Load Transfer in Rock-Socketed Drilled Shafts

• Load distribution and deformation of rock-socketed drilled shafts subjected to axial loads are evaluated by a load transfer method.
• Emphasis is on quantifying the effect of coupled soil resistance in rock-socketed drilled shafts using 2D elasto-plastic finite element analysis.
• Slippage and shear-load transfer behavior at the pile-soil interface are investigated by using a user-subroutine interface model (FRIC).
• Coupled soil resistance acts as pile-toe settlement as the shaft resistance is increased to its ultimate limit state.
• The coupling effect is closely related to the ratio of the pile diameter to soil modulus (D/Es) and the ratio of total shaft resistance against total applied load (Rs/Q).
• 2D numerical analysis reasonably estimated load transfer of pile and coupling effect through comparison with field case studies.
• The prediction of load deflections of drilled shafts sees a significant improvement using this method.

Introduction

• The load transfer method has been widely used to predict the load transfer characteristics of piles subjected to axial loads.
• This method is applicable to any complex composition of soil layers with a nonlinear stress-strain relationship, non-homogeneous medium, and any variation in the sections along a pile.
• The pile is modeled by discrete elements and the soil is represented by a set of load transfer curves, which represent the soil resistance as a function of pile displacements at several discrete points along the pile, including the pile-toe.
• The spring (soil) modulus is not constant, but a nonlinear function of depth and pile deflection.
• A realistic representation of the subgrade reaction can be established directly in terms of coupled soil resistance using nonlinear load transfer curves.

Vesic's Pile-Toe Settlement

• Vesic reported that pile-toe settlement (wt) can be classified into two components.
• One is the settlement caused by load transmitted at the pile-toe (Wbp), and the other is the settlement caused by the load transmitted along the pile shaft (Wbs).
• Traditional load transfer method without the wbs component cannot consider the coupling effect between shear transfer loading and pile-toe displacement, and thus underestimates the pile-toe displacement.
• Rock-socketed drilled shafts typically carry most of their working load in shaft resistance because the ultimate shaft resistance is generally mobilized at smaller interface displacements between the shaft and surrounding rock than ultimate toe resistance.
• Load transmitted to the pile-toe is typically 10-20% of the axial load applied at the pile head at general working loads.
• So it's more important to consider additional pile-toe displacements caused by shear loading transferred from the pile shaft for reasonable designs of rock-socketed drilled shafts in a working limit state.
• The numerical modeling techniques based on the finite element (FE) or finite difference (FD) methods are becoming increasingly used in geotechnical engineering and to investigate pile behavior.
• Fellenius et al. performed 2D FE analysis for piles subjected to bidirectional loading using the thin layer element, and Nam and Bui et al. conducted 2D FD analysis using the strength reduction factor.
• Rowe and Armitage, Lee, Jeong et al., and Sheng et al. used slip interface elements for simulated relative displacement to consider slip behavior.
• Hassan and O'Neill and Drumm et al. used a sinusoidal profile for numerical modeling of socket roughness, and Kong et al. performed both 2D FE analysis and the Rocket program.
• These works were primarily based on basis of Coulomb's frictional law or Patton's theory.
• FEA is a continuum approach, so it can consider coupled soil resistance of piles automatically, which traditional load transfer method cannot.
• FEA was conducted to examine the coupled behavior of rock-socketed drilled shafts by simulating slippage and shear-load transfer behavior at the pile-soil (or pile-rock) interface with a user-subroutine interface model.
• The validity of numerical modeling was tested against field observation, and the major parameters that influence coupled soil resistance are discussed.

Finite Element Modeling Procedure

• The commercial finite-element package, ABAQUS version 6.5, was used in this study.
• Analyses adopted circular piles in 2D axi-symmetric conditions.
• The model boundaries comprise a width of 20 times pile diameter (D) from the pile center and a height of pile length (L) plus a further 1.5 L below pile-toe level.
• These dimensions were considered adequate to eliminate the influence of boundary effects on the pile performance.
• Allows for rigorous treatment of the soil-structure interaction by modeling both the pile and soil using finite elements.
• Both soil and the pile are represented by eight-node, second-order quadratic elements.
• A relatively fine mesh was used near the pile-soil interface and the pile-toe, and became coarser farther from the pile.
• Studies were conducted with full modeled mesh, including the overburden soil layer and the individual interface of shaft layers, to more realistically simulate and compare with field measurement.

Material Properties

• An isotropic elastic model was used for the pile and a Mohr-Coulomb model was used for the soil.
• The rocks were assumed to be elastic-plastic and were represented by a Drucker-Prager model.
• The dilation angle in the Drucker-Prager model was assumed to be half of the angle of friction to avoid unrealistically high dilation due to the normality rules.
• Poisson's ratio of the rock was assumed to be 0.3.
• Other material properties represented a soil or rock based on the results of a soil investigation in the field cases.

