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

In urban environments, temporary excavation support systems (ESSs) are intensively recommended during the construction process of structures with underground levels to preserve nearby structures and maintain the excavation sides. Once the foundations and basements are constructed, these systems are rendered useless. As a result, integrating the temporary ESS into the building foundation may have significant benefits. Therefore, the main aim of this paper was to investigate the behavior of Secant Pile Walls (SPWs) through fifteen model tests with an acceptable scale on an axially loaded SPW embedded in medium and dense sand. This study considered several factors to define wall behavior, such as normalized lateral deflection (δh/Ht%), the vertical deflection of the SPW (δvw/Ht%), vertical ground settlement (δv/Ht%), and settlement influence zone (Do). These factors were investigated and analyzed under the influence of a set of parameters including normalized penetration depth (He/Hc), sand relative density (Dr), and surcharge load density (Wsur). The findings demonstrated that SPWs had structural and overall stability features to withstand lateral earth pressures as well as applied axial loads. Generally, increasing the He/Hc ratio further than a limit value of 2.0 for the same surcharge load had a limited impact on the ultimate axial capacity, particularly in the case of dense sand. The location of the pivot point (ε′) extended from 0.24 to 0.41He from the wall tip, with a mean value of 0.34He and 0.29He for the values of Dr = 80 ± 2%, and 60 ± 2%, respectively. Other issues were also discussed for selected samples, including an analysis of the wall's bending moments and any potential wall buckling. Finally, to correlate the experimental data with the theoretical values, a modification factor for the pile static formula was developed by using nonlinear regression analysis with a significant prediction accuracy with an R2 of 0.94.


H e /H c Penetration depth ratio δ h
Lateral deflection of the piled wall δ v Vertical ground settlement behind the piled wall δ vw Vertical deflection of the wall δ ih-max Maximum lateral deflection of the piled wall (without axial loading) δ iv-max Maximum vertical settlement behind the piled wall (without axial loading) δ h-max Maximum lateral deflection of the piled wall at ultimate axial loading δ vw-max Maximum vertical deflection of the wall at ultimate axial loading δ vg-max Maximum  Effective overburden pressure at the center of the layer P b Effective overburden pressure beneath the wall base ὴ Modification factor for static method

