Seismic Stability Evaluation of Soil–Rock Mixture Slopes Using Upper-Bound Finite Element Limit Analysis Considering Effective Rock Content

Soil–rock mixtures are composed of various constituents, including rock blocks, soil matrix, and pores. The stability of slopes formed by such materials is significantly affected by rock content, block location, and block gradation. However, most existing studies have used the overall rock content as the primary index to characterize the role of rock blocks. This index is essentially a global averaged parameter and therefore cannot accurately reflect the actual contribution of rock blocks to slope stability. To overcome this limitation, stochastic numerical models of soil–rock mixture slopes were established based on real rock-block contours, and the seismic stability of these slopes under pseudo-static horizontal seismic loading was investigated using the upper-bound finite element limit analysis method. On this basis, the concept of effective rock content was proposed to quantify the actual participation of rock blocks within the governing sliding zone. Comparative analyses based on selective rock-block removal further demonstrated the limitation of the overall rock content index. When the rear rock blocks were removed while the effective rock content remained unchanged, the safety factor changed only slightly from 0.882 to 0.881. In contrast, after removing the leading-edge rock blocks, the effective rock content of the slope decreased to 0. The safety factor dropped to 0.774, close to the safety factor of 0.772 for a homogeneous soil slope. Quantitative sensitivity analysis further showed that the effective rock content plays a controlling role in the slope safety factor. Compared with the overall rock content, it can more effectively characterize the actual contribution of rock blocks to the seismic stability of soil–rock mixture slopes and can be regarded as the governing structural parameter controlling slope stability. Furthermore, the effects of gradation and the spatial distribution of oversized rock blocks on the stability of soil–rock mixture slopes can both be interpreted through their regulation of the effective rock content and the rock-skeleton effect. In general, the beneficial influence of the spatial location of oversized rock blocks on slope stability follows the order: slope toe > slope face > slope crest > inside the slope > behind the slope. These findings indicate that effective rock content can serve as a key index for characterizing the seismic stability of soil–rock mixture slopes and provide a new analytical framework for the stability assessment of such slopes in seismic regions.