This paper revisits a classical problem of geotechnical engineering involving the stability of shallow circular tunnels excavated in frictional cohesive materials. The problem is of practical interest since, among others, it allows establishing conditions of stability for the front of tunnels in soils excavated manually or using mechanized methods. A historical background of computational methods developed to establish the stability conditions of shallow cavities in soils is presented first. In particular, analytical models based on lower and upper bound theories of plasticity are discussed. Thereafter a classical lower bound model due to Caquot is analyzed and extended to account for the presence of a surface surcharge and water in the soil being excavated. This model is proposed as a means of getting a first estimate of the stability conditions of shallow tunnels under various hydraulic conditions, using a closed-form solution. The concept of factor of safety, traditionally used in the assessment of stability of slopes in frictional cohesive materials, is also included in the model. Results obtained with the extended Caquot's model are shown to be in accordance with those obtained with more sophisticated finite element and finite difference methods. A computer spreadsheet including the implementation of Caquot's extended solution is also provided in the paper.
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