The geotechnical behavior of soils is highly influenced by their composition, granulometry, and plasticity. In this study, six soil samples were collected from different locations within the Penka-Michel region (West Cameroon) to characterize their physical and mechanical properties. The classification of these soils follows the Unified Soil Classification System (USCS), which differentiates soil types based on grain size distribution and plasticity indices.

The collected soil samples exhibit significant variations in fines content, with a predominance of clay and silt fractions. The first three samples (EI.01, EI.02, and EI.03) consist primarily of fine-grained soils. Sample EI.01, obtained from Wassa (5˚27'54.7''N, 10˚15'57.75''E), and sample EI.03, from Balessing (5˚29'41.229''N, 10˚13'36.137''E), are classified as highly plastic clays (CH), whereas sample EI.02, from Batchoua (5˚29'37.46''N, 10˚14'58.062''E), consists of highly plastic silty and clayey materials (OH). These fine soils exhibit high water retention capacity and significant plasticity, making them prone to settlement and volume changes under loading conditions.

The remaining three samples (EI.04, EI.05, and EI.06) are predominantly sandy-clayey soils with lower plasticity. Sample EI.04, obtained from Meha (5˚26'28.376''N, 10˚12'54.27''E), and sample EI.06, from Tami 1 (5˚27'20.686''N, 10˚13'9.224''E), are classified as clayey sands (SC). Sample EI.05, collected from Bamendou (5˚27'10.28''N, 10˚14'15.769''E), consists of low-plasticity clays (CL). These soils exhibit better load-bearing capacity compared to fine-grained soils due to their granular nature, which provides higher shear resistance and reduced compressibility.

Grain size distribution and Atterberg limits ( Table 1 ) were used to assess the physical properties of the soils ( Table 1 ). The proportion of fines (<0.08 mm) varies significantly among the samples, ranging from 41.8% in EI.06 (clayey sand) to 90.2% in EI.02 (silty clay). These high fines content in fine-grained soils contributes to their low permeability and high plasticity. The liquid limit (wL) ranges from 48.4% in EI.05 to 61.5% in EI.03, while the plasticity index (PI) varies between 18.9% (EI.05) and 30.8% (EI.02), indicating considerable differences in soil plasticity.

The fines content (<0.08 mm) averages 69.37%, with a standard deviation of 18.18%, indicating significant variation in soil composition. The liquid limit (wL) has a mean value of 53.38% and a standard deviation of 5.16%, suggesting moderate variability among samples. Meanwhile, the plasticity index (PI) averages 24.37%, with a standard deviation of 4.35%, highlighting a range from low-plasticity clays to highly plastic silty-clay soils.

The statistical distribution highlights the heterogeneity of the soils in the study area, with a marked distinction between fine-grained and sandy-clayey soils. The results confirm that fine soils (CH and OH) exhibit higher plasticity and fines content, whereas sandy-clayey soils (SC and CL) are more stable with lower compressibility. These findings emphasize the importance of soil classification in predicting foundation behavior and settlement potential under loading conditions.

The mechanical behavior of soils plays a crucial role in determining the stability and performance of shallow foundations. Soil strength and deformability are influenced by several factors, including cohesion, internal friction angle, compressibility, and stiffness. In this study, the mechanical properties of the six selected soil samples were evaluated using laboratory tests and numerical modeling. The results are summarized in Table 2 .

The soils in the study area exhibit significant variations in their geomechanical properties, reflecting differences in composition and structure. The cohesion values range from 20.09 kPa (EI.04) to 27.40 kPa (EI.01), indicating that fine-grained soils have higher cohesion due to their clay content. Cohesion is a critical parameter for soil shear strength, as it determines the soil’s ability to resist deformation under load ( Terzaghi, 1943 ; Meyerhof, 1953 ).

The internal friction angle (φ) varies between 15.33˚ (EI.01) and 31.86˚ (EI.04). Fine-grained soils (CH and OH) generally exhibit lower friction angles due to their high plasticity and particle cohesion, whereas sandy-clayey soils (SC and CL) have higher friction angles, which contribute to their improved load-bearing capacity ( Imanzadeh et al., 2015 ; Abdi, 2019 ; Ibrahim & Al-Obaydi, 2021 ).

Compressibility is assessed using the oedometric modulus (Eeod), which measures the soil’s resistance to deformation under loading. The values range from 2306 kPa (EI.01) to 4765 kPa (EI.05), highlighting the greater stiffness of sandy soils compared to fine-grained soils. This difference is expected, as sandy soils exhibit immediate settlement due to particle rearrangement, whereas clay-rich soils undergo progressive settlement over time ( Tchouani Nana & Callaud, 2004 ).

