Guidelines and Precautions for Continuum Analysis

Continuum analysis is gaining importance nowadays in all the design offices. Complex multi stage models can be easily created and quickly analyzed as the computing power is increasing day by day. But the irony is, sometimes, the users are not powerful enough, with little understanding (of both - the problem at large and the physics behind the code). In retrospect, during past 5 years of my experience as a design engineer, I have run umpteen number of numerical analysis but hardly any of them was perfect (from my current standpoint). However, it has been improving continuously with experience. It is not an area which could be mastered overnight, anyway. 

During my current course in Politecnico di Torino, I am able to interact with different experts and learn from different practicing engineers about the efficient and practical way of Tunnel continuum analysis. I want to summarize my understanding and the guidelines given in different books regarding the Continuum Analysis of Tunnels, to share with other aspiring Tunnelling engineers (I intend to update this post as the course progresses).

General procedure and precautions to be taken in numerical modelling:

• Step 1: Assess the requirement and purpose of continuum analysis. Precaution in selection of selecting FoS. Safety factors and load factors commonly used in conventional methods should not be used in Numerical analysis.
• Step 2: Choose suitable material model, anaysis dimension (2D/3D) and computing technique (FEM/DEM/BEM) / software based on the purpose of the analysis. Summary of different numerical modeling programs and their applications are summarized in Table 6-12 of FHWA-NHI-10-034 [2]
• Step 3: Stress state: Effective stress is more appropriate for saturated rock masses and for sedimentary rocks (Warpinski and Teufel 1993, Berge, Wang and Bonner 1993, Bellwald 1992)
• Step 4: Mesh Size and Boundary Condition: Depends on the hydrologic conditions. Approx. boundaries at 5 to 10 times the size of the opening from centerline. 
• Step 5: Construction sequence: Main sequence to be modelled in numerical simulations are: excavation/ material removal (in steps, if required), liner/support installation (in steps). To simulate the lag time in shotcrete strength gain, one way of modelling is to sequence installation when shotcrete develops its full strength.
• Step 6: Support installation near the face is a 3D problem. However, to simulate this in 2D model, the rock is allowed to deform a percentage of its otherwise free deformation prior to “installation” of the support. This percentage ranges between 50 and 90 percent (Schwartz, Azzouz, and Einstein 1980) depending on how far the supports are installed behind the tunnel face and can be judged using convergence-confinement method. Discussed in detail in my blog post, here)
• Step 7: In a 2D analysis, the properties of bolts and lattice girders are "smeared" along the length of the tunnel. Equivalent properties (per unit length of tunnel) to be used in analysis.
• Step 8: Analysis approach: Unless required, the number of details in performing the analysis should be maintained minimum and Accuracy of results should be read with the accuracy of input data in mind.
• Step 9: Interpretation: Key aspects to be investigated

1. Is the deformation according to the expected trend
2. Compatibility between support system deformations and rock deformations
3. Compatibility between stress state and failure criterion
4. Numerical Convergence
5. Evaluation of support system performance and redesign (if required)
6. Prepare capacity diagrams
7. Parametric studies to develop design charts for other opening size
8. Check yielded and overstressed rockmasses. Check for spalling etc.
9. Pore-pressure distribution and check direction of water flow

Also refer my previous post on 2008 Kresten Lecture for specific learnings from this paper.

References:
[1] Chapter 8, Tunnels and Shafts in Rock, US Army Corps of Engineers (EM 1110 2 2901), Washington, May 1997.
[2] Chapter 6, Technical Manual for Design and Construction of Road Tunnels (FHWA-NHI-10-034), Washington, December 2009.
[3] Hoek, Evert, et al. "The 2008 Kersten Lecture Integration of geotechnical and structural design in tunneling." 56th Annual Geotechnical Engineering Conference. 2008 (available for educational purpose at: Hoek's Corner)