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Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
237
DOI: 10.4408/IJEGE.2013-06.B-21
ESTIMATION OF THE WATER WAVES GENERATED
BY THE LANDSLIDE IN THE GRIJALVA RIVER, MEXICO, 2007
J
ersain
GÓMEZ nÚÑeZ & V
erduZco
M
oisés
BereZoWsKY
Universidad Nacional Autónoma de México - Instituto de Ingeniería - Ciudad Universitaria, D.F, México, C.P. 04510
landslide overtopped the dam and destroyed Longa-
rone town downstream; nearly two thousand people
were killed by the water wave (s
chnitter
, 1964).
If a chronological point of view is chosen, there
are three characteristics stages in landslide waves. The
first is the generation as a consequence of the impact
of the landslide on the water body; the second phase
is the propagations, dissipation and dispersion of the
waves as they travel through the water body. The last
stage corresponds to the interaction of the waves with
the hillsides around the water body and with the dam
or other infrastructure around; this last stage includes
the wave reflection and run-up.
The most complex part of the phenomena is that
related to the wave generation. This is because there is
an interaction of the solid material entering the water
body; this combination of a water displacement, flow
resistance, disintegration of the landslide, etc., makes
ABSTRACT
Large-scale water waves generated by landslides
are one of the most dangerous events in reservoirs.
Although the probability of occurrence is low, the
consequences can be catastrophic as historical events
have shown. The process of generation of the water
waves is very complex, and has been studied with the
aid of analytical, computational and physical models;
empirical equations to estimate the characteristics of
the water waves have been obtained depending on the
parameters of the landslide. The paper presents a set of
equations derived from physical models and real cases
studies. The range of parameters and the hypothesis
made in the experiments are discussed. Some of those
equations are used to estimate the magnitude of the
water waves generated as a result of a landslide of 50
Mm
3
in the Grijalva River, Chiapas, Mexico, occurred
in November 2007. The results are compared with re-
corded data. The expressions that reproduce better that
particular event are brought out and discussed.
K
ey
words
: water waves, landslide, Grijalva
INTRODUCTION
Water waves formed in coastal regions, a lake or
reservoir due to impact of an earth or rock landslide,
an avalanche, the fall of a glacier, or even the fall
of a meteorite can be catastrophic. One of the most
relevant and well documented of these events was in
Vajont Reservoir in 1963. The wave generated by a
Fig. 1 - Water waves generation by landslide
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J. GÓMEZ NÚÑEZ & V.M. BEREZOWSKY
238
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
periments with moving sand bags were (d
aVidson
&
M
c
c
artneY
, 1975).
The Laboratory of Hydraulics, Hydrology and
Glaciology of Zurich (VAW-ETH), (h
uBer
, 1980 &
1982) reproduced the deformation and the poros-
ity of the slide material using a granular mass. (F
ritZ
et alii, 2003 & 2004; Z
WeiFel
, 2004; Z
WeiFel
et alii,
2006; h
eller
, 2007; h
eller
et alii, 2009; h
eller
&
h
ager
, 2010) also worked in that laboratory. Accord-
ing to what we call the Swiss School the wave forma-
tion depends of the landslide velocity, V
s
, the bulk slide
volume, Vol
s
, the slide thickness, s, the landslide width
b, the landslide density, ρ
s
, the porosity, n, the slide
impact angle, α, and the water depth, h. On 2D experi-
ments, the wave propagation is in the x direction and in
3D models the angle, γ, for the point where the wave is
studied is also required.
2D EXPRESSIONS
Most of the already cited experiments were de-
veloped in flumes, so the characteristics of the water
waves are just of a 2D wave and its one-directional
movement in front of the landslide.
In order to reduce the number of variables, di-
mensional analysis is used. For (K
aMphuis
& B
oWer
-
ing
, 1970) the relative wave height, H(x)⁄h (where h is
the water depth); the dimensionless landslide volume
per unit with, Vol*=Vol⁄(bh
2
) (where b is the landslide
width); the impact Froude number, F=V
s
/√gh (where
V
s
is the landslide velocity and g is the acceleration
due to gravity); and the relative propagation distance,
X=x/h as is shown in the following equation:
(1)
As shown in equation 1, according to these au-
thors, the waves decay exponentially.
h
uBer
& h
ager
(1997) using (h
uBer
, 1980) data
formulated the next equation in which the impact an-
gle and the specific gravity G=ρ
s
w
are considered:
(2)
where ρ
s
is the landslide bulk density and ρ
w
is the
water density.
