influences of soil water characteristic curve on rainfall-induced shallow landslides

ORIGINAL ARTICLE

Influences of soil water characteristic curve on rainfall-inducedshallow landslides

Tung-Lin Tsai

Received: 5 March 2010 / Accepted: 16 November 2010 / Published online: 1 December 2010

� Springer-Verlag 2010

Abstract The analysis of slope instability induced by

rainfall was usually performed using the main drying curve

as the measurement of the main wetting curve is a more

time-consuming and costly task. In this study, the influ-

ences of the main drying and wetting curves on rainfall-

induced shallow landslides are examined. Three designed

scenarios and a real case scenario are used to conduct this

examination. The prediction of shallow landslide occur-

rence is related to the main drying and wetting curves due

to the strong relation between groundwater pressure head

and hysteresis effect. The main wetting curve may have a

less minimum landslide-triggering rainfall amount and a

less rainfall duration threshold for landslide occurrence

than the drying wetting curve. For safety’s sake, an

underestimation of shallow landslide occurrence may be

produced by the commonly used main drying curve. In

addition, besides the shallow landslide occurrence, the

failure depth and the time to failure are also influenced by

the main drying and wetting curves. The hysteresis effect

should be taken into account for assessing rainfall-induced

shallow landslides.

Keywords Shallow landslides �Soil water characteristic curve �Main drying and wetting curves

List of symbols

C The change in volumetric water content per unit

change in pressure head

c0 Effective cohesion

dZ Water depth

dLZ Slope depth

FS Factor of safety

Gs The specific gravity of soil solid

IZ Rainfall intensity

Ks Saturated hydraulic conductivity

KL Hydraulic conductivity in lateral direction

(x and y)

Kz Hydraulic conductivities in slope-normal

direction (z)

RS The resisting stress

S The degree of saturation

SS The sliding stress

Sr The residual degree of saturation

Se The effective saturation

M Shape parameter

N Shape parameter

T Rainfall duration

ua Pore air pressure

uw Pore water pressure

Z The coordinates

r Total normal stress

w Groundwater pressure head

h Soil volumetric water content

hs Saturated volumetric water content

hr Residual volumetric water content

a Slope angle

/0 Effective friction angle

n Shape parameter

nd Shape parameter in main drying curve

nw Shape parameter in main wetting curve

T.-L. Tsai (&)

Department of Civil and Water Resources Engineering,

National Chiayi University, 300 Sefu Road,

Chiayi City 60004, Taiwan

e-mail: [email protected]

123

Environ Earth Sci (2011) 64:449–459

DOI 10.1007/s12665-010-0868-9

v Effective stress parameter

c The depth-averaged unit weight of soil

cw The unit weight of water

Introduction

Rainfall-induced landslides pose substantial threats to both

lives and property in many countries such as Japan, Hong

Kong, and Taiwan. The empirical rainfall threshold concept

and the physical-based model are two commonly used

approaches to the assessment of shallow landslides. The

empirical rainfall threshold concept can be very simply

applied to the assessment of rainfall-induced shallow land-

slides, but it seems to provide a minimal amount of insight

into the actually physical processes that trigger shallow

landslides. Therefore, to investigate in more detail landslide

occurrence, the physical-based model needs to be used.

With assumptions of steady or quasi-steady groundwater

table, and groundwater flows parallel to hillslope, various

physical-based models coupling the infinite slope stability

analysis with hydrological modeling (Montgomery and

Dietrich 1994; Wu and Sidle 1995; Borga et al. 1998) were

developed to assess shallow landslides induced by land use

and hydrological conditions. Iverson (2000) further devel-

oped a flexible modeling framework of shallow landslide

with the approximation of the Richards’ equation (1931)

valid for hydrological modeling in nearly saturated soil. This

led to the use of the linear diffusion-type Richards’ equation

for modeling rainfall infiltration. The extension version of

Iverson’s model was proposed to take variable rainfall

intensity into account for hillslope with finite depth (Baum

et al. 2002). Without the assumption of constant infiltration

capacity, the Iverson’s model was modified by amending the

boundary condition at top of hillslope to consider more

general infiltration process (Tsai and Yang 2006). Due to its

efficiency the physical-based model with the hydrological

modeling in nearly saturated soil (Iverson 2000; Baum et al.

