Numerical model

4.6.1.1 Description of finite element model

The pile-soil system is modeled employing a 3D quarter cylindrical mesh. The pile was placed along the axial z-direction of the model. The helical plate was idealized as planar disk for numerical simplification. Figure 4 - 17 presents the model geometry for a single pile of configuration C subjected to axial loading.

The soil medium and the pile were simulated using 8-noded, first order, and reduced integration continuum solid elements (C3D8R) having three active translational degrees of freedom at each node and one integration point located at the centroid. The location of the boundaries was optimized to minimize the boundary effects on the results while reducing the computational effort. The radius of the soil cylinder extended 2.5 m (i.e. 10 times the largest shaft diameter) from the center of the pile shaft. The bottom horizontal boundary was placed at 1.95 m below the pile toe, which is equivalent to 5 helix diameters.

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Figure 4 - 17: Finite element model geometry – undeformed mesh-PC1

A stress-free boundary was considered for the soil top surface. The translation of the bottom boundary was restrained in X, Y and Z directions. The vertical boundaries of the soil were restrained from translating in X (Y) direction and rotating around Y and Z (X and Z) where applicable to simulate the case of a full model. The back of the soil quarter cylinder was restrained from moving in X and Y directions (movement along Z direction was allowed).

Mesh refinement at stress/strain concentration zones was necessary to ensure the accuracy of the results. Accordingly, a series of models was developed where the mesh was incrementally refined and the results were compared. When the difference between the results of two consecutive models (i.e. refinements) became less than 2.5%, the most refined model was considered. The elements were most refined along the pile-soil interface and around the helical plate and then their size gradually increased towards the model

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boundaries. This process resulted in mesh configurations consisting of 37 309/28 553 elements for pile configurations A/C, with maximum elements side dimension ranging from 250 mm/330 mm at the model boundaries to 20 mm/25 mm at the pile-soil interface. The pile mesh consisted of 1609/1451 for configurations A/C.

4.6.1.2 Soil model

The soil is simulated as an elastic-perfectly plastic isotropic continuum. The soil plasticity and failure were modeled using the Mohr-Coulomb yield criterion where values of the

critical state angle of internal friction, cs, cohesion yield stress, cʹ and the dilation angle,

ψ. Poisson’s ratio, ν, and Young’s modulus, Es defined the soil elasticity.

The soil domain was divided into three main sections:

 The top soil (0.5m) layer was modeled with reduced strength and stiffness reflecting the soil disturbance induced during the initial predrilling process;

 Soil along the pile shaft;

 Soil beneath the helix pate was modeled using higher stiffness to account for the soil densification during the installation process.

The soil properties representing the conditions after pile installation were established through the calibration of the numerical model using monotonic compression field test results as presented in Chapter 3. The same soil properties, presented in Table 4 - 7, are used herein. Additionally, the analysis of the uplift testing results confirmed their validity.

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Table 4 - 7: Soil parameters considered in FE model (calibrated and verified in Chapter 3) Depth (m) cs(o) c’ (kPa) ψ ( o₎   Es (MPa)  (kN/m3)

From To PA2 PC1 PA2 PC1

0 0.5 32 4 4 4 0.3 35 35 17 0.5 Helix level 32 4 6 4 0.3 70 60 18 Helix level End of model 32 4 6 6 0.3 91 94 18

In order to account for disturbance of soil above the helix plate during the compression loading, a cylindrical disturbed zone assigned above the helix plate extending to a distance equal to Dhelix = 0.39m. The properties of soil in this zone were obtained from the

calibration process using the uplift results, which yielded friction angle  = 27o and Es = 9

MPa. These values reflect the loose state of the disturbed zone and sheared sands and fall within the typical values for very loose sands (Bowles, 1996).

4.6.1.3 Pile Model

The pile was simulated as linear elastic-perfectly plastic material. The elastic behavior was defined by Poisson’s ratio, νp, and Young’s modulus, Ep. The plastic behavior was

represented by the yield strength of the pile material. The mechanical properties of the piles materials are presented in Table 4 – 8. Weaker strength parameters were considered for the helix and base plate welds to accommodate the weld defects observed prior to the piles installation.

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Table 4 - 8: Pile mechanical properties considered in FE model

Component Young’s Modulus Ep (kN/m2) Poisson’s ratio p Unit weight p (kN/m3) Yield strength Fy (MPa) Shaft- configurations A and

B 1.69E08 0.28 77 314

Shaft - configuration C 2.0E08 0.28 77 370

Helix and base plates

welded connections 2.0E08 0.28 77 170

4.6.1.4 Pile-Soil Interface Model

The pile-soil interface was simulated using the penalty-type tangential behavior Coulomb’s frictional model. No relative tangential motion occurs until the surface traction reaches a critical shear stress value, which is taken as the lesser of the interface shear strength or a fraction of the interface pressure. Pile-soil interface strength is given by tan = 0.78 and 0.5 for tapered and straight piles, respectively. While the first was determined by studying the pile surface roughness in comparison to the soil mean particle size as mentioned in Chapter 3, the latter was considered in accordance to the suggested values by the Canadian Foundation Engineering Manual (2006). These values were calibrated with the axial tests results in Chapter 3. Slippage along the soil-pile interface was allowed.

4.6.1.5 Loading Sequence

An initial loading step of geostatic stresses and equilibrium was applied to consider the initial soil stresses, wishing the pile in. This was followed by a displacement-controlled analysis where the pile was subjected to monotonic compression loading. The compression loading was then reset followed by a displacement-controlled uplift applied to the pile at reference points rigidly connected to the top loading plates.

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