Vardanega, P. J. (2015). Sensitivity of simplified pile settlement calculationsto parameter variation in stiff clay. In M. G. Winter, D. M. Smith, P. J. L.Eldred, & D. G. Toll (Eds.), Geotechnical Engineering for Infrastructure andDevelopment: Proceedings XVI European Conference on Soil Mechanicsand Geotechnical Engineering (Vol. 7, pp. 3777-3782). London: ICEPublishing. DOI: 10.1680/ecsmge.60678.vol7.595

Publisher's PDF, also known as Version of record

Link to published version (if available):10.1680/ecsmge.60678.vol7.595

Link to publication record in Explore Bristol ResearchPDF-document

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This document is made available in accordance with publisher policies. Please cite only the publishedversion using the reference above. Full terms of use are available:http://www.bristol.ac.uk/pure/about/ebr-terms

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Proceedings of the XVI ECSMGEGeotechnical Engineering for Infrastructure and DevelopmentISBN 978-0-7277-6067-8

© The authors and ICE Publishing: All rights reserved, 2015doi:10.1680/ecsmge.60678

Even though it could be possible to increase the tip normal stiffness, in the presence of very long piles no significant variations are expected to take place. In fact, load is transferred to the tip only when relevant pile displacement are obtained. Consequently, the initial stiffness of the simulated load-displacement curve would not change as a function of the tip stiff-ness parameter.

The soil stiffness can be increased as shown in Figure 10, according to G-γ curves presented by Seed and Idriss (1970). The pile load test curve can therefore be easily back analyzed, as shown in Fig.11.

During Calibration #2 the frictional interfaces de-fined in Equation 1 and reported in Fig. 2a have been adopted, assuming the values of βi shown in Fig. 7a (design β). In this way, the effect of the confining pressure is properly taken into account and the em-bedded pile approach is suitable to better reproduce the raft and group pile influence.

0

10

20

30

40

50

60

70

0 50000 100000 150000 200000

z(m)

E(kN/m2)

ENspt E=Ecalibr

Figure 10. Calibration #2: a) calibrated values for the soil strata stiffness (E calib);

0

10000

20000

30000

40000

50000

60000

70000

0 0.05 0.1 0.15 0.2 0.25 0.3

Q [k

N]

uz [m]

E=Ecalibr

Pile A E=Ecalibr

Figure 11. Calibration #1: simulations of pile load test curve

5 CONCLUSIONS

A specific methodological path for the proper inter-face law calibration is presented. A case study related to an in situ pile load test (50 m long pile with a di-ameter of 2 m loaded with two Osterberg cell) is con-sidered in order to validate the calibration of a single embedded pile. Two different calibration procedures are presented and an extensive parametric study is performed in order to clarify the role of both stiffness and strength parameters in the embedded pile ele-ment interface with respect to the soil interfaces. The effectiveness of the adopted frictional law for em-bedded piles is demonstrated in the capability of simulating a full scale single pile test in layered soil. The soil stiffness of the strata is alighted to be the critical point to get a satisfactory simulation of the in situ pile load test. As a consequence a slightly higher values are considered as it results from a back-analyses procedure. The presented calibration proce-dure should be considered as a sort of academic exer-cise to get practical suggestions in order to retrieve the necessary engineering parameters from in situ pile load tests when embedded piles are considered.

ACKNOWLEDGEMENTThe financial and technical support provided by Arup to the first author's PhD research is gratefully acknowledged; notes by by prof. Claudio di Prisco and eng. Bruno Becci are also gratefully acknowledged.

REFERENCES

Becci, B., Nova, R., Baù, A. and Haykal, R. (2007), Prove di carico su pali di grande diametro mediante l’impiego di celle Osterberg, Rivista Italiana di Geotecnica (RIG), 41(4), 9-28, in Italian.Murrells, C., Ibrahim, K. & Bunce, G. (2009), Foundation design for the Pentominium tower in Dubai, UAE, Proceedings of the ICE - Civil Engineering, 162 (6), 25–33.Sadek, M. & Shahrour, I. (2004), A three dimensional embedded beam element for reinforced geomaterials, International Journal for Numerical and Analytical Methods in Geomechanics, 28 (9), 931–946.Seed, H. and Idriss, I. (1970), Soil moduli and damping factors for dynamic response analyses, Rap. tecn., Earthquake Engineering Research Center, Berkeley, California.

