Performance Analysis of Axially Loaded Secant Pile Wall Embedded in Sand: An Experimental Investigation

Table 1 lists the geotechnical characteristics of the sand used in this study (average of three tests). According to the Unified Soil Classification System (USCS), the sand utilized in this study is poorly graded (SP). The jar method was employed to identify the specific gravity of the sand particles. Three tests were carried out. Dry sieving analysis in accordance with ASTM [67] was utilized to obtain the particle size distribution. A direct shear test was utilized to measure the internal friction angle of the used sand for the cases of maximum and minimum densities as well as various relative densities.

Additionally, the ratio between the suggested pile diameter (D_p) and the sand median size (D₅₀) must not be less than 45 in order to eliminate the impact of grain size distribution on the pile-soil interaction [68]. Franke and Muth [69] recommended that the ratio be at least 30D_p for the exact modeling of the sand-pile interaction. While Taylor [70] recommended that the ratio of D_p/D₅₀ must be at least 100D_p. As a result, the scaling law condition is met in this research study because the ratio of D_p/D₅₀ is approximately 146.34.

The geometrical features of the used prototype for modeling were widespread secant pile walls with a diameter of 600 mm, an overlapping width of 120 mm, and a length of 15,000 mm, as proposed by El-Nimr et al. [62]. According to the test conditions and the profitability of the test operation, the dimensions of the model were reduced by 1/10. The Buckingham theory was used to obtain the similarity ratios between physical variables [71, 72]. As a result, the length, diameter, and overlapping width of the model piles should be 1500, 60, and 12 mm, respectively. Also, the width of the wall was taken as 300 mm. The test model's similarity law and similarity constants are displayed in Table 2. For steel configuration, a stirrup bar with a diameter of 4 mm was spaced 100 mm apart, and four longitudinal threaded rods with a diameter of 6 mm were also utilized. Figure 1a shows the cross-section dimension of the SPW model. The components of the concrete mixture and the material characteristics were acquired from El-Nimr et al. [62].

For controlling the quality of the concrete pouring, all test samples were made in a cylindrical metal mold made of demountable curved metal strips (8 mm thick) linked by screw bolts (Fig. 1b).

To choose the tank dimension, Rankine's earth pressure theory was utilized, and the effect zone for the piled wall was computed. The net dimensions of the soil tank were chosen to reduce the excavation's boundary effects and to fulfill the settlement influence zone. According to El-Nimr et al. [16], and Leung and Ng [37], the influence area (D_o) extended to an average distance of 2.5H_c behind the wall. In addition to achieving the above, the tank should be as small as possible to facilitate its use. Considering the previous, the soil tank was a rectangular steel tank of interior dimensions 3300 × 300 mm, with a 2100 mm depth (all dimensions have a tolerance of not more than + 1%). The distance between the wall toe and the tank base was not less than 500 mm (> 8D_pile). As a result, the dimensions of the soil tank were adequate to reduce the impacts of the boundary conditions on the SPW's performance and the settlement influence area. In order to avoid any lateral deformation, 10-mm-thick steel plates and 110 × 80 × 6.0 mm horizontal steel hollow sections were utilized to stiffen the sides of the soil tank. Additionally, to enhance the tank's rigidity, vertical steel ribs (I.P.N.) were placed on the sidewalls. The soil tank was sitting on a rigid steel base which horizontally oriented on the ground of the laboratory. The test setup was leveled vertically and horizontally using a spirit level. For easy filling and emptying of the soil tank, two sides of the tank were made with opening and closing features. Also, one side of the tank was made of transparent tempered glass 20 mm thick to visually monitor the movement of the soil and the wall. The soil tank is shown in Fig. 2.

