Optimization of steel anchor pile configurations for enhanced pullout resistance in expansive soil foundations

Abstract

This study aims to predict the pullout behavior of steel anchor piles in saturated expansive soil using finite element method-based PLAXIS 3D CONNECT Edition V22 software. It inspects the effects of varying pile parameters and spacings for a displacement of 10% of the pile diameter. The study evaluates the performance of single and group anchor piles by comparing square configurations (2 × 2, 3 × 3, and 4 × 4) at varying centre-to-centre (c/c) spacings of 2.5D, 3D, and 3.5D, where D is the pile diameter. The numerical analysis reveals that increasing the pile length (L) and diameter (D) significantly improves the uplift (pullout) capacity of the piles. Furthermore, the group efficiency—defined as the ratio of the total uplift capacity of a pile group to the sum of individual pile capacities—was assessed to understand the interaction effects among piles at different spacings. Results indicate that optimal spacing enhances efficiency by minimizing negative group interaction and maximizing load resistance. The pullout force in pile groups increases with the number of piles, but group efficiency decreases as the number of piles rises. The efficiency of the anchor pile system showed minimal variation when spacing increased from 3 D to 3.5 D, suggesting that 3 D is the optimum spacing for group anchor pile systems. The findings contribute to a better understanding of how pile configuration and spacing influence uplift resistance in expansive soils, aiding in the practical design and optimization of foundation systems.

Introduction

Expansive soils, which undergo substantial swelling and shrinkage with changes in moisture content, present critical challenges for civil engineering infrastructure. These volume changes frequently cause foundation instability, leading to cracks, uplift, and eventual failure in structures such as overhead tanks, high-rise buildings, chimneys, and transmission towers^1,2. Light structures such as pavements and runways are particularly vulnerable, especially during wetting-drying cycles, which induce soil movement and settlement. In India, expansive soils cover nearly 20% of the land area, amplifying their impact across a wide geographic region. Traditional mitigation techniques for expansive soils include physical methods like sand cushions and CNS layers³, chemical stabilization using lime, fly ash, and Portland cement, and mechanical approaches involving under-reamed piles and belled piers⁴. However, these methods are often expensive, labor-intensive, and less effective in resisting tensile uplift loads over time⁵. An innovative and increasingly adopted solution involves the use of Granular Anchor Piles (GAPs) and Granular Pile Anchor Foundations (GPAFs), which incorporate anchor plates at the base to resist both compressive and uplift loads effectively^1,6. GPAFs have demonstrated high performance in expansive clays, showing up to 96% reduction in heave and a 20% increase in undrained shear strength⁷.The inclusion of geogrid or geotextile reinforcements further enhances their pullout capacity due to improved interfacial friction^6,8. Recent studies reveal that increasing pile diameter, embedded length, and relative density significantly improves uplift resistance⁹, with optimal L/D ratios around 10 and pile spacing of 2.5D to 3D reducing stress interference^5,10 (Singh et al., 2019; Abhishek & Sharma, 2019b). GPA systems also outperform traditional concrete piles under both saturated and unsaturated conditions, exhibiting over twice the pullout resistance^11,12. However, group installations of GPA can lead to reduced efficiency due to overlapping pressure zones⁹. The major key differences between the recent studies have been highlighted in Table 1.

Table 1.

Major differences among recent studies.

Authors	Soil type	Focus area	Methodology
Sharma and Sharma (2021)14	Cohesionless soil	Geogrid-encased granular piles	Experimental
Malhotra and Singh (2021)9	Sandy soil	Pullout of anchor piles	Experimental & numerical
Vashishtha and Sawant (2021)13	Clayey soil	Single GPA pullout response	Experimental
Joseph et al. (2022)12	Clayey & sandy soil	GPA vs. helical anchor	Model testing
Kumari and Sharma (2025)15	Loose sandy soil	Uplift of anchor pile	Numerical analysis

The numerical investigation on anchor piles in case of weak soils performed by various researchers showed satisfactory results towards pullout resistance. The above literature studies highlight the resistance capacity of anchor piles against pullout forces using experimentally and numerically in sand and clay both. The pullout capacity of group of anchor piles using numerical analysis in expansive soils has not been broadly explained by any of the researcher and needs to be explored. Keeping this in view, the present study aims to predict the pullout behaviour of steel anchor piles group installed in saturated expansive soil by varying pile parameters using finite element method based PLAXIS 3D software. An effort has been made to study the effects of various parameters and spacings of anchor piles for a prescribed displacement of 10% of pile diameter. The study also compares the results of single and group anchor piles, efficiency of various square pile configuration (22, 33 and 44) and efficiency of various c/c spacing (2.5 D, 3 D and 3.5 D) between anchor piles.

