A Study on Seepage Through Earthen Dams By Using Analytical Methods 1 D.Ashok Kumar, 2 A. Mohan

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1 A Study on Seepage Through Earthen Dams By Using Analytical Methods 1 D.Ashok Kumar, 2 A. Mohan 1 Assistant Professor, Department of Civil Engineering, Vignan s,institute of Technology & Aeronautical Engineering, Pochampalli , Telangana, India 2 Professor & Director, KSRM College of Engineering, Kadapa , AndhraPradesh, India ABSTRACT The flow or seepage of water through soil medium is one of the important problems of geotechnical engineering. In recent years various theories are proposed for unconfined seepage analysis through soil medium. They include both analytical and graphical methods. Recently numerical modelling techniques are developed for seepage analysis. Among all the methods analytical method can handle difficult problems involved in the soil properties. In the present work, a comparative study on seepage analysis methods is undertaken. For the study: two analytical methods viz. Casagrande s and Dupuit s, are considered for estimating seepage rate through homogenous bund sections for the laboratory scale models. For these tests two types of bund sections and three types of soils are used for the study. The soil samples are selected such that a wide range of hydraulic conductivity is covered. The results are compared between analytical methods for the laboratory scale models and the values are found to be in good agreement with each method. KEYWORDS: Earthen dam model; Flow net; Permeability; Study state flow; Seepage flow rate; Analytical methods. 1. INTRODUCTION The flow or seepage of water through soil medium is one of the important problems of Foundation engineering. Seepage through soil can be either confined or unconfined. Unconfined seepage is more involved than confined seepage because the phreatic surface is unknown in unconfined seepage. Many hydraulic and other civil engineering structures involve both confined and unconfined seepage flow analysis. Accurate analysis for seepage is a major concern for geotechnical engineers. A dam is a barrier constructed across a river to store water in a reservoir for later use. Water flow through and below an earthen dam and below gravity dam plays an important role in determining the stability of such dams. Seepage analysis is required for estimating water losses and pore-water pressure. Pore-water pressures influence the shear strength and volume change characteristics of soil and hence influence the stability of sloping soil stratum. 1.1 METHODS FOR SEEPAGE ANALYSIS: Exact analysis of the flow of water through soil either analytically or numerically can be very complex. Steady state flow analysis is relatively simple compared to transient flow analysis. Transient flow analysis is best performed by iterative numerical

2 methods. The differential equation governing 2Dsteady seepage flows through the soil porous medium has given by the Laplace equation: where k x and k y are permeability in x and y direction and h is the total available head under which steady seepage occurs. If the medium is isotropic and homogeneous, then k x = k y = k and the equation is reduced to: To find quantity on seepage through the earth dam, it is very essential to locating the top flow line of seepage.the upper most boundary is a free water surface and will be referred as the seepage line or top flow line, which separates saturated and unsaturated zones with the body of the dam. The main problem is loss of seepage through an earthen dam primarily involves prediction of position of the seepage line in the cross-section. From the experimental studies on earthen dam models that the line of seepage assumes as a basic parabola and also, assuming that hydraulic gradient i is equal to the slope of the free surface and constant with depth (Dupuit s theory), the resulting solution of the top flow line is parabola.in some sections a little divergence from a regular parabola is required particularly at that top surface of entry and discharge of the line of seepage. Fig.1. Phreatic line for an earth dam without toe filter Every point on the parabola is equidistant from focus and directrix.therefore FA=AB. Also, FG = GE = p = S/2. Focus = (0, 0). Any point, A on the parabola is given by A = A(x,z). Using AF 2 = AB 2, we get or 2.1 CASAGRANDE S SEEPAGE ANALYSIS In homogeneous earth dam with no drainage filter, the phreatic line ends at some point on the downstream face of the dam; focus on the parabola in this case happens to be the downstream toe of the dam as shown in Fig.1 The analysis was conducted based on the procedure, and quantity of seepage flow through was computed from the following equations: where, k is the coefficient of permeability of the soil 2.2 DUPUIT S SEEPAGE ANALYSIS The figure shows the section of an earth dam in which the phreatic surface, i.e., the uppermost line of seepage. The quantity of seepage through a unit length at perpendicular angles to the cross section is given by Darcy s law as q = kia. In dupuit s method assumes that the hydraulic gradient is equal to the slop of the free surface and is constant with depth i.e., i = dz/dx. The equation represents a parabolic free surface.

3 Fig.2.Dupuit's solution for seepage through earth dam 3 EXPERIMENTAL SET UP It consists of an enclosing tank made of 12 mm thick sheet glass. The size of tank is cm. The tank is provided with an inlet, outlet and six Piezometer tapings are protected with filter paper to avoid clogging. A glass wall of six centimeter height is provided at the tank floor to simulate impervious ground or foundation. Fig.5. Fully developed phreatic line in Bund BH Table.1. Geometry and material properties of Bund BH Bund height 12.0 cm Bund base width 54.0 cm Bund top width 6.0 cm Height of water Free board Bund upstream slope Bund downstream slope 10.0 cm 2.0 cm 2H:1V 2H:1V Fig.3.Enclosure tank with inlet, outlet and piezometers 3.1TEST BUND SECTION BH This section is designated as BH for Bund with High permeability material. The purpose of this section is to observe the development of phreatic line and its shape under steady state flow condition. The bund material is Ennore sand of grades II and III mixed in the proportion of 30:70. Fig.4.Geometry of Bund section BH C/s area of bund section 300 cm 2 Permeability of bund cm/sec material The section is compacted by tamping. The geometry of bund is given in Table III.1. The upstream face is projected against collapse by providing rip-rap with 20 mm pebbles. The model is tested for seepage by admitting water on upstream side and maintaining constant height of water at 10 cm. The discharge is collected at the downstream side into a measuring jar. Testing is continued until steady state flow is established when equal volumes of water are collected in equal intervals of time. After attaining steady flow, dye is introduced into the flow to observe phreatic line development. 3.2 TEST BUND SECTION BM The soil used for this bund has medium hydraulic conductivity (among the three samples selected for model testing). Hence, this is designated as Bund BM. The bund section for this is a 1:100 scale model of Thimmapur Reservoir earth dam section. The bund section has stepped side slopes. The intermediate berm width is 5 cm. The side slopes