2002; Tsai and Yang 2006) was commonly used for the

assessment of shallow landslides triggered by rainfall (Crosta

and Frattini 2003; Keim and Skauqset 2003; Frattini et al.

2004; Lan et al. 2005; D’Odorico et al. 2005; Tsai 2008).

It had been observed that the soil failures could be caused

not only by the increase of positive pore water pressure in

saturated soil due to the groundwater table rise, but also by

the loss in unsaturated shear strength due to the dissipation of

matric suction. The physical-based model with the hydro-

logical modeling in nearly saturated soil could not assess the

shallow landslides caused by the dissipation of matric suc-

tion, as the linear diffusion-type Richards’ equation rather

than the complete Richards’ equation was used for modeling

rainfall infiltration, and the effect of matric suction on the

unsaturated shear strength was not reliably considered to

examine the soil failures. Therefore, many physical-based

shallow landslide models using the complete Richards’

equation and the extended Mohr–Coulomb failure criterion

(Fredlund et al. 1978) valid for describing the shear strength

of unsaturated soil were developed (Anderson and Howes

1985; Tarantino and Bosco 2000; Collins and Znidarcic

2004; Tsai et al. 2008). However, in those physical-based

shallow landslide models, the unit weight of soil was

assumed constant rather than varying with the degree of

saturation. In addition, the shear strength of unsaturated soil

also remained unchanged in spite of the degree of saturation,

that is, the nonlinearity in the shear strength of unsaturated

soil was not taken into account (Gan et al. 1988; Escario et al.

1989; Vanapalli et al. 1996). Tsai and Chen (2010) further

developed the physical-based shallow landslide model with

considering the effect of degree of saturation on the unit

weight and the shear strength of unsaturated soil.

The slope instability can be caused by the decrease in shear

strength owing to the dissipation of matric suction resulting

from rainfall infiltration into soil slopes (Tsai et al. 2008; Tsai

and Chen 2010). The soil water characteristic curve (SWCC),

representing the relationship between suction (or pore water

pressure) and volumetric water content, is needed to model

rainfall infiltration into soils. The complex nature of the

liquid-phase configuration in an unsaturated porous medium

leads to the non-unique relationship between suction and

volumetric water content. This hysteresis effect displays a

volumetric water content that is less for a wetting process than

for a drying process at a given suction. The analysis of slope

instability induced by rainfall was usually performed using

the main drying SWCC due to the fact that the measurement

of the main wetting SWCC is a more time-consuming and

costly task (Lu and Likos 2004). It needs to be noted that the

soil is in wetting process during rainfall infiltration as it gains

moisture, and neglecting the main wetting SWCC could

affect the assessment of rainfall-induced shallow landslides.

In this study, the influences of the main drying and wetting

curves on rainfall-induced shallow landslides are examined

by three designed scenarios and a real case scenario. The

physical-based shallow landslide model developed by Tsai

and Chen (2010) is employed for this investigation. In the

used model, the rainfall-induced shallow landslides are ana-

lyzed by taking into account the unit weight and the shear

strength of soil as a function of degree of saturation.

Framework of shallow landslide modeling

Hydrological modeling

The unsteady and variably saturated Darcian flow of

groundwater in response to rainfall infiltration of hillslope

450 Environ Earth Sci (2011) 64:449–459

123

can be governed by the Richards’ equation with a local

rectangular Cartesian coordinate system (Bear 1972;

Hurley and Pantelis 1985) as follows:

owot

dhdw¼ o

oxKL wð Þ ow

ox� sin a

� �� þ o

oyKL wð Þ ow

oy

� ��

þ o

ozKz wð Þ ow

oZ

� �� cos a

� �ð1Þ

in which w is groundwater pressure head; h is volumetric

water content; a is the slope angle; and t is time. The

coordinate x points down the ground surface; y points

tangent to the topographic contour that passes through the

origin; and z points into the slope, normal to the x–y plane.

