Determination of Coefficient of Modulus of Sub-Grade Reaction for Free Head Short Pile-Paper

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The study develops a method for estimating the coefficient of horizontal subgrade reaction (ηh) for free-head piles under lateral loading, without constructing p–y curves. Experiments used hollow cast-iron model piles, 24 mm in diameter, with length-to-diameter ratios (L/d) of 8, 10, and 15, embedded in homogeneous sand at relative densities from 33% to 90%.<br /><br />The experimental results were compared with three-dimensional finite-element analyses using PLAXIS 3D. Predicted ultimate loads agreed reasonably well with test results. The authors then applied a finite-difference method to PLAXIS load–deflection and pile-response data to estimate the subgrade reaction at different depths. These estimates were within about 10% of values obtained from the numerical results.<br /><br />The study found that ηh and the normalized flexibility ratio increased with both sand relative density and pile L/d ratio. Using these trends, the authors developed a design relationship and chart connecting the flexibility ratio to relative density and L/d, for the parameter range studied. A separate test using a CPVC pile produced an ηh estimate within 5% of the numerical value, providing an additional check on the proposed approach.<br /><br />The findings suggest that the method can support practical analysis of laterally loaded short piles in homogeneous cohesionless soils. Its applicability is limited to conditions similar to those investigated, particularly relative densities up to 90% and L/d ratios up to 15.

Keywords

horizontal subgrade reaction

free-head piles

lateral loading

p-y curves

finite-element analysis

PLAXIS 3D

sand relative density

flexibility ratio

pile response

cohesionless soils