Validation of methods for assessing tunnelling-induced

technical note

ground engineering march 2011 25

Validation of methods for assessing tunnelling-induced settlements on pilesMike Devriendt, Arup Michael Williamson, University of Cambridge & Arup

AbstractFor tunnelling projects, settlements of structures supported on piles are often appraised by using simplistic empirical assumptions. These include assuming the greenfield tunnelling-induced ground movement a given distance down the pile represents the displacement at the pile head.

This paper compares two com-monly used empirical assumptions with an analytical method of analy-sis. The analytical method has the advantage that the mobilisation of shaft friction and axial loading down the pile can be calculated. Analysis using the analytical meth-od takes very little time to carry out, is an improvement in sophistication relative to empirical methods and is less time consuming than carrying out more rigorous analysis using finite element or finite difference methods.

A sample set of calculations is provided that illustrates several important features of the analytical method and provides a compari-son with results from the empirical methods. To validate the use of the analytical method a back analysis is presented comparing results with those obtained from an instrument-ed pile test during tunnelling for the Channel Tunnel Rail Link in north London.

1. Introduction1.1 GeneralA requirement of tunnelling projects carried out in urban areas is to assess its impact on third party assets. The impact on masonry buildings founded on shallow foot-ings has been discussed by many authors and methods for their assessment are provided by Burland (1995) and Cording et al (2001). The impact on structures founded on piles, however, is covered less extensively. Examples of the effect of tunnelling on piles in recent years include studies from Loganathan et al (2000) and Selemetas (2005), which provide results from centri-

fuge modelling and field testing.Practising engineers carrying out

impact assessments of structures founded on piles commonly resort to making empirical assumptions relating to the settlements that occur to piles and the overlying building as a consequence of tunnelling-induced displacements. Further details of these simplifying assumptions are provided and discussed in Section 2.

Many low-rise masonry structures built in recent years are supported on individual piles with relatively low stiffness sub-structure linking the piles. In such instances a plausible method to assess the impact on the overlying structure is by calculat-ing the pile head displacements and imposing these onto a simple beam type analysis proposed by Burland (1995). Given the relative lateral flexibility of the piles and limited restraint offered by the sub-struc-ture, greenfield horizontal strains at sub-structure level arising from tun-nelling-induced horizontal ground movements are sometimes conserva-tively used in these analyses.

From the authors’ experience, the widespread use of empirical methods for calculating vertical displacements of the piles relates to a perception that more refined analysis takes much longer to carry out and requires the use of numeri-cal methods such as finite element analysis. While this may be carried out where structures are considered to be at higher risk of damage, vali-dation of the empirical assumptions for the less sophisticated analyses is not well documented.

This paper describes an analytical method of assessment using exist-ing published techniques that can be carried out quickly and provides the engineer with an understand-ing of the pile behaviour subjected to ground movements. The results presented in the paper also provide some evidence to support the use of the empirical techniques described in Section 2.

Both the empirical and analytical

methods could be used as part of a Stage 2 or 3 analysis when assessing impact on buildings as described in accordance with Burland (1995). More refined methods such as using finite element analysis may also be considered necessary to supplement the results from the empirical and analytical methods.

1.2. Constraints of paperThe examples used in this paper are limited to reviewing settlement characteristics of single piles located above tunnels. When appraising set-tlements, consideration is also given to the axial stress in the pile and mobilisation of shaft friction. Only piles with toes in soil that do not derive a significant amount of their capacity from the toe of the pile are considered.

The paper does not consider pile groups or lateral deflections of piles caused by tunnelling works. Further assessments would be required to assess these scenarios and the result-ing impact on the pile(s) and overly-ing structure above. It is also real-ised that the stiffness of buildings and sub-structure founded on piles (for instance those supported by piled rafts) will have a significant effect on the resulting pile displace-ment and building distortion.