4 are 2H: 1V for both upstream and downstream slopes. Table.2. Geometry of Bund sections BM and BL Bund height Bund base width 12.0 cm 64.0 cm Bund top width 6.0 cm Fig.6.Geometry of Bund Section BM and BL Locally available soil is selected for Bund BM. Soil samples are tested in laboratory for physical and engineering properties. The IS classification of the soil sample is SC and its permeability is The properties of soil are in given in Table.3. The properties are determined as per the relevant IS code procedures. The bund is made-up by compacting the soil to maximum dry density at optimum moisture content. Dried soil sample is mixed with water and seasoned for 24 hours before preparing the bund. A core is taken from bund and tested for density. It is observed that the compacted density is 98% of the laboratory MDD. The model is tested for seepage by admitting water on upstream side and maintaining constant height of water at 10 cm. It took nine days for the bund to get saturated and discharge on the downstream. 3.3 TEST BUND SECTION BL Bund section BL is same as that of Bund BM. However, the soil sample used for the bund has the lowest (among the three samples studied) hydraulic conductivity. The soil sample is collected from Chennuru village of Kadapa. Intermediate berm width 5.0 cm Height up to intermediate berm 5.0 cm Height of water 10.0 cm Free board 2.0 cm Bund upstream slope 2H:1V Bund downstream slope 2H:1V C/s area of bund section 410 cm 2 Table.3. Properties of the soil for Bund BM IS classification SM D D D Uniformity coefficient C u 11.7 Curvature coefficient C c 0.78 Liquid limit 25% Plastic limit Non-plastic Plasticity index Non-plastic MDD g/cc OMC 11%

5 Permeability cm/s 1) Sample seasoning 2) First layer compacted 3) Second layer compacted The bund is made-up by compacting the soil to maximum dry density at optimum moisture content. Dried soil sample is mixed with water and seasoned for 24 hours before preparing the bund. A core is taken from bund and tested for density. It is observed that the compacted density is 96% of the laboratory MDD. The model is tested for seepage by admitting water on upstream side and maintaining constant height of water at 10 cm. It took seventeen days for the bund to get saturated and discharge on the downstream. The discharge is collected at the downstream side into a measuring jar. Testing is continued until steady state flow is established when equal volumes of water are collected in equal intervals of time. Phreatic line could not be ascertained as the capillary effect saturated total body of the bund. 4) Final bund section Table.4. Properties of soil for Bund BL IS classification SC D D D Uniformity coefficient C u 5.38 Curvature coefficient C c 1.13 Liquid limit 36% Plastic limit 14% Plasticity index 22% MDD g/cc OMC 16% Permeability cm/s 4. RESULTS 4.1 RESULTS FOR BUND BH Casagrande s method Dupuit s method per cm length of bund Fig.7.Stages in fabrication of Bund BL

6 4.2 RESULTS FOR BUND BM Casagrande s method per cm length of bund Dupuit s method classification Permeability, cm/s q by Casagrande s method, cm 3 /s/cm q by Dupuit s method, cm 3 /s/cm Model studies are useful tools for hydraulic simulation 4.3 RESULTS FOR BUND BL Casagrande s method 2. All method of analysis give comparable results 3.The analytical methods considered here cannot be applied to transient analysis. REFERENCES 1.Casagrande, A. (1940). Seepage through dams, in Contributions to Soil Mechanics , Boston Society of Civil Engineers, Boston, MA, pp BM Das, 2008, Advanced Soil Mechanics, per cm length of bund Dupuit s method 5.CONCLUSIONS An experimental earth dam model of trapezoidal cross-section was set up and tested with three different types of soils obtained from i) Ennore sand, ii) locally available soil in the College and iii) Chennuru village. The bund models are fabricated in glass chamber with a facility to drain water on the downstream side. Summary of Test Results: Bund Designation BH BM BL Taylor and Francis, UK, 3rd Edition 3.Terzaghi, K., and Peck, R. B., Soil Mechanics Engineering Practice, John Wily and Sons, U.S.A, Harr, M. E. _1962_. Ground water and seepage, McGraw-Hill, New York. 5.Anand V, 2012, Seepage through Earthen Dams: Estimation of Filter Dimensions, Summer Training Report, Department of Civil Engineering, Indian Institute of Technology, Guwahati, India. 6.Casagrande, A. (1937). Seepage through earthern dams. J. New England Water Works Association, reprinted in Contribution to soil mechanics , Boston Society of Civil Engineers, Boston, Sharma,H.D (1991).Embankment dams, Oxford & IBH, New Delhi. Soil S SM SC

7 8. Lot, R. C. Y. Steady seepage with free surface. Ph.D. Thesis,Harvard University, Cambridge, MA, Casagrande, A. (1937). Seepage through earthern dams. J. New England Water Works Association, reprinted in Contribution to soil mechanics , Boston Society of Civil Engineers, Boston, Cedegren, H.R., (1989). "Seepage, Drainage, and Flow Nets." John Wiley & Sons, U.S.A.