The Importance of the Precipitation and the Susceptibility of the

Anuncio
Natural Hazards 21: 65–81, 2000.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.
65
The Importance of the Precipitation and the
Susceptibility of the Slopes for the Triggering of
Landslides Along the Roads
CLEMENTE IRIGARAY1 , FRANCISCO LAMAS1, RACHID EL
HAMDOUNI1, TOMÁS FERNÁNDEZ2 and JOSÉ CHACÓN1?
1 Departamento de Ingeniería Civil, Universidad de Granada, Facultad de Ciencias, Avda.
Fuentenueva s/n, 18071 Granada, Spain; 2 Departamento de Ingeniería Cartográfica, Geodésica y
Fotogrametría, Universidad de Jaén, Spain
(Received: 3 December 1998; in final form: 22 April 1999)
Abstract. In order to characterise the influence of the heavy rains on the observed landslides during
the 1996–1997 hydrological cycle, rainfall records for the last 100 years are analysed from 104
stations in eastern Andalusia. Regarding the amounts of rain recorded between October 1996 and
March 1997 in the 104 stations studied, 31 presented new all-time records; 15 presented values that
were 80–100% of the pre-1995 record; 49 stations, 80–50%; and 9 stations, <50%. A map has
been devised of the susceptibility of the materials through which the south-eastern Andalusian road
network crosses, together with an inventory of the damage caused by instability phenomena on banks
and cuttings of the road network during the winter of 1996–1997. The relationships between the
rainfall during the study period, the damage caused to the road network and the susceptibility of the
materials affected are analysed. The results indicate that there is a clear correspondence between the
rainfall recorded and the susceptibility of the materials with the inventoried damage. It is concluded
that the widespread serious damage caused in early 1997 to the roads and surrounding areas in the
Alpujarra region and the coast of the Province of Granada was mainly caused by the extraordinarily
heavy rains. However, considerably less damage was observed where the susceptibility of the terrain
is low, thus highlighting the extreme usefulness of terrain-susceptibility maps for risk prevention and
territorial planning.
Key words: Slope movements, heavy rainfall, damage, road network, susceptibility, south-eastern
Spain.
1. Introduction
The mechanisms that cause slope instability due to the effect of water are complex
and difficult to quantify for large-scale regions. The rainfall that has the most effect
on slopes may be the rain falling during the period before the collapse (accumulated
rainfall), the most recent downpour or the maximum diurnal rainfall (Crozier, 1986;
? Author for correspondence: José Chacón, Departamento de Ingenierı́a Civil, Universidad de
Granada, Facultad de Ciencias, Avda. Fuentenueva s/n, 18071 Granada, Spain; phone/fax: +34-958
24 33 67; e-mail: [email protected]
66
CLEMENTE IRIGARAY ET AL.
Figure 1. Location of the study area.
Romana Ruiz, 1992). Nevertheless, there is a direct relationship between rainfall
levels and the occurrence of landslides (Finlay et al., 1997), which, in turn, depends on the properties of the soil. Beside, the instability processes along the road
corridors depend on the landslide susceptibility of the terrain and also on several
other factors related with the road construction itself as the increased weight on
the slope head from fills deposits, the slope angle increase by the excavations, the
removal of slope support in road cuts, and the alteration of surface runoff paths
including increased depth and rates of runoff (Larsen and Parks, 1997).
In this paper a study is presented on the relationships between accumulated
rainfall, the distribution of damage to the road network of the study area (Figure
1) and the susceptibility of the affected materials, with a view to determining to
what extent the damage caused can be considered as being directly dependent on
the extraordinarily intense nature of the rains that fell, or other unrelated factors.