Before applying the surcharge load, the sand in the tank is left for 24 h after filling the tank. Then the surcharge load is applied using three calibrated pneumatic pistons. The utilized pneumatic pistons have a bore size of 50 mm, a movement tolerance of 50 mm, and a pressure range of 0.1–0.9 MPa (1.0–9.0 bar). Medium-pressure air compressor (Fig. 2) which has an outlet pressure of 1.04 MPa (10.40 bar) is used to feed three pneumatic pistons. Each loading point (piston) is converted into two points by a metal frame, each end of which rests on a metal plate with dimensions 300 × 160x20 mm. It should be mentioned that the sand was gradually dug at 125 mm layers to reach the needed excavation depth (H_c) only after the observed data were essentially steady (generally, there was a minimum 2-h wait). Then, using a calibrated hand-controlled loading mechanism (Hydraulic manual pump SPX 700 bar and hydraulic cylinder piston with axial capacity 258 KN), the vertical centric load was applied (Fig. 2). Each increment was maintained until there was no noticeable change in the SPW deformations (i.e., for 3 readings under the same load, the change between two consecutive readings should be less than 0.01 mm every 5 min). The corresponding SPW's lateral deflection and vertical ground movement behind it were measured using dial gauges. No rotation was permitted during these loading tests, and any variations in the vertical or horizontal dial gauge readings were rejected.

To monitor the strain response of the SPW, five couples of strain gauges were glued on the front and back surfaces of the tested wall with their axes parallel to the SPW length (Fig. 3). Strain gauges were placed at the mid-reinforced pile of the SPW. The utilized strain gauges had 120 ± 0.5 ohms resistance, a gauge factor of 2.1, and a gauge length of 60 mm.

Each strain gauge was connected to UCAM-550A strain data logger instrument to collect the deformation of samples (Fig. 4a). In the process of measuring, strain reading may be affected by temperature, and relative humidity (RH) data recorder was used to monitor the temperature and RH (Fig. 4b). The measured temperature during the tests ranged from 27.1° to 28.9°, while the RH values were between 39.5% and 46.9%. Additionally, two horizontal digital dial gauges with a measuring range of 50 mm and an accuracy of 0.01 mm were utilized to monitor the lateral deflections of the SPW head. Also, one vertical dial gauge with a measuring range of 100 mm (accuracy of 0.01 mm) was employed to detect the wall's vertical settlement (Fig. 5a). Furthermore, five vertical digital dial gauges at least with a measuring range of 50 mm (accuracy of 0.01 mm) were employed to monitor the soil surface settlements behind the SPW (Fig. 5b).

Currently, laser scanning technologies are being employed for both monitoring and obtaining three-dimensional geometry [73, 74]. Laser scanning could significantly minimize field time and accuracy errors related to field measurement surveys [75]. Laser scanning was also used to assess the overall performance of the retaining structure [73]. Consequently, the Topcon terrestrial laser scanner (GLS-2000 3D) was employed to monitor the wall movement as well as the soil through the tank's transparent glass face. The scanning distance is up to 350 m, and the accuracy is 2 mm/150 m [75]. Fixed points are made along the length of the SPW, and the locations of these points are monitored using the Topcon Laser Scanner (TLS) device at intervals. The obtained data from TLS scans were handled and processed using the MAGNET COLLAGE Program (Copyright Topcon 2021). This software can process TLS data and accurately detect deformations [75, 76]. One observation is obtained for each excavation stage in addition to the four that are taken during axial loading (at 0.25 P_ult, 0.50 P_ult, 0.75 P_ult, and 1.0 P_ult).

In this research, the performance of axially loaded secant pile walls in medium and dense sand was studied. Several factors were considered, including normalized lateral deflection (δ_h/H_t%), the vertical deflection of the wall (δ_vw/H_t%), vertical ground settlement (δ_v/H_t%), and settlement influence zone (D_o). These factors were investigated under the influence of a set of parameters including normalized penetration depth (H_e/H_c), sand relative density (D_r), and surcharge load density (W_sur), as explained below. Figure 6 shows the model test setup and parameters. The testing program and variables that were investigated are shown in Table 3. Table 3 indicates that the excavation depth of the sand (H_c) ranges from 250 to 750 mm.