Introduction
Excavation support systems (ESSs) are generally categorized according to a variety of factors: system stiffness (rigid or flexible), load support mechanism (externally or internally stabilized), construction method (fill or cut), construction material, stability mechanism, lifespan (permanent or temporary systems), and applications [1].Based on stability mechanisms, Clayton et al. [2] proposed a categorization of different types of ESSs.They divided them into three categories: composite/hybrid walls, embedded piled walls, and gravity walls.Embedded piled walls, such as diaphragm walls (DWs), contiguous bored pile walls (CPWs), secant walls (SPWs), soil mixing walls (SMWs), and sheet pile walls (SHPWs), are frequently utilized [3,4].In general, piled walls are employed extensively due to their capability to retain soil and the ability to create continuous barriers [5].In comparison with other types, CPWs and SWPs have proven to be moderately cost-effective and very competitive [3].
In urban areas, ground movements induced by excavations will have a serious impact on the nearby infrastructure, buildings, and tunnels, which is a major concern for their safety [6][7][8][9][10].If the ground movements and the wall lateral deflection in the vicinity of the excavation area are too large, surrounding structures will be threatened [11,12].This might potentially lead to a major accident or tragedy [13,14].As a result, the control criteria in deep excavation design and construction have changed from bearing capacity to deformation-based criteria, particularly for systems embedded in cohesionless soil [3].So, controlling the environmental consequences of a deep excavation requires an understanding of its deformation behavior [15].The deformations of excavations have been investigated by several researchers via theoretical analysis, numerical modeling, model testing, full-scale testing, and field observations.In general, the performance of the ESSs can typically be described by lateral wall deformations, and vertical ground settlements behind the wall [16][17][18][19].
Clough and O'Rourke [20] proposed profiles of the wall deflection and the ground settlement due to excavation activities.The wall will be deflected as a cantilever in the initial phases of excavation and before installing the lateral supports.At the same phase, the largest vertical settlement value was observed relatively near the wall head, and the settlement pattern was presented as triangular-shaped.Lateral supports are positioned when the excavation reaches deeper heights to restrict the upper movement of the wall head.During this phase, deep inward wall movements take place.Cantilever and deep inward profiles combine together to cause cumulative wall and ground movements.Regarding the effects of wall deformation, Boone and Westland [40] concluded the same result.When cantilever movements predominate, settlements typically take the shape of a triangle.They may also adopt the same pattern during excavations in hard clays and sands [20].Hsieh and Ou [32] reached similar conclusions and developed the spandrel and concave settlement profiles based on a variety of case studies.To understand the overall deformation behavior of deep excavation support systems, El-Nimr et al. [16] conducted a detailed literature review.They concluded that the normalized lateral deflection (δ h-max /H c %) ranges between 0.07 to 1.5, with a mean value of 0.58, and 0.2% for soft clay and sands, respectively.Also, normalized vertical settlement (δ v-max /H c %) ranged between 0.02 to 1.10%, with a mean value of 0.49 and 0.24 for soft soil, and sands, respectively.The settlement influence zone (D o ) reached a mean distance of 2.3H c , which falls within D o = 1.5-3.5Hc with a mean distance of 2.0H c and 3.0H c in the case of sands and other stiff clay soils, respectively.
According to the design requirements, cast-in-place secant pile walls may be divided into two categories [41].The first type, commonly known as the hard/hard or reinforcedreinforced-reinforced (RRR) type, is mainly constructed of Reinforced Concrete Piles (RCPs) which are placed consecutively.The second type, also known as the hard/firm or Plain-Reinforced-Plain (PRP) type, is typically comprised of plain and reinforced concrete piles, which are alternately set.The secant pile wall is typically simplified for designing or modeling purposes as an equivalent continuous wall, and hence the intersection of the SPWs' faces is considered entirely bonded [42][43][44].The limit equilibrium methods (LEMs) developed by Blum [45], Krey [46], Rowe [47], and Hansen [48] are used to obtain the lateral earth pressure distribution in cohesionless soil.The previously mentioned methods exclude surcharge loads from the analysis [49].The piled wall is considered to rotate rigidly around a pivot point that is near the wall's tip.To apply the LEM, two unknown parameters should be obtained.Generally, these parameters often refer to the pivot point's location (ε ) and the embedded depth (He) needed to prevent collapse [50].According to King [51], the pivot point might be positioned at (ε = 0.35He) from the wall's tip.It should be highlighted that the LEMs depend on the soil strength, so they do not indicate wall movements [52].As a result, a number of researchers have tried to relate the growth in lateral earth pressure with the retaining wall movements [53][54][55][56][57].
The SPWs have been studied in a few field tests [58,59], case histories [36,38,60,61], and scaled laboratory tests [41,62].Liao et al. [41] examined the interface and the interaction between secant piles under tension, shear, and bending loads.They concluded that the early strength of primary piles, the time intervals of bonding (TIB), and the effects of bonding quality could be a source of wall stiffness reduction.El-Nimr et al. [62] investigated the structural performance of the 1/10th scaled model of RC secant pile wall using two types of tests: bending and axial compression.They suggested a selfcompacting concrete mix.They also confirmed the validity of the tested models by comparing results with some empirical equations for calculating the modulus of elasticity and critical buckling load.In conclusion, there is a dearth of laboratory research on the behavior of secant pile walls under combined loads.
On the other side, in urban environments, temporary ESSs are intensively recommended during the construction process of structures with underground levels to preserve nearby structures and maintain the excavation sides.Once the foundations and basements are constructed, these systems are rendered useless.From the literature, up to date, the majority of researchers have concentrated only on employing piled walls as retaining structures.So, the design strategy is basically controlled by lateral forces.Despite that, a few researchers have investigated utilizing piled walls to withstand both vertical structure loads and lateral pressures [4,5,[63][64][65].This concept was investigated through smallscale laboratory tests [4], full-scale field tests [64,66], and case studies [63].All these investigations were performed on steel-piled walls where integrating the temporary ESS into the building foundation may have significant benefits.The utilization of ESS as a foundation element could decrease the required materials for foundation construction (a smaller number of needed piles) and the construction time.This also will element the reduction in the building footprint.Furthermore, SPWs have the structural features to withstand both lateral earth pressures and vertical loads of structures [63,65].However, this concept has not reached the final design stage due to the absence of well-documented laboratory tests or case histories involving heavily instrumented, full-scale axial load tests on piled walls that accept them as bearing elements.Thus, the main aim of this paper was to investigate the behavior of axially loaded secant pile walls (concrete models), embedded in medium and dense sand, through a set of laboratory tests using a large-scale model.

