Convergence-Confinement Curve based on Depth

Last week, we had an interesting discussion among classmates regarding Convergence-Confinement Curve. This interesting discussion led to further reading on this topic and helped us to understand the influence of depth on convergence-confinement curve. As it gave me a good insight on the behavior of the system with respect to depth and reference to few landmark research articles, I decided to blog on this topic.

From the beginning of this course, our understanding of convergence-confinement curve is as shown in figure below [1]. This concept was described and a spreadsheet for parametric analysis was shared in my previous blog here.

Convergence Confinement Curve

But during the Lecture by Prof. Galler on 3^rd March (details), he gave us a different behavioral concept, as shown in figure below [1]:

NATM - Convergence Confinement Curve

Second behavior as explained by Prof. Galler was proposed by Pacher [2], [3], with a trough-shaped ground response curve. This concept became a main argument point of NATM technique – In order to keep the load upon lining as low as possible, the support-reaction line should intersect the ground reaction line at point minimum point (Point B).

This concept was however questioned by Kovari [4] and was criticized by saying that the minimization of the lining resistance is not possible at all, because its prerequisite of trough-shaped ground response curve could not be explained theoretically.

Several authors [1], [5], [6] defended Pacher’s [2] trough-shaped response curve using numerical calculations, justifying that the variation could be because of the depth of the considered tunnel. It was demonstrated that the trough-shape response curve (as depicted in all NATM literature) are realistic for shallow tunnels and is due to the material softening [5], [6]. Softening is related with loosening and is responsible for increase of the ground pressure relative to the increase of convergence. The deeper the tunnel, the smaller is the softening behaviour and thus trough-shape behavior is not observed in numerical models of deeper tunnels [7].

Softening Behaviour

Further, it is to be noted that softening occurs both for friction angle and the cohesion. Cohesion softening is more dangerous than friction softening as it can lead to sudden loss of stability (as cohesion is destroyed completely after small deformations) [6], [8].

Significance:

For shallow tunnels, cohesion softening is proven by researchers [8] and hence this has to be considered in the numerical modeling. For an excavation with Shield TBM, the excavation face is supported by the TBM itself. Whereas in NATM (shallow tunnel), cohesion softening would play a vital role in stability of the tunnel. Vermeer [9] has also suggested to use 3D tunnel-heading stability and 3D settlement analysis for shallow analysis, if possible.

References:

[1]      D. Kolymbas, Tunnelling and tunnel mechanics: A rational approach to tunnelling. Springer, 2005.

[2]  Pacher, “Deformationsmessungen im Versuchsstollen als Mittel zur Erforschung des Gebirgsverhaltens und zur Bemessung des Ausbaues,” in Grundfragen auf dem Gebiete der Geomechanik/Principles in the Field of Geomechanics (in German), Springer, 1964, pp. 149–161.

[3]      L. Müller and E. Fecker, “Grundgedanken und Grunds{ä}tze der‘ Neuen {Ö}sterreichischen Tunnelbauweise’, Felsmechanik Kolloquium Karlsruhe” (in German), Trans Tech Publ., Claustal, 1978.

[4]      K. Kovári, “Erroneous Concepts behind NATM,” in Rabcewicz-Geomechanical Colloquium, Salzburg, 1993, p. 21. (Available at Swiss Federal Institute of Technology site, here)

[5]    G.-M. Vavrovsky, “Development of groundpressure, deformation and tunnel design (in German),” Felsbau, pp. 312–329, 1994.

[6]      P. A. Vermeer, T. Marcher, and N. Ruse, “On the Ground Response Curve,” Felsbau, vol. 20, no. 6, pp. 1–8, 2002.

[7]      C. Bliem and W. Fellin, “Die ansteigende Gebirgskennlinie,” Bautechnik, vol. 78, no. 4, pp. 296–305, 2001.

[8]      S. C. Moller, P. A. Vermeer, and T. Marcher, “NATM-tunnelling in softening stiff clays and weak rocks,” Numer. Model. Geomech., p. 407, 2004 (available at Stuttgart Univ. site, here)

[9]      P. A. Vermeer, S. C. Moller, and N. Ruse, “On the application of numerical analysis in tunnelling,” Post Proceeding 12th Asian Reg. Conf. soil Mech. Geotech. Eng. (12 ARC), Singapore, pp. 1539–1549, 2003 (available at Stuttgart Univ. site, here)

PS: Citations managed using Mendeley. Started trying Mendeley for research papers and reports and found it amazing :)

Week 7 Tunnelling & TBM Course: NATM, Ground Reinforcement & Ground Monitoring

Week 7 (3rd Mar '14 to 7th Mar '14) of 2nd Level specializing course in Tunnelling and TBM started with a lecture by Prof. Galler on NATM technique (details here). Followed by lectures on Geotechnical Monitoring, Ground Reinforcement and Lining Segments.

