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Geotechnical News • March 2013
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end loader, backhoe, bottom dump
bucket, conveyor system or ready
mix truck. Soil or granular in-
fill material should be about 2 cm
above the top of the cells and com-
pacted to the required density
5. Finishing details
• Seeding with suitable essences al-
lows fast vegetation. Seeded areas
may be protected with synthetic or
natural fiber blankets (jute).
Dimensional analysis
Dimensional analysis is a method to
describe a phenomenon by develop-
ing a dimensionally correct equation
among certain variables. There are
two objectives of dimensional analy-
sis:
1. To reduce the number of variables
for subsequent analysis, and
2. To provide dimensionless param-
eters that numerical values are in-
dependent of any system of unit.
Dimensional analysis provides a
similarity law for the phenomenon
under consideration. Similarity means
certain equivalence between two
physical phenomena that are actu-
ally different. By using dimensional
analysis, a model can be related to
a prototype. Sets of independent
parameters are chosen to build up the
complete characteristics of the actual
event. Then dimensional analysis
will reduce the quantity of variables
and produce dimensionless param-
eters. Experiments or tests need to be
carried out to verify these parameters.
Dimensionless values often used for
interpreting the prototype value from
small model tests. Similarity between
model and prototype is attained when
the dimensionless parameters have the
same value in both model and proto-
type.
Buckingham’s Pi theorem
Buckingham Pi Theorem is the basis
of most dimensional analysis, asserts
that any complete physical relation-
ship can be expressed in term of a set
of independent dimensionless products
composed of the relevant physical
parameters. Bridgman has stated that,
“If the equation F(q1, q2, q3 … qn)
= 0 is complete, the solution has the
form f(π1, π2, π3 …πn-k) = 0, where
the π terms are independent products
of the parameters q1, q2, etc., and
are dimensionless in the fundamen-
tal dimensions.” In other word, a
complete dimensional homogeneous
equation, relating n physical quanti-
ties which are expressible in term
of k fundamental quantities can be
reduced to a functional relationship
between n-k dimensionless products.
For example, if there are nine physical
quantities involved in the relationship
of the physical problem and three fun-
damental physical quantities, six set of
dimensionless groups would be form.
Laboratory simulation of rainfall
and erosion
Experiments for erosion can be
classified as field experiments and
laboratory experiments. Field experi-
ments principally involve long-term
measurement of soil loss in small
fractional-acre plots under natural
conditions. Such field tests are often
expensive and time consuming, but are
useful in gaining data on actual soil
loss under various land management
practices. However, they are not use-
ful in studying the physics of the soil
erosion process. Laboratory experi-
ments are carried out under the control
over meteorological conditions where
rainfall intensity, soil type, slope and
other conditions can be controlled and
varied in a logically designed experi-
ment. Laboratory tests measure the
rate of soil loss under conditions that
simulate natural conditions and pro-
cess. The factors that can be varied in
the laboratory test are:
a. The
amount,
intensity,
and
frequency of rainfall
b. Soil properties such as mean par-
ticle size, size distribution, surface
texture, clay and organic content,
bulk density, and moisture content
c. Slope and length of the flow path
d. Surface cover such as vegetation
and/or erosion control system.
Various laboratory systems have been
developed to generate rainfall and
overland flow in order to study runoff,
infiltration and erosion. Conditions
simulated include of rainfall with
various average drop sizes, range of
drop sizes, terminal fall velocities
and intensities; controlled discharge
at ground level to generate varying
levels of overland flow; and slope with
adjustable inclinations and lengths.
Rainfall is considered the most impor-
tant and difficult to simulate. The
design of simulators should be able to
reproduce drop-size distribution, drop
velocity at impact, and intensity of
natural rainfall with a uniform spatial
distribution. The energy of natural
rainfall is generally regarded as less
important in the rainfall simulators
(Bubenzer, 1979). Numerous types of
rainfall simulators have been devel-
oped. Bubenzer (1979) have reviewed
a large number of simulators produced
by different researchers and classified
the simulators into two group. The
first group uses a series of nozzles
of sprinklers to produce rain with a
widely varying drop size and size dis-
tribution. These systems are easy to
install and maintain, but they generally
produce non-uniform rainfall distribu-
tion. Also, the drop trajectories are not
generally vertical when they impact
the ground. This is of concern when
trying to simulate soil detachment by
raindrop. The second group of rainfall
simulators uses modules of multiple
drop formers to generate a near-uni-
form rainfall distribution with drops
of uniform and controlled size. The
early simulators used pieces of yarn to
form the raindrop that more uniform
than those produced by nozzles.
However, the raindrop formed by the
yarn was found to change, resulting in
non-uniform drop size. Then the later
systems used small diameter tubing
fixed to the bottom of a rigid plate.
Other types of drop former are glass
capillary tubes, hypodermic needles,
and polyethylene, copper, brass or