2. Analysis methods2.1 Commonly used empirical methods2.1.1 Assumed depth down pile approach (2/3 depth approach)Ground movements are commonly calculated at a given distance down the pile length (1/2, 2/3, 3/4 or pile toe depth). The displacement calcu-lated at this given depth is assumed to also occur at the head of the pile. Generally for tunnelling induced ground movements, for pile toes located above the tunnel, the closer to the toe the displacement is cal-culated, the larger the assumed pile movement will be and the more con-servative the approach.

The authors do not know the

basis for these assumptions. How-ever, they believe engineers are extrapolating theories relating to the loading of pile groups and assump-tions that settlements can be calcu-lated by assuming an equivalent raft 2/3 down the pile (see Tomlinson, 1994). For the remainder of this paper, the settlement 2/3 down the pile will be used for comparisons with the other methods.

A perceived drawback with the approach is that settlements will vary depending upon the location of the pile relative to the tunnel. Buildings generally have many piles that will vary in position relative to the tunnel.

Therefore, making a constant assumption on the depth to assume ground settlement represent pile head displacement appears concep-tually to have drawbacks.

2.1.2 Neutral axis approachThe position of the neutral axis (NA) of the pile is calculated (ie where the pile shaft moves from being in com-pression to tension). Various empiri-cal or analytical approaches can be used to calculate the position of the neutral axis. The tunnelling-

α = adhesion factor between soil and pilecu = undrained soil shear strengthE = soil Young’s modulus. Represents both fine and coarse grained soils (undrained & drained response), see Table 1 E concrete = Young’s modulus of pile concreteEu = Undrained soil Young’s modulusk = tunnelling settlement trough width parameter at surfacekN = kilo NewtonL = length of pile m = metresMN = mega NewtonmOD = metres Ordnance DatumTBM = tunnel boring machinez = depth below ground level or point of reference

Key to notation

26 ground engineering march 2011

induced settlement at this posi-tion is assumed to represent the pile head displacement.

The disadvantage with this approach is that the pile may not have a neutral axis position if it is situated to one side of the tunnel (ie only the top section of a pile is affected by settlement, or the soil adjacent to the lower section of the pile settles less than the soil adjacent to the upper section of the pile). Under these circumstances the pile may be under compression along the entire shaft length.

2.2 Analytical methodThe method discussed in this paper was developed by Poulos and Mattes (1968, 1969) and Mattes and Poulos (1969) and is based upon lin-ear elastic theory. An individual pile is discretised into a number of ele-ments. Loads may be applied down the pile and displacements of the soil adjacent to the pile specified. A single Young’s modulus is speci-fied for the soil adjacent to the pile and a Young’s modulus specified for the soil below the base of the pile. A

Poisson ratio is specified for the soil. A rigid boundary is set at an appro-priate distance below the pile base. A Young’s modulus is also speci-fied for the pile shaft and the pile is assumed to behave elastically.

Limiting values of shaft skin friction are specified at each ele-ment position and slip between the soil and pile shaft occurs once this value has been reached. The elastic analysis described above is modi-fied to take account of this. First the displacements are calculated on the assumption that all elements are elastic. From the displacements, the shear stresses calculated are compared with the specified limit-ing stresses. The extra displacement caused by the out of balance force is calculated and added to the previous elastic solution. The shear stresses are then calculated again based on the modified displacements. This procedure is repeated until all shear stresses do not exceed the specified limiting shear stress.

The pressure at the base of the pile is calculated from elastic theory and considering the displacement at

the base of the pile. This assumption and those related to the tunnelling-induced soil displacement assumed at the pile/soil interface will be dis-cussed further in Section 3.1.

Figure 1 summarises some of the analysis assumptions in Sections 2.1 and 2.2 for the empirical and ana-lytical methods.

The analytical method is described in the commonly used text book by Fleming et al (1992). The method is also used in the OASYS program PILE.

