A Semi-Probabilistic Approach to the Design of Jet Grouted Umbrellas in Tunnelling

A possible approach is shown for the design of jet grouted umbrellas, which are often used as temporary supports in tunnelling practice. In the paper, it is argued that such an approach cannot be but probabilistic or semi-probabilistic. Based on published experimental data and statistical analysis of diameter and centroid position along the axis of jet grouted columns, in the paper a series of Monte Carlo simulations were carried out to find the influence of possible defects within the column in the umbrella static performance, with reference to two extreme subsoil conditions, that is clay and sand. Geometrical considerations on the minimum overlapping among columns necessary for continuity on the whole span of the umbrella are first drawn. It is shown that, due to defects, the real shape of jet grouted umbrellas is not that of a regular frustum of cone, and overlapping decreases along the span. There is a critical length after which structural continuity is difficult to obtain, depending on the statistical characteristics of the jet columns. Defects in axis orientation play the major role on this critical length. Static conditions are also analysed, assuming a simplified 2D arch scheme, with reference to the part of umbrella in which continuity is guaranteed with the assumed level of confidence (95%). The minimum average thickness of the jet grouted umbrella necessary for equilibrium is than found, which of course increases as the umbrella opens up along its axis. By combining geometric and static considerations, a simple yet conservative criterion to plan the number of layers of jet columns, their spacing and minimum required diameter (therefore, their initial overlapping) for the design of tunnelling supporting umbrellas is than proposed.