# Characterization and numerical verification of seepage scenarios in anisotropic soils under retaining structures and in unconfined aquifers due to pumping wells"

- Iván Alhama Manteca Director

Defence university: Universidad Politécnica de Cartagena

Fecha de defensa: 01 June 2021

- Teresa Maria Bodas Freitas Chair
- Juan Francisco Sánchez Pérez Secretary
- Matteo Icardi Committee member

Type: Thesis

## Abstract

Resumen de la tesis: The main objective of this thesis is the search and verification of the dimensionless groups that govern the geotechnical problems of flow through porous media under gravity dams with or without a sheet pile at its base and groundwater flow in unconfined aquifers due to a pumping well. The aim is to find the groups which the dimensionless unknowns of interest depend on. These unknowns (groundwater flow, pore pressure, average exit gradient, seepage surface, etc) change according to the chosen scenario. The methodology to obtain these groups is the discriminated nondimensionalization of the governing equation. The solutions are displayed in universal abaci that depict values of monomial and dimensionless variables. The curves have been represented after carrying out a large number of simulations. These models, also shown in the thesis, have been specifically designed according to the network method. Chapter I thoroughly explains the objectives of the thesis. Chapter II gathers the theoretical fundaments of the thesis. Firstly, references and different governing equations of flow through porous media are presented. It is basically focused on the scenarios studied along the thesis. The following section is a historical overview of electrical analogy, with different application examples. Afterwards, discriminated nondimensionalization is explained: different aspects, steps to apply the technique and examples in which it has been employed. In the following section, the bases of the network simulation method are presented, as well as examples of engineering problems in which this methodology has been successfully applied. The rest of the sections of the second chapter show the tools that have been used for the development of the compute programs employed for characterizing the problems researched in this thesis, Ngspice (software for compilation) and Matlab (programming language for creating the models in text files and graphically processing the solutions). Chapter III consists in a study of the dimensions of the soil parameters that are related to flow through porous media, that is permeability and hydraulic conductivity. The chapter starts revising the few references where the quantities involved in permeability are contemplated employing classical dimensional analysis, according to which quantities are measured in the same unit independently to the spatial direction in which they are measured. No satisfactory conclusion is reached, and the same happened when applying discriminated dimensional characterization, a methodology with which quantities are considered as distinct when measured in different directions or if they are of diverse nature. For this reason, the parameters are studied introducing quantities related to flow energy in the dimensional basis of the phenomenon, which does allow characterizing the units of hydraulic conductivity. Chapter IV presents the application of dimensional nondimensionalization to different scenarios of flow through porous media: flow under gravity dams without a sheet pile, flow under gravity dams with a sheet pile located at its base, flow under dams in infinite media and flow in unconfined aquifers due to a pumping well. For each of these scenarios, governing equations, monomials ruling the phenomenon and groups involving unknowns are presented and universal abaci obtained from numerous simulations are depicted. Moreover, for the last problem there is a table where it is demonstrated that, for the same dimensionless scenario (although the values of the dimensional variables are different) the dimensionless unknowns remind the same. Chapter V collects the models designed for the scenarios studied in this thesis: their boundary conditions, the cell structure, etc. The models, which are written as text files, include devices and routines that provide the unknown variables of interest for each of the scenarios as output information. Two codes have been developed: DamSim for flow under dams and WaWSim for flow due to a pumping well. Both simulation tools, in a Windows environment, are free, potent and reliable. Matlab codes have been employed for programming the model text files and the interfaces, and Ngspice for numerical simulation. Chapter VI shows an inverse problem in which radial and vertical conductivities in a free aquifer are calculated from values measured in field in a pumping well. The problem is studied from two points of view: employing the universal abaci and the designed code. In both cases, the errors between real and estimated values are calculated. After this, a study has been carried out in order to understand the effect of possible measure errors in the filed variables on the deviations of the estimated hydraulic conductivity values. Chapter VII presents a set of application: i) flow under gravity dams without a sheet pile; ii) flow under gravity dams with a sheet pile located at its base; and iii) flow in unconfined aquifers due to a pumping well. In addition, for each of the scenarios one of the variables have been compared with analytical or experimental results that can be found in references. http://repositorio.bib.upct.es/dspace/