3.Sample calculations3.1 GeneralTo provide a comparison between the methods described in Section 2, a series of calculations have been carried out for the scenario defined in Figure 2. The input parameters for the calculations are also given.

The Mair et al (1993) method is used to calculate the sub-surface set-tlement adjacent to the pile shaft. The analytical method described in Section 2 relies on relative displace-ments between pile shaft and soil being specified along the pile length. If all of the pile is in the settlement trough, the pile head and toe dis-placement is considered prior to the analysis. The lesser settlement of these two is noted and this set-tlement is subtracted from all of the settlements calculated down the pile shaft to form the input relative pile shaft/soil displacement. Follow-ing completion of the analysis, the lesser settlement calculated prior to the analysis is added to the results of all settlements of the pile to provide the overall pile settlement.

The analytical method also cal-culates a settlement from initially imposing the 1MN load prior to applying the tunnelling-induced soil displacements. A load of 1MN corresponds with a factor of safety of approximately 3.5 for the soil parameters and pile defined in Fig-ure 2. This initial loading settlement is subtracted from the results pre-sented in the paper.

For Pile A, initial calculations using the PILE program indicated that a pressure in the base of the pile was developing despite the soil adja-cent to the toe settling more than the pile toe. In such instances it would be reasonable to expect the pile toe to generate zero pressure. The error arises from PILE assuming that the displacement of the soil or rock beneath the toe to be zero and calculating a pressure using elastic theory from the pile base displace-ment. The error may be overcome by specifying a low stiffness for the soil beneath the base. This does not introduce subsequent errors on other parts of the calculation.

Where the pile toe settles more than the adjacent ground, it is not necessary to make this correction. This may be the case if a pile is locat-ed a given lateral distance from the tunnel and the toe is not influenced by the tunnelling induced settlement.

3.2 ResultsFigures 3 and 4 present results from the analysis for Pile A located above the centre line of the tunnel and Pile B located 10m from the centre line respectively. A sequence of graphs is shown in these figures to provide

technical note

Figure 1: Empirical and analytical approaches Figure 2: Example scenario for comparison calculations

2/3L

A

B

Greenfield displacement from tunnel at B assumed to be pile head displacement at A

Empirical assumed depth down pile approach

A

B

Greenfield displacement from tunnel at B assumed to be pile head displacement at A

Empirical neutral axis approach

Axial load in pile

Neutralaxis

Model requires following inputs:

• Poisson ratio of soil • Young’s modulus of pile • Young’s modulus of soil adjacent to shaft • Young’s modulus of soil beneath base • Skin friction limit down shaft to achieve mobilisation • Soil displacement adjacent to pile shaft • Pile load • Depth to rigid boundary

Analytical approach

Rigid boundary

Specify soil displacement and limiting shaft friction at nodal positions

Pile A20m length, 0.6m diameter pile

10m

Pile B20m length, 0.6m diameter pilePile 10m from tunnel centreline Pile directly over tunnel centreline

Applied load of 1MNApplied load of 1MN

25m depth to tunnel centreline

7.08m diameter1% volume lossMair et al (1993) settlement calc

Analytical modellingassumptionsα = 0.5cu = 50 + 10z (z depth (m) below surface) Eusoil adjacent to shaft = 60,000kN/m 2

Eusoil below toe = 100,000kN/m2 (for pile loading only – for other analyses please refer to Section 3.1 for modelling assumptions)Poisson ratio of soil = 0.5Rigid boundary 40m below ground levelE concrete = 20 x 106 kN/m 2

Not to scale

Ground level at +40mOD


0

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2/3 depth down pile approachTake settlement at 26.66mOD from Mair et al (1993)Settlement = 19.2mm

Neutral axis position approachNA (ie tension to comp point) = 29.6mODSettlement from Mair et al (1993) = 17.2mm