Sensitivity of simplified pile settlement calculations to parameter variation in stiff clay

Sensibilité des calculs simplifiés de règlement des tas de variation de paramètre dans l'argile raide

P.J. Vardanega*1

1 University of Bristol, Bristol, United Kingdom * Corresponding Author

ABSTRACT Pile settlement is a key geotechnical design consideration. The serviceability limit state for deep foundations cannot be ig-nored and yet many design methods merely assume that large factors of safety are sufficient to prevent excessive settlements. A simplemodel, supported by previously published databases of load testing on bored piles founded in London clay, is used to make predictions ofsettlement for bored pile foundations in the same geological deposit. The results of a detailed sensitivity study of the key parameters that af-fect the performance of bored piled foundations are presented. The parameters studied include: the mobilisation factor; the mobilisationstrain; the elastic modulus of the concrete; the undrained shear strength profile; the pile length and the pile diameter. Based on the prelimi-nary results of this sensitivity study, design guidance is presented and a rank of order of the parameters is given in order of their influenceon the settlement calculation result. The influence of soil non-linearity is also studied. RÉSUMÉ L’implantation des pieux est une considération de conception géotechnique majeure. L’état limite de service pour les fondationsprofondes ne peut être ignoré et encore beaucoup de méthodes de conception prennent simplement pour acquis que les grands facteurs desécurité suffisent à prévenir les implantations excessives. Un modèle simple, soutenu par des bases de données sur les essais de chargementdes pieux forés dans l’argile de Londres précédemment publiées, est utilise pour établir des prédictions d’implantation de fondations enpieux forés dans le même dépôt géologique. Les résultats d’une étude détaillée de sensibilité des paramètres les plus importants affectait lesperformances des fondations en pieux forés sont présentés. Les paramètres étudiés incluent : le facteur de mobilisation, l’effort de mobilisa-tion, le module élastique du béton, l’allure de la force de cisaillement non drainée, la longueur du pieu et le diamètre du pieu. Basé sur lesrésultats préliminaires de cette étude de sensibilité, un guide de conception est présenté et un rang est attribué aux paramètres en fonctionde leur influence dans les résultats des calculs d’implantation. L' influence du sol non - linéarité est également étudié.

1 INTRODUCTION

Simple methods for the estimation of pile settlement are useful for geotechnical engineers. Generally piled foundations in the UK are designed on the basis of collapse considerations as opposed to serviceability considerations (Vardanega et al. 2012a).

This paper presents a generalized version of the simple MSD-style calculation for pile settlement in stiff clay (Vardanega et al. 2012b and Vardanega 2012). MSD for piles is reminiscent of traditional p-y calculations for piled foundations (Bouzid et al. 2013). The calculation method used in this paper is inspired by the formulation of Randolph (1977). It

makes use of the strain to mobilize half the undrained shear strength (also used in the early work of Mat-lock, 1970) and the power-law formulation for soil-stress strain presented and calibrated in Vardanega & Bolton (2011a). The method has been shown (in Vardanega et al. 2012b) to reasonably match the gen-eralized pile-settlement curves for the database of tests in London clay presented in Patel (1992). The simple model also reasonably matched data from centrifuge model tests in kaolin (Williamson, 2014) and for two pile tests at a site in the Jurassic clay in the Moscow region (Kolodiy et al. 2015).

This paper presents the results of a sensitivity analysis aimed at assessing the relative influence of

Geotechnical Engineering for Infrastructure and Development

3778

the key design parameters using the previously pub-lished calculation method and the results of previous-ly published databases. The baseline condition is considered to be a typical characterization of the rel-evant design parameters for the London clay deposit.

2 PILE SETTLEMENT MODEL

Equation 1 is the simple power-law model for strength mobilization that has been calibrated with a large database of tests on clays and silts (Vardanega & Bolton, 2011a),

b

MucM

2

5.01

5>M>1.25 (1)

where, b = non-linearity factor determined from curve fitting analyses; cu = undrained shear strength; τ = mobilized shear stress; γ = shear strain; γM=2 = shear strain to half mobilisation (0.5cu) and M = mo-bilisation factor.

Equation 2 is Randolph’s approximate equation of radial reduction of shear stress (Randolph, 1977; Fleming et al. 2009)

rr00 (2)

where, τ0 = shear stress on the pile shaft; r0 = pile ra-dius and τ = shear stress at radius, r (see Figure 1).

