Introduction

Helical piles (also called screw or threaded piles) are formed by a central square or circular steel shaft to which one or more circular plates are attached in a helical shape [1]. Although, in principle, helical piles were used as anchors to withstand lifting loads, in recent decades, their application and use have increased, being widely used as a foundation solution in low compacted terrain, supporting lifting, compression, and lateral loads [2]. Its ease of installation using torque and downward pressure represents a significant advantage since it reduces the impact on neighboring structures, decreases installation times, and has greater capacity than perforated piles due to the helical plates increasing the piles' support area [3, 4].

The torque requirement for the installation of helical piles depends mainly on the ground conditions and the geometry of the pile [5]. The improvement in equipment to generate torsion allows the use of larger diameter helical piles in response to the increased design requirements, and its use is suitable for any project, from the foundation of light poles and wind turbines to the foundation of residential and commercial buildings [6]. The capacity can be analytically assessed by a failure of the individual helical plates or through cylindrical shear failure, which depends on the spacing between the plates [2, 7].

Considering the benefits of installing helical piles as foundation elements, different authors have researched the use, capacity, and mechanical behavior of these piles to resist axial loads in compression and traction in different soil types. Hence, numerous investigations have been undertaken to assess the capacity of helical piles, providing further solutions to various challenges encountered in geotechnical engineering.

The capacity of helical piles is usually determined experimentally from static load tests, which are often time-consuming and expensive. Therefore, it is increasingly common to propose high-deformation dynamic tests to determine the capacity of large-diameter helical piles. Sakr [8] evaluated the static capacity of helical piles, comparing the results of static load tests with the results of dynamic load tests, and determined the efficiency of using high-deformation dynamic tests. He concluded that dynamic load tests could be a helpful tool to assess the static capacity of helical piles, taking advantage of the speed with which the test can be performed.

Elkasabgy and El Naggar [9] carried out experimental tests of axial load for helical piles of different lengths in cohesive soils to determine the mechanism of load transfer and their ultimate capacity. They concluded that the ultimate capacity is affected by changing parameters such as diameter and number of helical plates. Other authors conducted similar experimental studies on different soil types. For instance, Fatnanta and Satibi [10] researched peat soils, while Tsuha et al. [11] conducted a parametric study in sandy soil.

Polishchuk and Maksimov [12] used helical piles in clay for experimental testing and numerical analysis using the MIDAS GTS NX program. They observed that a double-helix pile developed a cylindrical shear behavior and had a higher load-bearing capacity than a single-helix pile. Similarly, Salem and Hussein [2] conducted a parametric study using ADINA finite element software. Their results were verified based on an experimental study, which led to the modeling of different pile geometries, concluding that some parameters have a greater effect on the capacity of the pile than others.

Similarly, various studies conducted by Al-Baghdadi [13, 14] have investigated the behavior of helical piles as offshore foundations through physical small-scale tests, finite element analysis (FEA), and numerical analysis. These studies subjected the piles to lateral, vertical, and combined loading using PLAXIS 2D and 3D software while modifying parameters such as helical plate spacing and pile geometry.

Cerfontaine et al. [15] investigated the behavior of helical piles subjected to tension in sandy soils using finite element modeling (FEM); they developed PLAXIS 2D models to simulate the behavior of helical piles subjected to successive loading/unloading on the piles; and the results obtained from the modeling were compared with results from other tests; the authors proposed a numerical methodology to predict the load–displacement relationship in helical piles on sandy soils. Additionally, they determined the failure modes in this type of soil and the ultimate loads for different geometries used in the helical piles.

Alwalan and Naggar [16] propose a finite element analysis for helical piles subjected to high-deformation dynamic tests using PLAXIS; in this study, the influence of the number of helical plates was determined, as well as the spacing between helical plates, the weight of the hammer, and the drop height in the static capacity of helical piles.

