Application of finite element method in highway base and subbase layers

ABSTRACT

Highways are essential components of transportation infrastructure, and their performance depends critically on the mechanical behavior of multilayered pavement systems. This study investigates stress distribution in layered highway structures under circular loading using the Finite Element Method (FEM). A multilayered model including asphalt, base, subbase, and subgrade soil layers was developed, and vertical stress increments were evaluated for each layer. Results show that rigid upper layers, such as asphalt and base, concentrate stresses near the surface, while softer subbase and subgrade layers distribute stresses over a wider area. FEM results were quantitatively compared with analytical solutions based on Boussinesq theory, revealing a maximum deviation of approximately 7% in stress predictions, confirming the model’s accuracy. The study demonstrates that FEM-based simulations provide detailed insights into load transfer mechanisms and layer interactions, supporting optimized pavement design and reduced maintenance requirements.

Keywords:
Highways; Pavement system; Finite Element Method; Boussinesq theory; Simulation

1. INTRODUCTION

Transportation networks, particularly highways, play a critical role in modern infrastructure by connecting cities and regions, supporting economic development, and facilitating social interactions. The design of highway structures must accommodate high traffic volumes, variable environmental conditions, and regional characteristics while ensuring durability and ease of maintenance [¹, ²].

Highways consist of multiple layers, including pavement, base, subbase, and subgrade soil, each engineered to efficiently support and distribute traffic loads [³]. The base and subbase layers are especially important for structural stability, providing uniform load transfer to the underlying soil. The increase in stresses cause deterioration in the pavement and decrease in road service capability [⁴, ⁵] The selection of materials and construction techniques directly affects pavement performance, maintenance requirements, and sustainability [⁶, ⁷].

Recent advancements in numerical modeling, particularly the Finite Element Method (FEM), have enabled more accurate predictions of stress distribution in multilayered pavement systems [⁸]. FEM discretizes structures into small elements, allowing precise analysis of mechanical behavior under various loading and boundary conditions. Beside, FEM reveals a strong correlation between the experimental test results and numerical estimations in terms of stresses [⁹]. Simulia Abaqus/CAE is widely used for such analyses, offering capabilities to model different material behaviors, including elastic, elastoplastic, and viscoelastic properties [¹⁰, ¹¹]. However, in this study, materials are assumed to behave as linear elastic, which simplifies the model. Future work could incorporate elastoplastic or viscoelastic models to capture more complex soil and pavement behavior, enhancing accuracy and reliability [¹², ¹³].

This study aims to investigate vertical stress distribution in multilayered highway systems under circular loading using FEM and Simulia Abaqus/CAE. The novelty of this work lies in:

1. Developing a detailed multilayered model with realistic material properties.

2. Quantitatively comparing FEM results with analytical solutions to evaluate model accuracy.

3. Highlighting the impact of different layer stiffness on stress concentration and load distribution, providing guidance for optimized pavement design.

By integrating numerical simulations and analytical comparisons, this study provides engineers with reliable insights into the structural behavior of pavement systems and supports cost-effective, durable, and sustainable highway design.

2. MATERIALS AND METHODS

This study investigates the distribution of stresses within the multilayered soil and the stress increments resulting from external loads applied to highway structures. Accurate stress calculation is crucial for evaluating soil bearing capacity, settlement analysis, and overall stability.

Stresses within the soil are composed of two main components: natural stresses and additional stresses. Natural stresses arise from the self-weight of soil particles, while additional stresses develop due to externally applied surface loads.

These stresses are explained using Terzaghi’s effective stress principle (σ′ = σ − u), where σ represents total stress, σ′ is the effective stress, and u is the pore water pressure.

The distribution of total and effective stress varies depending on the groundwater level and flow conditions. For example, in a steady groundwater condition (no-seepage), pore water pressure increases hydrostatically below the water table, and effective stress follows a linear trend. Upward seepage reduces effective stress, and under critical conditions, soil liquefaction may occur. In fine-grained soils, capillary rise can locally increase effective stress and modify soil behavior [¹⁴, ¹⁵].

All layers in the model were assumed to behave as linear elastic, characterized by their respective elastic moduli and Poisson’s ratios (Table 1). Linear elasticity was chosen to simplify stress analysis while providing sufficient accuracy for preliminary design comparisons with analytical solutions. Although all layers are modeled as linear elastic for simplicity, this assumption does not capture nonlinear, time-dependent, or plastic behavior of pavement materials. Future studies may incorporate elastoplastic or viscoelastic models to enhance predictive accuracy.

