Accepted Manuscript Investigation of the influence of vertical loads on the lateral response of pile foundations in sands and clays Lassaad Hazzar, Mahmoud N. Hussien, Mourad Karray PII:
S1674-7755(16)30043-9
DOI:
10.1016/j.jrmge.2016.09.002
Reference:
JRMGE 274
To appear in:
Journal of Rock Mechanics and Geotechnical Engineering
Received Date: 5 July 2016 Revised Date:
1 September 2016
Accepted Date: 4 September 2016
Please cite this article as: Hazzar L, Hussien MN, Karray M, Investigation of the influence of vertical loads on the lateral response of pile foundations in sands and clays, Journal of Rock Mechanics and Geotechnical Engineering (2016), doi: 10.1016/j.jrmge.2016.09.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Investigation of the influence of vertical loads on the lateral response of pile foundations in sands and clays
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a
Department of Civil Engineering, Faculty of Engineering, Sherbrooke University, Sherbrooke, QC, Canada Department of Civil Engineering, Faculty of Engineering, Assiut University, Assiut, Egypt
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Corresponding author. Tel: + 1 819 821-8000 (63922) E-mail adresses:
[email protected] (L. Hazzar),
[email protected] (M.N. Hussien),
[email protected] (M. Karray).
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Lassaad Hazzara,*, Mahmoud N. Hussiena, b, Mourad Karraya
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Abstract
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Although the load applied to pile foundations is usually a combination of vertical and lateral components,
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there have been few investigations on the behavior of piles subjected to combined loadings. Those few studies
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led to inconsistent results with regard to the effects of vertical loads on the lateral response of piles. A series
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of three-dimensional finite differences analyses is conducted to evaluate the influence of vertical loads on the
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lateral performance of pile foundations. Three idealized sandy and clayey soil profiles are considered: a
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homogeneous soil layer, a layer with modulus proportional to depth, and a two-layered stratum. The pile
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material is modelled as linearly elastic, while the soil is idealized using the Mohr-Coulomb constitutive model
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with a non-associated flow rule. In order to confirm the findings of this study, soils in some cases are further
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modelled using more sophisticated models (i.e., CYsoil for sandy soils and MCC for clayey soils). Numerical
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results showed that the lateral resistance of the piles does not appear to vary considerably with the vertical
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load in sandy soil especially at the loosest state. However, the presence of a vertical load on a pile embedded
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in homogeneous or inhomogeneous clay is detrimental to its lateral capacity, and it is unconservative to
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design piles in clays assuming that there is no interaction between vertical and lateral loads. Moreover, the
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current results indicate that the effect of vertical loads on the lateral response of piles embedded in multi-
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layered stratum depends on the characteristics of soil not only surrounding the piles but also those located
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beneath their tips.
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Keywords: Pile foundations, Vertical loads, Lateral loads, Finite differences, Mohr circle.
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1. Introduction Pile foundations are extensively used in many civil structures to support vertical and lateral loads.
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In conventional design methods, the vertical and lateral responses of piles are often evaluated
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separately neglecting their possible interaction. This would lead to an erroneous design, as pile
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foundations for several types of structures are often subjected to simultaneous vertical and lateral
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loading. The separate consideration of the vertical and lateral loading therefore cannot be expected to
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account properly for the pile behavior (Georgiadis and Saflekou, 1990; Zhang et al., 2002; Hussien et al.,
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2014a, 2014b).
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The behavior of pile foundations under either vertical or lateral loads has been investigated for
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more than a century through full-scale tests (e.g., Brown et al., 1987, 1988; Rollins et al., 1998,
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2005), centrifuge model tests (e.g., McVay et al., 1995, 1998; Tobita et al., 2004), and analytical
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(e.g., Matlock and Reese, 1960; Randolph and Wroth, 1978; Zhu and Chang, 2002) as well as numerical
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solutions (e.g., Ottaviani, 1975; Hussien et al., 2010, 2012; Hazzar et al., 2013) among others. The
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procedures used for modelling soil range from rigorous soil continuum discretization such as finite
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element (FE) or finite differences (FD) formulation to simplified interaction models such as the
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subgrade reaction approach. In the conventional subgrade reaction approach, soil is modelled by
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spring elements attached to the pile at different depths. These springs generally have nonlinear load-
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displacement characterizations called (t-z) and (p-y) curves for vertical and lateral loading,
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respectively. These two types of springs are generally uncoupled and therefore soil reactions along
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the corresponding degrees of freedom are also uncoupled. In other words, the influence of load
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acting in one direction on the characteristics of the spring in the other direction is neglected (Hussien
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et al., 2014a). Anagnostopoulos and Georgiadis (1993) have reported through model tests supported
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by two-dimensional (2D) FE analysis that the modified status of soil stresses and local plastic
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volume changes in the soil continuum under combined vertical and lateral loads cannot be accounted
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for in general by the subgrade reaction and elastic half space methods of analysis. Therefore, they
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suggested using a nonlinear three-dimensional (3D) FE or FD technique for analyzing the problem.
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Achmus and Thieken (2010) used the 3D FE to investigate the behavior of piles in non-cohesive soil
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under combined lateral and vertical loading, and they reported that the combined loading on piles
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induces interaction effects due to simultaneous mobilization of passive earth pressure due to lateral
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loads and pile skin friction due to vertical loads. Karthigeyan et al. (2006 and 2007) showed through
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a series of 3D FE analyses on piles that the presence of vertical loads increases the lateral load
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capacity of piles in sandy soils and decreases it in clayey soil. Hussien et al. (2012, 2014a and
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2014b), using simplified soil-pile interaction FE models, reported a little increase in the lateral
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capacity of free-head piles installed in sandy soil due to the presence of vertical loads and attributed
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this increase to the increase in the confining pressures in the sand deposit surrounding the upper part
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of the pile. In fact, the scopes of the previous attempts examining this problem using 3D FE models
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have been limited to the behavior of piles installed in homogeneous sandy or clayey soils. Little
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work has been devoted to the behavior of piles subjected to combined effects of vertical and lateral
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loads in inhomogeneous and/or layered soils which is often encountered in geotechnical projects.
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Moreover, the mechanisms regarding the influence of vertical loads on the lateral response of pile
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foundations in inhomogeneous and/or layered soils may be quite different from those of piles in
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ideal homogeneous situations.