Figure 1. Displacement of a single pile (plot adapted from Vardanega et al. 2012b)

Noting that the downward displacement of the

pile, w is equal to the integral of the shear strain with

respect to the radii of concentric surfaces (Randolph, 1977) (Equation 3 and Figure 1), we can say

drwor

(3)

substituting in Equations 1 and 2 we get

or

b

uM

b drrc

rw)/1(

002

)/1(2 (4)

bMsoil

MDw

12

(5)

where, wsoil = computed pile settlement (soil contri-bution) and D = pile diameter and

112

2 )/1(

b

b

(6)

The estimation of the contribution of compression of the concrete component to the total pile settlement is given in Vardanega et al. (2012b).

Equation 7 shows the generalized form of the bored pile settlement equation shown in Vardanega et al. (2012b) (see also Williamson, 2014)

2

)/1(2 2

DL

EMc

MDw

c

ub

Mh (7)

where, wh = computed pile head settlement (total); Ec = elastic modulus of the concrete pile and L = length of pile in the clay.

Equation 7 makes use of the assumed stress distri-bution in Figure 1 and the simple pile geometry and soil strength profile shown in Figure 2. It is acknowl-edged in Vardanega et al. (2012b) that a more rigor-ous non-linear model could make use of full load-transfer (e.g. Fleming et al. 2009) and in such analy-sis inclusion of the base resistance is possible.

Vardanega et al. (2012b) explain that for the col-lapse condition for bored piles (i.e ‘α-method’) to hold then Equation 8 (which links the factor of safety F [shaft] to the adhesion value, α and the mobiliza-tion factor, M) should also hold when using Equation 7 for settlement checks:

MF (8)

For example, if α = 0.45 (Skempton, 1959) then the lower ‘realistic’ limit of M is about 2.2 and if α = 0.6 (Patel, 1992) the lower realistic limit of M is about 1.7. This simple analysis shows why relatively large M values are needed to deal with both collapse and serviceability considerations in bored pile design.

Figure 2. Idealized soil strength profile and pile geometry 3 BASELINE VALUES (LONDON CLAY)

3.1 Soil stress-strain variation

The η term in Equation 7 allows for varying values of b which has a mean value (μ) of about 0.6, based on the database of 115 tests on 19 natural clays and silts presented in Vardanega & Bolton (2011a), with a standard deviation (σ) of about 0.15. Vardanega & Bolton (2011b) show that based on 17 reported tests on London clay b is on average 0.6 with a standard deviation of 0.12, i.e. very similar to the values from the larger database. The standard deviation of γM=2 is much lower for the London clay tests – around 0.002 and this value will be used in this paper. The varia-tion of η with b is given in Table 1. Table 1. Variation of η with b

b η 0.36 (-2 σ) 1.93 0.48 (-1 σ) 1.96 0.60 (mean) 0.72 (+1 σ) 0.84 (+2 σ)

2.38 3.37 5.99

3.2 London clay cu-profile variation

The values used in for the sensitivity of the cu-profile (shown in Table 2 and plotted on Figure 3) are de-rived using the Graphical Three-Sigma Rule (e.g. Duncan, 2000) and the database of mean undrained

strength profiles in London Clay collected by Patel (1992).

Table 2. Variation cu-profile in London Clay (based on the data-base presented in Patel 1992) [d as defined in Figure 2]

cu-profile lowest conceivable -2 σ

cu (kPa) = 5.7d + 25 cu (kPa) = 6.2d + 40

-1 σ cu (kPa) = 6.7d + 55 μ +1 σ +2 σ highest conceivable

cu (kPa) = 7.2d + 70 cu (kPa) = 7.7d + 85 cu (kPa) = 8.2d + 100 cu (kPa) = 8.7d + 115

Figure 3. Results of ‘graphical three sigma’ construction (e.g. Duncan, 2000) to the database of Patel (1992). N.B. Only one site in the database has data that is close to the upper bound line (as drawn) at depth and is therefore considered to be an outlier

3.3 Concrete elastic modulus variation

It is difficult to sensibly assign a population μ and σ value to Ec. In this paper simple range of values (10 to 30GPa) is used and a baseline value of 20GPa is adopted as was done in Vardanega et al. (2012b).

3.4 Mobilization factor

Vardanega et al. (2012a) show that for six codes of practice the factor of safety (F) demanded for bored pile design can range from about 1.7 to upwards of 3 with a typical value of 2.5. Noting that we are study-ing London clay (α≈0.6), the range of F implied by

3779

the key design parameters using the previously pub-lished calculation method and the results of previous-ly published databases. The baseline condition is considered to be a typical characterization of the rel-evant design parameters for the London clay deposit.

