senting conditions at the above field site was also performed. The advantage of the laboratory model was the ability to investigate a broad range of variables and flow conditions not readily achievable in a field setting. For the model, an instrumented 3D block mold was constructed that could be rotated with respect to the flow direction to study the influence of discontinuity orientation on block erodibility. As would be expected, the block erodibility threshold was found to be highly dependent on the flow direction. This can be attributed to changes in kinematic constraints associated with the block mold geometry in the downstream direction as well as the relative profile of block protrusion above the channel bottom. Three separate block response types were observed which are closely associated with block kinematic resistance. Pressure values, represented by the dimensionless average dynamic pressure coefficient, Cp, were determined as a function of the block mold orientation, turbulence intensity, block protrusion height, and flow velocity. Overall, the average hydrodynamic pressures on block faces were found to be adequate in the evaluation model block stability. Accordingly, the data presented herein may be applied to a variety of flow conditions.
A reliability-based, block theory framework was also developed for evaluation of 3D block erodibility given parameter uncertainty associated with the inherent variability within the rock scour process. Block theory provides a rigorous analytical methodology to identify removable blocks, determine potential failure modes, and assess 3D block stability. Block stability is evaluated in a pseudo-static manner using block theory limit equilibrium and kinematic constraint equations. Theoretical predictions for block erodibility threshold compare well with those obtained from hydraulic model testing for both high and low turbulence flows. Improved prediction was observed for some cases when a mobilized joint friction angle was used.
Applicability of the reliability-based, block theory methodology was demonstrated through two example analyses for the field site in northern California. Removable blocks from the spillway channel were identified and analyzed deterministically to determine their erodibility threshold. Variability in rock mass parameters was included based on statistical analysis of the LiDAR data set to calculate the failure probability of the block with the lowest erodibility threshold. FORM analysis for parameter importance indicates block protrusion height, followed by rock joint orientations and flow velocity, are the most influential variables on block stability, while joint friction angle is relatively insignificant.
From a design standpoint, the benefit of the proposed methodology is that 3D, site-specific geologic structure information can be incorporated into evaluation of rock mass erodibility. Variability in site parameters can be addressed in a probabilistic manner to classify locations most susceptible to erosion as well as identify the most influential variables affecting rock block stability. This can lead to more efficient scour remediation designs as well as more focused field and laboratory efforts to investigate parameters with the most impact on the system. Furthermore, reliability data can be useful for designers and infrastructure owners in decision making and management of risk at a specific site.