Knappett et al. [17] conducted a parametric study on helical piles in sands to investigate their compressive behavior when used as foundations for offshore marine renewable energy (MRE) devices in deep waters. For the study, they used scaled experimental data with sands of varying densities to subsequently validate the obtained data through a PLAXIS 2D modeling, where they varied the helix spacing ratio (s/D) and the helix to shaft diameter ratio (D/Dshaft). After the study, the authors suggested failure mechanisms in these types of soils, correlations with the pile load capacity, and optimal parameters for designing helical piles.

Knappett et al. [18] presented simple procedures for finite element modeling (FEM) to estimate the load-settlement behavior of continuous helical displacement (CHD) piles in sands. The authors concluded that it is possible to estimate the load-settlement behavior of CHD piles using the proposed procedures in the research based on geotechnical data from the site. There is more research whose results obtained from finite element models conform to the results of experimental tests [19,20,21].

The finite element model calibrated from the results of experimental work has allowed an improved understanding of the behavior and capacity of helical piles under compression and tension loads. Based upon the above, this research seeks to carry out a parametric study into helical piles through calibrated numerical models to determine the influence of the number of helical plates, the diameter of the plates, and the spacing ratio on the compressive and tensile capacity of helical piles.

Materials and Methods

Site Investigation

This study considered the field test data from experimental research by Livneh and El Naggar [22] at the University of Western Ontario, London, who determined the soil composition of two sites by triaxial and SPT tests. The profiles obtained from the research suggested that the soils are composed of clayey and sandy silt layers. Both layers cover deep deposits of stiff clayey silt (site 1) or dense fine sand (site 2). The site's groundwater table elevation varied between 5.2 and 6.5 m below the ground surface. The soil is overconsolidated in both sites with high cohesion values.

The Mohr–Coulomb elastic–plastic model was used to approximate the behavior of the soil. This model is based on five input parameters: Young's modulus (E), Poisson's ratio (ν), friction angle (ϕ), dilation angle (ψ), and cohesion (C) [6].

With the soil characterized in the field, two boreholes were made using a hollow stem auger mounted on a platform, and an empirical correlation factor (KT) was used to generate the least possible disturbance in the soil surrounding the pile during the installation process. During the installation of the piles, the annular cavity created by the square shaft of the pile and the broad cross section of the forged socket of the coupling medium were filled with cement-based grout. After curing, the union between the grout and the square section allowed a composed circular section to be generated. The reaction piles were installed at a distance of 2.7 m from the test piles, at approximately the same depth as the test pile, to anchor the test frame effectively.

At site 1, a pile under tension with a total length of 5.5 m was installed, while at site 2, the pile under compression with a length of 4.5 m was located. The soil parameters are shown in Tables 1 and 2, while the helical pile's parameters are shown in Table 3.

Table 1 Soil properties of the site 1
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Table 2 Soil properties of the site 2
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Table 3 Properties of the helical pile
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Model Development

The PLAXIS 2D finite element software was used to model the piles, which makes it possible to perform stress deformation analysis and predict the behavior of piles subjected to static and dynamic axial loads [16, 23].

The study focused on the behavior of the helical piles in regard with varying parameters such as the number of helical plates, plate diameter, and plate spacing for a set of load cases based on the allowable load of the numerical model; considering the symmetry of the pile and the helical plates, the axisymmetric model of PLAXIS was used for its appropriateness to circular foundations with radial cross section, in addition to being the most often used for the modeling of piles [24,25,26]. In the axisymmetric model, the x-axis is used as the radius, while the z-axis is the symmetric axis of the ground, as shown in Fig. 1. Triangular elements of 15 nodes were used to provide highly accurate; this choice was based on the need to achieve a high level of precision in representing the behavior of the pile and its helical plates.