Prof. C. Oggeri explained us about the concepts and importance of Ground monitoring with case studies. Ground response monitoring forms a key aspect of Observational Method / NATM Technique.

Observational Design Cycle

For further reading on Ground Monitoring, we referred to the book by Dunnicliff [1]. In the latter part of the week, we were given the basic concepts of Ground Reinforcements and Ground Improvement for Tunnelling applications, detailed discussion to follow in Week 8. 

References:

[1]   Dunnicliff, John. "Geotechnical instrumentation for monitoring field performance." (1993).

Prof. Robert Galler's Lecture on NATM & Case studies

Prof. Robert Galler at Politecnico di Torino, Italy

Today (March 3rd, 2014) we had a special lecture by Prof. Robert Galler (official page) from University of Leoben, Austria. Prof. Galler gave us an overview of the NATM Technique with few examples. Basically, the lecture was a brief of the contents presented in his book "NATM - The Austrian Practice of Conventional Tunnelling" published by Austrian Society of Geomechanics (review of this book was covered in my blog, here) and his paper on New NATM Guidelines[1]. Prof. Galler explained us about the Design stage workflow and construction stage followed in NATM with emphasis on monitoring and role of a Geotechnical engineers during construction.

Prof. Galler also explained in brief, about the Austrian Practice of "Works Contracts" for Underground works based on Austrian Standard ÖNORM B2203-1. This standard addresses the need for flexibility in contracts in order to take advantage of NATM's strength. ÖNORM B2203-1 proposes costing guidelines to prepare Advancement (Round Length) vs Support Factor Matrix for deciding different support classes.

Example of Costing matrix proposed in B2203-1 [2]

Also we received a personalized signed copy of the book "The Austrian Art of Tunnelling in Construction Consulting and Research" (link) from Prof. Galler.

The Austrian Art of Tunnelling - ISBN 978-3-433-02924-4

References:

[1] Galler, R., et al. "The New Guideline NATM–The Austrian Practice of Conventional Tunnelling." BHM Berg-und Hüttenmännische Monatshefte 154.10 (2009): 441-449.

[2] The Austrian Practice of NATM Tunnelling Contracts, Austrian Society of Geomechanics, ÖGG Salzburg, 2011 (available at ÖGG's website)

Week 6 Tunnelling & TBM Course: Shotcrete and Lining Design

Week 6 (24th Feb '14 to 28th Feb '14) of 2nd Level specializing course in Tunnelling and TBM was on Shotcrete and Design of lining, including the use of support interaction capacity curves. Majority of this week's time was spent on understanding the evolution of design philosophy for tunnel liners using shotcrete and steel-sets. 

Initial Support & Lining System Used in Current Practice [1]

It is understood from the above figure that the application of Shotcrete + Steelsets is used for wide range of ground conditions and is one of the most widely used support system. 

Concepts of three main design methods: Distributed ground pressure approach, subgrade reaction approach and Ground-support interaction approach were discussed. The paper on composite supports (Steel-sets + Shotcrete) by Hoek's research group (Carranza-Torres et al) [2] was helpful in understanding the concepts of Capacity diagrams.

Other paper which was reviewed during this week was Oreste (2007) which is on Hyperstatic reaction (numerical method) to simulate interaction between the support and rock surroundings using springs. Based on several calculation using Hyperstatic Reaction Method (HRM), design tables are presented for dimensioning support system (with Steel-sets + Shotcrete).

For complete understanding of shotcrete usage and admixtures used, we had invited lectures by  Mr. Enroco Dal Negro, Carlo Pistolesi and Cristiano Maltese (from Maipei) on practical aspects of shotcrete use in a site and on Concrete Technology.

Also during this week,  we had a special lecture by Mr. Juha Kukkonen (from Sandvik) on Drilling Jumbos and tools. This is in continuation with the Drill and Blast lecture series which was covered during Week 4 of this course.

Mr. Juha Kukkonen and Mr. Giovanni De Mattia from Sandik

References:

[1] Transportation Research Board (2006). "Making Transportation Tunnels Safe and Secure", NCHRP Report 525, Vol. 12.

[2] Carranza-Torres, C., and M. Diederichs. "Mechanical analysis of circular liners with particular reference to composite supports. For example, liners consisting of shotcrete and steel sets." Tunnelling and Underground Space Technology 24.5 (2009): 506-532.

[3] Oreste, P. P. "A numerical approach to the hyperstatic reaction method for the dimensioning of tunnel supports." Tunnelling and underground space technology 22.2 (2007): 185-205.

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)