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An Empirical Method for Analysis of Load Transfer and Settlement of Single Piles

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Abstract

An empirical method is developed for estimating the load transfer and deformation of drilled, in situ formed piles subjected to axial loading. Firstly, governing equations for soil–pile interaction are developed theoretically, taking into account spatial variations in: (a) shaft resistance distribution and (b) ratio of load sharing between the shaft and base. Then generic load transfer models are formulated based on examination of data from 10 instrumented test piles found in the literature. The governing equations and load transfer models are then combined and appropriate boundary conditions defined. Using an incremental-iterative algorithm whereby all the boundary conditions are satisfied simultaneously, a numerical scheme for solving the combined set of equations is developed. The algorithm is then developed into an interactive computer program, which can be used to predict the load-settlement and axial force distribution in piles. To demonstrate its validity, the program is used to analyse four published case records of test piles, which other researchers had analysed using the following three computationally demanding tools: (a) load transfer (t–z), (b) finite difference and (c) finite element methods. It is shown that the proposed method which is much less resource-intensive, predicts both the load-settlement variation and axial force distribution more accurately than methods: (a–c) above.

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Abbreviations

A:

\( {\frac{{\left[ {f_{s} (z)} \right]_{z = L} }}{{\left[ {f_{s} (z)} \right]_{z = 0} }}} \)

B:

0.001%L

C:

Compound parameter (see Eq. 6b)

D b :

Diameter of pile base

D s :

Diameter of pile shaft

E p :

Elastic modulus of pile material

E i :

Initial tangent modulus of soil

E u :

Undrained modulus of deferomation of soil

I :

Intercept on the P s /√Δ s axis of the best line of fit of P s /√Δ s versus √Δ s

L :

Total pile length

L c :

Length of permanent casing for pile (or length of upper pile segment not embedded in soil or passing through weak soil)

L s :

Length of pile shaft transferring load to soil by means of shaft resistance

N c :

Bearing capacity factor

N i :

SPT blow count for the ith stratum along pile shaft

N s :

Average value of N SPT along pile shaft, after weighting with respect to strata thickness

N SPT :

Number of blow count in standard penetration test

P b :

Mobilised base resistance of pile

P h :

Applied pile head load

P s :

Mobilised shaft resistance of pile

P ub :

Ultimate pile base resistance

P uh :

Maximum pile head capacity

P us :

Maximum shaft resistance of pile

P(z) :

Axial force in pile at depth z below pile head level

S i :

Tangent slope, at the origin, of the curve of unit base resistance versus base movement of pile

c u (z) :

Undrained shear strength of soil at depth z

e p :

Compression of pile

f b :

Unit base resistance of pile mobilised at a particular loading stage

f max :

Maximum unit shaft resistance at a certain depth along pile (Kim et al 1999 and Balakrishnan et al 1999)

f s :

Average unit shaft resistance of pile mobilised at a particular loading stage

f s (z) :

Local unit shaft resistance mobilised at depth z along pile

f ub :

Maximum unit base resistance of pile

f us :

Maximum unit shaft resistance of pile

j :

Number of Δb increments applied in SEM analysis program

\( \left\{ \begin{gathered} k_{1} \hfill \\ k_{2} \hfill \\ \end{gathered} \right. \) :

Empirical constants in the expression for n (Eq. 15a)

l i :

Thickness of ith stratum along pile shaft

m s :

Gradient of the regression trend line of P s /√Δ s versus √Δ s

n :

Critical shaft settlement divided by pile shaft diameter (i.e., Δsc/Ds)

r 2 :

Correlation coefficient in linear regression

w(z):

Pile movement at depth z below pile head level

z :

Depth below pile head level

α:

Adhesion factor

α1, α2, α3, α4 :

Compound coefficients in the modelled functions: f s(z) and P(z)

α z :

f s (z)/c u (z)

Δ b :

Pile base displacement

Δ bc :

Critical pile base displacement (Δb corresponding to P ub )

Δ h :

Pile head settlement

Δ s :

Average shaft settlement

Δ sc :

Critical shaft settlement (Δs corresponding to P us)

τ1, τ2, τ3 :

Shear strength of 1st, 2nd, 3rd soil layer respectively along pile shaft

τ b :

Shear strength of soil at pile base level

τ s :

Average shear strength of soil around pile shaft, weighted with respect to strata thickness

ω:

Value of z/L at the point of maximum f s(z)

ψ :

Mobilised shaft resistance divided by pile head load

References

  • Ahmadi MM, Khabbazian M (2009) End bearing capacity of drilled shafts in sand: a numerical approach. Geotech Geol Eng J 27:195–206

    Article  Google Scholar 

  • Jamiolkowski M et al (1979) Design parameters for soft clays. In: Proceedings of the 7th European conference on soil mechanics and foundation engineering. Brighton, vol 5, pp 21–57

  • Balakrishnan EG, Balasubramaniam AS, Phien-wej N (1999) Load deformation analysis of bored piles in residual weathered formation. J Geotech Geoenviron Eng ASCE 125(2):122–130

    Article  Google Scholar 

  • Bowles EB (1996) Foundation analysis and design, 5th edn. McGaw-Hill Co., New York, p 887