2. Analysis of Rainfall
The Mediterranean climate presents a varied rainfall pattern with long, dry summers with violent storms and generally wet winters (Novoa, 1984), although over
67
THE IMPORTANCE OF PRECIPITATION
Table I. Distribution of observation points by basin, indicating those for which the previous
all-time record (AR) was broken during the winter of 1996–1997
BASIN
Guadalhorce
Vélez
Guadalfeo
Adra
Genil
Guadiana Menor
Total
Observation point
Record broken
Record broken by
(% of the observation points)
44
14
30
11
3
2
5
5
16
5
0
0
11.4
35.7
53.3
45.5
0
0
104
31
29.8
the last decade an extended period of drought was recorded with values well below
the expected average. However, in the year 1996–1997 the rainfall was so heavy
that the average of the previous years was more than doubled.
The rainfall records used were mostly obtained from data supplied by the Water
Commission of the Southern Spain Water Authority and the Water Commission
of the Guadalquivir Water Authority. Additional data obtained from the Spanish
National Meteorological Institute (an agency of the Ministry of the Environment)
were also used.
The data were grouped by hydrographic basin and further broken down by
altitude, in order to estimate for each altitude interval the most representative alltime record rainfall figure. Thus, extremely comprehensive data sets were obtained
for each observation point, generally starting in the 1930s, although some sets
date back to the turn of the century. 104 control points were selected for the 6
hydrographic basins within the study area (Table I).
For each of these points data were obtained for the daily rainfall, monthly
averages and accumulated monthly values. The rainfall values corresponding to
the period between October 1996 and March 1997 were isolated to analyse their
relative importance in comparison with the data set as a whole. The all-time record
monthly value was calculated for each altitude interval and for each basin. The
monthly rainfall value is represented for all the points included in these categories
compared with the all-time record and monthly average.
2.1.
AVERAGE MONTHLY RAINFALL
As Table II shows, for each altitude interval the monthly average was calculated
from the entire data set, which in general were fairly homogeneous. They range
between a minimum of 50 mm/month (Adra, alt. 270–500 m, December) and a
maximum of 153 mm/month (Genil, alt. >2000 m, January). However, the distri-
68
CLEMENTE IRIGARAY ET AL.
Table II. All-time record rainfall levels and monthly averages in
winter
BASIN
Altitude
(m)
All-time record
(mm/month)
Monthly average
(mm/month)
Guadalhorce
0–100
100–250
250–500
500–750
750–1000
630 – Nov.
580 – Dec.
620 – Dec.
450 – Jan.
695 – Dec.
87 – Dec.
90 – Dec.
92 – Dic.
97 – Dec.
95 – Dec.
Vélez
0–100
100–250
500–750
750–1000
550 – Jan.
575 – Nov.
632 – Dec.
783 – Nov.
90 – Nov.
87 – Nov.
109 – Dec.
100 – Dec.
Guadalfeo
0–100
100–250
250–500
500–750
750–1000
1000–1500
1500–2000
>2000
392 – Jan.
420 – Jan.
470 – Dec.
375 – Dec.
600 – Dec.
550 – Dec.
610 – Jan.
620 – Jan.
76 – Jan.
100 – Nov.
97 – Dec.
100 – Dec.
87 – Dec.
104 – Dec.
110 – Nov.
117 – Dec.
Adra
0–100
100–250
250–500
500–750
750–1000
1000–1500
1500–2000
220 – Jan.
600 – Oct.
319 – Jan.
223 – Jan.
295 – Jan.
302 – Jan.
450 – Dec.
53 – Dec.
78 – Dec.
50 – Dec.
60 – Dec.
70 – Jan.
53 – Jan.
87 – Dec.
Genil
500–750
750–1000
1000–1500
>1500
601 – Jan.
650 – Jan.
712 – Dec.
735 – Jan.
85 – Nov.
78 – Dec.
135 – Dec.
153 – Jan.
bution of all-time record monthly values varies greatly, as was to be expected given
the Mediterranean climate of the region. During the winter period from November
to February, the average values for 91.2% of the stations ranged between 117
mm/month and 60 mm/month, indicating the homogeneity of the average data.
69
THE IMPORTANCE OF PRECIPITATION
During the period from 1986 to 1995 there was a drought with values considerably below the expected monthly averages, whereas in 100% of the data for the
winter of 1996–1997 the average values obtained exceeded the previous all-time
record by at least 30%, indicating the extraordinary intensity of the rainfall in the
area during that period.
