3.1. Experimental Results
Figure 7 displays the results of the previously conducted experiments. In
Figure 7a, the load-displacement curves can typically be simplified into three distinct regions: initial linear (zone I), transition (zone II), and final linear (zone III), according to Kulhawy [
43]. Even if all the deformations remain in the elastic zone, the pile bearing capacity remains in the initial linear zone and other zones match the pile failure.
In compression tests, the type 1 pile helix exhibits the least favorable performance due to its greater displacement of up to 38 mm at 14.5 Tn. However, the other piles show comparable displacements, ranging from 12 to 10.8 mm. A decrease in displacement is observed as the number of helices increases. The analysis of pile types 3 and 4, each consisting of three helices, reveals that the layout of spirals along the pile has a role. An equidistant distribution (type 3) produces smaller displacements (10.8 mm) than a non-homogeneous distribution (type 4) with a higher displacement value (11.1 mm). In the case of the present study, only industrial helical piles are considered, where the helix and the shaft are made of the same type of steel and of similar thickness—a configuration relatively easy to reproduce using industrial tools.
In the case of pile type 1, the displacement is still small (2 mm) until reaching a force of 8.5 Tn. Beyond this threshold, there is a noticeable linear increase in displacement. However, for the rest of the piles, the critical force at which the minimal displacement occurs is around 10 Tn.
Regarding lateral (or shear) tests, the outcomes exhibit comparable curves. Nevertheless, pile type 1 shows a substantial displacement with minimal initial force. The rest of the piles exhibit perfect resistance up to 3 Tn. The one-helical pile (type 1) presents a higher maximum displacement of 63 mm compared to the 18 mm reached in the two-helices pile (type 2), the 14.4 mm of the irregular three-helices pile (Type 4), and the 13.5 mm obtained in the homogeneously dispersed three-helices pile (Type 3). Regarding the compression test, the piles show reduced resistance under lateral loading conditions, indicating that the loads required for the same arbitrary displacement value are lower than in the shear test for the same pile type.
3.2. Numerical Results
Using the UC3MLib software, curves practically equal to the experimental ones are obtained with errors of 0.1–0.4 mm for the compression test and 0.1–0.75 mm for the lateral load test. These values are adequate compared to pile dimensions and displacement, therefore the model is suitable for helical pile computations. Note that numerical results are not graphically represented because it is invaluable to see the graphical difference. Therefore, a differential displacement plot between the experimental and numerical results is plotted in
Figure 8.
Additionally, the average error is still consistent across various pile types, indicating that it is independent of pile geometry. In lateral cases, the distribution of average error exhibits greater variability compared to axial compression load. Furthermore, the average error, ranging from 0.34 to 0.29 mm, reduces as the load increases. On the other hand, the error distribution is scattered and somehow depends on the pile geometry. The error is smaller and distributed more regularly for piles with multiple helices.
The following interpretation can be derived: the total displacement is composed of pile bending and soil deformation for high loads. Under conditions where the load is relatively low (namely, within the elastic domain of the pile or near the plasticity threshold), the only deformation is due to the soil. With increasing load, the total deformation is composed almost entirely of pile shaft bending, and the soil displacement stays almost linear. This means that the error between the test data and simulation decreases.
In
Figure 8c,d, a high correlation between experimental and numerical data is obtained with R-squared values of R
2 = 1 (Type 1), R
2 (Type 2) = 0.9995, R
2 = 0.9995 (Type 3), and R
2 = 0.9991 (Type 4) for the compression tests. For the lateral tests, an R-squared value of R
2 = 0.9999 (Type 1), R
2 = 0.9994 (Type 2), R
2 = 0.9996 (Type 3), and R
2 = 0.9992 (Type 4) are obtained. With these values obtained, it is proved that the RBF method developed is a helpful tool for predicting the piles’ vertical and lateral displacement.
Once the numerical model has been developed using the RBF method and validated with the experimental results, it is used to investigate the effect of the number of helices and their spacing.
