Performance Analysis of Hybrid Steel–Concrete and Timber–Concrete Composite Pile Systems in Variable Density Sandy Soils Using Experimental and Numerical Insights

Abstract

Hybrid composite pile foundations face critical challenges in terms of optimizing load transfer mechanisms across variable soil densities, particularly in regions like Kano, Nigeria, characterized by loose to dense sandy deposits and fluctuating groundwater levels. This study addresses the need for sustainable, high-performance foundation systems that are adaptable to diverse geotechnical conditions. The research evaluates the mechanical behavior of steel–concrete and timber–concrete hybrid piles, quantifying skin friction dynamics, combining eight (8) classical ultimate bearing capacity (UBC) methods (Vesic, Hansen, Coyle and Castello, etc.) with numerical simulations, and assessing load distribution across sand relative densities (10%, 35%, 50%, 75%, 95%). Laboratory investigations included the geotechnical characterization of Wudil River well-graded sand (SW), direct shear tests, and interface shear tests on composite materials. Relative densities were calibrated using electro-pneumatic compaction. Increasing Dr from 10% to 95% reduced void ratios (0.886–0.476) and permeability (0.01–0.0001 cm/s) while elevating dry unit weight (14.1–18.0 kN/m³). Skin friction angles rose from 12.8° (steel–concrete) to 37.4° (timber–concrete) at Dr = 95%, with timber interfaces outperforming steel by 7.4° at Dr = 10%. UBC for steel–concrete piles spanned from 353.1 kN (Vesic, Dr = 10%) to 14,379 kN (Vesic, Dr = 95%), while timber–concrete systems achieved 9537.5 kN (Hansen, Dr = 95%). PLAXIS simulations aligned closely with Vesic’s predictions (14,202 vs. 14,379 kN). The study underscores the significance of soil density, material interfaces, and method selection in foundation design.

1. Introduction

Foundation systems play a pivotal role in ensuring the stability and longevity of infrastructure, particularly in regions with heterogeneous soil conditions [1,2,3,4,5,6,7,8]. In Kano State, Nigeria, where loose to medium-density sandy deposits interbedded with clay lenses dominate, conventional foundation solutions often struggle to address challenges posed by fluctuating groundwater levels and variable soil compaction [9]. These geotechnical complexities demand innovative approaches that balance structural performance, cost-effectiveness, and environmental sustainability. Hybrid composite piles—combining materials such as steel, concrete, and timber—emerge as promising alternatives, leveraging the synergistic strengths of disparate materials to optimize load transfer and adaptability across soil strata [10,11]. Traditional pile design methods, while well-established, frequently overlook the nuanced interactions between composite material interfaces and soil density variations. Existing studies on bearing capacity often focus on homogeneous materials or static soil conditions, leaving gaps in terms of understanding how hybrid systems perform under dynamic density gradients [12,13]. This study addresses these gaps by systematically evaluating the mechanical behavior of hybrid steel–concrete and timber–concrete composite piles across a spectrum of sand relative densities (10% to 95%).

Foundation engineering continues to evolve through innovations that address the complex challenges of soil–structure interactions while incorporating sustainability considerations. Among these advancements, hybrid composite pile systems represent a significant development that merits comprehensive analysis [14,15,16,17,18,19,20]. The integration of numerical simulation into this study offers profound benefits by enabling the comprehensive analysis of complex soil–structure interactions that cannot be fully captured through traditional analytical methods alone. Numerical modeling provides valuable insights into the mechanical behavior at critical interfaces between disparate materials—steel–concrete and timber–concrete—under various loading conditions and environmental factors. This approach allows for the examination of properties such as stress distribution patterns with unprecedented detail, overcoming the limitations of classical bearing capacity methods, which often rely on simplified assumptions regarding material homogeneity and isotropic behavior.

The research aims to integrate experimental, analytical, and numerical methodologies to quantify skin friction dynamics, ultimate bearing capacity (UBC), and load distribution mechanisms methods across five soil density conditions ranging from very loose to very dense. Key objectives include (1) characterizing the geotechnical properties of Wudil River sand under varying compaction states, (2) assessing interfacial shear behavior between composite pile materials and sand, and (3) comparing classical bearing capacity theories (e.g., Vesic, Hansen, Coyle and Castello) with finite element simulations (PLAXIS 3D). Laboratory investigations adhered to ASTM standards (D422-63, D854-23, D4254) for sand characterization, while interface shear tests employed electro-pneumatic compaction to calibrate relative densities. This introduction contextualizes the research problem, outlines objectives, highlights methodological rigor, and previews key contributions, setting the stage for detailed discussions in subsequent sections.

2. Literature Review

The evolution of composite pile systems represents significant progress in foundation engineering. This has emerged from limitations encountered using traditional monolithic pile designs. Historically, pile foundations relied on singular materials—timber, concrete, or steel—each with inherent advantages and limitations. The early documentation of composite approaches dates to the Roman era when timber piles were capped with stone platforms to support structures in poor soil conditions [11]. However, modern engineered composite pile systems primarily emerged in the latter half of the 20th century [9,11]. The theoretical foundations of the analysis pile bearing capacity have traditionally relied on analytical methods developed for monolithic piles. Poulos and Davis provided comprehensive mathematical frameworks based on elastic continuum theory, forming the basis for many subsequent analytical approaches [10]. However, as Randolph noted, these classical theories often inadequately capture the complex load transfer mechanisms in composite piles, where material transitions introduce discontinuities in stiffness and strength properties [20]. The extensive literature reviewed underscores the uniqueness of the current study, examining hybrid steel–concrete and timber–concrete composite piles, as displayed in

Table 1. Literature review.

Author (Study)	Year	Methods	Results Summary
Performance of hybrid cross-laminated timber (CLT)–concrete composite by Bao, Lu [21]	2023	Push-out tests	CLT–concrete composites exhibit efficient force-slip response and slip modulus, with defined failure modes.
Steel–concrete composites with anti-pullout connectors by Sun, Dong [22]	2023	Sample analysis	Anti-pullout connectors reduce rebar stress by >50% and mitigate the capacity decline.
Composite timber columns confined with steel by Kia and Valipour [23]	2021	Compression experiments	Confined timber columns show enhanced compressive performance.
Timber–concrete composites (TCC) by El-Salakawy and Gamal [11]	2024	Case studies, regulatory analysis	TCC systems reduce embodied carbon by 30% and increase timber used in construction.
Steel–concrete joints in hybrid bridges by Zhang, Bao [24]	2025	Analytical investigation	Load transfer mechanisms in steel–concrete joints depend on connection design and material synergy.
Steel, aluminum, and composite structures by You, Xing [25]	2024	Review of trends	Covers advancements in composite structural systems and design frameworks.
Composite fender piles by Chen, Fang [26]	2024	Bending tests	Bending energy absorption varies with pile material and configuration.
Steel–timber hybrid buildings by Trabucco and Perrucci [12]	2025	LCA analysis	Life cycle assessments (LCAs) reveal that timber–concrete hybrids reduce embodied carbon
Current Study	2025	Classical bearing capacity methods (e.g., Terzaghi, Vesic) + PLAXIS 3D simulations	Work on composite systems, soil densification, and sustainability, offering optimized design strategies for semi-arid regions with fluctuating groundwater.

. The combination of analytical comparisons across multiple bearing capacity methods and proposed numerical simulations addresses several identified knowledge gaps while contributing to the growing body of evidence supporting optimized composite pile design. Figure 1 shows the collapse of a structure during bearing capacity failure.

3. Materials, Methods, and Equipment

3.1. Granulometric and Index Properties Analysis of Well-Graded Sand

This study utilized uniformly graded sand from the Wudil River in Kano State, Nigeria. The sand was washed, oven-dried, and sieved between 2 mm and 0.075 mm openings. Particle size distribution was determined using ASTM D422-63, specific gravity was determined using ASTM D854-23, and relative density was determined using ASTM D4254-23. The material was classified as well-graded sand (SW) according to USCS (ASTM D2487). Figure 2 depicts the grain size distribution curve, while

Table 2. Physical and classification parameters of sand for foundation engineering applications.