    Google Scholar 

  • British Standards Institution (1986) BS 8004-Code of practice for foundations. BSI, Milton Keynes

    Google Scholar 

  • Carrubba P (1997) Skin friction of large diameter piles socketed into rock. Can Geotech J 34:230–240

    Article  Google Scholar 

  • Chandler RJ, Foster A (2001) Engineering in Mercia mudstone. Report C570. Construction Industry Research Information Association (CIRIA), London, pp 39

  • Chang MF, Broms BB (1991) Design of bored piles in residual soils based on field-performance data. Can Geotech J 28:200–209

    Article  Google Scholar 

  • Chin FK (1972) The inverse slope as a prediction of ultimate bearing capacity of piles. In: Proceedings of 3rd south east Asian conference on soil engineering, Hong Kong, pp 83–91

  • Coyle HM, Reese LC (1966) Load transfer for axially loaded piles in clay. J Soil Mech Found Eng Div ASCE 92((SM2)):1–26

    Google Scholar 

  • Darrag AA (1987) Capacity of driven piles in cohesionless soils including residual stresses. Ph.D. Thesis, Purdue University, West Lafayatte, Indiana

  • Delpak R, Robinson RB, Omer JR (2000) Assessment of the performance of large diameter, bored cast in situ piles in Mercia mudstone. Research Project 576: The Engineering Properties of the Mercia mudstone Group. Construction Industry Research Information Association (CIRIA), London, pp 36–63

  • Hirayama H (1990) Load-settlement analysis for bored piles using hyperbolic transfer functions. Soils Found Jpn Soc Soil Mech Found Eng 30(1):55–64

    Google Scholar 

  • Jardine R, Fourie A, Maswose J, Burland JB (1985) Field and laboratory measurements of soil stiffness. In: Proceedings of the 11th international conference on soil mechanics and foundation engineering, San Francisco, vol 2, pp 511–514

  • Kim S, Jeong S, Cho S, Park I (1999) Shear load transfer characteristics of drilled shafts in weathered rocks. J Geotech Geoenviron Eng ASCE 125(11):999–1010

    Article  Google Scholar 

  • Lin SS (1997) Use of filamented beam elements for bored pile analysis. J Struct Eng ASCE 123(9):1236–1244

    Article  Google Scholar 

  • Omer JR (1998) Numerical analysis of test pile data from instrumented large diameter bored piles formed in Keuper marl (Mercia Mudstone). Ph.D. Thesis, University of Glamorgan, UK

  • Reese LC (1978) Design and construction of drilled shafts. J Geotech Eng Div ASCE 104(GTI):91–116

    Google Scholar 

  • Reese LC, Touma FT, O’Neill MW (1976) Behaviour of drilled piers under axial loading. J Geotech Eng Div ASCE 102(GT5):493–510

    Google Scholar 

  • Schmertmann JH, Hartman JP, Brown PR (1978) Improved strain influence factor diagrams. Proc Am Soc Civil Eng 104(GT8):1131–1135

    Google Scholar 

  • Schmidt HH, Rumpelt TK (1993) Pile load capacity in pre-consolidated Keuper marls of South West Germany: design and performance. In: Proceedings of the international symposium on geotechnical engineering of hard soils-soft rocks, Balkema, vol 2, pp 1021–1027

  • Stroud MA (1974) The standard penetration in insensitive clays and soft rock. In: Proceedings of the 1st European seminar on penetration testing (ESOPT I), Stockholm, vol 2, issue 2, pp 366–375

  • Tomlinson MJ (1994) Pile design and construction practice, 4th edn. E&F.N. Spon, London

    Google Scholar 

  • Vijayvergiya VN (1977) Load-settlement characteristics of piles. In: Proceedings of Port ‘77 conference, Long Beach, pp 269–284

  • Wright SJ, Reese LC (1979) Design of large diameter bored piles. Ground Eng 12(6):17–23

    Google Scholar 

  • Zhu H, Chang MF (2002) Load transfer curves along bored piles considering modulus of degradation. Am Soc Civil Eng J Geotech Geoenviron Eng 128(9):764–774

    Article  Google Scholar 

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Acknowledgments

The authors are grateful to The Royal Society, London, for awarding a generous Fellowship to the first author in order to carry out a significant part of the research at Lankelma CPT, East Sussex, U.K. Special appreciation is due to Mr J. Powell of the Building Research Establishment, Watford, UK, for his valuable discussions and support. Other thanks go to the University of Glamorgan, UK, for allowing use of various facilities.

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Authors and Affiliations

  1. Faculty of Engineering, Kingston University, London, KT1 2EE, UK

    J. R. Omer

  2. Faculty of Advanced Technology, University of Glamorgan, Wales, CF37 1DL, UK

    R. Delpak & R. B. Robinson

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  1. J. R. Omer
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  2. R. Delpak
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  3. R. B. Robinson
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Correspondence to J. R. Omer.

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Omer, J.R., Delpak, R. & Robinson, R.B. An Empirical Method for Analysis of Load Transfer and Settlement of Single Piles. Geotech Geol Eng 28, 483–501 (2010). https://doi.org/10.1007/s10706-010-9307-7

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