Calculation of uniformly distributed strip load and the most dangerous sliding surface

In order to search an economical and safe method for calculating the uniformly distributed strip load, based on the formula for stability factor proposed by Professor Sha Hunianci, the formula for the total stress of foundation is substituted and derived. Thus a “general formula” for the elasticity, plasticity, critical edge and extreme stress load is obtained. In addition, this study demonstrates that there exists the smallest stability factor along the load midline from 0 to 90 degrees under the action of load. The point N on the midline of dangerous view’s vertex can be obtained on the premise that the minimum stability factor is presupposed. It increases and decreases with the magnitude of the load. Based on the theory of additional stress formula, the arc ANB from the base to both sides can be drawn through the point N. The arc is the location of the most dangerous sliding surface. On the sliding surface, the stability factor is the smallest at the top and the largest at the bottom. It is exactly the maximum depth of plastic area when K₀=1. During the process of applying load, the stress at each point in the foundation increases and the stability factor decreases. Therefore, the original minimum stability arc ANB moves up to a new place on the arc <>AMB. If we stipulate the minimum value K₀ at point M on the arc AMB, then as long as the minimum value K₀ produced by the preset load at point <>M on the arc <>AMB is within the specified scope, the load is defined to be the design load.