Page 83 - Geotechnical Engineering Soil and Foundation Principles and Practice

Soils That Are Sediments
78 Geotechnical Engineering

4.6.2 Playfair’s Law and Horton’s Demonstration
This relationship between stream size and valley size was noted by John Playfair,
a Scottish mathematician and philosopher, in 1802, and he reasoned that streams
therefore must cut their valleys. A relationship to geomorphic landform was
formulated in 1945 by an engineer, R. E. Horton. Horton defined the smallest
headwater streams as first-order streams. Two or more first-order streams then
combine to make a second-order stream; two or more second-order streams
combine to make a third-order stream; and so on. The highest-order stream in
North America is the Mississippi River, which is tenth order. Through this simple
numbering system Horton showed that the higher the stream order, the larger the
drainage basin.

4.6.3 Base Level
The term ‘‘base level’’ was proposed in 1875 by an American geologist, John Wesley
Powell, a civil war veteran whose expedition was the first to traverse the Grand
Canyon in boats. Powell saw firsthand that the depth of cutting by a stream is
governed by thresholds of hard rock that create a base level. The ultimate base level
is sea level; the bottom of a river bed can erode below sea level, but this depth is
limited because the water must run downhill. Localized base levels can occur
anywhere along the length of a river or stream where it encounters harder rock,
or where an excess of sediment is carried in and deposited by a tributary stream.

Because of the existence of an ultimate base level, the gradient or slope of rivers
generally increases upstream, and in general the lower the stream order, the higher
the stream gradient.

4.6.4 Meandering Streams

As downward erosion is halted by a base level, excess energy becomes directed
toward meandering, or lateral erosion into a series of sinusoidal loops that
lengthen the river channel and therefore decrease its gradient, which in turn slows
the flow and decreases erosion. Meanders normally are spaced at an interval of
about five to seven river widths, so small rivers have small meanders and large
rivers have large meanders.

Meandering streams still erode, as the momentum of water flowing around
a meander loop carries it to the outside of the bend, where it erodes the channel
wider and deeper. The main thread of flow, called a ‘‘thalweg,’’ moves back and
forth across a meandering river in order to impinge on the outside of each
meander. The straight section between adjacent meanders is a relatively shallow,
sandy reach. The changing depths of a meandering river channel become obvious
to the boater as a boat drags bottom in the reaches. Prior to the use of bridges and
ferries, reaches were sought out for fording, but can be areas of quicksand, which
is discussed in Section 14.9.

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