Modeling of Installation and Quantification of Shaft Resistance of Drilled-Displacement Piles in...

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MODELING OF INSTALLATION AND QUANTIFICATION OF SHAFT RESISTANCE

OF DRILLED-DISPLACEMENT PILES IN SAND

Prasenjit Basu1, A.M. ASCE; Monica Prezzi2, A.M. ASCE; Rodrigo Salgado3, F. ASCE

ABSTRACT

Drilled-displacement (DD) piles are installed using a drilling tool consisting of a partial-flight

auger and a displacement body. This tool is inserted and advanced in the ground by both a

vertical force and a torque. Despite the widespread use of DD piles throughout the world, most

of the design methods available for calculation of shaft capacity were developed based solely on

the results of pile load tests for which only the pile head capacity was known (no instrumentation

that allowed separation of shaft and base loads was used in those tests). The shaft capacity of a

pile depends on the stress state of the soil surrounding the pile that results after its installation.

Proper analysis of the impact of installation of DD piles on the stress state in the in situ soil is

fundamental to the development of reliable design methods. This paper presents the results of

one-dimensional, quasi-axisymmetric FEAs performed with an advanced sand constitutive model

that capture the essential stages of the installation and loading of DD piles in sand. In addition, a

set of equations is proposed for the estimation of the unit limit shaft resistance of DD piles

installed in sand that takes into account the initial soil state and the rate of penetration of the

drilling tool into the ground during pile installation.

Keywords: numerical modeling and analysis, finite element, shaft capacity, piles, drilled-

displacement, screw, sands, plasticity Number of words in main text (including headings and list of references): 8041 Number of Figures: 18 Number of Tables: 1

1 Assistant Professor, Department of Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA 16802; [email protected]; Corresponding Author. 2 Professor, School of Civil Engineering, Purdue University, West Lafayette, IN 47907; [email protected] 3 Professor, School of Civil Engineering, Purdue University, West Lafayette, IN 47907; [email protected]

International Journal of Geomechanics. Submitted July 13, 2012; accepted March 7, 2013; posted ahead of print March 9, 2013. doi:10.1061/(ASCE)GM.1943-5622.0000303

Copyright 2013 by the American Society of Civil Engineers

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INTRODUCTION

Drilled-displacement (DD) piles are rotary displacement piles installed by inserting a specially

designed drilling tool consisting of a partial-flight auger and a displacement body into the ground

and advancing it using both a vertical force and a torque. The soil is displaced laterally within

the ground (with minimal spoil generated), and the void created is filled with concrete or grout.

These piles are also known as screw piles in Europe and augered displacement piles in the U.S.

(Brown and Drew 2000; Brown 2005; Prezzi and Basu 2005; Basu et al. 2010). Basu et al.

(2010) provide an overview of DD piling technologies available around the world. DD piling

technology is distinctively different from the helical piling technology in which a single- or

multiple-helix steel auger is screwed into the ground to form the piles, which are similar to

helical ground anchors.

The soil displacement produced during the installation of DD piles can vary from that of

a partial- to a full-displacement pile depending on the design of the drilling tools and piling rig

technology. The installation of DD piles produces greater radial soil displacement than that

produced by continuous-flight-auger (CFA) or auger cast-in-place (ACIP) piles (CFA and ACIP

piles are generally associated with small soil displacement). As a result, higher capacity can be

expected from DD piles than from CFA or ACIP piles of similar geometry. The main

advantages of DD piles are: (i) ease of construction with minimal vibration or noise, (ii) minimal

soil spoil (this is particularly important for contaminated sites) and (iii) high load carrying

capacity due to full or partial displacement of the soil surrounding the pile. However,

notwithstanding the widespread use of these piles, no theoretical research has been performed to

assess the effect of the various installation methods on the shaft resistance of these piles.



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Over the last few decades, researchers have correlated the capacity of DD piles with the

results of different in situ tests (NeSmith 2002; Brettmann and NeSmith 2005; Bustamante and

Gianeselli 1993, 1998; Van Impe 1986, 1988, 2004; Bauduin 2001; Holeyman et al. 2001; De

Vos et al. 2003; Maertens and Huybrechts 2003). These design methods rely mostly on

empirical relations that were developed based on the results of field pile load tests performed on

certain types of DD piles and, therefore, are applicable only to the specific type of DD pile

considered and soil conditions of the test sites. Park et al. (2012) calculated the fitting

parameters for a soil spring model (an approximate model to capture soil-pile interaction through

a series of springs positioned along the pile shaft and at the pile base) to match the load-

settlement behavior of DD and ACIP piles installed in sand. The fitting parameters were

determined based on regression analyses so that the load and settlement measured at pile head

could be reproduced. Such an approach falls short of capturing the complex pile-soil interaction

and thus, cannot describe the mobilization of local shaft and base resistances with sufficient

rigor. There has been no theoretical research done so far on studying the effect of installation on

the capacity of DD piles.

This paper investigates the development of the shaft resistance of DD piles with nearly

straight shafts (installed using drilling tools that have enlarged, large-diameter displacement

bodies; e.g., Auger Pressure-Grouted Displacement, Omega and De Waal piles) in sand using

one-dimensional, quasi-axisymmetric finite element analysis (FEA). The analysis captures the

essential stages of the installation and loading of DD piles in sand: (i) expansion of a cylindrical

cavity and shearing of soil (both downward and torsional) along the shaft-soil interface during

drilling, (ii) upward shear unloading along the borehole wall caused by removal of the drilling

tool, and (iii) shaft loading, which causes further vertical shearing along the shaft-soil interface.



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The FEAs, which use a two-surface plasticity constitutive model, are based on the assumptions

that: i) the borehole wall neither ‘caves in’ nor ‘bulges out’ during concrete (or grout) placement

and hardening, ii) the pile shaft is perfectly rigid (a reasonable assumption given the large

concrete-to-soil stiffness ratio), and iii) the lateral expansion of the shaft due to any vertical

loading is negligible. Based on the FEA simulation results, a set of equations is proposed for the

estimation of the lateral earth-pressure coefficient and thus the unit limit shaft resistance of DD

piles installed in sand that takes into account the initial soil state and the rate of penetration of the

drilling tool during pile installation.

SOIL PROPERTY-BASED METHOD FOR CALCULATING SHAFT RESISTANCE

The limit unit shaft resistance, which is mobilized at very small pile head displacements, is used

in the calculation of the axial capacity of piles along the entire pile length under most conditions

(except for long floating piles, which rely on incomplete mobilization of shaft resistance along a

lower portion of their length). In the soil property-based approach, the limit unit shaft resistance

qsL of an axially loaded pile is expressed as:

sL v0 v0tanq K (1)

where K is the coefficient of lateral earth pressure, is the friction angle mobilized at the pile

shaft-soil interface, and v0 is the in situ vertical effective stress (before pile installation) at the

depth where the shaft resistance is calculated. The earth pressure coefficient K depends on soil

state (i.e., void ratio and mean effective stress). For DD piles, K can be substantially greater than

the at-rest lateral earth pressure coefficient K0 since installation causes substantial radial

displacement of the soil surrounding the pile shaft. The friction angle mobilized at the

interface is a function of the pile surface roughness (Fioravante 2002; Colombi 2005).



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During installation of a DD pile with a straight shaft, as the drilling tool is extracted from

the ground, concrete or grout is pumped (sometimes under pressure) into the nearly cylindrical

borehole created by drilling. Fresh concrete (or grout) fills the irregularities of the borehole wall

caused by drilling. As concrete hardens, strong bonding develops at the pile shaft-soil interface,

which can be considered to be rough. For a rough interface, shearing occurs within the soil

immediately adjacent to the shaft, and limit shaft resistance is reached through the formation of a

shear band parallel to and adjacent to the shaft (Randolph and Wroth 1981, Potts and Martins

1982, Azzouz et al. 1990, Loukidis and Salgado 2008, Basu et al. 2011). Therefore, the limit

shaft resistance of DD piles is controlled purely by the shear strength of the soil, and takes the

value of the mobilized friction angle The value of the limit interface friction angle is usually

expressed in terms of the critical-state friction angle c of the soil because the large shear strains

that develop near the pile shaft at ultimate load levels cause the soil adjacent to the pile shaft to

reach critical state. According to Potts and Martins (1982), for a perfectly rough interface,

correlates with the critical-state friction angle cSS under simple shear conditions following the

relation tan sin cSS. Therefore, the value of appearing in Equation (1) can be chosen with

reasonable accuracy. In contrast, K depends not only on the initial relative density and confining

stress of the soil (Salgado 2008), but also on the evolution of the values of these parameters

during pile installation.

