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Module 1: Fundamentals of Reservoir and Farm Ponds

Module 2: Basic Design Aspect of Reservoir and Far...

Module 3: Seepage and Stability Analysis of Reserv...

Module 4: Construction of Reservoir and Farm Ponds

Module 5: Economic Analysis of Farm Pond and Reser...

Module 6: Miscellaneous Aspects on Reservoir and F...

5 April - 11 April

12 April - 18 April

19 April - 25 April

26 April - 2 May

## Lesson 15 Seepage Analysis I

**15.1 Introduction**

Many soils are formed in horizontal layers as a result of sedimentation through water. Because of seasonal variations such deposits tend to be horizontally layered and this results in different permeability’s in the horizontal and vertical directions.

**15.2 Permeability of Layered Deposits**

Consider the horizontally layered deposit (Fig. 15.1), which consists of pairs of layers the first of which has a permeability of *k _{1}* and a thickness of

*d*

_{1}overlaying a second which has permeability

*k*and thickness

_{2}*d*.

_{2}

**Fig. 15.1. Layered soil. (Source: ****https://www.u-cursos.cl/ingenieria/2008/1/CI44A/2/material_docente/objeto/175689****.)**

First consider horizontal flow in the system and suppose that a head difference of ∆h exists between the left and right hand sides (Fig. 15.2).

It then follows from Darcy’s law that,

It, therefore, follows:

**Fig. 15.2. Horizontal flow through layered soil.**

**(Source: ****https://www.u-cursos.cl/ingenieria/2008/1/CI44A/2/material_docente/objeto/175689****.)**

Next consider vertical flow through the system, shown in fig.15.3. Suppose that the superficial velocity in each of the layers is *v* and that the head loss in layer 1 is *∆h _{1}*, while the head loss in layer 2 is

*∆h*.

_{2}In layer 1:

Similarly in layer 2,

**Fig. 15.3. Vertical flow through layered soil.**

**(Source: ****https://www.u-cursos.cl/ingenieria/2008/1/CI44A/2/material_docente/objeto/175689****.)**

The total head loss across the system will be *∆h=∆h _{1}+∆h_{2}* and the hydraulic gradient will be given by,

For vertical flow Darcy's law gives,

Total head loss is, ∆h =, we can write,

**15.3 Flow Nets for Soil with Anisotropic Permeability **

Flow in a plane in an anisotropic material having a horizontal permeability *k _{H}* and a vertical permeability,

*k*is governed by the equation:

_{v }The solution of this equation can be reduced to that of flow in an isotropic material by the following simple device. Introduce new variables defined as follows:

Dividing the equation by, the seepage equation then becomes

Thus by choosing:

It is found that the equation governing flow in an anisotropic soil reduces to that for an isotropic soil, viz.:

and so the flow in anisotropic soil can be analyzed using the same methods (including sketching flow nets) that are used for analyzing isotropic soils.

**15.4 Seepage in Anisotropic Soil: Example**

Suppose we wish to calculate the flow under the dam as shown in Fig. 15.4:

**Fig. 15.4. Dam on a permeable soil layer above impermeable rock (natural scale).**

**(Source: ****https://www.u-cursos.cl/ingenieria/2008/1/CI44A/2/material_docente/objeto/175689****.)**

For the soil shown in Fig.15.4 it is found that *k _{H}*= 4

*k*

_{V}. Therefore,

Transformed co-ordinates of a dam on a permeable layer over an impermeable rock and its flow net are shown in Fig.15.5and Fig.15.6, respectively. A rigorous proof of this result will not be given here, but it can be demonstrated to work for purely horizontal flow as:

**Fig. 15.5. Dam on a permeable layer over impermeable rock (Transformed scale).**

**(Source: ****https://www.u-cursos.cl/ingenieria/2008/1/CI44A/2/material_docente/objeto/175689****.)**

**Fig. 15.6. Flow net for transformed geometry.**

**(Source: ****https://www.u-cursos.cl/ingenieria/2008/1/CI44A/2/material_docente/objeto/175689****.)**

Figure 15.7 shows horizontal flow through anisotropic soil in natural and transformed scale.

**Fig. 15.7. Horizontal flow through anisotropic soil.**

**(Source: ****https://www.u-cursos.cl/ingenieria/2008/1/CI44A/2/material_docente/objeto/175689****.)**

**Key words**: Anisotropic soil, Flow net, Seepage

**References**

Suresh, R. (2002). Soil and Water Conservation Engineering. Fourth Edition. Standard Publishers.

https://www.ucursos.cl/ingenieria/2008/1/CI44A/2/material_docente/objeto/175689.)

**Suggested Readings**