Environ Earth Sci (2014) 71:2911–2923
DOI 10.1007/s12665-013-2666-7

ORIGINAL ARTICLE

Analysis of infiltration processes into fractured and swellingsoils as triggering factors of landslides
A. Galeandro • A. Doglioni • V. Simeone •J. Šimůnek

Received: 26 February 2013 / Accepted: 5 July 2013 / Published online: 13 July 2013
Ó Springer-Verlag Berlin Heidelberg 2013

Abstract Rainfall infiltration can cause a dramatic
decrease of suction in unsaturated soils and, consequently,of shear strength, triggering various instability phenomena,such as the slip of steep surface soil layers. Swelling of
cracked soils and capillary barrier effects, induced by finegrained soils overlying a more permeable material, can also
affect water flow through this type of soil systems. In thepast, few studies on infiltration and rainfall-induced landslides considered the simultaneous effects of surface
cracks, swelling materials, and/or the capillary barrier
phenomenon. To this purpose, this paper presents theresults obtained by a dual-permeability model, which
simulates water flow through a fractured swelling soil
overlying a more permeable soil and focusing on theinfluence of these phenomena on triggering of landslides.
Numerical results show that for high-intensity precipitations, flow through fractures quickly reaches significant
depths and the capillary barrier is broken, while soil
swelling leads to a uniform narrowing of cracks. On theother hand, for low-intensity precipitations, fracture flow
and swelling are limited only to the first 30–50 cm of the
topsoil, while cracks almost completely closed. Evaluations of the slope stability show that prolonged lowintensity rainfalls might be more dangerous than shorthigh-intensity rains in triggering surface landslides.

A. Galeandro (&)  A. Doglioni  V. Simeone
Department of Civil Engineering and Architecture, Technical
University of Bari, Via Orabona, n. 4, 70125 Bari, Italye-mail: annalisa.galeandro@poliba.it
J. Šimůnek
Department of Environmental Sciences, University of California
Riverside, Riverside, CA 92521, USA

Keywords Infiltration  Dual-permeability model 
Rainfall-induced landslides  Rainfall thresholds 
Shallow landslides

Introduction
Rainfall-induced landslides are hot topics for scientific
literature about landslides, especially for the evaluation of
rainfall thresholds, triggering slope failure (Guzzetti et al.
2008; Frattini et al. 2009; Rahardjo et al. 2010; Doglioni
et al. 2012). These landslides are characterized by a combination of very complex hydrological and mechanicalprocesses. They are strongly influenced by the site stratigraphy (Tsai and Chiang 2013), while their complex
processes hindered the development of reliable hydrological models for the prediction of these thresholds. In fact,
low-intensity prolonged rainfalls can sometimes be moredangerous than short and intense ones (Doglioni et al.
2011; Galeandro et al. 2013), showing how the singularityof an event is often more critical than its exceptionality.
A detailed analysis of infiltration processes, accounting
for particular stratigraphic conditions, can lead to a better
understanding of the influence of rainfall intensity andduration on the distribution of soil suction and pore pressure
in surface soils, and then on triggering of shallow landslides.
During rainfall infiltration, the soil suction of unsaturated
soil layers and the corresponding shear strength significantly
decrease, producing slope instability. In fractured soils, thepresence of preferential flow paths boosts rainfall infiltration
and affects variations of pore pressure as consequence ofrainfall intensity and soil properties (Beven and German
1982; Jarvis et al. 1991; Yang et al. 2013; Zhou et al. 2013).
Shrinking and swelling phenomena of clayey soils can
induce opening or closing of cracks and significantly affect