Fig. 1
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Axisymmetric model of finite elements. Taken from [23]

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In order to avoid any mechanical interference resulting from the limitations of the numerical model, the impact of the model boundaries on the stress–strain curve of the pile was evaluated. The model's horizontal limit was considered 1.5 times the total length of the pile, while the lower limit was set at a depth of 2.5 times the total length of the pile (1.5 L * 2.5 L). These values are greater than the minimums (L * 2 L) recommended by Alwalan and El Naggar [16]. The lateral boundaries allow vertical displacements and restrict horizontal displacements and rotations, while the lower boundary restricts all displacements and rotations. Figure 2 shows the layers that are part of the model's geometry, whose parameters are detailed later. The mesh of the FEM is refined in the area near the pile to increase the accuracy of the load and displacement results obtained. Zone 3 has a coarse refinement, while in zone 2, a medium refinement is used, and in zone 1, a fine refinement is used, considering that it is around the pile.

Fig. 2
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Case model. Case 1 model: a helical pile and soil–pile interface, b model geometry, and c generated mesh. Case 2 model: a helical pile and soil–pile interface, b model geometry, and c generated mesh

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A linear elastic model was utilized for the helical pile, which only requires two parameters for elastic stiffness: Young’s modulus (E) and Poisson's ratio (ν). The interaction between the soil and the pile was simulated by constructing the interface between the pile shaft, the helical plates of the pile, and the soil. PLAXIS employs a reduction factor for interface resistance \(\left({R}_{{\text{inter}}}\right)\) to control small displacements (elastic behavior) and permanent sliding (plastic behavior) within the interface. The parameters, such as the interface's shear strength or the roughness of the interface between the soil and the pile, are controlled by the \(\left({R}_{{\text{inter}}}\right)\) value used in the model. The \(\left({R}_{{\text{inter}}}\right)\) value used for the current analysis was 0.70 [23].

Geometry and Parameters of the Model

The FEM was carried out on a full scale, adopting almost all the geometry of the pile model by Livneh and El Naggar [22], as shown in Fig. 3. Only three aspects of the pile geometry changed in the FEM relative to the experimental model: Since it is an axisymmetric model, it is not possible to consider a central axis with a square cross-section, so the central shaft of the pile was considered to be a circular cross-section with a diameter of 44.5 mm. On the other hand, the helical plates were modeled as circular discs and not as inclined plates. In addition, the pile tip was taken as flat and not beveled as in the experimental model. The number of helical plates, diameter, and spacing were kept equal to the experimental model. A pile subjected to compression with a total length of 4.5 m and a pile of 5.5 m subjected to tension was modeled.

Fig. 3
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Geometry of the experimental model pile and the PLAXIS model pile

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Ultimate Capacity of the Pile

Experimental load tests, and in particular the FEM, do not always explicitly show the maximum capacity of a pile, so it is necessary to estimate the ultimate capacity from the load–displacement curve that describes the behavior of the pile.

The load–displacement curve obtained from the FEM can be divided into three distinct zones as shown in Fig. 4: (1) the initial linear zone ending in Li has an elastic behavior with pronounced slope, (2) the nonlinear transition zone between Li and Lf where the shift is considered disproportionate to the load increase, and finally, (3) the final linear zone where the slope is not so steep, which indicates little rigidity, and where greater displacements for small increments of load can be found.

Fig. 4
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Geometry of the experimental model pile and the PLAXIS model pile

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Considering that a pile reaches its maximum capacity when large displacements occur in small increments, Elkasabgy and El Naggar [9] establish that the ultimate capacity of a pile is in the non-linear transition zone before the start of the final linear zone.

Other studies determine the maximum capacity of a helical pile considering its geometry (Table 4) and the shape of the load–displacement curve. Most authors agree that the diameter of helical plates is the characteristic dimension of helical piles, so the maximum displacement criterion before failure is given by the diameter of the helical plate (D) and the elastic deflection of the pile.

