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 :)