2.2.
ALL - TIME RECORD RAINFALL
From the data sets of all-time record values, calculated for each altitude interval
in each of the basins studied, a profile is obtained of the maximum rainfall over
a hypothetical year. This provides a “peak altitude” of comparison throughout the
hydrological year. Each datum is the maximum monthly sum for each month over
the years measured, obviously excepting those corresponding to the winter months
of 1996–1997.
In the study area there was a fairly wide variation in the all-time record values,
with a January maximum of 783 mm/month in the river Vélez basin in the 750–
1000 m altitude interval and a January minimum of 220 mm/month in the river
Adra basin in the 0–100 m interval. The all-time record was about 464% of the
monthly average, reaching 915% in the most extreme case.
2.3.
RAINFALL BETWEEN OCTOBER
1996
AND MARCH
1997
The rainfall between October 1996 and March 1997 was by anyone’s reckoning
quite extraordinary. For 100% of the observation points, the accumulated monthly
rainfall was not only greater than the previously established monthly average, but in
100% of cases it was over twice of this value. Moreover, during the months from
November to January, for 100% of the measurement points, the monthly rainfall
was over 200% the monthly average, and, as Table I shows, in 29.8% of the data
the previous all-time record was exceeded. Figure 2 shows an accumulated monthly
value for some rainfall stations of this region.
2.4.
LINEAR RAINFALL MAP
From the above data a linear map was drawn along the main road network, indicating the rainfall during the hydrological year 1996–1997 compared with the all-time
record before 1995. The values obtained were classified into three categories: (1)
rainfall <50% than the previous all-time record; (2) 50–80%; and (3) >80% (Figure 3). The distribution of each of these categories is shown in Figure 4. Almost
92% of the study area presented rainfall that was over 50% of the previous all-time
record and in 26.4% of the study area it was over 80% higher. The heaviest rains
fell in the Alpujarra region and certain places on the coast (the Motril area and
Rábita). In the rest of the study area, except in a belt between Dúrcal and Padul,
rainfall was 50–80% of the previous all-time record.
70
CLEMENTE IRIGARAY ET AL.
Figure 2. Some rainfall-stations data in the Guadalfeo basin for the hydrological year
1996–1997 compared with all-time record rainfall data before 1995.
THE IMPORTANCE OF PRECIPITATION
71
Figure 3. Linear map of rainfall during the winter of 1996–1997 compared with the all-time
record value before 1995 (AR).
3. Damage to the Road Network and Susceptibility of the Materials Affected
Table III shows a summary of the main slope movements that affected the road
network in the study area. The major damage occurred on the local roads in the
Alpujárra region (C-332, C-333, C-411 and C-421), on the N-323 trunk road between
Lanjarón and Vélez de Benaudalla and on the N-340 trunk road in the Almuñécar area. Using this data, completed with the inventories available on the damage
caused to the road network between November 1996 and January 1997 (Fernández
et al., 1997; El Hamdouni et al., 1997), a linear map has been drawn for all the main
routes to provide a qualitative indication of the density of damage per kilometre of
road, classified into three categories: (1) no damage or minor damage; (2) isolated
or moderate damage; and (3) general or serious damage (Figure 5). Figure 6 shows
the distribution of each of these categories. Damage (moderate or serious) affected
60% of the road network studied.
No.
