Limit Analysis for Tunneling

The proposed research aims at improvements in numerical predictions in geomechanics with particular emphasis on tunnelling with the New Austrian Tunnelling Method (NATM) by approaching the problem from two aspects. The first one is the finite element modelling employing advanced constitutive models. The second one is the limit analysis, also based on numerical procedures. The advantage of the limit analysis approach is that, once the complex numerical algorithms required for the optimization procedure are sorted out, run times on the computer are very low, i.e. solutions for the problem at hand are obtained typically in the order of minutes. The disadvantages of the method are that only limit loads can be obtained, yielding no information on the stress and displacement field before failure and severe restrictions with respect to geometric conditions which can be handled apply. The contrary holds for finite element techniques employing highly advanced constitutive models. Here stresses and displacements are obtained for working load conditions as well as for near failure conditions. If appropriate models are implemented accounting for strain softening behaviour the post failure regime can also be investigated. The disadvantage of this approach is twofold. First, run times are very high due to the complex solution strategies required. Second, material parameters are not always easy to determine for such complex models. In addition, only limited experience is available from the field because failures are often not very well documented. It is therefore essential that such highly complex models are validated against well proven other methods, and one of these methods are limit analyses. As mentioned previously these methods are restricted to certain boundary conditions and furthermore simplify the material behaviour significantly. However, the more versatile finite element method addressed above can model those conditions as a special case and thus results obtained from both approaches can be compared. This gives an excellent opportunity to validate finite element results. On the other hand, it serves also to show the limitations of the limit analysis approach. For these reasons the research proposed from the applicants is complimentary in the sense that the main expertise of the main applicant is in limit analysis and the co-applicant has significant experience in finite element modelling applying advanced constitutive models. It is thought that the exchange of experience will be very beneficial to both sides leading to an enhancement of knowledge in the difficult field of assessing failure mechanisms in tunnelling constructed due to the principles of the NATM.