This paper quantifies the effect of installation on the shaft resistance of a DD pile through

the K/K0 ratio (= r/ r0; where ′r is the radial effective stress acting on the pile shaft at limit

loading conditions and ′r0 is the in situ radial effective stress at the depth considered). K/K0 is

expressed as a function of the initial in situ vertical effective stress v0, relative density DR and

an installation rate parameter expressed as:



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θ

z1tanuu

(2)

where uz and u are the vertical and rotational (torsional) displacements of the drilling tool used

in pile installation. The installation parameter represents the ratio of the advancement

(penetration) of the drilling tool into the ground and the rotation of the drilling tool (Figure 1a).

Lower values of imply slower rate of penetration of the drilling tool into the ground during

drilling (as expected for installation in dense sands), while higher values of imply easier

drilling conditions (as expected for installation in loose sands). For a drilling condition in which

the auger rotates a single full rotation to penetrate a length equal to the pitch length of the auger,

is the flight angle of the auger.

SIMULATION OF DD PILE INSTALLATION AND LOADING

The installation of a DD pile causes complex changes to the state (i.e., void ratio e and mean

effective stress p′) of the in situ soil surrounding it. The key steps of the installation of a DD pile

are: (I) drilling (during which both rotation of the drilling tool and the crowd (axial) force,

typically applied by hydraulic rams, help advance the drilling tool); (II) removal of the drilling

tool from the ground, (III) pumping of concrete or grout through the casing as the drilling tool

and the casing are extracted from the ground and placement of the reinforcement cage (either

before or after concrete placement), and (IV) hardening of the concrete. A soil element in the

vicinity of any segment of the shaft of a DD pile experiences the effects of not only these four

installation steps but also an additional loading step (step V) due to either construction of the

superstructure or performance of a pile load test. The borehole wall neither ‘caves in’ nor

‘bulges out’ during steps (III) and (IV). This assumption allows consolidation of the five



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installation and loading steps into three idealized FEA stages. Analysis stages 1 (drilling into the

ground) and 2 (removal of the drilling tool) represent steps (I) and (II), respectively. Analysis

stage 3 (loading of the pile) represents step (V).

Figure 1b shows schematically the idealized stages used to model the installation and

loading of a DD pile. The insertion of the drilling tool with a large-diameter displacement body

into the ground and its extraction cause shearing of the soil through a combination of three

loading modes: i) cavity expansion, ii) torsional shearing on the borehole wall, and iii) vertical

shearing on the borehole wall (downward during drilling and upward during extraction of the

drilling tool). Additional downward shearing occurs along the pile shaft-soil interface during

loading of the pile. Before the drilling tool is inserted into the ground, the soil element A shown

in Figure 1b is subjected to the in situ stress state. As the drilling tool passes element A (Stage

1), this element is pushed radially away from the path of the drilling tool (simulated by

expansion of a cylindrical cavity starting from a very small cavity radius) and also undergoes

torsional and vertical shearing. At the end of the cavity expansion process, the left boundary of

element A merges with the wall of the displacement body of the drilling tool. After the cavity

expansion phase is complete, torsional and vertical shearing are simultaneously applied to soil

element A (which is now adjacent to the wall of the displacement body). This part of the

analysis indirectly accounts for any torsional and vertical shearing that may occur when the

drilling tool passes element A, which reaches critical state by the end of Stage 1, which means

that a shear band forms in the vicinity of the borehole wall.

Coupled analyses, in which cylindrical cavity expansion is coupled with vertical and

torsional shearing, were also performed to model the drilling process. The main uncertainties

involved in these coupled analyses are related to the ratios of the radial, vertical and torsional



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displacements. For this reason, a parametric study was done to quantify the effect of the coupled

displacement application during Stage 1 on the limit unit shaft resistance of the pile.

Stage 2 represents the extraction of the drilling tool from the ground. During this

process, the displacement body applies an upward drag force on the soil adjacent to it. This is

modeled by applying upward vertical shearing on the left boundary of element A until a limit

state (the critical state) is reached. The analysis simulates Stage 3 (loading of the pile) by re-

applying downward vertical shearing on the left boundary of element A, which is now adjacent

to the pile shaft-soil interface and once again reaches a limit state at the end of Stage 3.

Between Stage 1 and Stage 2 (extraction of the drilling tool), soil element A looses radial

support from the large-diameter displacement body. This is because the casing attached to the

top of the displacement body usually has a diameter smaller than that of the displacement body.

As a result, element A may undergo some negative radial displacement (i.e., displacement

towards the pile axis). However, during the extraction of the drilling tool (Stage 2), the soil is

again pushed away from the path of the drilling tool. During this process, element A returns to

its previous position, and its left boundary merges with the wall of the displacement body. As

indicated earlier, the inward movement (at the end of Stage 1) and outward movement (during

Stage 2) of the soil element are not considered in the analyses since the effects of these two

intermediate stages counterbalance each other and do not impose any net change on the state of

the soil surrounding the pile. During extraction of the drilling tool from the ground, fresh

concrete is pumped into the borehole, providing lateral support to the surrounding soil, and no

further change in the lateral stress in the soil adjacent to the pile occurs as the concrete hardens.



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FINITE ELEMENT MODELING

This paper investigates the effects of DD pile installation and loading on the stress state of a soil

disk around the pile shaft by assuming that the vertical normal strain in the soil surrounding the

pile shaft is negligible and that there is no bending deformation. These are reasonable

assumptions at a depth sufficiently away from both the ground surface and the pile base. Using

these assumptions, the analysis becomes independent of the thickness of the soil disk and thus

one-dimensional (1-D). A similar 1-D approach was also used to investigate the shaft resistance

of full-displacement and nondisplacement piles in clays and sands (Randolph and Wroth 1978;

Potts and Martins 1982; Loukidis and Salgado 2008; Basu et al. 2011; Chakraborty et al. 2013;

Basu et al. 2012).

Mesh and Boundary Condition

Figure 2 shows the FE mesh, boundary conditions, and nodal constraints used in the analyses.

The mesh consists of a row of 8-noded, rectangular, quasi-axisymmetric elements with 4 Gauss-

quadrature points. In addition to the in-plane degrees of freedom (DOFs) uz and ur (for vertical

and radial direction, respectively), each node of these elements has an out-of-plane DOF u .

This out-of-plane DOF at every node is required to simulate the torsional shearing associated

with the drilling. The elements used in this study represent an axisymmetric geometry; however,

the presence of an additional out-of-plane DOF at each node separates these elements from

conventional 8-noded axisymmetric rectangular elements. Gens and Potts (1984) also used such

quasi-axisymmetric elements to solve boundary value problems with axisymmetric geometry

subjected to nonaxisymmetric loading. The quasi-axisymmetric element was implemented in the

finite element code “Solid Nonlinear Analysis Code” (SNAC; Abbo and Sloan 2000).



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All DOFs of nodes lying along a vertical line are tied together to enforce the condition of

zero normal vertical strain. Imposition of this constraint also guarantees that there is no bending

deformation of the sides of any element during shearing in the vertical and in the angular

(torsional) directions. The constraint applied at the nodes also makes the analysis independent of

the height of the rectangular elements. The nodes at the outer boundary of the disk are fixed in

all directions to ensure zero displacement at a distance far from the pile shaft. Displacement

increments are applied at the nodes on the left boundary of the domain. At the end of the

cylindrical cavity expansion phase (but before the vertical and torsional shearing start), the

thickness of the smallest (leftmost) element is consistent with typical values of shear band

thickness (i.e., 5 to 20 times the mean particle diameter D50) observed in sand.

Specified Displacement Increments

The analyses were displacement-controlled analyses, in which the displacement increments ur,

uz and u were applied at the nodes on the left boundary of the domain where the reactions

were monitored, as shown at different stages of the analyses in Figure 3. The analyses are based

on the conventional, small-strain finite element formulation but with updating of the position (x

and y coordinates) of the nodes after the application of each displacement increment (an

approach often referred to as Updated Lagrangian). The FE code SNAC was modified to handle

node updating after each solution increment; this is needed for proper simulation of a large-

deformation problems like the one addressed in this paper. Basu et al. (2011) demonstrated the

validity of this approach by comparing the results obtained from FEAs (with node updating) of

cylindrical cavity expansion problems with the solutions proposed by Yu and Houlsby (1991),

Collins et al. (1992) and Salgado and Randolph (2001).



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Horizontal displacement increments ur were applied to the leftmost nodes of the domain

to simulate the cavity expansion phase associated with the penetration of the drilling tool (Figure

3a). At the end of the cavity expansion phase, vertical and torsional (angular) displacement

increments ( uz and u , respectively) were applied simultaneously at the nodes of the leftmost

boundary of the domain to simulate vertical and torsional shearing during drilling (Figure 3b).

No interface elements were placed at the left boundary. Any slippage between the drilling tool

(when the displacement body completely passes the soil disk) and soil was simulated by the

formation of a shear band inside the soil adjacent to the displacement body. This condition

corresponds to a perfectly rough interface between the displacement body and the cavity wall.