Table 4 Configuration of helical piles to analyze the effect of the number of helical plates
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In this study, the fault criterion of Elkasabgy and El Naggar [9] was adopted, considering that it was developed for helical piles with geometry like that of the FEM, and in addition, the ultimate load is in the non-linear transition zone. The ultimate pile load is set as the load needed to generate a total displacement in the pile head equal to 3.5% of the diameter of the largest helical plate plus the elastic deformation of the pile. When determining the displacements at the tip, the criterion does not require considering the elastic deformation of the pile.

Validation of Modeling

The calibration of the numerical models consisted of comparing the load–displacement curves obtained in the experimental tests with the curves produced in the numerical models; the soil parameters were defined according to the results of the field and laboratory tests carried out by Livneh and El Naggar [22] at the University of Western Ontario.

The performance of the models was evaluated through a statistical procedure of relative error between two groups of data, which correspond to the mean magnitude of the relative error (MMRE) of data from the numerical model with respect to the data from the experimental test, which is expressed in the following equation:

$${\text{MMRE}}=\frac{1}{n}*\sum_{i=1}^{i=n}\left(\frac{\left|{x}_{i}-{x}_{i}^{*}\right|}{{x}_{i}}\right)$$
(1)

where xi is the experimental value for data i, \(x_{i}^{*}\) is the model value for each data i, and n is the total number of data.

Values closer to zero indicate a better fit. However, a model can be considered sufficiently accurate for most purposes when the value of the MMRE parameter is less than 0.25 [27].

Case 1: Pile Tested in Tension at Site 1

The pile at site 1 was tested in tension according to the experimental study and had a total length of approximately 5.5 m. The load–displacement curve of the FEM has a behavior similar to the curve of the experimental model (Fig. 5). Initially, the modeled soil has greater resistance than the real soil due largely to the high elasticity moduli established. However, after deforming 13 mm, it begins to behave identically to the real ground of site 1.

Fig. 5
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Load–displacement values of the experimental model and FEM pile tested in site 1

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Statistically, the MMRE result is 0.24, obtaining an MMRE value less than 0.25 for the model, which is considered sufficiently precise, and therefore, its use is justified. Considering that the curves present a good relationship according to the MMRE criterion, it is determined that the FEM for site 1 satisfactorily describes the real behavior of the soil.

Case 2: Pile Tested in Compression at Site 2

The helical main plate of the pile is located at a depth of three meters, with approximately 4.5 m of total length. Figure 6 shows that the load–displacement curve of the FEM with the parameters of site 2 coincides with the curve of the results of the experimental model.

Fig. 6
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Load–displacement values of the experimental model and FEM of pile tested in site 2

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Statistically, the MMRE result is 0.11, obtaining an MMRE value less than 0.25 for the model, which is considered sufficiently precise, and therefore, its use is justified. The statistical validation of the load–displacement curves indicates that the numerical model allows the correct description of the compressive behavior of the soil at site 2.

Parametric Analysis

Calibrated FEM was used to perform a parametric study where the properties of the materials were preserved while the geometry of the pile was changed in order to investigate the effect that different parameters have on the compression and tension capacity of helical piles.

The parametric study was carried out by developing 12 models of the pile under tension and 12 models of the pile under compression. To determine the effect of the number of helical plates on the pile's tensile and compression capacity, piles with 1, 2, 3, and 4 helical plates were considered. The diameter (Di) of the first helical plate of the calibrated model was used for the single-helix pile, that is, 200 mm; the diameter of the other helix is a function of the initial diameter, increasing by a factor of 0.25Di as the number of helical plates in the pile increases. Table 4 summarizes the variations made.

To assess the effect of the diameter of the helices on the behavior of helical piles, a pile with three plates of ascending diameter was considered according to the calibrated model, and the diameters of the helices were varied. The diameter of the helical plates was established as a function of the ratio D/Di, where D is the diameter of each helical plate and Di is the diameter of the first helical plate of the experimental model pile (200 mm). Table 5 summarizes the variations made to consider the effect of diameter.