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In view of the above mentioned issues, this paper presents and discusses the results of a series of
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3D FD analyses carried out using FLAC3D (Itasca, 2009) in order to recapitulate and to evaluate the
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influences of vertical loads on the lateral response as well as internal forces of piles installed in four
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idealized sandy and clayey soil profiles: a homogeneous sandy layer; a clayey layer with constant
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undrained shear strength; a clayey layer with undrained shear strength proportional to depth, and a
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two-layered stratum. Numerical models are validated and then analyses were carried out to
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investigate the influences of vertical loads on the lateral capacity and bending moment of piles as
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affected by typical soil characteristics such as relative density of sandy soil and undrained shear
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strength as well as over-consolidation ratio (OCR) of clayey soils. Combined load analyses were
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performed for vertical loads equal to 25 %, 50 %, 75 %, and 100 % of the ultimate vertical load
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capacity of the pile, Vult.
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2. Finite differences modeling and parameters identification
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2.1. Finite differences
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The 3D FD program FLAC3D (Itasca, 2009) was employed to study the behavior of piles under
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lateral and vertical loading. Full 3D geometric models were used to represent the coupled soil-pile
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system. Taking advantage of symmetry, only half of the actual model was built, thus significantly
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reducing the computational effort. Fig. 1 shows the general layout and meshing of the FD half model
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used for the analysis of the soil-pile system. A floating pile with a diameter, B was embedded in the
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soil to a depth of L while the total thickness of the soil stratum was selected at L+6B. The soil-pile
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system was meshed with 8-node brick elements, and the soil elements are fairly small adjacent to the
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pile and gradually increase in size as they move away from it. The soil element size was kept
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uniform at 0.5 m in the vertical direction. The total mesh size was extended to a horizontal distance
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of 16B from the center of the pile. This distance was decided after performing a number of initial
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trial analyses with several horizontal distances until the displacements and stresses of the pile did not
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change significantly with further increasing of the distance. All displacements were restrained at the
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bottom of the meshes while those at the vertical “external faces” were fully fixed in the x- and y-
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directions. The symmetry face (indicated in red in Fig. 1) were fixed against displacement normal to
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the symmetry plane, but were free to move on the surface of the plane.
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2.2. Soil model
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The Mohr-Coulomb model, extensively used in geotechnical engineering practice, was adopted in
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this study to simulate the nonlinear behavior of soil. In FLAC3D, six parameters are required to
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effectively define the soil behavior. These parameters are: the elastic bulk modulus, K; the elastic
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shear modulus, G; the mass density, ρ; the friction angle, φ; dilatancy angle, ψ; and the cohesion, c.
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2.3. Pile model
The pile is modelled as linear-elastic material. Three parameters are required to define the pile
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material behavior. These parameters are: the elastic bulk modulus, Kp; the elastic shear modulus, Gp;
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and the mass density, ρp.
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2.4. Soil-pile interface model
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The constitutive model of the soil-pile interface is defined in FLAC3D by a linear Coulomb shear-
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strength criterion that limits the shear force acting at an interface node. The shear-strength criterion
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is given by (Itasca, 2009):
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Fs max = ci A + tan φi ( Fn − pA )
(1)
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Where Fsmax is the limiting shear force at the soil-pile interface, Fn is the normal force, ci is the
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cohesion along the interface, φi is the friction angle of the interface surface, p is the pore pressure
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(interpolated from the target face), and A is the area associated with an interface node. The shear
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strength was defined with zero cohesive strength and 2/3 of the friction angle for sandy soils. In the
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case of clayey soils, the interfaces were assumed to have a zero friction angle and the same cohesive
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strength of the surrounding soil. Separation would cause a significant increase in displacements and
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therefore the interface elements are allowed to separate if tension develops across the interface and
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exceeds the tension limit of the interface. Once gap is formed between the soil-pile interfaces, the
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shear and normal forces are automatically set to zero (Itasca, 2009). The normal and shear forces at
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the interface nodes are determined by:
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Fsi( t +∆t ) = Fsi(t ) + ks ∆ u (sit + 0.5 ∆t ) A + σ si A
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(2)
(3)
Where Fn and Fsi are the normal and shear force, respectively, kn and ks are the normal and shear
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stiffness, respectively, ∆usi is the incremental relative shear displacement vector, un is the absolute
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normal penetration of the interface node into the target face, σn is the additional normal stress added
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due to interface stress initialization, and σsi is the additional shear stress vector due to interface stress
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initialization (Itasca, 2009).
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In the current study involving nonlinear analysis; high soil-pile interface stiffness is assigned to
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minimize the contribution of soil-pile interface elements to the accumulated pile displacements.
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According to the results of trial numerical analyses conducted to identify an appropriate stiffness
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value, a value of 105 kPa/m for both kn and ks was found to be sufficient to ensure that no additional
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deflections were attributed to the pile due to the deformation of the springs representing the
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interface. The use of such considerably higher values is tempting as it could be considered as more
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appropriate, but in that case the solution convergence would be very slow. In that way, the interface
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elements behave practically as a slider with a rigid/plastic behavior.
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2.5. Analysis scheme
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The model is brought to an equilibrium stress-state under gravitational loading before the
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installation of the pile. In the next stage of analysis, the model is brought into equilibrium after the
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installation of the pile. The installation is modeled by changing the properties of the pile zones from
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the properties representing the soil material to those representing the pile material. The pile is then
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loaded vertically. The ultimate vertical capacity (Vult) of the pile is evaluated by applying a vertical
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velocity at the pile head while the pile load and settlement are monitored. According to CGS (2013),
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the value of Vult is defined as the vertical load corresponding to the point with maximum curvature
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on the vertical load-vertical displacement curve. After the pile is loaded vertically, the pile top is
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then displaced laterally for a deflection of 0.1B, a value that was fixed in all studied cases to
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minimize the number of parameters involved. The vertical load is kept constant while applying the
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lateral displacement. It is fair to mention that the pile is assumed to be in a stress-free state at the
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beginning of the analysis, and thus the effect of the pile installation is ignored in the analysis.
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3. Validation of the FD model
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Before describing the numerical results on the influence of vertical loads on the lateral response of
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pile foundations, the applicability of the adopted model was verified by predicting the pile response
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in three published pile loading tests. The first case corresponds to a full scale pile loading test under
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pure lateral load; the second case corresponds to a full scale test on a pile installed in sandy soil and
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subjected to the combined action of vertical and lateral loads; and the third case corresponds to a
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laboratory test on a model pile embedded in clay under combined vertical and lateral loadings.
