Discrete Element and Experimental Investigations of theEarth Pressure Distribution on Cylindrical Shafts

Viet D. H. Tran1; Mohamed A. Meguid2; and Luc E. Chouinard, M.ASCE3

Abstract: Experimental and numerical studies have been conducted to investigate the earth pressure distribution on cylindrical shafts in softground. A small-scale laboratory setup that involves a mechanically adjustable lining installed in granular material under an axisymmetric con-dition is first described. The earth pressure acting on the shaft and the surface displacements aremeasured for different inducedwallmovements.Numerical modeling is then performed using the discrete element method to allow for the simulation of a large soil displacement and particlerearrangement near the shaft wall. The experimental and numerical results are summarized and compared against previously published theo-retical solutions. The shaft-soil interaction is discussed, and conclusions regarding soil failure and the earth pressure distributions in both theradial and circumferential directions are presented. DOI: 10.1061/(ASCE)GM.1943-5622.0000277. 2014 American Society of CivilEngineers.

Author keywords: Cylindrical shafts; Soil arching; Lateral earth pressure; Retaining structures; Discrete element method.

Introduction

The discrete element method (DEM) has gained popularity in thepast few decades among geotechnical engineers and researchersinvolved in studying soil-structure interaction problems. Since itwas first proposed by Cundall and Strack (1979), the method hasbeen used extensively to understand the micromechanical and ma-cromechanical behavior of granular material (e.g., Jiang et al. 2003;Cui and OSullivan 2006; Yan and Ji 2010; Chen et al. 2012). Oneapproach to implement DEM into geotechnical engineering analysisis by fitting the measured macroscale response for a given problemwith that predicted using the DEM method. Although extensiveresearch has been reported on quantitative DEM validation usingstandardized laboratory tests, such as direct shear and triaxial ex-periments (Liu et al. 2005; Cui and OSullivan 2006; Belheine et al.2009; OSullivan and Cui 2009), DEM validation conducted usinglarge-scale problems (Jenck et al. 2009; Chen et al. 2012) is con-sidered to be limited.

This study aims at providing a quantitative DEM validation of apractical geotechnical problem involving a buried structure inter-acting with the surrounding soil. The active earth pressure distri-bution on cylindrical shafts is selected because it involves largedisplacements and particle movements under an axisymmetric con-dition. This problem has received extensive research attention in an

effort to understand the mechanics behind the observed lateral earthpressure distribution along vertical shafts using experimental andtheoretical investigations. Among the reported experimental studiesthat involved measuring lateral earth pressure due to the movementof a shaft wall are those of Walz (1973); Lade et al. (1981); Koniget al. (1991); Chun and Shin (2006); and Tobar and Meguid (2011).Theoretical solutions have also been proposed by researchers to cal-culate lateral earth pressures on cylindrical structures, taking into ac-count the interaction between the cylindrical wall and the surroundingmaterial (e.g., Cheng and Hu 2005; Cheng et al. 2007; Salgado andPrezzi 2007; Andresen et al. 2011; Osman and Randolph 2012).

An attempt has been made by Herten and Pulsfort (1999) to usethe DEM to simulate a laboratory size shaft construction in granularmaterial. Although the study provided useful results, the circularshaft was assumed to behave as a small flat wall, which has lead to aninadequate simulation of the arching effect and the stress distributionaround the shaft. Furthermore, a quite small segment of the shaftgeometry was modeled, resulting in the presence of rigid boundariesclose to the investigated area. Therefore, there is a need for animproved DEM simulation of the problem, considering the problemgeometry as well as realistic soil properties.

In this paper, an experimental study of a model shaft installed ingranular material is first presented. The recorded lateral earth pres-sures acting on the shaft with different wall movements is measured.ADEMmodel that has been developed to simulate the shaft model isthen introduced. A suitable packing method to generate the soildomain is proposed, and a calibration test is conducted to determinethe input parameters needed for the simulation. The results of theexperimental and numerical studies are then analyzed, and con-clusions are made regarding the distribution of the radial and cir-cumferential stresses around the shaft as well as the extent of soilshear failure.