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water flow (Vogel et al. 2005; Türköz and Tosun 2011).
Finally, the presence of a more permeable layer underlying
surface fine-grained unsaturated soils can create a capillarybarrier effect (Mancarella and Simeone 2012). This retains
water at the bottom of cracks and fine-grained matrix, until
critical conditions for further downward infiltration arereached. All these processes (i.e., cracks, swelling, and water
retention at the interface between soil layers) contribute tovariations of the soil pressure head, which affect the slope
stability of unsaturated soils.
Existing models do not consider all these processes orare not yet applied to evaluate the slope stability and/or to
predict rainfall thresholds triggering landslides. The
empirical models, developed during the last few decades(Caine 1980; Guzzetti et al. 2008; Brunetti et al. 2009;
Sheng et al. 2011, and others), do not account for many
physical phenomena affecting soils and do not consider
how hydrological processes, land use, and climate affectlocation, timing, and rates of landslides (Iverson 2000).
Several theoretical models evaluating landslide phenomena(Tsai and Yang 2006; Pagano et al. 2010, and others) arebased on topographical, geological, and hydrologicalvariables, and on changes of the land use. Many numericalcodes, such HYDRUS (Šimůnek et al. 2008) or MACRO(Jarvis 1994; Larsbo et al. 2005), are also available tosimulate water flow through soil. However, these models
are not yet able to evaluate interactions between surface
landslides, rainfall, and other relevant processes according
to their full complexity. To fully analyze rainfall-induced
landslides, a reliable model should be developed, considering all relevant processes affecting the behavior of
unsaturated soils. This would lead to a better understandingof the influence of rainfalls on triggering landslides and to amore reliable description of associated hydrological risks.
This study investigates a dual-permeability model(Galeandro and Simeone 2010a, b, 2012; Galeandro et al.
2011), in which fractures behave as open channels,
becoming progressively narrower during infiltration, due tomatrix swelling (Fig. 1). The model additionally considers
the presence of a coarse-grained soil underlying a finetextured fractured layer, which creates a capillary barrier
effect at the contact between the two types of soils. Rainfall
intensity is assumed to be constant during a particularrainfall event and all rainfall water infiltrates into fractures,
thus there is no shallow ponding, until fractures completely
close. These assumptions are an acceptable approximation
for systems characterized by low permeability soils withwide cracks (Römkens and Prasad 2006), particularly forhorizontally stratified soils, in which the vertical permeability is significantly lower than the horizontal one.
The model is applied to a soil system consisting of afractured sandy loam, overlying a coarse sandy layer, aquite frequent scenario in south Italy. Mancarella and123

Environ Earth Sci (2014) 71:2911–2923

Simeone (2012) (and many others) observed in Campania asignificant number of landslides, which were triggered byprolonged, low-intensity rainfalls at the beginning of thewarm season in May 1998. In addition, these were likely
affected by vertical shrinkage cracks that significantly
influenced the infiltration process. The proposed model
attempts to simulate these phenomena and shows how theinfiltration process and the water content distribution ofsoil can be strongly affected by the rainfall intensity,
swelling phenomena, the presence of swelling cracks, andthe underlying capillary barrier. Results allow for evaluating the influence of the pressure head distribution on thedecrease in the slope safety factor, consequently affecting
the overall slope stability.

The model
The used model (Galeandro and Simeone 2010a, b, 2012;
Galeandro et al. 2011) simulates water flow throughswelling fractured surface soils, overlying a coarse soil
layer, working as a capillary barrier. The model is based ona dual-permeability concept, in which fractures represent
the macroporous domain and the soil matrix between them
represents the microporous domain. The soil system issimplified as a homogeneous porous medium, with paralleland perpendicular vertical fractures (Fig. 1), which get
progressively narrower during the infiltration process dueto the swelling dynamics of the matrix.
Rainfall water flows directly into the fractures, while
only lateral flow is assumed in the soil matrix, between
fractures. By assuming that vertical infiltration into thematrix can be neglected and water flows vertically only inthe fractures allowed us to focus on the main flow processes,that is water infiltration into the fractures, its downward
percolation in the fractures, and the mass exchange at thefracture/matrix interface. Moreover, this is reasonable forparticular conditions with compacted surface soil layers, inwhich the hydraulic conductivity along horizontal direction
is significantly higher than along vertical direction. The
computations are carried out only for one fracture and halfblock (L/2) of the soil matrix (Fig. 1), without considering
two-dimensional interactions between cracks/fractures andthe soil matrix. These assumptions greatly simplify thecomplexity of the system. However, note that this approachallows to obtain results, which are consistent with the onedimensional slope stability approach such as the infinite
slope method. Since it is assumed that all infiltrating water
moves directly into the fractures, the flow model does notmake any assumptions about the slope inclination, only
about the length of the surface, from which water flows into
the fracture. The slope inclination is considered only whenevaluating the slope stability.

