Performance of Screw Piles Under Axial Loading

Abstract

Piles with continuous helix (referred to herein as “screw pile”) is a new configuration of helical piles. It features a continuous helix spiraling several pitches around a smooth shaft forming a “threaded shaft”. This study investigates the compressive capacity and behavior of helical and screw piles using 3D numerical models calibrated and validated against full-scale field testing. The bearing capacity factor, $N_c$, for helical piles is back-calculated from the numerical results and compared against standard theoretical assumptions to evaluate their accuracy in predicting ultimate capacity. Parametric studies are conducted considering screw piles configuration, including shaft diameter, pitch size, helix diameter, as well as soil strength. The results reveal that shaft resistance accounts for up to 89% of the total capacity. Analysis of load distribution, shear contours, and displacement contours at failure allowed for the identification of different failure modes of soil adjacent to the pile’s threaded shaft: Individual Bearing Mode (IBM), Cylindrical Shear Mode (CSM), and a combined mode. The study identifies specific parametric thresholds for these modes in both sand and clay layers. Furthermore, varying clay strength is found to alter the development of the shear surface, transitioning from localized bearing to continuous shearing along the threaded shaft. Finally, apparent shaft resistance factors, $\alpha$ and $\beta$, are back-calculated to provide practical parameters for evaluating the resistance of threaded shafts in layered soil.

1. Introduction

Helical piles have become a popular choice in the construction industry as a reliable, easy to install foundation system. To efficiently meet different loading and installation conditions, several variations evolved out of the traditional helical pile configuration. One of these variations is the continuous helix screw pile referred to herein as “screw pile”. The main feature of this new configuration is the shape of the helix, which is forged as one continuous helix spiraling several rounds around a steel cylindrical shaft. The ratio of continuous helix diameter to shaft diameter is smaller than that of the conventional helical pile, which reduces the required installation torque [1]. Screw piles are used in soil conditions where it is difficult or inefficient to install helical piles. For example, very stiff clay or soils with high gravel or cobble content.

There is a limited number of studies on the performance of screw piles subject to axial loading. Most studies have assumed that theories established for axial capacity of helical piles remain applicable to screw piles. Guo and Deng [2] conducted forty full-scale field tests of six configurations of screw piles. The tested pile configurations consisted of smooth steel cylindrical shaft, followed by a threaded shaft and a tapered threaded shaft with pointed end. Subsequent studies have evaluated the performance of screw piles through full-scale field testing in various soil types and under different loading conditions, considering the same general configuration proposed by Guo and Deng. These studies referred to screw piles as a “new generation of micropiles” [3,4,5,6]. In these studies, the theoretical capacity of screw piles is evaluated using the cylindrical shear failure mode (CSM), same as that used for helical piles. The strain gauge results obtained from load tests on instrumented screw piles revealed that screw piles derive their capacity primarily from the threaded shaft resistance [2,3,6]. Mneina et al. [7] investigated the comparative performance of screw and helical piles installed in stiff clay under uplift loading and reported similar observations. Andreasen and Ibsen [8] presented the results of full-scale testing of screw piles installed in sand in the laboratory. They investigated the installation rate of screw piles and its effect on the pile compression capacity and the capacity-torque correlation factor.

Conducting field tests on fully instrumented screw piles is limited by cost, time, and site-specific soil conditions. finite element modeling (FEM) can be used as a reliable method to simulate different soil and pile conditions and parameters to evaluate the performance of screw piles. FEM not only allows the evaluation of pile behavior under different conditions but also provides detailed insight into the stress distribution around the helices across different soil layers. The literature is well established in terms of numerical methods to model helical piles; however, no publication to date has addressed the modeling of steel continuous helix screw piles subjected to axial loading. The majority of published research represents the helices as idealized plates rather than true helical geometries, and in some cases, the problem is further simplified by modeling the pile as a two-dimensional axisymmetric system to reduce complexity and computation time [9,10,11,12,13,14]. This simplification is acceptable when the helices are sufficiently spaced such that the contribution of the helical pitch to helix interaction is negligible. However, in the case of a continuous helix, the pitch forms an integral part of the geometry and cannot be disregarded. Consequently, modeling the helix as a three-dimensional volume is essential to accurately capture the behavior of screw piles. Pucker and Grabe [15] performed numerical simulations of the full displacement pile installation process to investigate its effects on the surrounding soil and to interpret field measurement results. By modeling the pile as a volumetric rigid body, they were able to analyze reaction forces and the influence of different velocity ratios between rotation and penetration on soil displacement, stress states, and void ratio changes. The resulting simulations successfully reproduced qualitative field observations, including the increase in cone penetration resistance and horizontal soil deformations.

In this study, the axial performance of screw piles is analyzed using finite element modeling. The developed models are calibrated and validated against the results of instrumented full-scale tests on helical and screw piles under axial compression. The experimental field test results are reported by Mneina et al. [7]. The preliminary soil parameters are estimated from the observations of six boreholes and associated SPTs and laboratory testing of soil samples.

1.1. Pile Axial Capacity

The pile capacity is estimated from the load–settlement curves using the graphical L1–L2 method developed by Hirany and Kulhawy [16]. In this method, the pile load–settlement curve is divided into three segments. The first segment represents the initial elastic deformation of the pile, extending from zero load to a load value of L1. The second segment corresponds to the nonlinear response of the pile, occurring between load levels L1 and L2. Beyond L2, the curve transitions into a final semi-linear segment with a flatter slope. Two tangential lines are drawn: the first is the tangent to the initial linear segment to point L1; the second line is drawn tangent to the latter, flatter portion of the curve at L2 as shown in Figure 1. The pile capacity is defined as the intersection point of the two tangents.

Another common method for helical pile is to estimate the pile capacity from the load–settlement curve based on a limiting settlement criterion defined as a percentage of the average helix diameter ($D_h$), typically ranging from 5%$D_h$ for helix diameters greater than 610 mm to 10%$D_h$ for helix diameters less than 305 mm [11].

1.1.1. Theoretical Capacity of Helical Piles

The theoretical pile capacity for helical piles is estimated using the individual bearing mode (IBM) since all piles comprise a single helix embedded in clay, i.e.,

$$Q_{total}=Q_{shaft\_sand}+Q_{shaft\_clay}+Q_{helix}$$

(1)

$$Q_{shaft\_sand}={\displaystyle \frac{\pi d}{2}}{L}_s\times {\sigma }_v^{\prime }{K}_{s}tan\delta ={\displaystyle \frac{\pi d}{2}}{L}_s\times \beta {\sigma }_v^{\prime }$$

(2)

$$Q_{shaft\_clay}=\pi d{L}_c\alpha S_u$$

(3)

$$Q_{helix}={\displaystyle \frac{\pi }{4}}{D}_h^2\times S_u{N}_c$$

(4)

where $Q_{total}$ is the pile compression capacity, $Q_{shaft\_sand}$ and $Q_{shaft\_clay}$ are the contribution of the smooth shaft in sand and clay respectively, d (m) is the shaft diameter, $L_s$ and $L_c$ (m) are the embedded length of the smooth shaft in sand and clay respectively, ${\sigma }_v^{\prime }$ (kPa) is the average effective vertical stress along the shaft, $K_s$ is the lateral earth pressure coefficient, $\delta$ is the interface friction angle between the pile material and the surrounding soil, $\beta$ is the combined shaft resistance factor, $\alpha$ is the adhesion factor, $S_u$ is the undrained shear strength of clay, and $N_c$ is the bearing capacity factors for clay. The components of the helical pile capacity are shown in Figure 2a.