Sand
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 (D 50 ) 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 /D 50 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 /D 50 is approximately 146.34.

Size Selection and Preparation of Samples
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 Stress, β 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).

Soil Tank and Loading Mechanism
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 0.1-0.9MPa (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.

Monitoring Scheme
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 ).

Test Parameters
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.

Working Process of the Testing Model
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.

Failure Criteria
The concept of LEM is the forecast of the excavation's maximum height while preserving static equilibrium [80].This is referred to the limited equilibrium condition.Generally, the LEM is used to design the piled walls, although this approach ignores the wall deformations that are essential for the wall's serviceability.Serviceability concerns related to the wall lateral deflection and the vertical settlement of adjacent structures induced by excavations are significantly more common than failures [81][82][83].As mentioned previously in the literature review, the control considerations in deep excavation systems' design have altered from loadcarrying capacity to deformation-based criteria, particularly for systems embedded in cohesionless soil [3].Accordingly, the lateral behavior of the SPW under an applied axial concentric load was the main emphasis of this work for various investigated variables.According to Milligan [84], and Clough and Rourke [20], when the curves cannot clearly indicate a failure (peak) point, the ultimate piled wall capacity is defined as the load at which rotational failure occurred as a result of both peaks lateral and vertical movements.Furthermore, Rowe and Peaker [85] found that the acceptable limit for maximum lateral deflection at the head of the piled wall is δ h-max = 5.0% of the wall height, and this point can be considered as a failure point.For sandy soil, very minor ground movements are considered significant since they might result in the complete mobilization of strength and cause failure.Also, according to SNI-8460 [86], the allowable wall lateral deflection ranges from 0.5 to 1.0%H based on the proximity of the excavation to adjacent buildings or infrastructures.In this research, the value of δ h-max /H t % was considered equal to 1.0 as a limit for comparing the results.

Testing Results and Discussion
All samples were loaded to the failure point (δ h-max /H t = 1.0%) under a monotonous constant load with regular increments to ensure the consistency of the collected data.

SPW's Performance Under the Effect of Lateral Loads Only
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 excavationinduced lateral and vertical movement profiles at different phases of excavation.The surcharge load, in this case, was W sur = 8.0 kN/m 2 .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 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/m 2 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/m 2 .These ratios also reduced to minimal values when W sur = 4.0 kN/m 2 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 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 (R 2 ) 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/m 2 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.

SPW's Response to Vertical and Lateral Loading
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/m 2 ) 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.

Effect of Penetration Depth on Maximum Lateral Deflection
As mentioned before, Fig. 11 shows the axial loadmovements (lateral and vertical) relationships for each experiment in groups at different sand densities and different surcharge loads.For the wall lateral movement, the analysis is presented in terms of the ratio of maximum lateral deflection to total SPW's height (δ h-max /H t ). Figure 11 shows that for all sand densities, the increase in penetration depth resulted in a considerable reduction in the lateral deflection of the tested SPW.This can be explained that the increase in penetration depth provides conditions for fixed soil support and increases the overall stability of the wall under the applied axial load with less lateral deflection.This is further supported by the berm hypothesis of Georgiadis and Anagnostopoulos [89], who demonstrated that constructing a berm in the passive zone may greatly enhance penetration depth and, as a result, reduce the wall lateral deflection.Additionally, it was noticed that for all sand relative densities, the penetration depth ratio of 5.0 gave the highest movement reduction and markedly decreased the lateral deflection.It's possible that this higher ratio worked as a berm in the passive zone, increasing wall resistance and maintaining the stability of the piled wall.As previously mentioned, in this research, the value of δ h-max /H t % was considered equal to 1.0 as a limit for comparing the results.