Environ Earth Sci (2014) 71:2911–2923

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Fig. 1 Schematic
representation of the studied soil
system (modified from
Galeandro and Simeone 2012):
a vertical cross section; b top
view

Fractures work as channels, in which flow can becharacterized as open channel flow. The absorption processof the soil matrix starts at fracture walls and is treated ashorizontal infiltration due to ponding. It is assumed that thehalf-fracture behaves like a channel with a rectangularcross section and that its flow can be treated as open
channel flow. Then, water flow through fractures can be
described using the kinematic wave equation (a simplified
form of de Saint–Venant equations). The continuity equation of kinematic wave is:
oQ oA
þ
¼q
oz
ot

ð1Þ

where Q (m3s-1) is the flow rate, which passes through thecross section characterized by an area A (m2). The sink/
source term q represents the amount of water, which
laterally infiltrates into the matrix, and which is below
described. Assuming uniform flow, the equation of motion
can be expressed as:
A ¼ a Q bð2Þwhere a* and b* parameters are calculated using Manningequation (Manning 1890), depending on the wetted
perimeter, the hydraulic gradient, and Strickler roughness
coefficient cs (m1/3s-1). Equation (1) can then be expressed
only in terms of the variable Q as follows: oQ  b 1 oQ
þa b Q¼q
ð3Þ
oz
ot
Equation (3) is solved, given initial and boundary
conditions. The initial condition is:
Q0 ¼ 0ð4Þ

and the top, boundary condition is:
Qttop ¼r  ðL þ dÞ2
48t [ 0where r is the rainfall intensity (cm s-1).

ð5Þ

Water flow through the matrix is described using themixed form of Richards equation for horizontal infiltration:


oh
o
ow
¼
KðwÞ
ð6Þ
ot ox
ox
where w is the pressure head (cm), h is the water content(cm3cm-3), and K(w) is the unsaturated hydraulic conductivity (cm s-1), evaluated using the van Genuchten(1980) and Mualem (1976) relationships (Mualem 1976;
van Genuchten 1980).
The initial water content is assumed to be constant for
the entire soil matrix. Since the flow system is assumed tobe symmetric, a zero flux boundary condition is considered
for the matrix at the right-hand side of the system (in the
middle of the matrix block, Fig. 1):
qx ¼ KðwÞ

ow
¼0
ox

ð7Þ

On the left side of the matrix, at the time step k ? 1, for
the ith interface element, the boundary condition isexpressed as:


k
kþ1
hkþ1
¼
min
h
þ
A
=A
;
h
ð8Þ
tot
sat
i
i;1
i;1
where

 b
Akþ1
¼ a Qkþ1
i
i

ð9Þ

and
Atot ¼ L  dkþ1i

ð10ÞThe water content distribution in the soil matrix is used
to estimate the amount of water, which laterally propagates
into the matrix, and to update the flow rate thoughfractures, by subtracting this amount from the flow rate
profile.
A linear relationship between the soil element volume V(cm3) and its water content h (cm3cm-3) is used to evaluatematrix swelling (Novák et al. 2000, 2002):

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Environ Earth Sci (2014) 71:2911–2923

V ¼ c1 h þ c2

ð11Þ

where c1 and c2 are parameters calibrated to havemaximum swelling equal to 0.5 % of the initial volume
at saturation. Assuming no vertical deformation of soil, thelateral expansion DL (cm) of each element is obtained asfollows:
DL ¼

V
 dx
dz

ð12Þ

where dx (cm) and dz (cm) are in the order the initial widthand height of the soil element. Finally, the half crack’s
opening d (cm) at each depth can be obtained as follows:Xd ¼ d0  DLtot ¼ d0 
DLi
ð13Þ
i

where d0 is the initial half width of the crack.
The model additionally implements a capillary barrier
below the shallow fractured soil. The capillary barrier is aconsequence of the presence of a course-textured layer
underlying a fractured fine-textured shallow soil layer.
Water accumulates on the cracks and in the matrix above
the interface between the two layers. Water is stored in thefractures up to the highest capillary height that can exist
between two parallel walls and depending on the crack
opening at the bottom of the fractures, expressed as:
hkþ1
¼
c