Steel anchor pile concept

Anchor pile foundations consist of tall, deep vertical piles driven into the ground, which are equipped with guy wires or anchors to act as a single unit. These guy wires provide tensioned lateral support, enhancing the structural stability by effectively resisting lateral forces. Anchor pile foundations are a modern and efficient method to address compressive and pullout loads. This method employs an axial-resistance anchor pile designed to handle both pullout and axial forces (Fig. 1). This is achieved by a mild steel tendon that connects an anchor plate at the bottom to a top base plate. The circular base plate transfers stress to the pile material, compressing it and creating anchoring effects. The system relies on two main factors: the self-weight of the anchor pile material and the frictional resistance between the surrounding soil and the pile. In resisting pullout forces, frictional resistance is the primary factor, while the self-weight is less significant in small-scale tests. Various factors affect frictional resistance, including lateral swelling pressure, overburden pressure, and effective shear strength parameters. Lateral swelling pressure notably restricts pile movement, thereby preventing pullout.

Fig. 1.

Group anchor pile system subjected to pullout loading.

Research methodology

The soil used in this study was expansive soil; further modeling conducted using PLAXIS 3D software. The soil parameters were taken from a reference paper⁵. In the present study, the expansive soil was modeled in PLAXIS 3D using the Mohr–Coulomb model, which effectively captures elastic-plastic soil response under fully saturated conditions. To represent the critical uplift condition, the entire soil mass was considered as saturated, and corresponding swelling pressures were incorporated indirectly through predefined initial stresses. Additionally, interface elements with a reduced interaction factor (R-interaction = 0.7) were introduced between the pile and soil, enabling simulation of the relative displacement and the development of negative skin friction along the pile shaft. The soil had a saturated unit weight (γ_saturated) of 19 kN/m³, an unsaturated unit weight (γ_unsaturated) of 17 kN/m³, an undrained cohesion () of 25 kN/m², an angle of shearing resistance (Φ) of 0°, a modulus of elasticity (E) of 4 MPa, and a Poisson ratio () of 0.4. Steel was used as the material for anchor piles with an unsaturated unit weight (γ_unsaturated) of 78.5 kN/m³, a modulus of elasticity (E) of 21 × 10⁴ MPa, and a Poisson ratio () of 0.3. The base plate and anchor plate, both constructed from rigid mild steel with a diameter matching the anchor pile and a thickness of 4 mm, had E value 2 × 10⁵ MPa and 0.15. Stainless steel tendon, a pullout wire with a 4 mm diameter and a modulus of elasticity of 1.96 × 10⁵ MPa, was utilized to facilitate pullout tests. A mild steel, with high flexural rigidity, was used for both the anchor rod and anchor plate to prevent buckling and deformations. Table 2 shows the various pile parameters utilized in numerical modelling.

Table 2.

Various pile parameters utilized in numerical modelling.

Length of anchor pile (L) (m)	Diameter of anchor pile & anchor plate (D) (m)	Thickness of anchor/base plate (mm)	Spacing (S)	Slenderness ratio(L/D)
3	0.6, 0.4, 0.3	5	2.5 D, 3 D, 3.5 D	5, 7.5, 10
4	0.8, 0.533, 0.4	5	2.5 D, 3 D, 3.5 D	5, 7.5, 10
5	1, 0.7, 0.5	5	2.5 D, 3 D, 3.5 D	5, 7.5, 10

Numerical modelling

PLAXIS 3D software was utilized to model group anchor piles installed in expansive soil by varying both pile and soil parameters. The project and model properties were used to define the model’s characteristics, with units of measurement being meters (m) and kilo Newtons (kN). The unit weight of water (_water) was set at 10.00 kN/m³, and the acceleration due to gravity was 9.81 m/s².

The group anchor pile system was surrounded by expansive soil extending to a depth of 10 m below the ground surface. The soil layer was simulated using the borehole option in PLAXIS 3D, with appropriate plan dimensions selected. To avoid boundary condition effects, the soil layer’s plan dimensions were varied as follows:

To investigate the pullout capacity of a group anchor pile system installed in expansive soil under fully saturated conditions, PLAXIS 3D software was employed to model the system for varying L/D ratios at various spacing values of anchor pile. The configurations modeled included anchor piles in a 2 × 2, 3 × 3 and 4 × 4 in square pattern, with S = 2.5 D, 3 D, and 3.5 D, to assess the influence of these variables on the pullout capacity. The equations shown in Table 3 were derived to evaluate the dimensions of the soil mass and the base plate:

Table 3.