Effect of Penetration Depth on Maximum Vertical Settlement
As noted earlier, the lateral behavior of the SPW under an applied axial concentric load was the main emphasis of this work for various investigated variables.The maximum normalized vertical settlement of the wall (δ wv-max /H t ) was considered when the value of δ h-max /H t % equals 1.0.For all sand densities, increasing the H e /H c ratio resulted in a considerable increase in the vertical settlement of the SPW.This can be explained by the fact that the value of the vertical settlement is related to the value of the applied load.Also, as mentioned previously, the increase in the H e /H c ratio leads to a considerable increase in the ultimate axial capacity.Hence, it is logical that the greater the H e /H c ratio, the greater the corresponding vertical settlement.However, increasing the H e /H c ratio further than a limit value of H e /H c = 2.0 for the same surcharge load had no discernible impact on the vertical settlement of the SPW, particularly in the case of dense sand, as shown in Fig. 12. Figure 13 illustrates the relationship between the ultimate axial capacity of the SPW (P ult ) and maximum normalized vertical settlement (δ wv-max /H t ) at various sand relative densities.This demonstrates that increasing the applied axial load causes an increase in the vertical deflection, as expected, and that the relationship is closer to being a linear relationship.Also, in comparison, the vertical deformation of the tested samples in medium sand (D r = 60 ± 2%) was significantly greater and evolved much faster than the tested samples in dense sand (D r = 80 ± 2%) at the same axial loading for both sand densities, as predicted.As a result, the piles must be sufficiently embedded in the passive zone to maximize the benefit of the penetration depth.

Effect of Penetration Depth on the Ultimate Axial Capacity
Where the piled walls with sufficient penetration depth result in a notable increase in both the interface area and the passive wedge zone [85,89].But, as Fig. 14 illustrates, beyond a limit value of H e /H c = 2.0, there was no meaningful advantage to increasing the penetration depth for surcharge load density of W sur = 4.0 kN/m 2 .Generally, beyond this ratio, H e /H c had a relatively little effect on the ultimate axial capacity of the wall.In contrast, the ultimate capacity (P ult ) significantly decreased for penetration depth ratios H e /H c < 2.0.In this case, the ultimate capacity (P ult ) was significantly decreased since the penetration depth only offered a small wedge area in the passive zone.

Effect of Surcharge Loading on the Ultimate Axial Capacity
Equipment, existing buildings, storage facilities, construction materials, vehicles, or highway loads, as well as other considerations, may result in surcharge loads.The SPW experiences increased lateral pressures as a result of the surcharge loads, which force the piled wall outward.The tests were carried out at uniform surcharge intensities of 4.0, 8.0, and 12.0 kN/m 2 .The effect of the uniform surcharge is to increase the effective vertical soil pressure and hence cause additional lateral pressures on the SPW system.Overall, due to the presence of these surface loads near the excavation area, the lateral earth pressure along the SPW in the active zone was considerably increased, which increased the lateral deflection of the SPW (Fig. 11).Therefore, the ultimate capacity of the SPW (P ult ) was decreased due to the rapid generation of wall lateral movement, especially at a high surcharge load intensity.Also, the existence of such a surcharge effectively increases the frictional resistance at the upper elevations of the wall [90].Therefore, with an increase in the surcharge load, the vertical movement of the wall relatively decreases.Figure 15 illustrates the applied surcharge load (W sur ) in relation to the ultimate capacity (P ult ) at different ratios of H e /H c . Figure 15 shows that at W sur = 8.0 kN/m 2 and D r = 80 ± 2%, the ultimate capacity (P ult ) decreased by 9.42, 21.80, and 40.47% for the penetration depth ratios of H e /H c = 5.0, 2.0, and 1.0, respectively, compared with the

Effect of Sand Relative Density on the Ultimate Axial Capacity
The findings showed that the relative density of the sand greatly affected the ultimate capacity (P ult ) of the SPW.As shown in Fig. 15, at the ratio of H e /H c = 5.0, increasing the sand relative density up to 80 ± 2% distinctly increased the ultimate load by as much as 52.89, 51.61, and 44.31% of the medium sand values (D r = 60 ± 2%) for W sur = 4.0, 8.0, and 12.0 kN/m 2 , respectively.At the ratio of H e /H c = 2.0, when the sand relative density increased up to 80 ± 2%, the ultimate load distinctly increased by as much as 58.65, 62.50, and 78.64% of the medium sand values (D r = 60 ± 2%) for W sur = 4.0, 8.0, and 12.0 kN/m 2 , respectively (Fig. 15).The average rates of increase in the ultimate axial capacity were about 49.60%, and 66.60% with changing the sand density from medium to dense sand for penetration depth ratios of 5.0, and 2.0, respectively.This may be ascribed to the following: (1) when relative density increases, the relative stiffness ratio and lateral subgrade reaction of sand also increase [91]; (2) compacted soil particles are more closely interlocked in dense sand than in medium sand, which makes their movement more difficult in the dense sand [92].

