# Finite Difference Solution to Dam seepage Problems Report

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Updated: Mar 31st, 2022

## Introduction

There are seepage problems which are found in the application of the civil engineering. The nonlinear numbering systems can be useful in finding the free-surface which provides a hindrance to the flow boundaries. This can incorporate the finite difference method that has an adaptive mesh. The Extended Pressure method is among the very efficient systems. This has been used in many free-surface seepage problems and also the numerical solution has been used. In engineering, the numerical solutions are not commonly used. The reason being, they need complicated ways of deriving and implementing them. Currently there is another approach to finite difference where spreadsheets are used in the calculation of the seepage which is not confined (Bardet 1997).

## Measures of seepage control

Seepage water can cause a lot of damage unless it is controlled. The major reason of using a dam foundation to control seepage water is to avoid the materials of the foundation being washed away causing the destruction of the soil structure. Seepage is also controlled to avoid uplift pressures of the foundation. There are some benefits to the stilling basin slab when the filters are put under a dam to cut off the extra uplift pressure (Friedmann 1982).

In foundation seepage, there are the problems of rock, soil and the pile foundations. This causes the damage of the foundation material. To avoid this, seepage control is done by site-specific method of the cut-off. Can be slurry cut-offs or the impervious cut-offs (Cryer 1970).

In abutment seepage, to avoid the bypass of the dam by the stream and to avoid the falling of the bank, the abutments should be made into a strong bank tie-in structure or the cut-offs and the slopes of the bank should be very well taken care of through adequate protection.

Seepage analysis is very important. This is essential in finding out the effect of seepage. The rock of the concrete gravity dams foundation should be drained this is essential for the defective and the formation of sound. A good program for grouting will control seepage and also expose the weaknesses in the foundation which are not identified hence improving the defects which are present. Such a good program will provide safety measures (Westbrook 1985).

The most used design of grout is where one line of grout holes is placed on the upstream dam’s side. Another line of holes which is parallel to the upstream one is placed downstream. A series of holes will be then drilled on the gallery if it is provided. Control grouting pressure in order to prevent the rock lifting and splitting of the rock. When there is a presence of the stilling basin on the rock, make some drain holes with some system for discharge at the foundation edge for pressure relief. The cut-offs will avoid the piping which occurs on the material of the foundation caused by the pressure of the seepage. Make sure an underneath drainage system is established to aid in the relief of the pressure (Varga 1963).

The trenches are made from the ground level of the soil dam to the top level of the layer which is pervious and lower to the impervious layers of the soil which is also known as the bedrock. There is a shallow cut-off in the concrete cut-off walls. These are made where the trenches are not deep and they can be dug and then filled again with concrete. This method is applicable when the piers of the navigation dam have a good spacing and which are wide. In such, the dam pier doesn’t need a transverse width which is very wide (Lacy and Prevost 1987).

The slurry trench method can be used to obtain the intermediate depth cut-offs. A specific tool is applied in the digging of the trench. Slurry is then provided to give support to the sides of the dug–out. When a required depth is obtained, the material which is impervious is put in to give a good cut-off. The slurry should be in combination with some concrete (Cryer 1970).

The concrete cut-offs with greater depths are called deep cut-offs. Special equipment is used to dig it out and slurry is used to offer support to the walls.

The piling cut-off walls for the steel sheet which are continuous are made use of in soil and pile supported dam structures made of concrete (Darcy 1856).

The impervious layer in the upstream has advantages for the soil and pile dams, this because it makes longer the paths for the seepage. This action makes the uplift pressure to be low (Schwartz and Zhang 2008).

## Conclusion

In conclusion we can say that, there are many solutions to the seepage problems. The choice of the solution to use will depend on the type of the soil, seepage and the equipment to be used.

## References

Alt, H.W., 1980. Numerical Solution of Steady-state Porous Flow Free Boundary Problems. Numer. Math., 36(3), pp.73-98.

Bardet, J.P., 1997. Experimental Soil Mechanics. Upper Saddle River, NJ: Prentice- Hall.

Cryer, C.W., 1970. On the approximate Solution of Free Boundary Problems using Finite Differences. Journal of the ACM, 17(3), pp.397-411.

Darcy, H., 1856. Les Fontaines Publiques de la Ville de Dijon. Paris: Dalmont.

Friedmann, J.A., 1982. Variational Principles and Free-Boundary Problems. New York: Wiley.

Lacy, S.J and Prevost, J.H., 1987. Flow through Porous Media: A procedure for locating the free surface. Int. J. Num. Anal. Meth. Geomechanics, 11(1), pp. 585–601.

Schwartz, F. and Zhang, H., 2008. Fundamentals of Ground Water. New York: Wiley.

Varga, R.S., 1963. Matrix Iterative Analysis. New Jersey: Prentice Hall.

Westbrook, D.R., 1985. Analysis of inequalities and residual flow procedures. New York: Kindle.

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