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Details of these three cases will be discussed next.
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3.1. Case study 1
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Comodromos (2003) has reported the response of a 52 m long and 1.0 m diameter bored pile
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under pure lateral loads installed at a bridge site in Greece. The subsoil at the site consists of a thick
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soft silty clay layer extending to a depth of 36.0 m, overlying a medium stiff clay layer of 12.0 m
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thickness and followed by a very dense sandy gravel layer. Geotechnical properties of soil layers in
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the test site are summarized in Table 1. In the current analysis, the behavior of the test pile is
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analyzed by FLAC3D as well as the p-y method according to Matlock (1970). Properties of various
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soil layers and the pile adopted in the 3D FD analyses are identical to those reported by
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Comodromos (2003). The same sequence of load application used in the field test was followed in
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the current FD analysis. The lateral load-lateral deflection curve obtained using the current FD
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analysis is compared to both the measured and the estimated p-y responses in Fig. 2a. The present
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numerical results overestimate the lateral capacity of the pile at all deflection levels compared to the
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p-y results, and the difference reaches to 15 % at the maximum lateral deflection of 100 mm. In spite
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of this, the 3D numerical result is fully consistent with the experimental result reported by
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Comodromos (2003).
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3.2. Case study 2
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The validity of the FD model to the analysis of pile in sandy soil and subjected to both vertical and
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lateral loads was verified by back predicting the pile response from a test data reported by Karasev et
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al. (1977). The length and diameter of the test pile were 3.0 m and 0.6 m, respectively. The pile was
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embedded in a soil strata consisting of very stiff sandy loam with shear strength parameters of c = 18
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kPa and φ = 18°. The soil shear modulus considered by Karasev et al. (1977) (9295 kPa) was used in
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the current analysis. The Poisson’s ratio of the soil was assumed of 0.35. The field tests were
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conducted by loading the pile in the vertical direction and then the lateral loads were applied while
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the vertical load was kept constant. The sequence of the load application used in the current FD
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analysis is the same as that followed during the pile test. The FLAC3D results are in accordance with
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and the reported test as shown in Fig. 2b.
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3.3. Case study 3
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The validity of the FD model to the analysis of pile in clayey soil and subjected to both vertical
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and lateral loads was verified by back predicting the pile response from a test data reported by
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Anagnostopoulos and Georgiadis (1993). This case study pertains to laboratory model tests on
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aluminium closed-ended piles of 19 mm outside diameter and 1.5 mm wall thickness, jacked 500
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mm into a prepared soft clay bed (cu = 28 kPa). The laboratory test was performed on a single pile
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under both vertical and lateral loads applied to the pile head at ground elevation through dead
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weights. The combined vertical and lateral loads were applied in two stages, in the first stage a
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vertical load of 160 N was applied and in the second stage the lateral load of 130 N was applied
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incrementally while the vertical load was kept constant. In the current analysis, the Young’s modulus
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(Es) of the soil was selected at 7500 kPa following the empirical relation Es ≈ 250-400×cu, (Poulos
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and Davis, 1980). The Poisson’s ratio of the clayey soil was selected at 0.49 assuming an undrained
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response during the load test. The comparison between the test data and the predicted results of piles
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under pure vertical load and combined vertical and lateral loads are shown in Fig. 2c and 2d. The FD
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prediction in both the cases matched well with the test data.
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Based on the comparative results shown in Fig. 2, it could be concluded that the numerical scheme
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adopted in the present investigation is capable of modeling the soil-pile interaction under vertical,
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lateral, and a combination of vertical and lateral loads.
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4. Parametric studies
FLAC3D was employed to study the behavior of piles under combined vertical and lateral loading
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in different soil profiles. Four idealized sandy and clayey soil profiles were considered: a
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homogeneous sandy layer, a clayey layer with constant shear strength, a clayey layer with shear
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strength proportional to depth, and a two-layered medium. Due to the abundant number of
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parameters involved, this study focuses on a selected number of parameters. These parameters
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include relative density of sandy soil, shear strength and shear stiffness as well as over-consolidated
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ratio (OCR) of clayey soil. A floating concrete pile, conformed to a grade M25, with a diameter, B of
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1.0 m was embedded in the soil to a depth, L of 10.0 m while the total thickness of the soil stratum
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was selected at 16.0 m. The elastic modulus (Ep) and Possion’s ratio (υp) of the pile were set to be
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25.00 GPa and 0.15, respectively. Soil parameters considered in the analyses are summarized in
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Tables 2 and 3 for sandy and clayey soils, respectively. For each sand density, the adopted friction
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angle and the corresponding relative density (Dr) were chosen referring to Skempton (1986) and
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A.P.I. (1993). Elastic shear modulus (G), was taken as 300cu; within the typical range for a clay
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(CGS, 2013). A gravitational acceleration vector (g) of 10 m/s2 was applied in the negative z-
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direction. Stresses within the model were initialized with an in situ earth pressure coefficient, K0 = 1.
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The response of piles to pure lateral loads was first evaluated for each case considered. Then, the
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response of piles to combined vertical and lateral loads is examined for different values of vertical
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loads ranging from 25 to 100 % of Vult. The combined loads are applied in two stages. In the first
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stage, vertical loads were applied and then in the second stage, lateral loads were applied while the
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vertical load was kept constant. The numerical results under pure lateral loads and combined lateral
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and vertical loads on piles are presented and discussed separately for sandy layer, clayey layer, and
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two-layered stratums. In order to confirm the finding of this study, soils in some cases (dense sand and medium clay) is
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further modelled using more sophisticated models: namely a friction hardening/softening elasto-
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plastic constitutive model (CYsoil) for sandy soils and the modified Cam-Clay model (MCC) for
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clayey soils. Details of these soil models are given next:
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The CYsoil model is characterized by a frictional Mohr-Coulomb shear envelope (zero cohesion)
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and an elliptic volumetric cap in the (p´, q) plane. The input parameters are: elastic tangent shear
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modulus, Geref, at reference effective pressure pref (100 kPa), failure ratio, Rf, which is a constant and
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smaller than 1 (0.9 in most cases), ultimate friction angle, φf, and calibration factor, β. The material
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properties adopted in the analyses for dense sand case are presented in Table 4.