Based on the findings from both experimental and numerical analyses, including extra helices in a pile does not significantly enhance its bearing capacity. The increase in capacity is approximately 40% when comparing piles with one and two helices and an average of 10% when comparing piles with two and three helices. However, considering the considerable costs associated with manufacturing and installing piles with additional helices, to obtain a considerable gain in vertical bearing capacity of a helical pile under an axial load, adding a second helix for a 50% vertical bearing capacity increase and two extra equally spaced helices for a gain of 40% of horizontal bearing capacity is a reasonable compromise.
Our results differ from the conclusions of Shao et al. [
5]. They numerically analyzed the influence of the helices spacing on the bearing capacity of the pile in sandy soils. However, we conducted a numerical simulation of a pile with four and five helices, depicted in
Figure 9, which yielded the following results compared to the pile with double helices.
The numerical results of the force-displacement curve comparison from one to five helices are shown in
Figure 10. For piles with two or more helices, it is shown that the increase in bearing capacity is quite negligible. Therefore, it can be concluded that selecting three helices for a six-meter pile in sand strikes an acceptable compromise between achieving optimal bearing capacity and minimizing manufacturing expenses.
The behavior of the pile, when more than three helices are included, can be attributed to two factors: the destabilization of the ground due to its non-homogeneity on one side, and the three possible states that a loaded pile can be in.
In the initial stage of small loads, most of the load is supported by the lateral section of the pile shaft through pure friction. In the second state, there is a buildup of non-reversible shear deformations. The frictional resistance on the sides of the pile decreases to its lowest values, particularly for weak soil layers. Additionally, there is a redistribution of forces from the main body of the pile to its base. In the third stage, when the loads are close to their maximum, the primary source of the pile’s work is the soil resistance near the pile’s tip.
Only the initial stages of pile work are affected by helices positioned on the upper portion of the pile.
As previously mentioned, the force-displacement plots can be divided into three regions: initial linear (zone I), transition (zone II), and final linear (zone III), according to Kulhawy [
43]. An analysis has been performed to obtain the regression line of zone 3 (
) to analyze the influence of the number of helices.
Table 11 shows the linear regression curves.
It seems that parameter “a” has an increasing tendency with the number of helices. However, the most significant parameter is given for the number of helices equal to two. This leads to more tests to verify the influence of the number of helices on the linear part of the F-d curve.
Four different distributions are generated to examine the impact of the spacing between helices, focusing on the piles of two and three helices for compression and shear loads. The distributions of each setup are presented in
Table 12.
Figure 11 shows the results of the analysis of the influence of the helices spacing. In the case of two-helices piles shown in
Figure 11a, the bearing capacity decreases slightly with the decreasing helix spacing. However, these changes are negligible since the helices remain on the same horizon.
In the case of three-helical piles in compression, the bearing capacity of the pile increases while the spaces between helices become larger according to Shao et al. [
38] (
Figure 11b). For shorter helices spacing (test 3), the displacement increases (12 mm in the case of test 3). However, for the initial disposition, the displacement is slightly lower (10.7 mm).
Figure 11c,d shows the piles’ lateral bearing capacity results. Similar conclusions are obtained in the case of the application of shear loads. Getting helices closer to each other reduces the bearing capacity of the pile, however, fewer displacements are obtained with a double helix than a triple helix pile for the same load.
Some general considerations drawn from the results are that the pile with several helices works as a ground drill, mostly in non-homogeneous soils. The drill’s rotation destroys natural connections in the ground, decreasing the Winkler stiffness and subsequently reducing its bearing capacity. Nevertheless, if more than one helix is added, the contact area between the pile and the ground increases and the pile becomes embedded in the anchoring horizon (patella-type for a single helix, embedding for a multi-helix pile).
Enlarging the space between helices does not damage the soil during installation and does not cause interference between ground components contained between the helices.
The optimal relationship between the pile bearing capacity and the manufacturing cost, as well as the optimized necessary installation torque, leads us to determine the most efficient configuration of the pile.