Configuration details of anchor piles system.

Anchor pile configuration	Base plate dimension ()	Soil mass dimension ()
1 × 1	D	5D
2 × 2	Eq. 1	Eq. 4
3 × 3	Eq. 2	Eq. 4
4 × 4	Eq. 3	Eq. 4

Where,.

is the dimension of soil mass.

is the dimension of base plate.

is the spacing between anchor piles.

is the diameter of anchor pile.

N is the number of anchor piles.

For a 1 × 1 anchor pile configuration, base plate diameter (D) equaled anchor plate diameter, and soil plan dimensions (M × M) were 5 D × 5 D (Fig. 2a). In 2 × 2 configuration, base plate dimensions (P × P) were determined using Eq. (1) with soil plan dimensions of 5 P × 5 P (Fig. 2b); for 3 × 3 configuration, base plate dimensions were calculated using Eq. (2) with soil plan dimensions of 5 P × 5 P (Fig. 2c); and in 4 × 4 configuration, base plate dimensions were determined using Eq. (3) with soil plan dimensions of 5 P × 5 P (Fig. 2 d). The soil mass dimensions for all group anchor pile configurations were calculated using Eq. (4).

Fig. 2.

Different anchor pile confingrations used in study.

The group anchor pile system was modeled using poly-curve and extrude options in PLAXIS 3D software. The anchor plate and base plate were modeled with plate elements. The pullout wire, connecting the base plate, anchor plate, and anchor pile into a single unit, was modeled using a node-to-node element (Fig. 3). A linear elastic model was used for the node-to-node anchor, pile material, and plate elements. The modified Mohr-Coulomb criterion was applied to expansive soil. Each model applied an upward displacement at pile base plate equal to 10% of pile diameter to determine the resulting pullout. The volume elements were represented by ten-node tetrahedral elements, while plate elements were modeled with six-node triangular elements.

Fig. 3.

Anchor pile system’s modelling (4X4).

For the analysis of foundation failure, mesh aperture plays a crucial role. The geometry in PLAXIS 3D was divided into basic element types and compatible structural elements using the fully automatic mesh generation method. PLAXIS 3D offered five different mesh densities: very coarse, coarse, medium, fine, and very fine. Initial tests were carried out with these five different mesh densities under identical conditions. It was observed that when using a very fine mesh, the results were more accurate and precise. Hence, a very fine mesh density was selected for the present study (Fig. 4).

Fig. 4.

Generated mesh of anchor pile group.

A base plate matching the diameter of the anchor plate was designed at the top of the anchor pile system. The total displacement during pullout was shown in the z-direction (Figs. 5, 6 and 7), with different color schemes representing various displacement stages. Displacement patterns observed during system failure are illustrated in Fig. 5 for the 2 × 2 configuration, Fig. 6 for the 3 × 3 configuration, and Fig. 7 for the 4 × 4 configuration. Dark blue indicates minimal displacement, while dark red shows the maximum displacement. Areas with significant displacement have a denser mesh, while areas with minimal displacement have a coarser mesh. The deformed mesh (u) of the group anchor pile system during pullout, highlighting stress points near the bulged area, is shown in Fig. 8. Figures 9 and 10, and 11 present the deformed mesh (u) of the group anchor pile system during pullout.

Fig. 5.

Total displacement (u_z) of anchor pile during pullout for group anchor pile system (2× 2)

Fig. 6.

Total displacement (u_z) of anchor pile during pullout for group anchor pile system (3× 3)

Fig. 7.

Total displacement (u_z) of anchor pile during pullout for group anchor pile system (4× 4)

Fig. 8.

Deformed mesh (u) of group anchor pile system during pullout showing stress points near bulged area.

Fig. 9.

Deformed mesh (u) of group anchor pile system during pullout loading (2× 2).

Fig. 10.

Deformed mesh (u) of group anchor pile system during pullout loading (3× 3).

Fig. 11.

Deformed mesh (u) of group anchor pile system during pullout loading (4× 4).