2 PILE SETTLEMENT MODEL

Equation 1 is the simple power-law model for strength mobilization that has been calibrated with a large database of tests on clays and silts (Vardanega & Bolton, 2011a),

b

MucM

2

5.01

5>M>1.25 (1)

where, b = non-linearity factor determined from curve fitting analyses; cu = undrained shear strength; τ = mobilized shear stress; γ = shear strain; γM=2 = shear strain to half mobilisation (0.5cu) and M = mo-bilisation factor.

Equation 2 is Randolph’s approximate equation of radial reduction of shear stress (Randolph, 1977; Fleming et al. 2009)

rr00 (2)

where, τ0 = shear stress on the pile shaft; r0 = pile ra-dius and τ = shear stress at radius, r (see Figure 1).

Figure 1. Displacement of a single pile (plot adapted from Vardanega et al. 2012b)

Noting that the downward displacement of the

pile, w is equal to the integral of the shear strain with

respect to the radii of concentric surfaces (Randolph, 1977) (Equation 3 and Figure 1), we can say

drwor

(3)

substituting in Equations 1 and 2 we get

or

b

uM

b drrc

rw)/1(

002

)/1(2 (4)

bMsoil

MDw

12

(5)

where, wsoil = computed pile settlement (soil contri-bution) and D = pile diameter and

112

2 )/1(

b

b

(6)

The estimation of the contribution of compression of the concrete component to the total pile settlement is given in Vardanega et al. (2012b).

Equation 7 shows the generalized form of the bored pile settlement equation shown in Vardanega et al. (2012b) (see also Williamson, 2014)

2

)/1(2 2

DL

EMc

MDw

c

ub

Mh (7)

where, wh = computed pile head settlement (total); Ec = elastic modulus of the concrete pile and L = length of pile in the clay.

Equation 7 makes use of the assumed stress distri-bution in Figure 1 and the simple pile geometry and soil strength profile shown in Figure 2. It is acknowl-edged in Vardanega et al. (2012b) that a more rigor-ous non-linear model could make use of full load-transfer (e.g. Fleming et al. 2009) and in such analy-sis inclusion of the base resistance is possible.

Vardanega et al. (2012b) explain that for the col-lapse condition for bored piles (i.e ‘α-method’) to hold then Equation 8 (which links the factor of safety F [shaft] to the adhesion value, α and the mobiliza-tion factor, M) should also hold when using Equation 7 for settlement checks:

MF (8)

For example, if α = 0.45 (Skempton, 1959) then the lower ‘realistic’ limit of M is about 2.2 and if α = 0.6 (Patel, 1992) the lower realistic limit of M is about 1.7. This simple analysis shows why relatively large M values are needed to deal with both collapse and serviceability considerations in bored pile design.

Figure 2. Idealized soil strength profile and pile geometry 3 BASELINE VALUES (LONDON CLAY)

3.1 Soil stress-strain variation

The η term in Equation 7 allows for varying values of b which has a mean value (μ) of about 0.6, based on the database of 115 tests on 19 natural clays and silts presented in Vardanega & Bolton (2011a), with a standard deviation (σ) of about 0.15. Vardanega & Bolton (2011b) show that based on 17 reported tests on London clay b is on average 0.6 with a standard deviation of 0.12, i.e. very similar to the values from the larger database. The standard deviation of γM=2 is much lower for the London clay tests – around 0.002 and this value will be used in this paper. The varia-tion of η with b is given in Table 1. Table 1. Variation of η with b

b η 0.36 (-2 σ) 1.93 0.48 (-1 σ) 1.96 0.60 (mean) 0.72 (+1 σ) 0.84 (+2 σ)

2.38 3.37 5.99

3.2 London clay cu-profile variation

The values used in for the sensitivity of the cu-profile (shown in Table 2 and plotted on Figure 3) are de-rived using the Graphical Three-Sigma Rule (e.g. Duncan, 2000) and the database of mean undrained

strength profiles in London Clay collected by Patel (1992).

Table 2. Variation cu-profile in London Clay (based on the data-base presented in Patel 1992) [d as defined in Figure 2]

cu-profile lowest conceivable -2 σ

cu (kPa) = 5.7d + 25 cu (kPa) = 6.2d + 40

-1 σ cu (kPa) = 6.7d + 55 μ +1 σ +2 σ highest conceivable

cu (kPa) = 7.2d + 70 cu (kPa) = 7.7d + 85 cu (kPa) = 8.2d + 100 cu (kPa) = 8.7d + 115

Figure 3. Results of ‘graphical three sigma’ construction (e.g. Duncan, 2000) to the database of Patel (1992). N.B. Only one site in the database has data that is close to the upper bound line (as drawn) at depth and is therefore considered to be an outlier

3.3 Concrete elastic modulus variation

It is difficult to sensibly assign a population μ and σ value to Ec. In this paper simple range of values (10 to 30GPa) is used and a baseline value of 20GPa is adopted as was done in Vardanega et al. (2012b).

