for which the structure can be assessed. This paper provides a method of obtaining this parameter for long structures within a range of stiffness (EI) values.   2 Euston Square Station  In November 1996, London Electricity plc (LE) constructed a 3m diameter tunnel under the existing Metropolitan Line at Euston Square station (Lu et. al., 1999, Samuel et. al., 1999). This tunnel was driven within London Clay to achieve a clearance of approximately 7m between the two structures (see Figure 1 for plan of crossing).  The Metropolitan Line was built in 1863 (Baker, 1885), and the section under Euston Road was a brick arch constructed using the cut and cover method. The foundations of the arch were just into London Clay and the arch was covered with about 8m of Terrace Gravel and made ground.  A site investigation was conducted and brick cores were taken from the masonry to obtain both strength and stiffness parameters. The unconfined compressive tests produced a range of strengths between 6.9 and 22 N/mm2 and the average Young’s modulus was 8500 N/mm2.  During the LE tunnel construction, precise levelling was carried out to measure the displacements along the walls and the crown. This surveying method was accurate to 1mm and the measured data at the axis and foundation (P6 and P7 respectively) is shown in Figure 2. The predicted greenfield settlement curve, based on a value of i calculated as half the depth between the LE tunnel axis and the arch foundations, is also shown. The back analysis of the settlement data showed a ‘best fit’ Gaussian curve with the point of inflexion, i, equal to 1.5 times the depth between the LE tunnel axis and the arch foundation. The actual settlement curve was 3 times wider than the greenfield condition and the volume loss was 2.5% one week after construction. Lu, Bloodworth & Gleig 3 of 9  Figure 1. Plan at Euston Square Station.  Distance from station headwall,  mSettlement, mm0-4-8 P6     P7    - Gaussian Curve2010 300  Figure 2. Observed and predicted settlements at tunnel axis and foundation levels, Euston Square Station.  Lu, Bloodworth & Gleig 4 of 9  3 Longford Street Spur Tunnel  A spur tunnel was excavated from an electricity substation to intersect the main tunnel drive, described in Section 2 above, at a point approximately 400m to the east of Euston Square. The spur tunnel was 77m long and 2.9m in diameter and was hand excavated in London clay on a decline at shallow depth, ranging from 4m to 15m beneath an existing structure (Bloodworth and Macklin, 1999).   The structure comprised a single-storey reinforced concrete frame which was the former basement of a substantial office development, demolished in 1996 to ground level (Figure 3). The basement extended over a wide area either side of the tunnel axis. The frame consisted of columns at 7m centres in both directions and a ground level slab. At basement level, a reinforced concrete slab was cast against the columns but was not structurally connected to them. The vertical separation of ground and basement level slabs was 4m. The columns were founded on pad footings 2m below basement slab level, approximately at the top of the London Clay. Precise level monitoring of the columns above the tunnel axis (points A – C), the basement slab over a wide area each side of the tunnel (points 1 –29) and for subsurface settlements 4m below basement slab level at a point where the tunnel axis was 8m below basement slab level (points 101 – 103) was carried out.  The settlement results at the chainage of the subsurface monitoring points are shown in Figure 4. The back analysis of the settlement data showed a volume loss of 0.8%, which was consistent with the depth of the tunnel below basement slab level and the stability number of the heading (Macklin, 1999). The trough width parameter i at the level of the subsurface monitoring points was found to be approximately twice the width predicted by methods based on subsurface settlement trough width in London clay (Mair et al, 1993). This widening of the trough was also observed at basement slab level.    