On the Role of Analytical Solutions for the Evaluation of Soil Deformation Around Tunnels
The role of analytical solutions in the evaluation of stress and displacement fields around tunnels is commented. The paper is divided into two parts. In the first part, ground loss and tunnel distortion are evaluated from elastic and elastic-plastic solu
- PDF / 1,989,064 Bytes
- 22 Pages / 482 x 692 pts Page_size
- 98 Downloads / 256 Views
C. Sagaseta University of Cantabria, Santander, Spain
ABSTRACT: The role of analytical solutions in the evaluation of stress and displacement fields around tunnels is commented. The paper is divided into two parts. In the first part, ground loss and tunnel distortion are evaluated from elastic and elastic-plastic solutions, starting from the basic case of a circular tunnel at infinite depth and with uniform and isotropic initial stresses, and by introducing the effect of uneven stresses and finite depth. The second part deals with the analysis of distant deformations. Available solutions are used to derive surface and deep displacements. The results of observations in actual cases are used to assess the applicability of the solutions presented. INTRODUCTION The use of analytical solutions has been reduced in the last decades due to the large development of numerical methods. Finite element analyses in· 2 or 3 dimensions, with nonlinear soil behaviour, simulation of construction phases, and coupled deformation and flow are now possible in a portable computer, with commercially available programs. Under these conditions, the old analytical solutions, requiring drastic simplifications of the problem geometry and stress-strain properties are no longer a usual tool. However; they can play still an important role for several reasons: first, they are the reference benchmarks for the results of numerical analyses; they are useful for sensitivity analysis and to identify problem variables; and finally, they provide in some cases simple useful results, either directly or with some empirical corrections (see, for instance, Booker, 1988).
A. Cividini (ed.), Application of Numerical Methods to Geotechnical Problems © Springer-Verlag Wien 1998
C. Sagaseta
4
In any case, analytical solutions, used in conjunction to numerical methods and interpretation of actual observations form the basis for the prediction of performance in engineering problems. This is particularly evident in the present case of soil deformation around tunnels. This problem can be divided into two parts, of very different nature. On one hand, the construction of the tunnel produces a deformation in its immediate vicinity. Its magnitude and distribution are strongly dependent on the soil mechanical behaviour and the tunnel construction process. These factors are difficult to consider, given the three-dimensional character of the problem, the non-linearity and time-dependency of soil deformability, and the nature of construction details. This poses a serious problem, and even the most refined numerical analyses require some empirical correction factors. This deformation attenuates with the distance to the tunnel. The distribution of soil movements depends only on a limited number of factors. The kinematical constrains of the problem are strong, the strain level is moderate or small, and the problem geometry is relatively simple. As a result, the pattern of soil displacements at some distance from the tunnel does not vary significantly between different case
Data Loading...