Type
Location
Date
Observations
1
2
3
4
Co (Sl-Rf)
Rf
5
6
7
Rf
Rf
Rf
C-333, km 53 (Orgiva-Albuñol)
C-451 (Orgiva-Vélez Benaudalla)
Gr-SO2 (Suspiro del Moro–Coast), Lentejı́ crossroads
8
9
10
11
Sl
Sl
Sl
Co (Sl-Rf)
C-411 (Bubión–Capileira)
N-323, Miriñaque area
N-323, near Béznar
N-323, Vélez de Benaudalla
12
Co (Sl-Rf)
N-323, Lanjarón
13
14
Rf
Rf
N-323, km 171
N-323, km 175 (opposite Izbor)
15
16
Rf
Sl
C-332, km 1,5 (Orgiva–Torvizcón)
N-323, km 171
17
18
19
20
21
Rf
Rf
Rf
Rf
Co (Sl-Fl)
C-332 (Orgiva–Torvizcón) at Ujı́jar
Road between Pitres and Bubión
Gr-SO16, 400 m from Fornes
C-421 (Pampaneira–Orgiva) Fuente del Portillón
C-420 Cenes de la Vega
8/1/97
8/1/97
8/1/97
21/12/96
2/01/97
20/12/96
20/12/96
20/12/96
2/01/97
11/11/96
31/01/97
31/01/97
12/11/96
20/12/96
12/11/96
20/12/96
8/1/97
1/01/97
31/1/97
12/11/96
25/12/96
3/01/97
12/11/96
12/11/96
5/01/97
6/01/97
10/09/96
Uneven road surface
Rf
N-340, km 316 (Almuñecar)
N-340, km 354 (Rubite)
N-340, Tamaray (Almuñecar)
N-340, km 357 (Rubite-Almerı́a)
Volume: 200,000 m3
Collapse of hard shoulder
Collapse of one lane
Rainfall: 87 l/m2 in 24 h
Rubble along route
Collapse of road
Collapse of one lane and earth fallen onto roadway
Collapse of one of the lanes
Rainfall: 46.6 l/m2 in 24 h
Collapse of a new bridge
Volume: 500 m3
Volume: 100 m3
CLEMENTE IRIGARAY ET AL.
Co: complex; Rf: rockfalls; Sl: slides; Fl: flows.
72
Table III. Summary of the main slope movements, indicating the damage caused in the study area during the winter of 1996–1997
THE IMPORTANCE OF PRECIPITATION
73
Figure 4. Distribution of 1996–1997 rainfall compared with the 19950 all-time record (AR) in
the study area.
Landslide susceptibility can be defined as the tendency for a landslide to be
generated in a specific area in the future; this can be measured from the correlation between determining factors together with the spatial distribution of the
movements (Brabb, 1984), such that the susceptibility map represents a zoning
in which each degree of susceptibility indicates a greater or lesser tendency for
a slope movement to be generated. The susceptibility map used for this study was
based on a 1:200000-scale slope-movement map of the Province of Granada drawn
up by the Ministry of Public Works and Urban Development (MOPU, 1987). In
this map, the slope stability degree is assessed considered in one hand the percentage of surface affected by landslides and, in the other, the type of instability
(active and dormant or potential). For the linear susceptibility map (Figure 7) three
susceptibility categories were classified: (1) low; (2) moderate; and (3) high. Highsusceptibility land (25.3%) corresponds to schist and Alpujárride phyllite units that
are broadly subjected to instability processes related to the deeply incised fluvial
network of the region (Fernández et al., 1997). In moderate-susceptibility land
(30.8%) the predominant materials are Nevado-Filábride and Alpujárride marble,
schist and quartzite. The remainder of the study area (43.9%) presents low levels
of susceptibility (Figure 8).
4. Rainfall–Damage–Susceptipility Relationship
Once the linear maps of susceptibility, rainfall during the winter of 1996–1997
and damage caused to the road network had been drawn up, they were converted
to digital format and entered into the SPANS Geographical Information System
74
CLEMENTE IRIGARAY ET AL.
Figure 5. Linear map of damage caused to the road network during the heavy rains of
1996–1997.
(Tydac, 1993) to enable a quantitative analysis to be made of these three factors in
order to determine whether there is any relationship between them. To this end, a
map of unique conditions was generated to define 18 categories that are the result
of all the possible combinations between the categories defined for the three factors
considered (Table IV).
