Improved R-F relations for the transversal seismic analysis of rectangular tunnels

The R-F method is commonly implemented in design practice to evaluate the response of rectangular tunnels subjected to ground seismic shaking in the transversal direction. The efficiency of the method depends significantly on the so-called R-F relations, which correlate the flexibility ratio, F, expressing the soil to tunnel relative stiffness, with the racking ratio, R, that is used to account for the soil-tunnel interaction effects in the evaluation of the seismic racking distortion of the tunnel and subsequently in the evaluation of the seismic lining forces. This study presents a set of new R-F relations that were developed for a wide range of rectangular tunnels based on a comprehensive set of numerical parametric analyses, conducted to elaborate on the experimentally and numerically observed coupled racking-rocking response of this type of structures during transversal ground shaking. The new R-F relations account for the dynamic soil-tunnel interaction effects, as well as for the inherent effect of the rocking response of the tunnel section on the numerically computed racking ratios. Additionally, the study provides insights on the rocking response of the rectangular tunnels during shaking, by quantifying this response on the basis of normalized sectional rotation-flexibility ratio (θ/γff -F) relations. The efficiency of the R-F method, when the new R-F relations are used, is examined by comparing its predictions, in terms of seismic bending moment at critical sections of the tunnel lining, with relevant results of rigorous dynamic analyses. The predictions of the 'improved' R-F method are compared very well with the full dynamic analysis results, especially for the cases of rigid tunnels compared to the surrounding ground. Along these lines, the proposed relations may be used in practice, improving the accuracy of the R-F method in common engineering projects.