Acta Geotechnica

, Volume 5, Issue 4, pp 273–286 | Cite as

Effect of local nonlinearity in cohesionless soil on optimal radius minimizing fixed-head pile bending by inertial and kinematic interactions

Research Paper

Abstract

This study presents the effects of a local nonlinearity in cohesionless soil upon the optimal radius minimizing the bending strains of a vertical, cylindrical fixed-head pile embedded in a layered soil stratum in a soil–pile–structure system where the kinematic interaction dominates. The seismic deformation method (SDM) with discretized numerical models is applied since the SDM is a static numerical method that can easily consider realistic conditions of layered soil strata and the nonlinearity of the soil. In the numerical models, the local nonlinearity of the soil in the vicinity of the pile is represented by subgrade springs having bi-linear skeleton curves with a simple hysteretic loop. Various amplitudes of the lateral displacements of the soil and the lateral forces at the head of the pile are considered as numerical parameters. The results of parametric analyses reveal the presence of an optimal pile radius that locally minimizes the bending strains of the piles under strong nonlinearity of the soil, and the optimal pile radius tends to increase as the degree of nonlinearity increases. Criteria are presented for predicting the increment in the optimal radius of soil–pile–structure systems under strong nonlinearity in the soil.

Keywords

Dynamic analysis Nonlinearity Seismic design Seismic deformation method Soil–structure interaction Soil–pile interaction 

List of symbols

a

Radius of pile

\( {a \mathord{\left/ {\vphantom {a {H_{{{\text{opt}} .}} }}} \right. \kern-\nulldelimiterspace} {H_{{{\text{opt}} .}} }} \)

Optimal slenderness ratio

Eb

Young’s modulus of bedrock

Eg

Young’s modulus of soil

Egi

Young’s modulus in the ith layer of soil

Ep

Young’s modulus of pile

H

Length of pile

hi

Length of beam element in the ith layer

I

Geometrical moment of inertia of pile

Ki

Horizontal deformation of subgrade of the ith layer of soil

Kie

Initial stiffness of the horizontal subgrade spring of the soil at the ith node of pile

Kr

Rotational stiffness at the toe of pile

ki

Horizontal subgrade spring of soil at the ith layer of soil

N

Total number of layers

Pie

Ultimate strength of the horizontal subgrade spring of the soil Pie at the ith node of pile

piI

Ultimate soil reaction of the ith layer of soil

ϕi

Angle of shearing resistance of the ith soil layer

ϕr

Phase lag of lateral load with respect to mean shear strain

up

Horizontal displacement of pile with respect to bedrock

usi

Relative displacement of the ith soil layer with respect to bedrock

V

Lateral load acting at the top of the pile

Vs

Shear velocity of soil

Vsb

Shear velocity of bedrock

\( \gamma_{i}^{\prime } \)

Effective unit weight of the ith soil layer

γs

Mean shear strain of soil stratum

ν

Poisson’s ratio of soil

νb

Poisson’s ratio of bedrock

ρb

Mass density of bedrock

ρg

Mass density of soil

References

  1. 1.
    Badoni D, Makris N (1995) Nonlinear response of single piles under lateral inertial and seismic loads. Soil Dynamics Earthquake Eng 15:29–43CrossRefGoogle Scholar
  2. 2.
    Borowicka H (1943) Über ausmittig belastete starre Platten auf elastisch isotropem Untergrund. Ingenieur-Archiv 1:1–8CrossRefMathSciNetGoogle Scholar
  3. 3.
    Broms BB (1964) Lateral resistance of piles in cohesionless soils. J Soil Mech Found Div, ASCE 90(SM3):123–156Google Scholar
  4. 4.
    Broms BB (1964) Lateral resistance of piles in cohesive soils. J Soil Mech Found Div, ASCE 90(SM2):27–63Google Scholar
  5. 5.
    Gazetas G, Dobry R (1984) Horizontal response of piles in layered soils. J Geotech Eng, ASCE 110(6):937–956Google Scholar
  6. 6.
    Gerolymos N, Gazetas G (2005) Phenomenological model applied to inelastic response of soil–pile interaction systems. Soils Found, JGS 45(4):119–132Google Scholar
  7. 7.
    Luo X, Murono Y, Nishimura A (2002) Verifying adequacy of the seismic deformation method by using real examples of earthquake damage. Soil Dynamics Earthquake Eng 22:17–28CrossRefGoogle Scholar
  8. 8.
    Matlock H (1970) Correlations for design of laterally loaded piles in soft clay. Paper No. OTC 1204, Proceedings of the 2nd annual offshore technology conference, Houston, Texas I:557–594Google Scholar
  9. 9.
    Murono Y, Nishimura A (2000) Evaluation of seismic force of pile foundation induced by inertial and kinematic interaction. Paper No. OTC 1496, Proceedings of the 12th world conference on earthquake engineering, New ZealandGoogle Scholar
  10. 10.
    Mylonakis G (2001) Simplified model for seismic pile bending at soil layer interfaces. Soils Found JGS 41(4):47–58Google Scholar
  11. 11.
    Reese LC, Cox WR, Koop FD (1975) Field testing and analysis of laterally loaded piles in stiff clay. Paper No. OTC 2312, Proceedings of the 7th annual offshore technology conference, Houston, Texas II:672–690Google Scholar
  12. 12.
    Saitoh M (2005) Fixed-head pile bending by kinematic interaction and criteria for its minimization at optimal pile radius. J Geotech Geoenviron Eng, ASCE 131(10):1243–1251CrossRefMathSciNetGoogle Scholar
  13. 13.
    Trochanis A, Bielak J, Christano P (1991) Simplified model for analysis of one or two piles. J Geotech Eng, ASCE 117(3):448–466CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Graduate School of Science and EngineeringSaitama UniversitySakura-KuJapan

Personalised recommendations