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The Modified Cam-Clay model (MCC) (Roscoe and Burland, 1968) was adopted as quite
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appropriate, particularly for materials whose behavior is influenced by volume variation. In fact, the
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MCC may be used to represent materials when the influence of volume change on bulk property and
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resistance up to failure should be taken into consideration. In this study, The MCC is used to model
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the case of medium clay (cu = 39 kPa). Eight material parameters were required to specify the soil
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model, including either the elastic bulk modulus, K, or elastic shear modulus, G, the mass density, ρ,
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the Poisson’s ratio, υ, the slope of the normal consolidation line, λ, the slope of the elastic swelling
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line, κ, the frictional constant, M, the pressure of reference, p1, and the specific volume at pressure of
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reference, p1, on the normal consolidation line, υλ. The material properties adopted in the analyses
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for medium clay case are presented in Table 4.
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5. Results and discussions
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5.1. Sandy soils
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The ultimate vertical capacities of piles installed in sandy soils with different states of density are
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evaluated by applying vertical velocities at the piles heads and monitoring the piles loads variation
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with their settlements as plotted in Fig. 3. The value of Vult is selected as the vertical load
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corresponding to the point with maximum curvature on the vertical load-vertical displacement curve
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as defined by CGS (2013). Fig. 3 indicates that the ultimate bearing capacity of the pile is
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approximately 162 kN, 180 kN, 200 kN, and 246 kN for very loose, loose, dense, and very dense
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sand, respectively. Figs. 4a-d show the influence of a vertical load of Vult on the lateral response of piles installed in
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sandy soils. Each graph in Fig. 4 corresponds to a different state of sand density including very
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loose, loose, dense, and very dense. It is appeared from Fig. 4 that the lateral capacity of the pile is
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slightly affected by the presence of the vertical load in all states of density considered. At lateral
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deflection of 0.1B (100 mm), the presence of a vertical load of Vult is slightly increase the lateral
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capacities of piles by 0.1 %, 3.7 %, 4.6 % and 4.8 % in very loose, loose, dense, and very dense
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sand, respectively. This result is full consistent with those reported earlier by Hussien et al. (2012
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and 2014b).
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The influence of Vult on the lateral response of a pile installed in dense sand layer (Fig. 4c) is
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further investigated using the CYsoil model and the results are shown in Fig. 5. Although there are
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some differences in the initial slopes of the lateral load-deflection curves as well as the values of the
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pile ultimate capacities between Fig. 4c and Fig. 5, both figures indicate a slight increase in the pile
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lateral capacity due to the presence of vertical loads.
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An attempt to identify the mechanism of the little increase in the lateral capacities of piles
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installed in sandy soil due to the vertical load application was made by plotting the stress state (Mohr
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circle) of a soil element adjacent to the pile and at a depth of 3 m. The major (σ1) and the minor (σ3)
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principal stresses corresponding to the stress state of the soil element after 0.1B lateral deflection of
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a pile installed in dense sand are plotted in Fig. 6a for both the cases with (V = Vult) and without (V =
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0) vertical loads. As expected, Fig. 6a shows that the inclusion of a vertical load increases the major
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principle stress relative to that corresponds to the case of a pile under pure lateral load. On the other
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hand, the corresponding σ3 slightly increases. The increase in the major stress then increases the
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mobilized shear strength, τfm of the soil according to:
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τ fm =
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σ1 − σ 3 2
sin(90 + φ )
(4)
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Fig. 6a also confirms that the soil shear strength is reached in the case of V = Vult, while more
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lateral pile deflection is needed in the other case (V = 0) for the soil to reach its shear strength. A
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little increase in the confining pressure of the soil in the vicinity of the pile installed in very dense
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sand is also shown in Fig. 6b. This little increase in the confining stress of soil, then, slightly
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increases the resistance of the soil-pile system to lateral loading. Fig. 6d shows the stress paths of
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soil elements attached to the pile installed in dense sand and at different depths for both the cases
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with (V = Vult) and without (V = 0) vertical loads. For all considered depths, Fig. 6d confirms that the
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soil element in the case of (V = Vult) reached the failure surface earlier than that in the case of (V =
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0). Moreover, the soil element located at 1.0 m reached the failure surface before the other soil
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elements at deeper depths due to the load transfer from the pile to the adjacent soil. It could be also
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noted a little curvature in stress paths of soil elements at different depths due to the interaction with
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other soil elements. The variation of stresses (major, minor, vertical, horizontal) of a soil element
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adjacent to the pile, installed in dense sand and at a depth of 3 m, with lateral deflections are plotted
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for both the cases with (V = Vult) and without (V = 0) vertical loads in Fig. 6c. Fig. 6c indicates that
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the presence of vertical load slightly increases the soil stresses compared to the corresponding
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stresses in the case of pure lateral loading. Fig. 6c shows also that the orientation of the minor
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principle stress σ3 and the major principle stress σ1 in both analyses with and without vertical loads
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are similar up to the maximum lateral deflection of 100 mm. In addition, Fig. 6c illustrates a
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principle stress rotation after 8 mm lateral deflection since the horizontal stress σx becomes larger
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than the vertical stress σz.
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The little increase in lateral soil stresses σxx is further examined through the contours of normal
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stresses around the pile under pure lateral load and in the presence of a vertical load corresponding
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to V = Vult in Figs. 7a and 7b. These contours are plotted for a lateral deflection equal to 0.1B and at
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a depth of 3.0 m from the ground surface (i.e., the depth where maximum difference in lateral soil
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stresses occurs, Fig. 6b). Similarly, the little increase in shear stresses, σxy over the pile’s frictional
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face is also examined through the contours of shear stresses around the pile under pure lateral load
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and in the presence of a vertical load corresponding to V = Vult in Figs. 7c and 7d. These contours are
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plotted at a lateral deflection of 0.1B and at a depth of 3.0 m from the ground surface. It is clear that
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the lateral soil stress and the mobilized shear stresses of soil around the pile are almost the same in
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the presence of vertical load as compared to the pure lateral load case.
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5.2. Clayey soils with constant cu
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In the analyses of piles installed in clayey soils, two main cases have been considered. In the first
332
case (S1), the shear modulus of the soil was evaluated according to the value of cu (G = 300cu). In
333
the second case (S2), the shear modulus was assumed to be constant (G = 38.5 MPa) for all clayey
334
soils considered in Table 3.