W
alder
et alii (2003) worked on underwater
landslides; they added the dimensionless underwater
travel time, T
s
:
it almost impossible to consider a general solution be-
cause there are a lot of variables involved (Fig. 1). This
is why most of the cases are studied experimentally
although the mathematical models have improved con-
siderably in recent years. In addition, several studies
have been developed in laboratory flumes or tanks in
order to control the variables and be able to measure
and observe the wave development, and compare pre-
dictions against observed historical events.
In the following, empirical expressions reported
in the literature, mostly experimentally obtained, are
presented and discussed. Some of them are applied for
the prediction of the characteristics of the water waves
generated after the Grijalva Landslide that occurred in
November, 2007. The computed values are compared
to the documented observations of the event.
EXPERIMENTAL STUDIES
There are several experimental studies related
to impulse waves. Most of them were developed for
flumes, where it is possible to control the relevant vari-
ables of the slide as its velocity, the angle of the slide,
its density, etc.
One of the applicable results of the experimental
studies are expressions for the maximum wave ampli-
tude, a
M
, or the total wave height, H
M
, at the zone just
in front of the landslide; additionally, there are some
expressions for these variables as they travel from
the above point, a(x) and H(x). These expressions are
function of the physical characteristics of the slide and
of the body of water where the landslide impacts.
d
i
r
isio
et alii (2011) summarized the subject.
Here we discuss the most relevant results that can
be applied to our case. The first experiments report-
ed went back to the XIX Century (r
ussell
, 1838 &
1845). Solitary waves generated by the vertical falling
box were studied. (W
iegel
, 1955) was the first to study
the waves generated by the impact of solid boxes slid-
ing down inclines.
c
ruicKshanK
(1969) found that the shape of the
box, the slide impact angle, and the vertical distance
from the centroid of the mass sliding to the bottom of
the flume are meaningless in the wave formation. He
found that the relevant variables are the water volume
displaced and the time the slide is moving in the water.
n
oda
(1970) classified the water waves as a
function of the slide Froude number and the rela-
tive height of the slide. The first that reported ex-
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ESTIMATION OF THE WATER WAVES GENERATED BY THE LANDSLIDE IN THE GRIJALVA RIVER, MEXICO, 2007
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
239
Z
WeiFel
(2004) experiments and proposed to include
the impulse product parameter:
(12)
with experimental ranges: 0.17≤P≤8.13
This parameter is used in the following set of
equations for near field (if X<5.5P
(1/2)
)
(13)
(14)
For far field (if X≥5.5P
(1/2)
)
(15)
(16)
3D EXPRESSIONS
The first experiments in a tank were reported by
J
ohnson
& B
ernal
(1949), however S
ingerland
&
V
oight
(1979) summarized their experimental results
in the following equation:
(17)
p
aniZZo
et alii (2005), using a rigid block in a rec-
tangular tank, measured the 3D wave propagation and
proposed the next equation:
(18)
h
uBer
& h
ager
(1997) using h
uBer
(1980) ex-
periments proposed the next 3D expression:
(19)
Finally,
heller
et alii (2009) using the scale mod-
el experiments of Lituya Bay and the Lucerne Lake,
and their 2D flume experiments, proposed the next
equation valid for far field (X≥5.5P
(1/2)
):
(20)
The all dimensionless quantity ranges of the ex-
perimental parameters are reported below in Tab. 1.
(3)
T
s
is a function of the dimensionless landslide
length L=l/h.
(4)
This last Equation has been criticized because it
does not involve the kinetic energy of the slide.