The vertical and torsional loading stage following the cavity expansion phase is stopped when

normal, tangential and torsional reactions at the left boundary of the domain stabilized and a

limit condition (critical state) was reached along the borehole (cavity) wall. This limit state

represents the end of drilling and also the end of analysis Stage 1.

Negative (upward) vertical displacement increments (− uz) were applied at the nodes

lying on the left boundary of the domain (Figure 3c) to simulate the extraction of the drilling tool

from the ground. This stage was stopped when both the normal stress and vertical shear stress

along the left boundary of the domain stabilized and a limit condition was reached. At this stage,

the vertical shear stress on the left boundary of the domain reached a negative limiting value. In

practice, the drilling tool may be rotated clockwise during its extraction from the ground.

However, the present analysis does not simulate this rotation of the drilling tool during the

extraction process. At the end of the extraction stage (i.e., analysis Stage 2), the nodes lying on

the left boundary of the domain were on the pile shaft-soil interface.



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The transition between analysis Stages 1 and 2 and that between analysis Stages 2 and 3

was automated based on a convergence criterion: for three consecutive displacement increments,

the corresponding shear and normal stress values differed only by a value equal to or less than

10-7 kPa. This criterion was applied simultaneously to both the normal and tangential reactions

to guarantee that the limit state was indeed reached. In analysis Stage 3, positive (downward)

vertical displacement increments uz were applied to the nodes lying on the left boundary of the

domain (which represented the pile-soil interface) to simulate loading of the pile (Figure 3d).

In the case of the coupled analyses, during the cavity expansion phase, vertical and

angular (torsional) displacement increments were also applied at the nodes on the left boundary

of the domain (Figure 3e). The analyses started from a small cavity radius r0 with radial

displacement increments applied until the cavity radius r became equal to the maximum radius R

of the displacement body. Both vertical and angular (torsional) displacement increments were

applied until a limit state was reached. The next loading stages (corresponding to the extraction

of the drilling tool and loading of the pile) remained the same, as shown in Figures 3c and 3d.

Constitutive Model and Solution Algorithms

A two-surface plasticity model based on critical-state soil mechanics was used to simulate the

mechanical response of sand. The model accounts for both stress-induced and inherent (fabric)

anisotropy. This constitutive model for sand was originally proposed by Manzari and Dafalias

(1997) and subsequently modified by Li and Dafalias (2000), Papadimitriou and Bouckovalas

(2002), Dafalias et al. (2004), and Loukidis and Salgado (2009). The present analyses used

model parameter values calibrated for dry-deposited/air-pluviated Toyoura sand. This model

was calibrated to correctly predict the stresses at the boundary of sand specimens used in



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laboratory tests, such as drained biaxial compression tests, direct simple shear tests and torsional

shear tests in the hollow cylinder apparatus.

The modified Newton-Raphson method was used to solve the global nonlinear load-

displacement system of equations. The elastic global stiffness matrix was used in the modified

Newton-Raphson scheme. The constitutive model equations were integrated using a semi-

implicit algorithm adapted with sub-incrementation and error control (Loukidis and Salgado

2009) using relative stress error tolerance equal to 10-4. The displacement at the inner boundary

was applied in increments of 4 10-4mm.

ANALYSIS RESULTS

The effective stress analyses were performed for normally consolidated Toyoura sand with

different values of relative density DR (= 30, 45, 60, 75 and 90%), different values of initial

vertical effective stress 'v0 (= 25, 50, 100, 200 and 400 kPa) and K0 = 0.45 (a value appropriate

for normally consolidated sand). Two different values of 10° and 20°) were considered. The

pile diameter B was equal to 0.33 m. The main output of the FEA was the value of K/K0 at the

end of loading. An additional set of FEAs were performed with ° to obtain an approximate

measure of K/K0 values (through interpolation between the values of K/K0 obtained for = 0°

and 10°) for DD piles installed with values less than 10°. To assess the effect of inherent

(fabric) anisotropy, which is due to the preferred orientation of the sand particles, on the pile-soil

load-transfer behavior, two sets of analyses were done: i) considering fabric anisotropy and ii)

ignoring fabric anisotropy (by switching off the constitutive model components pertaining to

fabric anisotropy and thus having an isotropic fabric tensor). These two sets of analyses, referred

to as anisotropic and isotropic, respectively, were performed for several reasons. First, not all



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sands have fabrics that are as anisotropic as that of Toyoura sand. Additionally, an initially

anisotropic sand fabric may evolve significantly and become progressively more isotropic during

pile installation. Thirdly, cavity expansion involves stress paths with large increments of mean

stress p relative to deviatoric stress ones. These stress paths are different from the stress paths

followed in elemental shearing tests in the triaxial, plane-strain or hollow-cylinder equipment

(which impose predominantly deviatoric stress increments to soil specimens). The calibration of

the constitutive model parameters pertaining to fabric anisotropy for Toyoura sand is based on

these elemental tests. Finally, cylindrical cavity expansion imposes kinematic constraints on the

soil elements that could cause the effects of fabric anisotropy to be more muted.

Evolution of Normal and Shear Stresses

Figure 4 shows the evolution of normal (radial) stress r′ acting on the cavity wall during the

cavity expansion (CE) phase of drilling (i.e., analysis Stage 1). Cavity expansion starts from a

very small initial radius r0 (= 0.015 m) and ends when the cavity radius r becomes equal to the

maximum radius R (= 0.165 m = B/2; with B being the pile diameter) of the displacement body

(which is equal to the pile radius). Starting from a finite cavity radius is theoretically equivalent

to modeling the expansion of an existing cavity, while, in reality, a cavity is created (expanded

from zero radius) in the soil during installation of a DD pile. With a sufficiently small initial

cavity radius (compared to the final radius), the cavity pressure at the end of the cavity expansion

process (i.e., when r/r0 = 11) practically matches the limit cavity pressure (Figure 4). The values

of torsional and vertical shear stresses ( and z, respectively) remain zero throughout the CE

phase.



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Figures 5 and 6 show (for ′v0 = 200 kPa, DR = 75%, and = 10° and 20°) the evolution

of r′, and z at different stages of pile installation and loading. These stresses act on the outer

wall of the large-diameter displacement body during drilling and removal of the drilling tool, and

on the DD pile shaft during loading of the pile. The initial values of r′ (point A) in these figures

are equal to those at the end of the CE phase. As the shearing (both torsional and vertical) phase

(associated with drilling; analysis Stage 1) starts, the sand behavior becomes purely contractive,

leading to a loss of radial stress r′. This happens because the direction of loading changes from

horizontal during the CE phase to a direction consistent with the value of used during the

shearing phase. Upon such changes in the shearing direction, the soil surrounding the drilling

tool switches from a dilative to a contractive response. This change in soil behavior is

adequately captured by the constitutive model used in the analyses. As the limit condition is

reached at the end of the shearing phase associated with drilling, more than half of the initial

limit cavity pressure is lost due to the net contractive behavior of the soil surrounding the pile.

Critical state is reached in the first element adjacent to the drilling tool at the end of drilling as

and z reach their respective limiting values (point B in Figures 5 and 6).

During the extraction of the drilling tool (analysis Stage 2), all the stresses acting on the

interface between the displacement body and the soil element adjacent to it decrease

continuously as upward vertical shearing is applied. At the end of pile installation (point C in

Figures 5 and 6), z reaches a negative limiting value and becomes equal to zero. At the end of

loading (point D in Figures 5 and 6), both r′ and z acting on the pile shaft-soil interface reach

their limiting values. During loading of the pile (Stage 3), remains equal to zero at the pile

shaft-soil interface since this stage is associated purely with vertical shearing along the pile shaft-

soil interface. A small loss or gain in radial stress is observed due to dilation, especially after the



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peak in shear stress response, as the limit (critical) state is approached during the extraction of

the drilling tool and during loading of the pile (Figures 5 and 6).

Figure 7 shows (for ′v0 = 200 kPa, DR = 75%, and = 0°, 10° and 20°) the stress path in

void ratio e – mean effective stress p′ space for the leftmost quadrature point in the first

(leftmost) element of the mesh. The soil element adjacent to the displacement body dilates

during the CE phase, and as a result, p′ increases from its in situ value to a value corresponding

to point A in Figure 7. As the shearing (both torsional and vertical) phase associated with

drilling (Stage 1) starts, the contractive behavior of sand leads to a loss of mean effective stress

p′. Towards the end of drilling, the soil element adjacent to the displacement body dilates

(without any change in p′) to reach the limiting condition at critical state (point B in Figure 7a).