1.1.2. Theoretical Capacity of Screw Piles

The theoretical capacity of screw piles is influenced by the shape of the multi-pitch helix and is complicated due to the uncertainty of the mode of failure (IBM or CSM or a combination of both). In general, the compressive capacity of screw piles comprises three components as shown in Figure 2b. The first component is the frictional resistance along the smooth part of the pile shaft $Q_{smooth}$, which is embedded in sand. The second component is derived from the soil resistance along the pile threaded shaft $Q_{th}$, which is calculated assuming either CSM or IBM.In CSM, the threaded shaft resistance is calculated assuming a cylindrical soil column formed at the outer perimeter of the helices. In IBM, the threaded shaft resistance is calculated assuming each helix is an individual bearing plate. The third component of the pile capacity is the base bearing resistance $Q_b$, which is provided by the underlying clay layer. The following equations can be used to calculate the different components of screw pile capacity [17]:

$$Q_{smooth}={\displaystyle \frac{\pi d}{2}}{L}_s\times {\sigma }_v^{\prime }{K}_{s}tan\delta ={\displaystyle \frac{\pi d}{2}}L\times \beta {\sigma }_v^{\prime }$$

(5)

$$Q_{th\_sand\_CSM}=\pi D_h\times L_{c1}\times {\sigma }_v^{\prime }{K}_{s}tan{\varphi }^{\prime }$$

(6)

$$Q_{th\_sand\_IBM}=\pi D_h^2{\displaystyle \sum _{i=1}^n}{\gamma }_i{H}_i{N}_q$$

(7)

$$Q_{th\_clay\_CSM}=\pi D_h\times L_{c2}\times S_u$$

(8)

$$Q_{th\_clay\_IBM}=\pi D_h^2{\displaystyle \sum _{i=1}^n}{S}_{ui}{N}_c$$

(9)

$$Q_b={\displaystyle \frac{\pi }{4}}{D}_h^2\times S_u{N}_c\mathrm{For} \mathrm{pile} \mathrm{toe} \mathrm{embedded} \mathrm{in} \mathrm{clay}$$

(10)

$$Q_b={\displaystyle \frac{\pi }{4}}{D}_h^2\times {\sigma }_v^{\prime }{N}_q\mathrm{For} \mathrm{pile} \mathrm{toe} \mathrm{embedded} \mathrm{in} \mathrm{sand}$$

(11)

where $Q_{th\_sand\_CSM}$, $Q_{th\_sand\_IBM}$, $Q_{th\_clay\_CSM}$, and $Q_{th\_clay\_IBM}$ represent the threaded shaft capacities for sand and clay under both CSM and IBM, respectively, $L_{c1}$ and $L_{c2}$ are the length of the threaded shaft in sand and clay, respectively, n is the number of threads, ${\gamma }_i$, $H_i$, and $S_{ui}$ are the unit weight, embedment depth, and undrained shear strength of the ith thread, and $N_q$ is the bearing capacity factors for sand.

Lutenegger [18] observed that the mode of failure in multi-helix piles is progressive and changes from one mode to another throughout loading. They reported that at small load levels, specifically settlement less than 5% of the helix diameter, behavior in stiff clays is entirely controlled by IBM for spacing ratios ($S/D_h$) above 1.5, and as loads increase toward ultimate capacity (e.g., 20% of the helix diameter), the behavior shifts toward CSM. A similar observation was reported by Lanyi-Bennett and Deng [19] through analysis of strain gauge results obtained from the inter-helix segment of a pile with $S/D_h$ ratios of 5 and 3. They observed a progressive increase in inter-helix shaft resistance at higher load levels for piles that initially behaved as IBM, indicating a progressive shift from IBM to CSM. Lanyi-Bennett [20] proposed a model to describe this transition, which involves the progressive growth of a soil cylinder under the upper helix. As the load increases, this soil cylinder extends toward the lower helix, increasing the contribution of CSM to the overall capacity.

Given the unique geometry of screw piles, compared to conventional helical piles, it is necessary to understand the applicable failure mode to enable the derivation of a reliable method to evaluate their compressive capacity. Therefore, this study conducts a comprehensive numerical investigation to identify the failure mode and establish a physics-based method for calculating the compressive capacity of screw piles.

2. Preliminary Soil Parameters

The test site is located in north-eastern London, Ontario, Canada (${43}^{\circ }{02}^{\prime }{03}^{″}$ N, ${81}^{\circ }{09}^{\prime }{47}^{″}$ W), and six boreholes are drilled along with SPT tests at the test site. Split spoon samples are collected and analyzed in the laboratory for unit-weight, particle size, Atterberg limits, and soil classification. The average results of the six boreholes are used to establish the generalized soil profile to be modeled in the finite element software. The resulting soil profile and estimated parameters are shown in

Table 1. Soil profile and preliminary parameters.

Depth (m)	Soil Type	SPT N Value	Consistency	${\mathit{\varphi }}^{\prime }$ $\left(\mathbf{deg}\right)$	${\mathit{S}}_{\mathit{u}}$ $\left(\mathbf{kPa}\right)$	${\mathit{\gamma }}_{\mathit{bulk}}$ $\left(\mathbf{kPa}\right)$
0	FILL	8	loose	29	-	19
0.762	Clayey Sand	6	loose	28	-	21
1.524	Poorly Graded Sand with Silt	10	loose	29	-	20
2.286	Sandy Lean Clay	18	Stiff	-	88.3	23.5
3.048	Sandy Lean Clay	39	Very stiff	-	176.6	23
3.81	Sandy Lean Clay	88	Hard	-	267.5	22.5
4.572	Sandy Lean Clay	115	Hard	-	267.5	22.7

${\varphi }^{\prime }$ is the soil internal friction angle, and ${\gamma }_{bulk}$ is the unit weight.

.