Secondary influence zone
Primary influence zone

Effect of Axial Loading on the Settlement Influence Zone Width (D o )
The vertical ground settlement profiles behind the tested secant pile walls in the laboratory were determined, as illustrated in Fig. 16.The analysis is presented in terms of variation of the normalized ground settlement  Generally, it can be concluded that the axial loading relatively increases the influence zone width behind the wall, and this depends on the value of the applied axial load, the applied surcharge density, penetration depth ratio, and sand relative density.Also, as shown in Fig. 16, the influence zone is divided into two zones: the primary influence zone and the secondary influence zone.The primary influence zone occurs approximately at a distance of 0.94 H c in dense sand (Fig. 16a) and at a distance of 1.60 H c in medium sand (Fig. 16b) from the wall.The curves in this zone were comparatively steep, and if the value of δ v is large enough, this might severely damage the nearby structures.In contrast, the secondary influence zone had a gentler slope which means that nearby structures may be less influenced.Moreover, Fig. 17 illustrates some images of the settlement influence zone behind the tested SPW.
According to descriptive statistics, at the ultimate loading case, the maximum normalized ground settlement (δ vg-max /H t ) ranged from 1.45 to 1.86 H t , with a mean value of 1.60 H t and 1.78 H t for the relative density of D r = (80 ± 2) % and (60 ± 2) %, respectively.

Evaluation of the SPW Buckling
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.

Bending Moment Analysis of the SPW
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; 1 1 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 1 2 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 123 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 1.0:0.13for H e /H c ratios of 2.0, and 1.0, respectively.

Proposed Equation for Estimating Ultimate Axial Capacity of the SPW
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][95][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 (R 2 ) 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 (R 2 ) 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/m 2 , 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/m 2 , 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.

Conclusions
The main aim of this paper was to investigate the behavior of secant pile walls through fifteen model tests with an acceptable scale on an axially loaded secant pile wall embedded in the sand.Many factors, such as 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 ), were considered in this study.Other issues were also considered for selected samples, including an analysis of the wall's bending moments and any potential wall buckling.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 ).Based on the results and analyses of this research, the following conclusions are drawn: (1) The concluded δ ih-max /H c % values ranged from 0.14 to 1.28, with a mean value of 0.38.Besides that, it was found that the increase in sand density significantly decreases the lateral deflection of the wall where the mean δ ih-max /H c % value increased by 16 to 30% in the case of medium sand over the values in the case of dense sand.(2) δ iv-max /H c % values range between 0.12 to 1.07, with a mean value of 0.40.Besides that, the mean δ ih-max /H c % value increased by 18 to 26% in the case of medium sand over the values in the case of dense sand.
(3) The settlement influence zone (D io ) extended from 1.81 to 2.10 H c from the wall head, with a mean value of 1.95 H c .Besides that, it was found that the increase in sand density significantly decreases the settlement influence zone (D o ).Where the mean value of  (7) By increasing the sand's relative density, the ultimate capacity of the SPW also increased.The average rates of increase in the ultimate axial capacity were about 49.60%, and 66.60% with changing the sand density from medium to dense sand for H e /H c of 5.0, and 2.0, respectively.(8) Beyond a limit value of H e /H c = 2.0, there was no meaningful advantage to increasing the penetration depth.Generally, beyond this ratio, H e /H c had a relatively little effect on the ultimate axial capacity of the wall.In contrast, the ultimate axial capacity of the SPWs significantly decreased for penetration depth ratios H e /H c < 2.0.(10) The settlement influence zone is divided into two zones: the primary influence zone and the secondary influence zone.In the primary zone, the curves have a relatively steep slope, while the secondary influence zone has a gentler slope.The primary influence zone occurs at a mean distance of 0.94 H c , and 1.60 H c from the wall for dense and medium sand, respectively.(11) The SPW rotates semi-rigidly around a pivot point located near the wall tip.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 the values of D r = (80 ± 2) %, and (60 ± 2) %, respectively.(12) For the selected three samples, the ratio between the maximum positive and negative bending moments at the ultimate axial loading is 1.0:0.80,1.0:0.58,and 1.0:0.13for H e /H c of 5.0, 2.0, and 1.0, respectively.As a result, the distribution of reinforcing bars within the cross-section of the wall must be reconsidered according to the H e /H c ratio.The presence of P ult increased the positive moment by as much as 82.5% of the initial values (without axial load) for H e /H c = 5.0.Also, the presence of P ult decreased the positive moment by as much as 5.80%, and 55.11% of the initial values (without axial load) for H e /H c = 2.0, and 1.0, respectively.( 13) To correlate the experimental data with the theoretical values, linear and nonlinear regression analysis was utilized to develop a modification factor for the pile static formula.The best-achieved model showed a significant prediction accuracy with an R 2 of 0.94.Generally, 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.