3.4 Mobilization factor

Vardanega et al. (2012a) show that for six codes of practice the factor of safety (F) demanded for bored pile design can range from about 1.7 to upwards of 3 with a typical value of 2.5. Noting that we are study-ing London clay (α≈0.6), the range of F implied by

Vardanega

Geotechnical Engineering for Infrastructure and Development

3780

the range 5>M>1.7 is 3>F>1. This range of ‘sensible’ M values will be used in the analysis, with M=3 taken as a baseline value (it is conceded that values of μ and σ cannot be realistically assigned for the M pa-rameter). The influence of the pile base is neglected in this analysis. 4 SENSITIVITY ANALYSIS

For the analysis the listed baseline values in Table 3 are used. The aim (where possible) is to examine the influence of each parameter listed in Table 3 ± 2σ. Table 3. Baseline values for sensitivity analysis

≈ μ ≈ σ Source Ec GPa 20 Vardanega et al. (2012b) M 3 Vardanega et al. (2012a) cu kPa 70+7.2d Figure 3 and Table 2 b 0.6 0.12 Vardanega & Bolton (2011b) γM=2 0.007 0.002 Vardanega & Bolton (2011b)

4.1 Influence of pile diameter

Figure 4 shows the influence of pile diameter on the computed pile head settlement. As the pile lengthens the influence of pile diameter becomes more marked.

0.0

1.0

2.0

3.0

0 10 20 30 40 50 60 70

wh/D (%

)

L/D

D = 1.5m

D = 1.2m

D = 0.9m

D = 0.6m

D = 0.3m

D (m) variesEc (GPa)  = 20 M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = 70+7.2dM = 3

Figure 4. Computed pile head settlement varying with pile length for different diameter piles (results plotted on dimensionless axes)

4.2 Influence of cu-profile variability

Figure 5 shows that as the soil undrained shear strength is increased the normalized pile settlement increases. This is because a pile founded in strata with a stronger cu-profile can carry a higher load be-fore the ultimate condition is reached. Therefore, at higher loads more concrete compression is expected,

leading to more settlement. This trend becomes in-creasingly apparent as the L/D ratio increases.

0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50 60 70

wh/D(%

)

L/D

40+6.2d

55+6.7d

70+7.2d

85+7.7d

100+8.2d

D (m)  = 0.6Ec (GPa) = 20 M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = variesM = 3

(a)

L= 20m

wh = 10mm

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70

wh/D (%

)

L/D

40+6.2d

55+6.7d

70+7.2d

85+7.7d

100+8.2d

D (m)  = 1.2Ec (GPa) = 20 M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = variesM = 3

(b)

wh = 10mm

L= 20m

Figure 5. Normalized pile head settlement (wh/D) with increasing L/D with a varying cu-profile (a) D = 0.6m; (b) D = 1.2m

4.3 Influence of non-linearity factor

Figure 6 shows the influence of the non-linearity fac-tor, b on the computed normalized pile head settle-ment. Clearly as b increases there is a marked in-crease in the computed settlements. Figure 6 shows the magnitude of the effect as remaining relatively consistent across the range of L/D ratios.

4.4 Influence of mobilization strain

Figure 7 shows that the mobilization strain parameter has a more limited effect on the computed normal-ized pile-settlement than the non-linearity parameter, b. The variation of normalized pile settlement shown on Figure 7 relates to changes of γM=2 of approxi-mately ±2σ, and indicates that at least for London clay the variation does not have a significant effect. However, for other soil deposits where γM=2 can vary more significantly the trend shown on Figure 7 may not necessarily hold and the influence of γM=2 may be more considerable.

0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50 60 70

wh/D (%

) 

L/D

b=0.36

b=0.48

b=0.60

b=0.72

b=0.84

D (m)  = 0.6Ec (GPa) = 20 M=2 = 0.007b = variesη = variescu (kPa)  = 70+7.2dM = 3

L= 20m

wh = 10mm

(a)

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70

wh/D

(%)

L/D

b=0.36

b=0.48

b=0.60

b=0.72

b=0.84

D (m)  = 1.2Ec (GPa) = 20 M=2 = 0.007b = variesη = variescu (kPa)  = 70+7.2dM = 3

wh = 10mm

L= 20m

(b)

Figure 6. Normalized pile head settlement (wh/D) with increasing L/D with a varying b (and η) (a) D = 0.6m; (b) D = 1.2m