3. Finite Element Model

Midas GTS NX software (version 1.1) [21] is used to simulate the axial field tests of single screw and helical piles in three-dimensional space. The soil domain is modeled as an $8\mathrm{m}\times 8\mathrm{m}\times 6\mathrm{m}$ block consisting of two layers: a $2.3\mathrm{m}$ thick silty sand layer overlying a $3.7\mathrm{m}$ thick hard clay layer as shown in Figure 3a. The boundaries of the soil block represent the soil mass extending 24 times the helix diameter from the centerline of the pile to the lateral boundary, and 2 times the pile length below the tip of the screw pile. A mesh sensitivity analysis is performed to ensure that the soil mass dimensions will not affect the accuracy of the results. It is found that a soil block $14\mathrm{m}\times 14\mathrm{m}\times 12\mathrm{m}$ would give the same results as the $8\mathrm{m}\times 8\mathrm{m}\times 6\mathrm{m}$ block in this particular model; therefore, the smaller size is used for faster computation time. The pile helix geometry is modeled to reflect the actual pile features as a continuous helix for screw piles, and as a helical plate for helical piles. The soil and pile are discretized using four-node tetrahedral elements. The soil–pile interaction is modeled using the plane interface element with the Coulomb-friction criterion. An interface mesh is constructed for each soil layer. Figure 3b,c show the pile models and interface elements used in the analysis.

The calibration and validation phases are based on six pile types, four of which are screw piles (S1, S2, S3 and S4) with two different shaft, helix diameters and pile lengths. The other two are helical piles (H1 and H2) with varying depth, shaft diameter, and helix diameter. The shorter screw pile types (S1 and S3) are instrumented with strain gauges at 5 different levels along the pile length. The geometric parameters of the piles are illustrated in Figure 3b and are listed in

Table 2. Geometric parameters and number of samples of the screw and helical piles in the field experimental program [7].

Pile	Type	L1 (mm)	L2 (mm)	d (mm)	${\mathit{D}}_{\mathit{h}}$ (mm)	Pitch (mm)	Number of Piles
S1	Screw pile	1650	1150	76	127	76	3
S2	Screw pile	1900	1150	76	127	76	4
S3	Screw pile	1550	1240	89	152	89	4
S4	Screw pile	1850	1240	89	152	89	3
H1	Helical pile	3650	-	76	254	76	3
H2	Helical pile	3350	-	89	356	89	6

.

Mesh refinement is applied to increase the accuracy of the model at critical regions. A $3\times 3\times 6\mathrm{m}$ fine mesh with a maximum element size of 300 mm is generated around the pile, while a coarse mesh surrounded it with an element size gradually increased to 1 m near the model boundaries. The mesh refinement of the soil block is illustrated in Figure 4a. The pile mesh is generated using a 20 mm element for the pile shaft, 12 mm element for the continuous helix and a 5 mm element at the toe to avoid concentration of stresses that and facilitate convergence. The helix of the helical pile is generated using 5 mm elements. The pile mesh refinement is illustrated in Figure 4b.

The hardening soil (HS) constitutive model is adopted to simulate soil behavior, as it provides a more realistic representation compared to the Mohr–Coulomb or Drucker–Prager models. The HS model accounts for stress-dependent stiffness, nonlinear stress–strain behavior, and plastic straining under both primary loading and unloading–reloading conditions, thereby offering a more accurate description of soil response under pile loading [22,23].

4. Hardening Soil Model Properties

The hardening soil model, first formulated by [24], is a stress-dependent constitutive model with a hyperbolic stress–strain relationship, which offers a clear advantage over the Mohr–Coulomb constitutive model. The preliminary HS model parameters are determined using correlations from SPT data collected from the six boreholes drilled in the field. These properties are fine-tuned during the model calibration phase to match the field load–settlement curves.

4.1. Stiffness Moduli

The HS model requires the definition of three types of stiffness moduli, all measured at a specific reference confining pressure ($p^{ref}$): the secant stiffness modulus in standard drained triaxial test ($E_{50}^{ref}$), the tangent stiffness modulus for primary oedometer loading ($E_{oed}^{ref}$), and the unloading–reloading stiffness modulus ($E_{ur}^{ref}$). In numerical modeling, it is assumed that $E_{50}^{ref}$ = $E_{oed}^{ref}$ = ${\displaystyle \frac{1}{3}}\times E_{ur}^{ref}$ [23,25,26,27]. For the sand layer, the stiffness modulus is estimated based on their relative density ($D_r$) [26]:

$$E_{50}^{ref}=E_{oed}^{ref}={\displaystyle \frac{1}{3}}{E}_{ur}^{ref}=60000\times \%D_r\left(\mathrm{kPa}\right)$$

(12)

where $D_r$ is estimated using the correlation %$D_r=100\sqrt{{\displaystyle \frac{{\left(N_1\right)}_{60}}{60}}}$ [28].

For the clay layer, the stiffness moduli are estimated based on the correlation suggested by [27]:

$$E_{50}^{ref}=\left(1100\mathrm{to}2500\right)N_{60}\left(\mathrm{kPa}\right)$$

(13)

The stiffness values estimated from Equations (12) and (13) are all based on reference confining pressure $p^{ref}=100$$\left(\mathrm{kPa}\right)$.

Poisson’s ratio $\nu =0.3$ is assumed for sand in drained conditions and $\nu =0.495$ for clay in undrained conditions [29,30].

4.2. Pressure Constant (m)

The pressure constant $\left(m\right)$ controls the degree of pressure dependency for the elastic moduli, where $m=0.5$ corresponds to hard soils and $m=1.0$ corresponds to soft soils [23,25]. For the sand layer, m is estimated using the Brinkgreve’s correlation [26]:

$$m=0.7-{\displaystyle \frac{\%D_R}{3.2}}$$

(14)

For the clay layer, the value of $m=0.8$ is adopted to represent hard clay [27].

4.3. Failure Ratio

The failure ratio ($R_f$) defines the ratio between the deviatoric stress at which failure is considered to occur and the ultimate deviatoric stress. The value of $R_f$ ranges from 0.75 to 1.0 and can be taken as 0.9 as a default value [23]. The values used for sand and clay layers in the numerical model are 0.96 and 0.8, respectively.

4.4. Strength Parameters

Several correlations are available in the literature to estimate the soil internal friction angle ${\varphi }^{\prime }$ for sand and the undrained shear strength $S_u$ for clay from SPT blow-count and soil consistency. The preliminary friction angle is estimated based on the suggested range for loose sand by Bowles [17]. However, the friction angle is reduced by $5^{\circ }$ during calibration as recommended by Look [31] for clayey sand. A final friction angle of 25° is adopted for the sand layer. To ensure numerical stability in the analysis, a negligible cohesion (1.0 kPa) value is assigned to the sand. The dilation angle $\psi$ for loose sand and undrained clay is taken as zero [29,30,32].

The undrained shear strength ($S_u$) is estimated using the following correlation for low-plasticity clay [33]:

$$S_u=5.36N_{60}\left(\mathrm{kPa}\right)$$

(15)

The undrained shear strength is set to increase linearly from 88 (kPa), at the top of the clay layer, to 267 (kPa) to reflect the actual soil condition.

Table 3. Main hardening soil model parameters used for MIDAS GTS NX input for soil materials.