Soil density influences both bearing capacity and settlement behavior. The dry unit weight (γunsat) varies from 13.39 kN/m³ (EI.02) to 20.60 kN/m³ (EI.06), while the saturated unit weight (γsat) ranges from 18.32 kN/m³ (EI.02) to 23.14 kN/m³ (EI.06). The higher densities observed in sandy soils (EI.04, EI.05, EI.06) indicate a more compact structure with lower compressibility, whereas fine-grained soils tend to retain more water, leading to lower densities and increased settlement potential.

To better understand soil property variability, a statistical analysis was conducted on the mechanical parameters. The average cohesion is 24.56 kPa, with a standard deviation of 2.88 kPa, showing moderate variation, with higher values in fine-grained soils and lower values in sandy-clayey soils. The internal friction angle (φ) has a mean of 22.94˚ and a standard deviation of 6.43˚, highlighting significant differences between fine-grained and sandy soils. The oedometric modulus (Eeod) averages 3343 kPa, with a standard deviation of 978 kPa, reflecting a wide range of compressibility among soil types. Additionally, the dry unit weight (γunsat) has a mean of 16.81 kN/m³ with a standard deviation of 2.89 kN/m³, while the saturated unit weight (γsat) averages 20.53 kN/m³ with a standard deviation of 1.86 kN/m³, confirming the higher density and superior compaction of sandy soils.

The statistical analysis confirms that soil behavior varies significantly across the study area, with fine-grained soils demonstrating higher cohesion and lower friction angles, while sandy-clayey soils exhibit greater stiffness and load-bearing capacity. These differences directly influence foundation settlement and stability. Fine soils, due to their lower strength and higher compressibility, are more susceptible to settlement and deformation, particularly under eccentric loading conditions ( Waheed & Asmael, 2019 ; Al-Dawoodi et al., 2021 ).

Given these variations, foundation design in Penka-Michel must account for the specific geotechnical properties of each soil type. Foundations on sandy-clayey soils can support higher loads with minimal settlement, whereas those on fine-grained soils require careful consideration of bearing capacity reductions and settlement control measures, such as soil improvement techniques or deeper foundation solutions.

Numerical modeling is a powerful tool in geotechnical engineering, enabling a detailed assessment of soil-structure interaction under various loading conditions. Unlike traditional analytical methods, which rely on simplified assumptions, numerical techniques provide a more accurate representation of complex soil behavior by incorporating non-linearity, heterogeneity, and load distribution effects ( Waheed & Asmael, 2019 ; Al-Dawoodi et al., 2021 ). In this study, Plaxis 2D, a finite element method (FEM)-based software, was employed to analyze the influence of eccentricity on the bearing capacity and settlement of shallow foundations resting on tropical soils in Penka-Michel.

Plaxis 2D is widely used for geotechnical analysis, as it solves plane-strain and axisymmetric problems related to soil stability and deformation. The FEM discretization method involves dividing the soil domain into small triangular elements (meshes), where differential equations governing stress-strain relationships are solved numerically. The accuracy of the model depends on mesh refinement, with finer meshes providing better stress distribution but increasing computational cost. In this study, 15-node triangular elements were used to enhance precision in stress and strain calculations.

The soil was modeled as a 5 × 5 m homogeneous, isotropic medium, on which a square 1 × 1 m shallow foundation was placed. The boundary conditions were set to prevent displacement along the model’s edges while allowing free movement in the vertical direction at the top surface. Ground layers affected by the analysis are well above the water table. However, the groundwater has no impact on the behavior of the shallow foundations, as they are located more than 30 m below the footings.

The Mohr-Coulomb (M.C.) constitutive model was selected to describe soil behavior, as it provides a reasonable approximation for small-strain problems in geotechnical engineering ( Abdi, 2019 ; Mansouri, 2019 ).

The numerical model integrated key geotechnical parameters from laboratory tests, including soil density, cohesion, internal friction angle, and Young’s modulus. Soil behavior was represented as a linear elastic-perfectly plastic material following the Mohr-Coulomb failure criterion. A flexible footing was modeled under a vertically applied load with varying eccentricities (0 cm, 10 cm, 20 cm, 30 cm). Fully drained conditions were assumed, neglecting excess pore water pressures during loading. A uniformly distributed vertical load of 100 kPa was applied, simulating typical structural loading conditions in tropical regions.

