The significance of the selection of a tunnel analysis method lies in obtaining accurate and reliable results, understanding complex interactions, optimizing the design, and efficiently utilizing resources. The chosen method should align with the project's objectives, scope, and constraints to ensure a robust and cost-effective tunnel design and construction process. In this article, we explore two commonly used methods for analyzing tunnels and their interaction with surrounding soil: Soil spring analysis and finite element analysis. The following paragraphs explain the concept, advantages and limitations of each method, and illustrate the analysis results for a TBM tunnel, modeled and analyzed with our shoring and tunnel design software, DeepEX.
B. SOIL SPRING ANALYSIS APPROACH
Soil spring analysis is a simplified approach used to model the interaction between a tunnel lining and the surrounding soil, assuming that the soil behaves like a series of nonlinear elastoplastic springs, providing resistance to the tunnel lining.
The main advantage of this approach is that it is relatively simple and quick to perform compared to more complex numerical methods. The Soil springs approach can provide a reasonable estimation of tunnel behavior for preliminary design purposes. The method is particularly useful for analyzing tunnels in a relatively simple soil stratigraphy as soil properties are only represented at the lining perimeter.
On the other hand, the soil springs approach relies on simplified assumptions and may not capture the full complexity of the soil-structure interaction. The method might not be accurate for tunnels in highly variable or layered soil conditions. Finally, soil springs cannot capture localized stress concentrations or complex deformation patterns.
The following figure illustrates a TBM tunnel in stiff clay soil. The tunnel was simulated in DeepEX software, considering the segmental concrete lining.
Figure 1: TBM Tunnel Model in DeepEX Software
Figure 2 below presents the tunnel lining moment graphs in the last construction stage (lining activation). Figure 3 presents the tunnel lining displacement graph and the estimated surface settlement.
Figure 2: TBM Tunnel Soil Springs Method – Tunnel lining moment & moment capacity
Figure 3: TBM Tunnel Soil Springs Method – Tunnel lining displacement and surface settlements
C. FINITE ELEMENT ANALYSIS METHOD (FEM)
Finite element analysis is a numerical method widely used for simulating the behavior of structures, including tunnels, in complex soil conditions. FEM divides the soil and tunnel into a mesh of small elements, allowing for a detailed analysis of stress, deformation, and soil-structure interaction. The method considers material properties, boundary conditions, and nonlinearity to simulate realistic behavior.
The main advantage of the Finite Elements approach is that it provides a more detailed and accurate representation of the soil-structure interaction. FEM can handle complex soil conditions, including layered or non-homogeneous soils. The method allows for analyzing localized stress concentrations and deformations.
On the other hand, FEM requires expertise and computational resources to set up and analyze the model. FEM simulations can be time-consuming, especially for large-scale or complex tunnel systems. Finally, the accuracy of the results depends on the quality of the input parameters, soil properties, and modeling assumptions.
The same TBM tunnel model described above is analyzed with the FEM approach in our DeepEX software. Figure 4 below presents the tunnel lining moment and moment capacity graphs. Figure 5 illustrates the generated mesh, the tunnel lining displacement graphs and the soil mass settlement shading. Figure 6 presents the segmental lining joint stresses and the lining shear graph.
Figure 4: TBM Tunnel FEM – Tunnel lining moment & moment capacity
Figure 5: TBM Tunnel FEM – Tunnel lining displacement graph, soil mass settlements shading
Figure 6: TBM Tunnel FEM – Tunnel lining shear graph, segmental lining joint stresses
In practice, the selection between soil spring analysis and finite element analysis depends on several factors such as the project's complexity, available resources, and desired level of accuracy. As presented above, our DeepEX software can perform tunnel analysis with both methods. This can make a difference for several reasons:
- Flexibility and Comparison: Different projects may have different requirements and constraints, and having the capability to choose between soil spring and finite element analysis allows for flexibility in the analysis approach. DeepEX enables engineers to select the most suitable method based on the project's complexity, available data, time constraints, and desired level of accuracy. Additionally, being able to compare the results obtained from both methods can provide valuable insights and help validate the analysis.
- Transition from Preliminary to Detailed Design: A software that offers both analysis methods facilitates a seamless transition from preliminary design to detailed design stages. Engineers can start with simpler soil spring analysis during the initial stages to quickly evaluate design options and identify key parameters. As the design progresses and more detailed information is required, DeepEX can seamlessly switch to finite element analysis to provide a more comprehensive understanding of the tunnel's behavior under complex soil conditions.
- Training and User Familiarity: A software that supports both analysis methods allows engineers and analysts to work within a familiar environment. It reduces the need to switch between multiple software tools, thereby streamlining the workflow and reducing training requirements. Engineers who are already proficient in DeepEX interface and options can leverage their expertise in both soil spring and finite element analyses, leading to increased efficiency and productivity.
In summary, the fact that DeepEX software offers both soil spring and finite element analysis capabilities provides flexibility, efficiency, and the ability to handle a wide range of tunnel analysis scenarios. Our software empowers engineers to make informed decisions, optimize designs, and ensure the safety and performance of tunnel projects.