Table 5 Configuration of helical piles for diameter effect analysis
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The effect of helical plate spacing was analyzed from four models of helical piles with spacing (s/D) equal to 2.5, 3, 3.5, and 4 where s is the spacing and D is the diameter of the lower helical plate. Table 6 shows the synthesis of the pile’s variations with three helical plates.

Table 6 Configuration of helical piles for the analysis of the effect of spacing
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Results and Discussion

Effect of the Number of Helical Plates on Load Capacity

The results obtained in the compress and tensile models show that the pile's capacity increases proportionally with the number of helical plates, as shown in Fig. 7. The final loads obtained for the pile subjected to compression (Fig. 7b) are approximately 99 kN, 168 kN, 267 kN, and 360 kN, with the largest capacity being that of the pile with four helical plates. The two-helix pile increased its capacity by 69% compared to the single-helix pile, while the three-helix pile increased its capacity by 58%. By increasing the number of helical plates to four, a capacity increase of 34% was obtained. Similarly, for the pile subjected to tension (Fig. 7a), the final loads are approximately 64 kN, 92 kN, 156 kN, and 240 kN, where the two-helix pile increased its capacity 43% compared to the single-helix pile; when using three helical plates, the capacity increased 69%, and increasing the number of helical plates to four resulted in a 53% capacity increase, suggesting that the capacity increases as the number of helical plates increases, similar to what was found by Rawat and Gupta [23].

Fig. 7
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Load–displacement curves from FEM for helical piles with different number of plates: a tension and b compression

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These results are consistent with those obtained by Elkasabgy and El Naggar [9], who reported that installing a single helical plate increases the capacity of a pile by 18% compared to a driven pile with the same characteristics. Salem and Hussein [2] determined that the number of helical plates is the most effective parameter for increasing pile capacity; their research concluded that increasing the number of helices from 2 to 5 resulted in an almost 86% increase in the tensile capacity of the helical pile, similar to the results obtained in this investigation. Consequently, increasing the number of helical plates enhances the extraction capacity of the piles. Not only does it increase the support area, but it also compacts the soil between the helical plates, thereby raising the angle of internal friction and subsequently improving the bearing capacity.

On the other hand, contrary to the findings of the present parametric study, research by Nabizadeh and Choobbasti [7] suggests that an increase in the number of helical plates leads to greater soil disturbance, negatively impacting the performance of helical piles. They concluded that the performance of three-helix piles is inadequate compared to double-helix piles. Similarly, the study conducted by Sharif et al. [28] supports the investigation of soil disturbance caused by helical pile installation using the discrete element method (DEM).

Effect of Helical Plate Diameter on Load Capacity

Maintaining three helical plates and a constant spacing between plates, the change in diameter generated changes in the extraction and compression capacity of the helical pile. Figure 8a, b shows an increase in the ultimate pile capacity as a function of the increase in diameter. Considering the criterion of failure of the pile to extraction (Fig. 8a), it is observed that it increased its capacity by approximately 28% when it increased its diameter from 0.75D to 1D while increasing its capacity from 1D to 1.25D by 24%. Similarly, Fig. 8b shows that the capacity of the pile subjected to compression increased when the diameter of the helical plates was increased; thus, the capacity was 205kN in the pile with plates of diameter 0.75D and increased 28% in the pile with plates of diameter 1D, while increasing 27% for the pile with plates of diameter 1.25D. The results indicate that the capacity of the piles subjected to extraction and compression increases with the increase in the diameter of their helical plates.

Fig. 8
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Load–displacement curves from FEM for helical piles with different diameters: a tension and b compression

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The results show a behavior similar to Rawat and Gupta's [23], indicating that the capacity of piles subjected to extraction and compression increases with the diameter of their helical plates. This increase in pile capacity was expected, considering that increasing the diameter of the plates directly increases the bearing area, introducing friction between the pile and the soil.

