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


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.


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

List of symbols


Radius of pile

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

Optimal slenderness ratio


Young’s modulus of bedrock


Young’s modulus of soil


Young’s modulus in the ith layer of soil


Young’s modulus of pile


Length of pile


Length of beam element in the ith layer


Geometrical moment of inertia of pile


Horizontal deformation of subgrade of the ith layer of soil


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


Rotational stiffness at the toe of pile


Horizontal subgrade spring of soil at the ith layer of soil


Total number of layers


Ultimate strength of the horizontal subgrade spring of the soil P i e at the ith node of pile


Ultimate soil reaction of the ith layer of soil


Angle of shearing resistance of the ith soil layer


Phase lag of lateral load with respect to mean shear strain


Horizontal displacement of pile with respect to bedrock


Relative displacement of the ith soil layer with respect to bedrock


Lateral load acting at the top of the pile


Shear velocity of soil


Shear velocity of bedrock

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

Effective unit weight of the ith soil layer


Mean shear strain of soil stratum


Poisson’s ratio of soil


Poisson’s ratio of bedrock


Mass density of bedrock


Mass density of soil


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

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

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