The critical state (in e-p′ space) reached at the end of drilling is similar to the one reached at the

end of the CE phase (point A in Figure 7a); however, both are significantly different from those

reached at the end of extraction of the drilling tool (point C in Figure 7a) and at the end of

loading of the pile (point D in Figure 7a). This is because the loading conditions imposed on the

surrounding soil during different pile installation phases are different. Extraction of the drilling

tool and axial loading of the pile impose simple shear loading conditions to the soil surrounding

the pile shaft. Consequently, the points C and D fall on a critical-state line (in e-p′ space) that

corresponds to a simple shear loading condition. The loading conditions during CE and drilling

are complex; these loading conditions correspond to a critical-state line (in e-p′ space) that is

different from the critical-state line corresponding to simple shear loading. However, the stress

path in q-p′ space (Figure 8) illustrates that the soil adjacent to the pile shaft reaches almost the

same stress ratio (q/p′) at the end of different phases of installation and loading.



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At the end of drilling (point B in Figure 7a), no variation is observed in the stress paths

(in e-p′ space) for different values of (Figure 7a). Beyond point B (during extraction of the

drilling tool and loading), the stress paths for different values of differ slightly from each other.

As the value of increases, the soil response becomes more contractive leading to greater loss of

p′. Figure 7(b) shows the stress paths (in e-p′ space) for quadrature points at different distances

(B, 2B, 4B and 10B) from the pile axis. At a distance of 10B from the pile axis, the installation

and loading of a DD pile does not impose any significant change in the stress state of the in situ

soil.

Effect of Installation on the Surrounding Soil

Installation of a DD pile causes significant changes to the stress state of the soil surrounding the

pile. For example, for ′v0 = 200 kPa and DR = 75%, the normal (radial) stress ′r acting at a

point on the pile shaft at the end of pile installation in initially anisotropic and isotropic sand

fabric are, respectively, 4.6 and 10 times the in situ normal (radial) effective stress ′r0 acting at

that depth before pile installation (Figure 9). For pile installation in an initially anisotropic sand

fabric, the increase in the radial effective stress ′r due to pile installation becomes less than

0.13 ′r0 beyond a distance of 20B from the pile axis; in the case of an initially isotropic sand

fabric, this increase in ′r is 0.4 ′r0. Figure 9 shows that most of the changes in the in situ normal

stress due to installation and loading of a DD pile occur within a distance of 10B from the pile

axis.

Figure 10 shows the influence of DD pile installation on the mean effective stress p′

acting at different points within the surrounding medium. Results of an anisotropic analysis with

′v0 = 200 kPa, p′0 = 126.67 kPa and DR = 75% shows that p′ increases from its initial value



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within a zone of radius equal to 5B around the pile axis. The maximum increase in p′ is observed

adjacent to the pile shaft; at the end of pile loading, p′ adjacent to the pile shaft becomes 2.4

times its initial value p′0 (Figure 10a). A small decrease in p′ (from p′0) is observed within a

zone between radii 5B and 11B from the pile axis; beyond a radial distance of 11B from the pile

axis, p′ remains unchanged (Figure 10a). For an isotropic analysis with the same initial

conditions, the increase in p′ becomes insignificant beyond a distance of 15B from the pile axis

(Figure 10b).

Soil within a small zone (of radius equal to 1.3B and 3.6B from the pile axis for

anisotropic and isotropic analysis) surrounding the pile shaft dilates due to DD pile installation

(Figure 11). A contractive zone surrounds this dilative zone. For an initially anisotropic sand

fabric, the contractive zone is observed between radial distances of 1.3B and 11B from the pile

axis (Figure 11a); for an initially isotropic sand fabric this contractive zone is smaller (Figure

11b).

For different values of , Figure 12 shows (for anisotropic analysis with ′v0 = 200 kPa,

′r0 = 90 kPa and DR = 75%) the profiles of normal effective stress, mean effective stress and

void ratio at different radial distances from the axis of a DD pile at the end of installation. At a

point just adjacent to the pile shaft, a maximum variation of 15% is observed for the normal and

mean effective stresses as the value of changes from 0° to 20°. The value of does not have

any influence on the values of the normal effective stress and mean effective stress beyond radial

distances of 16B and 10B (from the pile axis), respectively. The void ratio is insensitive to ,

varying less than 1% at a point just adjacent to the pile shaft.



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ESTIMATION OF LATERAL EARTH-PRESSURE COEFFICIENT K

The ratio K/K0 (= ′r/ ′r0) is estimated from the recorded normal reaction on the pile shaft at the

end of loading of the pile. The following mathematical expressions resulted from the FEAs:

0.11

v0 R A

0 A v0

0.33 exp 3.59 0.53ln 1 0.11tan100D pK

K p (3)

for anisotropic sand fabric, and

0.11

v0 R A

0 A v0

1.30 exp 2.91 0.38ln 1 0.12 tan100D pK

K p (4)

for isotropic sand fabric, where DR is expressed as a percentage (%) between 0 and 100 and pA

is a reference stress (=100 kPa or equivalent in other units).

Figures 13 and 14 show the variation of K/K0 (for = 10° and = 20°) with DR for

different initial vertical effective stress levels calculated using Equations (3) and (4) together

with the values resulting from the FEAs. K/K0 increases with increasing relative density and

decreasing initial confinement (a direct consequence of the increased soil dilatancy). The ratio

K/K0 for DD piles installed in sand with initially anisotropic fabric is always smaller than that

installed in sand with initially isotropic sand fabric. This is because the installation of a DD pile

involves stress paths and loading modes in which the direction of the major principal stress

increment is closer to the horizontal plane (which is also the preferred orientation of the particle

long axis for sands deposited under the action of gravity) than to the vertical plane. In such case,

sand with an anisotropic fabric exhibits a more pronounced contractive (or less dilative)

response, has less strength and is more compliant (Oda 1972; Tatsuoka et al. 1986; Tatsuoka et

al. 1990; Yoshimine et al. 1998; Basu et al. 2011).



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Effects of K0 and Pile Diameter B on the Earth-Pressure Coefficient K

Equations (3) and (4) are based on the FEAs performed for a 0.33 m-diameter DD pile installed

in normally consolidated Toyoura sand with an assumed value of K0 equal to 0.45. The effects

of K0 and B values on the earth-pressure coefficient K at limit state were investigated, with

results shown in Figures 15 and 16. Figure 15 shows that for installation in dense sand (DR =

90%) with K0 = 0.6 (an overconsolidated sand), the ratio K/K0 differs only by 7.5% (for = 10°)

and 6.4% (for = 20°) from its value obtained using K0 = 0.45. For a medium-dense sand (DR =

45 to 75%), the value of K0 has minimal effect on the ratio K/K0. The small difference in the

ratio K/K0 for different values of K0 is due to the varying extent of initial stress-induced

anisotropy: the lower the value of K0, the higher the stress-induced anisotropy is. For the same

value of initial vertical effective stress, a lower value of K0 would suggest a lower value of initial

mean effective stress; therefore, a more dilative response is expected for lower values of K0.

Similar dependence of K/K0 on the value of K0 is observed in the analyses of nondisplacement

and displacement piles in sand (Loukidis and Salgado 2008; Basu et al. 2011). Figure 16 shows

the variation of K/K0 at limit state conditions for two different pile diameters, B = 0.33 m and 0.6

m. The ratio K/K0 (for different values) differs by no more than 1.6% as the pile diameter is

changed. Irrespective of B, the same limit state is reached at the end of cavity expansion, and

therefore, B does not have a significant effect on the value of K/K0 at limit loading conditions.

Comparison of K/K0 Obtained from Coupled and Uncoupled Analyses

The expressions for K/K0 given by Equations (3) and (4) were obtained from uncoupled analyses

in which no shear displacements were applied during the CE phase of drilling (Stage 1).

However, some shearing may be associated with the cavity expansion phase as well. An



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additional set of coupled FEAs were performed to evaluate the effect of additional shearing (both

torsional and vertical) during the cavity expansion phase on K/K0. In the case of coupled FEAs,

equal radial and torsional displacement increments (i.e., ur = u ) were applied during the CE

phase. The vertical displacement increments applied during the CE phase of the coupled FEAs

were determined based on Equation (2). The CE phase ends when the cavity radius became

equal to the radius of the pile. Torsional and vertical shearing are continued until a limit

(critical) state that signifies the end of drilling is reached. Figure 17 shows K/K0 ratios obtained

from the coupled FEAs (for DR = 45, 60, 75, and 90%; ′v0 = 50, 100, 200, and 400 kPa; = 10°

and 20°) superposed with those obtained from the uncoupled FEAs. The values of K/K0 obtained

from the coupled FEAs are 10 to 20% higher than those obtained from the uncoupled FEAs. The

differences observed for the K/K0 values obtained from coupled and uncoupled analyses are due

to the inherent nonlinear mechnical behavior of soils and its dependence on the loading path.

DESIGN EXAMPLE AND COMPARISON

Detailed records of instrumented load tests on DD piles in sand appear to be scarce in literature.

