Contribution to the forecast of horizontal displacements in continuous flight auger piles in granular soil profile

This article presents a series of propositions for the prediction of horizontal displacements for continuous flight auger piles in granular soil profiles through modifying the parameters A y and B y from the method proposed by Matlock and Reese (1961). Empirical proposals were also presented for calculating the horizontal soil reaction coefficient ( n h ) for granular soils. Data from ten horizontal static load tests, conducted in the city of Paulino Neves (State of Maranhão, Brazil) were used to develop and validate the propositions. The data regarding results of nine static load tests (PCH 1 to PCH 9) were used to develop the propositions, whereas results for PCH 10 and other data from other studies (Cases A and B) were used in the validation step. Modifying the parameters used in Matlock and Reese’s method resulted in convergent and coherent predictions for all the propositions assessed in this study. In addition, predictions made for piles used in the validation phase yielded results very congruent with experimental displacements.


Introduction
The prediction of horizontal displacements in piles is a topic that has been addressed in diverse ways by several authors. The most recent works have focused on numerical modeling (Abagnara, 2009;Faro, 2014;Abreu, 2014;Ballarin, 2016;Santos et al., 2016) that allows for more elaborate predictions. However, these tools usually demand more complex analyses and are performed at high computational costs.
The analytical methods (Miche, 1930;Hetenyi, 1946;Matlock and Reese, 1961) are simpler and have been used in studies like Guo and Lee (2011), who concluded that the equation proposed by Hetenyi (1964) is comparable to numerical approaches if Winkler's parameters are estimated using the load transfer factor described in his study. Del Pino Jr. (2003) and Albuquerque et al. (2019) obtained values for the horizontal coefficient of the soil using retro analysis, according to the method suggested by Matlock and Reese (1961). Zammataro (2007) showed that excluding the equation term that considers the distance between ground level and load application axis can influence the coefficient of horizontal soil reaction. Phanikanth et al. (2010) obtained new coefficients A y and B y for the equation proposed by Matlock and Reese (1960), whereas Silva (2017) verified that, for the This study presents a contribution to the prediction of horizontal displacements in piles, through modifying the parameters used in the method proposed by Matlock and Reese (1961), using the experimental results from horizontal static load tests as a reference, aiming at obtaining more convergent predictions.
To this end, the coefficients A y and B y and the relative pile-soil stiffness pa-rameter (T) from the equation proposed by Matlock and Reese (1961) were modified. Correlations were also proposed to obtain nh from the SPT N-values of sandy soils.

Materials e methods
In this study, horizontal static load tests were performed on ten continuous flight auger piles (workload of 30 kN), installed in the town of Paulino Neves, State of Maranhão, Brazil. The ten piles had 600 mm of diameter and their lengths varied from 16.96 to 28.08 m, as detailed in Table 1.
One percussion drilling (SP) was conducted where each pile was executed. Figure 1 shows the results for drilling SP 02, conducted in the vicinity of PCH 2, exhibiting subsurface layers, water level, and SPT N-values along soil depth.   HT 3 EI piles assessed in his work, the method suggested by Hetenyi (1964) resulted in more accurate predictions for the horizontal displacements than those proposed by Miche (1930) and Matlock and Reese (1961).
However, it is worth mentioning that results of the analytical analyses might be discordant with experimental values, both due to its more simplistic nature and for the fact that they can be influenced by variables that do not contemplate the particularities of each situation or analyzed scenario.
In order to estimate horizontal dis-placements (y o ), Matlock and Reese (1961) proposed the following expression, which encompasses the dimensionless constants A y and B y and variables H (horizontal load), M (moment applied to pile head), T (relative pile-soil stiffness), E (deformation modulus), and I (moment of inertia):  As shown in Figure 2, the SPT Nvalues varied between 1 and 7 up to a depth of 4 m, except for drilling SP 04, with a SPT N-value of 24 around 3 m below ground level. Between 5 m and 13 m in depth, the SPT N-values varied up to 32, and above 14 m in depth, the SPT N-values varied between 8 and 70.
