Environmental Engineering Reference
In-Depth Information
16
Landslides, Rockfalls
and Sandpiles
Stefan Hergarten
Karl-Franzens-Universitat Graz Institut fur Erdwissenschaften, Graz, Austria
What do landslides, earthquakes and forest fires have in
common? Obviously, they are among the major natural
hazards in many regions on Earth. However, from a more
quantitative point of view, the statistical distribution of
event sizes is their most striking similarity. For all these
processes, it roughly follows a power law at least over
some orders of magnitude. If
s
is the event size, the
number of events with a size greater than
s
within a given
region and time span can be described by the relation
(2004) compiled landslide data sets from several regions,
each of them consisting of about 1000 to 45 000 events.
Some of them were derived from historical inventories,
whereas others consist of events attributed to one trigger-
ing event (rapid snowmelt, a rainstormor an earthquake).
Figure 16.1 shows the frequency density of the eight
data sets taken from the papers of Hovius
et al
. (1997)
and Malamud
et al
. (2004) where the area is taken as
a measure of landslide size. The diagram displays the
frequency density instead of the cumulative distribution
F
(
s
) according to Equation 16.1. The frequency density
f
(
s
) is similar to the probability density in statistics; it is the
product of the probability density and the total number
F
(
s
)
∼
s
−
b
(16.1)
Earthquakes were the first phenomenon in the context
of natural hazards where such a power-law distribution
was found. It is directly related to the Gutenberg-Richter
law, which is more than half a century old (Gutenberg
and Richter, 1954). It has been supported by an enormous
amount of data and was found to be applicable over a
wide range of earthquake magnitudes globally as well as
locally, with quite a small variability in the power-law
exponent
b
(e.g. Frohlich and Davis, 1993).
The power-law distribution of the areas destroyed by
forest fires was discovered much later (Minnich and
Chou, 1997; Malamud
et al
., 1998; see also Chapter 3). In
contrast to earthquake statistics, the power-law exponent
shows a considerable variability.
Extensive landslide statistics have been collected for
several decades, too. More than 40 years ago, Fuyii (1969)
found a power-law distribution in 650 events induced by
heavy rainfall in Japan. In a more comprehensive study,
Hovius
et al
. (1997) analysed about 5000 landslides in the
western Southern Alps of New Zealand. Malamud
et al
.
of events. It is defined in such a way that
s
2
s
1
f
(
s
)
ds
is
the number of events with sizes between
s
1
and
s
2
and is
related to
F
(
s
)as:
F
(
s
)
f
(
s
)
=−
(16.2)
In the case of a power-law distribution,
f
(
s
) also follows
a power-law:
d
dx
s
−
b
s
−
b
−
1
s
−
β
∼
∼
=
f
(
s
)
(16.3)
with an exponent
1.
Malamud
et al
. (2004) found
β
=
b
+
4 at large landslide
sizes with little variation between the data sets considered.
The rollover of the frequency density at small sizes indi-
cates a lack of small landslides in all data sets. Although the
authors suggest a function to describe it quantitatively, its
origin is still unclear, but it seems not to be an artefact of
incomplete sampling.
β
≈
2
.
Search WWH ::
Custom Search