To guarantee that sand was formed uniformly, with an accuracy of 0.001 kN, a predetermined weight of sand was compacted into a specific volume of the soil tank to achieve the target relative density and a specific depth [4, 77]. After conducting a test, the sand's relative density was validated by gathering samples in small metal tins with specified volumes which were put at various points in the soil tank before the test [78, 79]. In the soil tank, a bed of stratified sand was created, with each layer 100 mm thick. Using a sharpened straight steel plate, the compacted sand was leveled. After that, on the top surface of the compacted bed layer (at a height of 500 mm), a spirit level was used to ensure that the SPW was vertical on the bed layer and perpendicular to the tank's sides. The desired height (at a height of 1500 mm above the bed layer) on both sides of the SPW was then achieved by adding sand in the way previously mentioned. The desired excavation depth was then progressively achieved by excavating the soil in front of the SPW at 250 mm levels (H_c). In each excavation phase, the vertical ground movement and the lateral wall deflection were measured concurrently. Also, Fig. 7 shows some images from the working process of the model testing.

As depicted in Fig. 8, the wall deflected as a cantilever element in conjunction with the various excavation phases and before applying the axial load. Figure 8 shows the excavation-induced lateral and vertical movement profiles at different phases of excavation. The surcharge load, in this case, was W_sur = 8.0 kN/m². As seen in Fig. 8, the maximum lateral deflection at the SPW head (δ_ih-max) is around (0.2–0.78%) H_c, and also grows approximately linearly with excavation depth. The pile head experienced the maximum value of lateral deflection, while the SPW toe did not move since the penetration depth was adequate for the wall stability. The obtained lateral profiles agreed well with the suggested lateral wall deformation profiles suggested by Clough and O'Rourke [20]. Also, settlements can be presented by a trilinear settlement profile. The observed settlement profiles and the suggested Spandrel Settlement Profile (SSP) suggested by Ou et al. [29] were consistent. The maximum vertical settlement value behind the wall was observed quite near the SPW head.

Figure 9 shows the normalized lateral deflection (δ_h/H_c%) as well as the vertical ground settlement (δ_v/H_c%) of the secant pile wall with respect to normalized penetration depth (H_e/H_c) at various sand densities. For all applied surcharge intensities, an increment in penetration depth ratio (H_e/H_c) resulted in a substantial reduction in the lateral deflection of the SPW. Also, in the range of H_e/H_c > 2.0, there was insignificant variation in the normalized maximum lateral deflection (δ_ih-max/H_c%) for all sand densities. As shown in Fig. 9, the growth rate of lateral and vertical movements increased significantly with raising the value of the applied surcharge load at the same normalized penetration depth (H_e/H_c), especially at the ratio of H_e/H_c = 1.0. In general, the normalized maximum horizontal deflection (δ_ih-max/H_c%) at surcharge load of W_sur = 12.0 kN/m² was found to be δ_h-max/H_c% = 0.25, 0.48, and 1.28% for the normalized penetration depth of H_e/H_c = 5.0, 2.0, and 1.0, respectively. These ratios were found to be δ_ih-max/H_c% = 0.20, 0.1, and 0.81% at W_sur = 8.0 kN/m². These ratios also reduced to minimal values when W_sur = 4.0 kN/m² to δ_ih-max/H_c% = 0.14, 0.15, and 0.31% for the corresponding penetration depth. It is reasonable to conclude that vertical ground settlement behavior is compatible with the horizontal deflection behavior of the wall. However, when the penetration depth ratio was increased above, H_e/H_c = 2.0, there was no significant change in the values of δ_ih-max or δ_iv-max for the same surcharge load.