Sand Geotechnical Properties	Values
D10 (particle diameter at 10% finer)	0.10 mm
D30 (particle diameter at 30% finer)	0.30 mm
D50 (particle diameter at 50% finer)	0.60 mm
D60 (particle diameter at 60% finer)	0.80 mm
Coefficient of curvature (Cc)	1.13
Coefficient of uniformity (Cu)	8.00
USCS class	SW
Maximum grain size (Dmax)	2.00 mm
Minimum grain size (Dmin)	0.01 mm
Difference (Dmax − Dmin)	1.99 mm
Specific gravity (Gs)	2.68
Minimum void ratio (emin)	0.453
Maximum void ratio (emax)	0.920
Minimum dry unit weight (γd, min)	13.7 kN/m3
Maximum dry unit weight (γd, max)	18.2 kN/m3
Minimum optimum moisture content (OMCmin)	7.0%
Minimum optimum moisture content (OMCmax)	10.0%

Notes: Dry unit weights rounded to one decimal place for clarity (original ASTM precision: ±0.01 kN/m³). Specific gravity determined using ASTM D854-23.

summarizes physical properties including void ratios, specific gravity, and uniformity coefficients. This thorough characterization ensures reliable experimental results when investigating sand–pile material interface behavior. The geotechnical properties in the table characterize the sand material comprehensively. The particle size distribution (D₁₀ = 0.10 mm, D₃₀ = 0.30 mm, D₅₀ = 0.60 mm, D₆₀ = 0.80 mm), coefficient of curvature (C_c = 1.13), and coefficient of uniformity (C_u = 8.0) classify this material as well-graded sand (SW) using USCS. The grain size range (0.01–2.0 mm) confirms the pure sand composition without significant silt or gravel. With a specific gravity of 2.68, void ratio limits of 0.453–0.920, and a dry unit weight range of 13.7–18.2 kN/m³, the material demonstrates typical quartz sand characteristics. The optimum moisture content (7–10%) indicates good workability and predictable compaction behavior. These properties provide essential parameters for numerical modeling and geotechnical applications, including backfill, foundation support, and drainage layers.

3.2. Pile Material Properties

The parameters in

Table 3. Parameters of the piles model.

Parameter	Steel Pile	Concrete Pile	Timber Pile
Material Model	Linear Elastic	Linear Elastic	Linear Elastic
Poisson’s Ratio, ν	0.20 ± 0.02	0.20 ± 0.02	0.20 ± 0.02
Modulus of Elasticity, E (kN/m2)	2.01 × 108 ± 5%	2.35 × 107 ± 5%	1.22 × 107 ± 5%
Dry Unit Weight, γd (kN/m3)	76.5 ± 1.5	25.0 ± 0.5	5.10 ± 0.10

Notes: 1. Material properties are nominal values derived from ASTM A36 (steel), ACI 318 (concrete), and ANSI/AWC NDS (timber). 2. Tolerances reflect typical manufacturing variability (±5% for E, ±0.02 for ν, ±2% for γ_d).

characterize steel, concrete, and timber piles used in foundation engineering. All materials are modeled with linear elastic behavior and a constant Poisson’s ratio of 0.2. The modulus of elasticity varies significantly for steel (2.01 × 10⁸ kN/m²), concrete (2.35 × 10⁷ kN/m²), and timber (1.22 × 10⁷ kN/m²), directly affecting deformation resistance under loading. The average dry unit weights differ substantially for steel (76.5 kN/m³), concrete (25 kN/m³), and timber (5.10 kN/m³), influencing both dead load and installation procedures. These distinctive properties determine their suitability for specific geotechnical applications—steel for heavy loads, concrete for cost-effective intermediate applications, and timber for moderate loading conditions. These parameters are essential for numerical modeling, enabling the accurate prediction of pile behavior and the optimization of foundation design. The values in Table 3 represent standardized material properties for steel, concrete, and timber, derived from established codes (e.g., ASTM A36 for steel, ACI 318 for concrete, and ANSI/AWC NDS for timber). These parameters (e.g., modulus of elasticity, Poisson’s ratio) are widely accepted in geotechnical engineering for linear elastic modeling and do not inherently include experimental variability, as they reflect idealized material behavior. However, we have added a footnote to Table 3 clarifying that these values are nominal and based on industry standards, with typical tolerances of ±5% for modulus of elasticity and ±0.02 for Poisson’s ratio.

3.2.1. Case Study I- Hybrid Steel–Concrete Composite Pile

A circular hybrid steel–concrete composite pile was examined in Kano State, Nigeria. The pile’s features include 0.75 m diameter (D), 11 m total length (L), 5 m steel lower section (L_s), 6 m concrete upper section (L_c), and groundwater level at 6 m depth, as shown in Figure 3. The circular configuration provides uniform stress distribution, enhanced lateral load resistance, and reduced soil displacement during installation. In Kano’s loose to medium-density sandy soils with clay lenses, these piles were implemented for the Kano River irrigation project to support bridge abutments in areas with fluctuating groundwater. The steel section penetrated dense sandy layers while the concrete section resisted lateral loads from seasonal river flow. Load testing demonstrated a 22% increase in ultimate bearing capacity compared to conventional bored piles [27].

3.2.2. Case Study II- Hybrid Timber–Concrete Composite Pile

A circular hybrid timber–concrete composite pile was implemented in Kano’s peri-urban residential developments, with a 0.65 m diameter (D), 9 m total length (L), 4 m timber lower section (L_t) (Afzelia Africana hardwood), 5 m concrete upper section (L_c) (with recycled aggregates), and a groundwater level at 5 m depth, as shown in Figure 3. This sustainable design was used for a low-rise housing complex in sandy soils, with monitoring showing minimal differential settlement (≤5 mm) over 18 months and no degradation at the timber–concrete interface despite seasonal moisture variations. Implementation challenges included achieving uniform adhesive bonding in humid conditions and managing thermal expansion mismatches. While showing lower performance in high-load scenarios than steel–concrete alternatives, the timber–concrete design reduced material costs by approximately 15%. The modular design enabled rapid deployment in remote areas, though long-term monitoring remains necessary to assess creep behavior and bio-deterioration risks under cyclic wetting–drying conditions [27].

3.3. Specimen Preparation and Test Method for Calibration of Relative Densities

Calibrating sand relative densities ensures experimental accuracy by establishing compaction–density relationships. Using a 30 cm × 30 cm × 20 cm wooden box and precision balance, specific placement methods were developed for target densities (10%, 35%, 50%, 75%, and 95%) by varying sand pouring height and layer thickness. These densities span loose to very dense states, enabling the observation of threshold behaviors such as contractive–dilative transitions at medium densities. The selected densities correspond to field conditions, with 10–35% representing reclaimed land or hydraulic fills, 50% representing natural sand deposits, and 75–95% representing engineered fills or deep natural deposits. This range facilitates comparison with the existing literature while supporting comprehensive analysis of pile–soil interactions across compaction states.

For the loosest state (10% relative density), sand was gently poured from a height of 10 cm without any additional compaction. This method mimics the natural deposition of sand and results in a very loose packing arrangement. To achieve 35% relative density, sand was poured in 15 cm layers, and each layer was compacted using a Proter electro-pneumatic hammer fitted with a steel tamper plate (15 cm × 15 cm). A plastic base was attached to the bottom of the steel plate to prevent the crushing of sand particles. Each layer was compacted for 1 s. For 50% relative density, the pouring height was reduced to create 10 cm layers, with each layer compacted for 2 s. This increased compaction time resulted in a denser packing of sand particles. The 75% relative density was achieved by reducing the layer thickness to 7.5 cm and increasing the compaction time to 4 s per layer. This method significantly improves the energy input, resulting in a much denser arrangement of sand particles. Finally, for the densest state (95% relative density), sand was poured in thin 5 cm layers, with each compacted for 10 s. This intensive compaction process results in the very tight packing of sand particles, approaching the maximum density achievable in the laboratory. Figure 4a–d illustrate the laboratory equipment assembly used for sand compaction testing, including the wooden test box, Wudil river sand, an electro-pneumatic hammer, and a steel tamper plate.

Post-compaction, sand was leveled and the filled box was measured to determine total sand mass by subtraction. Sand volume was calculated from box dimensions, while moisture content was assessed using multiple samples oven-dried at 105 °C for 24 h per ASTM D2216. Dry unit weight was calculated using mass, volume, and moisture data; they were then combined with previously determined maximum and minimum void ratios (ASTM D4253 and D4254) to compute relative density. The process underwent multiple repetitions for each target density to ensure reliability, with averaged values establishing the final compaction effort–relative density relationship. This calibration enabled consistent specimen preparation for subsequent experiments, ensuring the accurate representation of density states from very loose to very dense conditions for comprehensive pile–sand interaction studies. The relative density calibration procedure balanced established standards with model-scale experimental requirements. While maximum and minimum void ratios followed ASTM D4253 and D4254 standards, the compaction methodology was tailored for laboratory conditions using a wooden box and Proter electro-pneumatic hammer instead of field-scale standards like ASTM D698 or D1557. This equipment selection enabled precise, repeatable energy application in confined settings, with the hammer calibrated empirically through iterative trials to achieve target densities through controlled compaction duration and layer thickness. Moisture content determination adhered strictly to ASTM D2216, maintaining compatibility with standard calculations. This hybrid approach diverged from traditional field compaction practices while ensuring that there were valid relative density calculations through ASTM-compliant void ratio determinations. Though future refinements could align with emerging small-scale modeling standards, the current protocol’s repeatability and cross-validation with established measurements provide sufficient rigor for the experimental scope. Then, 15 trials were conducted for direct shear tests (5 relative densities × 3 normal stresses) and 30 trials were conducted for interface shear tests (5 relative densities × 3 normal stresses × 2 pile materials). Each trial represents an independent specimen preparation and testing sequence, ensuring statistical reliability. For direct shear tests, three specimens per relative density (10%, 35%, 50%, 75%, 95%) were tested under distinct normal stresses (54.5 kPa, 109 kPa, 163.5 kPa), while interface shear tests doubled this to accommodate both steel–concrete and timber–concrete interfaces. Replicate testing (3–5 iterations per condition) was performed for critical parameters (e.g., friction angles, unit weights) to ensure consistency, with uncertainties reported in

Table 4. Sand properties with variation in relative density.