Fig. 1
Fig. 1 Preparation of samples a sample cross-section dimension, b dismountable mold for RC SPW making

Fig. 2
Fig. 2 Image of soil tank and the loading instruments

Fig. 3 Fig. 4
Fig. 3 Strain gauges' positions a layout of strain gauges on SPW model b Image of SPW model

Fig. 5 Fig. 6
Fig. 5 Image of measuring points a dial gauges on the SPW head b vertical dial gauges behind the wall

Fig. 7
Fig. 7 Images from the working process of the test model

Fig. 10
Fig. 10 Bending moment on the tested samples (D r = 80 ± 2%, W sur = 8.0 kN/m 2 ), a variation of the maximum bending moment with the excavation depth; b bending moment distribution along the length of the wall

Fig. 11 2 (
Fig. 11 Load-normalized movements (lateral and vertical) relationships at different sand relative densities and different penetration depths

Figure 14
Figure14depicts the ultimate axial capacity of the SPW (P ult ) in relation to normalized penetration depth (H e /H c ) at two different relative densities (80 ± 2% and 60 ± 2%).It is obvious that when the H c /H e ratio increased, the ultimate capacity (P ult ) increased as well.Figure14shows that at H e /H c = 2.0 and D r = 80 ± 2%, the ultimate axial capacity of the SPW increased by as much as 60.10%, 98.12%, and 148.35% for surcharge load densities of W sur = 4.0, 8.0, and 12.0 kN/m 2 , respectively, compared to the result for the same

Fig. 12 Fig. 13 Fig. 14
Fig.12 Variation of maximum normalized vertical settlement of the wall (δ vw-max /H t ) with normalized penetration depth ratio (H e /H c )

Fig. 15 Fig. 16
Fig.15 The relationship between the ultimate capacity of the SPW (P ult ) and applied surcharge load (W sur ) (δ v /H t ) with respect to normalized distance from the excavation area (D o /H c ) at different axial loading conditions.According to descriptive statistics, the settlement influence zone (D o ) extended from 2.22 to 2.68 H c from the wall head, with a mean value of 2.45 H c .Besides that, according to the findings, the ground surface settlement was considerably reduced by increasing the sand's relative density where the mean value of settlement influence zone (D o ) of medium sand (D r = 60 ± 2%) increased by 20.72% over the values of dense sand (D r = 80 ± 2%).In general, for the relative density of D r = (80 ± 2) % and (60 ± 2) %, the presence of the ultimate axial load increased the influence zone width (D o ) by 22.60% and 27.70%, respectively, from the initial values of the same relative density (without axial load).

Fig. 17
Fig. 17 Images of lateral deflection profile and settlement zone behind the SPW from the laboratory tests

Fig. 18
Fig. 18 Lateral deflection profile along the length of the wall and potential buckling profile (D r = 80% ± 2, W sur = 8.0 kN/m 2 ), a H e /H c = 5.0; b H e /H c = 2.0; c H e /H c = 1.0

Fig. 19
Fig. 19 Bending moment distribution along the length of the wall for different loading stages (D r = 80% ± 2, W sur = 8.0 kN/m 2 )

Fig. 20
Fig. 20 Model output statistics, a obtained ultimate load values against predicted values, b variation of modification factor with penetration depth ratios

( 9 )
The axial loading relatively increases the settlement influence zone width behind the wall.In general, the presence of the ultimate axial load increased the influence zone width (D o ) by as much as 22.60, and 27.70% of the initial values (without axial load) for the values of D r = (80 ± 2) %, and (60 ± 2) %, respectively.Also, the mean value of D o increased by 20.72% in the case of medium sand (D r = 60 ± 2%) over the values of dense sand (D r = 80 ± 2%).
ground settlement behind the piled wall at ultimate axial loading D io Initial width of the settlement influence zone (without axial loading) D o Initial width of the settlement influence zone at ultimate axial loading

Table 3
Testing program and measured variables