Engineers Australia

Revisiting the applicability of Voussoir Beam Theory for tunnel design in Sydney

D.A.F. Oliveira and P.J.N. Pells


The design of semi flat-roofed tunnels, i.e. with a high arch radius to roof span ratio, in Sydney has been proven successful over time. The horizontally bedded nature of Sydney’s Hawkesbury Sandstone draws designers to the voussoir beam theory. Such analogy and the associated method of analysis can be easily implemented in computer spreadsheets, which significantly facilitates the design of semi flat-roofed tunnels in geological conditions such as Hawkesbury Sandstone. Like any other engineering simplified model or theory, the voussoir beam theory has some limitations. However, it seems that some of these limitations are not well understood and often ignored and/or misinterpreted. Such lack of understanding of the theory and its limitations often raises question about the applicability of the analytical solution in practice, misleading engineers to believe that the only reliable and comprehensive design method is through numerical analysis such as Distinct Element Method (DEM). This paper investigates the applicability of the analytical or closed-form solution of the voussoir beam theory through comparison with numerical modelling, focusing on some of the perceived limitations and their impact on the design of tunnels in Sydney. The results illustrate that the voussoir beam theory can be confidently used in practice if its limitations are well understood and good engineering judgment is applied to take the local geology into account. In addition, the results also demonstrate that some of the limitations can be on the conservative side. For example, the potentially positive effect of high horizontal stresses ignored in the voussoir beam theory may explain why some of the unfavourable conditions are less pronounced in practice.