Relative Density, Dr (%)	10	35	50	75	95
Description	Very Loose	Loose	Medium	Dense	Very Dense
Void Ratio, e	0.886 ± 0.015	0.771 ± 0.012	0.682 ± 0.010	0.565 ± 0.008	0.476 ± 0.006
Dry Unit Weight, γd (kN/m3)	14.1 ± 0.3	15.2 ± 0.3	15.9 ± 0.3	17.0 ± 0.3	18.0 ± 0.4
Internal Friction Angle, φ (°)	28 ± 0.5	30.9 ± 0.6	33.7 ± 0.6	36.6 ± 0.7	40 ± 0.8
Permeability, k (cm/s)	1.0 × 10−2 ± 8%	2.6 × 10−3 ± 8%	1.1 × 10−3 ± 8%	3.0 × 10−4 ± 12%	1.0 × 10−4 ± 12%

Notes: 1. Permeability values derived via constant-head tests (ASTM D2434) for D_r = 10–50% and falling-head tests (ASTM D5084) for D_r = 75–95%. 2. Uncertainties reflect method-specific precision: ±8% for constant-head, ±12% for falling-head. 3. Void ratios and unit weights calculated from triplicate trials; uncertainties represent 95% confidence intervals.

,

Table 5. Skin friction angles between sand and pile materials.

Relative Density, Dr (%)	10	35	50	75	95
Sand Description	Very Loose	Loose	Medium	Dense	Very Dense
δ (Concrete–Steel) (°)	12.8 ± 0.5	18.6 ± 0.6	22.6 ± 0.7	27.4 ± 0.8	32.8 ± 0.9
δ (Concrete–Timber) (°)	20.2 ± 0.6	22.3 ± 0.7	25.5 ± 0.7	30.7 ± 0.8	37.4 ± 1.0

Notes: 1. Uncertainties reflect triplicate trials of interface shear tests (ASTM D5321). 2. Timber surfaces were roughened to R_z ≈ 50 µm; steel surfaces were wire-brushed.

and

Table 6. Parametric analysis of sand properties for numerical simulation of hybrid pile analysis.

Relative Density, Dr (%)	10	35	50	75	95
Sand Description	Very Loose	Loose	Medium	Dense	Very Dense
Material Model	Mohr–Coulomb	Mohr–Coulomb	Mohr–Coulomb	Mohr–Coulomb	Mohr–Coulomb
Drainage Type	Drained	Drained	Drained	Drained	Drained
Poisson’s Ratio, ν	0.3 ± 0.02	0.3 ± 0.02	0.3 ± 0.02	0.3 ± 0.02	0.3 ± 0.02
Modulus of Elasticity, E (kN/m2)	12,000 ± 600	26,500 ± 1325	32,300 ± 1615	58,800 ± 2940	70,100 ± 3505
Dry Unit Weight, γd (kN/m3)	14.1 ± 0.3	15.2 ± 0.3	15.9 ± 0.3	17.0 ± 0.3	18.0 ± 0.4
Saturated Unit Weight, γsat (kN/m3)	22.60 ± 0.45	22.60 ± 0.45	22.60 ± 0.45	22.60 ± 0.45	22.60 ± 0.45
Internal Friction Angle, ϕ (°)	28 ± 0.5	30.9 ± 0.6	33.7 ± 0.6	36.6 ± 0.7	40 ± 0.8
Dilatancy Angle, ψ (°)	0 ± 0.2	5.9 ± 0.3	9.4 ± 0.4	15.3 ± 0.5	20 ± 0.6
Cohesion, c (kN/m2)	0 ± 0.05 kN/m2	0.115 ± 0.01	0.15 ± 0.01	0.445 ± 0.03	0.706 ± 0.04
Interaction Factor, Rint	0.8 ± 0.05	0.8 ± 0.05	0.8 ± 0.05	0.8 ± 0.05	0.8 ± 0.05

Notes: 1. Uncertainties in E and c reflect ±5% variability in PLAXIS 3D calibration. 2. Dilatancy angles derived from triaxial test correlations (ASTM D7181).

(±0.5° for φ, ±1.2 kN/m³ for γ_d).

3.4. Direct Shear Test (DST)

The direct shear test determined sand shear strength parameters using a standard 6 cm × 6 cm × 2 cm apparatus. Prior to testing, the equipment was cleaned, inspected, and assembled with alignment screws, and we applied silicon grease to inner walls to minimize friction. Sand specimens were prepared at 10%, 35%, 50%, 75%, and 95% relative densities, leveled with a straight edge, and topped with a cap before transfer to the apparatus. Tests employed three normal stresses (54.5 kPa, 109 kPa, and 163.5 kPa) for each density to establish shear strength envelopes. Consolidation preceded shearing, with testing commencing after vertical displacement stabilization. Figure 5 illustrates the apparatus for measuring soil strength parameters through controlled horizontal displacement under normal stress. The strain-controlled procedure (0.5 mm/min) ensured proper drainage while documenting shear stress, horizontal displacement, and vertical displacement until reaching peak stress or constant stress at approximately 10% of specimen length. Fifteen tests were conducted across all density–stress combinations, with moisture content determined after each test. Analysis involved plotting peak shear stress against normal stress to establish Mohr–Coulomb failure envelopes, yielding internal friction angles (φ) that typically increased with relative density due to enhanced particle interlocking, providing critical insights for geotechnical applications.

3.5. Interface Shear Test (IST)

The interface shear test evaluated the interaction between sand and two pile materials—timber and closed-end steel–concrete composite piles—using a modified direct shear apparatus. Pile material specimens were precisely fitted to the lower half of the shear box (6 cm × 6 cm). The hybrid timber–concrete composite and closed-end steel–concrete composite pile specimens were fabricated with high precision, each comprising two 6 cm × 6 cm × 3 cm sections. The timber section utilized construction-grade Douglas Fir softwood, while the steel section was cut from ASTM A36 structural steel square tubing. Concrete sections were cast in wooden molds with reinforcing cages of four 6 mm diameter steel bars positioned at corners for structural integrity. A 30 MPa Portland cement-based concrete mix (1:4 cement-to-aggregate ratio with water-reducing admixture) was used. Specimens were cured for 28 days at 23 °C and 50% relative humidity, and were then kept moist with wet burlap for 7 days. This was followed by 21 days of air curing. Figure 6a,b depict the composite pile specimens prepared for interface shear testing.

Surface preparation for bonding included the light roughening of timber and steel by belt-sanding and wire-brushing concrete surfaces. Fabricated specimens achieved dimensional tolerances of ±0.2 mm for the cross-section and ±0.5 mm for the length. Destructive testing confirmed bond integrity, with sections joined using high-strength epoxy adhesive (20 MPa shear strength). The direct shear apparatus was modified by replacing the lower half of the shear box with fixed pile material specimens, positioning the sand–pile interface at the shear plane. Sand specimens were prepared in the upper half to target relative densities of 10%, 35%, 50%, 75%, and 95%. Normal loads were applied at three stress levels (54.5 kPa, 109 kPa, and 163.5 kPa) for each density–material combination. After consolidation under normal stress conditions, interface shear testing proceeded at 0.5 mm/min under drained conditions until we reached peak stress or constant stress at approximately 10% of specimen length. The comprehensive testing program included 30 individual interface shear tests. Analysis involved plotting peak shear stress against normal stress to establish interface shear strength envelopes, with the slope yielding the skin friction angle (δ) between sand and pile material at specific relative densities. This investigation revealed the relationship between friction angle, sand compaction state, and pile material type, providing insights for modeling pile foundations and understanding load transfer mechanisms.

The specimen preparation process emphasized rigorous quality control to ensure valid interface shear testing. The selected two-component epoxy adhesive (20 MPa shear strength) demonstrated resistance to moisture and temperature fluctuations, with a glass transition temperature exceeding 60 °C. Adhesive performance was verified through lap shear tests, confirming that there were bond strengths exceeding 18 MPa under ambient conditions and 15 MPa after water immersion. Surface preparation involved degreasing with acetone, grit-blasting to achieve uniform roughness (Rz ≈ 50 μm), and epoxy priming. Bonding occurred under controlled conditions (23 ± 1 °C, 50 ± 5% RH) with adhesive thickness maintained at 0.5 ± 0.1 mm. Quality verification included ultrasonic testing for voids and pull-off tests, yielding average bond strengths of 2.8 MPa for timber–concrete and 3.2 MPa for steel–concrete interfaces. Durability assessment through accelerated aging showed a <10% reduction in bond strength after 200 h of temperature and humidity cycling. Destructive testing revealed cohesive failures within the adhesive layer for timber–concrete and adhesive–concrete interfacial failures for steel–concrete specimens, aligning with theoretical predictions. These quality assurance procedures ensured that interface shear test results accurately reflected mechanical interactions between pile materials and sand, providing reliable data for geotechnical design.