The areas with no damage mainly correspond to low susceptibility levels, regardless of the rainfall recorded, although it was generally under 80% of the previous all-time record. Moderate damage was generally associated with rainfall more
than 50% of the previous all-time record, with moderate or high susceptibility
levels, although moderate damage was also observed on low susceptibility levels
when the rainfall was above a certain level. Finally, the most serious damage was
generated either at high susceptibility levels with rainfall that was 50–80% of the
previous all-time record or at moderate susceptibility levels with rainfall that was
over 80% of the previous all-time record.
75
THE IMPORTANCE OF PRECIPITATION
Figure 6. Distribution of damage categories in the road network studied (1. No/minor damage,
2. Moderate, 3. Serious).
Table IV. Result of the unique conditions of the categories defined for the three
factors considered
Category
Length (km)
%
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
45.8
26.1
184.0
49.1
22.4
13.4
80.6
53.3
105.3
34.7
65.2
28.5
14.6
7.4
41.3
2.2
62.8
18.7
5.36
3.05
21.51
5.74
2.62
1.57
9.43
6.23
12.31
4.06
7.62
3.33
1.70
0.86
4.83
0.25
7.34
2.19
Tota1
855.5
100.00
Damage
Rainfall
Susceptibility
1
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
3
3
1
1
2
2
2
3
2
2
2
3
3
3
2
2
2
3
3
3
1
2
1
2
3
1
1
2
3
1
2
3
1
2
3
1
2
3
76
CLEMENTE IRIGARAY ET AL.
Figure 7. Linear map of susceptibility to slope movements (based on MOPU, 1987).
Table IV was used to devise cross matrices (contingency tables) between the
categories defined for rainfall and damage caused in each susceptibility category,
as well as the categories resulting from combining damage with susceptibility for
each rainfall category.
In order to evaluate the degree of significance of the relationship between the
damage observed and rainfall, the contingency coefficient, the Gamma of Goodman–Kruskal, Spearman’s Rho coefficient and the Chi-squared test (Goodman and
Kruskal, 1954; Kendal and Stuard, 1967; Davis, 1986) were calculated for each
susceptibility category (Table V).
These coefficients indicate that, in general, there is a considerable correlation
between the damages generated in the road network and intensity of rainfall. However, when the results are analysed for each susceptibility category, this correlation
is found to be significant for moderate susceptibility levels but not for low or high
levels. One would assume that if the susceptibility is low, no movements would be
generated regardless of the rainfall value, so there would be no damage. Equally,
77
THE IMPORTANCE OF PRECIPITATION
Figure 8. Distribution of the susceptibility-map categories defined in the study area.
Table V. Association coefficients obtained between the damage and rainfall
categories defined for each susceptibility class and jointly
Coefficient
Pearson Chi-square
Contingency coefficient
Goodman–Kruskal Gamma
Spearman Rho
Value
Prob.
Susceptibility
Low
Moderate
High
Total
6.883
0.142
0.373
0.759
0.376
0.0
1.000
0.0
0.440
0.193
28.529
0.000
0.477
0.803
0.519
17.443
0.002
0.607
0.936
0.708
if the susceptibility is very high, considerable movements might well be expected
even with moderate rainfall values. Only, then, if susceptibility values are moderate
would the appearance of damage be closely conditioned by the intensity of the
rainfall.
Figure 9 shows the relative frequency for each susceptibility level of the parts of
the road network that suffered damage or suffered no damage. It can be seen that
for low susceptibility levels, only 35.2% of the road network presents damage.
Where the road network crosses materials of moderate susceptibility, this proportion rises to 71.5%; and where susceptibility is high, more than 89% of the
road network underwent landslide processes. As we have observed, in the study
area, high-susceptibility areas correspond to schist and Alpujárride phyllite units
that are broadly subjected to instability processes related to the excavation pro-
78
CLEMENTE IRIGARAY ET AL.
Figure 9. Relative frequency of the damaged areas of the road network for each susceptibility
level.
cesses generated by the fluvial network of the region (Fernández et al., 1997).