Results and discussion

Influence of varying c/c spacing between anchor piles on pullout capacity

This section discusses the impact of varying center-to-center spacing between anchor piles on pullout capacity of a group anchor pile system. To evaluate this effect, 2 × 2 configuration piles with c/c spacings of 2.5 D, 3 D, and 3.5 D were modeled, keeping L/D = 5. For a 3 m anchor pile, the pullout force was 2751.44 kN for 2.5 D spacing, 3358.19 kN for 3 D spacing, and 3520.43 kN for 3.5 D spacing (Fig. 12). The pullout capacity increased by approximately 22% and 5% when c/c spacing was increased from 2.5 D to 3 D and 3 D to 3.5 D respectively. This indicates that pullout capacity increases with c/c spacing up to an optimum value (3 D), beyond which the increase is not significant.

Fig. 12.

Upward displacement versus pullout force of anchor pile for varying lengths.

Graphs plotting upward displacement on X-axis and ultimate pullout force on Y-axis (Fig. 12 (a), (b), (c)) show that ultimate pullout force increases with larger c/c spacing between anchor piles. The variation in pullout capacity with increasing c/c spacing of anchor piles exhibits a nonlinear behavior, primarily influenced by the complex interactions between soil and structural elements, load distribution efficiency, and failure mechanisms. In the initial phase, when c/c spacing is relatively small (≤ 2.5D), the stress bulbs or zones of influence of adjacent piles tend to overlap significantly. This overlapping effect leads to an interaction between piles that reduces their ability to mobilize full individual pullout resistance, as the available surrounding soil is shared among multiple piles, thereby diminishing the overall effectiveness of the system. However, as the c/c spacing is progressively increased towards an optimal range (3D), these stress zones become more distinct, minimizing interference between adjacent piles. This increased spacing allows each pile to engage independently with the surrounding soil, resulting in enhanced mobilization of shaft friction along the pile-soil interface, which is a primary contributor to pullout resistance. Additionally, at these optimal spacing values, improved soil arching effects occur, wherein the movement of one pile transfers load effectively to the adjacent soil mass, enhancing the confining pressure around the piles and increasing the overall load-bearing capacity of the system. As spacing continues to increase beyond the optimal value (> 3D), the efficiency of load transfer among the piles begins to diminish. This is because the degree of pile-soil interaction is reduced, leading to weaker lateral confinement and a reduction in soil arching effects. The decreasing effectiveness of soil confinement results in a loss of mutual support among the piles, causing them to behave more independently rather than as a cohesive group. Consequently, beyond a certain spacing threshold, the pullout capacity per pile may continue to increase slightly, but the overall group efficiency of the pile system begins to decline. This occurs because the additional spacing no longer contributes proportionally to load distribution improvements, leading to diminishing returns in pullout resistance enhancement. Furthermore, in large-spacing configurations, the system loses the advantage of stress redistribution among piles, making the soil-structure interaction less efficient and reducing the anchoring effect that was beneficial at lower spacing values. Another crucial factor influencing pullout behavior is the material response of the piles themselves. When subjected to increasing tensile forces, an anchor pile initially deforms elastically, meaning that displacement occurs in direct proportion to the applied load. However, once the tensile force exceeds the material’s yield strength, the pile undergoes plastic deformation, leading to strain hardening. At this stage, the crystalline structure of the pile material changes, increasing its strength but simultaneously reducing its ductility. This alteration in mechanical properties means that further deformation requires significantly greater forces, causing the pullout force-displacement relationship to reach a plateau. As a result, the system exhibits noticeable upward displacement without a corresponding increase in pullout force, limiting the efficiency of the anchor pile system under extreme loading conditions. Thus, determining the optimal c/c spacing (~ 3D) is critical to achieving the best balance between soil-pile interaction, stress distribution, and structural load mobilization. At this spacing, the piles effectively utilize the surrounding soil, minimize stress overlap, and maintain sufficient load-sharing characteristics without unnecessary material inefficiencies or excessive deformation risks. Beyond this point, excessive spacing compromises the structural integrity and stability of the system by reducing confinement effects and load redistribution benefits, highlighting the importance of an optimized spacing strategy in anchor pile design for expansive soil conditions. Previous study has shown the similar findings that pullout capacity increases with c/c spacing up to an optimum value (3D), beyond which the increase is not significant⁸.