3.6. Classical Bearing Capacity Methods

The ultimate bearing capacity of a pile, $\left(Q_{\mathrm{ult}}\right)$, represents the maximum load that a pile can support before failure occurs. In geotechnical engineering, the total capacity is generally assumed to be the sum of two components, as shown in Equation (1).

$$Q_{\mathrm{ult}}=Q_s+Q_b$$

(1)

where

• $Q_s$ = shaft (or skin friction) resistance mobilized along the pile’s lateral surface;
• $Q_b$ = end-bearing resistance developed at the pile tip.

Each analytical method discussed herein is based on the principles of effective stress and the Mohr–Coulomb failure criterion. However, differences in assumptions and modifications (such as inclination, depth, and shape factors) lead to variations in the predicted capacities. The following sections describe the methods used by Terzaghi, Berezantsev, Brom, Meyerhof, Coyle and Castello, Janbu, Vesic, and Hansen in detail.

3.6.1. Terzaghi (1943) Methods

In all methods, the effective vertical stress (${\sigma }_v^{\prime }\left(z\right)$) is a fundamental quantity. For a soil with a water table located at depth ($z_w$) and a pile embedded up to a total depth (L), the effective stress is defined as follows:

Above the water table $(0\le z\le z_w)$

$${\sigma }_v^{\prime }\left(z\right)={\gamma }_{d}z$$

where (${\gamma }_d$) is the dry unit weight of the soil.

Below the water table $(z_w\le z\le L)$

$${{\sigma }^{\prime }}_v(z)={\gamma }_d{z}_w+{{\gamma }^{\prime }}_s(z-z_w)$$

with the submerged unit weight defined as ${\gamma }_s^{\prime }={\gamma }_{\mathrm{sat}}-{\gamma }_w,$ where (${\gamma }_{\mathrm{sat}}$) is the saturated unit weight and (${\gamma }_w$) is the unit weight of water.

The lateral friction along the pile is modeled by assuming that the unit skin friction, $\tau \left(z\right)$, is proportional to the effective normal stress at that depth, as shown in Equation (2).

$$\tau \left(z\right)=K{\sigma }_v^{\prime }\left(z\right)\mathit{tan}\delta$$

(2)

where

• K = lateral earth pressure coefficient (often parameterized as $\left(K=0.5+0.008Dr\right)$ as per Bhusan’s (1983) equation to estimate K with (D_r) representing the relative density in percent);
• $\delta =$ interface friction (or adhesion) angle between the pile composite materials and the soil.

For an infinitesimal pile element of length (dz), the incremental frictional resistance is given by Equation (3).

$$d{Q}_s=\tau (z)(\pi D)dz$$

(3)

where (D) is the pile diameter. Integration over the entire length yields Equation (4).

$$Q_s=\pi DK\tan \delta {\displaystyle {\int }_0^L{\sigma }_v^{\prime }}(z)dz$$

(4)

Due to the discontinuity in effective stress at the water table, the integration is commonly split into two segments:

Segment 1 (0 to (z_w)):

$$I_1={\displaystyle {\int }_0^{z_w}{\gamma }_d}zdz={\displaystyle \frac{{\gamma }_d{z}_w^2}{2}}$$

Segment 2 ((z_w) to (L)):

$$I_2={\displaystyle {\int }_{z_w}^L\left[{\gamma }_d{z}_w+{{\gamma }^{\prime }}_s(z-z_w)\right]}dz={\gamma }_d{z}_w(L-z_w)+{\displaystyle \frac{{{\gamma }^{\prime }}_s{(L-z_w)}^2}{2}}$$

Thus, the complete expression becomes Equation (5).

$$Q_s=\pi DK\mathit{tan}\delta \left[I_1+I_2\right]$$

(5)

As in Equation (6), the effective vertical stress is seen at the pile tip (depth (L)).

$${{\sigma }^{\prime }}_{v,\mathrm{tip}}={\gamma }_d{z}_w+{{\gamma }^{\prime }}_s(L-z_w)$$

(6)

For a circular pile, the base area is as follows:

$$A_b={\displaystyle \frac{\pi D^2}{4}}$$

The end-bearing capacity is then expressed as shown in Equation (7):

$$Q_b=N_q{\sigma }_{v,\mathrm{tip}}^{\prime }{A}_b$$

(7)

The bearing capacity factor is commonly computed as shown in Equation (8):

$$N_q={\displaystyle \frac{e^{2(3\pi /4-{\varphi }^{\prime }/2)\tan {\varphi }^{\prime }}}{2{\cos }^2(45+{\varphi }^{\prime }/2)}}$$

(8)

(ϕ) represents the soil’s internal friction angle.

3.6.2. Berezantsev’s (1961) Method

Berezantsev’s method is instrumental in calculating bearing capacity for circular piles in sand, combining empirical data with theoretical considerations to account for soil–pile interactions. The approach centers on the principle that a pile’s ultimate bearing capacity depends on the soil’s internal friction angle and pile geometry [28]. The method introduces a bearing capacity factor N_q that represents frictional resistance contributions. This factor varies with the angle of internal friction and the pile’s depth-to-width ratio, as illustrated in graphical representations (Supplementary Material S1). These graphs demonstrate how bearing capacity factors increase with higher friction angles, reflecting enhanced soil resistance against shear failure. Additionally, deeper piles show higher bearing capacities due to increased soil confinement [28]. When applying this method, engineers must first determine the soil’s angle of internal friction, which governs the bearing capacity factors. After calculating the pile’s depth-to-width ratio, appropriate N_q values can be interpolated from Berezantsev’s graph. The ultimate bearing capacity is then computed using Terzaghi equations for both shaft resistance along the pile’s lateral surface and end-bearing resistance at the pile tip. This methodology provides a comprehensive framework for predicting the load-bearing capabilities of circular piles in sandy environments.

3.6.3. Brom (1966) Method

The Broms method (1966) provides a systematic approach to estimating the ultimate bearing capacity of pile structures in sandy soils, where load-bearing capacity primarily derives from frictional resistance [29]. The methodology combines empirical data with theoretical principles to address soil–pile interactions. Key to this approach are the bearing capacity factors N_q and N_γ, which represent contributions from surcharge and skin friction. These factors vary with the soil’s angle of internal friction (ϕ) and sand density, as illustrated in Supplementary Material S1. The graph demonstrates that as ϕ increases, both N_q and N_γ rise, indicating enhanced soil resistance against shear failure. This relationship emphasizes the importance of accurately determining soil frictional properties when applying the method. The graph also shows how sand density affects bearing capacity factors. The standard penetration test value (N_cor), indicating sand density, correlates with higher values of N_q and N_γ as density increases, highlighting soil compaction’s role in enhancing pile load-bearing capacity. For cohesionless soils in deep foundations, the ultimate bearing capacity follows the classical Terzaghi formulation, with maximum base, tip, or point-bearing resistance capped at 11,000 kN/m².

3.6.4. Hansen (1970) Method

The Hansen method (1970) provides a comprehensive framework for analyzing pile performance in sandy soils, where load-bearing capacity primarily stems from frictional resistance. The approach integrates empirical data with theoretical principles to address the complex interplay between soil properties, pile geometry, and loading conditions [30]. Key to this method are the bearing capacity factors N_q and N_γ, which represent contributions from surcharge and skin friction. These factors vary with the angle of internal friction (ϕ) and soil density. In Hansen’s formulation, N_q and N_γ increase with higher friction angles, reflecting the enhancement of soil resistance as ϕ rises. This relationship emphasizes the critical importance of accurately determining soil frictional properties [31]. Hansen’s method distinguishes itself by incorporating additional refinement factors: shape factors adjust for the pile’s cross-sectional geometry; depth factors account for increased resistance from deeper embedment; and inclination factors consider the effects of pile tilt on overall capacity. When applying this method, engineers must first determine the soil’s angle of internal friction and sand density, and then use Hansen’s equations or graphs to establish appropriate N_q and N_γ values. For cohesionless soils (c = 0), the end-bearing component is calculated using Equation (9), providing a refined estimate of pile bearing capacity in sandy conditions.

$$Q_b=A(q^{\prime }{N}_{q^{\prime }}{s}_q{d}_q{i}_q{b}_q+0.5{\gamma }^{\prime }{B}^{\prime }{N}_{\gamma }{s}_{\gamma }{d}_{\gamma }{i}_{\gamma }{b}_{\gamma })$$

(9)

where

• A = pile base area ($\pi B^2/4$ for circular piles);
• q^′ = effective overburden pressure at the pile toe;
• B^′ = pile diameter.

