On a Paradox of Elasto-Plastic Tunnel Analysis

Elasto-plastic tunnel analysis may produce a paradox in the calculation of ground pressure whereby ground pressures appear to increase in relation to higher ground quality. More specifically, for an overstressed ground in combination with a stiff support, analysis may indicate greater loading of the support with a ground of high strength than with a ground of low strength (all of the other parameters being equal). This counter-intuitive outcome appears in all of the common calculation models (analytical plane strain analysis, numerical plane strain analysis and numerical axisymmetric analysis), although it does not correspond either to the ground behaviour that is intuitively expected or to ground behaviour observed in the field, thus raising doubts over the predictive power of common tunnel design calculations. The present paper discusses the assumptions made in the models that are responsible for the paradox: the assumption that ground behaviour is time-independent (whereas in reality overstressed ground generally creeps) and the assumption that the support operates with full stiffness close to the face (which is not feasible in reality due to the nature of construction procedures). When proper account is taken of either or both of these assumptions in more advanced models, the paradox disappears. As the models which generate the paradox are very commonly used in engineering and scientific practice, the investigations of the present paper may be of value, helping the engineer to understand the uncertainties inherent in the models and to arrive at a better interpretation of the results they produce.