Based on the logarithmic spiral collapse mechanism

and with considering the heterogeneity of clayey soil

the optimal upper bound solution of the face supporting pressure is obtained in heterogeneous soil in which the cohesive force varies linearly. The validity of the proposed solution is demonstrated by comparing the calculated results with the monitoring data and the results of model tests. In addition

the optimal supporting pressures and the logarithmic spiral sliding surfaces are analyzed in details for various soils. It is shown that in heterogeneous soils the soil cohesion and internal friction angle are the controlling factors. A design chart is developed for the limit supporting pressures in heterogeneous soils.