Eccentric loading is a major factor influencing soil settlement and bearing capacity, as it causes uneven stress distribution beneath the foundation. In Plaxis 2D, eccentricity (e) was simulated by offsetting the point of load application relative to the foundation centroid. Three eccentricity values were analyzed:

The model calculates stress-strain relationships at Gaussian integration points, rather than at the mesh nodes, ensuring accurate assessment of stress redistributions caused by eccentric loading. The failure mechanism and settlement trends were examined by analyzing the plastic deformation zones and displacement contours generated by the simulation.

The numerical results were validated by comparison with classical analytical solutions ( Terzaghi, 1943 ; Meyerhof, 1953 ). As expected, increasing eccentricity led to a reduction in bearing capacity due to a decrease in effective footing width, an increase in settlement causing differential deformation, and a non-uniform stress distribution that shifted the load toward the footing edge, potentially compromising stability. The analysis of failure patterns, displacement contours, and stress-strain distributions provided valuable insights into the effects of eccentric loading on shallow foundations in tropical soils.

The numerical simulations conducted in this study provide a detailed assessment of the influence of load eccentricity on the bearing capacity and settlement of shallow foundations resting on tropical soils. The results reveal significant variations in soil response depending on both the type of soil and the magnitude of the eccentricity. The main findings, including bearing capacity and settlement values for different eccentricity levels, are presented in Table 3 .

The numerical analysis shows a clear trend of bearing capacity reduction with increasing eccentricity. For centered footings (e = 0 cm), the bearing capacity ranges from 4.20 bars (EI.01) to 10.00 bars (EI.04), demonstrating the inherent variability in soil strength across the study area. However, as eccentricity increases to 10 cm, 20 cm, and 30 cm, a progressive decrease in bearing capacity is observed. In fine-grained soils (EI.01, EI.02, EI.03), every 10 cm increase in eccentricity results in an approximate 5% reduction in bearing capacity, while in sandy-clayey soils (EI.04, EI.05, EI.06), the decrease is more pronounced, reaching 8% per 10 cm increment. This confirms previous studies indicating that load eccentricity significantly reduces effective contact pressure and load-bearing efficiency ( Meyerhof, 1953 ; Abdi, 2019 ; Mansouri, 2019 ).

For the maximum eccentricity analyzed (e = 30 cm), the bearing capacity drops to 3.50 bars (EI.01) and 7.97 bars (EI.04), representing an overall reduction of 16.7% and 20.3%, respectively, compared to the centered loading case. The reduction is more severe in sandy soils due to their lower cohesion and increased sensitivity to stress redistribution under eccentric loads ( Waheed & Asmael, 2019 ; Al-Dawoodi et al., 2021 ).

Settlement values increase significantly as eccentricity grows, with fine-grained soils exhibiting the highest deformation. For centered loading, settlement values range from 4.00 cm (EI.04) to 8.95 cm (EI.01). However, when eccentricity reaches 30 cm, maximum settlements of 24.09 cm (EI.01) and 10.00 cm (EI.06) are recorded.

Fine-grained soils (CH and OH) exhibit higher settlement due to their lower stiffness and higher compressibility, which is consistent with previous research indicating that settlement in saturated fine soils is one of the most critical parameters affecting structural stability ( Tchouani Nana & Callaud, 2004 ). In contrast, sandy-clayey soils show lower settlement values due to their granular structure, which provides greater resistance to deformation under load.

The results confirm that eccentric loading increases differential settlement, leading to non-uniform stress distribution beneath the foundation. This effect is particularly problematic for fine soils, where large settlements can lead to excessive tilting and potential structural damage ( Salih, 2021 ).

Statistical analysis of data in Table 3 revealed significant variability in bearing capacity and settlement. For centered loading (e = 0 cm), the mean bearing capacity was 6.61 bars (standard deviation 2.38 bars, CV 36.0%), and mean settlement was 6.12 cm (standard deviation 2.02 cm). Eccentric loading (e = 30 cm) resulted in a 27.3% reduction in mean bearing capacity (4.81 bars) and a 122.5% increase in mean settlement (13.62 cm), with a higher dispersion in settlement values (CV 41.7%) likely due to soil heterogeneity.

These statistical results confirm that bearing capacity reduction and settlement increase are strongly dependent on soil type and eccentricity level. Fine-grained soils are more susceptible to settlement due to their lower stiffness, while sandy-clayey soils exhibit greater resistance to deformation but still experience significant bearing capacity loss under eccentric loads.

This study highlights the crucial role of load eccentricity in shallow foundation design for tropical soils. Eccentricity exceeding 10 cm should be avoided in fine-grained soils to mitigate excessive settlement and instability. While sandy-clayey soils exhibit greater stability, significant bearing capacity reductions necessitate reinforcement or increased footing size. Differential settlement, especially across heterogeneous soil layers, must be considered in structural analysis. These findings corroborate previous research ( Mehdi et al., 2013 ; Abdi, 2019 ; Mansouri, 2019 ), demonstrating that foundation stability depends not only on soil type but also on load distribution.