pc2  pc1 2r cos c2  2r cos c1
¼
qg
2dqg

ð14Þ

where pc1 and pc2 are interface capillary pressures, defined
k?1
as pc = pair - pwater and pc = 2r cosk/2dk?1
nz , where 2dnz
is the distance between walls and equal to the crack
opening at the bottom, r is the surface tension (0.073 N/m), and k is the contact angle.
Excess water flows into the lower coarse-textured layer.
Due to lateral water diffusion, water is stored by the matrix
until the pressure head at the interface between the twolayers reaches a critical breaking value, which is approximately equal to the water entry pressure head of the lower
coarse layer (Shackelford et al. 1994; Stormont andAnderson 1999; Morris and Stomont 1999; Mancarella andSimeone 2012).

The case study
The proposed dual-permeability model is applied to a
stratified soil system, in which a fractured sandy loam soil
overlies a coarse sand substratum. The matrix of the upper
soil layer is characterized by low permeability, while thesubstratum is assumed to be quite permeable. The finetextured soil layer is assumed 150 cm thick, having soil
cracks 80 cm apart, with an initial fracture opening of
4 mm. Roughness value cs is assumed to be 1 m1/3s-1.

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Parameters of the fracture network and the soil matrix aresummarized in Table 1.
The soil system is spatially discretized into small finite
elements (5 cm 9 1 cm), resulting into 30 vertical soil
sub-layers and 40 horizontal elements. A water entry
pressure head equal to -200 mm, which is appropriate forcoarse sand (Stormont and Morris 1998), is considered as
the critical value for capillary barrier break at the interface
between soil layers.

Results and discussion
The model is used to simulate 10 different rainfall events,
which are divided into two groups: the former five events(A–E) have a total rainfall amount of 20 mm, while thelatter five events (F–L) of 100 mm. Each rainfall event has
different duration and different intensity, ranging between
2 and 50 mm/h (Table 2); therefore, the total amount of
rainfall water in each event of the two groups is the same. It
is then possible to compare different behaviors of the soil
system, with respect to different rainfall intensities, forevents of each group. The behavior of the soil system, i.e.
pressure head distributions and crack closure dynamics(Figs. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11), is analyzed for eachconsidered rainfall event, to examine effects of different
rainfall intensities and durations, such as short highintensity storms and/or long low-intensity rains.
Pressure head distributions
Figures 2a, 3a, 4a, 5a, 6a show pressure head distributionsof rainfall events with total rainfall height of 20 mm(events A–E). It is possible to observe how slow waterflows into the fracture for low-intensity (2–5 mm/h) rains.
The maximum depth reached by infiltrating water is only
about 25 cm for event A (2 mm/h) (Fig. 2a). While events
B and C (5 and 10 m/h, respectively) have deeper corresponding infiltration fronts (Figs. 3a, 4a). Event D shows
infiltrating water, reaching the bottom of fine soil limit(Fig. 5a). Finally, event E (Fig. 6a) shows water reaching
the bottom of fractures quite quickly (after about 5 min),allowing for accumulation of water inside the fractures,
depending on rainfall duration, crack opening, and capillary forces defining the maximum height of water column.
Since for rainfall events F–J (with the total rainfall
height of 100 mm) rainfalls last longer than events A–E,
water can go deeper into fractures. During the lowest
intensity rain (2 mm/h, Fig. 7a), water slowly flows
through the fractures, reaching a maximum depth of 25 cm,
which is just slightly higher than at the end of event A. In
fact, a complete closure of fractures limits rainfall watersupply. While for event G (5 mm/h, Fig. 8a), water reaches

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Table 1 Parameters characterizing fractures and soil material (datafrom Carsel and Parrish 1988)
Fractures

Upper soil layer (loamy sand)Spacing, L (cm)80

Residual water content,
hres (m3m-3)

0.065

Half opening,d (cm)

0.2

Saturated water content,
hsat (m3m-3)

0.41

Thickness, s (cm)150

Initial pressure head winit
(cm)

-1000

Roughnesscoefficient,cs (m1/3 s-1)

1

Saturated hydraulicconductivity, Kms (cm/s)

1.2 9 10-3

a (van Genuchten 1980)(cm-1)

0.075

n (van Genuchten 1980)