Analytical approach (from PILE)Pile head settlement = 18.9mm

Tunnel geometry7.08m diameter1% volume lossaxis level = 25m below ground level

Pile geometry0.6m diameter20m length

Ground and pile displacement Pile displacement from relativepile/soil settlement

Shaft friction Axial stress in pile

Ground displacement (Mair et al)Pile displacement

1MN load, no downdrag1MN load, no downdrag1 MN load, downdragNo pile load, downdrag1MN load, downdragNo pile load, downdrag

1MN load, no downdrag1 MN load, downdragNo pile load, downdrag

1MN load, no downdrag1MN load, downdragNo pile load, downdrag


1MN load, no downdrag1MN load, downdragNo pile load, downdrag

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2/3 depth down pile approachTake settlement at 26.66mOD from Mair et al (1993)Settlement = 9.1mm

Neutral axis position approachNA (ie tension to comp point) = not present

Analytical approach (from PILE)Pile head settlement = 9.1mm

Tunnel geometry7.08m diameter1% volume lossaxis level = 25m below ground level

Pile geometry0.6m diameter20m length

Ground and pile displacement Pile displacement from relativepile/soil settlement

Shaft friction Axial stress in pile

Ground displacement (Mair et al)Pile displacement

1MN load, no downdrag1MN load, no downdrag1 MN load, downdragNo pile load, downdrag1 MN load, downdragNo pile load, downdrag





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Figure 3: Results from Pile A above centreline of tunnel

Figure 4 - Results from Pile B, 10m from tunnel centreline

results from some of the calcula-tions carried out using the analytical approach. The top left graph shows the greenfield ground movement from Mair et al (1993) and those calculated for the pile from the pro-posed analytical approach. The pile settlement has been calculated from the method described in Section 3.1.

The top right graph provides the displacements calculated from the analytical method for various analy-ses. The series in the graphs provide the displacement from loading the pile with 1MN, settlement from applying the relative settlement on the pile from the tunnelling induced settlement (referred to as “down-drag” in the graph series title) and the combination of both settlement and pile loading. The bottom left and bottom right graphs show the shaft friction mobilised down the pile and the axial stress within the pile shaft.

A comparison is given at the bottom of each figure describing the pile head settlement calculated from the empirical and analytical approaches. For the pile located above the centreline the analytical and 2/3 depth approach calculate very similar pile head settlements (approx 19mm), while the neutral axis approach calculates a margin-ally smaller settlement (17.2mm). For the pile located 10m from the centreline, the analytical and 2/3 depth approach calculate the same pile head settlement (approx 9mm). There is no neutral axis position in the pile, therefore, the neutral axis approach yields no result.

Figure 5 (overleaf) shows further results varying the position of Pile B and shortening the pile to 10m in length for providing further compar-ison of the pile head displacement against the empirical methods. The graph illustrates the limitations of the NA approach identifying that it can only be used where the pile being assessed is close to the cen-treline of the tunnel. The analyti-cal (PILE) analysis and 2/3 depth approach produce similar results for varying the position of the pile relative to the tunnel centreline and varying the pile depth.

The analytical approach has the further advantage that an under-standing of the pile behaviour can be gained by review of the mobi-lisation of shaft friction and axial loading in the pile. An appreciation of the axial loading can be used for further calculations where the struc-tural capacity of the pile is checked.

4. Comparison with case study displacements4.1 GeneralThe study described in Section 3 identifies comparisons and drawbacks with the empirical and


technical noteanalytical approaches. A further

study has been carried out to back analyse case study observations of a pile subjected to tunnelling induced settlements.

Results of pile settlements as a consequence of tunnelling have been obtained from Selemetas (2005). A summary of the work may be found in Selemetas (2004) and Selemetas et al (2006). The references include results from the Channel Tunnel Rail Link (CTRL) London tunnels construction beneath a series of test piles installed ahead of the tun-nel drives. The tunnels are 8.15m in diameter with tunnel axis level 18.9m below ground level.