Parameter	Sand Layer	Clay Layer
${\gamma }_{bulk}$ (kPa)	20	21
$E_{50}^{ref}$ (MPa)	13.8	50
$E_{oed}^{ref}$ (MPa)	13.8	50
$E_{ur}^{ref}$ (MPa)	41.4	150
m	0.63	0.8
${\varphi }^{\prime }$	25	-
$S_u$ (kPa)	-	88 to 267
$\nu$	0.3	0.495
$R_f$	0.97	0.8

lists a summary of the main HS parameters used in the MIDAS GTS NX software model for each of the soil layers.

5. Soil–Pile Interface Model

The soil–pile interface is modeled using the interface element mesh tool in the Midas GTS NX software with Mohr–Coulomb friction criteria. The interface reduction factor ($R_i$) is applied to the stiffness and strength parameters of the adjacent soil to estimate the interface parameters assuming a virtual thickness factor ($t_v$) of 0.1 and a constant Poisson’s ratio of ${\nu }_i=0.45$. The normal and shear stiffness of the interface are calculated following Equations (16)–(19) [34].

$$E_{oed,i}=2G_i{\displaystyle \frac{(1-{\nu }_i)}{(1-2{\nu }_i)}}$$

(16)

$$G_i=R_i^2\times G_{soil}$$

(17)

$$K_n={\displaystyle \frac{E_{oed,i}}{t_v}}$$

(18)

$$K_t={\displaystyle \frac{G_i}{t_v}}$$

(19)

where $E_{oed,i}$ is the oedometer modulus of the interface material; $G_i$ and $G_{soil}$ are the shear moduli of the interface and the soil, respectively; $K_n$ and $K_t$ are the normal and shear stiffnesses of the interface, respectively.

The strength parameters of the interface are calculated as follows:

$${\varphi }_i={tan}^{-1}(R_i\times tan{\varphi }_{soil})$$

(20)

$$S_{ui}=R_i\times S_u$$

(21)

where ${\varphi }_i$ and ${\varphi }_{soil}$ are the friction angles of the interface and soil materials, respectively; $S_{ui}$ and $S_u$ are the undrained shear strength parameters of the interface and soil materials, respectively.

6. Analysis Method

The analysis is performed in three construction stages. In the first stage, the in situ vertical and lateral stresses in the soil are calculated prior to pile installation by assigning soil material properties to the entire mesh block, including the pile mesh. A rigid link is used instead of the interface element to simulate an integral soil block rather than a pile–soil interface. In the second stage, pile material properties are assigned to the pile mesh, the interface meshes are activated, and the rigid link mesh is deactivated. In the third stage, the load is applied as pressure to a rigid plate attached to the pile head. The numerical modeling results are presented sequentially, beginning with the complex two-layer profile as it represents the actual field site conditions used for physical validation, model calibration, and initial parametric evaluations. Following this, further parametric simulations are conducted on simplified homogeneous profiles to isolate and evaluate the independent mobilization mechanisms of the screw piles in uniform sand and clay soils.

7. Calibration and Validation

The model parameters are first calibrated against the field compression test results of three helical piles H1 (Table 2). The soil and interface properties are fine-tuned during the calibration phase, and after several trials, the model matched the field results with a settlement root-mean-square error (RMSE) of only 1.6 mm, or 4.6% of the total settlement range in the field test. The calibrated soil parameters are listed in Table 3. The calibrated model is further validated with field compression test results of screw piles S1, S2, S3 and S4 in addition to the field tension test of pile S4 and compression test of helical pile H2 with good agreement between the measured and FEM curves. Interface reduction factors of 0.6 and 0.4 are applied to the sand and clay layers respectively for helical piles type H1 to match the field results. Different reduction factors are applied to different pile types depending on penetration depth and the amount of soil disturbance due to installation. The interface reduction factors used for different pile types are shown in

Table 4. Interface reduction factors for different pile types installed at different depths.

Pile Type	Test	Installation Depth (m)	${\mathit{R}}_{\mathit{i}}$ for Sand	${\mathit{R}}_{\mathit{i}}$ for Clay
S1	Compression	2.8	0.6	0.3
S2	Compression	3	0.6	0.5
S3	Compression	2.8	0.5	0.3
S4	Tension	3	0.6	0.5
S4	Compression	3	0.6	0.5
H1	Compression	3.6	0.6	0.5
H2	Compression	3.3	0.4 to 0.5	0.2 to 0.25

. All piles are used to validate the model in compression, except type S4, of which both compression and tension results are used, as they are both obtained at similar installation torque levels. The tension resistance for helical pile H2 is substantially lower than the compression resistance. This is because the soil above the helix experienced more disturbance than soil below the helix. The results of FEM and field measurements are shown in Figure 5 for piles in compression and in Figure 6 for the S4 pile in tension.

By comparing the tension and compression results of the capacity-torque correlation factor ($k_t$) for the larger helical pile H2 presented by Mneina et al. [7], it is found that $k_t$ in tension is 50% less than in compression, indicating high installation disturbance which is common in most helical piles. Moreover, the theoretical uplift capacity of H2 piles is 69% higher than the average field capacity. This indicates that disturbance is probably the main factor causing the $R_i$ to be as low as 0.2 in H2 piles.

It should be noted that $R_i$ was used as a calibration parameter to account for installation-induced soil disturbance in the numerical model, and it cannot be directly quantified from the available field measurements. Therefore, the reported $R_i$ values are specific to the investigated pile geometries, installation conditions, and soil profiles, and should not be interpreted as universally applicable design values.

8. Parametric Analysis

Based on the validated numerical model, two main parametric analyses are performed. The first parametric study (Study 1) focuses on a layered soil profile consisting of 2.3 m of sand overlying a thick clay layer; this study is subdivided into two groups, Group 1 which examines variation in pitch and helix diameter, and Group 2 which investigates variations in clay strength. The second parametric study (Study 2) considers a single homogeneous soil layer across seven soil types. The comprehensive plan for these studies is illustrated in the flowchart in Figure 7. The following sections detail the parameters and configurations for each case conducted.

8.1. Pile in Layered Soil (Study 1)

This parametric analysis is performed using the validated model, with the focus on screw pile type S4 considering different geometry parameters (Group 1) and common clay types (Group 2). In Group 1, the varied parameters are helix pitch ($p=$ 60, 89 (original S4 pile), 135 and 176 mm), and helix diameter ($D_h=$ 120, 140, 152 (original S4 pile), 160 and 170 mm). Each of the helix and pitch parameters is changed independently while fixing the other parameter to the original pile value. For Group 2, the original S4 pile is modeled with the bottom clay layer varying in strength from very soft to stiff-to-hard, while the top layer is fixed as the original loose sand. The geometric variable parameters and the properties of the different clay types used in the parametric analysis are listed in

Table 5. Variable parameters considered in Group 1 parametric analysis.

Case	Shaft Diameter (mm)	Helix Diameter (mm)	Helix Pitch (mm)
Original pile S4 (D152 P89) *	89	152	89
D120	89	120	89
D140	89	140	89
D160	89	160	89
D170	89	170	89
P60	89	152	60
P135	89	152	135
P176	89	152	176

* The letters D and P in the case name denote the helix diameter and pitch respectively.

and

Table 6. Clay parameters considered Group 2.