1.89

Table 2 Rainfall events and inflow rates for half-fracture
Total
rainfallheight,H (mm)

Rainfallevent

Rainfallintensity,i (mm/h)Duration,T (h)Inflow rate to ahalf-fracture(cm3/s)

20 mm

A

2

10

0.09

100 mm

B

5

4

0.22

C

10

2

0.45

D

20

1

0.89

E

50

0.4

2.23

F

2

50

0.09

G

5

20

0.22

H

10

10

0.45

I

20

5

0.89

J

50

2

2.23

a depth of 105 cm, for events H, I, and J (Figs. 9a, 10a,11a), water reaches the bottom of the fractures, and starts
accumulating there.
Lateral adsorption of water into the soil matrix involves
initially only few centimeters of the soil near the interface.
Further infiltration depends on flow through the fractures,
rainfall intensity, rainfall duration, and soil swelling, which
may close fractures preventing further infiltration. Lateralabsorption increases for events with long low-intensity
rains (events A and B; Figs. 2a, 3a), for which almost theentire soil matrix between the fractures is moist at the endof rainfalls (Table 3). At the end of the rainfall event C(10 mm/h), due to its short duration, the lateral water
infiltration is less significant than the two preceding events,
i.e. A and B, while for events D and E horizontal water
absorption occurs for only few centimeters of the soil.
The lateral diffusion process increases for events F-J,
with longer rainfalls. It involves the entire soil matrix for
events F, G, and H (Figs. 7a, 8a, 9a). Water front reaches a
shorter distance for event I (Fig. 10a) and only about halfdistance for event J (Fig. 11a). The lateral infiltration into
the soil matrix depends on the rainfall duration and matrix
swelling, which leads to different water content distributions at the end of different rainfall events. The interface
between fractures and soil matrix reaches full saturation for
all rainfall events.
All rainfall events with total rainfall height of 20 mm(events A–E) averagely produce similar saturation of soil
matrix (13–22 %). The average saturation of the first
20 cm of the matrix reaches 77 % for event A and 53 % forevent B. High-intensity precipitations produce the average
saturation of the first 20 cm of the matrix at the end of theFig. 2 Pressure head distribution and crack closure dynamics for event A (i = 2 mm/h, T = 10 h)

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Fig. 3 Pressure head distribution and crack closure dynamics for event B (i = 5 mm/h, T = 4 h)Fig. 4 Pressure head distribution and crack closure dynamics for event C (i = 10 mm/h, T = 2 h)

rainfall corresponding to: 39 % for event C, 29 % for event
D, and 20 % for event E. Rainfall events with total rainfall
height 100 mm (events F–J) produce an average saturation
ranging between 17 % for the lowest intensity rainfall and
57 % for the highest-intensity rainfall. The average saturation of the first 20 cm of the soil matrix reaches 98 % forevents F and G. On the other hand, for high-intensity
precipitations, at the end of rainfall, it is equal to 81 % forevent H, 59 % for event I, and 39 % for event J.
Cracks closure dynamics
Cracks start closing at the soil surface and closure propagates towards the bottom depending on lateral water
adsorption. Crack narrowing is quite irregular for lowintensity rains (Figs. 2b, 3b, 4b, 7b, 8b, 9b), when soil

123

initially swells at the surface, inducing cracks closure,while deeper layers of soil are not yet reached by infiltrating water. For less intense rainfalls, a smaller amount ofwater goes deeper. The result is less intensive swelling
process and then fracture openings remain quite wide.
Event A shows quite intense horizontal infiltration at the
topsoil, where the swelling process causes a significant
crack closure (about 1.6 mm of the 2-mm half-fracture),
while at the bottom, the width of cracks remains equal tothe initial value (4 mm). On the other hand, for events F
and G, the swelling process causes a complete closure ofcracks after 14.4 h of rain precipitation.
The crack closure is similar for events B, C, and H(Figs. 3b, 4b, 9b, respectively). Although these eventsshow non-uniform swelling, involving only topsoil, there isno complete closure of fractures. As shown by Table 4, theEnviron Earth Sci (2014) 71:2911–2923