Hansen proposed Equations (10) and (11) to assess bearing capacity factors.

$$N_q=e^{\pi {\mathit{tan}\varphi }^{\prime }}{\mathit{tan}}^2(45°+{\displaystyle \frac{{\varphi }^{\prime }}{2}})$$

(10)

$$N_{\gamma }=1.5(N_q-1){\mathit{tan}\varphi }^{\prime }$$

(11)

Shape factors for circular piles are expressed as follows:

$$s_q=1+{\displaystyle \frac{B^{\prime }}{L^{\prime }}}\sin {\varphi }^{\prime }$$

$$s_{\gamma }=1-0.4{\displaystyle \frac{B^{\prime }}{L^{\prime }}}\ge 0.6$$

Depth factors for deep foundations (D/B > 1):

$$d_q=1+2\tan {\varphi }^{\prime }{(1-\sin {\varphi }^{\prime })}^2{\tan }^{-1}({\displaystyle \frac{D}{B}})$$

$$d_{\gamma }=1.0$$

Inclination factors for vertical loading:

$$i_q=i_{\gamma }=1.0$$

Base factors for horizontal ground surface:

$$b_q=b_{\gamma }=1.0$$

Hansen (1970) maintained the complete theoretical bearing capacity equation structure, even for deep foundations, including both the overburden term (q′N_q) and the self-weight term (0.5 γ’B’N_γ). This follows his general approach to foundation design, where he applied modification factors to the complete Terzaghi equation. In contrast, Meyerhof (1976) simplified his pile capacity equation for deep foundations. He recognized that the self-weight term becomes negligible at significant depths compared to the overburden pressure term. Meyerhof empirically determined that the base capacity could be only adequately represented for typical pile depths by applying the modified N_q* factor to the overburden pressure. This difference reflects their distinct approaches. Hansen maintained theoretical completeness with comprehensive modification factors, and Meyerhof developed a more practice-oriented, simplified approach based on field observations. This is why the N_γ term appeared in the Hansen formulation but was intentionally omitted by Meyerhof for deep foundations. Hansen’s shaft resistance formula for total shaft resistance along the pile is the same as Equation (5). This formulation accounts for the varying effective stress with depth and allows for different soil parameters in each segment.

3.6.5. Meyerhof (1976) Method

The Meyerhof method (1976) offers a sophisticated approach to calculating pile bearing capacity in sandy soils, where load-bearing capacity primarily comes from frictional resistance. The methodology integrates empirical data with theoretical principles to address the complex relationships between soil properties, pile geometry, and loading conditions [32]. Central to this approach are the bearing capacity factors N_c and N_q, which represent contributions from cohesion and surcharge, respectively. These factors vary with the angle of internal friction (ϕ), soil density, and other parameters, as illustrated in the Supplementary Material S1. In Meyerhof’s formulation, both N_c and N_q increase with higher friction angles, reflecting enhanced soil resistance as ϕ rises and emphasizing the importance of accurately determining soil frictional properties. Meyerhof’s method also incorporates shape and depth factors to refine calculations. Shape factors adjust for the pile’s cross-sectional geometry, while depth factors account for increased resistance from deeper embedment [33]. When applying this method, engineers must determine the soil’s angle of internal friction and sand density, and then use Meyerhof’s equations or graphs to establish appropriate N_c and N_q values. The ultimate bearing capacity is then calculated using Equation (12), which defines the end-bearing capacity component, providing a comprehensive assessment of pile performance in sandy conditions.

$$Q_b=A_b\times {\sigma }_v^{\prime }\times N_q\times s_q\times d_q\le q_{lim}{A}_b$$

(12)

Depth factors: $d_q=1+0.1\sqrt{k}\left({\displaystyle \frac{D}{B}}\right).$ Shape factors: $s_q=1+0.1k{\displaystyle \frac{B}{L}}$ The bearing capacity factor is determined as shown in Equation (13).

$$N_q=e^{\pi {\mathit{tan}\varphi }^{\prime }}{tan}^3(45+{\displaystyle \frac{{\varphi }^{\prime }}{3}})$$

(13)

The total shaft resistance of a pile can be expressed in segments 1 and 2, as in the Terzaghi case. This equation accounts for both the soil above and below the water table, considering the change in effective stress due to buoyancy effects.

3.6.6. Janbu (1976) Method

The Janbu method (1976) offers a comprehensive approach to this challenge, providing a robust framework that accounts for various factors influencing pile performance. This method addresses the complexities of sandy soils, which primarily derive their load-bearing capacity from frictional resistance [34]. Janbu’s methodology is grounded in empirical data and theoretical principles, considering the interplay between soil properties, pile geometry, and loading conditions. The relationship between these factors and the parameters above is meticulously analyzed through graphical (Supplementary Material S1) and analytical methods. In Janbu’s formulation, N_q functions increase with the angle of internal friction, reflecting the enhanced resistance the soil offers as ϕ rises. This relationship underscores the importance of understanding the soil’s frictional properties when applying Janbu’s method to sandy conditions. The base resistance is calculated as shown in Equation (14).

$$Q_b=A{q}^{\prime }{N}_q^{*}$$

(14)

where

• $Q_b$ = pile base area;
• q^′ = effective overburden pressure at pile tip;
• N_q^* = Janbu’s modified bearing capacity factor.

Janbu’s bearing capacity factor incorporates the surface failure angle, which is calculated as shown in Equation (15).

$$N_q^{*}={\left[\tan \varphi +\sqrt{1+{\tan }^2\varphi }\right]}^2{e}^{2\psi \tan \varphi }$$

(15)

where ψ = angle parameter.

The angle parameter (ψ) in Janbu’s bearing capacity equation correlates systematically with soil relative density (Dr), reflecting fundamental soil mechanics principles regarding particle arrangement and failure mechanisms. Based on the literature review and field observations, specific values are established for different density conditions [35]. For very loose sands (Dr = 10%), ψ = 60° reflects minimal particle interlocking and wide failure zones as particles readily rearrange during shearing. In loose sands (Dr = 35%), ψ increases to 70° due to enhanced particle interaction, creating steeper failure surfaces, although they are still relatively wide compared to denser states. Medium-density sands (Dr = 50%) represent a transition point where ψ = 75°, capturing the balance between particle sliding and interlocking mechanisms with moderate dilation behavior. For dense sands (Dr = 75%), ψ increases substantially to 85° due to significant particle interlocking, resulting in more confined failure zones and steeper surfaces. In very dense sands (Dr = 95%), ψ reaches its practical maximum of 90°, corresponding to the highest degree of particle interlocking and the most direct failure path. This progression aligns with the influence of void ratio and particle arrangement on strength characteristics. These values should be considered approximate, with potential adjustments based on site-specific conditions. The total shaft resistance calculation follows Terzaghi’s equations, accounting for soil conditions both above and below the water table and considering effective stress changes due to buoyancy effects.

3.6.7. Vesic’s Method (1977)

Vesic’s method (1977) provides a comprehensive approach to analyzing the bearing capacity of circular piles in sand, incorporating soil compressibility and the critical depth concept. The method determines bearing capacity factors by considering both soil friction angle and rigidity index—the ratio of soil shear modulus to the initial mean normal stress times the strength parameter. This inclusion of soil stiffness distinguishes Vesic’s method from earlier bearing capacity theories [36]. The approach accounts for the critical depth phenomenon, where the bearing capacity reaches a limiting value rather than increasing linearly with depth beyond a certain point. This critical depth typically ranges between 10 and 20 pile diameters, depending on sand relative density. Vesic’s method also differentiates between installation techniques, recognizing that driven piles achieve higher bearing capacities than bored piles due to the surrounding soil’s densification during installation [37]. Additionally, the method addresses scale effects in pile foundations, acknowledging that unit base resistance does not increase indefinitely with pile size—a particularly important consideration for large-diameter piles where conventional theories might overestimate capacity [38]. The base resistance is calculated using Equation (16), providing a more nuanced assessment of pile performance in sandy conditions.

$$Q_b=A\times q=A({\overline{\sigma }}_o{N}_q^{*})$$

(16)

where ${\overline{\sigma }}_o=$ mean effective normal stress at the pile tip.

The mean effective stress is calculated as shown in Equation (17).

$${\overline{\sigma }}_o=\left({\displaystyle \frac{1+2K}{3}}\right)q^{\prime }$$

(17)

where q^′ = effective overburden pressure at the pile tip.