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Similar to sandy soil cases, the ultimate vertical capacities of piles installed in clayey soils with
336
different cu are evaluated by applying vertical velocities at the piles heads and monitoring the piles
337
loads variation with their settlements as plotted in Fig. 8. Fig. 8 shows that Vult of the pile installed in
338
clayey soil (S1) is approximately 255 kN, 410 kN, 550 kN and 1000 kN in soft (cu = 20 kPa),
339
medium1 (cu = 30 kPa), medium2 (cu = 39 kPa) and stiff (cu = 64 kPa) clay, respectively.
340
Fig. 9 shows the variation of the lateral load as a function of lateral deflection of piles in clayey soils
341
(S1). A different trend is observed than that in the case of sandy soils. In the presence of vertical
342
loads, the lateral capacities developed at all deflections are less than the corresponding load
343
developed under pure lateral load. Karthigeyan et al. (2007) have reported similar findings for piles
344
in clayey soils through 3D FE analysis of single pile under combined loads and attributed the
345
reduction in the pile capacity to the early failure of soil-pile interfaces in the presence of vertical
346
loads.
347
Similar to the sand case, the influence of Vult on the lateral response of a pile installed in medium
348
clay (cu = 39 kPa; S1) (Fig. 9c) is further investigated using the MCC model as shown in Fig. 10.
349
Both the lateral load-lateral deflection curves presented in Fig. 10 and the corresponding curves
350
presented in Fig. 9c show a decrease in the pile lateral capacity due to the application of vertical
351
loads with percentages of decrease at 0.1B lateral deflection of 16.21 % and 13.92 %, respectively.
352
The differences in the initial slopes of the lateral load-deflection curves as well as in the values of
353
the pile ultimate capacities may attributed to the differences in soil modelling.
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The bending moment (M) developed in each pile section was calculated by the summation of the
355
product of the vertical stress (σzz,i) at each element, the plan area of that element (Ai) and the x-
356
distance from the center of the pile to the centroid of the element (xci).
357
M = ∑σ
n
359 360 361 362
zz ,i
× Ai × xci
(5)
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i =1
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Similar decreases were induced in the maximum bending moment in the pile for both studied cases considered (S1 and S2). The percentage of decrease in lateral capacity (DLC) has been defined to measure the influence of vertical loads on the lateral capacity of the piles: DLC =100 ×
PV =0 − PV =v PV =0
(6)
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363
where PV=v is the lateral capacity with vertical loads and PV=0 is the lateral capacity under pure
364
lateral loads. In the same context, the percentage of decrease in maximum moment (DMM) has been
365
also defined:
366
DMM = 100 ×
367
where MmaxV=v is the maximum bending moment with vertical load and MmaxV=0 is the maximum
368
bending moment under pure lateral load. The variation of the DLC and DMM values with cu for V =
369
0.5Vult, V = 0.75Vult and V = Vult at 0.1B lateral deflection is presented in Fig. 11 for the two cases (S1
370
and S2).
M maxV = 0 − M maxV =v M maxV = 0
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(7)
Figs. 11a and c (S1) show that up to cu of 16 kPa, the DLC and DMM values is equal to 0 (the
372
vertical load has no effect below this value). With the increase in soil cohesion (cu > 16 kPa), the
373
DLC and DMM values increase with the increase in cu as well as with the increase in vertical loads.
374
Figs. 11b and d (S2) show that the increase in DLC and DMM is more affected by Vult than cu. The
375
comparative results shown in Fig. 11 confirm that the estimation of the soil shear modulus, G based
376
on the undrained shear strength, cu is as important as the value of the undrained soil shear strength in
377
the design of pile foundation under the combined action of vertical and lateral loading.
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The mechanism of the decrease in both lateral capacity and bending moment of a pile installed in
379
clayey soil under the action of vertical loads has been also examined by plotting the stress state
380
(Mohr circle) of a soil element adjacent to the pile and at a depth of 3 m. The ultimate shear stress
381
τult, corresponding to the failure, can be calculated by:
382
τ ult =
2
= cu
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σ1 − σ 3
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(8)
The σ1 and σ3 corresponding to stress state of the soil element before and after the application of a
384
vertical load on a pile installed in clay are plotted in Fig. 12 for both the cases with (V = Vult) and
385
without (V = 0) and for all cu values considered in the (S1) case. When Vult is applied to the pile, it is
386
clear that the Mohr circles will have larger radii than those corresponding to (V = 0). Thus, the
387
presence of the vertical load decreases the lateral resistance of soil and subsequently leads to the
388
development of lower resistance to the lateral pile deformation. Fig. 13a shows the stress paths of
389
soil elements attached to the pile in medium clay (cu = 39 kPa; S1) at different depths for both the
390
cases with (V = Vult) and without (V = 0) vertical loads. For all considered depths, the soil element in
391
the case of (V = Vult) reached the surface failure earlier than the soil element in the case of (V = 0).
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The variation of stresses (major, minor, vertical, horizontal) of a soil element adjacent to the pile,
393
installed in medium clay (cu = 39 kPa; S1) at a depth of 3 m, with lateral deflections are plotted for
394
both the cases with (V = Vult) and without (V = 0) vertical loads in Fig. 13b. Fig. 13b indicates that
395
the inclusion of vertical load decreases the soil stresses compared to the corresponding stresses in the
396
case of pure lateral loading. Fig. 13b shows also that the orientation of the minor principle stress σ3
397
and the major principle stress σ1 in both analyses with and without vertical loads are similar up to
398
the maximum lateral deflection of 100 mm. Also, Fig. 13b shows a principle stress rotation after 8
399
mm lateral deflection since the horizontal stress σx becomes larger than the vertical stress σz.
400
5.3. Clayey soils with cu proportional to depth
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According to Mesri (1993), cu can be defined as a function of OCR and effective overburden
402
stress, σ v' :
403
cu = α ⋅ σ p' = α ⋅ OCR ⋅ σ v'
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Mesri (1993) demonstrated also that the value of the constant α is about 0.24 for Champlain clay
405
(Quebec, Canada). In the analyses, different values of OCR are considered. For each value of OCR
406
(1.5, 2.5 and 4.0), cu is assumed to be proportional to depth and the pile responses under combined
407
load obtained are compared to the corresponding responses for constant cu.