Descriptive analyses were carried out to evaluate changes in average normalized lateral deflection of the SPW (δ_ih-max/H_c%), ground settlement (δ_iv-max/H_e%), and settlement influence zone (D_o) for different relative densities and different normalized penetration ratios (H_e/H_c). The concluded δ_ih-max/H_c% values ranged from 0.14 to 1.28, with an average of 0.38. Also, the concluded average δ_ih-max/H_c% value, in this case, was very close to the findings of several researchers, including Moormann [60] and Wang et al. [34]. Besides that, according to the findings, the lateral deflection of the SPW was considerably reduced by an increase in the sand's relative density where the mean δ_ih-max/H_c% value increased by 16 to 30 for medium sand (D_r = 60 ± 2%) over the values of dense sand (D_r = 80 ± 2%). δ_iv-max/H_c% values ranged between 0.12 to 1.07, with an average of 0.40. Also, the average δ_ih-max/H_c% value was very close to the findings of several researchers, including Moormann [60], and Wang et al. [34]. In addition, the mean δ_ih-max/H_c% value increased by 18 to 26 for medium sand (D_r = 60 ± 2%) over the values of dense sand (D_r = 80 ± 2%). The settlement influence zone (D_o) varied between 1.81 Hc and 2.10 Hc from the SPW head, with a mean value of 1.95 H_c. Also, the ground surface settlement was considerably reduced by increasing sand relative density where the mean value of settlement influence zone (D_o) increased by 17% for medium sand (D_r = 60 ± 2%) over the values of dense sand (D_r = 80 ± 2%).

The section modulus required for the safe design of the secant pile wall depends on the maximum bending moment experienced by it. So, the effect of excavation depth is analyzed on the behavior of the cantilever secant pile wall. As shown in Fig. 10a, the maximum bending moment is increasing approximately linearly with increasing the penetration depth ratio (H_e/H_c) as concluded by Zhang and Liu [87]. The induced maximum bending moment is about (−0.17 (H_e/H_c) + 0.89) kN.m/m, with a high coefficient of determination (R²) equals 0.897. When excavation goes deeper, the maximum curvature of the bending moment curve is observed to be increasing. Figure 10b shows the variation of bending moment along the normalized depth of the cantilever secant pile wall for surcharge load W_sur = 8.0 kN/m² and for different penetration depth ratios (H_e/H_c = 5.0, 2.0, and 1.0). Normalized depth (z/H_t) is defined as the ratio of wall depth from the ground surface to the wall length. The maximum bending moment observed for H_e/H_c = 5.0, 2.0, and 1.0 was 0.06 kN.m/m, 0.34 kN.m/m, and 0.82 kN.m/m, respectively. It was noted that at the penetration depth ratio of H_e/H_c = 1.0, and 2.0, the bending moment is doubled by about 13.4, and 5.6 times the bending moment at the H_e/H_c ratio of 5.0, respectively. This proves that the maximum bending moment is increasing significantly with excavation depth.

In Fig. 11, the load-normalized displacement relationships (lateral and vertical) for each investigation are depicted by groups. The curves were arranged in accordance with the normalized penetration depth ratio (H_e/H_c) for various conditions of surcharge load (W_sur) and sand relative density (D_r). The curves cannot clearly indicate a failure (peak) point. Consequently, to compare the results, the ultimate axial capacity of the SPW was defined as the axial load at which the value of δh-max/Ht% equals 1.0.