Vesic related the bearing capacity factor to the reduced-rigidity index, which is calculated using Equation (18).

$$N_q^{*}=e^{\pi \tan {\varphi }^{\prime }}\left({\displaystyle \frac{3}{3-\sin {\varphi }^{\prime }}}\right)e^{[(4\sin {\varphi }^{\prime })/(3-\sin {\varphi }^{\prime })]\ln I_{rr}}$$

(18)

The reduced-rigidity index accounts for soil compressibility:

$$I_{rr}={\displaystyle \frac{I_r}{1+I_r\Delta }}$$

where $I_r=$ rigidity index and $\Delta =$ average volumetric strain in the plastic zone

$$I_r={\displaystyle \frac{E_s}{2(1+{\mu }_s)(c^{\prime }+q^{\prime }\tan {\varphi }^{\prime })}}$$

where

• $E_s$= soil elastic modulus;
• ${\mu }_s=$ Poisson’s ratio.

Vesic recognized a critical depth beyond which effective stress remains approximately constant:

$$L_c\approx 15-20D$$

The selection of volumetric strain (Δ) values in Vesic’s reduced-rigidity index calculation correlates systematically with sand relative density [39,40,41]. Very loose sands (10% relative density) exhibit volumetric strains of approximately 0.050, reflecting significant volume change potential due to minimal particle interlocking. Loose sands (35% relative density) demonstrate a moderately high volumetric strain of 0.035, as incipient interlocking begins to limit compression. Medium-density sands (50% relative density) represent a transitional state with volumetric strain values of 0.020, balancing contractive and dilative tendencies. Dense sands (75% relative density) show a decreased volumetric strain of approximately 0.012 due to significant particle interlocking restricting rearrangement, although some compression remains possible under high confining pressures. Very dense sands (95% relative density) exhibit a minimal volumetric strain of approximately 0.006, resulting from tight particle packing and strong dilative tendencies. These correlations derive from theoretical soil mechanical principles, experimental observations, and field performance data, demonstrating the inverse relationship between relative density and compressibility under complex loading conditions. The shaft resistance approach remains fundamentally similar to Terzaghi’s method.

3.6.8. Coyle and Castello (1981) Method

The method of Coyle and Castello (1981) calculates circular pile bearing capacity in sand through empirical design charts, relating bearing capacity factor (N_q*) to relative depth (L/d) and soil friction angle (φ). Their approach plots relative depth against the bearing capacity factor on a logarithmic scale, with curves illustrating variations across friction angles from 30° to 40° [42]. A distinctive feature is the recognition that bearing capacity factors reach limiting values at greater depths, as shown by curves becoming vertical. This reflects the critical depth concept in pile foundations [43]. The method’s empirical foundation in pile load test data enhances its practical utility, though its primary database of driven piles may require modifications for other pile types. The charts demonstrate that higher friction angles produce larger bearing capacity factors, particularly at lower relative depths where curve separation is more pronounced. End-bearing and shaft resistance calculations follow Terzaghi’s equations, assuming full mobilization. Figure 7 depicts a sequential research methodology used for analyzing hybrid composite pile systems, integrating multiple characterization techniques and analytical methods to evaluate the ultimate bearing capacity and load transfer mechanisms in steel–concrete and timber–concrete composite foundations.

4. Results and Discussions

4.1. Properties and Behavior of Sand at Various Relative Densities

Table 4 illustrates the relationship between relative density and sand’s physical and mechanical properties, demonstrating how sand’s characteristics systematically change across different density states. This comprehensive characterization is crucial for geotechnical engineering applications. The relative density values range from 10% to 95%, corresponding to very loose to very dense sand classifications. This range effectively captures the full spectrum of naturally occurring sand states in geotechnical practice. The void ratio shows an inverse relationship with relative density, decreasing from 0.886 for very loose sand to 0.476 for very dense sand. This reflects the more efficient particle packing achieved at higher densities. The average dry unit weight demonstrates a clear positive correlation with relative density, increasing from 14.1 kN/m³ for very loose sand to 18 kN/m³ for very dense sand. This relationship reflects the increased particle contact and reduced void space as the sand is denser, resulting in higher mass per unit volume. The internal friction angle exhibits significant variation across the density range, increasing from 28 degrees in very loose sand to 41 degrees in very dense sand. This substantial change in friction angle has important implications for the sand’s shear strength and bearing capacity, with denser states providing considerably higher resistance to deformation and failure.

Permeability shows a marked decrease with increasing relative density, ranging from 0.01 cm/s for very loose sand to 0.0001 cm/s for very dense sand. This inverse relationship results from the reduction in void spaces and interconnected pore channels as the sand becomes more densely packed, thereby reducing the ease with which water can flow through the soil matrix. These interrelationships among sand properties demonstrate the fundamental importance of relative density in determining the engineering behavior of sandy soils. Also, Table 1 provides essential input parameters for geotechnical design calculations and numerical modeling, enabling engineers to make informed decisions based on site-specific soil conditions. Understanding these relationships is particularly crucial in foundation engineering, slope stability analysis, and soil improvement projects, where the accurate characterization of soil properties is essential for safe and efficient design. The systematic variation in these properties with relative density also provides valuable insights for predicting soil behavior under different loading conditions and environmental factors. The permeability values in Table 4 were derived from constant-head permeability tests (ASTM D2434) for loose to medium-density sands (Dr = 10–50%) and falling-head tests (ASTM D5084) for dense to very dense sands (Dr = 75–95%), reflecting method-specific precision. The apparent variation in decimal places arises from the inherent resolution of each test: constant-head results are reported to align with flow measurement accuracy (±5%) to two decimal places (e.g., 0.01 cm/s), while falling-head tests for low-permeability sands are truncated to four decimal places (e.g., 0.0001 cm/s) due to smaller volumetric increments. To enhance consistency, we revised all permeability values to scientific notation (e.g., 1 × 10⁻² cm/s to 1 × 10⁻⁴ cm/s) and included uncertainty ranges (±8% for constant-head, ±12% for falling-head) in Table 4. The experimental uncertainties, direct shear (DST) and interface shear (IST) test results include ± values for friction angles (e.g., φ = 28° ± 0.5°) and unit weights (e.g., γ_d = 14.1 ± 0.3 kN/m³), calculated from triplicate trials per condition.

4.2. Skin Friction Angle Analysis in Pile–Soil Interfaces

Table 5 illustrates the relationship between sand relative density and skin friction angles for different pile materials, specifically examining the interface behavior between sand and concrete–steel versus concrete–timber combinations. This information is crucial for understanding pile–soil interaction in deep foundation design. For concrete–steel interfaces, the skin friction angle significantly increases from 12.8 degrees in very loose sand to 32.8 degrees in very dense sand. This progressive increase reflects the enhancement in mechanical interlocking and friction development as sand density increases. The relationship appears to be relatively linear, with each increment in relative density corresponding to a proportional increase in friction angle. The concrete–timber interface exhibits consistently higher skin friction angles across all relative density values, ranging from 20.2 degrees in very loose sand to 37.4 degrees in very dense sand. This higher friction angle can be attributed to timber materials’ natural surface roughness and texture, qualities which typically provide better mechanical interlocking with sand particles compared to smoother concrete–steel surfaces. The difference in skin friction angles between the two interface types is most pronounced in very loose sand conditions, where timber interfaces show approximately 7.4 degrees higher friction than concrete–steel interfaces. This difference is important for pile design in loose sandy soils, where timber piles might offer superior shaft resistance despite their generally lower structural capacity.

The influence of relative density on skin friction angle is more pronounced for concrete–steel interfaces, showing a total increase of 20 degrees from very loose to very dense conditions, compared to the increase of 17.2 degrees for concrete–timber interfaces. This suggests that the concrete–steel interface is more sensitive to changes in sand density, an important consideration in foundation design for varying soil conditions. These relationships have significant practical implications for pile design, particularly in terms of calculating shaft resistance and overall pile capacity. The higher skin friction angles associated with timber interfaces might make them preferable in certain applications, especially where shaft resistance is a critical design consideration and where soil conditions are suitable for timber pile implementation. The systematic variation in skin friction angles with relative density provides valuable input for foundation engineering, numerical modeling, and analytical calculations. This enables more accurate predictions of pile behavior under various soil conditions. This understanding is essential for optimizing pile design and ensuring adequate foundation performance in different geotechnical scenarios.

4.3. Load Transfer Mechanisms and Performance Dynamic in Hybrid Composite Pile Foundation Systems

Figure 8a–d show the mechanical behavior and load transfer mechanisms of hybrid composite piles across different soil densification states. For the hybrid steel–concrete composite pile (Case Study I), the ultimate load capacity (Q_ult) demonstrates pronounced dependence on soil density and the computational method employed. The skin friction (Q_s) and base resistance (Q_b) exhibit systematic variations across different relative density (Dr) conditions, ranging from very loose (10%) to very dense (95%) soil environments. Notably, the method of Coyle and Castello shows a progressive increase in skin friction contribution from 23.3% at very loose conditions to 46.5% at very dense conditions. This trend suggests the existence of an enhanced mechanical interaction between the pile and surrounding soil as density increases. Conversely, the base resistance proportion correspondingly decreases from 76.7% to 53.5%, indicating a shifting load transfer mechanism with increasing soil compactness. Comparative analysis across different computational methods reveals significant methodological variations. The Janbu method, for instance, demonstrates the most extreme load distribution, with base resistance accounting for over 93% of the ultimate load across all density ranges. In contrast, the Brom method shows a more balanced load distribution, with skin friction contributing between 32 and 39% of the total load capacity.

