The Role of Finite Element and Difference Methods.
Why Ground Behaviour Modelling Matters
In ground engineering and construction, one of the most complex and critical challenges is predicting how the soil conditions and ground behaviour will respond to loading and excavation. Numerical modelling techniques such as the Finite Element Method (FEM), Finite Difference Method (FDM), and Finite Element Limit Analysis (FELA) are transforming how geotechnical engineers simulate soil-structure interaction with accuracy and insight. For developers, structural engineers, and project managers, these models offer a powerful tool to de-risk projects, optimise designs and communicate complex subsurface behaviours clearly.
What Is Numerical Modelling in Geotechnical Engineering?
Numerical modelling involves using advanced mathematical techniques to simulate how soil properties, soil behaviour and rock behave under different loads and conditions. When combined with field and lab data, a digital model can be constructed to analyse and simulate real-world scenarios — from how a foundation settles under long-term loading to how an underground tunnel may be affected due to the construction of a new high rise building above.
Common approaches include:
- Finite Element Analysis (FEA)
- Finite Difference Method (FDM)
- Finite Element Limit Analysis (FELA)
The Finite Element Method (FEM) and Finite Difference Method (FDM) are both numerical techniques used to solve differential equations, but they differ in their approaches and applications. The FDM is found to be easier to implement and computationally efficient for simple problems, while FEA offers greater flexibility for complex geometries and material properties. FELA is specifically used for determining the collapse load of structures and often employs upper and lower bound theorems of plasticity to provide bounds on the collapse load. The choice between the three methods often depends on the specific problem being solved, acknowledging any limitations of the methods employed.
These tools are crucial for understanding soil-structure interaction, especially where conditions are complex or standard empirical methods fall short.
Practical Applications: From Tunnels to Tower Foundations
Numerical modelling and numerical simulation are widely used across geotechnical services, including:
- Deep Basement Excavations: Predicting wall movements and ground deformation to protect nearby assets.
- Tunnelling Projects: Simulating face pressure and ground loss to optimise lining design.
- Pile Foundation Design: Modelling settlement and lateral response under structural loads.
- Retaining Structures and Slopes: Assessing stability under changing groundwater levels or seismic loads.
- Ground Improvement: Evaluating how techniques like wick drains or vibro-compaction affect settlements and bearing capacity.
Case Studies: Numerical Modelling in Practice
To illustrate the value of numerical modelling in geotechnical engineering, here are three real-world applications and an example our team has analysed using FEA and FELA techniques.
a) Pile Design in Layered Soils
In a study of single piles and pile groups embedded in layered soil, we used finite element simulations to investigate and analyse how a weaker layer below the pile group toe affects settlement. Results showed that:
- Settlement increases by up to 2.8 times when a weaker stratum is close to the pile base.
- Increasing the distance between the pile toe and the weaker layer significantly reduces settlement.
- A stiffer upper layer (relative to the lower) further reduces total settlement.
These insights help engineers assess whether conventional pile design might underestimate settlement — especially in layered soil profiles. We developed design charts that allow preliminary assessments using dimensionless ratios (L/D, E1/E2, h/D), and influence factors (I) to adjust for layered ground conditions.
b) Working Platform Design Optimisation
3D FELA (OptumG3) is used to assess the bearing capacity of working platforms — allowing for true 3D failure mechanisms and refined estimates.
In one case, the limit analysis predicted higher bearing capacity than the standard BRE method, allowing us to reduce platform thickness from 1.0 m to 0.9 m.
The sustainability impact?
- ~2 tonnes less CO₂ per 1,000 m² of platform
- Fewer truck movements and reduced material use
These gains demonstrate how modelling supports both cost savings and environmental targets.
c) Solar Farm Foundations: Managing Soil Movement
Solar projects often rely on pile foundations in expansive soils. Traditional methods (like the Nelson test) design piles to anchor below the active depth — often leading to excessively long and costly piles.
Instead, we apply finite element models that consider:
- The dual stabilising/destabilising forces in the active zone
- The flexibility of the solar structure
- Accurate soil parameters (e.g., c’, ϕ’, E, γ)
This approach results in more realistic and sustainable designs, especially when consequences of movement are low and cost efficiency is essential.
Benefits to Project Teams: Better Design, Fewer Surprises
For project managers, structural engineers, and developers, numerical modelling offers more than technical assurance:
- Risk Mitigation: Models reveal potential failure modes before construction begins.
- Optimised Design: Avoids overdesign by simulating real conditions — reducing material use.
- Clearer Communication: Visual outputs help explain ground behaviour to non-specialists and stakeholders.
- Cost & Time Savings: Early insights lead to smarter decisions and fewer delays.
With geotechnical modelling embedded early in the design phase, your project benefits from fewer surprises and more control over ground-related risk.
The Future of Ground Engineering is Predictive
As geotechnical challenges become more complex — from deeper excavations to climate-driven changes in groundwater — predictive tools like FEA,FDM and the FELA methods are essential. Numerical modelling and geotechnical analysis brings clarity to uncertainty, supporting better decisions across all project stages.
At Douglas Partners, we specialise in advanced geotechnical engineering and modelling services, helping clients achieve safer, more efficient outcomes.
Contact us to speak with our geotechnical specialists.
Our experts are also actively contributing to the broader geotechnical community through applied research and knowledge sharing including:
- Richard Merifield, Geotechnical Engineer and Principal at Douglas Partners, has co-authored a detailed technical paper published in Computers and Geotechnics, 2021 titled “Finite element modelling of pile groups founded above compressible layers”. This work provides valuable insights into how compressible strata can influence the performance of pile groups and how advanced finite element modelling can be used to predict and manage these effects.
- Sean Goodall and Richard Merifield, fellow geotechnical engineers, co-authored the paper “ Working Platforms And Bearing Capacity Assessments Of Sand Overlying Clay Using Finite Element Limit Analysis “. This research uses finite element limit analysis solutions are used to produce charts to assist designers with estimating the ultimate bearing capacity of granular working platforms overlying clay. The paper also aims to highlight some important considerations when adopting the BRE-470 guideline to design granular working platforms overlying clay.
- Sean Goodall, Caitlyn Todd, and Richard Merifield, fellow geotechnical engineers, co-authored the paper “P-Y analysis of shallow embedded solar farm piles in reactive clay”. This research investigates the challenges of designing solar farm foundations in expansive soils, where movement due to soil reactivity can impact structural performance. Through a combination of numerical modelling and P-Y curve analysis, the study proposes more efficient and site-responsive approaches to foundation design.
As the complexity of infrastructure projects increases, so does the importance of staying at the forefront of modelling technology and best-practice design methodologies. We believe that ensuring reliability through rigorous research and shared knowledge are essential to lifting the standard of geotechnical outcomes across the industry.
We invite you to explore these publications for a deeper understanding of the sophisticated modelling techniques that underpin many of our projects, and how research-driven insights continue to shape best practices in geotechnical engineering. These papers underscore the importance of a research-informed approach in a field where ground behaviour is often unpredictable and site-specific.
As the industry continues to evolve, particularly in response to environmental and sustainability pressures, our ability to integrate research into design workflows will be critical.
