# Experimental conceptualisation of the Flow Net system construction inside the body of homogeneous...

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- 1. Experimental Conceptualisation of the Flow Net System Construction inside the Body of Homogeneous Earth Embankment Dams Dr. Costas I. Sachpazis Civil & Geotechnical Engineer (BEng (Hons) Civil Eng. UK, Dipl. Geol, M.Sc.Eng UK, Ph.D. NTUA (...), Post-Doc. UK, Gr.m.ICE). Associate Professor, Lab of Soil Mechanics, Department of Environmental Engineering, Geotechnical Engineering Division, Technological Educational Institute of Western Macedonia. Killa 50100, Kozani, Greece. Ph: (+30) 210-5238127; Fax: (+30) 210-5711461. e-mail the author: costas@sachpazis.info ABSTRACT By means of a drainage and seepage tank, an experimental flow net system inside the body of a homogeneous earth embankment dam model, formed from Leighton Buzzard Silica sand, was developed and studied in this experimental research paper. Water flow through dams is one of the basic problems for geotechnical engineers. Seepage analysis in an important factor to be considered in the proper design of many civil engineering structures. Seepage can occur in both through the structure itself as the case of earth dams and under foundations of an engineering structure. Successful seepage analysis is achieved on the proper and accurate construction of a flow net. Amongst the various existing methods of seepage analysis, the Finite Element Method and the method of Experimental Flow Nets are the most widely used ones. Construction of a flow net is mainly used for solving water flow problems through porous media where the geometry makes sometimes analytical solutions impractical. This method is usually used in soil mechanics, geotechnical or civil engineering as an initial check for problems of water flow under hydraulic structures like embankments or dams. As such, a grid obtained by drawing a series of equipotential lines and stream or flow lines is called a flow net. In this procedure the Laplace equation principles must be satisfied. Hence, the construction of a flow net is an important tool in analysing two-dimensional irrotational flow problems and provides an approximate solution to the flow problem by following simple rules, as initially set out by Forchheimer, 1900, and later refined by Casagrande,1937. It can also be very useful tool even for problems with complex geometries, as proven in this experimental research paper. The objectives of this experimental research paper are: To determine the position and shape of the flow line representing the uppermost free water surface inside the body of a dam by using a drainage and seepage tank, To conceptualise the flow lines system and to demonstrate that each flow line starts perpendicular to the upstream slope of the dam and that that slope is a boundary equipotential line, To construct an experimental flow net and subsequently to verify and analyse it by the FEA method, To calculate the rate of seepage through the dam body, and To summarise the calculations and experimental findings in a concise and readable format. In order to achieve these objectives, an experimental flow net system inside the body of a homogeneous earth embankment dam model was formulated by using a drainage and seepage tank. From the constructed flow net in the present experimental research paper, an attempt has been made to analyze, determine and present the following parameters: - 2113 -

2. Vol. 19 [2014], Bund. J 2114 The pressure drop from one side of the embankment to the other, The seepage flow rate in each flow channel, The total seepage flow rate, and The pore pressure ratio, ru, for the embankment. KEYWORDS: Earth Embankment Dams; Flow Net; Flow Lines; Equipotential Lines; Seepage Flow Rate; Pore Pressure Ratio; Experiment Model; Pressure Drop; Experimental Conceptualisation; Permeability; Bilinear Shape Functions; Seepage analysis; Finite Element; Steady-State; Unconfined flow; Free surface; Saturated Soil; Unsaturated Soil; Hydraulic Structures; Phreatic Surface; Drainage and Seepage Tank. INTRODUCTION Dams are constructed to impound water for irrigation, water supply, energy generation, flood control, recreation as well as pollution control. Moreover, disastrous effects of water are significant on them. It has been implicated that seepage plays a major role on dam failures due to its potential to cause endogenous rather than exogenous eruption of soil mass (Cedergen, 1989), as well as slope instability and failure (Sachpazis, 2013); hence embankment dams and especially earthfill dams require seepage control (Fell, 1992; Fredlund et al, 1994). Many researches indicated that failure of embankment dams due to seepage alone stands for about 25% of the total failure cases, apart from overtopping, piping, internal erosion, etc (Singh, 1995). Free-surface, i.e. unconfined seepage problems are commonly encountered in geotechnical engineering. In these problems, the determination of the free surface and the calculation of