Asymetric Buckling Of Circular Rings in a Confined Environment. “Amstutz Buckling” – An Enhanced Approach

"""The theory of buckling of shafts and Steel tunnel-linings"" was published by E. Amstutz in 1970 and commented on by S. Jacobsen in 1974. The authors have revised and enhanced Amstutz’s work to address Jacobsen's comments on its limitations and to extend its validity over a wider range of pipe/shaft geometries, including those commonly found in deep mine access shafts. The author has looked at Amstutz’s assessment of strengthening with flexible shear anchorages and adapted the theory of non-linear shear deformation response of bolts to develop a method of assessing increased buckling capacity utilising the full plastic shear capacity of studs. INTRODUCTION “Amstutz Buckling” refers to the buckling of pipe embedded in concrete under external uniform pressure. In terms of a mining environment, this relates directly to the design of a watertight shaft. This load case will commonly occur where a main shaft is cast against a geostatically stable primary liner and the only load applied to the final shaft is that of a uniform ground water load. Ernst Amstutz wrote his first paper on buckling of pressure-shaft steel linings in 1950 and subsequently improved his theory (Amstutz, 1970), which was then widely adopted for use within the industry. Years later, an alternative approach (Jacobsen, 1974) was proposed. Within his paper Jacobsen critiques Amstutz work, identifying some mathematical inconsistencies and highlighting limitations of the theory imposed by approximations adopted by Amstutz. Despite these limitations Amstutz work has still been used as the favoured design theory for use in the mining industry. In reviewing this body of work the author realised that with the advent of readily available computing software it was possible to adopt an iterative approach using Amstutz approximate formulae to find a solution to the original precise formulae, thus eliminating the limitations highlighted by Jacobsen The shear deformation to load characteristics of bolts has long been established (Crawford & Kulak 1968) and used for the plastic design of bolted connections in shear. This relationship is directly transferable to the design of shear studs, typical properties are well known, and actual values easily established in simple lab tests. The author has taken this relationship and modified Amstutz theory (Amstutz, 1970) for shear anchored strengthened liner buckling, to give a more efficient solution, using readily available material properties."