Soil Type	${\mathit{\gamma }}_{\mathit{b}}$  $(\mathbf{kN}/{\mathbf{m}}^3)$	${\mathit{E}}_{\mathit{ur}}$ (MPa)	${\mathit{E}}_{50}$ (MPa)	${\mathit{S}}_{\mathit{u}}$ (kPa)
Very soft Clay	15	10.5	3.5	10
Soft	16	16	5.3	18
Firm	18	26.7	8.9	40
Stiff	20	59	19.6	75
Very Stiff to Hard *	21	150	50	88–267

* Represented by the original pile S4 (D152 P89) Group 1.

.

8.2. Pile in Homogeneous Soil Layer (Study 2)

This parametric analysis is conducted on the validated screw pile S4 to assess the performance of screw piles in a homogeneous single-layer soil. Seven different cases are considered with three sand types and four clay types with varying strengths. The properties of the soil in this analysis are listed in

Table 7. Soil parameters for Study 2.

Soil Type	Relative Density %	${\mathit{E}}_{\mathit{ur}}^{\mathit{ref}}$ MPa	${\mathit{E}}_{50}^{\mathit{ref}}$ MPa	$\mathit{\psi }$	$\mathit{\varphi }$	${\mathit{S}}_{\mathit{u}}$ (kPa)
Loose Sand	15	41.4	13.8	0.0	25	0
Medium Dense Sand	50	72	24	4.0	35	0
Dense Sand	75	158.4	52.8	7	42	0
Very Soft Clay	-	10.5	3.5	0	0	10
Soft Clay	-	16	5.3	0	0	18
Firm Clay	-	26.7	8.9	0	0	40
Stiff Clay	-	59	19.6	0	0	75

$\psi$ is the dilation angle.

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9. Results and Discussion

9.1. Helical Pile Capacity

The numerical pile capacity determined using the graphical method is compared with the theoretical capacity calculated using Equations (1)–(4). The load distribution obtained from the numerical model at the graphical capacity load level is in good agreement with the theoretical load distribution for the H2 pile (Figure 8b). In contrast, for the H1 pile, the theoretical capacity is approximately 37% lower than the numerical estimate. The graphical numerical capacities for the H1 and H2 (upper-bound) piles are only 1% and 10% higher, respectively, than the field results. The pile capacities correspond to a pile settlement of 6%$D_h$ in both H1 and H2 piles. A summary of the estimated helical pile capacities is presented in

Table 8. Axial capacity of helical piles obtained from numerical, theoretical and field (graphical and 10%$D_h$) results.

Pile	H1	H2
Numerical (graphical) (kN)	189	254
Numerical (10%$D_h$) (kN)	238	320
Theoretical (IBM) (kN)	138	217
Field (graphical)	188	230
Field (10%$D_h$)	249	315

. Overall, the results demonstrate that the graphical method provides a reliable and consistent estimate of helical pile capacity, with close agreement between numerical predictions and field measurements, while the theoretical approach tends to underestimate the capacity.

Figure 8 compares the theoretical and numerical load distribution profiles along the pile shaft for helical piles H1 and H2. It shows that the piles acted mainly as bearing piles, which is expected in helical piles with a single helix. The main factor that affects the theoretical capacity is the bearing capacity factor in clay $N_c$, which is assumed to be equal to 9 for undrained conditions and for $D-h<0.5$ m [35]. The helix contribution to the overall capacity is 86% and 90% for H1 and H2 respectively. By back-calculating $N_c$ from Equation (4), values of approximately 12.7 and 10.2 are obtained for the H1 and H2 piles, respectively. These results are consistent with the findings of Elsherbiny and El Naggar [11], who concluded that $N_c$ is underestimated and recommended a value of 12.

The difference between the back-calculated $N_c$ values for H1 and H2 is attributed to the influence of helix diameter on the bearing failure mechanism. Classical bearing capacity theory indicates that $N_c$ is not strictly constant, particularly for deep foundations and circular bearing elements. Smaller helix diameters tend to develop more confined plastic zones and higher normalized bearing stresses, resulting in larger apparent $N_c$ values. Conversely, increasing the helix diameter enlarges the failure zone and reduces the normalized bearing resistance, resulting in relatively lower $N_c$ values. This behavior is consistent with observations reported in the literature for deep foundations in undrained clay [35].

The percentage contribution of shaft and helix resistances to the overall load carrying capacity is shown in Figure 9. It indicates that for the H1 pile with a shaft diameter of 76 mm, the shaft contribution varied from 43% at the beginning of loading to 13% at settlement of approximately 3%$D_h$ (7.5 mm). For the H2 pile with an 89 mm shaft, the shaft contribution varied from 23% to 8% at a settlement of 1%$D_h$ (3.5 mm). This indicates that the shaft resistance is mobilized at a settlement of approximately 1% to 3%$D_h$. Similar trends are reported by Elsherbiny and El Naggar [11].

9.2. Screw Pile in Layered Soil (Study 1)

9.2.1. Pile Capacity

The screw pile capacity is estimated theoretically based on different failure modes for threads in each of the sand and clay layers. The instrumented pile load testing program [7] concluded that for screw piles S1 and S3 installed up to 2.8 m deep, the failure mode in sand is primarily CSM while the failure mode in the clay layer is closer to IBM. However, for longer S2 and S4 piles, the behavior of the threaded shaft within the clay layer indicated a combination of both modes (IBM + CSM). As S4 piles are not instrumented with strain gauges, their behavior is further evaluated using finite element modeling. The failure-mode cases investigated in this study are listed in

Table 9. Different failure-mode cases for theoretical capacity calculation of screw piles.

Soil Layer	Case 1	Case 2	Case 3	Case 4	Case 5
Sand	CSM	CSM	IBM	CSM	IBM
Clay	CSM	IBM	IBM	IBM + CSM	IBM + CSM

. Two groups of parametric analyses are performed on the S4 piles: Group 1, in which the helix diameter ($D_h$) and helix pitch (p) are varied, and Group 2, in which the strength and stiffness parameters of the clay layer are varied (Table 5 and Table 6). The load–settlement curves resulting from the parametric analysis are shown in Figure 10.

The pile capacity is estimated using the graphical method and 10%$D_h$ failure criterion. Both interpretation methods yielded closely aligned results, with discrepancies ranging from 2% to 7% for piles featuring $p/D_h$ ratios of 0.39 and 0.89. However, for pile P176 ($p/D_h=1.16$), the load determined at $10\%D_h$ settlement is 15% lower than the capacity calculated via the graphical method. In varying clay consistencies, the observed differences are generally between 0.7% and 6%, with an exception to the case of screw pile in very soft clay where the 10%$D_h$ criterion resulted in a capacity 26% higher than the graphical estimate. However, the absolute difference between the ultimate load obtained from the two methods is less than 6 kN. The estimated capacities of both methods are summarized in

Table 10. Pile capacity obtained from Study 1 results using the graphical and 10%$D_h$ methods.