seepage usually requires sophisticated numerical techniques, unfamiliar to most engineers. Different methods have been identified to study the extent of seepage in earth dams. Due to its relative simplicity, flow net is the most commonly used amongst these methods. For simple embankment dams such as a homogeneous earthfill dam with simple configurations, the configuration of a flow net is relatively straightforward in the determination of seepage quantity. However, especially for zoned earthfill dams or embankment dams with different coefficients of permeability for each zone, the complexity of seepage behaviour increases dramatically. Therefore, seepage modelling using a drainage and seepage tank as well as a finite element analysis technique can help to solve the problem promptly, thus saving funds and time, but immolating a marginal reduction of accuracy. Several authors such as Papagianakis, 1984, Lam et al, 1988, Potts et al, 1999, Rushton et al, 1979, Vandammea et al, 2013, had performed seepage analysis using either finite element or drainage and seepage tank apparatus method. Historically, Stelzer et al, 1987, presented an introductory scheme for plotting contours that are traced along paths of constant function values. Desai et al, 1988, presented a detailed theoretical development of Residual Flow Procedure (R.F.P.) for three dimensional seepage, and a scheme for locating of the three dimensional free surface. Fan et al, 1992, presented a simple and unique method for generating flow nets based on nodal potentials and bilinear shape functions. The method reduces the work of performing a second FEM to compute the stream potentials at the nodes. Mathematically, the process of making out a flownet consists of contouring the two harmonic or analytic functions of potential and flow line function. These functions both satisfy the Laplace equation and the contour lines represent lines of constant head, i.e. equipotentials, and lines tangent to flowpaths, i.e. streamlines. Together, the potential function and the stream function form the complex potential, where the potential is the real part, and the stream function is the imaginary part. 3. Vol. 19 [2014], Bund. J 2115 n this experimental study, a model of the body of a homogeneous earth embankment dam was formed by means of a drainage and seepage tank and by using Leighton Buzzard Silica sand. In this set up a flow net system was developed and the flow and seepage characteristics were studied, as outlined below. THE EXPERIMENT MODEL SET UP An experimental earth dam model of trapezoidal cross-section was formed from Leighton Buzzard Silica sand in the Drainage and Seepage Tank. The general Drainage and Seepage Tank setup configuration showing the Steady State Seepage conditions through an earth dam model is presented in Figure 1. The particular experiment set up of the earth dam model is presented in Figure 2. The Flowlines through this earth dam model are also shown in this figure. The base of the dam model was exactly 153.2 mm above the bottom of the tank. The width of the base of the dam model was exactly: 1250 mm. The upstream slope was steeper than the downstream one and its toe was approximately at the overflow outlet. The illustration of the exact dimensions and upstream and downstream slope inclinations of the experiment set up of the earth dam model is shown in Figure 3. The dam model cross section was constructed with an upstream slope inclination of exactly 1 : 1.70 (Height : Length) and a downstream slope inclination of exactly 1 : 3.37 (Height : Length). The height of the dam model was exactly 240 mm, and the crest width was exactly 80 mm. The upstream water level was stabilised exactly 30 mm below the dam crest, and the downstream level was stabilised exactly 17.5 mm above the bottom. The height of the upstream water level was exactly 210 mm above the bottom of the dam model, and hence the water head level difference between the upstream and the downstream water level was exactly 192.5 mm (see fig. 3). When the dam model was constructed, water was first poured into the downstream pool and only after it was full the upstream pool was filled up. The rate of filling was slow enough in order not to cause any dam model collapse due to increased internal seepage forces. Two drainage pipes, one upstream and the other downstream, were introduced to keep both water levels controlled in specific head heights as shown in figure 1, and by this way a Steady State Seepage condition through the earth dam model experiment was achieved. When the upstream water level was stabilised, potassium permanganate grains were placed just below the surface of the upstream slope close to the glass side of the tank. The first grain was placed at the junction with the water surface and flowlines were forming over a period of appropriate and relevant to soil permeability time. 4. Vol. 19 [2014], Bund. J 2116 Figure 1: The Drainage and Seepage Tank setup configuration showing the Steady State Seepage conditions through the eart