Influence of varying slenderness ratio (L/D) on group anchor pile system’s pullout capacity

The effect of varying the L/D ratio on the pullout capacity of a group anchor pile system was evaluated numerically. Four anchor piles (2 × 2) with different L/D ratios (5, 7.5, and 10) were modeled for lengths of 3 m, 4 m, and 5 m, respectively, with a constant center-to-center spacing of 3 D. Pullout loads were calculated for a constant upward displacement of 150 mm, and graphs were plotted for piles installed in fully saturated soil having E = 4 MPa. For 3 m anchor pile, pullout forces observed were 1040 kN, 1485 kN, and 2700 kN for L/D = 10, 7.5 and 5 respectively; for 4 m pile, pullout forces observed were 1742 kN, 2450 kN, and 4400 kN for L/D = 10, 7.5 and 5 respectively; for 5 m pile, pullout forces observed were 2610 kN, 4080 kN, and 7100 kN for L/D = 10, 7.5 and 5 respectively. The graphs showed that reducing the slenderness ratio from 10 to 7.5 resulted in a 42% increase in pullout capacity for 3 m and 4 m piles and a 55% increase for 5 m piles, while further reducing the slenderness ratio to 5 from 7.5 resulted in an 81% increase for 3 m piles, 80% for 4 m piles, and 75% for 5 m piles.

The increase in pullout capacity with a decreasing slenderness ratio (L/D) is attributed to a larger surface area available for load transfer and better mobilization of frictional resistance between the soil and the anchor pile. As the L/D ratio decreases, the pile diameter (D) becomes larger in comparison to its length (L), providing more contact area for interaction with the surrounding soil. This larger interface results in improved shaft friction, which plays a crucial role in resisting pullout forces, especially in cohesive and expansive soils where confining pressure affects load mobilization. Shorter piles are inherently more rigid and less flexible than longer ones, which influences their load transfer characteristics and deformation patterns. In the case of long piles, tensile loads can cause bending and lateral displacement, leading to partial force dissipation and uneven pullout resistance along the shaft. On the other hand, shorter piles distribute stress more uniformly and depend more on shaft friction for load resistance, improving their overall pullout strength. Additionally, reduced bending in shorter piles enhances lateral confinement, increasing the passive resistance from the surrounding soil. In geotechnical terms, the relationship between slenderness ratio and pullout behavior is also associated with the failure mechanism of the pile-soil system. Piles with a high L/D ratio primarily fail due to shaft friction mobilization along their length, where elongation and deformation influence performance. Conversely, lower L/D ratio piles exhibit a mixed failure mode involving both shaft friction and base resistance, where the enlarged base provides additional support against tensile loads, further improving resistance. Overall, piles with lower slenderness ratios demonstrate superior pullout performance due to their greater surface area for frictional resistance, improved lateral confinement, reduced flexibility, and better load distribution. These characteristics make them particularly effective for foundations in weak or expansive soils, where stable anchorage under tensile loads is essential (Fig. 13). Previous research has reported similar findings that there was an increase in pullout capacity with decrease in slenderness ratio for all pile lengths^7,8.

Fig. 13.

L/D ratio versus pullout force of anchor pile at upward displacement (u_z) of 0.15 m for S/D = 3.

Influence of varying number of anchor pile on pullout capacity

The effect of varying the number of anchor piles on the pullout capacity of a group anchor pile system was numerically assessed. Configurations of 2 × 2, 3 × 3, and 4 × 4 piles for L/D = 5, 7.5, and 10, were modeled for 3 m long anchor piles, keeping S = 3 D. The pullout force (F_z) for these systems in fully saturated soil with a modulus of elasticity of 4 MPa was evaluated.

