A simple model of internal erosion in embankment dams

Embankment dams are water barriers constructed of earth and rock. They are the most common type of dams used to impound water for a variety of purposes such as for water supply, irrigation, navigation and power generation. The failure of an embankment dam will generally lead to catastrophic consequences such as the loss of life as well as economic losses. The two principal causes of failure in an embankment dam is due to prolonged overtopping at the crest or by uncontrolled internal erosion leading to a phenomenon known as 'piping'. This thesis is an attempt to model the second failure mechanism, i.e. internal erosion which if unchecked may lead to destruction. In particular, an attempt has been made to develop a numerical model based on a simplified representation of the physically based processes that underlies the phenomenon.An analysis of the most recent theoretical and experimental work on internal erosion reveals that what may happen in an embankment dam as the pressure gradient increases is still largely unpredictable. Based on a series of experimental studies, Bendahmane and his co-workers (2005) concluded that the erosion rate of fine particles in a porous matrix should be directly proportional to q(1-&phis)/&phis, where q is the filtration velocity and &phis is the porosity of the medium. In an independent series of experimental tests, Vardoulakis and co-workers (1996) found that the erosion rate should vary as q(1-&phis)C where C is the concentration of eroded particles that move with the water. According to the erosion rate found by Bendahmane et al. (2005) the porosity of the medium would be expected to remain spatially uniform during the whole process. This may be true only during the so-called suffusion process. From the erosion rate found by Vardoulakis et al. (1996) however, the porosity of the medium would be expected to increase in the downstream direction. This non-uniform erosion may occur in the so-called backward erosion process where a 'tunnel' could gradually make its way upstream, from the (downstream) exit point of the water into the interior of the dam. To unify these two situations, the key question is to find a model equation for the rate of erosion in terms of the most significant parameters of the problem. The strategy adopted in this work is to construct a model of internal erosion by considering the fluid-particle and particle-particle interactions as two simultaneous eroding mechanisms. Initially, the shear force effects of the interstitial flow on the erosion rate of the soil structure are considered. Subsequently, it is postulated that these suspended particles detached from the soil structure and transported by the flow may have the effect of successfully dislodging (by collision) additional particles bound to the exposed soil structure. By combining these two mechanisms of erosion, namely the fluid-particle interactions and the particle-particle interactions, it has been possible to construct a mathematical model that appears to describe both the suffusion as well as the backward erosion phenomena. In fact, the results obtained previously by Bendahmane and Vardoulakis may be recovered as two limiting cases of the present model. The results obtained with this model indicate that it may be used to simulate the evolution of internal erosion in a variety of situations, from the slow suffusion process to the strong backward erosion stage, leading to the piping failure. These results also provide guidance towards searching for a more general model to predict the erosion process in a greater class of problems. As the present model stands, it can in no way be considered a predictive tool but rather as an aid to understanding what is obviously a complex process.Internal erosion is a process by which soil particles from the interior of the dam are detached and carried downstream by the seepage (water) flow when the pressure gradient across the dam exceeds a certain critical value. The duration of the erosion process, from the inception of erosion to the complete breakdown of the dam may vary from a few hours to many years. Clearly, the problem is not trivial and to predict the likelihood of failure requires an understanding of the intrinsic processes together with their associated time scales. It may then be possible to make an assessment of the stability of the structure for purposes of dam safety analyses.