KL and Kz, a function of soil properties and w, are hydraulic

conductivities in lateral direction (x and y) and slope-nor-

mal direction (z), respectively.

For the case of shallow soil and a rainfall time shorter

than the time necessary for transmission of lateral pore

water pressure, Eq. 1 can be simplified in vertical direction

(Iverson 2000) as follows:

CðwÞowot¼ cos2 a

o

oZKzðwÞ

owoZ� 1

� �� ð2Þ

where CðwÞ ¼ dh=dw is the change in volumetric water

content per unit change in groundwater pressure head. The

elevation Z is vertically measured downward from a hori-

zontal reference plane that passes through the origin on the

ground surface.

The appropriate initial and boundary conditions are

needed for solving Eq. 2. For the initial steady state with

the groundwater table of dZ in vertical direction, the initial

condition in terms of groundwater pressure head can be

expressed as

wðZ; 0Þ ¼ ðZ � dZÞ cos2 a ð3Þ

For a hillslope soil with depth of dLZ measured in

vertical direction, the impervious and pervious boundary

conditions in terms of groundwater pressure head at bottom

of hillslope soil can be, respectively, written as

owoZ

dLZ; tð Þ ¼ cos2 a ð4Þ

and

wðdLZ; tÞ ¼ ðdLZ � dzÞ cos2 a ð5Þ

The ground surface of hillslope subjected to the rainfall

with intensity of Iz yields

owoZð0; tÞ ¼ �IZ=ðKZÞZ¼0 þ cos2 a if wð0; tÞ� 0 and t\T

ð6Þwð0; tÞ ¼ 0 if wð0; tÞ[ 0 and t\T ð7Þ

owoZð0; tÞ ¼ cos2 a if t [ T ð8Þ

where T is the rainfall duration. (KZ)Z=0 denotes the

hydraulic conductivity at ground surface of hillslope.

Equations 2–8 need to be numerically solved with an

iterative procedure. The groundwater pressure head at

ground surface of hillslope, i.e., w(0, t), is first obtained by

assuming that the infiltration rate equals the rainfall

intensity shown in Eq. 6. If w(0, t) is less than or equals

zero, that is, the ponding does not happen, the calculated

results are accepted. The computation moves forward to the

next time step. If the calculated w(0, t) is greater than zero,

that is, the ponding occurs, with neglecting the water depth

of overland flow (Hsu et al. 2002; Wallach et al. 1997; Tsai

et al. 2008) w(0, t) = 0 is used as boundary condition to

recalculate once more for the same time step.

In addition, for solving the Richards’ equation shown in

Eq. 2 the implicit finite-difference scheme (Celia et al.

1990) is used in conjunction with the function of soil water

characteristic curve proposed by van Genuchten (1980) as

follows:

S ¼ h� hr

hs � hr

¼ 1

1þ ½njwj�N

!M

ð9Þ

KZðhÞKs

¼ h� hr

hs � hr

� �1=2

1� 1� h� hr

hs � hr

� � 1M

" #M8<:

9=;

2

ð10Þ

where S is the effective degree of saturation; hs denotes the

saturated volumetric water content; hr represents the

residual volumetric water content; and Ks is the saturated

hydraulic conductivity. n, N, and M are shape parameters,

with M related to N by

M ¼ 1� 1

Nð11Þ

The conceptual and empirical models are two main

approaches used to describe the hysteresis effect in SWCC.