Experimental Study

An experimental study was performed to investigate the active earthpressure on circular shafts in dry sand. During the experiment, theshaft diameter was uniformly reduced while the radial earth pres-sures at different depths were recorded. The experimental setup

1Graduate Student, Dept. of Civil Engineering and Applied Mechanics,McGill Univ., 817 Sherbrooke St. West, Montreal, QC, Canada H3A 2K6.E-mail: viet.tran@mail.mcgill.ca

2Associate Professor, Dept. of Civil Engineering and Applied Mechan-ics, McGill Univ., 817 Sherbrooke St. West, Montreal, QC, Canada H3A2K6 (corresponding author). E-mail: mohamed.meguid@mcgill.ca

3Associate Professor, Dept. of Civil Engineering and Applied Mechan-ics, McGill Univ., 817 Sherbrooke St. West, Montreal, QC, Canada H3A2K6. E-mail: luc.chouinard@mcgill.ca

Note. This manuscript was submitted on June 2, 2012; approved onDecember 4, 2012; published online on December 6, 2012. Discussionperiod open until July 1, 2014; separate discussions must be submitted forindividual papers. This paper is part of the International Journal ofGeomechanics, Vol. 14, No. 1, February 1, 2014. ASCE, ISSN 1532-3641/2014/1-8091/$25.00.

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http://dx.doi.org/10.1061/(ASCE)GM.1943-5622.0000277mailto:viet.tran@mail.mcgill.camailto:mohamed.meguid@mcgill.camailto:luc.chouinard@mcgill.ca

consisted of an instrumented shaft installed in soil contained withina cylindrical concrete tank. Details of the test setup and procedurehave been reported elsewhere (Tobar and Meguid 2011) and arebriefly summarized subsequently.

Model Shaft

The model shaft consisted of six curved lining segments cut from asteel tube with an outer diameter of 101.6 mm and a thickness of 6.35mm.The lining segmentswerefixed in segment holders, which in turnwere attached to hexagonal nuts using steel hinges (see Fig. 1). Thenuts could move vertically along an axial rod that could be rotatedusing a precalibrated handle. The shaftwas placed on a Plexiglas plateattached firmly to the base of the container. The initial diameter ofthe shaft is 150 mm, and the length of the shaft is 1,025 mm, witha surrounding soil height of 1,000 mm. Shims bent from gauge steelstripswereused to cover the spaces between the lining segments. Theywere placed on the outer surface of the lining and overlapped the steelsegments such that one edge of each shim was fixed to one liningsegment, whereas the other edge was free to slide over the liningsegment. This mechanism keeps the shaft segments from collidinginto one another during the inward movement and at the same timeassures a gap-free circumference reduction process [Fig. 1(c)].

To reduce the shaft diameter, the axial rod is rotated, forcing thehexagonal nuts to move vertically; the segment holders and the liningsegments are then pulled radially inward. These movements force theshaft diameter to decrease uniformly. Two additional segment guidedisks were also installed [Fig. 1(b)] to protect the shaft linings fromrotational movement or sliding out of the segment holders.

Concrete Container

A cylindrical concrete tank with an inner diameter of 1,220 mmprovided the axisymmetric condition for the experiment. The tank

diameter was chosen to minimize the boundary effects on the be-havior of the soil-shaft interaction during the experiment. Previousexperimental results of Chun and Shin (2006) and Prater (1977)suggest that the soil failure zone extends laterally from one to threetimes the shaft radius. Therefore, negligible soil movement is ex-pected in the present investigation at a radial distance of 240 mmfrom the outer perimeter of the shaft lining. The depth of the containeris 1,070 mm to support the full length of the shaft. The interior side ofthe container was smoothed and linedwith plastic sheets to reduce thesoil-wall friction. In addition, a sand auger systemwas used to removethe sand after each test through a circular hole 150 mm in diameterlocated sideways at the base of the container. Fig. 1(a) shows anoverview of the experimental setup and model shaft.