In the absence of field test data quantifying the shaft resistance of DD piles in sand, a design

example is used to demonstrate the application of the proposed equations and to compare the

limit shaft capacity calculated using Equation (3) with that calculated using three different

empirical design methods: Method A (NeSmith 2002; Brettmann and NeSmith 2005), Method B

(Bustamante and Gianeselli 1993, 1998) and Method C (Van Impe 1986, 1988, 2004; Bauduin

2001; Holeyman et al. 2001; De Vos et al. 2003; Maertens and Huybrechts 2003a). These

empirical design methods were developed in different parts of the world based on load tests on

DD piles installed under different site conditions. The load tests used for the development of

these design methods did not allow the separation of shaft and base resistances. In order to gage



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the variability that might be expected when different methods are used for the calculation of

shaft capacity of DD piles in sand, the shaft capacity calculated using the proposed FEA-based

equations is compared with that obtained using three different empirical design methods

routinely used in practice. Details of these empirical design methods are summarized in Basu et

al. (2010).

The limit shaft capacity is calculated for a 0.5-m-diameter DD pile installed in a naturally

deposited, multilayered (relative density varying with depth), normally consolidated (K0 = 0.45,

c = 30°) sand deposit (Figure 18). The local values of unit limit shaft resistance qsLi are

calculated at the mid-depth of each segment and those values are multiplied by the available

shaft area Asi (= B L; L is the length of each segment and chosen to be equal to 1 m for the

calculation presented in this paper) of each segment to obtain the shaft resistance available from

each pile segment. The total shaft capacity of the pile is obtained by adding up the resistance

values calculated for all the pile segments.

The sample calculation is presented for a pile segment (Segment # 6) between depths 5 m

and 6 m from the ground surface. The mid-depth of this segment is at 5.5m from the ground

surface. At depth 5.5m, the in situ vertical stress ′v0 = 5.5×20 = 110kPa. Given DR = 60% and

K0 = 0.45, the value of earth-pressure coefficient K at limit loading condition can be calculated

using Equation (3) as:

22.1

10tan11.01110100

ln53.059.310060

exp100110

45.033.0

tan11.01ln53.059.3100

exp33.0

011.0

0

11.0

00

v

AR

A

v pDp

KK



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As discussed earlier in this paper, the interface friction angle can be calculated from the

critical-state friction angle c as = tan-1(sin c) = 26.6°. The limit shaft resistance available at a

depth 5.5m is qsLi, at 5.5 m = K ′v0 tan ×110×tan(26.6°) = 66.9 kPa. The available shaft area

Asi (= B L) for each pile segment is equal to 1.6m2. Thus, the available shaft resistance QsLi

from this pile segment (Segment # 6) will be: QsLi = qsLi Asi = 66.9×1.22= 105.1 kPa.

Similarly, QsLi for all other pile segments are calculated and added up to obtain the limit shaft

capacity QsL (= 1266.9 ≈ 1267 kN) of the pile.

Table 1 summarizes the calculation results for all pile segments. This table also shows the

results obtained by using design methods A, B and C. The cone penetration test (CPT) resistance

profile used in calculations done with the empirical design methods was obtained from the soil

profile shown in Figure 18a. The following expression proposed by Salgado and Prezzi (2007) is

used to calculate qc as a function of horizontal effective stress ′h, DR (expressed in %) and c:

0.841 0.0047

hR

A

1.64exp 0.1041 0.0264 0.0002RD

cc c

A

qD

p p (5)

The qc profile (Figure 18b) calculated using Equation (5) is used in the calculation of the

limit shaft resistance using the empirical design methods (i.e. Methods A, B, and C). The limit

shaft capacity of the DD pile calculated using the proposed equation for an initially anisotropic

sand fabric (Equation 3) compares well with that predicted by the design methods B and C (with

differences equal to 11.2 and 7.6%, respectively). The prediction using Method A is,

respectively, 27.5%, 18.4% and 21.5% higher than the limit shaft capacity values calculated

using the FEA-based equation proposed in this paper, Method B and Method C. To facilitate

application of the proposed FEA-based equations in real-life design, predictions using the



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proposed equations may need further verification with results from instrumented load tests on

DD piles in sand as such results become available.

CONCLUSIONS

The shaft resistance of DD piles installed in sand is studied using 1-D, quasi-axisymmetric

FEAs. Installation of a DD pile is modeled as a combination of three deformation modes: (i)

cavity expansion, (ii) vertical shearing and (iii) torsional shearing. The FEAs are performed for

different initial soil states using an advanced constitutive model suitable for sand. Two series of

FEAs were performed: one considers fabric anisotropy and one ignores it. Based on the results

of the FEAs, equations were proposed to calculate the ratio K/K0 which can be used to calculate

limit shaft resistance of a DD pile. The FEA results show that the value of K/K0 ratio increases

with increasing DR, decreasing ′v0 and decreasing . The limit shaft resistance of a DD pile

installed in an ideal sand deposit with isotropic fabric is always greater than of a DD pile with

the same geometry installed in a natural sand deposit with an anisotropic fabric. In the absence

of data from instrumented load tests on actual DD piles, limit shaft capacities of an example DD

pile installed in multilayered sand deposit is calculated using equation proposed in this paper for

initially anisotropic sand fabric and compared with those predicted by three available empirical

design methods. The comparison of limit shaft capacity values calculated using the proposed

method and empirical methods proposed in the literature reveals that, for an initially anisotropic

sand fabric, the prediction using the proposed FEA-based equation is in close agreement with the

predictions of these design methods.



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LIST OF REFERENCES Abbo, A.J. and Sloan, S.W. (2000). Solid nonlinear analysis code (SNAC), User manual version

2.0, Department of Civil, Surveying and Environmental Engineering, University of Newcastle, Australia.

Azzouz, A.S., Baligh, M.M., and Whittle, A.J. (1990). Shaft resistance of piles in clay. Journal

of Geotechnical Engineering, ASCE, Vol. 116, No. 2, pp. 205-221. Basu, P., Prezzi, M., and Basu, D. (2010). Drilled Displacement Piles – Current Practice and

Design. DFI Journal: The Journal of the Deep Foundations Institute, Vol. 4, No. 1, pp. 3-20. Basu, P., Loukidis, D., Prezzi, M., and Salgado, R. (2011). Analysis of Shaft Resistance of

Jacked Piles in Sand. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 35, Issue. 15, pp. 1605-1635.

Basu P., Prezzi, M., Salgado, R. and Chakraborty, T. (2012). Shaft Resistance and Setup Factors

for Piles Jacked in Clays. Under review in the Journal of Geotechnical and Geoenvironmental Engineering, ASCE.

Bauduin, C. (2001). Design procedure according to Eurocode 7 and analysis of the test results.

Screw Piles – Installation and Design in Stiff Clay, Holeyman (ed.), Swets and Zeitlinger, Lisse, pp. 275-303.

Brettmann, T. and NeSmith, W. (2005). Advances in auger pressure grouted piles: design,

construction and testing. Advances in Designing and Testing Deep Foundations, Geotechnical Special Publication No. 129, ASCE, pp. 262-274.

Brown, D. and Drew, C. (2000). Axial capacity of augured displacement piles at Auburn

University, New Technological and Design Developments in Deep Foundations. Proceedings of sessions of Geo- Denver 2000, Geotechnical Special Publication No. 100, ASCE, pp. 397-403.

Brown, D.A. (2005). Practical considerations in the selection and use of continuous flight auger

and drilled displacement piles. Advances in auger pressure grouted piles: design, construction and testing. Advances in Designing and Testing Deep Foundations, Geotechnical Special Publication No. 129, ASCE, pp. 251-261.

Bustamante, M. and Gianeselli, L. (1993). Design of auger displacement piles from in-situ tests.

Deep Foundations on Bored and Auger Piles, BAP II, Balkema, Rotterdam, pp. 21-34. Bustamante, M. and Gianeselli, L. (1998). Installation parameters and capacity of screwed piles.

Deep Foundations on Bored and Auger Piles, BAP III, Balkema, Rotterdam, pp. 95-108.



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Chakraborty, T., Salgado, R., Basu, P., and Prezzi, M. (2013). The Shaft Resistance of Drilled Shafts in Clay. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 139, No. 4, pp. 1-16.

Collins, I.F., Pender, M.J., and Yan, W. (1992). Cavity expansion in sands under drained loading

conditions. International Journal of Numerical and Analytical Methods in Geomechanics, Vol. 16, No. 1, pp. 3-23.

Colombi, A. (2005). Physical modeling of an isolated pile in coarse grained soil. Ph.D. Thesis,

University of Ferrara. Dafalias, Y.F., Papadimitriou, A.G., and Li, X.S. (2004). Sand plasticity model accounting for

inherent fabric anisotropy. Journal of Engineering Mechanics, ASCE, Vol. 130, No. 11, pp. 1319-1333.