The conceptual models are originally based on the

independent domain theory. This theory assigns soil water

to domains and each domain wets and dries at different water

pressures regardless of the neighboring domains. The

modifications to the independent domain theory have been

proposed by taking into account interactions between

domains (Topp 1971; Mualem 1984). Based on an analysis

of SWCC shape and properties the empirical models use

closed-form expressions to represent hysteresis effect (Scott

et al. 1983; Jaynes 1984; Pickens and Gillham 1980). This

study adopts the formulation of Kool and Parker (1987) who

coupled the function of soil water characteristic curve pro-

posed by van Genuchten (1980) as shown in Eqs. 9 and 10

Environ Earth Sci (2011) 64:449–459 451

123

with an empirical model developed by Scott et al. (1983) to

describe the hysteresis effect in soils. The shape parameter N,

the saturated volumetric water content hs, and the residual

volumetric water content hr are assumed the same for main

drying and wetting curves, but the shape parameter n varies

in main drying and wetting curves, respectively, denoted as

nd and nw. Based on the analysis of different kinds of soils,

the relation of shape parameters nd and nw could be assumed

as nd ¼ nw=2 (Kool and Parker 1987). The empirical model

proposed by Kool and Parker (1987) had been applied to

analyze hysteresis effect on irrigation problems (Elmaloglou

and Diamantopoulos 2008; Kerkides et al. 2006) and tidal

capillary fringe dynamics in a well-sorted sand (Wener and

Lockington 2003).

Soil failure modeling

The shear strength of soil can be represented by the

extended Mohr–Coulomb failure criterion (Bishop 1954) as

follows:

s ¼ c0 þ ½ðr� uaÞ þ vðua � uwÞ� tan /0 ð12Þ

where c0 is the effective cohesion; /0 represents the

effective friction angle; r is the total normal stress; ua and

uw denote pore air pressure and pore water pressure,

respectively; ua–uw is the matric suction; and x is the

effective stress parameter. There are many experimental

evidences showing that the effective stress parameter is a

highly nonlinear function of the matric suction (Gan et al.

1988; Escario et al. 1989; Vanapalli et al. 1996). A

convenient and accurate representation of effective stress

parameter (Vanapalli and Fredlund 2000; Lu and Likos

2004) was proposed as follows:

Table 1 Hillslope conditions and hydrological conditions

Scenario

1

Scenario

2

Scenario

3

Soil depth, cm (dLZ) 210 210 280

Water depth, cm (dZ) 303 253 353

Slope angle, � (a) 35 35 33

Saturated hydraulic conductivity,

cm/s (Ks)

0.00123 0.00083 0.00323

Saturated volumetric water content

(hs)

0.47 0.45 0.48

Residual volumetric water content

(hr)

0.06 0.06 0.04

Fitting parameters (nw, N) 0.07, 1.8 0.05, 1.6 0.06, 1.7

Effective friction angle, � (/0) 30 30 28

Effective cohesion, N/m3 (c0) 2,700 2,500 2,500

Unit weight of water, N/m3 (cw) 9,810 9,810 9,810

Specific gravity of soil solid (Gs) 2.6 2.6 2.6

Rainstorm amount (mm) 600 400 600

Rainstorm duration, h (T) 15 20 20

0

50

100

150

200

t = 0t = 4 hrst = 12 hrst = 16 hrst = 24 hrst = 48 hrs

0

50

100

150

200

t = 0t = 4 hrst = 12 hrst = 17.1 hrst = 24 hrst = 48 hrs

-250 -200 -150 -100 -50 0 -250 -200 -150 -100 -50 0

-180 -160 -140 -120 -100 -80 -60 -40 -20 0 -180 -160 -140 -120 -100 -80 -60 -40 -20 0

0

50

100

150

200


0

50

100

150

200


Scenario 1 Scenario 1


gnitteWgniyrD

gnitteWgniyrD

Groundwater pressure heads (cm)

Dep

ths

(cm

)

