A Hyperbolic p–y Criterion for Flexible Piles in Weathered Rock Mass
Publication: International Journal of Geomechanics
Volume 23, Issue 10
Abstract
Bored piles (drilled shafts) socketed in weathered rock mass are frequently used to transfer higher lateral loads from superstructures to competent underlying rock mass. A common method for analyzing the response of laterally loaded bored piles is to use nonlinear p–y curves to represent the rock mass resistance. This paper presents the development of a hyperbolic p–y criterion for flexible bored piles in weathered rock mass under static loading. The hyperbolic p–y criterion was derived based on the Hoek–Brown failure criterion. The ultimate resistance of the rock mass and the initial stiffness of the p–y curve were proposed based on mathematical and statistical analyses. The effectiveness of the proposed p–y criterion was verified with finite-element analysis and full-scale tests. Finally, recommendations for choosing the rock mass parameters to establish the p–y curve were provided.
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Data Availability Statement
All data that support the findings of this study are available from the corresponding author upon reasonable request.
Notation
The following symbols are used in this paper:
- AbΔ, Ab
- area of the wedge bottom surface for the triangular and rectangular areas, respectively;
- As
- area of the wedge side surface;
- a, mb, mi, s
- constants of the Hoek–Brown failure criterion;
- c′
- effective cohesion;
- D
- disturbance factor;
- d
- pile diameter;
- dref
- reference pile diameter;
- Ee
- effective Young’s modulus of the pile;
- Ei
- Young’s modulus of intact rock;
- Em
- Young’s modulus of rock mass;
- Ep
- Young’s modulus of the pile;
- (EI)c
- actual bending rigidity of the pile;
- Em1
- Young’s modulus of rock mass (Liang et al. 2009);
- Em2
- Young’s modulus of rock mass (proposed p–y criterion);
- Fnb, Fsb
- normal and shear forces applied to the wedge bottom surface;
- FnbΔ,
- normal force applied to the wedge bottom surface for the triangular and rectangular areas, respectively;
- FsbΔ,
- shear force applied to the wedge bottom surface for the triangular and rectangular areas, respectively;
- Fns, Fss
- normal and shear forces applied to the wedge side surface;
- Ft
- total resistance force;
- G
- shear modulus of the rock mass;
- G*
- equivalent shear modulus of the rock mass;
- GSI
- geological strength index;
- H
- wedge height;
- Ip
- moment of inertia of the pile;
- Ki
- initial stiffness of the p–y curve;
- Ko
- earth pressure coefficient at rest;
- ki
- dimensionless constant;
- L
- pile length;
- MR
- modulus ratio;
- PL
- normal limit stress;
- P
- resistance of rock mass per unit length;
- Pu
- ultimate resistance of rock mass per unit length;
- RQD
- rock quality designation;
- y
- lateral displacement;
- z
- depth below the rock surface;
- ƒ
- reduction factor;
- β
- wedge bottom angle;
- γ′
- effective unit weight of rock mass;
- δ
- Radial angle;
- θ
- wedge fanning angle;
- ν
- rock mass Poisson’s ratio;
- major effective principal stresses;
- minor effective principal stresses;
- σci
- unconfined compressive strength of the intact rock;
- σn
- normal stress;
- overburden pressure;
- τ
- Shear stress;
- τmax
- rock–pile interface side shear resistance; and
- φ′
- effective friction angle.
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Received: Oct 1, 2022
Accepted: Apr 17, 2023
Published online: Aug 8, 2023
Published in print: Oct 1, 2023
Discussion open until: Jan 8, 2024
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