Date of Award

12-14-2015

Document Type

Open Access Dissertation

Department

Civil and Environmental Engineering

First Advisor

M. Hanif Chaudhry

Abstract

Both numerical and experimental investigations are conducted to study the failure of earthen dams and levees. Boussinesq equations describing one-dimensional unsteady flow including non-hydrostatic pressure distribution are solved numerically along with Exner equation for the sediment mass conservation to include the effects of the streamline curvature on the failure of non-cohesive earthen embankments. In addition, the effects of the steep bottom slope on the flow variables during the failure are studied by solving the Saint- Venant equations modified for steep bed slope along with the Exner equation to simulate non-cohesive earthen embankment failure due to overtopping. The Boussinesq equations are solved by using the two-four finite-difference scheme which is second order accurate in time and fourth order accurate in space, while the modified Saint-Venant equations are solved by using the MacCormack finite-difference scheme which is second order accurate in time and space. The performance of three sediment transport formulae, namely Ashida and Michiue, Meyer-Peter and Müller, and Modified Meyer-Peter and Müller for steep slope is compared. The comparison of the numerical results with the experimental results shows that: (1) The improvement in the prediction of the breach evolution and the downstream hydrograph by including the Boussinesq terms is minimal; (2) The predicted results by using the modified Saint-Venant equations are slightly better than those calculated by using the classical Saint-Venant equations; (3) Ashida and Michiue transport equation overestimates the erosion rate which results in an overestimation of peak discharge but predicts the time to peak fairly well; (4) Meyer-Peter and Müller and Modified Meyer-Peter and Müller equations give almost the same results for the top elevation of the eroded dam and the water surface levels, and the peak value and time to peak of the downstream hydrograph. A number of non-dimensional equations are presented to relate different model variables to the peak discharge of the downstream hydrograph. A sensitivity analysis of different model parameters to determine the most dominant factor affecting the peak downstream discharge indicates that the most dominant factor affecting the peak discharge is the upstream reservoir volume, while the sediment grain size shows very little effect on the peak discharge. The lateral outflow through a levee breach may be computed as an outflow over a broad-crested side weir. The lateral outflow has been computed previously by assuming the flow in the main channel to be one-dimensional, and most of the equations for computing the outflow are based on the local flow variables near the breach. These are unknown and difficult to measure during a flood. In this study, a numerical model is developed to solve the two-dimensional, shallow water equations using MacCormack finite-difference scheme. The model is applied to a breach in a rectangular channel. A comparison of the numerical results with the experimental measurements shows satisfactory agreement. Different cases are simulated by varying the breach width, the bottom level of the breach, and the discharge in the main channel. Comparison between the breach outflows obtained using the numerical model with the results of a simple one-dimensional approach indicates that the breach outflows are overestimated by the latter. A new discharge correction factor is introduced for the lateral breach outflow predicted using the simple one-dimensional approach. The correction factor is a function of the submergence ratio of the breach, breach width, and inlet Froude number. An accurate prediction of the evolution of the breach resulting from overtopping of a non-cohesive earthen levee is important for flood mitigation studies. Laboratory experiments are conducted with various inlet discharges, and downstream water depths. The breach shape is recorded using a sliding rods technique. A sequence of discrete mass failure of the sides of the breach due to slope instability is observed during the failure process. A simple geostatic failure mechanism is suggested to calculate the lateral sediment load due to the mass failure. This mechanism is implemented in a two-dimensional numerical model which solves the shallow water equations along with the sediment mass conservation. In order to assess the effect of the lateral sediment load resulting from slope instability on the failure process, the predicted breach shape evolution and breach hydrograph with and without the slope failure mechanism are compared with the experimental results. The predicted breach shape is improved by adding the lateral sediment inflow due to slope instability especially in terms of the maximum depth of erosion. Also, the peak discharge of the breach hydrograph is captured more accurately by adding the slope failure mechanism.

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