In such areas, if the rainfall is extraordinarily high, the mobilisation of slopes
may well be generalised, largely due to the reactivation of pre-existing unstable
masses. In moderate-susceptibility areas, mostly composed of Nevado-Filábride
and Alpujárride marble, schist and quartzite, the amount of mobilisation observed
(71.5%) indicates just how heavy the rains were (the rainfall recorded was at least
200% of the monthly average during the period from November 1996 to January
1997). These results show the importance of having susceptibility maps available
to predict the spatial distribution of future slope movements, so that the appropriate
preventive and palliative measures can be taken.
As we can see, the susceptibility of the land plays a major role in the distribution
of the damage that was suffered by the road network. However, to bring to light the
relevance of rainfall in the distribution of this damage, Figure 10 shows the relative
frequency of the parts of the road network affected by slope movements for each
rainfall-intensity level. Thus, we observe that when the rainfall was low (less than
50% of the all-time record), no damage was observed at any susceptibility level.
When the rainfall was 50–80% of the all-time record, 54.2% of the road network
was damaged, of which 68% corresponds to moderate or high susceptibility levels.
Finally, when rainfall was high (over 80% of the record level), the area damaged
was almost 96%, of which under 12% corresponds to low susceptibility categories.
Furthermore, in order to determine the importance of rainfall, taking into account the susceptibility of
Pthe terrain, Figure 11 shows the quotient between the
mi /ti ratio and the sum
mi /ti , multiplied by 100, for each susceptibility cat-
THE IMPORTANCE OF PRECIPITATION
79
Figure 10. Relative frequency of the damaged parts of the road network for each rainfall level
(AR: all-time record).
egory. The value mi represents the length of the damaged parts of the road network
for each rainfall level, while ti is the total length for the rainfall level in question.
This coefficient (Irigaray et al., 1997) shows the relative distribution of the damage
and defines the degree of adjustment between the damage observed and the rainfall
recorded. As we can see, rainfall plays a major role, inasmuch as, regardless of
the susceptibility level of the terrain, in order for damage to be generated the
rainfall must be greater than 50% of the all-time record level. When the rainfall is
below this value there is no appreciable damage – not even when the susceptibility
level is high. In general, the area damaged increases as the rainfall increases. This
tendency is quite striking for the low-susceptibility category, where 68.3% of the
damage produced occurred where the rainfall was greater than 80% of the alltime record. This tendency becomes less clear as the susceptibility increases, such
that for the high-susceptibility category the damage was distributed almost equally
between rainfall levels 2 (50–80% of the all-time record) and 3 (>80% of the alltime record), which probably indicates that a rainfall threshold of instability was
attained.
5. Discussion and Conclusions
The irregularity of the weather patterns is a fact of life in the Mediterranean climate; year after year new averages and record levels are set, and the statistical
values that are used must be constantly updated. There can be little doubt that
the climatic data set available has not so far been comprehensive enough to make
80
CLEMENTE IRIGARAY ET AL.
Figure 11. Degree of adjustment between the damage observed and the rainfall recorded for
each susceptibility category (AR: all-time record).
predictions from the short term to the long term. However, with such data as is
available it is possible to draw certain conclusions about the relationships between
the heavy rains of the winter of 1996–1997, the susceptibility of the terrain and the
generation of the slope movements that affected the road network of south-eastern
Andalusia.
The rains that winter were extraordinarily heavy, with values of at least 200%
of the monthly average for the period between November 1996 and January 1997;
nearly 92% of the area studied presented rainfall that was over 50% of the previous
all-time record and in 26.4% of the terrain it was over 80% the all-time record.
It is obvious that the unprecedented nature of the rains was a major factor in
the damage caused to the area and responsible for the cause-and-effect relationship
between rainfall and damage. The threshold rainfall value necessary for generalised
slope movements is over 50% of the previous all-time record, since at lower levels
no appreciable damage was observed.
Nevertheless, the meteorological variability of the region, with new peaks and
records being set every year, including the start of the meteorological year 1997–
1998, means that we should consider whether these new values should be included
within the immediate environment, rather than long-term scenario, for the design
of infrastructures.