The normalized wall movements (lateral and vertical) δ_h/H_t, and δ_vw/H_t against the applied axial load (kN/m) are presented in Fig. 11. Based on the penetration depth ratio (H_e/H_c), sand relative density (D_r), and surcharge load density (W_sur), the secant pile wall was found to be vertically settled and laterally displaced with different values of axial load. The maximum lateral deflection at the top of SPW and the wall's vertical settlement gradually decreased as the penetration depth ratio and sand density increased. This is explained by the fact that increasing the wall penetration depth increased the friction resistance between the soil and the wall, which also improved the axial capacity of the SPW. It was also noted that the applied axial load significantly contributed to the extra lateral top deflection of the SPW due to the asymmetrical lateral earth pressure. Generally, the overall lateral deflection of a piled wall is often affected by the unloading due to the excavation area, the elastic deformation of the wall, shear deformations of the earth's body, and soil movement beneath the wall [88]. The wall lateral deflection caused by axial loading effects could be reduced with an increase in the H_e/H_c ratio as the passive resistance in the embedded part of the SPW will form a sufficient wedge region. As a result, stability for the SPW was achieved. Additionally, when the SPW was placed with an adequate He/Hc ratio and with low surcharge load density (H_e/H_c = 2.0; W_sur = 4.0 kN/m²) in dense soil (D_r = 80 ± 2%), the overall SPW's movements (lateral and vertical) were relatively small in comparison to other tests. Generally, and as shown in Fig. 11, the applied axial load can modify the lateral and vertical load–displacement response of the SPW according to penetration depth ratio, applied surcharge load, and sand relative density. According to the testing results, the secant pile walls offered both lateral and vertical bearing capacity, which might aid to retain the excavation sides and bear axial loading at the same time.

As previously mentioned, the Topcon GLS-2000 3D device was employed to monitor the wall movement through the tank's transparent glass face and MAGNET COLLAGE software was used to process the data obtained from TLS scans. Figure 18 shows lateral deflection profiles along the length of the wall and the potential buckling profiles for different loading stages at different penetration depth ratios (H_e/H_c). As can be observed, the wall rotated semi-rigidly around a pivot point that is located near the wall's tip. Soil pressure changes from active to passive earth pressure below the pivot point, with passive pressure on the retained side. In cohesionless soils, King [51] stated that the pivot point (ε′) for embedded cantilevered walls might be at (ε ′ = 0.35H_e), where H_e is the penetration depth. According to descriptive statistics, the location of the pivot point (ε′) extended from 0.24 to 0.41 H_e from the wall tip, with a mean value of 0.34 H_e and 0.29 H_e for relative density of D_r = (80 ± 2) %, and (60 ± 2) %, respectively. Figure 17 shows some images of the lateral deflection profile of the SPW from the laboratory tests. As observed from Fig. 18(a, b), the lateral deflection profiles of the SPWs show a reverse ‘‘S’’ shape, for H_e/H_c = 5.0, and 2.0. These profiles agree with the hypothesis of Aristizabal-Ochoa [93] who assumed that the structural elements, with sideway, partially inhibited and with rotational and lateral end restraints under combined loading (lateral and axial loading), would be deformed as an ‘‘S’’ shape. Also, as observed from Fig. 18, when the depth of the excavation grows, the lateral dent of the wall increases toward the excavation area above the excavation surface, and this is clearly shown in Fig. 18c. This can be attributed to several considerations, including the fact that increasing the depth of excavation increases the lateral loads resulting from lateral soil pressure and also increases the free length of the wall subjected to lateral loads, as well as the presence of axial load works to semi-restrict the upper movement.

Only three samples were chosen for the bending analysis since the primary aim of this study was to evaluate the deformation behavior rather than the structural behavior (Table 3). The bending moment of the selected three samples can be calculated based on the strain measurements of the secant pile walls. According to Li et al. [71], the bending moment, in this case, can be given by the following equation:where M is the bending moment at a definite point on the SPW; S is the elastic section modulus in bending; E_s is the elastic modulus of SPW; Ɛ₁ is the strain at the point of measurement on the SPW's front surface (for simplicity, the front surface of the SPW refers to the surface facing the excavation, and the rear surface refers to the surface opposite the higher ground level), and Ɛ₂ is the strain at the measurement point on the rear surface of the SPW. Figure 19 shows the bending moment distribution along the length of the SPW for different loading stages at different penetration depth ratios (H_e/H_c). On the near-pit side, the moment on the SPW is defined as negative. It can be concluded that the applied axial load can modify the bending moment distribution along the length of the SPW. Moreover, it was found that the distribution of bending moments along the wall length differed according to the penetration depth ratio (H_e/H_c). This is mainly due to the two reasons mentioned below. Firstly, the horizontal forces acting on the SPWs are different. Specifically, the greater the depth of excavation, the greater the horizontal forces caused by the soil's lateral pressure. Secondly, the wall is subjected to combined loads (axial and lateral loads), which affects the buckling behavior of the wall and, as a result, the deformations are distributed differently along the length of the wall, as shown in Fig. 19(a–c). According to Fig. 19(a–b), the bending moment distribution on the tested SPWs under different loading stages showed a reverse (S) shape, which is compatible with the buckling/deformation shape. The positive bending moment is often distributed above the excavation bottom, whereas the negative bending moment is typically spread below. Nevertheless, the lower part of the SPW bears little force due to the rotation of the wall.