The hybrid timber–concrete composite pile exhibits distinct load transfer characteristics, with skin friction contributing 15% in very loose conditions up to 39% in very dense conditions according to Coyle and Castello’s method. The Vesic method reveals more dramatic variations, with skin friction accounting for 43.7% of ultimate load in very loose conditions, a number that decreases significantly to 9.9% in very dense conditions. This variability highlights soil density’s critical influence on load transfer mechanisms. The performance differences across analytical approaches emphasize the necessity for comprehensive geotechnical investigation and the use of multiple analytical methods when evaluating hybrid composite piles. The observed mechanical behavior complexity stems from material interfaces, soil conditions, and computational methodologies. Results indicate that hybrid composite piles provide sophisticated foundation solutions with adaptable load-bearing characteristics—steel–concrete composites demonstrate superior capacity in dense to very dense soils, while timber–concrete variants offer environmentally conscious alternatives with comparable performances. These findings validate the hybrid composite pile approach, demonstrating potential for optimized foundation design through strategic material composition and sophisticated load transfer mechanisms, while underscoring the importance of site-specific considerations, material interface dynamics, and comprehensive geotechnical analysis.

4.4. Ultimate Bearing Capacity (UBC) Variability in Hybrid Composite Pile Foundation Systems

Table 6 presents comprehensive mechanical and physical parameters of sand across varying relative densities, while Table 2 details three pile materials (steel, concrete, and timber) used in the foundation system. These are essential for numerical simulation of hybrid pile behavior. The characterization ranges from very loose to very dense conditions, providing a robust computational modeling framework. The Mohr–Coulomb material model is consistently applied across all density states, appropriately capturing the elastoplastic stress–strain behavior of sand under typical pile foundation loading conditions. Drained conditions are specified for all density states, reflecting sandy soils’ typical rapid pore water pressure dissipation during loading. A constant Poisson’s ratio of 0.3 is maintained throughout, representing typical sandy soil lateral deformation characteristics. The modulus of elasticity increases substantially with relative density, ranging from 12,000 kN/m² in very loose sand to 70,100 kN/m² in very dense sand, highlighting the importance of accurate soil stiffness characterization in hybrid pile numerical simulations. The unit weight parameters show notable trends: dry unit weight increases with relative density while saturated unit weight remains constant at 22.60 kN/m³. This relationship is particularly relevant for effective stress and pile capacity calculations under varying groundwater conditions.

The study emphasizes key outcomes of PLAXIS 3D simulations (e.g., total displacement patterns, UBC validation); detailed mesh parameters were streamlined to focus on soil–structure interaction trends. The finite element model employed 15-node tetrahedral elements with adaptive mesh refinement, achieving convergence at a global tolerance of 0.1%. Mesh sensitivity studies confirmed stable results (±2.1% variation in UBC) across three refinement levels (coarse: 12,500 elements; medium: 34,000 elements; fine: 68,500 elements). These details can be further expanded, including displacement contours and stress distributions across mesh configurations. The research’s prioritization of analytical comparisons aligns with its goal of balancing technical depth with readability for engineering practitioners.

The friction angle increases progressively from 28° to 40° with increasing relative density, while the dilatancy angle shows a more dramatic range from 0° to 20°—significantly influencing the shear strength behavior and volume change characteristics in the numerical model. Cohesion values increase slightly with relative density (0 to 0.706 kN/m²), and the constant interaction factor (R_int) of 0.8 across all density states indicates consistent pile–soil interface behavior. These parameters enable the comprehensive numerical simulation of hybrid pile behavior, facilitating the detailed analysis of load transfer mechanisms and foundation performance across various soil conditions.

The finite element analysis (Plaxis 3D) results shown in Figure 9a–e and Figure 10a–e illustrate the total displacement patterns of hybrid steel–concrete and timber–concrete composite piles under varying relative soil density conditions. Maximum displacements primarily occur at pile heads, reaching approximately 1.35 × 10⁻³ m (steel–concrete) and 1.55 × 10⁻³ m (timber–concrete) in the lowest-density conditions. Displacement magnitude progressively decreases as soil relative density increases, with displacement distribution evolving from concentrated deformation at pile heads in looser soils to a more distributed displacement along pile shafts in denser conditions. The timber–concrete system exhibits larger maximum displacements than its steel–concrete counterpart under identical conditions, attributable to timber’s lower elastic modulus (1.22 × 10⁷ kN/m² versus 2.01 × 10⁸ kN/m² for steel). Increasing soil relative density from loose to dense conditions reduces maximum pile displacement by 40–50% in both systems, though this effect is more pronounced in the timber–concrete configuration. The steel–concrete composite consistently outperforms its timber counterpart, exhibiting 15–25% lower total displacements across all density scenarios despite the different foundation systems. These simulations effectively capture soil–structural interaction mechanisms, demonstrating the design’s optimization potential when composite pile systems are appropriately matched to site-specific conditions.

Figure 11a–e and Figure 12a–e reveal intricate performance characteristics across different computational methodologies and soil density conditions for hybrid steel–concrete and timber–concrete composite piles. The results demonstrate substantial variability in load-bearing capacities, with significant divergences observed between analytical methods. For the hybrid steel–concrete composite pile, the ultimate bearing capacity exhibits a pronounced scaling effect with the increasing relative density. At very loose soil conditions (10% Dr), the ultimate bearing capacity ranges from 353.1 kN (Vesic method) to 2287.8 kN (Hansen method), representing a remarkable threefold to sixfold variation. As soil density increases to very dense (95% Dr), this methodological disparity becomes even more pronounced, with capacities ranging from 7474 kN (Brom method) to 14,379 kN (Vesic method). The finite element method (FEM) using PLAXIS 3D software provides additional insights, demonstrating remarkable alignment with the Vesic method at very dense conditions. At 95% Dr, the PLAXIS simulation yields 14,202 kN, which is remarkably close to the Vesic method’s result of 14,379 kN, suggesting the computational validation of theoretical predictions. The hybrid timber–concrete composite pile exhibits similar methodological variations, but with less extreme magnitudes. In very loose soil conditions, ultimate bearing capacities range from 244.1 kN (Vesic method) to 1593.5 kN (Hansen method). The progression to very dense conditions reveals capacities spanning from 6149.8 kN (Berezantsev method) to 9537.5 kN (Hansen method).

Different analytical methods (Coyle and Castello, Vesic, Janbu, Terzaghi, Berezantsev, Brom, Hansen, Meyerhof, and FEM) yield varying results, highlighting the complexity of geotechnical bearing capacity predictions while consistently demonstrating the steel–concrete composite’s enhanced load-bearing characteristics, particularly in dense and very dense soil conditions. Material composition, interface characteristics, and soil density critically influence the ultimate bearing capacity of hybrid composite piles, with the steel–concrete variant consistently outperforming its timber–concrete counterpart due to superior material properties and structural integrity. Comparative analysis shows that in very dense conditions, the steel–concrete pile’s ultimate bearing capacity is approximately 1.8 to 2.3 times higher than that of the timber–concrete alternative, depending on the computational method used. The Janbu and Hansen methods consistently produce higher ultimate bearing capacity estimates compared to other analytical approaches, suggesting potentially conservative design considerations, while the Vesic, Coyle and Castello, and FEMs tend to yield more moderate capacity estimates, potentially reflecting more nuanced soil–structure interaction modeling. This remarkable variability in ultimate bearing capacity emphasizes the importance of comprehensive geotechnical investigation and multi-method analytical approaches. The divergence in predictive models highlights the complex mechanical behavior of hybrid composite piles, influenced by intricate interactions between material properties, soil conditions, and computational methodologies. These findings validate the innovative potential of hybrid composite pile systems and demonstrate their adaptability across varied geotechnical environments, while underscoring the necessity of site-specific analysis, sophisticated computational modeling, and interdisciplinary approaches in foundation engineering design.

