## 97

NONSTEADY (TRANSIENT) FLOW

Nonsteady or transient flow in aquifers occurs when the pressure and head in the aquifer change gradually until steady-state conditions are reached. During the course of transient flow, water can be either stored in or released from the soil. Storage has two possibilities. First, water can simply fill the pore space in soil without changing the soil volume. This storage is called phreatic storage, and usually occurs in unconfined aquifers as the groundwater table moves up or down. In the other storage, water is stored in the pore space increased by deformation of the soil and involves a volume change. This storage is called elastic storage and occurs in all types of aquifers. However, in confined aquifers, it is the only form of storage.

Transient Confined Flow (Elastic Storage)

In a completely saturated confined aquifer, water can be stored or released if the change in aquifer pressure results in volumetric deformation of the soil. The problem is complex because the constitutive equations for soil are highly nonlinear even for dry soil, and coupling them with groundwater flow increases the complexity.

The basic equation for the phenomenon is the storage equation (Strack 1989), as

where o = volume strain, and 3 = compressibility of water. From soil mechanics

where mv = modulus of volume change. Equation 9.7(1) can then be written as

pP 3t

When the variation of K, H, and p with time are neglected, then

3t 3t

KH 3p pg 3

so that Equation 9.7(3) can be written as

3t Ss where Ss [(1/m)] is the coefficient of specific storage

If the compressibility of water 3 is ignored, then Ss = pgmv.

Some typical values of mv are given in Table 9.7.1. Equation 9.7(5) can also be written in terms of ^ as

where Se = coefficient of elastic storage = Ss • H.

Transient Unconfined Flow (Phreatic Storage)

The vertical movement of a phreatic surface results in water being stored in soil pores without causing the soil to m

TABLE 9.7.1 TYPICAL VALUES OF COMPRESSIBILITY (m)

Compressibility, (m2/N or Pa1)

TABLE 9.7.1 TYPICAL VALUES OF COMPRESSIBILITY (m)

Compressibility, (m2/N or Pa1)

Clay |
10-6-10-8 |

Sand |
10-7-10-9 |

Gravel |
10-8-10-10 |

Jointed rock |
10-8-10-10 |

Sound rock |
10-9-10-11 |

Water (ß) |
4.4 X 10-10 |

Source: R.A. Freeze and J.A. Cherry, 1979, Groundwater (Prentice-Hall, Inc.).

Source: R.A. Freeze and J.A. Cherry, 1979, Groundwater (Prentice-Hall, Inc.).

deform. Phreatic storage is, therefore, several orders of magnitude greater than elastic storage, which can be ignored.

The basic differential equation for the transient uncon-fined flow (Strack 1989), such as shown in Figure 9.7.1, can be given as

where Sp = coefficient of phreatic storage.

Equation 9.7(9) can be linearized in terms of the potential $ as or

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