Data Recording

Load cells and displacement transducers were used to measure earthpressure and wall movement during the test. Three load cells wereinstalled behind the lining segments at three locations along theshaft: 840, 490, and 240 mm below the sand surface, respectively.The load cells were equipped with sensitive circular areas of 1-in.diameter in contact with the soil. Two displacement transducerswere located near the top and bottom of the shaft lining. All loadcells and displacement transducers were connected to a data ac-quisition system and controlled though a personal computer.

Testing Procedure

Before each test, all instruments were examined and the shaft wasadjusted to have an initial diameter of 150 mm. The concrete con-tainer was then filled with coarse sand (Granusil silica 2075, UniminCorporation, St.-Adrien, Quebec, Canada) through a raining processwith a target depth of 1 m from the shaft base. Table 1 summarizesthe sand properties. A hopper positioned 1,500 mm above the tank

Fig. 1. (a) Overview of the experimental setup; (b) model shaft during assemblage; (c) lower-end section during assemblage (Tobar 2009; withpermission)

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was used to spread the sand uniformly over the container. Sand wasplaced in three layers, and as soon as the sand height reached slightlyover 1 m, the raining process was stopped and extra sand was re-moved. The sand height was checked using laser sensors to ensureconsistent initial conditions for each test. The shaft diameter wasthen reduced slowly, and readings were taken for each movementincrement. The test was stopped when the reduction in the shaftradius reached 5 mm. Selected experimental results are discussed inthe Results and Discussion.

Discrete Element Simulation

The DEM considers the interaction among distinct particles at theircontact points. Different types of particles have been developed,including discs, spheres, ellipsoids, and clumps. Particles in a sam-ple may have variable sizes to represent the grain size distribution ofthe real soil. The interaction among particles is regarded as a dy-namic process that reaches static equilibrium when the internal andexternal forces are balanced. The dynamic behavior is representedby a time-step algorithm using an explicit time-difference scheme.Newtons and Eulers equations are then used to determine particledisplacement and rotation. The DEM simulations in this study areconducted using the open source discrete element code YADE(Kozicki and Donze 2009; Smilauer et al. 2010). Spherical particlesof different sizes are used to represent sand particles throughout thenumerical investigation. The contact law among particles is brieflydescribed subsequently.

If two particles A and B with radii rA and rB are in contact, thecontact penetration depth is defined as

D rA rB2 d0 (1)

where d0 5 distance between the two centers of particles A and B.The force vector F, which represents the interaction between the

two particles, is decomposed into normal and tangential forces

FN KN DN , dFT 2KT dDT (2)

where FN and FT 5 normal and tangential forces; KN and KT5 normal and tangential stiffnesses at the contact; dDT 5 in-cremental tangential displacement; dFT 5 incremental tangentialforce; and DN 5 normal penetration between the two particles. Thestiffnesses KN and KT are defined by

KN kAn k

Bn

kAn kBn(3)

where kAn and kBn 5 particle normal stiffnesses.

The particle normal stiffness is related to the particle materialmodulus E and particle diameter 2r such that

kAn 2EArA, kBn 2EBrB (4)The stiffness KN can be rewritten as

KN 2EArAEBrBEArA EBrB (5)

The interaction tangential stiffness KT is determined as a givenfraction of the computed KN . The macroscopic Poissons ratio isdetermined by the KT=KN ratio, while the macroscopic Youngsmodulus is proportional to KN and affected by KT=KN . The tan-gential force FT is limited by a threshold value such that

FT FTkFTk kFNktanwmicro if kFTk$ kFNktanwmicro (6)

where wmicro 5 microscopic friction angle.To represent the rolling behavior between two particles A and B,

a rolling angular vector ur is used. This vector describes the relativeorientation change between the two particles and can be defined bysumming the angular vector of the incremental rolling (Belheineet al. 2009; Smilauer et al. 2010)

ur Pdur (7)

A resistant moment Mr is computed by

Mr 8