Very recently, F
ritZ
(2002), worked on a wave
flume at the VAW-ETH laboratory generating waves
with a pneumatic landslide generator. He measured
the velocity field using Particle Image Velocity
(PIV). His results are formalized in (F
ritZ
et alii,
2004) resulting in the next equation:
(5)
where S=s⁄h is dimensionless landslide thickness.
d
i
r
isio
(2005) extended the works of K
aMphuis
&
B
oWering
(1970) for vertical falling box or landslide
with α=90°, and proposed the following equations:
(6)
(7)
Z
WeiFel
et alii (2006) using F
ritZ
(2002) results
formulated the near field equation:
(8)
For the far field, they formulated the next equa-
tion useful to obtain a as a function of the distance, x:
(9)
a
taie
-
ashtiani
& n
iK
-
Khah
(2008) showed again
that the landslide shape does not strongly affect the
wave height. Instead, they included the new dimen-
sionless landslide length, L*=l/s:
(10)
Dimensionless underwater travel time, T
s
*, is
computed with the empirical equation of
paniZZo
et
alii (2005):
(11)
where A=bs⁄h
2
is dimensionless landslide front area.
h
eller
(2007) continued F
ritZ
, (2002) and
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J. GÓMEZ NÚÑEZ & V.M. BEREZOWSKY
240
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
in the region is relatively narrow (from 200 to 400 m
wide). About 100 m upstream the San Juan Grijalva
Village was located.
LANDSLIDE CHARACTERISTICS
According to (
doMíngueZ
, 2008), the main con-
trolling factors of the San Juan Grijalva Landslide
were a combination of:
• Intense precipitation
• Structural geology (faults and fractures)
• Water level changes and suction regime in the rock
layers and rock dipping
• Mechanical properties of materials, expressly of lu-
tites, which lowered their resistance when satu-
rated
• Spatial distribution and stratigraphic character of the
rock masses
• Local topography, although the slope gradient before
the landslide was slightly higher than 10 degrees
• River bank erosion
• Deforestation
Additionally, there was a M4.5 earthquake in the
region 5 days before.
More than 1,500 mm of rainfall were recorded
during October, and 1,160 mm in just nine days very
near the landslide date. The soil at the region was
completely saturated, limiting the infiltration, (h
ino
-
Josa
, 2011). The spillway of Peñitas Dam was operat-
ing in order to control the big flood that was occurring
at the basin. The water level at the reservoir was above
the maximum operation level.
THE EVENT
At 20:32 hrs of Sunday November 4
th
, 2007, the
Cerro La Pera, slid towards the Grijalva river. Field
CASE STUDY: SAN JUAN GRIJALVA
LANDSLIDE
The Grijalva Reservoir is located at the south-
east of Mexico; the watershed has about 60,000 km
2
,
mainly at the State of Chiapas, and ends in the Gulf
of Mexico (Fig. 2). At the upper part of the basin,
the average year precipitation varies between 1,200
and 1,700 mm meanwhile at the lower part is a lit-
tle above 4,000 mm, one of the biggest in Mexico.
These conditions are mainly due to the presence of
what meteorologist call tropical systems. The aver-
age volume at the mouth of the Grijalva River is
36,000 Mm
3
.
There are four dams in cascade used mainly for
hydroelectric generation and flood control; these are,
coming from upstream, Angostura, Chicoasen, Mal-
paso and Peñitas.
The San Juan de Grijalva landslide happened in
the Peñitas reservoir, in a huge river meander. Peñi-
tas dam is about 14 km downstream the landslide site
and Malpaso Dam is over 60 km upstream. The basin
Tab. 1 - Experimental range of empirical formulations
Fig. 2 - Location of the Landslide
Tab. 2 - San Juan Grijalva landslide data
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ESTIMATION OF THE WATER WAVES GENERATED BY THE LANDSLIDE IN THE GRIJALVA RIVER, MEXICO, 2007
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
241
RESULTS
In Table 4, the dimensionless parameter computed
using the most reliable data is reported
The computed wave characteristics are reported
in Table 5, for the different equations that can be ap-
plied in this case. (a
rViZu
et alii, 2008; h
inoJosa
et
alii, 2011) reported that the water wave at San Juan
Village was H(x)=50 m. The splash region of the land-
slide is so near the town, X<5.5P
(1/2)
, that the results
for H
M
could also be considered valid.
