Analytical Expression for Plastic Hinge Length in Extended Pile-Shafts-Paper

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The paper develops an analytical method for estimating the equivalent plastic-hinge length of reinforced-concrete pile-shafts extending above ground and embedded in clay or sand. This length is important in seismic design because equivalent cantilever models use it to relate local curvature ductility to overall displacement ductility.<br /><br />The method distinguishes the actual yielded region from the equivalent concentrated hinge. The actual plastic-zone length is derived from the difference between ultimate and first-yield bending moments and the surrounding soil resistance. Soil resistance is treated as approximately constant in clay and as increasing with depth in sand. A modification factor converts the actual yielded length to an equivalent hinge length by matching the plastic rotation represented by a rectangular curvature block to the rotation obtained from the distributed plastic-curvature profile. The formulation can reflect pile geometry, reinforcement, axial load, material properties, and soil conditions.<br /><br />The authors use the GSNAP nonlinear-analysis program, which models piles with fiber-based beam-column elements and soil with nonlinear springs. Its predictions are checked against full-scale pile tests in loose and dense sand and show good agreement with measured load–deflection responses. Pushover analyses are then conducted for piles in clay and sand under different soil conditions, aboveground heights, and axial-load ratios.<br /><br />Results indicate that the modification factor decreases from about 0.6 to 0.3 as displacement ductility increases from 1 to approximately 1.5, then remains near 0.3 at higher ductility. Thus, equivalent hinge length depends on displacement ductility, unlike the depth of the plastic hinge, which the study finds relatively insensitive to displacement level. The proposed approach offers a way to estimate hinge length more consistently for performance-based seismic design of extended pile-shafts.

Keywords

plastic hinge length

reinforced-concrete pile-shafts

seismic design

equivalent cantilever model

displacement ductility

plastic curvature

clay and sand

soil resistance

pushover analysis

GSNAP nonlinear analysis