Case	${\mathit{Q}}_{10\%{\mathit{D}}_{\mathit{h}}}$ (kN)	QL1–L2 (kN)	$\mathit{w}/{\mathit{D}}_{\mathit{h}}\%$ at QL1–L2 (mm)
Original pile S4 (D152 P89)	167	163	9%
D120	116	119	11%
D140	152	155	11%
D160	183	171	8%
D170	192	179	8%
P60	138	159	14%
P135	153	160	11%
P176	170	165	9%
Very Soft Clay	25	19	4%
Soft Clay	35	32	8%
Firm Clay	62	60	9%
Stiff Clay	106	107	10%

where w is the pile settlement and $Q_{10\%D_h}$ and Q_L1–L2 are the estimated capacities using 10%$D_h$ and graphical criteria respectively.

The parametric analysis results presented in Figure 10a,b, demonstrate that there are limitations beyond which further modifications to the pile geometry yield marginal capacity gains. Increasing the helix diameter beyond $D_h=160$ mm or reducing the pitch spacing below $p=89$ mm results in a distinct flattening of the load-settlement curves. Indicating that further enlargement of the helix or narrowing of the pitch no longer engages a larger soil failure zone. Consequently, a pitch-to-helix diameter ($p/D_h$) ratio between 0.4 and 0.6 represents the geometric optimum based on the parametric analysis, soil conditions, and pile dimensions investigated in this study.

Figure 11 presents the results of sensitivity analysis for the estimated capacity using the 10%$D_h$ method with respect to $p/D_h$ ratio and $S_u$. Figure 11 indicates that the screw pile capacity is significantly more sensitive to the helix diameter than to the pitch as represented by the steep slope of the helix diameter results in Figure 11a. A linear trend is observed in Group 2 where an increase of 10 kPa in S_u resulted in a 12 kN increase in capacity as shown in Figure 11. Similar results are concluded using the graphical method. Although the capacities obtained using the 10%$D_h$ and L1-L2 methods are generally comparable, larger differences were observed for cases with low p/Dh ratios. Therefore, the 10%$D_h$ criterion was adopted as the primary reference throughout this study to ensure consistency in the comparison of pile behavior and capacity.

9.2.2. Failure Mode of Threaded Shaft

The load distributions along the pile shaft at failure load are compared in Figure 12 and Figure 13 with the theoretical load distribution calculated using the failure-mode cases listed in Table 9. Through this comparison, the failure mode of threaded shaft is determined based on the alignment of the numerical load distribution curves with the theoretical distributions.

Inspecting Figure 12 to estimate the failure mode, it is noted that for Group 1, the failure mode in the sand layer indicates IBM, except for the two piles D170 and P60 with lowest $p/D$ ratios of 0.39 and 0.52, respectively, where the pile exhibits CSM failure. In the clay layer, IBM failure is observed up to $p/D$ ratio of 0.59 and transforming to combined IBM + CSM for $p/D$ ratios > 0.59. For Group 2, the load distribution in Figure 13 indicates that the failure mode of the threaded shaft within the sand layer is governed by the strength of the underlying clay. The threaded shaft in the sand layer exhibits a CSM when the underlying clay strength is $S_u\le 40\mathrm{kPa}$, and transitions to IBM when the clay strength exceeds $S_u=40\mathrm{kPa}$. While the clay layer failed in combined mode (IBM + CSM) at S_u = 75 kPa and in IBM at S_u > 75. The transition to the IBM + CSM failure mode in the clay layer occurs because the helix initially mobilizes end-bearing resistance, and as the bearing capacity is reached, the development of a displaced soil wedge induces interface shear with the adjacent soil, subsequently activating the CSM resistance. This mechanism is suggested by Lanyi-Bennett [20].

The displacement patterns in Figure 14 and Figure 15 show that the soil within the inter-helix zone in stronger clay layers undergoes settlement in a wedge-like form at the capacity load level. This behavior suggests partial mobilization of cylindrical shear resistance. In weaker clay layers, the development of the cylindrical shear form occurs earlier in the loading stage. This observation confirms the findings of Lanyi-Bennett [20].

Figure 16 summarizes the influence of studied parameters (i.e., pitch, helix diameter, $p/D_h$ ratio, and soil undrained shear strength) on the failure mode of the helices in both sand and clay layers. In the clay layer, the failure mechanism varies from IBM for $p/D_h=$ 0.39–0.59 to a combined mode for $p/D_h>0.59$, while in the sand layer, a transition from IBM to CSM is observed at $p/D_h>0.52$. Furthermore, Group 2 results indicate that the clay layer primarily exhibits a combined failure mode in very soft to stiff clays, transitioning to IBM in stiff-to-hard clays, while the sand layer exhibits CSM for very soft to firm clays before transitioning to IBM in stiff to stiff-to-hard clay conditions.

9.2.3. Shear Stress Distribution

Figure 17 shows the shear stress distribution for load that produces 10%$D_h$ settlement for Group 1. The contours show the formation of distinct shear planes in the sand layer, characteristic of IBM behavior for the majority of the piles. Notable exceptions are observed for piles D170 and P60 (Figure 17e,h), which exhibit CSM shear planes in the sand layer. This behavior is attributed to the increased helix diameter in D170 ($p/D_h=0.52$) and the reduced helix pitch in P60 ($p/D_h=1.48$), both of which promote a continuous cylindrical failure surface in sand.

In the clay layer, a full or partial development of cylindrical shear planes is observed in all configurations. Pile D120 (Figure 17a) exhibits the least pronounced CSM mobilization, with stress interference limited to the bottom three helices.

For Group 2, the shear stress distribution shown in Figure 18 indicates that the relative contribution of the shaft segment embedded in sand is highest for the weak clay layer condition and decreases as the strength of the clay layer increases. Full to partial CSM patterns are evident in the sand layer for piles embedded in weaker clays as can be observed from Figure 18a–c. Conversely, the IBM becomes more prominent in stiff and stiff-to-hard clays as shown in Figure 17c and Figure 18c (original S4 pile in stiff-to-hard clay).

Within the clay layer, a transition in failure mechanisms is observed as clay strength increases: the fully developed CSM observed in weaker clays gradually shifts toward a partial mobilization of cylindrical shear in stronger clays as indicated by the wedge-like (conical) shape of the shear planes in stronger clays.

Specifically, as $p/D_h$ increases, the clay layer shifts from an individual bearing mode toward a combined mode (CSM + IBM). This occurs because larger spacing allows shear zones around each pile to partially develop cylindrical confinement, while localized IBM interactions are still present.

9.2.4. Shaft Contribution

Unlike conventional helical piles, screw piles function primarily as friction piles, transferring most of the load through shaft resistance. For all configurations considered in the parametric analysis, the shaft contribution consistently accounted for 83% to 89% of the total capacity. The majority of this resistance is mobilized by the shaft segment within the stronger clay layer; therefore, clay strength significantly influenced the distribution. In very soft clay, the contribution to the overall capacity of the shaft segment in clay layer drops to 41%, compared to 73% for the stiff-to-hard clay (pile S4 (D152 P89)).