DISCUSSION
The water wave height and total wave height ob-
tained with Eqs. (1) (K
aMphuis
& B
oWering
, 1972),
(2) (h
uBer
& h
ager
, 1997), (6) (d
i
r
isio
, 2005), (14)
(h
eller
, 2007), for 2D models overestimate the val-
ues. The differences with the estimated waves char-
acteristics reported from in situ observations are re-
ported in the last column of Table 5.
observation and the stratigraphic and geological set-
ting of the region near San Juan Grijalva allows the
conclusion, according to (
alcántara
, 2008 &
usgs
,
2004) that there was a translational mass movement
and the slide surface took place on a lutite layer.
The size of the landslide was huge (more than 50
Mm
3
) and the river was completely closed. Moreo-
ver, part of the slide material rose on the opposite
river margin. The impact of the landslide generated
water waves that traveled upstream and downstream
the landslide site. Fortunately, the reservoir widens
considerably before the Peñitas Dam, so the waves
damped out almost completely. No damage was re-
ported at the dam infrastructure. On the contrary, as
the water waves travelled upstream, San Juan Grijal-
va Town was razed to the ground. The small village
was located 100 m upstream the face of the landslide
and, at the same river margin, so γ=90° as can be
seen in Fig. 3. The waves were dissipated as they
traveled upstream, and no more damage was report-
ed. No waves were reported at the town Raudales de
Malpaso, just downstream of Malpaso´s Dam.
The data in Table 2 was taken from (d
oMíngueZ
,
2008; a
lcántara
& d
oMíngueZ
, 2008; a
rViZu
et alii,
2008; h
ernándeZ
et alii, 2010, and h
inoJosa
et alii,
2011). As it is common for these kind of events, there
are differences in the data.
Other characteristics of the landslide are reported
in Table 3. Note that the water depth in the reservoir
at the site of the landslide is relatively small consider-
ing the total volume of the slide. For that reason, the
landslide closed completely the river
Fig. 3 - Landslide and San Juan Grijalva Village, (Ex-
tracted from Google Earth)
Tab. 3 - Landslide characteristics
Tab. 4 - Dimensionless parameters of San Juan Gri-
jalva Landslide
Tab. 5 - Water wave characteristic
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J. GÓMEZ NÚÑEZ & V.M. BEREZOWSKY
242
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
On the contrary, the 3D expressions, Eqs. (18)
(p
aniZZo
et alii, 2005), (19) (h
uBer
& h
ager
, 1997)
and (20) (h
eller
et alii, 2009); underestimate the
wave height.
These differences can be explained because in
the 2D experiments, the energy of the block is more
efficient transmitted to the water waves been gen-
erated; besides the propagation is just in the same
direction of the movement (γ=0°). Besides, in 3D,
the water waves disperse of the waves as they travel
through the reservoir.
Also, it can be noted that the equations for gran-
ular landslides give lower wave heights tan those of
block slides because the soil porosity permits to ab-
sorb part of the energy of the slide dynamics, mainly
after the impact of the slide with the reservoir.
We believe that the block dynamics as it is mov-
ing in the reservoir has a strong influence on the
water waves’ characteristics. The specific gravity
of the landslide is also important in the buoyancy
force that is in opposite direction to the movement
of the slide. The dimensionless landslide volume
per unit with is the relationship of the volume of
the block compared to the water depth. In the case
here discussed, Vol >> bh
2
; besides, the size of the
block is also bigger than the water depth (s>h S>1).
The landslide ended its movement with just a part
underwater and closing completely the river. This
situation is not considered in most of the equations.
CONCLUSIONS
Empirical equations were used in order to es-
timate the water wave height at San Juan Grijalva
Town, after the landslide of November 2007.
The 2D models overestimate the water wave
height (from 16% to 100%) if the values of 50 m
reported in the literature are considered. The loca-
tion of San Juan Grijalva Town and the direction of
the landslide suggest that a 3D description could be
more adequate. Nevertheless, the computed values
are under the 50 m height (from -36% to -57%). The
event characteristics of the San Juan landslide are
such than just the landslide Froude number is in the
rank of the experiments reported in the literature, but
the dimensionless landslide volume per unit width
and landslide thickness are much bigger of the ex-
perimental parameters for most of the equations.
Furthermore, experiments where the landslide ended
partially submerged are required (as it is the case in
the Grijalva Lanslide).
ACKNOWLEDGMENTS
The support of PAPIT project IN 116011 of DGA-
PA UNAM and of the Instituto de Ingeniería UNAM
are fully appreciated.
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i
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Editrice
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