This paper will consider settle-ments of Pile FO detailed in the references during the passage of the down line tunnel. Figures 6 and 7 provide an illustration of the tun-nels and pile test general arrange-ment. The ground and groundwa-ter conditions are also summarised in Figure 6. Pile FO was located approximately 7m from the Down Line centre line.

The pile was installed to a depth of 13m and had a diameter of 0.456m. The pile was installed by driving a steel tube into the ground, removing the soil within the tube, then installing grout within the tube. The tube was then removed and the instrumented reinforce-ment cage lowered into position within the grouted hole. Instrumen-tation comprising inclinometers, extensometers and piezometers were also installed.

This paper will consider the results from extensometer E3 alongside the results from Pile FO. Extensometer E3 was located 6m from the centreline of the down line tunnel.

Back analysing the data, Selemetas (2004) reported a volume loss of 0.5% and a trough width parameter, k of 0.42 during the drive of the Down Line tunnel beneath Pile FO. At surface level this corresponds with a distance, i from the maximum settlement to point of inflection on the settlement curve of approximately 8m.

4.2 Back analysesTo appraise whether the analytical method reproduces results similar to the case study, the following back analyses have been carried out:

a) Comparison of the load/set-tlement and axial stress response of the pile during loading of the pile with a load of 240kN;

b) Assessing the settlement and axial load in the pile caused by the tunnel when the face of the tunnel had progressed 34m past the pile position. This corresponds with approximately five days after the

tunnel face passed the pile position; c) Assessing the settlement and

axial load in the pile caused by the tunnel 22 days after the face of the tunnel had progressed past the pile position.

For assessing b and c, the displace-ments from Extensometer E3 have been applied to the analytical PILE analysis of the pile. A 1m lateral dif-ference between the offset from tun-nel centre line of the extensometer and the pile is acknowledged, but this is considered to only have a relatively small effect on the accuracy of the back analysis.

By carrying out calculations using the method proposed by Mair et al (1993), the difference is likely to equate to applying displacements that are approximately 1mm larger than the soil displacements adjacent to the pile.

4.3 Results4.3.1 Initial loading responseThe load/settlement response and load distribution in the pile observed during loading of pile FO and from the PILE back analysis is shown in Figure 8. Reasonable agreement is achieved between the observed load/displacement response and stress down the pile.

Table 1 provides the input parameters used for the PILE analysis. The following should be noted when considering the input parameters:n The stiffness of the ground adjacent to shaft and beneath the base was set at a high value relative to what may be used for conventional analysis. Such high values are plausible given the very low strains that the ground adjacent to the pile experienced. Another possible reason for the high stiffness used in the back analysis may be due to the partial driving pile construction method. For information, the stiffness beneath the base would approximately correspond to Eu = 2000cu;n The top of pile shaft skin friction in made ground was set at a relatively high value. Test results for the pressure down pile suggest this to be appropriate.

To achieve similarity between observed and back analysed load/settlement behaviour, the input parameters were amended in accord-ance with above noted observations.

4.3.2 Pile response when tunnel face is 34m past pile and 22 days following passage of tunnelThe settlement response of the head of Pile FO with time caused by the tunnel construction is shown in Fig-ure 9. The position of the face of the TBM is also shown on this graph. This figure has been taken from

0

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(mm

)

Distance from tunnel centreline (m)

5 10 15 20

20

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Analytical (PILE)Empirical (2/3 depth)Empirial (NA)

Analytical (PILE)

20m pile:

10m pile:

Empirical (2/3 depth)Empirial (NA)

X

X

13m

6m

7m

Not to scale

Pile FO, 0.456m diameter. Load ofapproximately 240kN applied to pile

Extensometer E3Depth belowground level (m)

Ground waterlevel (4m)

Down line tunnel,8.15m diameterAxis level 18.9m belowground levelCrown of tunnel 1.825mbelow toe of pile FO

0

3

7.5

11.2

Made ground

Alluvium

Terrace Gravels

London Clay

Figure 5: Pile head settlements for 10 and 20m piles

Figure 6: CTRL Down Line tunnel, Pile FO and Extensometer E3 general arrangement

Figure 7: Panoramic view of the CTRL test site showing the test set up for Pile FO and three other piles tested


Selemetas (2005) and extrapolation has been carried out (see vertical and horizontal lines on graph) to establish the settlement of the pile when the tunnel face was 34m past the pile position and 22 days after the passage of the tunnel face.