De Vos, M., Baudin, C., and Maertens, J. (2003). The current draft of the application rules of

Eurocode 7 in Belgium for the design of pile foundations. Belgian Screw Pile Technology – Design and Developments, Maertens and HuyBrechts (eds.), Swets and Zeitlinger, Lisse, pp. 303-325.

Fioravante V. (2002). On the shaft friction modeling of non-displacement piles in sand. Soils and

Foundations, Vol. 42, No. 2, pp. 23-33. Gens, A. and Potts, D.M. (1984). Formulation of quasi-axisymmetric boundary value problems

for finite element analysis. Engineering Computations - International journal for computer-aided engineering and software, Vol. 1, pp. 144-150.

Holeyman, A., Baudin, C., Bottiau, M., Debacker, P., De Cock, F.A., Dupont, E., Hilde, J.L.,

Legrand, C., Huybrechts, N., Mengé, P., Miller, J.P., and Simon, G. (2001). Design of axially loaded piles – 1997 Belgian practice. Screw Piles – Installation and Design in Stiff Clay, Holeyman (ed.), Swets and Zeitlinger, Lisse, pp. 63 - 88.

Li, X.S. and Dafalias, Y.F. (2000). Dilatancy for cohesionless soils. Géotechnique, Vol. 50, No.

4, pp. 449-460. Loukidis D. and Salgado R. (2008). Analysis of the shaft resistance of non-displacement piles in

sand. Géotechnique, Vol. 58, No. 4, 283-296. Loukidis, D. and Salgado, R. (2009). Modeling sand response using two-surface plasticity.

Computers and Geotechnics, Vol. 36, No. 1-2, pp. 166-186. Maertens, J. and Huybrechts, N. (2003). Results of the static pile load tests at the Limelette test

site. Belgian Screw Pile Technology – Design and Developments, Maertens and HuyBrechts (eds.), Swets and Zeitlinger, Lisse, pp. 167-214.



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Manzari, M.T. and Dafalias, Y.F. (1997). A critical state two-surface plasticity model for sands. Géotechnique, Vol. 47, No. 2, pp. 255-272.

NeSmith, W.M. (2002). Static capacity analysis of augured, pressure-injected displacement piles.

Proceedings of the International Deep Foundations Congress 2002, Geotechnical Special Publication No. 116, Vol. 2, ASCE, pp. 1174-1186.

Oda M. (1972). Initial fabrics and their relations to mechanical properties of granular material.

Soils and Foundations; Vol. 12, No. 1, pp. 17–36. Papadimitriou, A.G. and Bouckovalas, G.D. (2002). Plasticity model for sand under small and

large cyclic strains: a multiaxial formulation. Soil Dynamics and Earthquake Engineering, Vol. 22, No. 3, pp.191-204.

Park, S., Roberts, L. A. and Misra, A. (2012). Design methodology for axially loaded auger cast-

in-place (ACIP) and drilled displacement (DD) piles. Journal of Geotechnical and Geoenvironmental Engineering, ASCE; doi:10.1061/(ASCE)GT.1943-5606.0000727

Potts, D.M. and Martins, J.P. (1982). The shaft resistance of axially loaded piles in clay.

Géotechnique, Vol. 32, No. 4, pp. 369-386. Prezzi, M. and Basu, P. (2005). Overview of construction and design of auger cast-in-place and

drilled displacement piles. Proceedings of DFI’s 30th annual conference on deep foundations, Chicago, pp. 497-512.

Randolph, M.F. and Wroth, C.P. (1978). Analysis of deformation of vertically loaded piles.

Journal of Geotechnical Engineering, ASCE, Vol. 104, GT12, pp. 1-17. Randolph, M.F. and Wroth, C.P. (1981). Application of the failure state in undrained simple

shear to the shaft capacity of driven piles. Géotechnique, Vol. 31, No. 1, pp. 143-157. Salgado, R. and Randolph, M.F. (2001). Analysis of cavity expansion in sand. International

Journal of Geomechanics, Vol. 1, No. 2, pp. 175-192. Salgado, R. (2008). Engineering of Foundations. Mc Graw-Hill, New York, USA. Tatsuoka F, Sakamoto M, Kawamura T, Fukushima S. (1986). Strength and deformation

characteristics of sand in plane strain compression at extremely low pressures. Soils and Foundations; Vol. 26, No. 1, pp. 65–84.

Tatsuoka F, Nakamura S, Huang C-C, Tani K. (1990). Strength anisotropy and shear band

direction in plain strain tests of sand. Soils and Foundations; Vol. 30, No. 1, pp. 35–54. Van Impe, W.F. (1986). Evaluation of deformation and bearing capacity parameters of

foundations, from static CPT-results. Proceedings of the Fourth International Geotechnical Seminar: Field Instrumentation and In Situ Measurements, NTI, Singapore, pp 51-70.



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Van Impe, W.F. (1988). Considerations in the auger pile design. Proceedings of the 1st

International Geotechnical Seminar on Deep Foundations on Bored and Auger Piles, BAP I, Balkema, Rotterdam, pp. 193-217.

Van Impe, W.F. (2004). Two Decades of Full Scale Research on Screw Piles: An Overview.

Published by The Laboratory of Soil Mechanics, Ghent University, Belgium. Yoshimine M, Ishihara K, Vargas W. (1998). Effects of principal stress direction and

intermediate principal stress on undrained shear behavior of sand. Soils and Foundations; Vol. 38, No. 3, pp. 179–188.

Yu, H.S. and Houlsby, G.T. (1991). Finite cavity expansion in dilatants soils: loading analysis.

Géotechnique, Vol. 41, No. 2, pp. 173-183.



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Page 1 of 2

LIST OF FIGURES Figure 1 Schematic representation of (a) the rate of installation parameter and (b) idealized

installation and loading stages for a DD pile (torsional shear stress acting on the soil element A

in Stage 1 is not shown in the figure)

Figure 2 One-dimensional finite element mesh, boundary conditions, constraints, and applied

displacements

Figure 3 Applied displacement increments in different stages of the analysis: (a) cavity

expansion, (b) shearing (vertical and torsional) associated with drilling, (c) upward (negative)

shearing during the extraction of the drilling tool, (d) downward shearing during loading of the

pile, and (e) simultaneous application of radial, vertical and torsional displacement increments

during the cavity expansion phase of a coupled analysis

Figure 4 Normalized cavity radius r/r0 vs. normal stress on the cavity wall during expansion of

the cavity (limit cavity pressure is reached at the end of the cavity expansion)

Figure 5 Evolution of normal (radial) effective stress, torsional shear stress and vertical shear

stress (for anisotropic analysis) during installation and loading of a DD pile; (a) ′v0 = 200 kPa,

DR = 75%, = 10° and (b) ′v0 = 200 kPa, DR = 75%, = 20°

Figure 6 Evolution of normal (radial) effective stress, torsional shear stress and vertical shear

stress (for isotropic analysis) during installation and loading of a DD pile; (a) ′v0 = 200 kPa, DR

= 75%, = 10° and (b) ′v0 = 200 kPa, DR = 75%, = 20°

Figure 7 Stress paths in e-p′ space: (a) for different values of and (b) at different distances from

the pile axis for = 20°

Figure 8 Stress path (in q-p′ space) for the leftmost quadrature point in the first (leftmost)

element of the mesh during installation (with = 20°) and loading of a DD pile



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Figure 9 Effect of DD pile installation (with °) on the normal (radial) effective stress

acting in the surrounding soil: (a) anisotropic analysis and (b) isotropic analysis

Figure 10 Effect of DD pile installation (with °) on the mean effective stress p′ in the

surrounding soil: (a) anisotropic analysis and (b) isotropic analysis

Figure 11 Effect of DD pile installation ( = 20°) on the void ratio e of the surrounding soil: (a)

anisotropic analysis and (b) isotropic analysis

Figure 12 Effect of the angle on the stress state of the soil surrounding the pile just after the

installation of a DD pile: (a) normal (radial) effective stress, (b) mean effective stress and (c)

void ratio

Figure 13 K/K0 predictions for DD piles (anisotropic analysis): (a) = 10° and (b) = 20°

Figure 14 K/K0 predictions for DD piles (isotropic analysis): (a) = 10° and (b) = 20°

Figure 15 Effect of K0 on the earth-pressure coefficient K at limit state conditions (anisotropic

analysis with ′v0 = 100 kPa): (a) = 10° and (b) = 20°

Figure 16 Effect of pile diameter B on the ratio K/K0 at limit state conditions (anisotropic

analysis with ′v0 = 100 kPa): (a) = 10° and (b) = 20°

Figure 17 Comparison of K/K0 obtained from coupled and uncoupled analysis: (a) = 10° and

(b) = 20°

Figure 18 Pile and soil profile used in the design example: (a) the multilayered sand deposit (b)

CPT profile calculated using Equation (5).



