Relationship between input and output : a systematic study of the stability of highly fractured rock slopes using the Hoek-Brown strength criterion.

Abstract

Rock slope stability is a particularly important topic in rock engineering. The circular failure of highly fractured rock slopes is a critical failure mode that can cause severe damage. Over the past decades, significant research has been devoted to soil slopes and failure modes of rock slopes controlled by discontinuities. However, there have been few attempts to systematically study the circular failure mode of rock slopes. Circular failure is controlled by the strength of the rock mass. While the strength of a rock mass is difficult to measure directly, the Hoek-Brown (HB) strength criterion has proved effective and convenient for its estimation. This research presents a systematic study of the stability of highly fractured rock slopes using the HB strength criterion. Both deterministic analyses and probabilistic analyses are included. The relationship between the input (GSI, mi, σci, and their variability) and the output, Factor of Safety (FS) and Probability of Failure (PF), is investigated. Slide6.0 and a limit equilibrium model programmed in Matlab are used for FS calculations; Monte Carlo simulations are applied for PF calculations. The deterministic analysis aims to characterise the sensitivity of FS to the changes in HB parameters (FS sensitivity). A sensitivity graph analysis and an equation fitting analysis are developed. The sensitivity graph analysis displays the relationship between HB parameters and FS directly. The equation fitting analysis fits a large amount of data generated by Slide6.0 with an equation connecting HB parameters and FS, and then determines FS sensitivity from the derivatives of this equation with respect to HB parameters. It is found that slopes with the same geometry and the same FS (but different combinations of HB parameters) can have quite different sensitivity and GSI is the most critical parameter in this respect. With the increase in GSI, FS becomes increasingly sensitive to the change in GSI and that in σci. The probabilistic analysis investigates the relationship between the variability of HB parameters (quantified by the coefficient of variation COV and scale of fluctuation θ) and PF. Its effectiveness in assessing the impact of FS sensitivity on slope stability is also studied. A series of parametric studies are implemented. It is found that there is a strong relationship between FS sensitivity and PF: for slope cases with identical FS and the same COV of input HB parameters, a slope of higher FS sensitivity has a higher PF, indicating a higher risk. The relative contributions of the variability of HB parameters to PF are also compared. It is found that when the COV of GSI, mi, and σci are identical, the variability of GSI makes the largest contribution; however, when these COV are set to their upper-limit values observed in engineering practice, the high variability of σci makes the largest contribution. Finally, the investigation demonstrates that spatial variability of HB parameters (applicable to mi and σci in this study) has significant influences on slope stability. For a slope with FS > 1, the PF increases as the scale of fluctuation θ of HB parameters increases. Also, larger θ makes the effect of FS sensitivity on slope stability more significant.