0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50 60 70

wh/D (%

)

L/D

γM=2    0.003

γM=2    0.005

γM=2    0.007

γM=2    0.009

γM=2    0.011

D (m)  = 0.6Ec (GPa) = 20 M=2 = variesb = 0.6η = 2.38cu (kPa)  = 70+7.2dM = 3

(a)

wh = 10mm

L= 20m

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70

wh/D (%

)

L/D

γM=2    0.003

γM=2    0.005

γM=2    0.007

γM=2    0.009

γM=2    0.011

D (m)  = 1.2Ec (GPa) = 20 M=2 = variesb = 0.6η = 2.38cu (kPa)  = 70+7.2dM = 3

L= 20m

wh = 10mm

(b)

Figure 7. Normalized pile head settlement (wh/D) with increasing L/D with a varying γM=2 (a) D = 0.6m; (b) D = 1.2m

4.5 Influence of concrete modulus

Figure 8 displays the influence of concrete elastic modulus on the computed normalized pile head set-tlement. The settlement ratio increases as the con-crete modulus is reduced. This trend becomes espe-cially apparent at high L/D ratios. Given that concrete modulus clearly can have a major influence on the computed settlements it is a parameter worthy of fur-ther study by construction and geotechnical engi-neers.

0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50 60 70

wh/D

 (%)

L/D

Ec = 30 GPa

Ec = 25 GPa

Ec = 20 GPa

Ec = 15 GPa

Ec = 10 GPa

D (m)  = 0.6Ec (GPa) = varies M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = 70+7.2dM = 3

L= 20m

wh = 10mm

(a)

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70

wh/D(%

)

L/D

Ec = 30 GPa

Ec = 25 GPa

Ec = 20 GPa

Ec = 15 GPa

Ec = 10 GPa

D (m)  = 1.2Ec (GPa) = varies M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = 70+7.2dM = 3

wh = 10mm

L= 20m

(b)

Figure 8. Normalized pile head settlement (wh/D) with increasing L/D with a varying Ec (a) D = 0.6m; (b) D = 1.2m

4.6 Influence of mobilization factor

As the mobilization factor is increased the computed settlements are seen to decrease (Figure 9). Factoring down the undrained shear strength means that less load is transferred to the concrete pile (less concrete compression) and there is also less soil straining and hence a lower computed wsoil component (Equation 5). The effect of an increasing M value is more marked as the pile lengthens but it is still significant for shorter piles. Adjusting M can be used to control foundation movements, as shown in Vardanega et al. (2012b).

3781

the range 5>M>1.7 is 3>F>1. This range of ‘sensible’ M values will be used in the analysis, with M=3 taken as a baseline value (it is conceded that values of μ and σ cannot be realistically assigned for the M pa-rameter). The influence of the pile base is neglected in this analysis. 4 SENSITIVITY ANALYSIS

For the analysis the listed baseline values in Table 3 are used. The aim (where possible) is to examine the influence of each parameter listed in Table 3 ± 2σ. Table 3. Baseline values for sensitivity analysis

≈ μ ≈ σ Source Ec GPa 20 Vardanega et al. (2012b) M 3 Vardanega et al. (2012a) cu kPa 70+7.2d Figure 3 and Table 2 b 0.6 0.12 Vardanega & Bolton (2011b) γM=2 0.007 0.002 Vardanega & Bolton (2011b)

4.1 Influence of pile diameter

Figure 4 shows the influence of pile diameter on the computed pile head settlement. As the pile lengthens the influence of pile diameter becomes more marked.

0.0

1.0

2.0

3.0

0 10 20 30 40 50 60 70

wh/D (%

)

L/D

D = 1.5m

D = 1.2m

D = 0.9m

D = 0.6m

D = 0.3m

D (m) variesEc (GPa)  = 20 M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = 70+7.2dM = 3

Figure 4. Computed pile head settlement varying with pile length for different diameter piles (results plotted on dimensionless axes)

4.2 Influence of cu-profile variability

Figure 5 shows that as the soil undrained shear strength is increased the normalized pile settlement increases. This is because a pile founded in strata with a stronger cu-profile can carry a higher load be-fore the ultimate condition is reached. Therefore, at higher loads more concrete compression is expected,

leading to more settlement. This trend becomes in-creasingly apparent as the L/D ratio increases.