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The lateral load-lateral deflection curves at constant cu of 16 and 20 kPa are compared to those
409
obtained from the case of cu proportional to depth with an OCR of 1.5 in Fig. 14 for both the
410
analyses with and without vertical loads. In particular, Figs. 14a and b correspond to (S1) case while
411
Figs. 14c and d correspond to (S2) case. For piles subjected to pure lateral loads presented in Figs.
412
14a and c, the curve corresponding to OCR of 1.5 (denoted C1) is located between the two other
413
curves corresponding to cu of 16 kPa (denoted C2) and cu of 20 kPa (denoted C3). For piles subjected
414
to the combined action of vertical and lateral loads with V = Vult presented in Figs. 15b and d, the
415
curve (C1) is located between the two other curves (C2) and (C3) for (S1) case only.
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Based on the above comparisons, it is clear that the percentage decrease in lateral capacity, DLC,
417
of pile subjected to combined loads in clayey soil with constant cu is different from those
418
corresponding to analyses of piles with cu proportional to depth. This difference depends basically
419
on: (1) the choice between the case (S1) and the case (S2), (2) the ratio of vertical load relative to
420
ultimate vertical load of the pile as portrayed in Fig. 15.
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It is interesting to compare the results obtained from the case of cu proportional to depth to that of
422
a constant cu. For example, it is possible to compare the results corresponding to OCR of 1.5 with an
423
average value of 30 kPa (when OCR = 1.5, cu varies from 14.4 kPa at ground surface to 43.2 kPa
424
with average value of 30 kPa) to that of a constant cu of 30 kPa (Fig. 15). At lateral deflection of
425
0.1B and for the (S1) case, Fig. 15a shows that the maximum DLC is of the order of 8.3 % at
426
constant cu of 30 kPa and 5.7 % at OCR of 1.5. At the same lateral deflection and for the (S2) case,
427
Fig. 15b shows that the maximum DLC is of the order of 9.1 % for cu of 30 kPa and 17.4 % for OCR
428
of 1.5. For OCR = 2.5, cu varies from 20.0 kPa at ground surface to 52.8 kPa with an average value
429
of 39 kPa. At lateral deflection of 0.1B and for the (S1) case, Fig. 15a shows that the maximum DLC
430
is of the order of 16.2 % at uniform cu of 39 kPa and 9.2 % at OCR of 2.5. At the same lateral
431
deflection and for the (S2) case, Fig. 15b shows that the maximum DLC is of the order of 14.4 % for
432
cu of 39 kPa and 7.5 % for OCR of 1.5. These results indicate that the behavior of piles in clayey soil
433
under combined action of vertical and lateral loads when cu assumed to vary with depth significantly
434
differs from the pile behavior when cu is assumed constant.
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435 436
5.4. Two-layered stratum
In this section, the effect of vertical loads on the lateral responses of piles embedded in two-
438
layered strata consist of a combination of medium clay (cu = 39 kPa; S1) (Table 3) and dense sand
439
(Table 2) is studied. Different thicknesses (H) of the sand and clay layers are considered. The results
440
of the study case (S1) with and without vertical loads are presented and compared for two different
441
configurations of the two-layered stratum in Figs. 16a and 16b.
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Under pure lateral loads, Fig. 16a shows that the increase of the clay thickness from 2B to 10B
443
leads to a significant decrease in the lateral capacity of the pile. With further increase in the clay
444
thickness, the lateral capacity of the pile is not affected. In the same context, Fig. 16b shows that the
445
increase of the sand thickness from 2B to 10B leads to a significant increase in the lateral capacity of
446
the pile and with further increase in the sand thickness, the lateral capacity of the pile is slightly
447
affected. These results support the earlier recommendation of Reese and Van Impe (2001) who
448
suggest that the shallower depth up to 10B is of predominant importance in soil-pile interaction due
449
to lateral loading. On the other hand, Fig. 16a shows that the effect of vertical loads on the lateral
450
capacity of the pile embedded in two-layer stratum with a clay layer thickness (H) ranges from 2B to
451
10B is not significant and almost similar to that observed in dense sand (i.e., the end bearing
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stratum). When the clay thickness increases (H = L+6B), the effect of vertical loads becomes
453
pronounced and leads to a significant reduction in the lateral capacity of the pile. This difference in
454
vertical loads effects on the lateral capacities of piles (e.g., the dependence of vertical load effect on
455
the characteristics of the soil layer under pile tip) may be attributed to the difference in pile function
456
in term of load transfer. For (H) ranges from 2B to 10B, the pile serves as an end-bearing pile with
457
higher end-bearing capacity (reaction) as shown in Fig. 17a. This high end-bearing capacity is
458
associated with smaller settlement as well as smaller transfer of stress from pile to adjacent soil (Fig.
459
17b). In other words the vertical loads have little effects on the soil surrounding the pile. With
460
further increase in the clay thickness (H = L+6B), the pile no longer serve as an end-bearing type. It
461
serves primarily as a friction pile that has lower end-bearing reaction (Fig. 17a) and a significant
462
stress transfer a long its shaft (Fig. 17b).
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Fig. 16b shows that the effect of vertical loads on the lateral capacity of the pile embedded in two-
464
layer stratum with a sand layer thickness of 2B is similar to that observed in medium clay. With the
465
increase of the sand thickness, the effect of vertical loads becomes similar to that observed in dense
466
sand (i.e., the end bearing stratum). These results imply that although the above recommendation of
467
Van Impe (2001) works well in situations where pile foundations are subjected to pure lateral loads;
468
it cannot be applied if the piles are under the action of both vertical and lateral loadings. More
469
specifically, the current results indicate that the effect of vertical loads on the lateral response of
470
piles embedded in multi-layered stratum depends on the characteristics of soil not only surrounding
471
the piles but also those beneath located their tips.
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6. Conclusions
The influence of vertical loads on the behavior of laterally loaded pile in sand and clay was
475
investigated by means of numerical modeling. The numerical models were conducted using the
476
computer program FLAC3D and the models were verified using full-scale load and laboratory model
477
testing data. The verified numerical model was then used to perform a parametric study considering
478
different soil configurations and parameters to evaluate the lateral capacities and bending moments
479
of concrete piles subjected to both lateral and vertical loads. The results of the lateral capacities and
480
the bending moments of piles were determined and compared for piles subjected to pure lateral loads
481
and to combined vertical and lateral loads for several values of vertical loads corresponding to 25 %,
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482
50 %, 75 % and 100 % of the pile ultimate vertical capacity. Based on this comparison, the
483
following conclusions can be made. 1. The response of the piles in sandy soils under lateral loads is not influenced by the presence
485
of vertical loads. Indeed, the lateral load capacities is not changed for very loose sand and
486
slightly increased for loose, dense, and very dense sand.
