SOIL MECHANICS - CHAPTER 8 ppt

Chapter 8

GROUNDWATER FLOW

In the previous chapters the relation of the flow of groundwater and the fluid pressure, or the groundwater head, has been discussed, in the form

of Darcy’s law. In principle the flow can be determined if the distribution of the pressure or the head is known. In order to predict or calculate

this pressure distribution Darcy’s law in itself is insufficient. A second principle is needed, which is provided by the principle of conservation

of mass. This principle will be discussed in this chapter. Only the simplest cases will be considered, assuming isotropic properties of the soil,

and complete saturation with a single homogeneous fluid (fresh water). It is also assumed that the flow is steady, which means that the flow is

independent of time.

8.1 Flow in a vertical plane

Suppose that the flow is restricted to a vertical plane, with a cartesian coordinate system of axes x and z. The z-axis is supposed to be in

upward vertical direction, or, in other words, gravity is supposed to act in negative z-direction. The two relevant components of Darcy’s law

now are

qx = −k

∂h

∂x,

(8.1)

qz = −k

∂h

∂z .

Conservation of mass now requires that no water can be lost or gained from a small element, having dimensions dx and dz in the x, z-plane,

see Figure 8.1. In the x-direction water flows through a vertical area of magnitude dy dz, where dy is the thickness of the element perpendicular

to the plane of flow. The difference between the outflow from the element on the right end side and the inflow into the element on the left end

side is the discharge

∂qx

∂x dx dy dz.

In the z-direction water flows through a horizontal area of magnitude dx dy. The difference of the outflow through the upper surface and the

inflow through the lower surface is

∂qz

∂z dx dy dz.

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