0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50 60 70

wh/D(%

)

L/D

40+6.2d

55+6.7d

70+7.2d

85+7.7d

100+8.2d

D (m)  = 0.6Ec (GPa) = 20 M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = variesM = 3

(a)

L= 20m

wh = 10mm

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70

wh/D (%

)

L/D

40+6.2d

55+6.7d

70+7.2d

85+7.7d

100+8.2d

D (m)  = 1.2Ec (GPa) = 20 M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = variesM = 3

(b)

wh = 10mm

L= 20m

Figure 5. Normalized pile head settlement (wh/D) with increasing L/D with a varying cu-profile (a) D = 0.6m; (b) D = 1.2m

4.3 Influence of non-linearity factor

Figure 6 shows the influence of the non-linearity fac-tor, b on the computed normalized pile head settle-ment. Clearly as b increases there is a marked in-crease in the computed settlements. Figure 6 shows the magnitude of the effect as remaining relatively consistent across the range of L/D ratios.

4.4 Influence of mobilization strain

Figure 7 shows that the mobilization strain parameter has a more limited effect on the computed normal-ized pile-settlement than the non-linearity parameter, b. The variation of normalized pile settlement shown on Figure 7 relates to changes of γM=2 of approxi-mately ±2σ, and indicates that at least for London clay the variation does not have a significant effect. However, for other soil deposits where γM=2 can vary more significantly the trend shown on Figure 7 may not necessarily hold and the influence of γM=2 may be more considerable.

0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50 60 70

wh/D (%

) 

L/D

b=0.36

b=0.48

b=0.60

b=0.72

b=0.84

D (m)  = 0.6Ec (GPa) = 20 M=2 = 0.007b = variesη = variescu (kPa)  = 70+7.2dM = 3

L= 20m

wh = 10mm

(a)

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70

wh/D

(%)

L/D

b=0.36

b=0.48

b=0.60

b=0.72

b=0.84

D (m)  = 1.2Ec (GPa) = 20 M=2 = 0.007b = variesη = variescu (kPa)  = 70+7.2dM = 3

wh = 10mm

L= 20m

(b)

Figure 6. Normalized pile head settlement (wh/D) with increasing L/D with a varying b (and η) (a) D = 0.6m; (b) D = 1.2m

0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50 60 70

wh/D (%

)

L/D

γM=2    0.003

γM=2    0.005

γM=2    0.007

γM=2    0.009

γM=2    0.011

D (m)  = 0.6Ec (GPa) = 20 M=2 = variesb = 0.6η = 2.38cu (kPa)  = 70+7.2dM = 3

(a)

wh = 10mm

L= 20m

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70

wh/D (%

)

L/D

γM=2    0.003

γM=2    0.005

γM=2    0.007

γM=2    0.009

γM=2    0.011

D (m)  = 1.2Ec (GPa) = 20 M=2 = variesb = 0.6η = 2.38cu (kPa)  = 70+7.2dM = 3

L= 20m

wh = 10mm

(b)

Figure 7. Normalized pile head settlement (wh/D) with increasing L/D with a varying γM=2 (a) D = 0.6m; (b) D = 1.2m

4.5 Influence of concrete modulus

Figure 8 displays the influence of concrete elastic modulus on the computed normalized pile head set-tlement. The settlement ratio increases as the con-crete modulus is reduced. This trend becomes espe-cially apparent at high L/D ratios. Given that concrete modulus clearly can have a major influence on the computed settlements it is a parameter worthy of fur-ther study by construction and geotechnical engi-neers.

0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50 60 70

wh/D

 (%)

L/D

Ec = 30 GPa

Ec = 25 GPa

Ec = 20 GPa

Ec = 15 GPa

Ec = 10 GPa

D (m)  = 0.6Ec (GPa) = varies M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = 70+7.2dM = 3

L= 20m

wh = 10mm

(a)

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70

wh/D(%

)

L/D

Ec = 30 GPa

Ec = 25 GPa

Ec = 20 GPa

Ec = 15 GPa

Ec = 10 GPa

D (m)  = 1.2Ec (GPa) = varies M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = 70+7.2dM = 3

wh = 10mm

L= 20m

(b)

Figure 8. Normalized pile head settlement (wh/D) with increasing L/D with a varying Ec (a) D = 0.6m; (b) D = 1.2m

4.6 Influence of mobilization factor

As the mobilization factor is increased the computed settlements are seen to decrease (Figure 9). Factoring down the undrained shear strength means that less load is transferred to the concrete pile (less concrete compression) and there is also less soil straining and hence a lower computed wsoil component (Equation 5). The effect of an increasing M value is more marked as the pile lengthens but it is still significant for shorter piles. Adjusting M can be used to control foundation movements, as shown in Vardanega et al. (2012b).