Figure 19a,b indicate that for Group 1 the shaft contribution curves plotted against %$D_h$ on a logarithmic scale can be divided into three distinct stages: an initial plateaued stage (constant shaft contribution with increase in settlement), a transitional steep-slope stage, and a final plateaued stage. During the first stage, the shaft resistance is mobilized at the onset of loading, maintaining a stable contribution percentage up to a settlement of 1%$D_h$. The second stage starts beyond 1%$D_h$, where the shaft contribution begins to decrease as the load is progressively transferred to the pile toe, which is mobilized at this stage. The final stage begins at a settlement of 10%$D_h$, where the contribution curves for all piles with helix diameters ≥140 mm display a plateau again indicating that the toe resistance is approaching full mobilization. For pile D120, a final plateau in the shaft contribution curve is not observed within the investigated settlement range. This is attributed to its smaller helix diameter relative to the other piles in the group; the reduced toe area requires greater settlement to reach full toe mobilization.

Figure 19c illustrates the effect of different parameters on the shaft contribution to overall capacity. In stiffer clays (stiff to stiff-to-hard), the shaft carries over 90% of the load from the onset of loading, indicating that shaft friction is mobilized almost immediately. A three staged pattern is observed where an initial plateaued stage is maintained up to 1%$D_h$. Conversely, in very soft to soft clays, the shaft contribution starts significantly lower (as low as 65%) before peaking at settlement of approximately 0.6%$D_h$, 0.4%$D_h$ and 0.3%$D_h$ for very-soft, soft and firm clay, respectively. The distinct three-stage pattern diminishes in very-soft to firm clays transitioning into a peak and post-peak pattern. However, as settlement reaches the 1%$D_h$, all piles converge toward a shaft contribution range of 83% to 89%.

The shaft resistance factors, $\beta$ for the sand layer and $\alpha$ for the clay layer, are back-calculated at selected depths from the shaft resistance results of the parametric analysis. The shaft resistance at the threaded shaft segments of the pile is calculated assuming a shaft diameter equal to the helix diameter, which includes the resistance of the helical threads. As a result, the $\alpha$ and $\beta$ values in these segments are higher than 1.0. The resulting values are summarized in

Table 11. Back-calculated values of $\beta$ and $\alpha$ from the shaft resistance results of Study 1 parametric analysis.

Layer	Sand		Clay
Depth	0.9 m	2.0 m	2.6 m
Factor	$\mathsf{\beta }\mathbf{1}$	$\mathsf{\beta }\mathbf{2}$	$\mathsf{\alpha }$
S4 (D152 P89)	0.33	1.69	1.88
D120	0.48	1.57	1.16
D140	0.46	1.89	1.57
D160	0.43	2.55	1.97
D170	0.42	2.38	2.16
P60	0.29	3.12	2.01
P135	0.82	3.11	1.57
P176	0.90	2.51	1.43
V-soft clay	0.12	0.86	2.94
Soft clay	0.13	1.10	2.59
Firm clay	0.15	1.76	2.43
Stiff clay	0.23	1.35	2.65

.

9.3. Pile in Homogeneous Soil Layer

9.3.1. Pile Capacity

The load–settlement curves resulting from the finite element parametric analysis are shown in Figure 20. The 10%$D_h$ criterion is used to estimate the pile capacity for each soil type. These capacities are compared to the theoretical capacities calculated for both the CSM and IBM, as presented in

Table 12. Comparison between the 10%$D_h$ numerical capacity and theoretical (IBM and CSM) capacities for Study 2.

Soil Type	10%Dh Capacity (kN)	Theoretical IBM (kN)	Theoretical CSM (kN)
Loose Sand	55	173	49
Medium Dense Sand	170	338	158
Dense Sand	381	851	355
Very Soft Clay	20	18	9
Soft Clay	34	32	16
Firm Clay	71	70	35
Stiff Clay	138	132	66

. For piles in sand, the CSM yielded the lowest error, ranging from 6.8% to 11.7%. Conversely, for piles in clay, the IBM gives the most accurate predictions, with errors ranging from 1.5% to 10.2%.

9.3.2. Mode of Failure of Threaded Shaft

The theoretical load distribution along the pile length is calculated using Equations (8)–(10) for the clay layers, and Equations (6), (7) and (11) for the sand layers. The load distribution obtained from the numerical analysis is compared with these theoretical values and is plotted in Figure 21. The comparison demonstrates that at the 10%$D_h$ load level, the theoretical load distribution calculated using the CSM equations closely matches the FEM results for all piles in sand. The CSM equations yielded the most accurate predictions for the sand profiles, which closely agrees with the physical observations from the numerical displacement contours. These contours clearly illustrate that the sand trapped between the helices moves downward as a unified cylindrical block within the helix diameter, confirming the mobilization of a cylindrical shear failure mechanism rather than independent helix bearing. Conversely, the IBM equations provide the most accurate representation of the load distribution for all piles in clay layers. Unlike the layered soil profile, in homogeneous sand, the soil mass is continuous and uniform, allowing fully developed cylindrical shear zones to form around the screw pile.

In homogeneous clay, the pile predominantly displays IBM because clay under undrained conditions deforms in a localized manner. The shear resistance is governed by the undrained shear strength, and the soil tends to form independent failure zones around each helix rather than a continuous cylindrical shear surface.

The resulting vertical displacement contours at the 10%$D_h$ pile settlement for all cases are shown in Figure 22. These contours indicate that the soil is displaced as a cylindrical block in the sand layers, as illustrated in Figure 22a–c. However, in the clay layers, the soil block is displaced as a conical wedge, forming a bearing zone that characterizes the mobilization of the IBM. This wedge-like formation is consistent with the observations reported by [20].

9.3.3. Shaft Contribution

Figure 23 illustrates the shaft contribution to the overall capacity plotted against the settlement as a percentage of the helix diameter. Figure 23a shows that for piles in sand, the shaft resistance is fully mobilized at pile settlement of approximately 0.2%$D_h$ a cross all density cases. At this point, the pile toe begins to engage in load transfer, resulting in a noticeable decline in the relative shaft contribution in a peak post-peak pattern. At the 10%$D_h$ capacity criterion, the shaft contribution represents 80%, 87%, and 91% of the total capacity for loose, medium dense, and dense sand, respectively. For piles in clay (Figure 23b), the mobilization behavior varies with soil consistency. In firm and stiff clays, an initial plateau is observed up to a settlement of 0.7%$D_h$; following this, the shaft contribution diminishes gradually as the pile toe starts to mobilize, with no final plateau zone observed as in Study 1. Conversely, for very soft clay, the behavior exhibits a peak and post-peak pattern, where the shaft contribution reaches full mobilization at a settlement of 0.5%$D_h$. At 10%$D_h$, the shaft contribution for all clay types remains higher than in sand, ranging from 91% to 93% of the pile capacity.

