A semi-analytical model for predicting outflow concentration of vented turbidity currents with application in the Xiaolangdi reservoir

Turbidity current venting is an important way to reduce reservoir sedimentation. Existing methods to predict the outflow concentration of vented turbidity currents either depend on three-dimensional (3D) modelling with high computational cost or semi-empirical equation with a simple assumption of uniform velocity distribution. This study presents a semi-analytical model for predicting outflow concentration in turbidity current venting events, which accounts for the non-uniform and asymmetric velocity distribution in the withdrawal layer. Firstly, a 3D numerical model is established to facilitate the determination of withdrawal layer thickness and extraction of flow velocity within it, which is validated by simulating a group of venting experiments in the literature. Then, a velocity distribution equation for turbidity currents insusceptible to downstream disturbance is found to be applicable in the withdrawal layer, after relating the parameter controlling the velocity profile shape with the ratio of the outlet height to the layer thickness. Finally, the equation is derived for the relative concentration of outflow to the turbidity current concentration before the dam, whose solution is dependent on the proposed velocity distribution. Field measured data in the Xiaolangdi Reservoir and operation records of sediment release structures were collected and used to validate the model. A concept of nominal outlet width is proposed in order to apply the model in reservoirs with complex water releasing structures, which is calibrated along with the dimensionless parameter in the withdrawal layer thickness equation. The proposed model can help to optimize the design of sediment release structures and improve the venting operation.