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Page 1 of 1

LIST OF TABLES

Table 1 Calculation of limit shaft resistance for example DD pile using different design methods



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(a)

(b)

Figure 1 Schematic representation of (a) the rate of installation parameter η and (b) idealized installation and loading stages for a DD pile (torsional shear stress acting on the soil element A

in Stage 1 is not shown in the figure)

uθ

uzη

= − z1tanuuη

Stage3: Limit loading along

the pile shaft

τ3σ r3Aσ r0

Initial stage

Large-diameter displacement body

Sacrificial tip

Drilling tool Partial flight

auger segment

τ1

Stage 1: Displacement body passes element

A during drilling

σ r1

τ2

σ r2

Stage 2: Displacement body passes element A during removal of

drilling tool

Accepted Manuscript Not Copyedited



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Figure 2 One-dimensional finite element mesh, boundary conditions, constraints, and applied displacements

Q8 quasi-axisymmetric elements

~ 300B

Thickness of shear band (after cavity expansion and before shearing starts)

B

Applied displacements; out of the plane displacement uθ is used to simulate torsional shear

All degrees of freedom tied

Nodes with three degrees of freedom: ur, uz, uθ(radial, vertical and torsional displacements)

uzuθ

ur




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Figure 3 Applied displacement increments in different stages of the analysis: (a) cavity expansion, (b) shearing (vertical and torsional) associated with drilling, (c) upward (negative) shearing during the extraction of the drilling tool, (d) downward shearing during loading of the pile, and (e) simultaneous application of radial,

vertical and torsional displacement increments during the cavity expansion phase of a coupled analysis

Stage 1Shearing (downward and torsional)

(b)Δuz Δuθ

Cavity expansion

(a)

Δur

Pile axis

Stage 2

Upward shearing

(c)

−Δuz

Stage 3

Downward shearing

(d)

Δuz

ΔuzΔuθ

Δur

Pile axis

(e)

Cavity expansion phase for a

coupled analysis

Acc

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Figure 4 Normalized cavity radius vs. normal stress on the cavity wall during expansion of the cavity (limit cavity pressure is reached at the end of the cavity expansion)

1 3 5 7 9 11

Normalized cavity radius r/r0

0

5

10

15

20

25

30

35

Nor

mal

stre

ss o

n ca

vity

wal

l σ' r/

p A(r

efer

ence

stre

ss p

A =

100

kPa)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized cavity radius r/R

Isotropic Analysis, Toyoura sandInitial cavity radius r0 = 0.015 mDR= 60%, K0=0.45 σ'v0= 400 kPa

200 kPa

100 kPa

25 kPa

50 kPa




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(b)

Figure 5 Evolution of normal (radial) effective stress, torsional shear stress and vertical shear stress (for anisotropic analysis) during installation and loading of a DD pile; (a) σ v0 = 200 kPa, DR = 75%, η = 10° and (b)

σ v0 = 200 kPa, DR = 75%, η = 20°

-0.04 -0.02 0 0.02 0.04 0.06

Vertical shear displacement δz (m)

-400

0

400

800

1200

1600

Nor

mal

(rad

ial)

stre

ss σ

' r , v

ertic

al s

hear

stre

ss τ

z

and

tors

iona

l she

ar s

tress

τθ (

kPa)

DrillingExtraction ofdrilling toolLoading of pile

Normal (radial) stressVerticalshear stressTorsionalshear stress

A

B

C

C

D

A: End of CEB: End of drillingC: End of installationD: End of loading

A

Anisotropic analysis, Toyoura sandσ'v0 = 200 kPa, K0 = 0.45DR = 75%, η = 10o

0 0.02 0.04 0.06 0.08 0.1


-400

0

400

800

1200

1600

Nor

mal

(rad

ial)

stre

ss σ

' r , v

ertic

al s

hear

stre

ss τ

z

and

tors

iona

l she

ar s

tress

τθ (

kPa)

Normal (radial) stressVertical shear stressTorsional shear stress


DrillingExtraction of drilling toolLoading of pile

A

B

B

C

C

D

DA

Anisotropic analysis, Toyoura sandσ'v0 = 200 kPa, K0 = 0.45, DR = 75%, η = 20o

Acc

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(b)

Figure 6 Evolution of normal (radial) effective stress, torsional shear stress and vertical shear stress (for isotropic analysis) during installation and loading of a DD pile; (a) σ v0 = 200 kPa, DR = 75%, η = 10° and (b)

σ v0 = 200 kPa, DR = 75%, η = 20°

-0.06 -0.04 -0.02 0 0.02 0.04 0.06


-1000

0

1000

2000

3000

Nor

mal

(rad

ial)

stre

ss σ

' r , v

ertic

al s

hear

stre

ss τ

z

and

tors

iona

l she

ar s

tress

τθ (

kPa)

DrillingExtraction of drilling toolLoading of pileNormal(radial) stressVerticalshear stressTorsionalshear stress

A

B

C

D


Isotropic analysisToyoura sandσ'v0 = 200 kPa, K0 = 0.45DR = 75%, η = 10o

0 0.02 0.04 0.06 0.08 0.1 0.12


-1000

0

1000

2000

3000

Nor

mal

(rad

ial)

stre

ss σ

' r , v

ertic

al s

hear

stre

ss τ

z

and

tors

iona

l she

ar s

tress

τθ (

kPa)

Isotropic analysisToyoura sandσ'v0 = 200 kPa, K0 = 0.45DR = 75%, η = 20o

DrillingExtractionof drilling toolLoading of pile

Normal(radial) stressVerticalshear stressTorsionalshear stress


A

B

C

A

C

D

D

C

Acc

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(b)

Figure 7 Stress paths in e-p space: (a) for different values of η and (b) at different distances from the pile axis for η = 20°

100 1000200 400 600 800Mean effective stress p' (kPa)

0.68

0.72

0.76

0.8

0.84

0.88

Voi

d ra

tio e

Anisotropic analysis

σ'v0 = 200kPa, DR = 75% η = 0o

η = 10o

η = 20o

CSL for simple shearcondition

A

B

C

D

A: End of CEB: End of drillingC: End of installationnD: End of loading

100 1000200 400 600 800Mean effective stress p' (kPa)

0.5

0.6

0.7

0.8

0.9

Voi

d ra

tio e

At a distance BAt a distance 4BAt a distance 10BAdjacent to the pile shaft

100 1000p'0.68

0.7

0.72

0.74

e

Anisotropic analysis, Toyoura sandσ'v0 = 200kPa, DR = 75%

η = 20o

CSL for simple shear

Initial state

Initial state

A

BCD

A: End of CEB: End of drillingC: End of installationnD: End of loading A

ccep

ted

Man

uscr

ipt

Not

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Figure 8 Stress path (in q-p space) for the leftmost quadrature point in the first (leftmost) element of the mesh during installation (with η = 20°) and loading of a DD pile

0 200 400 600 800 1000Mean effective stress p' (kPa)

0

200

400

600

800

1000

1200

Dev

iato

ric s

tress

q (k

Pa)

Anisotropic analysis, Toyoura sandσ'v0 = 200kPa, K0 = 0.45, DR = 75%, η = 20o

Cavity expansionDrillingExtraction of drilling toolLoading

A

B

C

D

A: End of CEB: End of drillingC: End of installationnD: End of loading

CSL

Initial state




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(b)

Figure 9 Effect of DD pile installation (with η = 20°) on the normal (radial) effective stress acting in the surrounding soil: (a) anisotropic analysis and (b) isotropic analysis

0 4 8 12 16 20Normalized distance from the pile axis (r/B)

0

400

800

1200

1600

Nor

mal

(rad

ial)

stre

ss σ

' r (k

Pa)

Initial radial effective stress(σ'r0 = 90 kPa)At the end of CEAt the end of drillingAt the end of installation(just after the extraction of drilling tool) At the end of pile loading

Anisotropic analysis, Toyoura sandσ'v0 = 200 kPa, K0 = 0.45, DR = 75%

η = 20o


0

500

1000

1500

2000

2500

3000

Nor

mal

(rad

ial)

stre

ss σ

' r (k

Pa)

Initial radial effective stress(σ'r0 = 90 kPa)At the end of CEAt the end of drillingAt the end of installation(just after the extraction of drilling tool) At the end of pile loading

Isotropic analysis, Toyoura sandσ'v0 = 200 kPa, K0 = 0.45, DR = 75%

η = 20o

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(b)

Figure 10 Effect of DD pile installation (with η = 20°) on the mean effective stress p in the surrounding soil: (a) anisotropic analysis and (b) isotropic analysis


