Stability of rocks on mild slopes

Abstract

Since the behaviour of damage formation on steep slopes varies from mild slopes, a comprehensive definition of damage needs to be established for different situations. Knowledge about the transition of rock stability between steep and mild slopes is lacking. This study presents a reliable and efficient design method. The goal of this study is to describe the stability of rock slopes (1:6 - 1:10). Insight into governing processes and quantified damage characteristics are gained by analyzing wave attack in the transition zone of mild and steep slopes. The method is based on physical model test series with deep water wave conditions and perpendicular wave attack, which were performed to understand the stability of slope 1:6. The slopes were measured with stereophotogrammetry and processed in a 3D model with Agisoft Metashape software. Before wave attack, an initial profile is retrieved which can be compared with cumulative damaged profiles. Automatically detectable Ground Control Points are used as reference to assign scaling information and location recognition. The quantity and location of normative damage on mild slopes are identified for six damage parameters, based on different relations regarding erosion area and depth. The tests results have led to a number of key findings. Damage formations are developed by dominant downward (bar profile) or upward transport (berm profile). In general, a thicker layer and a milder slope give more upward transport. Besides the change in transportation direction, no significant differences in stability numbers were observed for various layer thicknesses with similar wave characteristics. For an increasing slope angle, the influence on stability significantly decreases between various wave steepnesses, due to the impact of a higher amount of more damaging plunging waves. The definition of initial, intermediate and failure damage limits are specified and the test profiles are matched per limit. Initial and intermediate damage are found at a constant value of _3_.3 for a varying layer thickness and slope angle based on the definition and matching profile analysis. Failure of the slope is defined by the event in which the impermeable layer or filter layer becomes visible, which occurs for a layer thickness of 2.53=50 at a damage level of _3_.3 = 1.5. Research at 1:6 slope shows that a higher failure limit is observed for layer thickness 53=50. Due to the lack of test results of other slopes (1:8 - 1:10), specific values cannot yet be indicated for the range 1:6 - 1:10. The lack of testing is also due to limits of the flume and wave machine. In order to remain at least 13=50 over the slope, an acceptable damage limit for a design with a layer thickness of 2.53=50 is found at _3_.3 = 0.9. For a layer thickness of 53=50, an acceptable value of _3_.3 = 1.5 holds a remaining layer of 2.53=50 due to the increase of bed mobility for higher damage numbers. The design formula of mild slopes is based on _3_.3 because this gives the lowest bias error, variability and measurement errors. The design formula for mild slopes is used to estimate stability, nominal rock diameter and acceptable damage for conditions within the applicability range of performed tests. This new method for mild slope design indicates that a higher allowable stability can be used compared to the previously used (extrapolated) method of Van der Meer (1988). A displacement is not necessarily linked to erosion due to alternating upward and downward transport on mild slopes. It can be discussed to what extent a rock, after displacement, contributes to the stability of the design. This can be investigated by the ratio of mobility and erosion over the entire slope. This study has shown that the damage parameters, based on displacements, are larger than the width-averaged erosion parameters. This appears to be a useful ratio for distinguishing mild slopes from steep slopes. In the latter these parameters are considered equal. Requirements for mild slope stability can also be imposed on the basis of the ratio between mobility and erosion as described in this research.