Based on the parametric analysis results of Study 2, the shaft resistance factors ($\beta$ for sand and $\alpha$ for clay) are back-calculated at selected depths and are presented in

Table 13. Back-calculated values of $\beta$ and $\alpha$ from the results of Study 2 parametric analysis.

Depth:	0.95 m	2.4 m
Sand Soils	$\mathsf{\beta }\mathbf{1}$	$\mathsf{\beta }\mathbf{2}$
Dense	8.6	9.2
Medium Dense	2.3	4.0
Loose	0.1	1.5
Clay Soils	$\mathsf{\alpha }\mathbf{1}$	$\mathsf{\alpha }\mathbf{2}$
Stiff	0.5	2.4
Firm	0.5	2.3
Soft	0.5	2.4
Very Soft	0.5	2.6

. The back-calculated $\alpha$ and $\beta$ values should be interpreted as apparent shaft resistance factors for the threaded shaft system rather than conventional interface factors used for smooth piles. Because the resistance provided by the continuous helical threads is included in the shaft resistance calculation, values greater than unity are expected. The results indicate that both $\alpha$ and $\beta$ are influenced by soil strength and pile geometry, with higher values generally associated with stronger soils and increased thread interaction. Therefore, these factors provide a practical means of representing the combined effect of shaft friction and thread-induced resistance within simplified analytical calculations.

It should be noted that the results presented in Study 2 are based on a numerical parametric analysis using a finite element model validated against field tests from a single site. Although the observed trends are consistent with established theoretical failure mechanisms for screw piles in sand and clay, additional validation against independent field and laboratory data is recommended before extending these findings to a wider range of geological conditions.

10. Conclusions

The compressive capacity and behavior of helical and screw piles were investigated using 3D numerical models, which were calibrated and validated against full-scale field tests. The estimated capacities were determined using two different criteria for comparison: the widely used 10%$D_h$ settlement method and the graphical method. The estimated capacities were compared to theoretical capacities calculated using established equations from the literature for helical piles. For the screw piles, a parametric analysis was conducted by varying the pitch, helix diameter, and clay strength for the layered soil profiles, as well as evaluating various sand and clay types for the single-layer soil profiles. A more detailed analysis was performed to examine the shear failure surface and determine the modes of failure by utilizing shear and displacement contour results at the failure load. The conclusions presented herein are based on the investigated screw pile geometries and soil conditions calibrated against field tests conducted in London, Ontario. Although the normalized trends and dimensionless resistance factors ($\alpha$ and $\beta$) provide valuable insight into the load-transfer behavior of screw piles, the investigated geometric parameters were limited to the range considered in this study. Further studies involving a wider range of shaft diameters, pile lengths, helix configurations, and geological profiles are recommended before extending these findings to broader empirical design applications. Based on the analysis of the numerical modeling and parametric studies, the following conclusions are drawn:

For helical piles:

• The bearing capacity factor obtained from the numerical results ranged from 12.7 for pile H1 to 10.2 for pile H2, suggesting that the standard assumption of $N_c=9$ for clay in undrained conditions underestimates helical pile capacity. These findings are consistent with previous research recommending a higher value of 12 for $N_c$.
• The pile capacities obtained from numerical models agree well with the field result’s pile settlement of $6\%D_h$, with deviations of only 1% and 10% for piles H1 and H2. This indicates the numerical modeling scheme employed in the analysis is suitable for simulating the behavior of helical and screw piles.
• While the numerical load distribution for pile H2 aligned well with theoretical values, the theoretical capacity for pile H1 was significantly more conservative, underestimating the numerical results by approximately 37%. This is due to the assumed $N_c$ value of 9 for both piles in theoretical capacity calculation, while the value of $N_c$ is a function of pile diameter and it is higher for smaller diameter piles [35].
• The shaft contribution to the helical pile capacity mobilizes rapidly at the onset of loading and stabilizes at pile settlement between 1% and 3% $D_h$. Its percentage contribution falls from initial values of up to 43% to a value of 8% to 13% at failure load.

For screw piles:

• The $10\%D_h$ and graphical methods generally yield closely aligned results with differences less than 0.7% to 7%; however, deviations occur in extreme cases, such as a 15% lower $10\%D_h$ capacity for large $p/D_h$ ratios (1.16) and a 26% higher $10\%D_h$ capacity in very soft clay.
• The percentage contribution of shaft resistance the total capacity of screw piles ranges between 83% and 89% at pile settlement equal to ($10\%D_h$).
• The mobilization of shaft resistance in screw piles occurs in three distinct stages: Initial Stage: high shaft contribution (up to 95% of total load) at the onset of loading until settlement of approximately $1\%D_h$. Transitional Stage: a steep decrease in shaft percentage contribution as the load is progressively transferred to the pile toe. Final Stage: a plateau is observed at settlement of $10\%D_h$ where the toe reaches full mobilization.
• For screw piles in layered soil, the failure mechanism of the threaded shaft in the clay layer varies from IBM for $p/D_h=0.39–0.59$ to combined mode for $p/D_h>0.59$. In sand layer, and a transition between IBM to CSM at $p/D_h>0.52$.
• For screw piles in sand–clay layered profile, the failure mode is primarily a combined mode for very soft to stiff clays, transitioning to IBM in stiff-to-hard clays. For the sand layer, the failure mode is IBM for very soft to firm clays, transitioning to CSM in stiff and stiff-to-hard clays.
• The failure mechanism of screw piles in homogeneous soil is highly dependent on soil type; CSM is the dominant mode in sand layers, whereas IBM (characterized by a conical wedge formation) dominates in clay layers.
• The shaft resistance factors ($\beta$ for sand and $\alpha$ for clay) back-calculated from the shaft resistance vary greatly for different pile configurations and soil types. $\beta$ values of threaded shaft segment ranged from 0.86 to 1.97 in Study 1, and from 1.5 to 9.2 in Study 2, values of $\beta$ of driven straight-shaft piles in sand reported by Fellenius [36] ranged from 1 to less than 4 at similar depths (about 2.0 to 2.4 m). $\alpha$ values of threaded shaft segment ranged from 1.16 to 2.94 in Study 1 and from 2.3 to 2.6 in Study 2, which are notably higher than the values suggested by the Canadian Foundation Engineering Manual [35] for driven straight-shaft piles ranging from 0.4 for stiff-to-hard clays to 2.8 for very soft clays, for similar $S_u$ values used in this research.

Future Work

While this study evaluates the short-term monotonic axial compression and tension behavior of individual continuous helix screw piles, several areas remain open for future investigation. Future research should address: (1) the performance and degradation of pile-soil stiffness under cyclic and dynamic loading conditions; (2) the long-term creep behavior and settlement profiles of these deep foundations over extended operational lifespans; (3) the group pile behavior and efficiency factors for closely-spaced screw pile configurations in multi-layered soil profiles; and (4) Evaluation of the pile’s lateral resistance, bending moment distribution, and kinematic soil-structure interaction during seismic shaking.