A simple analysis method suitable for the preliminary design of tunnel supports is developed. The analysis is generally intended for cylindrical tunnels with closed-ring primary support systems excavated full-face in ground masses that can for practical purposes be treated as time-independent continua. In this method, the complex ground-structure interaction phenomena around a tunnel are reduced to three essential components: (1) the decrease of support loads with decreasing stiffness of the support relative to the ground, (2) the decrease of support loads with increasing spatial lag or "delay" of the support construction behind the tunnel face, and (3) the increase of support loads accompanying yielding of the ground mass. Each of these factors is studied in detail using both closed-form analytical derivations and finite element numerical solutions. The simplified analysis method then quantitatively combines the effects of the three fundamental variables: a "basic support load, which depends primarily on the relative support stiffness and lateral in situ stress ratio, is calculated and multiplied by two correction factors for the effects of support delay and ground yielding. In order to verify the accuracy of the simplified method, it is applied to four tunnel projects (a total of ten tunnel sections) in which the actual support loads were measured during construction. The average error in the predicted support loads for these cases is only 30%.
Tunnel construction is undeniably an expensive endeavor. Recent bids for a 4325 ft. long section of twin mined tunnels for the Red Line subway extension in Boston were in excess of $47 million, or over $5400 per foot of tunnel. Support of these tunnels represented a substantial portion--more than 25%--of cost. A recent survey by Tse (1979) found that the ratio of support costs to total costs typically averages 30-35% for tunnels in urban environments and up to 40% for deep-lying tunnels in mountainous regions. As a step toward a more rational determination of this load, we have developed a Simplified Analysis Method (SAM) suitable for preliminary design. The SAM is generally intended for circular tunnels with closed-ring primary support systems excavated full-face in ground masses that can for practical purposes be treated as time-independent continua. Examples of practical tunneling situations that satisfy these requirements and are amenable to analysis by the SAM include--but are not limited to--tunnels in soil, heavily jointed rock, and massive rock formations supported with circular steel ribs, prefabricated segmented liners, and continuous shotcrete.
For excavations through non-swelling, non-squeezing, and reasonably continuous ground masses (e.g., soil; rock with either very widely or very closely spaced joints), there are three major components to the ground-structure interaction phenomena around a tunnell: (1) the decrease of support loads with decreasing stiffness of the support relative to the ground, (2) the decrease of support loads with increasing spatial lag or "delay" of the support construction behind the tunnel face, and (3) the increase of support loads accompanying any yielding that may develop within the ground mass.
