The effect of leakage on backward erosion piping: A modelling study in 2D and 3D

Abstract

In the Netherlands, dikes are the most commonly used structures to retain water and provide safety against flooding. In order to ensure the safety of these dikes against a number of different failure mechanisms such as backwards erosion piping, wave overtopping and macro stability, a detailed safety assessment has been created. The focus of this thesis is on the failure mechanism known as piping. Which consists of three different sub-mechanisms; uplift, heave and backwards erosion piping. The safety assessment against piping consists of a multi-step approach. First an elementary assessment is done, followed by a detailed assessment of the different sub-mechanisms and lastly a final analysis is done using more detailed data and software. Currently, Sellmeijer’s design rule is used in the detailed safety assessment to design against the sub-mechanism backwards erosion piping. His design rule is the starting point of this thesis. Before Sellmeijer was able to derive his design rules, he had to make a number of different assumptions and simplifications. The most significant being, simplifying the three-dimensionality of the piping process to a two-dimensional process, by neglecting the meandering nature of the pipe and excluding the effect of the lateral groundwater flow on the pipe progression. By limiting the problem to twodimensions Sellmeijer derived a mathematical model on which his design rule was based. In his design rule Sellmeijer relates the progression of a pipe to a hydraulic gradient. Over the years, Sellmeijer’s design rule has been adapted three different times. Each adaptation resulted in a more accurate design rule accounting for more and more parameters. However, with each adaptation, Sellmeijer’s design rule did not become more transparent. During the derivation of his design rule, Sellmeijer fails to account for the effect of a leaky layer on the critical hydraulic gradient for pipe progression. This limitation in his design rule is the focus of this thesis. In order to determine if leakage affects the critical hydraulic head for pipe rogression, a study is done using a two dimensional groundwater model in which his design rule is implemented. From these simulations it was observed that the presence of a leaky layer results in an increase in the critical hydraulic head. In the simulations studied, a maximum of 12 % increase is observed. Next an analysis is done on the results of these simulations. On the one hand an attempt is made to determine if and how leakage can be included in Sellemijer’s design rule. The simulations show that the effect of leakage on increasing the critical hydraulic gradient for pipe progression is largely dependent on the hydraulic conductivity of the cover layer. However, in order for a leakage term to be determined, and included in Sellmeijer’s design rule, additional simulations should be done. In MSeep it was also observed that leaky layers significantly impact the groundwater flow under the dike. The effect of this was quantified by looking at the effective depth. Which is defined as the portion of the aquifer which is responsible for groundwater flow towards the pipe and uplift channel. In order to further analyse the effect of leakage on groundwater flow, a number of quasi 3D and 3D scenarios were modelled in iMOD. For these simulations the effective depth, the effective width (in 3D) and the discharge in the well is determined. In this way, the effect of leakage can be quantified. In all three of the models similar trends are observed: a increase in the hydraulic conductivity of the cover layer resulted in the decrease of the effective depth. However, in the full 3D model the impact of leakage on the groundwater flow resulted in a larger range in the results. The results of this thesis, show that derivation of a leakage term would greatly benefit the output of the design rule. As a ’quick fix’ it is recommended to derive a leakage term which can be included in Sellmeijer’s design rule. However, further developments of a 3D model which correctly implements the effect of a pipe on the groundwater flow is also beneficial.