A comparison between observed and back analysed settlement and pressure distribution down the pile shaft is shown in Figure 10. For the back analysis the same input param-eters as given in Table 1 were used for the analysis.

The settlement obtained if the pile head displacement was assumed to be the greenfield displacement at an ele-

vation of 2/3 down the pile at Exten-someter E3 is also shown in Figure 10. Reasonable agreement is seen between the observed and back ana-lysed pile head displacement using either the analytical or 2/3 down the pile assumption. It is noticeable that the observed displacements are marginally less than the calculated displacements.

This may be attributed to the larger displacements taken from Extensometer E3 assumed in the back analysis relative to those likely to have occurred adjacent to Pile FO.

Using the analytical method, the

stress down the pile is slightly larger than observed from the case study. The greatest difference is seen at approximately 4m depth. The larger displacements taken from Extensom-eter E3 assumed in the back analy-sis relative to those likely to have occurred adjacent to Pile FO may partly explain why the back analysis over predicts the axial stress.

It should be noted that the back analysis has assumed a low soil stiffness at the toe of the pile because it has been inferred from the case study data that the soil beneath the pile toe is likely to have settled more or about the same magnitude as the

pile. Re-running the analysis with a higher soil stiffness at the toe would yield larger stresses in the pile.

5. ConclusionsThe back analysis and comparative studies contained in this paper pro-vide a reference for understanding the applicability of empirical and analytical methods to represent the behaviour of settlements arising from tunnelled excavations on sin-gle piles.

The empirical method of assum-ing the neutral axis (zero axial force) position in a pile corresponds with the head displacement shows

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Analytical (PILE) analysis

Pile FO measured

Analytical (PILE) analysis

Pile FO measured

Load/settlement response during loading of pile FO

Axial stress response during loading of pile FO

Figure 8: Measured and back analysed load/settlement and axial stress distribution of Pile FO during loading

Depth below Limiting friction Materialground level (m) (kN/m2) 0 0 Made ground 1 23 Made ground 2 46.1 Made ground 3 10 Alluvium 4 10 Alluvium 5 10 Alluvium 6 10 Alluvium 7 10 Alluvium 8 44.1 Terrace gravels 9 48.9 Terrace gravels 10 53.8 Terrace gravels 11 58.6 Terrace gravels 12 40.8 London Clay 13 46.8 London Clay

Additional parameters used: E concrete = 23.4 x 106 kN/m2

Rigid boundary set at 30m below ground levelE shaft = 90 x 103 kN/m2, E below base = 150 x 103 kN/m2

Load applied to pile = 240kN, Poisson ratio of ground = 0.25

Table 1: Parameters used in analytical (PILE) back analysis of Pile FO

Figure 10: Tunnelling-induced Pile FO response

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Pile axial stress response

500 1,000 1,500 2,000 2,50014

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TBM face 34m past Pile FOAnalytical (PILE) analysis:

22 days after TBM has passed

Pile FO measured after tunnelling - approx. 8 days after tunnel facepassed pile

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Pile settlement response

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TBM face 34m past pile

Analytical (PILE) analysis:

Pile FO measured:

22 days after TBM has passed pile




Extensometer E3 displacement:

2/3 depth extensometer E3 displacement:




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TBM face 34m past Pile FOPile head settlement:

TBM 22 days past Pile FO

TBM progress

Figure 9: Pile FO settlement/time response from passage of TBM


reasonable correlation with the 2/3 depth assumption and analyti-cal method. The neutral axis meth-od cannot be applied where no neu-tral axis occurs down the pile. This is found to be the case where a pile is located to the side of a tunnel.