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2. The presence of vertical loads decreases the lateral load capacity by as much as 20 % and
488
maximum bending moment by as much as 30 % of piles in clayey soil depending on the level
489
of vertical load and the value of the lateral deflection.
3. The dependence of the lateral response of piles under combined loading on the clay shear
491
strength, cu is also investigated, and the shear modulus, G, is evaluated in two different ways.
492
In the first (S1), G is considered dependent on cu while in the second (S2), G is assumed
493
constant irrespective of the adopted cu value. The maximum percentage decreases in lateral
494
capacity reach 20.3 % and 13.6 % for S1 and S2, respectively.
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4. The effect of vertical loads on the lateral capacity of a pile embedded in two-layer stratum
496
with a clay layer thickness (H) ranges from 2B to 10B is not significant and almost similar to
497
that observed in the sandy soil. When the clay thickness increases (H = L+6B), the effect of
498
vertical loads become pronounced and leads to a significant reduction in the lateral capacity
499
of the pile. The dependence of vertical load effect on the characteristics of the soil layer
500
under the pile tip may be attributed to the difference in pile function in term of load transfer.
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References
Anagnostopoulos, C., Georgiadis, M., 1993. Interaction of axial and lateral pile responses. J. Geotech. Eng.: ASCE 119 (4), 793–798.
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A.P.I. American Petroleum Institute, 1993. Planning, designing and constructing fixed offshore platforms. RP2A-LRFD, Section G, pp 64–77. Achmus, M., Thieken, K., 2010. On the behavior of piles in non-cohesive soil under combined horizontal and vertical loading. Acta Geotechnica 5 (3), 199–210. Brown, D.A., Reese, L.C., O’Neill, M.W., 1987. Cyclic lateral loading of a large scale pile group. J. Geotech. Eng. Div.: ASCE 113 (11), 1326–1343. Brown, D.A., Morrison, C., Reese, L.C., 1988. Lateral load behavior of pile group in sand. J. Geotech. Eng. Div.: ASCE 114 (11), 1261–1276.
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Canadian Geotechnical Society (CGS), 2013. Canadian Foundation Engineering Manual (4thEd.). Richmond, B.C., Canadian Geotechnical Society. Comodromos, E.M., 2003. Response prediction for horizontally loaded pile groups. J. Geotech. Eng.: Southeast Asian Geotechnical Society 34 (2), 123–33. Georgiadis, M., Saflekou, S., 1990. Piles under axial and torsional loads. Comput. Geotech. 9, 29–305.
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Hussien. M.N., Tobita, T., Iai, S., Rollins, K.M., 2010. Soil-pile separation effect on the performance of a pile
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Hussien, M.N., Tobita, T., Iai, S., Rollins, K.M., 2012. Vertical load effect on the lateral pile group resistance in sand response. Inter. J. Geomech. Geoengin. 7 (4), 263–282.
Hussien, M.N., Tobita, T., Iai, S., Karray, M., 2014a. Influence of pullout loads on the lateral response of pile
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group under static and dynamic lateral load. Can. Geotech. J. 47 (11), 1234–1246.
foundation. GeoRegina2014, Regina, Saskatchewan-Canada, September 28 - October 1, paper 316. Hussien, M.N., Tobita, T., Iai, S., Karray, M., 2014b. On the influence of vertical loads on the lateral response
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of pile foundation. Comput. Geotech. 55, 392–403.
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Hazzar, L., Karray, M., Hussien, M.N., Bouassida, M., 2013. Three dimensional modeling of a pile group
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under static lateral loading using finite differences method. GeoMontreal2013, Montréal, Québec-Canada,
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Karasev, O.V., Talanov, G.P., Benda, S.F., 1977. Investigation of the work of single situ-cast piles under
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different load combinations. J. Soil Mech. Found. Eng.: ASCE 14 (3), 173–177. Karthigeyan, S., Ramakrishna, V.V.G.S.T., Rajagopal, K., 2006. Influence of vertical load on the lateral response of piles in sand. Comput. Geotech. 33 (2), 121–131. Karthigeyan, S., Ramakrishna, V.V.G.S.T., Rajagopal, K., 2007. Numerical investigation of the effect of
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Itasca, 2009. User’s and theory manuals of FLAC3D: Fast Lagrangian analysis of continua in 3D, version 4.
vertical load on the lateral response of piles. J. Geotech. Geoenviron. Eng.: ASCE 133 (5), 512–521. Matlock, H., Reese, L.C., 1960. Generalized solutions for laterally loaded piles. J. Soil Mech. Found. Div.: ASCE 86 (SM5), 63–91.
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Matlock, H., 1970. Correlations for design of laterally loaded piles in soft clay. 2nd Offshore Technology Conference, Houston, Texas, pp. 577–594. Mesri, G., 1993. Initial investigation of the soft clay test site at Bothkennar. Discussion, Géotechnique 43 (3), 503–504.
McVay, M., Casper, R., Shang, T-I., 1995. Lateral response of three-row groups in loose to dense sands at 3D and 5D pile spacing. J. Geotech. Eng.: ASCE 121 (5), 436–441. McVay, M., Shang, L., Molnit, T., Lai, P., 1998. Centrifuge testing of large laterally loaded pile groups in sands. J. Geotech. Geoenviron. Eng.: ASCE 124 (10), 1016–1026.
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Ottaviani, M., 1975. Three-dimensional finite element analysis of vertically loaded pile groups. Géotechnique 25 (2), 159–174.
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Poulos, H.G., Davis, E.H., 1980. Pile foundation analysis and design. Wiley: Singapore.
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Roscoe, K.H., Burland, J.B., 1968. On the Generalized Stress-Strain Behavior of ‘Wet Clay’. Engineering
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Rollins, K.M., Peterson, K.T., Weaver, T.J., 1998. Lateral load behavior of full-scale pile group in clay. J. Geotech. Geoenviron. Eng.: ASCE 124 (6), 468–478.
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Reese, L.C., Van Impe, W.F., 2001. Single piles and pile groups under lateral loading. Rotterdam,
Rollins, K.M., Lane, J.D., Gerber, T.M., 2005. Measured and computed lateral response of a pile group in
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sand. J. Geotech. Geoenviron. Eng.: ASCE 131 (1), 103–114.