For L/D = 5 and an upward displacement (u_z) of 0.31 m, the pullout forces were 3330 kN, 6335 kN, and 10,560 kN for 2 × 2, 3 × 3, and 4 × 4 configurations, respectively, showing 90% and 66% increase in pullout capacity when the number of piles was increased from 2 × 2 to 3 × 3 and from 3 × 3 to 4 × 4, respectively (Fig. 14 (a)). Similarly, for L/D = 7.5 and an upward displacement (u_z) of 0.20 m, the pullout forces were 1728 kN, 3043 kN and 4917 kN for 2 × 2, 3 × 3 and 4 × 4 configuration, respectively, showing 76% and 61% increase in pullout capacity when no. of piles was increased from 2 × 2 to 3 × 3 and from 3 × 3 to 4 × 4, respectively (Fig. 14 (b)). For L/D = 10 and an upward displacement (u_z) of 0.15 m, the pullout forces were 1040 kN, 1879 kN and 2929 kN for 2 × 2, 3 × 3 and 4 × 4 configuration, respectively, showing 80% and 55% increase in pullout capacity when no. of piles was increased from 2 × 2 to 3 × 3 and from 3 × 3 to 4 × 4, respectively (Fig. 14 (c)). The increase in pullout capacity with a greater number of anchor piles can be attributed to multiple geotechnical factors, primarily expanded surface area for load transfer, improved stress distribution, and enhanced soil arching effects. As the number of piles in a group increases, the total contact area between the piles and surrounding soil also increases, thereby mobilizing greater shaft frictional resistance and passive resistance at the pile base. This results in a more efficient transfer of pullout loads, leading to an overall increase in pullout capacity. Moreover, the addition of more piles improves load distribution efficiency, as each pile shares a portion of the applied load, preventing excessive stress concentration on individual piles. This reduces the likelihood of localized failure and ensures that the load is distributed more uniformly across the entire pile group system, enhancing stability under tensile forces. Soil arching effects, a key mechanism in pile group interactions, also become more prominent with increasing pile numbers. Soil arching occurs when the displacement of one pile induces lateral soil movement, causing stress redistribution to adjacent piles and improving confinement pressure. This phenomenon enhances the load-bearing capacity of the system by increasing effective lateral resistance and preventing premature failure of individual piles. Additionally, pile group efficiency, defined as the ratio of the actual pullout capacity of a pile group to the sum of the individual pile capacities, is influenced by pile spacing, group configuration, and soil type. While a higher number of piles generally results in increased total pullout resistance, there exists an optimal pile arrangement that maximizes efficiency. Beyond a certain threshold, overlapping stress zones between piles can lead to reduced interaction efficiency, as excessive proximity between piles may limit the full mobilization of shaft friction due to interference effects. Thus, the increase in the number of anchor piles enhances the system’s overall resistance to pullout forces by expanding the surface area for frictional interaction, improving stress redistribution, and maximizing soil arching effects. However, achieving an optimal pile spacing-to-diameter (S/D) ratio is crucial to maintaining maximum efficiency and avoiding diminishing returns in pullout capacity. Some past studies revealed the similar results that pullout capacity increased on increasing the number of anchor piles^3,5.

Fig. 14.

Upward displacement versus pullout force of anchor pile for varying L/D ratios.

Single and group anchor pile systems comparison

The numerical analysis was conducted on single and group anchor piles with square configurations of 2 × 2, 3 × 3, and 4 × 4, an L/D ratio of 5, and a pile length of 3 m, maintaining a constant spacing of 3 D. Figure 15 illustrates the response of these piles under pullout loading in expansive soil. To compare group and single piles, the pullout force per pile in a group was calculated by dividing the total group pullout force by the number of piles in the group. The trend of increase in pullout force was almost similar for all pile configurations. As the number of piles in the group increased, the pullout force increased due to interaction effects. The difference in pullout behavior between single anchor piles and grouped anchor pile systems is largely influenced by soil-structure interaction, load distribution, and pressure bulb overlap. When a single anchor pile is subjected to an uplift force, the resistance is primarily mobilized through shaft friction along the pile-soil interface and base resistance at the pile tip. The surrounding soil offers relatively uniform confinement, allowing the full mobilization of pullout resistance without interference from neighbouring piles. However, in group anchor pile systems, the uplift force causes all piles in the group to move simultaneously, which leads to overlapping stress zones or pressure bulbs around adjacent piles. The pressure bulb refers to the region of mobilized soil stress surrounding each pile, which expands outward as the pile resists uplift forces. When piles are placed in close proximity, their pressure bulbs intersect, creating stress interference effects. This overlap reduces the efficiency of load transfer since the soil surrounding each pile is already partially mobilized due to the presence of adjacent piles. Consequently, the pullout resistance of each individual pile within the group is lower compared to an isolated single pile.

Fig. 15.

Response of group piles and a single pile in expansive soil under pullout loading.

Pullout capacity of anchor piles

Single anchor pile

A vertical pile experiencing an upward force installed within a saturated or nearly saturated expansive soil, characterized by an undrained cohesion is shown in Fig. 16. According to Eq. 5, the gross and net ultimate pullout capacities can be described as follows:

5

Fig. 16.

Various anchor pile systmes used in study.

