Shallow stability of subgrade slopes protected by rectangular frame structures and structural optimization

In order to understand the influences of frame protection structures on shallow stability of subgrade soil slopes, based on the infinite slope shallow translational slip, the mechanical effects induced by horizontal and vertical frame structures on shallow slope sliding was analyzed are investigated. The failure modes between frame structures and the determination method for their threshold are established. An optimization mode is proposed. It is indicated that there are two modes, shear sliding along the bottom of frame structures and passive earth pressure failure mode due to retaining effect of horizontal frame structures, and the threshold of modes, l_sp, is mainly affected by the soil property, shear strength index and the slope geometric parameters. The factor of safety for slope shallow stability increases linearly and exponentially with the increasing width and thickness of structures, respectively, and decreases with the increasing clear distances between structures. l_v=l_sp is the optimal vertical distance under the constant factor of safety for the slopes. The optimal vertical clear distance may be determined reasonably by the ratios of the construction cost to the total cost, and increases with the increasing percentage of construction fee per meter.