The numerical results obtained in this study confirm the significant impact of load eccentricity on the bearing capacity and settlement of shallow foundations. These findings align with established theoretical and experimental research, demonstrating that increasing eccentricity reduces soil strength while amplifying differential settlement. To better understand these effects, the numerical results were compared with Terzaghi’s (1943) and Meyerhof’s (1953) analytical methods, and a statistical analysis was conducted on the discrepancies observed in Table 4 .

Figure 2(a) illustrates the inverse relationship between eccentricity and bearing capacity, reinforcing previous studies that highlight the loss of load-bearing efficiency as load application shifts away from the footing centroid ( Abdi, 2019 ; Mansouri, 2019 ). When eccentricity increases from 0 cm to 30 cm, the mean bearing capacity drops from 6.61 bars to 4.81 bars, representing an average reduction of 27.3%.

A comparison with analytical methods shows that Plaxis 2D results are generally lower than Terzaghi’s predictions but closer to Meyerhof’s estimations. The relative deviation between numerical and analytical results increases with eccentricity:

This increasing deviation suggests that traditional methods might not fully account for stress redistribution effects and progressive soil failure in eccentric footings. The numerical simulations, by considering full soil-structure interaction, provide a more refined estimation of load-bearing performance, particularly in tropical fine soils, which exhibit complex deformation mechanisms ( Waheed & Asmael, 2019 ; Al-Dawoodi et al., 2021 ). These results are similar to those obtained by Bandaru & Pollayi (2025) who, using numerical simulation, show the impact of load eccentricity on the bearing capacity of foundations.

Figure 2(b) demonstrates a substantial increase in settlement with load eccentricity, especially in compressible fine-grained soils (CH and OH), exhibiting progressive plastic deformation ( Issiakou, 2016 ; Tchouani Nana & Callaud, 2004 ). Mean settlement increased 122.5% from 6.12 cm (e = 0 cm) to 13.62 cm (e = 30 cm), with silty-clayey soils reaching a critical 24.09 cm. Eccentric loading ( Figure 3 ) shifts the failure mechanism from symmetrical stress distribution (e = 0 cm) to asymmetrical stress concentration and tilting (e = 30 cm), increasing the risk of structural instability and differential settlement damage, especially in buildings with rigid superstructures ( Salih, 2021 ), underscoring the importance of considering load eccentricity in foundation design. Eccentric loading has an adverse effect on foundations. As shown in this study, eccentricity increases settlement. These results are in agreement with those found by Rahaman et al., (2023) .

Statistical analysis of Table 4 data compared numerical (Plaxis) and analytical (Terzaghi, Meyerhof) bearing capacity predictions. For centered loading (e = 0 cm), Terzaghi overestimated bearing capacity by 33.4% compared to Plaxis (6.61 bars, standard deviation 2.38 bars), while Meyerhof showed only a 9% deviation (7.36 bars). As eccentricity increased, the deviation between Plaxis and Meyerhof rose to 14% (e = 10 cm) and 39% (e = 30 cm), indicating Meyerhof’s decreasing accuracy at higher eccentricities, likely due to simplified stress redistribution assumptions ( Mehdi et al., 2013 ; Abdi, 2019 ). Settlement analysis (Plaxis) revealed a mean of 6.12 cm (standard deviation 2.02 cm) for e = 0 cm and 13.62 cm (CV 41.7%) for e = 30 cm, highlighting increased variability under eccentric loading, particularly in fine-grained soils due to delayed consolidation. These results underscore the need for numerical models, especially for accurately predicting settlement in soft soils under asymmetric loading.

This study emphasizes the critical need to account for load eccentricity in designing foundations, especially in high-plasticity, low-stiffness tropical soils. Design recommendations include minimizing eccentricity, particularly avoiding values over 10 cm in fine-grained soils (resulting in approximately 8% - 10% bearing capacity loss per 10 cm increment). Numerical modeling should complement analytical methods, given the tendency of latter to overestimate bearing capacity and underestimate settlement under high eccentricity. Reinforcement (e.g., soil stabilization, deep foundations, geosynthetics) is recommended where eccentric loads are unavoidable, especially in fine silty-clayey soils. Finally, structural design must account for potential differential settlement, especially in structures with rigid frames or masonry walls, to prevent cracking and long-term serviceability issues. These findings support previous research ( Ibrahim & Al-Obaydi, 2021 ) indicating that foundation behavior is governed by both soil type and load application.