On the other hand, in this case, the undrained cohesion Cu, the pile length L, and the pile cross section perimeter () determine the net ultimate pullout capacity, or:

6

where,

 is pile cross section perimeter.

 is adhesion at the pile-clay interface.

The undrained cohesion determines the adhesion. Consequently:

7

where,

 is nondimensional adhesion factor

8

9

where  is in .

Group anchor piles

Figure 16 illustrates the various parts group pile anchor system by varying number of piles. The group pile’s net and gross ultimate pullout capacity are related as follows:

10

where,

 is pile group gross ultimate pullout capacity.

is pile group net ultimate pullout capacity.

 is effective self-weight of the piles in the group and the pile cap

11

The net allowable pullout capacity for a group of piles with a conventional spacing of S = 3D to 4D can be calculated as follows:

12

where,

 is net allowable pullout capacity of a single pile.

 is net allowable pullout capacity of a group pile.

 is factor of safety ≈ 2 to 2.5.

Efficiency of group anchor pile system’s pullout capacity

Efficiency of different L/D ratio and anchor pile configurations

Numerical analysis was conducted on group anchor piles with L/D = 5, 7.5 and 10 keeping L = 3 m, and having constant S = 3 D. The pullout capacity and efficiency of different square pile group configurations (2 × 2, 3 × 3, and 4 × 4) for various L/D ratios is summarized in Table 4. The efficiency of group anchor pile system for a given upward displacement is calculated and is presented in Eq. (9).

13

Table 4.

Pullout capacity of the anchor pile system of different square pile groups configurations (2 × 2, 3 × 3 and 4 × 4) and spacings for different L/D ratios.

Parameter	2 × 2 pile groups configurations	3 × 3 pile groups configurations	4 × 4 pile groups configurations
Length (m)	3	3	3
Diameter (m)	0.6	0.4	0.3
L/D ratio	5	7.5	10
Pullout capacity of single pile	227	144	107
Pullout capacity of 2 × 2 pile group at S- 2.5 D	2751.04	1421.27	881.74
Pullout capacity of 2 × 2 pile group at S- 3.0 D	3358	1728	1040.56
Pullout capacity of 2 × 2 pile group at S- 3.5 D	3520.43	1834.19	1149.79
Efficiency of 2 × 2 pile group at S- 2.5 D (%)	303	247	206
Efficiency of 2 × 2 pile group at S- 3.0 D (%)	370	300	243
Efficiency of 2 × 2 pile group at S- 3.5 D (%)	388	318	268
Pullout capacity of 3 × 3 pile group at S- 2.5 D	5804.14	2814.52	1785.26
Pullout capacity of 3 × 3 pile group at S- 3.0 D	7084.27	3421.91	2106.75
Pullout capacity of 3 × 3 pile group at S- 3.5 D	7427.15	3632.01	2327.98
Efficiency of 3 × 3 pile group at S- 2.5 D (%)	284	217	185
Efficiency of 3 × 3 pile group at S- 3.0 D (%)	346	264	219
Efficiency of 3 × 3 pile group at S- 3.5 D (%)	363	280	241
Pullout capacity of 4 × 4 pile group at S- 2.5 D	10204.23	4958.06	3054.54
Pullout capacity of 4 × 4 pile group at S- 3.0 D	12454.81	6028.04	3604.6
Pullout capacity of 4 × 4 pile group at S- 3.5 D	13057.62	6398.16	3979.48
Efficiency of 4 × 4 pile group at S- 2.5 D (%)	281	215	178
Efficiency of 4 × 4 pile group at S- 3.0 D (%)	343	261	210
Efficiency of 4 × 4 pile group at S- 3.5 D (%)	359	278	232

For an upward displacement of 10% D, the group efficiency of the anchor pile system ranges from approximately 178–388% for all pile parameters (Fig. 17). Efficiency decreases as the number of piles increases at constant spacing because the overlapping stress zones reduce the load-carrying capacity of each pile. This efficiency decreases with increasing slenderness ratio may be mainly due to the reduced surface area and mobilized interface friction between soil and anchor pile. Some previous studies have shown similar results, indicating that efficiency decreases as the slenderness ratio increases^15–17.

Fig. 17.

Variation of the efficiency of an anchor pile system with L/D ratios.