Vardanega

Geotechnical Engineering for Infrastructure and Development

3782

0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50 60 70

wh/D

 (%)

L/D

M=5

M=4

M=3

M=2

M=1.7

D (m)  = 0.6Ec (GPa) = 20 M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = 70+7.2dM = varies

(a)

L= 20m

wh = 10mm

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70

wh/D(%

)

L/D

M=5

M=4

M=3

M=2

M=1.7

D (m)  = 1.2Ec (GPa) = 20 M=2 = 0.007b = 0.6η = 2.38cu (kPa)  = 70+7.2dM = varies

(b)

wh = 10mm

L= 20m

Figure 9. Normalized pile head settlement (wh/D) with increasing L/D with a varying M (a) D = 0.6m; (b) D = 1.2m

5 SUMMARY

This paper has reviewed the simple calculation meth-od proposed in Vardanega et al. (2012b) and shown the influence of variation of the London clay design parameters on the computed normalized head settle-ments of bored piles.

The results of the parametric study reveal that es-pecially as L/D increases the mobilization factor and the concrete elastic modulus tend to dominate the set-tlement response of the pile. The influences of the cu-profile and b appear to have a more moderate influ-ence while γM=2 tends to have a less significant effect on the computed settlements. The influence of b and γM=2 are more pronounced as L/D decreases. The re-sults of the parametric study are shown in Table 4.

Table 4. Rankings of the studied factors (for London clay)

Factor Rank M Ec

1 most influence 2

b (or η) cu-profile γM=2

3 4 5 least influence

ACKNOWLEDGEMENTS

Thanks are due to S. Alogna for her assistance pre-paring the French abstract. Thanks are also due to Dr M. Williamson for his helpful suggestions and com-ments that helped improve the paper. The author also thanks Professor M. Bolton for supervising his doc-toral studies.

REFERENCES

Bouzid, D.A., Bhattacharya, S. & Dash, S.R. 2013. Winkler Springs (p-y curves) for pile design from stress-strain of soils: FE assessment of scaling coefficients using the Mobilized Strength Design concept. Geomechanics and Engineering, 5, 379-399. Duncan, J. M. 2000. Factors of safety and reliability in geotech-nical engineering. Journal of Geotechnical and Geoenvironmental Engineering, 126, 307-316. Fleming, W.G.K., Weltman, A.J., Randolph, M.F. & Elson, W.K. 2009. Piling Engineering. 3rd Ed. Wiley, New York, USA. Kolodiy, E., Vardanega, P.J. & Patel, D.C. 2015. Settlement pre-diction of bored piles in stiff clay at a site in the Moscow region. (these proceedings). Matlock, H. 1970. Correlations for Design of Laterally Loaded Piles in Soft Clay. Proceedings 2nd Annual Offshore Technology Conference. Offshore Technology Conference, Texas. Patel, D. 1992. Interpretation of results of pile tests in London Clay. In: Piling Europe, Thomas Telford, London, UK. Randolph, M.F. 1977. A Theoretical Study of the Performance of Piles. Ph.D. thesis, University of Cambridge. Skempton, A.W. 1959. Cast in situ bored piles in London Clay. Géotechnique, 9, 153-173. Vardanega, P.J. & Bolton, M.D. 2011a. Strength mobilization in clays and silts. Canadian Geotechnical Journal, 48, 1485-1503. Corrigendum, 49, 631. Vardanega, P.J. & Bolton, M.D. 2011b. Predicting shear strength mobilization of London clay. Proceedings of the 15th European Conference on Soil Mechanics and Geotechnical Engineering. (Eds. Anagnostopoulos et al.), 487-492. IOS Press, Netherlands. Vardanega, P.J. 2012. Strength Mobilisation for Geotechnical De-sign & its Application to Bored Piles. Ph.D. thesis, University of Cambridge. Vardanega, P.J., Kolody, E., Pennington, S.H., Morrison, P.R.J. & Simpson, B. 2012a. Bored pile design in stiff clay I: codes of prac-tice. Proceedings of the Institution of Civil Engineers – Geotech-nical Engineering, 165, 213-232. Vardanega, P.J., Williamson, M.G. & Bolton, M.D. 2012b. Bored pile design in stiff clay II: mechanisms and uncertainty. Proceed-ings of the Institution of Civil Engineers – Geotechnical Engineer-ing, 165, 233-246. Corrigendum, 166, 518. Williamson, M.G. 2014. Tunnelling Effects on Bored Piles in Clay. Ph.D. thesis, University of Cambridge.