The horizontal load tests were conducted following the recommendations of the Brazilian technical standard NBR 12131/2006 (Piles -Static load test -Method of test) for the rapid test. The loading was conducted in sixteen stages, each of them maintaining the load for 10 minutes, with the respective displacements being measured during each stage. At maximum load, displacements were measured at 10 min, 30 min, 60 min, 90 min, and 120 min. The used measurement system consisted of a hydraulic jack-pump set and two 0.01 mm precision gauges and a 5 cm stroke, installed on a metal beam at the same level of application of the loads. Two precision gauges were also used to check the stability of the reaction anchor system, which consisted of concrete blocks.
The unloading comprised five stages, with displacements being measured every 10 min, except for the last stage, where two measurements were made (at 30 min and 60 min). It is worth mentioning that in each stage, the load corresponded to 10% of the pile horizontal workload and in the unloading stages, to 32% of pile horizontal workload. Figure 3 illustrates the load test performed in loco.
As can be seen in Figure 1, the first layer was 2.35-m-thick, with fine-tomedium, gray sand, loose, with an average SPT N-value of 3. A water level was found at 0.35 m below ground level. The second layer was 9.47-m-thick (between the depths of 2.35 m and 11.82 m), with fine, gray silty-sand, loose to compact, with an average SPT N-value of 14. The third layer was a clayey-sand, gray in color, moderately compact to compact, from 11.82 m to 14.20 m below ground level, and average SPT N-value of 19. The fourth layer was a fine-to-medium sand, gray in color, compact to very compact, from 14.20 m to 28.10 m below ground level, and average SPT N-value of 36. Finally, the last layer was a gray silty-sand, loose to compact, from 28.10 m to 33.0 m below ground level, and average SPT N-value of 14.
In order to obtain coefficients A y and B y of Matlock and Reese's equation (Matlock and Reese, 1961) and the relative pile-soil stiffness parameter (T) for the propositions developed in this study which would be consistent with the horizontal load tests experimental values, the authors used the Least squares method and the Generalized reduced gradient (GRG) algorithm.
And to obtain the propositions for the correlation regarding parameter nh based on SPT N-values, a range of displacements was taken as a reference (from 0.59 mm to 1.53 mm), considering the largest displacements obtained in each load test. This was used to ob-tain nh values through retro-analysis. The mean SPT N-value was also considered for the superficial soil layer (soil depth between 0 m and 2 m), where the largest horizontal displacements usually occur. Then two equations that correlated the variables nh and SPT N-values were obtained through nonlinear regression, for the considered range of displacements.
In the validation step, data regarding piles PCH 10, HC1-A (from Araújo, 2013), called Case A, and PC1-DP and PC4-DP (from Del Pino Jr., 2017), called Case B, were used. Table 2 presents the characteristics of Case A and Case B piles. Figure  4 shows the soil profiles obtained through the percussion drilling for Cases A and B.  As can be seen in Figure 4, the soil in Case A (Figure 4a) consisted of a fine-to-coarse sand, moderately com-pact to compact, with SPT N-values ranging from 6 to 30. Soils in Case B (Figure 4b) were also predominantly sandy, except for one gravel layer, located between12 m to 13 m below ground level. Figure 5 shows the results for all horizontal load tests (Figure 5a) and also the results for the two piles that had the largest (PCH 3) and the small-est (PCH 8) residual displacements (Figure 5b).

Results and discussion (a) (b)
As shown in Figure 5, the displacements measured in the horizontal load tests varied between 0.24 mm and 0.48 mm for the pile workload (30 kN) and between 0.59 mm and 1.53 mm for the maximum test load. The smallest residual displacement occurred in PCH 8, which was zero, and the largest for PCH 3 (0.26 mm).
Since the curves in Figure 5 presented a linear behavior and the displacement levels were quite small, it is possible to state that no piles failed and that all of them were working in the elastic regime.