Field performance data from Kano’s infrastructure projects validates theoretical calculations, with steel–concrete piles demonstrating a 22% increase in ultimate bearing capacity compared to conventional bored piles. This is particularly beneficial in the region’s interbedded sandy deposits with clay lenses. Timber–concrete piles built using locally sourced Afzelia Africana hardwood showed minimal differential settlement (≤5 mm) over 18 months despite seasonal moisture variations, confirming their durability in semi-arid conditions. The interface between composite materials emerges as a critical design consideration, evidenced by challenges in achieving uniform adhesive bonding between timber and concrete under humid conditions. This complexity is reflected in Table 1′s skin friction angles, where timber–concrete interfaces consistently demonstrate higher values than steel–concrete across all density conditions, with the most pronounced differential (4.6°) seen in very dense sand. The circular cross-section adopted for both pile types provides significant advantages in stress distribution and installation efficiency, which is particularly relevant to Kano’s soil profile. The modular nature of these hybrid designs offers practical benefits for remote construction sites while addressing region-specific challenges through locally available materials integration. Bearing capacity calculations show marked sensitivity to soil density. This is especially evident using the Vesic method, where steel–concrete pile capacity increases from 353.1 kN in very loose sand to 14,379 kN in very dense sand—a 40.7-fold increase. These findings demonstrate that hybrid composite pile design requires the careful consideration of material properties, soil conditions, and installation methods, while substantial variations in predicted capacities across analytical methods underscore the importance of employing multiple calculation approaches during design and validating predictions through field testing. Future implementation would benefit from continued monitoring to assess long-term performance under cyclic environmental conditions and optimize interface design.

The research does incorporate case studies I–II geometries from two infrastructure projects in Kano, Nigeria, as detailed in previously. For the steel–concrete composite piles, field load testing demonstrated a 22% increase in UBC compared to conventional bored piles, aligning closely with Vesic’s method predictions (14,379 kN simulated vs. 14,202 kN PLAXIS result at Dr = 95%). The timber–concrete system exhibited ≤5 mm differential settlement over 18 months, consistent with interface shear test results (δ = 37.4° at Dr = 95%). These measurements validate the analytical and numerical models, particularly the efficacy of Vesic’s method and PLAXIS simulations for high-density conditions. Comparative analysis explicitly correlates UBC and settlement data with predictions from eight classical methods. For instance, Hansen’s method overestimated the timber–concrete UBC by 18% compared to average measurements, while Coyle and Castello’s approach showed the closest match (±5%). These discrepancies highlight the influence of soil heterogeneity and installation effects, which classical theories often simplify. Future work will expand field instrumentation to include pore pressure and strain gauges for granular validation.

The hybrid composite pile systems presented in the case studies represent a significant advancement in foundation engineering when compared to conventional monolithic foundation solutions. These innovative designs, featuring steel–concrete and timber–concrete combinations, offer distinct performance characteristics that can be evaluated against established foundation alternatives and employ analytical methodologies beyond the classical bearing capacity approaches documented in the study. Drilled shaft foundations, which typically exhibit shaft resistance contributions of 70–90% in cohesive soils according to research by Tomlinson and Woodward, demonstrate fundamentally different load transfer mechanisms compared to the hybrid composite piles analyzed [44,45]. Regarding the steel–concrete composite pile in very dense sand, Coyle and Castello’s method indicates a shaft resistance contribution of 46.5%, which is substantially lower than that of typical drilled shafts but significantly higher than the 9.9% predicted by Meyerhof’s method for the same conditions. This variation highlights the unique load transfer characteristics of hybrid systems, which cannot be adequately captured through conventional monolithic foundation analysis. Driven precast concrete piles, commonly analyzed using wave equation methods such as GRLWEAP or CAPWAP, typically demonstrate ultimate capacities 15–20% lower than those predicted by static formulas due to installation effects [46,47,48]. This contrasts with the observed performance of hybrid steel–concrete piles in Kano’s irrigation project, which demonstrated a 22% increase in ultimate bearing capacity compared to conventional bored piles. This performance differential suggests that hybrid systems may mitigate some installation-related capacity reduction factors through their composite construction.

The β-method for estimating skin friction, which employs effective stress principles and empirical coefficients, represents an alternative analytical approach not covered in the study. Research by Randolph and Gourvenec indicates that β-values typically range from 0.25 to 0.35 for medium-density sands—a range that would yield shaft resistance values approximately 15–30% higher than those calculated using the Coyle and Castello method for similar conditions [49]. Applied to the hybrid timber–concrete pile in medium-density sand, this would potentially increase shaft resistance from 180.7 kN to 207.8–235 kN. The CPT-based methods developed by Schmertmann and later refined by Robertson offer direct correlations between cone penetration data and pile capacity that circumvent many assumptions inherent in classical theories [50]. These methods typically predict end-bearing capacities 10–25% lower than theoretical approaches such as Vesic in granular soils, which would potentially reduce the 8178.4 kN end-bearing capacity predicted for timber–concrete piles in very dense sand to a more conservative 6133.8–7360.6 kN. Helical piles, increasingly utilized for their installation advantages and vibration control, typically achieve bearing capacity through a combination of cylindrical shear and individual plate bearing mechanisms. Research by Perko demonstrates that helical piles in medium-density sand mobilize approximately 30–45% of capacity through shaft resistance [51,52], similar to the 38.7% shaft contribution predicted by Brom’s method for timber–concrete composite piles in medium-density conditions, suggesting potentially comparable performance characteristics.

The novelty of the hybrid composite pile systems lies in their strategic material distribution that optimizes performance across different soil strata while addressing sustainability considerations. Unlike conventional foundation systems that employ uniform materials throughout their length, these hybrids demonstrate adaptive capacity characteristics, with the timber–concrete system offering a 15% reduction in material costs while maintaining differential settlements below 5 mm over an 18-month monitoring period. The integration of locally sourced Afzelia Africana hardwood into the timber–concrete system represents a significant advancement in sustainable foundation engineering, maintaining comparable performance to conventional systems. Furthermore, the modular design approach, enabling effective material transitions at predetermined depths, constitutes a methodological innovation not adequately addressed by classical bearing capacity theories. This approach allows for optimized material utilization where the higher-strength components (steel or treated timber) are positioned below the groundwater table, while more economical or sustainable materials are utilized in the less aggressive environment above the groundwater level—a design philosophy that transcends the assumptions of homogeneous material behavior inherent in traditional analytical methods. Future studies should prioritize the long-term monitoring (≥5 years) of hybrid pile systems under cyclic moisture exposure to quantify creep behavior and bio-deterioration risks. Specifically, accelerated aging tests simulating 10–30% interface property degradation should be integrated with probabilistic models to refine service-life predictions. Additionally, optimizing adhesive formulations for timber–concrete bonds to achieve ≥20% improvement in moisture resistance is critical for enhancing durability in semi-arid regions.

5. Conclusions

This study investigated the performance of hybrid steel–concrete and timber–concrete composite pile systems using classical bearing capacity methods and numerical simulations. The key findings revealed significant improvements in load-bearing capacity, material efficiency, and adaptability to varying soil conditions. The integration of numerical modeling highlighted the complex interplay between soil density and material interfaces. Below are the conclusions and a future recommendation derived from this research.

• This study demonstrated the systematic relationship between sand relative density (Dr) and geotechnical properties, where increasing Dr from 10% to 95% reduced void ratios from 0.886 to 0.476, increased dry unit weight from 14.1 kN/m³ to 18.0 kN/m³, and elevated internal friction angles from 28° to 41°. Permeability decreased by three orders of magnitude (0.01 cm/s to 0.0001 cm/s), underscoring the critical role of compaction in enhancing soil strength and stability.
• Skin friction angles at pile–soil interfaces exhibited material-dependent behavior: concrete–steel interfaces increased from 12.8° (Dr = 10%) to 32.8° (Dr = 95%), while concrete–timber interfaces showed higher values, rising from 20.2° to 37.4° over the same Dr range. The 7.4° difference in very loose sand (Dr = 10%) highlights timber’s superior interfacial performance in low-density conditions.
• Load transfer mechanisms shifted significantly with soil density. For hybrid steel–concrete piles, skin friction contribution (Q_s) increased from 23.3% (Dr = 10%) to 46.5% (Dr = 95%), while base resistance (Q_b) decreased from 76.7% to 53.5%. Timber–concrete piles displayed a more variable response, with Q_s dropping from 43.7% to 9.90% under Vesic’s method, demonstrating density-dependent interaction dynamics.
• Ultimate bearing capacity (UBC) predictions varied widely across methods, with steel–concrete piles ranging from 353.1 kN (Vesic, Dr = 10%) to 14,379 kN (Vesic, Dr = 95%), a 40.7-fold increase. Timber–concrete piles showed capacities between 244.1 kN (Vesic, Dr = 10%) and 9537.5 kN (Hansen, Dr = 95%). PLAXIS 3D simulations validated theoretical results, yielding 14,202 kN for steel–concrete at Dr = 95%, closely matching Vesic’s prediction (14,379 kN).
• Field implementations in Kano, Nigeria, confirmed hybrid systems’ efficacy: steel–concrete piles achieved a 22% higher UBC than conventional bored piles, while timber–concrete systems exhibited minimal differential settlement (≤5 mm over 18 months). Volumetric strain values (0.050–0.006) and interface friction angles (δ = 32.8° for steel–concrete at Dr = 95%) aligned with performance metrics, validating the designs’ adaptability to regional soil conditions.