Table 1
Elastic moduli and Poisson’s ratios for each layers.

LAYERS OF SOIL	E	ν	H
Asphalt layer	7 × 10⁸ kPa	0.3	0.25 m
Base Layer	7 × 10⁷ kPa	0.3	0.5 m
Sub-base Layer	7 × 10⁶ kPa	0.3	0.5 m
Existing Soil Layer	7 × 10⁵ kPa	0.3	48.75 m

The soil system was modeled as an axisymmetric cylinder with a radius of 100 m and a height of 50 m. The bottom boundary was fixed in both vertical and horizontal directions, while the lateral boundaries were constrained horizontally to prevent radial displacement but allowed vertical movement. A uniform circular load of 10 kPa was applied at the surface over a radius of 0.5 m. These boundary conditions simulate realistic load transfer to the underlying soil while minimizing artificial boundary effects. A mesh sensitivity analysis was performed to ensure that the chosen element size provides accurate stress predictions while maintaining computational efficiency, and boundary conditions were selected to minimize artificial constraints on stress propagation.

A 2D axisymmetric finite element mesh was generated using four-noded linear quadrilateral elements. The mesh included 20 elements in the radial (X) direction and 40 elements in the vertical (Z) direction, with finer elements concentrated around the loaded area to capture stress gradients accurately. Preliminary checks confirmed that the chosen mesh density provides sufficiently accurate stress results while maintaining computational efficiency.

Vertical stress increments were calculated from the surface to a depth of 5 m and compared between layered and homogeneous soil conditions. The FEM results were validated against analytical solutions based on Boussinesq’s theory for a uniformly loaded circular area. This comparison demonstrates the accuracy of the FEM model and highlights differences caused by layering effects.

Elasticity theory-based solutions, such as Boussinesq and Westergaard methods, are commonly employed to estimate stress distribution in elastic, homogeneous, semi-infinite soil masses subjected to point or circular loads. This study applies these theoretical foundations and numerical modeling using ABAQUS, following Example 3.8 from Sam Helwany’s Applied Soil Mechanics with ABAQUS Applications [¹⁶,¹⁷,¹⁸].

This modeling approach provides a detailed layer-wise stress evaluation under circular loads, which is rarely reported in the literature for multilayered pavement systems using ABAQUS, thereby offering a practical reference for pavement design optimization. Similar multilayered FEM approaches have been successfully applied in recent studies [¹⁹,²⁰,²¹], demonstrating the capability of axisymmetric modeling in capturing stress distribution patterns and validating against analytical solutions.

3. FEATURE EXTRACTION AND RESULTS

In Example 3.8, a uniform load of 10 kPa is applied to a circular area of radius 0.5 m on four soil layers of different elasticity modulus and thickness. The aim is to calculate the vertical stress increase between z = 0 and 5 m and compare it with the results obtained for the homogeneous soil layer [¹⁹]. This approach allows evaluating stress distribution trends in multilayered pavement systems using FEM and ABAQUS software.

The soil mass is modeled as an axisymmetric cylinder with a radius of 100 m and a height of 50 m. All soil layers are assumed to behave as linear elastic materials. The base of the soil cylinder is fixed, and lateral boundaries are assumed free of stress.

The analysis was performed using the Finite Element Method (FEM). A 2D axisymmetric finite element mesh was created with 20 elements in the radial direction and 40 elements in the vertical direction. A finer mesh was applied around the loaded circular area to accurately capture stress concentration. Four-noded, linear axisymmetric quadrilateral elements were used. A preliminary mesh sensitivity assessment was performed near the loaded region to ensure that element discretization provides reliable stress predictions while maintaining computational efficiency.

Figure 1 shows the vertical stress increase within the layered soil due to the uniformly applied circular load. Figure 2 provides a comparison between FEM results and analytical predictions for the layered system. Stress development in the layered soil under the applied load is illustrated in Figure 3. The ABAQUS model of the circular loading is shown in Figure 4, while Figure 5 presents the model plot analysis diagram. Stress results were extracted from ABAQUS and plotted in Excel for visualization, as shown in Figure 6. Finally, Figure 7 compares FEM results with the expected analytical diagram.

Figure 1
Increase in stress within layered soil due to a uniformly applied circular load.

Figure 2
Comparison of FEM and analytical solutions for a layered system under a uniformly loaded circular area.

Figure 3
Stress development in layered soil under a uniformly applied circular load.

Figure 4
Circular loading model created on ABAQUS.