Lu, Bloodworth & Gleig 5 of 9 2.59 I.D.CABLETUNNELX XXXX XXXX XXXXXX X X XXXXXXXXXX12345678910111213141516171819202122232425262729 XXX28ABC101102103Notes(1)  POINTS 1 TO 29 ARE HILTINAILS IN BASEMENT SLAB(2)  POINTS A B & C ARE SOCKETSIN COLUMNS AT BASEMENT SLABLEVEL(3)  101 102 & 103 ARE SUBSURFACE LEVELLINGPOINTS 4m BELOW BASEMENT SLAB LEVELEXIT TO RESTOF CAR PARKENTRY FROMREST OF CARPARKAA2.44m ID BOLTEDLINING TO SPURTUNNEL101-103BHMade groundStiff to VeryStiff FissuredLondon ClayOriginal Building Demolished toground floor levelLONGFORDSTREETJUNCTIONCHAMBERWeathered London clayC B A+25m+20m+25mVerticalScalem AOD10m5m0mHorizontalScale24.0720.0SECTION A-APLANBasement Slab level Figure 3. Plan and Section of Longford Street Spur Tunnel.  012345678-10 -5 0 5 10Transverse Distance from Spur Tunnel Centreline, y (m)Settlement (mm) Predicted greenfield subsurface Observed subsurfaceObserved column C Observed basement slab Figure 4. Predicted and observed settlement above spur tunnel, Longford St. Lu, Bloodworth & Gleig 6 of 9   4 Analysis Considerations  The simplest method to assess the level of risk, due to tunnelling beneath a structure, was to assume a flexible structure with the greenfield ground displacements superimposed. From this deflected shape, the gradients along the structure were calculated and compared with published data of settlement damage to buildings (eg. Boscardin and Cording, 1989). This method yielded conservative results.  Potts and Addenbrooke (1997), proposed an alternative method, modelling the building as an elastic beam and defining relative bending and axial stiffnesses as  = EI/EsH4 and *= EA/EsH respectively, where Es was defined as the representative soil stiffness. When H, the half width of the beam, became infinitely long, both stiffnesses would reduce to very small values. In their Figure 6, the i/Z value then became 0.5 for all values of relative axial stiffness ratios and Z was defined as the depth between the structure foundation to the axis of the tunnel.  Based on the two cases presented, the contribution from the structure appeared to become significant when the clearance between the structure and the tunnel was reduced. This could be attributed to the reduced trough width and the ability of the structure to ‘bridge’ across the trough. In a limiting situation, when the stiff structure could span across a sufficiently narrow trough, very little structural deflections would be anticipated which implied a large i/Z ratio. This assumed that the ground was capable of carrying the increased pressure at the foundation.  A series of FLAC (Fast Lagrangian Analysis of Continua) models were developed to study the behaviour of long structures subjected to underground construction, with reference to the Euston Square Station case study (Lu et al., 1999). The structure was idealised as a long beam glued to the top of the grid. A surcharge was also included to model the material above the arch tunnel. The soil was modelled as a non-linear elastic, undrained London Clay of stiffness parameters stated in Jardine et. al.(1986). An initial analysis was conducted which excluded the structure and good agreement between the numerical and theoretical curves can be seen in the Figure 7 of Lu et. al., 1999.  Three Z values were included in the analyses, namely 4.5m, 9.5m and 15m respectively. Figure 5 and Figure 6 shows the deflected shape of the structure compared with the greenfield settlement trough of i/Z=0.5 for tunnels at depth, Z, of 4.5m and 15m respectively. Lu, Bloodworth & Gleig 7 of 9 Tunnel at z=4.5m-1.2-1.0-0.8-0.6-0.4-0.20.00 5 10 15 20 25Horizontal Distance From Tunnel Axis, mS/SmaxGreenfield Conditioni/Z=2.0 Figure 5. Deflected shape of structure for tunnel at Z=4.5m.  Tunnel at z=15m-1.2-1-0.8-0.6-0.4-0.200 5 10 15 20 25Horizontal Distance From Tunnel Axis, mS/SmaxGreenfield Conditioni/Z=0.75 Figure 6. Deflected shape of structure for tunnel at Z=15m.  