Solving Saturated/Unsaturated Water Flow Problems - Unsaturated Soil Mechanics in Engineering Practice - page 375

CHAPTER 8

Solving Saturated/Unsaturated Water Flow Problems

8.1 INTRODUCTION the highest coefficient of permeability when it is saturated,

and it starts to reduce when soil suction exceeds the air-
entry value of the soil (i.e., the degree of saturation reduces
below 100%). There is an exception to this rule for the
condition where the soil cracks as a result of increased soil
suction. In this case, the cracks can produce a saturated
coefficient of permeability that is greater than the saturated
intact coefficient of permeability.
Most soils show a gradual decrease in the coefficient of
permeability as soil suction is increased once soil suction
exceeds the air-entry value. The log-log representation of the
water permeability function generally produces a straight-
line relationship once the air-entry soil suction is exceeded.
All soils appear to become essentially impervious to liq-
uid water flow once soil suction exceeds residual suction
conditions.

Direct experimental measurements of the water coefficient-
of-permeability function for an unsaturated soil are difficult
and time consuming. Attempts have been made to calcu-
late the coefficient of permeability through use of theoret-
ical considerations of the soil pore-size distribution. Some
of these procedures were mentioned earlier as part of the
theory of flow through an unsaturated soil. A limited num-
ber of proposed estimation procedures have experienced the
greatest success for application in geotechnical engineering
practice. These procedures are either directly or indirectly
related to the features of the SWCC, and are commonly
referred to as indirect methods for the estimation of the
water permeability function.
The estimation procedures have found increasing accep-
tance as it has become evident that (i) the cost of directly
measuring the permeability function is prohibitive on most
engineering projects and (ii) the estimation techniques are
providing adequate information for engineering design pur-
poses. The success of applying unsaturated soil mechanics
in engineering practice has been closely related to the use
of the SWCC for estimating the water coefficient of perme-
ability. There is a clear linkage between the commencement
of desaturation of a soil (i.e., the air-entry value) and the
decrease in its coefficient of permeability. The relationship
between the SWCC and the water coefficient of permeabil-
ity is illustrated in Fig. 8.1 for two soil types, namely, sand
and clayey silt.
The water storage characteristics of the soil are also
required when modeling transient seepage problems. The
slope of the SWCC on the arithmetic soil suction scale
gives the water storage modulus m 2 at designated soil
suctions.
The soil suction at the air-entry value of a soil can range
from a low value for sand (e.g., < 10 kPa) to a high value
for intact clay soils (e.g., > 1000 kPa). The wide range of
potential soil suction values can be more clearly observed on
a plot of the logarithm of soil suction versus the logarithm of
coefficient of permeability, as shown in Fig. 8.2. A soil has

8.2 ESTIMATION OF PERMEABILITY FUNCTION
The estimation technique for describing the water perme-
ability functions can be subdivided into four categories
of models: (i) empirical models, (ii) statistical models,
(iii) correlation models, and (iv) regression models. These
categories provide a practical classification for estimated
permeability functions.
“Empirical” models recognize that there is a relationship
between the character of the SWCC and the permeabil-
ity function and proceed to utilize this relationship in an
empirical manner. The Brooks and Corey (1964) estima-
tion technique determines a pore-size distribution index and
uses the computed index for the estimation of the water
permeability function.
“Statistical” models start with a physical model of the
assemblage of pore channels through which water can flow.
The most common physical model used is that of Childs
and Collis-George (1950). A number of permeability func-
tions have been derived based on the suggested physical
assemblage of flow channels suggested by Childs and Collis-
George. Most permeability functions derived in this manner