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Fig. 5 Pressure head distribution and crack closure dynamics for event D (i = 20 mm/h, T = 1 h)Fig. 6 Pressure head distribution and crack closure dynamics for event E (i = 50 mm/h, T = 24 min)crack closure is equal to 53 and 38 % of the initial crack
opening in the order for events B and C, while event H hasclosure rate higher than 83 % of the initial fracture width.
Event D (Fig. 5b) presents irregular swelling process,inducing a closure equal to only 28 % of the initial fracture
width, but involving a significant depth of soil matrix(down to a 125 cm depth). For intense precipitations (event
E, Fig. 6b), the swelling process is quite uniform for theentire soil depth; the closure of fractures is almost constantand crack walls remain quite parallel to the initial configuration. At the end of the rainfall event E, the crack
opening is 1.6 mm across the entire depth. Also events I
and J present fracture walls almost parallel to the initialstate. However, swelling is more intense and induces crackclosure equal to 59 and 39 %, respectively.

Capillary barrier
The capillary barrier remains active for rainfall events withtotal rainfall height of 20 mm (A–E), except for event E(50 mm/h, 24 min). In this event, the capillary barrier isbroken in the fractures after 270 s (corresponding to arainfall height of 3.7 mm) and in the matrix after 370 s(corresponding to the rainfall height of 5.1 mm). Even if asmall amount of water reaches the bottom of the fractures
for event D, this is not sufficient to break the capillarybarrier in both domains. Water through fractures of events
A, B, and C does not reach the bottom. The pressure headat the interface between the two soil layers does not change
and cannot reach the critical water entry pressure head of
the coarse sand (20 cm).

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Fig. 7 Pressure head distribution and crack closure dynamics for event F (i = 2 mm/h, T = 50 h)Fig. 8 Pressure head distribution and crack closure dynamics for event G (i = 5 mm/h, T = 20 h)

The capillary barrier remains active in events with thetotal rainfall height of 100 mm only for low-intensity
rains (events F–G). During event H, while the capillarybarrier remains active in the matrix, it breaks down in
the fractures after 9.3 h (a rainfall height of 93 mm).
During event I, the barrier breaks down for both
domains: after 2.7 h in the matrix and after 1.3 h in thefractures (corresponding rainfall heights are 54 and26.3 mm, respectively). Event J produces similar results
like event E, i.e. the capillary barrier breaks down in thefractures after 270 s and in the matrix after 370 s. The
breakdown of the capillary barrier is a fast process forhigh-intensity rainfalls, which severely affects water flow
toward groundwater resources, while it does not occur
for low-intensity rains, even if prolonged, such as inevents F and G.

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Swelling significantly affects the capillarity barrier
effect as it induces narrowing of fractures over time due tothe increase in water content of matrix. Low-intensity andlong rainfalls could induce a complete closure of thecracks, preventing water flow in the fractures, facilitatingwater retention in the fractures, and changing the pressure
head at the interface. For high-intensity and short precipitations, a closure of fractures is quite regular and involves
the entire fracture depth, thus the amount of water, retainedby fractures due to capillary forces, gradually increases. In
particular, this water varies from an initial value of 5.7 mm
to final value of 6.9 mm at the end of event E, when thehalf-fracture opening is reduced from 2 to 1.6 mm; to
9.2 mm at the end of event I, when half fracture is 1.2 mm
wide, and to 10.1 mm at the end of event J, when the halffracture width is equal to 1.25 mm.

Environ Earth Sci (2014) 71:2911–2923

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Fig. 9 Pressure head distribution and crack closure dynamics for event H (i = 10 mm/h, T = 10 h)Fig. 10 Pressure head distribution and crack closure dynamics for event I (i = 20 mm/h, T = 5 h)

Implications on slope stability
Stability of steep slopes of fine-grained soils is often
related to soil suction. Pressure head distribution variations
due to infiltration may induce a decrease in soil suction andshear strength and then the slope failure (Iverson 2000;
Tsai and Chen 2010). The introduced numerical modelshows how low-intensity and prolonged rains may increase
the water content of the soil matrix of the surface soil layer
close to saturation, which corresponds to pressure heads
close to zero. Instead, high-intensity and short precipitations cause only small changes of water contents of soil
matrix and less significant changes of pressure head. These
results could be noteworthy if related to slope stability andshallow landslides in fine textured and fractured deposits.