The severity of the damage suffered in the study area was not homogeneous
for each rainfall level, i.e., the damage observed depended not only on the amount
of rainfall but also on the susceptibility of the terrain: at low susceptibility levels,
only 35.2% of the road network was damaged, while this value increases to 89.6%
for high-susceptibility areas. There is therefore a need to devise maps of the susceptibility to slope movements, which, even though they may not be capable of
determining the probability of occurrence over time, will at least provide valuable
information on the stability conditions of large regions. Such mapping would be
THE IMPORTANCE OF PRECIPITATION
81
extremely useful both at the planning stages of major public works and during
their execution, in order for the appropriate preventive and corrective measures to
be taken.
Acknowledgements
This research was made possible by the facilities offered by the Southern Spain
Water Authority and the Guadalquivir Water Authority, and was carried out as part
of the activities of the Environmental Research Group: Geological Risks and Land
Engineering, code RNM121, of the Andalusian Research Plan. It was partially
supported by the 1091.6 CICYT Project.
References
Brabb, E. E.: 1984, Innovative approaches to Landslide Hazard and Risk Mapping, Proc. IV
International Symposium on Landslides, Toronto, Vol. 1, pp. 307–324.
Crozier, M. J.: 1986, Landslides: Causes, Consequences and Environment, Routledge, London &
New York.
Davis, J. C.: 1986, Statistical and Data Analysis in Geology, John Wiley & Sons, Inc., New York,
2nd edn.
El Hamdouni, R., Irigaray, C., Pérez Romero, J., Fernández, T. y Chacón, J.: 1997, Exposición a riesgos derivados de los movimientos de ladera en el entorno de Albuñuelas (Granada): incidencia
de las lluvias de noviembre a enero de 1996/97, In: E. Alonso et al. (eds), IV simposio nacional
sobre taludes y laderas inestables, Granada, Vol. I, pp. 15–26.
Fernández, T., Brabb, E., Delgado Salazar, F., Martin-Algarra, A., Irigaray, C., Estévez Rubio, A.
y Chacón, J.: 1997, Rasgos geológicos y movimientos de ladera en el sector de Izbor-Vélez de
Benaudalla de la cuenca del río Guadalfeo (Granada), In: E. Alonso et al. (eds), IV simposio
nacional sobre taludes y laderas inestables. Granada, Vol. II, pp. 795–808.
Finlay, P. J., Fell, R., and Maguire, P. K.: 1997, The relationship between the probability of landslide
occurrence and rainfall, Can. Geotech. J. 34, 811–824.
Goodman, L. A. & Kruskal, W.H.: 1954, Measures of association for cross classifications, J. Am.
Statist. Assoc. 49, 732–764.
Irigaray, C., Fernández, T., y Chacón, J.: 1997, Validación de un método de análisis de la susceptibilidad a los movimientos de ladera. Aplicación al sector de Rute, In: E. Alonso et al. (eds), IV
simposio nacional sobre taludes y laderas inestables. Granada, Vol. I, pp. 39–49.
Kendall, M. G. and Stuard, A.: 1967, The Advanced Theory of Statistics. Vol. 2: Inference and
Relationship, Charles Griffin & Company Limited, London.
Larsen, M. C. and Parks, J.: 1997, How wide is a road? The association of roads and mass-wasting
in a forested montane environment, Earth Surface Processes and Landforms 22, 835–848.
Novoa, M.: 1984, Precipitaciones y avenidas extraordinarias en Cataluña, Simp. Inestabilidad de
laderas en el Pirineo, Univ. Pol. Barcelona. pp. I.1.1–I.1.15.
MOPU: 1987, Movimientos del terreno de la Provincia de Granada, Dirección General de Carreteras.
Servicios de Geotecnia, Madrid.
Romana Ruiz, M.: 1992, El Problema de la previsión de un talud en función de la Pluviometría, In:
E. Alonso et al. (eds), III Simposio Nacional sobre taludes y laderas inestables, La Coruña, Vol.
1, pp. 53–70.
Tydac: 1993, SPANS GIS Reference Manual, INTERA-TYDAC Technologies Inc.
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