Acta Geotechnica

, Volume 9, Issue 3, pp 455–467 | Cite as

Effects of soil nonlinearity on the active length of piles embedded in cohesionless soil: model studies

  • C. S. Goit
  • M. Saitoh
  • H. Oikawa
  • H. Kawakami
Research Paper


Dynamic experimental studies on the active lengths of a fixed-head floating pile under static and dynamic loading conditions are reported, focusing on the effects of local nonlinearity and resonant behavior of soil. Results obtained from the laterally loaded model soil-pile system subjected to low-to-high amplitude pile head loading suggest a strong influence of local nonlinearity on the active lengths of the pile. Such obtained experimental results are further compared with the available approximate equations for estimating the active lengths. The comparisons reveal the closeness in values for very low amplitude of loadings, but for intermediate-to-high amplitude of loadings, the experimental values are smaller than predicted by the approximate equations. Moreover, both the static and dynamic active lengths of the pile converge to an approximately identical value of six times the diameter of the pile for intermediate-to-high amplitude of loadings. This suggests that the active lengths of the pile are, in fact, the same for both the static and dynamic loadings, under nonlinear conditions. Additionally, results also suggest that the passive-type failures of soil induced by the applied lateral loadings in front of the pile govern the active lengths. Furthermore, the dynamic active lengths of the pile do not show any significant dependency on the resonance in the soil.


Active length Dynamic analysis Fixed-head pile Local nonlinearity Shaking table 


\( C_{\text{u}} \)

Coefficient of uniformity

\( d \)

Diameter of pile

\( D_{60,30,10} \)

Particle size parameters for soil

\( e_{\hbox{max} ,\hbox{min} } \)

Maximum/minimum void ratio

\( E_{\text{p}} \)

Young’s modulus of pile

\( {{E_{\text{p}} } \mathord{\left/ {\vphantom {{E_{\text{p}} } {E_{{{\text{s}} - {\text{eq}}}} }}} \right. \kern-0pt} {E_{{{\text{s}} - {\text{eq}}}} }} \)

Elasticity contrast

\( E_{\text{s}} \)

Young’s modulus of soil at a depth equal to the diameter of pile

\( E_{{{\text{s}} - {\text{eq}}}} \)

Equivalent Young’s modulus of soil

\( E_{\text{s}}^{{{\text{low}} - {\text{strain}}}} \)

Low-strain modulus of elasticity of soil at a depth equal to the diameter of pile

\( f_{\text{n}} \)

Natural frequency

\( G \)

Shear modulus of soil

\( G_{0} \)

Initial shear modulus of soil

\( G_{\text{m}} \)

Shear modulus of model

\( G_{\text{p}} \)

Shear modulus of prototype

\( G_{\text{s}} \)

Specific gravity of soil

\( H \)

Height of soil layer

\( L \)

Length of pile

\( L/d \)

Slenderness ratio of pile

\( l_{\text{d}} \)

Dynamic active length of pile

\( l_{\text{s}} \)

Static active length of pile

\( q \)

Applied acceleration amplitude in m/s2

\( s \)

Shape factor

\( u \)

Displacement applied at pile head

\( V_{\text{s}} \)

Shear wave velocity in soil

\( \lambda \)

Geometric scaling ratio of the model to prototype

\( \eta \)

Density scaling ratio of the model to prototype

\( \omega_{\text{m}} \)

Circular frequency of model

\( \omega_{\text{p}} \)

Circular frequency of prototype

\( \gamma_{\text{m}} \)

Dynamic strain in model

\( \gamma_{\text{p}} \)

Dynamic strain in prototype

\( \rho_{\text{s}} \)

Density of soil

\( \rho_{\text{p}} \)

Density of pile

\( \varphi \)

Friction angle of soil


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • C. S. Goit
    • 1
  • M. Saitoh
    • 1
  • H. Oikawa
    • 1
  • H. Kawakami
    • 1
  1. 1.Graduate School of Science and EngineeringSaitama UniversitySaitamaJapan

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