Figure 5
Model plot analysis diagram on ABAQUS.

Figure 6
Excel diagram created with data obtained on ABAQUS.

Figure 7
Comparing of the obtained diagram with the desired diagram.

The results indicate that the maximum vertical stress occurs directly beneath the center of the loaded area and decreases with depth. The FEM results closely match the analytical solution, confirming the validity of the model. This comparison also demonstrates the stress distribution trend in multilayered systems, highlighting the effect of each soil layer on the overall response.

Future studies may consider extending the model to include dynamic loads, temperature effects, or more advanced constitutive models for soil layers, which would further improve the robustness and reliability of stress predictions under varied traffic and environmental conditions. Integrating these factors would allow a more comprehensive understanding of pavement behavior and support the development of durable and sustainable highway structures.

Figures 8 and 9 illustrates the finite element model of the pavement system developed in ABAQUS, highlighting the applied boundary conditions. The model includes the subgrade, subbase, and base courses, each represented with appropriate material properties.

Figure 8
Model with applied boundary conditions created on ABAQUS.

Figure 9
ABAQUS model under a uniform 10 kPa circular surface load (radius 0.5 m).

Fixed boundary conditions were applied at the bottom of the subgrade to simulate the support from the underlying soil layer, preventing both translational and rotational movements. Lateral constraints were imposed on the sides of the model to replicate the continuity of the pavement in the transverse direction and to avoid unrealistic lateral displacements. The loading condition, representing a standard wheel load, is applied at the surface of the pavement to simulate traffic-induced stresses. This configuration ensures that the model realistically represents the mechanical behavior of a multilayered pavement structure under applied loads, enabling accurate stress and deformation analysis.

4. CONCLUSIONS AND DISCUSSIONS

In layered systems, the presence of rigid upper layers can result in higher-than-expected stresses in surface-level structural elements, such as asphalt pavements and road bases. This factor must be considered during the design phase to mitigate the risks of deformation or structural damage. Due to the heterogeneous nature of soil, each layer’s deformation characteristics influence load transfer, leading to varying stress distributions [²⁰].

The elastic modulus of each layer plays a critical role in load-bearing capacity and stress distribution. Rigid layers concentrate stresses near the surface, while softer layers distribute stresses over a wider area, which explains their widespread use in road pavement applications to reduce surface deformations. Additionally, the interaction of layered systems with groundwater and seepage effects must be considered. Differences in permeability across layers can alter water movement, leading to deviations in stress distribution within the soil mass [²¹].

While analytical solutions, such as Boussinesq’s equations, provide reasonable estimates for homogeneous soils, they are limited in capturing complex conditions in layered and heterogeneous soils. Boussinesq solutions assume an infinite, homogeneous soil mass, which may be misleading in practical applications involving multiple layers. FEM implemented through software such as ABAQUS, offers a more flexible and precise approach by allowing detailed modeling of stress concentrations and load transfer at layer interfaces [²², ²³].

This study applies FEM to model multilayered highway systems under circular surface loading, integrating realistic material properties and layer stiffness. Compared to traditional analytical methods, the FEM approach captures the nonlinear interactions between layers more accurately, providing high-resolution insights into stress distributions and potential deformation zones. Such analyses are particularly critical in applications involving heavy surface loads, including highways and airport runways. Soft subgrade layers beneath rigid pavements may be susceptible to excessive settlement, highlighting the importance of FEM-based assessments for safe and durable infrastructure design.

It should be noted that this study uses a linear elastic model, which simplifies soil behavior. While sufficient for capturing primary stress trends, future research should incorporate advanced constitutive models such as Mohr-Coulomb, Drucker-Prager, or Hardening Soil Models to account for plasticity, viscoelastic effects, and time-dependent deformations (e.g., creep and consolidation). Validating FEM predictions with field measurements or laboratory tests will further enhance model reliability and engineering applicability.

In conclusion, this study demonstrates that layered systems significantly influence vertical stress distribution under surface loads, and FEM provides a superior tool for analyzing these effects compared to traditional analytical solutions. Engineers are encouraged to adopt FEM in the design and analysis of multilayered pavement and soil systems to achieve optimized, cost-effective, and durable infrastructure. Future studies should consider dynamic loading, temperature variations, long-term consolidation effects, and advanced material behaviors to improve predictive accuracy and contribute to the development of more resilient highway systems.

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Publication Dates

• Publication in this collection
  28 Nov 2025
• Date of issue
  2025

History

• Received
  22 Apr 2025
• Accepted
  02 Oct 2025