A numerical approach to the hyperstatic reaction method for the dimensioning of tunnel supports

• Published in: Tunnelling and underground space technology Vol. 22; no. 2; pp. 185 - 205
• Main Author: Oreste, P.P.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.03.2007; Elsevier
• Subjects: Applied sciences; Buildings. Public works; Computation methods. Tables. Charts; Exact sciences and technology; Geotechnics; Structural analysis. Stresses; Structure-soil interaction; Tunnels, galleries; Validation; Support(construction); Rock mass; Displacement; Dimensioning; Geometry; Finite element method; Formulation; Static analysis; Numerical simulation; Structure soil interaction; Typology; Mathematical model; Computing method; Tunnels
• ISSN: 0886-7798; 1878-4364
• DOI: 10.1016/j.tust.2006.05.002

The hyperstatic reaction method is particularly suitable for the dimensioning of support structures. This method simulates the interaction between the support and rock surrounding the tunnel through independent “Winkler” type springs. It requires the definition of the active loads that are applied directly to the support structure by the rock mass. Further passive loads are due to the reaction of the rock mass to the displacement of the support structure. A numerical approach to the hyperstatic reaction method is presented in this paper. The parameters that condition the calculation and the dimensioning techniques of the support structures, on the basis of the results of the method, are also presented. A specific code, named FEMSUP, was developed using a FEM framework, to perform calculations with the HRM. This code is able to consider the effective geometry of the support and the horizontal active loads that are different from the vertical ones; it is therefore able to analyse the rock mass–structure interaction in detail. An extensive parametric analysis performed using FEMSUP has made it possible to define the necessary support structures (steel sets incorporated into a shotcrete lining) in a wide number of cases that cover the conditions that are generally encountered in excavation practice. Ten design tables were drawn up to summarise the results of the parametric analyses. From an examination of the tables, it is possible to verify the influence of the various calculation parameters on the dimensioning of the support structure and to obtain rough indications on the entity of the support structures in the preliminary stages of a project.