These analyses demonstrated that a reduced clearance between the tunnel and the structure would increase the trough width parameter, i/Z. The effect of the long structure would no longer be significant when the 3m diameter tunnel was more than 20m beneath it.   5 Proposed Design Chart and Analysis Method  A sensitivity study has been conducted to investigate the influence of the structural stiffness, EI, towards its deflected shape, where I was the gross section modulus. It was found that changing the EI from brick masonry to reinforced concrete would not have increased the trough width. The range of EI used in this work was between 1x107 and 1x108 kNm2/m. Figure 7 shows the semi-log plot for the i/Z Lu, Bloodworth & Gleig 8 of 9 to C/D ratios, where C was the clear space between the tunnel and structure. Data points in the figure also include the two case studies, Euston Square station and Longford Street. 1100 0.5 1 1.5 2 2.5i/ZC/DEuston Square Station,EI=4.25x107 kNm2/m.log10(C/D)=-0.56(i/Z)+1.06Longford Street,Approx. EI= 5x107 kNm2/m.* Numerical Analysis* Z=15m*Z=9.5m*Z=4.5m Figure 7. Proposed design chart.  The equation derived from the plot was log10(C/D) = -0.56 (i/Z) + 1.06, where the i/Z ratio should not be greater than 2 or less than 0.5. This range was perceived as the upper bound based on current work and the lower bound from observed greenfield data in stiff clay. From the plot, the limiting C/D ratio, for i/Z = 0.5, was 6.  The recommended procedure to assess the risk on a long structure due to tunnelling would be applying the known C/D ratio to the above equation to obtain the i/Z value. This point of inflexion, i, is then combined with the anticipated volume loss to produce a deflected shape of the structure, which is compared with published structure performance charts or tables to obtain the risk levels.   6 Conclusion  Using greenfield condition to predict structure response due to tunnelling, without accounting for the structural stiffness, will provide a conservative result. However, the relative depth of the tunnel beneath the structure will also influence its deflected shape. The ability of a long structure to bridge across a settlement trough will need to be taken into consideration in order to provide a realistic prediction of the structural deflections. Lu, Bloodworth & Gleig 9 of 9  ACKNOWLEDGEMENTS  The authors would like to thank the technical skill group leaders in Brown & Root Services, Mr G Wilkinson and Mr I Brough, for their support in the preparation of this paper.   REFERENCES  Baker, B. 1885. The Metropolitan and Metropolitan District Railways. Proceedings of the Institution of Civil Engineers. Vol. LXXXI, 1-33.  Bloodworth, A.G. and Macklin, S.R. (1999). Ground and structure response to a hand driven decline in London clay. Proc. International Symposium on Geotechnical Aspects of Underground Construction in Soft Ground, Tokyo, 75-80.  Boscardin, M D and Cording E J. (1989). Building Response to Excavation Induced Settlement. Journal of Geotechnical Engineering, ASCE, Vol. 115, No.1.  Jardine R J, Potts D M, Fourie A B and Burland J B (1986). Studies of the influence of non-linear stress-strain characteristics in soil-structure interaction. Geotechnique 36, No.3, 377-396.  Lu Y C, Samuel H R and Chudleigh I (1999). Response of a masonry arch tunnel to underground tunnelling. Proceedings of the 5th International Symposium on Field Measurements in Geomechanics, Singapore,.  Macklin, S.R. (1999). The prediction of volume loss due to tunnelling in overconsolidated clay based on heading geometry and stability number. Ground Engineering, Vol. 32, No. 4.  Mair, R.J., Taylor, R.N. and Bracegirdle, A. (1993). Subsurface settlement profiles above tunnels in clays. Geotechnique, Vol. 43, No. 2, 315-320.  Potts D M and Addenbrooke T I (1997). A structure’s influence on tunnelling-induced ground movements. Proc. Instn Civ. Engrs Geotech. Engng., 1997, 125 Apr., 109-125.  Lu, Bloodworth & Gleig 10 of 9 Samuel H R, Mair R J, Lu Y C, Chudleigh I, Addenbrooke T I and Readings P(1999). The effects of boring a new tunnel under an existing masonry tunnel. Proc. International Symposium on Geotechnical Aspects of Underground Construction in Soft Ground, Tokyo, 293-298.  

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Behaviour of long structures in response to tunnelling

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