Upper Bound Stability Analysis of Cracked Embankment Fill on Soil with Spatially Varying Shear Strength

A common approach for analyzing slope stability in normally consolidated or lightly overconsolidated clays assumes a linear variation of undrained shear strength with depth. However, the undrained shear strength of soil (cu) varies not only in the vertical direction, but also in the horizontal direction. An upper bound limit analysis method was presented to investigates the stability of cracked embankment slope fill on soil ground with spatial varying shear strength. The undrained shear strength of the foundation soil is assumed to increase linearly with depth and vary concurrently with horizontal distance. Based on the upper bound theorem of limit analysis, a rotational failure mechanism which combines log-spiral and circular arc failure surface is adopted in this paper. In addition, an analytical method is provided for calculating the critical height, minimum safety factor, and critical sliding surface, facilitating a quick assessment of stability in embankments with cracks. It is shown that a positive ‘i’ suggests greater undrained shear strength around the slope toe, enhancing the embankment’s stability. An increase in the undrained shear strength ratio M increases the stability of the embankment slope, with the most significant impact observed at lower values of M. Cracks at the top require a lower critical slope height for stability.