Model Simulation, 2D Finite Element Analysis – Structural Capacities
A. INTRODUCTION
Determining the moment and shear capacity of custom shape tunnel sections presents a formidable challenge. This article demonstrates the seamless process of drawing and generating custom tunnel section shapes within DeepEX – Shoring and Tunnel Design section. DeepEX, a robust software suite, empowers engineers to design and analyze deep excavations and tunnels effortlessly. With its interactive interface and implemented Finite Element Analysis engine, DeepEX enables detailed simulation of all objects within the soil mass, facilitating comprehensive analysis of stresses, moments, shears, displacements, settlements, and more, while considering full soil-structure interaction.
Figure 1: DeepEX 2D FEM analysis - Tunnel lining moments graph and settlement shadings
B. CUSTOM SHAPE SEM TUNNEL SIMULATION IN DEEPEX
In the subsequent sections, we showcase the simulation of a custom shape tunnel with shotcrete lining using DeepEX software. This simulation encompasses all intermediate construction stages for tunnel construction, including partial soil deactivation, final excavation, and activation of the shotcrete lining. Table 1 provides the soil properties and stratigraphy assumed in this example, offering a comprehensive basis for analysis.
Table 1: Assumed soil properties and stratigraphy
Soil | Top El. | Description | Unit Weight | Friction Angle | C’ or Su | Soil Behavior | Eload | exp |
(-) | (m) | (-) | (KN/m3) | (deg) | (kPa) | (-) | (kPa) | (-) |
F | 0 | Fill - Sand | 19.6 | 30 | 0 | Exponential | 15000 | 0.5 |
C | -2 | Undrained Clay | 20 | 0 | 150 | Exponential | 20000 | 1 |
R | -6 | Rock | 27 | 30 | 60 | Exponential | 500000 | 0.5 |
STEP 1: Define soil properties and stratigraphy
In DeepEX, engineers can conveniently define soil properties using a user-friendly dialog. This dialog allows for direct specification of the soil name, type, and general properties, including soil behavior properties such as constitutive law, modulus of elasticity, and exponent. Users have the flexibility to input these parameters manually or utilize the implemented soil estimation tools for expedited input. Furthermore, DeepEX facilitates the generation of stratigraphy by enabling engineers to define the top elevation and soil type for each soil layer, ensuring accurate representation of subsurface conditions in the model.
Figure 2: Editing the soil properties and stratigraphy in DeepEX
STEP 2: Add a tunnel in the DeepEX 2D model area
Within DeepEX, engineers can easily access the "Draw Supports" drop-down menu located in the general tab of the software. From this menu, users can select the "Draw a tunnel" tool to initiate the tunnel creation process. By clicking on the desired position within the model area, engineers can designate the center of the tunnel. A dialog will then appear, providing options to adjust the precise tunnel center position, edit the tunnel's structural section, and implement features such as partial deactivation of the tunnel in specific construction stages. This intuitive interface empowers engineers to customize tunnel designs with precision and efficiency, ensuring optimal performance within the simulation.
Figure 3: Adding a tunnel in a DeepEX model
Figure 4: Tunnel properties dialog in DeepEX - Define the tunnel position and section
STEP 3: Draw a custom tunnel shape and edit point coordinates
DeepEX includes a CAD tool equipped with basic drawing functions, enabling engineers to create any tunnel shape effortlessly. By simply clicking on points within the CAD area, users can generate the desired tunnel shape. Subsequently, engineers have the capability to define the exact coordinates for each point along the perimeter of the tunnel shape, ensuring precise customization to meet project requirements. This intuitive feature empowers engineers to design tunnels with intricate geometries and tailored specifications, enhancing flexibility and accuracy within the simulation environment.
Figure 5: Drawing a custom tunnel shape in DeepEX
STEP 4: Define the structural section for the tunnel lining
Within DeepEX, engineers can swiftly select the desired tunnel structural section type from a range of options, including reinforced concrete, precast concrete, steel plates, steel ribs, corrugated sheeting, and more. Once selected, engineers can directly define the section properties, tailoring them to project specifications. This includes specifying structural materials, lining thickness, rebar size, positions, and other relevant parameters. By providing this comprehensive range of options and customization capabilities, DeepEX empowers engineers to efficiently design tunnel structures that meet performance requirements and project constraints with precision.
Figure 6: Tunnel lining structural section properties in DeepEX
C. FEM ANALYSIS RESULTS & TUNNEL STRUCTURAL CAPACITIES
The generated tunnel model underwent analysis using the DeepEX Finite Element Analysis engine. DeepEX presents all results on the model area comprehensively, enabling engineers to swiftly evaluate them and identify potential issues. Figures 7 through 10 illustrate the calculated soil mass displacement shadings, tunnel lining stress results and capacities, as well as the moment-axial interaction diagram for the shotcrete lining section.
Figure 7: DeepEX FEM analysis - Soil mass shading settlements
Figure 8: Tunnel lining moment diagram and moment capacity
Figure 9: Tunnel lining shear diagram
Figure 10: Tunnel lining moment axial interaction diagram
D. CONCLUSION
In conclusion, DeepEX emerges as an indispensable tool for engineers grappling with the complex task of designing and analyzing custom shape tunnels. By providing a user-friendly interface, advanced FEM analysis capabilities, and comprehensive results visualization, DeepEX streamlines the design process and enhances precision. We invite all tunnel engineers to harness the power of DeepEX and elevate their tunnel design endeavors to new heights of efficiency and accuracy.