Using the infinite slope approach, which is a realistic
approach for soil landslides in surface soils up to a thickness of 150 cm, and assuming the failure surface at a depthh, the safety factor can be evaluated as follows:FS ¼c0 þ ðch cos2 b  uÞ tan /0ch sin b cos b

ð15Þ

where c0 is the cohesion (kPa), /0 is the friction angle, c isthe soil unit weight (kN/m3), b is the inclination of theslope, and u is the pore water pressure (kPa). If FS0 is thesafety factor before rainfall, the dimensionless parameter
is:
DFS ¼

FS  FS0
 100
FS0

ð16Þ

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Fig. 11 Pressure head distribution and crack closure dynamics for event J (i = 50 mm/h, T = 2 h)
Table 3 The maximum depth reached by water in the fractures, zmax,
the maximum horizontal distance reached by water in the matrix, dmax
(evaluated as the distance where h C hinit ? 0.05 (hsat - hinit)), andtime tbreak when water breaks through the capillary barrier for eachconsidered rainfall event

Total rainfall height, H (mm)

20

100

Event

A

B

C

D

E

F

G

H

I

J

Rainfall intensity, i (mm/h)

2

5

10

20

50

2

5

10

20

50

Duration, T (h)

10

4

2

1

24 min

50

20

10

5

2

zmax (cm)

25

70

95

150

150

35

105

150

150

150

dmax (cm)

39

26

20

14

10

40

40

39

28

19

tbreak (min)No breakNo breakNo breakNo break

4.5

No breakNo break560 (9.3 h)

78.8 (1.3 h)

4.5Table 4 Percentage of crack closure for each considered rainfall
event
Total rainfall height,
H (mm)

Event

Closure (%)

20

A (i = 2 mm/h, T = 10 h)83

B (i = 5 mm/h, T = 4 h)53

C (i = 10 mm/h, T = 2 h)

38

100

D (i = 20 mm/h, T = 1 h)

28

E (i = 50 mm/h, T = 24 min)19

F (i = 2 mm/h, T = 50 h)
G (i = 5 mm/h, T = 20 h)

100
100

H (i = 10 mm/h, T = 10 h)83

I (i = 20 mm/h, T = 5 h)59

J (i = 50 mm/h, T = 2 h)39

It represents the decrease in the safety factor due torainfall infiltration, expressed as a percentage and is ameaningful index assessing the influence of infiltration
phenomena on soil suction and on shear strength. Thisdimensionless parameter was chosen since its values are
more indicative than the safety factor itself, in showing the123variation of the stability conditions due to different rainfall
events. In fact, the single numerical value of the factor ofsafety is strictly related to geotechnical and geometricalparameters of the slope and it does not provide
immediately the evidence of variation of stability
condition due to rainfall.
To assess the decrease in slope safety, the dimensionlessparameter DFS is evaluated for a test slope with parameterssummarized in Table 5 and assuming the failure surface at
depths of 20 cm (DFS20), 50 cm (DFS50), 100 cm(DFS100), and 150 cm (DFS150). Results of these calculations are summarized by Table 6 and Figs. 12 and 13.
Low-intensity and prolonged rains can seriously affect thesafety factor at the failure surface. For events A and B(Fig. 12), and F and G (Fig. 13), the safety factor decreaseis more than 60 % (reaching 80 % for the longest rainfalls
F and G). More intense precipitations C, D, and E (Fig. 12)
do not significantly affect the stability of the soil for eachconsidered failure surface (DFS \ 40 %). At a depth of
50 cm, the slope stability seems to be affected mostly by
rainfalls with intermediate intensities and prolonged durations (events G and H, Fig. 13), inducing a decrease in theEnviron Earth Sci (2014) 71:2911–2923

2921

safety factor of more than 70 %. More intense precipitations (events I and J, Fig. 13) induce a decrease in thesafety factor between 30 and 50 %, slightly affecting thestability at each considered failure depth. In addition, themodel shows that fractures can strongly influence pressure
head changes depending on rainfall intensities and rainfallsof certain intensities and durations could cause a slope
failure.
A similar phenomenon was observed for the case of
Sarno landslides, which occurred on May 1998 in
Table 5 Properties andparameters considered in slope
stability calculations

c0 (kPa)5u0 (°)25c (KN/m3)

