E. Haugeneder, H.A. Mang, Z.S. Chen, R. Heinrich, G. Hofstetter, Z.K. Li, M. Mehl, P. Torzicky:
"3D Berechnungen von Tunnelschalen aus Stahlbeton";
Report for Bundesministerium für wirtchaftliche Angelegenheiten, Straßenforschung, Heft 382; 1990.
The purpose of the completed research project was to use and further develop EDP programs for 3-D tunnel calculations and for a relastic calculation of the bearing capacity of tunnel linigs. The project was divided into the following steps, in order to reach the set goals:- Developing a program, based on the boundary-element method, for the three-dimensional calculation of cavity enclosures on the premise of a linear-elastic behaviour of the mountain mass, assumed to be homogenous and isotropic, and linking the boundary-element program to finite-element program TPS 10.
- Developing a suitable material model for the reinforced concrete, in order to be able to calculate the bearing capacity of the shotcrete shell in the tunnel.
- Calculating tunnel projects, while giving due consideration to the proper sequence of the advance operations; dimenionsioning the shotcrete shell on the basis of limit-load calculations for the entire construction; i.e. tunnel/rock, and comparison with recorded data.
The calculations showed that the program based on the boundary-element method has particular merits whenever a first estimate is needed of any dislocations and tensions. With the boundary-element method, discretization is limited to the surface of the area under review, which means less input that in case a comparable finite-element calculation. The result, obtained with the boundary-element method, in particular for any tensions, are considerably more precise than those derived by means of the finite-element method. The boundary-element program is restricted to the linear-elastic behaviour of the material, which is a drawback.
The following findings can be derived from the results of the calculations:
a) 3-D calculations provide a realistic presentation of the deformations and tensions. The course of the settlement basin, in relation to the working front, coincides well with the empirical values. A comparison with the recorded results shows good qualitative and a varying degree of quantitative correlation. This is mainly due to the complex soil conditions in the measured area under review.
b) Since the fresh concrete offers little stability near the working front, cutting conditions of any magnitude in the shotcrete shell build up at some distance only. The stresses on the external tunnel shell extend therefore mainly in a transverse direction to the axis.
c) Even though the parameters may be calibrated sufficiently, 2-D calculations, by comparison, can only reflect the final status of a cycle "initial stress relief, excavation of roof section, excavation of bench".
d) Calculating the limit load of a circular tunnel shell shows that normal force causes the critical stress. Accordingly, normal force alone deterimes the dimensions. It may be assumed that this statement is generally valid, also for other tunnel cross-sections. Further calculations are necessary, though, in order to be able to make it.