Efficiency of different anchor pile c/c spacing

Figure 18 shows the impact of L/D ratio (for constant L = 3 m) on the efficiency of a 2 × 2 pile group at different spacings ranging from 2.5 to 3.5 D. The graph reveals that for a spacing of 2.5 D, the efficiency decreases by approximately 18.5% when the L/D ratio increases from 5 to 7.5, and by about 16.6% when L/D increases from 7.5 to 10. For spacings of 3 D and 3.5 D, efficiency decreases by about 18.9% and 18.04%, respectively, as L/D ratio increases from 5 to 7.5, and by about 19% and 15.7% as it increases from 7.5 to 10. Similar trends are observed for other pile lengths at the same spacings, as shown in Table 4. The efficiency changes negligibly when the spacing increases from 3D to 3.5 D, indicating that 3 D is the optimum spacing for group anchor piles. Similar findings are observed for other pile lengths of 4 m and 5 m.

Fig. 18.

Variation of the efficiency of an anchor pile system with L/D ratios.

Practical implications and engineering relevance of parameter analysis

1. Adopt 3D Spacing for Group Anchor Piles: Numerical analysis showed that a center-to-center spacing of 3 times the pile diameter (3D) provides the best balance between pullout capacity and group efficiency. This spacing should be used in design as it minimizes stress overlap and maximizes soil-pile interaction.

2. Use Lower Slenderness Ratios (L/D ≈ 5) for Maximum Uplift Resistance: Anchor piles with lower slenderness ratios offer significantly improved pullout resistance. Practical designs should target L/D ratios around 5, especially in uplift-critical applications such as transmission towers or pipeline foundations in expansive soils.

3. Optimize Pile Group Configuration (Prefer 2 × 2 or 3 × 3 Layouts): While increasing pile numbers raises total capacity, it also reduces efficiency. 2 × 2 or 3 × 3 configurations are recommended for maximizing performance without unnecessary material and cost increases.

4. Design for Saturated Soil Conditions: All simulations were conducted under fully saturated conditions to represent worst-case field scenarios. It is advised that practical designs also assume saturation when working in expansive soil environments to ensure safety under extreme moisture fluctuations.

5. Apply Prescribed Displacement Approach for Accurate Design: Using a 10% pile diameter prescribed displacement provides a reliable basis for evaluating uplift behavior. This method should be integrated into design practices and software simulations to more accurately predict performance.

Conclusions

This study provided a comprehensive numerical investigation of the pullout performance of steel anchor pile systems installed in saturated expansive soil. Based on parametric variations including pile configuration, slenderness ratio, and spacing, the following engineering conclusions can be drawn:

1. The pullout capacity of anchor piles significantly improves with increased pile diameter and length. This reinforces the need to prioritize geometric optimization of anchor elements during the early stages of design for expansive soils.

2. An optimal center-to-center spacing of 3D was identified for group pile systems. This spacing yields the most effective balance between individual pile performance and group interaction, offering a practical design benchmark to minimize material usage without compromising pullout capacity.

3. Lower slenderness ratios (L/D) enhance pullout resistance substantially due to greater surface area and more efficient load transfer. This insight is particularly useful for short, squat piles in constrained spaces, where maximizing resistance is crucial.

4. The number of piles in a group directly influences the total uplift resistance, though group efficiency tends to decrease with larger configurations. Designers should consider an optimal number of piles—not merely increasing quantity—to avoid diminishing returns due to stress overlap.

5. The group efficiency, although high in smaller configurations, tends to decline as pile count increases due to overlapping stress zones and reduced mobilization of soil resistance. This finding underlines the importance of evaluating soil-structure interaction beyond linear scalability assumptions.

6. For practical implementation, the study confirms that 3D spacing, L/D ratio around 5, and smaller groups (e.g., 2 × 2 or 3 × 3) are optimal for enhancing pullout resistance in expansive soil applications like transmission towers, lightweight structures, and pipeline anchoring systems.

This research not only validates the mechanical advantage of anchor piles under uplift loading in problematic soils but also serves as a design guide to optimize configurations for real-world engineering applications. Future studies may incorporate dynamic or seismic conditions and experimental validation to further strengthen the proposed recommendations.

Author contributions

AS conceptualized the study and supervised the research; AK assisted in literature review and manuscript drafting; AHA and SA provided domain expertise on expansive soils and model validation; KS and AKT supported data interpretation and model design; JQ contributed to geometric modeling and technical review; ASG led the numerical modeling, coordinated revisions, and is the corresponding author; GJ handled mesh refinement and graphical improvements; RG enhanced the theoretical framework and practical application section; AM edited the manuscript, ensured formatting consistency, and finalized figures and equations.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.