20

b (°)

45

Table 6 Safety factor decrease (DFSd) due to rainfall infiltration fordifferent rainfall events (A through J) at different depths (d) of a
failure surface
H (mm)

20

100

Event

A
(%)

B
(%)

C
(%)

D
(%)

E
(%)

F
(%)

G
(%)

H
(%)

I
(%)

J
(%)

DFS20

64

51

38

28

19

82

82

80

57

38

DFS50

0

0

34

28

19

0

75

79

57

38

DFS100

0

0

0

11

18

0

2

55

50

37

DFS150

0

0

0

0

18

0

0

0

43

37

Campania (south Italy), when a significant number ofdebris flows and debris avalanches were triggered by prolonged rainfalls. Landslides were triggered by sliding of
surface pyroclastic debris from the covering mantle, whichwere channeled as debris flows (Del Prete et al. 1998;
Fiorillo et al. 2001; Crosta and Dal Negro 2003; Mancarella
and Simeone 2012; Mancarella et al. 2012). Several
authors reported that these extreme instability phenomena
took place after a period of several days of non intense, butquite continuous rainfalls, which could not be characterized
by a relevant return period, to be considered hydrologically
exceptional, even if these events were anyway singular.
Landslides occurred at the beginning of the warm season,
when fine-textured soils were affected by vertical shrinkage cracks, likely affecting the infiltration process.
Prolonged low-intensity rains could be more dangerous
than intense ones in triggering a landslide in surface horizons, because they can produce lowering of pressure heads
to zero for about the first 20–50 cm of soil matrix, seriously
affecting shear strength. The use of a reliable infiltration
model is thus necessary to correctly evaluate the rainfall
threshold triggering slope instability.

Conclusions
This work presents an application of a new dual-permeability model, which simulates water infiltration into

Fig. 12 Decrease in the safety
factor (%) for rainfall events
A–E (the total rainfall heightequal to 20 mm), evaluatedassuming a slip surface at a
depth of 20 (DFS20), 50(DFS50), 100 (DFS100), and150 cm (DFS150)

Fig. 13 Decrease in the safety
factor (%) for rainfall events
F–J (the total rainfall heightequal to 100 mm), evaluatedassuming a slip surface at a
depth of 20 (DFS20), 50(DFS50), 100 (DFS100), and150 cm (DFS150)

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2922

unsaturated fractured swelling soils, using relatively simple
parameters (such as van Genuchten parameters) and relating matrix swelling with closure of fractures. The model isbased on the assumption of a progressive narrowing of
fractures and no vertical flow through the matrix. It also
simulates the presence of capillarity barrier effect. The
model was used to simulate infiltration processes into asandy loam with shrinking cracks for different values ofrainfall intensity and duration.
Results show that for high-intensity precipitations, vertical flow through fractures quickly reaches significant
depths, while for low-intensity precipitations, water flow is
initially limited to the upper 30–50 cm of the topsoil, due
to different inflow rates. Soil swelling is more uniform overdepth for intense precipitations than for low-intensity rains.
While in the earlier case fracture walls remain almost
parallel, in the latter case swelling is concentrated near the
topsoil and could induce a closure of cracks. The application of the model shows that for severe rainfalls, thecapillary barrier breaks down in the fractures in a very
short time, since infiltrating water reaches quickly thebottom.
Results additionally allow for investigating the relationship between the rainfall intensity and duration and theslope stability of surface fine-grained and fractured covers.
In particular, prolonged low-intensity rains are likely moredangerous than intense rains at triggering the failure of thesurface soil strata, due to very low suctions in the first
20–50 cm of the soil matrix, dramatically reducing theshear strength. The obtained results show that the proposedmodel can be a reliable tool for the evaluation of infiltration processes through this soil system. It can be particularly useful for evaluating the effects of infiltration
processes when a fine soil covers a coarse one.
Another interesting application of the model is the studyof the influence of rainfall on water content in surface soil
layers to evaluate more realistically and theoretically-based
rainfall thresholds for landslide activation. The implementation of a more specific infiltration model can contribute to the development of more reliable approaches tolandslide risk analysis. This shows how landslide susceptibility to rainfall can be influenced not only by rainfall
amount or intensity but also by the time distribution of
rainfall.

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