Using the Least squares method, the coefficients Ay and By were determined for all piles as 0.10 for A y and 0.65 for B y (R² = 0.78). This method was called Modified II. Method Modified I was developed by the authors and described in a different study but was not included in the analyses performed in this research. Figure 6 illustrates the comparison between displacements predicted using method Modified II (i.e., proposed coefficients Ay and By) and Cintra's method (Cintra, 1982) and experimentally measured displacements for piles PCH 1 and PCH 9. Cintra's method is considered by the authors to be the most complete method to estimate horizontal displacements under loads applied above the soil surface, this being the reason it was included among the methods assessed herein.
As seen in Figure 6, the percentage difference between the displacements predicted by method Modified II and those obtained experimentally for piles PCH 1 and PCH 9 consider-ing a pile workload of 30 kN was of 56% (~ 0 mm). These piles had the smallest and largest percentage differences obtained in this study. Predictions made using Cintra's method resulted in a percentage difference of 1,507% for PCH 1 and of 2,967% for PCH 9. Figure 7 shows the correlation obtained for n h for different soil types and Figure  8, for sandy soils exclusively.     As mentioned before, the authors used the data regarding the pile related to PCH 10 and the piles described in Table 2 in order to validate: (i) Proposition 1 (correlation nh versus SPT N-values for different types of soil); (ii) Proposition 2 (correlation nh versus SPT N-values for sandy soils only); (iii) Modified II method (for coefficients A y and B y ); and (iv) for the relative pile-soil stiffness parameter (T = 0.90). Results are displayed in Figures 9, 10 and 11. It is worth mentioning also that Proposition 2 showed an inconsistency for SPT N-values lower than two.
As mentioned before, the authors used the data regarding the pile related to PCH 10 and the piles described in Table 2 in order to validate: (i) Proposition 1 (correlation nh versus SPT N-values for different types of soil); (ii) Proposition 2 (correlation nh versus SPT N-values for sandy soils only); (iii) Modified II method (for coefficients A y and B y ); and (iv) for the relative pile-soil stiffness parameter (T = 0.90). Results are displayed in Figures 9, 10 and 11. It is worth mentioning also that Proposition 2 showed an inconsistency for SPT N-values lower than two. According to Figure 9, the proposition that provided the best predictions when compared to the experimental displacements for PCH 10 was the Modified II method, with a percentage difference of 38% (0.09 mm), considering a workload of 30 kN. Predictions made using Cintra's equation (Cintra, 1982) showed a percent-age difference was of 2,344%. All the other propositions in this study resulted in very consistent and coherent predictions when compared to the experimental results.
As seen in Figures 10 and 11, among the propositions presented in this study, the one providing the best convergence for Case A was that of T parameter (T = 0.90), with a percentage difference of 33% (0.63 mm) when compared to the experimental results for HC1-A pile under a load of 100 kN.
Regarding Case B, the proposition which resulted in the best convergence for PC1-DP pile was also the T parameter (T = 0.90), with a percentage difference of 12% (0.53 mm). As to PC4-DP pile, the best one was Proposition 1, with a percentage difference of 37% (0.96 mm), considering the load of 30 kN, which is the workload of the piles assessed in this research. It should be highlighted that all propositions here presented also had a particularly satisfactory performance for small horizontal displacements.
In this study, propositions were made to predict horizontal displacements based on modifications in (i) Matlock and Reese's equation (1961) -coefficients A y and B y -, (ii) relative pile-soil stiffness parameter (T), and (iii) horizontal reaction coefficient (n h ).
Analyzing the convergence of the results from the horizontal displacements in relation to pile diameter (y/D), the pre-   dictions for PCH 10 pile converged to a y/D of 0.1% and for HC1-A pile (Case A), to 0.6%. For the piles in Case B (PC1-DP and PC4-DP), the average y/D ratio found was 1.2%. Thus, it was verified that all the propositions presented herein were coher-ent with experimental values for small horizontal displacements as occurred in the analyzed dataset.