The analytical and 2/3 depth method showed good agreement with pile head displacements observed from the CTRL case study. The use of the analytical method also provides information about the mobilisation of shaft stresses and axial force down the pile as an out-put to the analysis.

For back analysing the CTRL case study, the analytical method calculated pile stresses that showed good agreement with the measured data for loading the pile. The ana-lytical method over-predicted pile stresses when back analysing the effects of tunnelling on the pile, however, this may partly be attribut-ed to assumptions made for the back analysis relating to the tunnelling induced soil displacements adjacent to the pile.

The analytical method appears to be appropriate for carrying out analysis in a time effi cient manner prior to the use of more sophisticat-

ed methods such as fi nite element analysis. The use of more sophis-ticated methods would also allow other aspects to be considered such as the pile cap, sub-structure and horizontal displacements.

Further comparisons between relatively simple analytical mod-els described in this paper and case study displacements should be car-ried out to supplement these studies. Future underground construction projects present an opportunity to obtain further data to carry out com-parative studies.

In addition, the analytical method may be of use for comparing with numerical models or providing a simple model to compare centrifuge modelling test results against.

AcknowledgmentsThe authors would like to thank Professor Robert Mair of Cambridge University, Alice Berry of Arup and David Harris for their constructive comments on the paper and discussion on the subjects contained in the paper. This work is funded by the EPSRC and Arup, and has been carried out as part of a PhD the second author is undertaking at University of Cambridge.

technical note

Burland J B (1995). Assessment of Risk of Damage to Buildings Due to Tunnelling and Excavation. Proceedings of 1st International Conference on Earthquake Geotechnical Engineering, IS- Tokyo.Cording E J; Long J H; Son M; and Laefer D F (2001). Modelling and Analysis of Excavation-Induced Building Distortion and Damage Using a Strain-based Damage Criterion. CIRIA SP201, Responses of Buildings to Excavation-Induced Ground Movements, Proceedings of the International Conference, Imperial College, London, pp 245-256.Fleming W G K; Weltman A J; Randolph M F and Elson W K (1992). Piling Engineering 2nd edition. E & FN Spon.Loganathan N; Poulos H G; Stewart D P (2000). Centrifuge Model Testing of Tunnelling-Induced Ground and Pile Deformations. Géotechnique 50 No. 3, pp283–294.Mair R J; Taylor R N; Bracegirdle A (1993). Subsurface Settlement Profi les Above Clay in Tunnels. Géotechnique 43 No. 2, pp315-320.Mattes N S; Poulos H G (1969).

Settlement of Single Compressible Pile. Journal of the Soil Mechanics and Foundation Division, Proc. of ASCE, Vol. 95, No. SM1, Jan 1969, pp189-206.Poulos H G; Mattes N S (1968). The Settlement Behaviour of Single Axially Loaded Incompressible Piles and Piers. Géotechnique 18, pp351-371.Poulos H G; Mattes N S (1969). The Behaviour of Axially Loaded End-bearing Piles. Géotechnique, Vol. 19, No 2, pp285-300.Selemetas D (2004). Pile Settlement Due to Tunnelling in London Clay: A Case Study. Ground Engineering, June 2004, pp29-32.Selemetas D (2005). The Response of Full-scale Piles and Piled Structures to Tunnelling. University of Cambridge.Selemetas D; Standing J R; Mair R J (2006). The Response of Full-scale Piles to Tunnelling. Geotechnical Aspects of Underground Construction in Soft Ground, pp763 – 769. Tomlinson M J (1994). Foundation Design and Construction, 6th edition. Longman.

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Validation of methods for assessing tunnelling-induced