Interface Modeling

• A numerical approach based on continuum analysis should be used with great care due to large deformation by the pile settlement behavior.
• Proper modeling of the interface behavior is of crucial importance due to conventional numerical analysis presents some difficulties at large strain.
• The ABAQUS interface modeling technique using a slip element, which is based on slave-master simulation, was used to simulate slippage at the pile-soil interface.
• The nodes of the pile elements in contact with the soil could slide along the pile-soil interface when the pile-top load is applied using duplicated nodes to form an interface of zero thickness.
• ABAQUS uses the Coulomb frictional law, where frictional behavior is specified by a coefficient of friction and a limiting displacement (ycrit) or a limiting shear stress (Tcrit).
• The friction models were used to model the more complex behavior of shear transmission between surfaces in contact by a user-subroutine called FRIC.
• Shear behavior at the pile-rock interface can be modeled as shear-load transfer (f-w) functions used in the load transfer method.
• The f-routines were coded so that f-w functions were incorporated into this FE analysis using a bi-linear f-w function for pile-soil interface, and nonlinear triple f-w functions for the pile-rock interface.
• The shear-load transfer behavior of rock-socketed drilled shafts is elastic, elasto-plastic, and plastic portion depending on the factors influencing the shaft resistance
• Described the nonlinear triple f-w function which models slippage at the pile-rock interface and frictional-dilative shear behavior, are empirically considered by the Hoek-Brown failure criterion and regression analysis with field tests.

Material Properties Equations

• Equations used to define key material properties:
  • f = 0.23σci B (for w≤ Wst)
  • f = 0.23σci B [[σno + Kn tan i (w-Wst)] - (σci / σno ) B ] / σno (for Wst<W Wmax)
  • f = fmax (for Wmax < w)
  • B = -0.008 GSI + 0.94 (for GSI < 45)
  • B = -0.002 GSI +0.67 (for GSI ≥ 45)
  • Kn = Δση / ∆r = Em / r(1 + Vm)

Analysis Process

• The initial equilibrium state is of great importance in numerical analysis.
• The specified initial stress distributions should match with the calculation based on the self-weight of the material.
• An applied loading was simulated by the application of a uniform vertical load on the top of the pile after the initial step.
• The effect of the pile installation is ignored and the pile is assumed to be in a stress-free state at the start of the analysis.

Comparison with field observations

• Validation of numerical model and interface modeling techniques are discussed based on the results of FEA for two field measurements:
  • Gyeonggi case
  • Hongkong case

Gyeonggi Case: Test Details

• Three instrumented drilled shafts piles were installed in completely or moderately weathered gneiss
• All of the test piles are 1000 mm in diameter and 13.8 m in length

Gyeonggi Case: Parameters

• Parameters listed:
  • UCS of the intact rock (oci), soil/rock mass moduli (Es), Poisson's ratio (v), internal friction angle ($), cohesion (c),unit weight (y), mean roughness angle (i), geological strength index (GSI), ultimate unit shaft resistance (fmax), and critical movement (Wmax) of the pile segment at which fmax

Gyeonggi Case: Roughness

• Roughness in the interface model is characterized by a chord length and the mean roughness angle, which are used to generate fractal roughness profiles for the socket wall.
• Interface roughness for rocks of more than oci = 20 MPa could be represented by a regular sawtooth with a chord length of 50 mm with roughness angle from 1.1 to 8.0°.
• The roughness angles (i) of test shafts were alternatively assumed to be the average value of 4.6°.
• The fmax used was determined by the empirical relations on the rock mass modulus.

Gyeonggi Case: Results

• The predictions by FE analysis are in good agreement with the general trend observed in field measurements.
• There are considerably larger settlements when compared with the results by the general load transfer method because the load transfer method ignores pile-toe displacement due to shaft shear loading, resulting in overestimates of the toe load transfer and smaller displacement in pile head movement.

Hongkong Case: Test Details

• Properties of the material and shear transfer functions were chosen based on soil borings and pile load tests and showed comparison of curves and axial load distributions for test piles
• Confirmed FE analysis accurately predicts results when compared with load transfer method

Effects of Coupled Soil Resistance: Test Details

• A series of FE analyses on rock-socketed drilled shafts were performed based on the major influencing parameters, such as the pile diameters (D), the soil modulus (Es), and the ratio of load distributions to examine the effects of coupled soil resistance.
• Piles 20m in length with diameters .5m and 1m
• Used defined interface of a bi-linear model, and addressed load distribution ratio of shaft

Effects of Coupled Soil Resistance: Results

• By the FE analysis for the piles, the effects of resistance can be compared.
• The axial load applied to the pile head is transferred to the ground through shaft resistance that develops at the pile-rock interface along the sides of the shaft, and toe resistance that develops at the pile-toe, so that shear transfer loads along the pile-rock interface affect the pile-toe displacement.
• When shaft resistance is defined as zero by the user-subroutine, on the other hand, an axial load applied to the pile-toe is transferred to the ground through only toe resistance, so there has been no coupled soil resistance.
• Wb (pile-toe displacement) considering also coupled soil resistance.
• Coupling effect is more significant for friction piles rather than end-bearing piles because rock-socketed drilled shafts typically carry most of their working load in shaft resistance.

Conclusions

• It as shown that FE analysis using a special (contact) interface model defined by a user-subroutine (FRIC) could simulate slippage and shear-load transfer behavior at the pile-soil interface.
• F‐w functions used in the traditional load transfer analysis could be incorporated for the pile-rock (or pile-soil) interface in FE analysis and the proposed method can better predict load transfer behavior.
• Numerical modeling for coupled behavior exhibits larger settlement compared to the more traditional load transfer method.
• It was found in parametric study using FE analysis that additional pile-toe displacement (Wbs) by coupled soil resistance increases proportionally until the shaft resistance reaches the ultimate state and depends on the ratio of the diameter to the rock-mass modulus (D/Es).
• As the ratio of total shaft resistance against total applied load (Rs/Q) increases, the effects of coupled soil resistance increase.
• The coupling effect is generally more significant for friction piles than for end-bearing piles.