0

200

400

600

800

1000

Mea

n ef

fect

ive

stre

ss p

' (kP

a)Initial mean effective stress (p'0 = 126.67 kPa)At the end of CEAt the end of drillingAt the end of installation(just after the extraction of drilling tool) At the end of pile loading


η = 20o


0

400

800

1200

1600

Mea

n ef

fect

ive

stre

ss p

' (kP

a)

Initial mean effective stress (p'0 = 126.67 kPa)At the end of CEAt the end of drillingAt the end of installation(just after the extraction of drilling tool) At the end of pile loading


η = 20o

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Figure 11 Effect of DD pile installation (η = 20°) on the void ratio e of the surrounding soil: (a) anisotropic analysis and (b) isotropic analysis

0 4 8 12Normalized distance from the pile axis (r/B)

0.66

0.7

0.74

0.78

0.82

0.86

Voi

d ra

tio e

Initial void ratio e0 = 0.692At the end of CEAt the end of drillingAt the end of installation(just after the extraction of drilling tool) At the end of pile loading


η = 20o

0 4 8 12Normalized distance from the pile axis (r/B)

0.66

0.7

0.74

0.78

0.82

0.86

Void

ratio

e

Initial void ratio e0 = 0.692At the end of CEAt the end of drillingAt the end of installation(just after the extraction of drilling tool) At the end of pile loading


η = 20o

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(c)

Figure 12 Effect of the angle η on the stress state of the soil surrounding the pile just after the installation of a DD pile: (a) normal (radial) effective stress, (b) mean effective stress and (c) void ratio


0

100

200

300

400

500N

orm

al (r

adia

l) st

ress

σ' r

(kPa

)

η = 0o

η = 10o

η = 20o

Initial radial effective stress (σ'r0 = 90 kPa)


Variation of σ'r at the end of installation(just after the extraction of drilling tool)


100

200

300

400

500

Mea

n ef

fect

ive

stre

ss p

' (kP

a)

η = 0o

η = 10o

η = 20o

Initial mean effective stress (p'0 = 126.67 kPa)

Anisotropic analysis, Toyoura sandσ'v0 = 200 kPa, K0 = 0.45, DR = 75%Variation of p' at the end of installation(just after the extraction of drilling tool)


0.66

0.7

0.74

0.78

0.82

0.86

Voi

d ra

tio e

η = 0o

η = 10o

η = 20o

Initial void ratio e0 = 0.692

Anisotropic analysis, Toyoura sandσ'v0 = 200 kPa, K0 = 0.45, DR = 75%Variation of e at the end of installation(just after the extraction of drilling tool)




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Figure 13 K/K0 predictions for DD piles (anisotropic analysis): (a) η = 10° and (b) η = 20°

20 40 60 80 100Relative density DR (%)

0

4

8

12

16

(K/K

0) η =

10o

From FEAUsing Equation (5-3)

σ'v0 = 25 kPa

50 kPa

100 kPa

400 kPa

200 kPa

Anisotropic analysis, Toyoura sandK0 = 0.45, η = 10o

(3)


0

5

10

15

(K/K

0) η =

20o


Anisotropic analysis, Toyoura sandK0 = 0.45, η = 20o

σ'v0 = 25 kPa

50 kPa

100 kPa

400 kPa

200 kPa

(3)

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(b)

Figure 14 K/K0 predictions for DD piles (isotropic analysis): (a) η = 10° and (b) η = 20°


0

10

20

30

40

(K/K

0) η =

10o


σ'v0 = 25 kPa

50 kPa

100 kPa

400 kPa

200 kPa

Isotropic analysis, Toyoura sandK0 = 0.45, η = 10o

(4)


0

10

20

30

(K/K

0) η =

20o


Isotropic analysis, Toyoura sandK0 = 0.45, η = 20o

σ'v0 = 25 kPa

50 kPa

100 kPa

400 kPa

200 kPa

(4)

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(b)

Figure 15 Effect of K0 on the earth-pressure coefficient K at limit state conditions (anisotropic analysis with σ v0 = 100 kPa): (a) η = 10° and (b) η = 20°

40 50 60 70 80 90 100Relative density DR (%)

0

2

4

6

8

(K/K

0) η =

10o

K0 = 0.45K0 = 0.6

Anisotropic analysis, Toyoura sandσ'v0 = 100kPa, B = 0.33m, η = 10o


0

2

4

6

8

(K/K

0) η =

20o

K0 = 0.45K0 = 0.6

Anisotropic analysis, Toyoura sandσ'v0 = 100kPa, B = 0.33m, η = 20o

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(b)

Figure 16 Effect of pile diameter B on the ratio K/K0 at limit state conditions (anisotropic analysis with σ v0 = 100 kPa): (a) η = 10° and (b) η = 20°


0

2

4

6

8

(K/K

0) η =

10o

B=0.33mB=0.6m

Anisotropic analysis, Toyoura sandσ'v0 = 100kPa, K0 = 0.45, η = 10o


0

2

4

6

8

(K/K

0)η

= 20

o

B=0.33mB=0.6m

Anisotropic analysis, Toyoura sandσ'v0 = 100kPa, K0 = 0.45, η = 20o

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(b)

Figure 17 Comparison of K/K0 obtained from coupled and uncoupled analysis: (a) η = 10° and (b) η = 20°

40 60 80 100Relative density DR (%)

0

2

4

6

8

10

12

(K/K

0) η =

10o

Coupled analysisUncoupled analysis

σ'v0 = 50 kPa

100 kPa

400 kPa

200 kPa

Anisotropic analysis, K0 = 0.45, η = 10o

Toyoura sandδr = δθ during the cavity expansion phase

40 60 80 100Relative density DR (%)

0

2

4

6

8

10

12

(K/K

0) η =

20o

Coupled analysisUncoupled analysis

σ'v0 = 50 kPa

100 kPa

400 kPa

200 kPa

Anisotropic analysis, K0 = 0.45, η = 20o

Toyoura sandδr = δθ during the cavity expansion phase

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(b)

Figure 18 Pile and soil profile used in the design example: (a) the multilayered sand deposit (b) CPT profile calculated using Equation (5).

2m

B = 0.5m

DR = 45%

γ = 20kN/m3

φc = 30°DR = 60%

DR = 75%

4m

4m

η = 10°

K0 = 0.452m

B = 0.5m

DR = 45%

γ = 20kN/m3

φc = 30°DR = 60%

DR = 75%

4m

4m

η = 10°

K0 = 0.45

10

8

6

4

2

0

Dep

th (m

)

qc profile(using Equation 5-6)

0 2 4 6 8 10 12 14 16

Cone resistance qc (MPa)

qc profile for use in design methods A, B and C; calculated using Equation (5)

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Table 1 Calculation of limit shaft resistance for example DD pile using different design methods

Pile segment

Mid-depth (m)

Relative density

(%)

Proposed MethodMethod A

(NeSmith 2002; Brettmann and NeSmith 2005)

Method B(Bustamante and Gianeselli 1993,

1998)

Method C(Van Impe 1986, 1988, 2004; Bauduin 2001; Holeyman et al. 2001; De Vos et al. 2003;

Maertens and Huybrechts 2003a)

′v0

(kPa)K/K0

qsLi

(kPa)QsLi

(kN)

Cone resistance qc

(MPa)

Design Curves

qsLi

(kPa)QsLi

(kN)qsLi

(kPa)QsLi

(kN)qsLi

(kPa)QsLi

(kN)

1 0.5 45 10 2.1 4.7 7.4 1.3 Q3 29.4 46.2 13.2 20.8 14.7 23.12 1.5 45 30 1.9 12.8 20.1 2.6 Q3 41.7 65.5 26.4 41.5 29.4 46.13 2.5 60 50 3.1 34.9 54.8 5.5 Q4 83.9 131.8 55.0 86.4 61.1 95.94 3.5 60 70 2.9 45.7 71.8 6.6 Q4 93.3 146.6 66.4 104.3 73.7 115.85 4.5 60 90 2.8 56.8 89.2 7.6 Q4 101.2 159.0 76.4 120.1 84.8 133.36 5.5 60 110 2.7 66.9 105.1 8.6 Q5 123.3 193.7 85.5 134.3 94.9 149.17 6.5 75 130 4.3 126.0 197.9 13.2 Q5 153.0 240.3 132.4 208.0 123.0 193.18 7.5 75 150 4.1 138.6 217.7 14.2 Q5 158.0 248.2 142.0 223.0 126.8 199.29 8.5 75 170 4.0 153.2 240.6 15.1 Q5 162.3 254.9 150.9 237.1 130.4 204.810 9.5 75 190 3.9 167.0 262.3 15.9 Q5 166.1 260.9 159.4 250.3 133.7 210.1

QsL (kN)… 1267 1747 1426 1371




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Modeling of Installation and Quantification of Shaft Resistance of Drilled-Displacement Piles in...

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