Reliability-Based Design of Spatially Random Two-Layered Clayey Slopes

Two-layered cohesive slopes are encountered in geotechnical applications involving embankments, dams, levees, and natural cut slopes. The reliability of two-layered slopes is highly affected by spatial variability in soil properties. Existing studies lack guidance on the reliability levels that are inherent in the design of two-layered slopes. This paper aims at developing simple mathematical tools for designers to evaluate the reliability levels that are inherent in the design of two-layered slopes consisting of a cohesive embankment or cut that is resting on a soft cohesive foundation. To achieve this objective, Monte Carlo simulations are performed using the finite difference software FLAC for practical scenarios that involve a stiff clay layer on top of a soft clay layer. The reliability is assessed for a variety of slope geometries and soil correlation structures. Results indicate that simple empirical mathematical expressions can be used to link the mean and coefficient of variation (COV) of the dimensionless stability factor of the two-layered slope with input parameters that include (1) the COV of the undrained strength, (2) the ratio of undrained strengths in the upper and lower layers, (3) the ratio of the height of the two-layered system to the height of the slope, (4) the angle of the slope and (5) the vertical scale of fluctuation. A simple design example is presented to illustrate the use of the envisaged procedure in the reliability-based design of two-layered slopes.