As shown in Fig. 19a, the presence of the ultimate axial increased the positive moment by as much as 82.5% of the initial values (without axial load) for the penetration depth ratio H_e/H_c = 5.0. Also, the ratio between the maximum positive and negative bending moments at the ultimate axial load is 1.0:0.80, respectively. In the same context, according to Fig. 19(b–c), the presence of the ultimate axial loading decreased the positive moment by as much as 5.80%, and 55.11% of the initial values (without axial load) for penetration depth ratio H_e/H_c = 2.0, and H_e/H_c = 1.0, respectively. Also, the ratio between the maximum positive and negative bending moments at the ultimate axial load is 1.0:0.58, and 1.0:0.13 for H_e/H_c ratios of 2.0, and 1.0, respectively.

The ultimate pile capacity can be calculated using several different code approaches, but the static formula is the most well-known, practical, and popular one [94‐96]. The ultimate pile capacity is assumed to be the sum of skin friction and end-bearing resistance, as shown in the following equations.where P_p(ult) is the ultimate vertical load of a pile, Q_f is the skin friction resistance, Q_b is the total end-bearing resistance, f is the unit skin friction capacity, A_s is the side surface area of the pile, q is the unit end-bearing capacity, A_b is the gross end area of the pile, P_o is the effective overburden pressure at the center of the layer, P_b is the effective overburden pressure at beneath the wall base, k_h is coefficient of lateral earth pressure (0.7–1.5 [94]), δ is the friction angle between the soil and pile wall (3/4φ [94]), and N_q is a dimensionless bearing capacity factor [97].

According to the similarity law shown in Table 2, the dimension and applied loads were multiplied in the similarity ratios to simulate the behavior of the prototype. By modifying Eq. 2 with a modification factor, an attempt was made to match the experimental data with the theoretical values. Linear and nonlinear regression analysis was employed to represent the relation between the modification factor (ὴ) as the dependent variable and two independent variables (surcharge load (W_sur) and penetration depth ratio (H_e/H_c). Several mathematical models of the independent variables were developed by regression analysis. The criteria utilized to evaluate the predictive accuracy of the models are as Pham [98]. Accordingly, the better the model's goodness-of-fit, the lower the value of MSE, RMSE, AIC, BIC, and AICC. Conversely, a higher (R²) value denotes a better match. The XLSTAT statistical software was used for conducting the statistical analysis. This software has been widely utilized by many researchers [99, 100]. According to the predetermined criteria, Table 4 lists the best-fit models for the modification factor. As shown in Table 4, the best model is model B which is generated from nonlinear 2nd-order regression analysis, with a high coefficient of determination (R²) equal to 0.94. Also, Fig. 20a depicts the measured values of the ultimate load (P_ult) plotted against the predicted ones. The modified equation can be given as follows:where P_ult is the ultimate vertical load of an SPW and ὴ is the modification factor. As shown in Fig. 20b, at a H_e/H_c ratio of 5.0 and a surcharge load of 40 kN/m², the value of the modification factor approaches 1.0. Conversely, at a H_e/H_c ratio of 1.0 and a surcharge load of 120 kN/m², the ὴ value drops to less than 0.2. As a result, when the penetration depth ratio increases, the behavior of the laterally and vertically loaded SPWs becomes closer to that of the vertically loaded piles, especially at low surcharge loads.