Effect of Spacing Between Helical Plates on Load Capacity

Figure 9a, b shows the change in the pile capacity for extraction and compression, respectively; while the other parameters remained constant, the spacing between helical plates was modified for a three-helix pile depending on s/D. The results allow us to determine in both cases that a spacing ratio s/D < 3 significantly decreases the capacity of the helical pile, and in turn, a spacing ratio s/D > 3 does not represent a significant increase in capacity; therefore, the conventional use of a s/D = 3 spacing ratio is successful, finding a behavior similar to that reported by authors such as Salem and Hussein [2], Knappett et al. [17], and Cerfontaine et al. [15]; they established that with a spacing ratio (s/D) greater than 3, it only shows a slight increase in helical pile capacity.

Fig. 9
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Load–displacement curves from FEM for helical piles with different spacing between plates: a tension and b compression

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The smaller the spacing ratio, the closer the failure behavior to that of a single-helix pile, with which its capacity decreases, explained because modifying the spacing ratio changes the type of failure generated in the ground. The failure mechanism of the piles subjected to extraction and compression according to their spacing ratio determined in the FEM is shown in Figs. 10 and 11, respectively. It was determined that a cylindrical shear failure is generated with a s/D  < 3 spacing ratio, while with a s/D  ≥ 3 spacing ratio, the generated failure is from individual plates. Also, the size of the failure surface according to the diameter of each helical plate is given in the figures; this indicates that the type of failure of a helical pile is largely due to the spacing between the plates and their respective diameters.

Fig. 10
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Failure mechanism for the helical piles from FEM. Pile under tension

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Fig. 11
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Failure mechanism for the helical piles from FEM. Pile under compression

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The type of failure and behavior of the helical pile depend on the helices' diameter and depth (H/D). In other words, the upper helix of the pile exhibited a superficial failure by forming an uplift wedge from the pile's helix to the ground surface (Fig. 10). On the other hand, the lower helix with a H/D ratio greater than 7 suggested a deep failure (Fig. 11), displaying a behavior similar to that reported by Cerfontaine [15].

Conclusions

  • The FEM carried out does not allow an explicit determination of the moment of failure and, therefore, is essential to adopt an adequate fault criterion to the ultimate capacity of helical piles according to the type of soil, the geometry of the piles, and the behavior of the load–displacement curve.

  • Increasing the number of helical plates, in effect, represents an increase in the ultimate capacity of the pile for extraction and compression. However, it should be noted that the increase in the number of helical plates implies an increase in the torque needed to install the piles.

  • The capacity of helical piles increases between 24 and 28% by increasing 0.25D the diameter of their helical plates; this increase in capacity is because the area that supports the load is also increased.

  • The type of failure generated depends directly on the spacing between the helical plates; thus, a s/D  < 3 spacing ratio develops a cylindrical shear failure, while a s/D  ≥ 3 spacing ratio generates a failure of individual plates; because of this, the use of a s/D = 3 spacing ratios is ideal, since a greater spacing does not represent significant increases in the capacity of the pile. On the other hand, cylindrical shear failure decreases the ultimate capacity of the pile to extraction and understanding, this loss occurs due to a decrease in the length of the failure surface.

  • The validation of the FEM results of the two case studies allowed a parametric analysis of models that represent the real behavior of helical piles installed on site; in turn, these results allowed us to generate practical recommendations for the implementation of helical piles. It is recommended to implement a propeller separation ratio s/D = 3; it is recommended to implement helical piles with the greatest number of helices possible according to the torque available for the installation, and it was determined that increasing the diameter of the helical plates increases the compression and tension capacity of the pile.

Recommendations

  • The geometry of a single-helix pile significantly affects its post-installation capacity; therefore, a discrete element modeling (DEM) study, following the approach of Sharif et al. [28], is suggested to investigate the soil–pile interaction based on the geometry.