Skempton, A.W., 1986. Standard penetration test procedure and effects in sands of overburden pressure, relative density, particle size, ageing and over-consolidation. Géotechnique 36 (3), 425-477. Tobita, T., Iai, S., Rollins, K.M., 2004. Group pile behavior under lateral loading in centrifuge model tests. Inter. J. Physical Modelling in Geotech. 4 (4), 1–11.
Zhang, L.M., McVay, M.C., Han, S.J., Lai, P.W., Gardner, R., 2002. Effects of dead loads on the lateral response of battered pile groups. Can. Geotech. J. 39 (3), 561–575.
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Randolph, M.F., Wroth, C.P., 1978. Analysis of deformation of vertically loaded piles. J. Geotech. Eng.:
Zhu, H., Chang, M.F., 2002. Load transfer curves along bored piles considering modulus degradation. J. Geotech. Geoenviron. Eng.: ASCE 128 (9), 764–774.
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Plasticity, Cambridge University Press, New York, pp. 535–609.
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Table 1 Geotechnical properties of soil layers from Comodromos (2003) study. Soil layer Depth Unit Undrained (m) weight shear strength γ (kN/m3) cu (kPa) Soft silty clay 0-36 20.0 27 Medium stiff clay 36-48 20.0 110 Very dense sandy gravel 48-70 22.0 0
584 585
Table 2 Model parameters of sandy soil used in the parametric study. Soil type Mass density Shear modulus Bulk modulus Undrained shear G (MPa) K (MPa) strength cu (kPa) ρ (kg/m3) Very loose 1600 4.6 10.0 Loose 1800 7.7 16.7 0 Dense 2000 19.2 41.7 Very dense 2200 26.9 58.3
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Angle of friction φ (°) 0 0 40
587 589
590 591
Undrained shear strength cu (kPa) 20 30 39 64
Table 4 Parameters of sandy and clayey soils used in CYsoil and MCC models. CYsoil model MCC model Soil type Dense sand Soil type Medium1 clay Geref (MPa) 19.20 G (MPa) 9.00 ref P (kPa) 100.00 0.45 υ Rf 0.90 0.13 λ 36.00 0.05 φf (degrees) κ β 2.35 M 0.77 p1 (kPa) 1.00 5.30 υλ
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Table 3 Model parameters of clayey soil used in the parametric study. Clay type Mass density Shear modulus Bulk modulus G (MPa) K (MPa) ρ (kg/m3) Soft 6.00 58.0 1 Medium 9.00 87.0 2 1600 Medium 11.70 113.1 Stiff 19.20 185.6
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Shear modulus G (MPa) 2.43 3.35 24.0
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20
Angle of friction φ (°) 26 (Dr = 0 %) 30 (Dr = 40 %) 36 (Dr = 60 %) 42 (Dr = 87 %)
Angle of friction φ (°)
0
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Fig. 1. The general layout and meshing of the FD half model used for the analysis of the soil-pile system.
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Fig. 2. Comparison between the present 3D FD results and: (a) test data of Comodromos (2003) and p-y method, (b) test data of Karasev et al. (1977), (c) test data of vertical loaded pile of Anagnostopoulos and Georgiadis (1993), and (d) test data of combined vertical and lateral loaded pile of Anagnostopoulos and Georgiadis (1993).
2
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Fig. 3. Vertical load-vertical displacement of piles installed in sandy soils with deferent densities.
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Fig. 4. Lateral load-lateral deflection curves of piles for the analyses with and without vertical loads: (a) very loose, (b) loose, (c) dense, and (d) very dense sand.
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Fig. 5. Lateral load–lateral deflection curves of pile installed in dense sand for the analyses with and without vertical loads adopting the CYsoil model.
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Fig. 6. Analyses of pile installed in dense sand with and without vertical loads: (a) Mohr circles of a soil element adjacent to the pile and at a depth of 3, (b) variation of the confining pressure along the pile, (c) stresses of a soil element adjacent to the pile at a depth of 3 m, and (d) stress paths of soil elements attached to the pile at different depths.
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Fig. 7. Normal and shear stress contours in xy-plane at 3.0 m depth from ground surface in dense sands: (a) σxx contours for pure lateral loading case, (b) σxx contours with vertical load of Vult, (c) σxy contours for pure lateral loading, and (d) σxy contours with vertical load of Vult.
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Fig. 8. Vertical load-vertical displacement of piles installed in clayey soils with deferent cu.
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Fig. 9. Lateral load–lateral deflection curves of piles installed in clayey soil (S1) for (a) cu = 16 kPa, (b) cu = 30 kPa, (c) cu = 39 kPa and (d) cu = 64 kPa.
9
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Fig. 10. Lateral load–lateral deflection curves of pile installed in medium clay for the analyses with and without vertical loads adopting the MCC model.
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Fig. 11. DLC and DMM versus cu at 0.1B lateral deflection: (a) DLC (S1); (b) DLC (S2); (c) DMM (S2); and (d) DMM (S2).
11
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Fig. 12. Mohr circles of a soil element adjacent to the pile and at a depth of 3 m in a clayey soil (S1) for: (a) cu = 20 kPa, (b) cu = 30 kPa, (c) cu = 39 kPa, and (d) cu = 64 kPa.
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Fig. 13. Analyses of pile installed in a medium clay (cu = 39 kPa) with and without vertical loads: (a) stress paths of soil elements attached to the pile, and (b) stresses of a soil element adjacent to the pile at a depth of 3 m.
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Fig. 14. Lateral load-lateral deflection curves of pile installed in clayey soil for (a) V = 0 (S1), (b) V = Vult (S1), (c) V = 0 (S2) and (d) V = Vult (S2).
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Fig. 15. DLC variation with the ratio of V/Vult at lateral deflection of 0.1B: (a) (S1) case and (b) (S2) case.
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Fig. 16. Lateral load-lateral deflection curves of piles in two-layered stratum (S1) for both analyses with and without vertical loads: (a) higher medium clay and lower dense sand and (b) higher dense sand and lower medium clay.
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Fig. 17. Stress conditions for soil elements in (H = L): (a) end-bearing stress versus V/Vult, (b) major principle stress with and without vertical loads adjacent to pile shaft at 3 m depth.
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