Geotechnical and Geological Engineering

, Volume 36, Issue 2, pp 793–811 | Cite as

Numerical Evaluation of Pile Response Under Combined Lateral and Axial Loading

  • Triada E. Zormpa
  • Emilios M. ComodromosEmail author
Original paper


Piled foundations are frequently subjected to simultaneous axial and lateral loadings. However, the interaction effects of the one loading on the other are, in most cases, disregarded for the sake of simplicity. With the aim of evaluating this effect, a detailed research work on the response of a single pile under simultaneous application of axial and lateral loading was carried out. A qualitative assessment of the effect was initially attempted and the effect was afterwards quantified, based on the results of an intensive three-dimensional parametric numerical analysis. The influence arising from pile head fixity and the second order phenomenon was examined, while the post-peak behaviour was also considered using a strain hardening/softening constitutive law. Interesting conclusions have been drawn, providing a qualitative and quantitative evaluation of the effect on clayey and sandy soils. It was also found that no loading interaction effect is developed, when ultimate limit state is applied for a piled foundation design. On the contrary, when the serviceability limit state is applied and if the pile capacity in both lateral and axial loading is simultaneously reached, a reduction in the pile axial capacity is observed in the case of clayey soils. On the contrary, in the case of sandy soils the action of a lateral load is leading to an increase of pile axial capacity.


Combined pile loading Lateral pile loading Axial pile loading Pile response Numerical analysis 

List of symbols


Area associated with an interface node


Boolean number associated with interface element i


Pile perimeter


Soil–pile adhesion


Undrained shear strength


Undrained shear strength before yielding occurs (strain softening/hardening model)


Mobilised undrained shear strength (strain softening/hardening model)

Epicentral angle at a pile segment (in radians)


Pile diameter


Soil modulus of elasticity


Pile modulus of elasticity


Shear stress at the soil–pile interface


Normal force at the interface


Shear force at the interface


Limiting shear force (interface element)


Horizontal pile load


Ultimate lateral fixed-head pile load capacity


Ultimate lateral free-head pile load capacity


Interface normal stiffness


Interface shear stiffness


Earth pressure coefficient at rest


Pile length


Length of a pile segment


Axial pile load


Ultimate axial pile load capacity


Pile section radius


Shaft resistance of the pile


Serviceability limit state


Normal penetration of an interface node


Shear displacement at interface node i


Ultimate limit state


Incremental relative shear displacement interface vector


Soil unit weight


Partial factor for a resistance


Plastic portion of the second invariant of the shear strain tensor (strain softening/hardening model)


Plastic portion of the second invariant of the shear strain tensor at critical state initiation (strain softening/hardening model)


Poisson’s ratio for the soil


Poisson’s ratio for the pile


Interface normal stress


Interface shear stress


Soil angle of internal friction


Soil angle of internal friction corresponding to critical state (strain softening/hardening model)


Soil angle of internal friction prior to soil yielding (strain softening/hardening model)


Mobilised soil angle of internal friction (strain softening/hardening model)


Angle of friction at the soil–pile interface


Residual angle of friction at the soil–pile interface after frictional shear failure (strain softening/hardening model)


Dilation angle


Dilation angle of friction before yielding occurs (strain softening/hardening model)


Mobilised dilation angle of friction (strain softening/hardening model)


Epicentral angle of interface element i (in radians)


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of ThessalyVólosGreece

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