Fig. 1 The simulated results of groundwater pressure heads from the main drying and wetting curves for scenarios 1 and 2


123

v ¼ h� hr

hs � hr

ð13Þ

Equation 13 can be further expressed as

v ¼ Se ¼S� Sr

1� Sr

ð14Þ

in which S denotes the degree of saturation, Sr is the

residual degree of saturation, and Se represents the effec-

tive saturation. It can be observed from Eqs. 9 and 13 that

there is indeed a highly nonlinear relation between effec-

tive stress parameter and matric suction. In addition, it can

be found from Eqs. 12 and 14 that the shear strength

depends on the degree of saturation. The effective stress

parameter ranges between zero and unity. If the soil is

saturated the effective stress parameter is identical to unity.

The effective stress parameter is zero when the soil has the

residual degree of saturation.

The infinite slope stability analysis is a preferred tool to

evaluate shallow landslide because of simplicity and

practicability (Montgomery and Dietrich 1994; Wu and

Sidle 1995; Borga et al. 1998; Iverson 2000; Morrissey

et al. 2001; Crosta and Frattini 2003; Collins and Znidarcic

2004; Tsai and Yang 2006; Tsai 2008). This concept is

generally valid for the case of landslide with a small depth

compared with its length and width. This assumption is

also compatible with that used for the hydrological mod-

eling in hillslope as shown in Eq. 2.

The soil failure is induced at depth Z where the sliding

stress is larger than the resisting stress due to friction and

0 20 40 60 80 100

0 20 40 60 80 100

-80

-70

-60

-50

-40

-30

-20

-10

0

main drying curvemain wetting curve

-50

-40

-30

-20

-10

0

Scenario 1

Z = 200 cm

Z = 185 cm

Time (hrs)

Gro

undw

ater

pre

ssur

e he

ad (

cm)

Scenario 2

Fig. 2 The simulated results of groundwater pressure heads at

Z = 200 and 185 cm, respectively, for scenarios 1 and 2

0

50

100

150

200

t = 0t = 4 hrst = 12 hrst = 16 hrst = 24 hrst = 48 hrsSF = 1

0

50

100

150

200

t = 0t = 4 hrst = 12 hrst = 17.1 hrs ( failure )t = 24 hrst = 48 hrsSF = 1

1.0 1.2 1.4 1.6 1.8 1.0 1.2 1.4 1.6 1.8

1.0 1.2 1.4 1.6 1.8 2.0 1.0 1.2 1.4 1.6 1.8 2.0

0

50

100

150

200

t = 0t = 4 hrst = 12 hrst = 17.9 hrs (failure)t = 24 hrst = 48 hrsSF = 1

0

50

100

150

200

t = 0t = 4 hrst = 12 hrst = 20 hrst = 24 hrst = 48 hrsSF = 1

1oiranecS1oiranecS


gnitteWgniyrD

gnitteWgniyrD

Z = 200 cm

Z = 185 cm

Dep

ths

(cm

)

Factors of safety

Fig. 3 The simulated results of

factors of safety from the main

drying and wetting curves for

scenarios 1 and 2


123

cohesion. Using the infinite slope stability analysis together

with the shear strength of soil given by Eq. 12, and

assuming that the pore air pressure is atmospheric, the

sliding stress SS can be given by

SS ¼ cZ cos a sin a ð15Þ

and the resisting stress RS can be written as

RS ¼ c0 þ cZ cos2 a tan /0 � cwwcv tan /0 � cwwp tan /0

ð16Þ

where cw represents the unit weight of water. c is the depth-

averaged unit weight of soil and can be expressed as

c ¼ 1

Z

ZZ

0

½ð1� hÞcwGs þ hcw� dZ ð17Þ

where Gs is the specific gravity of soil solid. In Eq. 16,

when the groundwater pressure head is negative, that is, the

soil is unsaturated, wc is equal to w which can be obtained

from Eq. 2, whereas wp is zero. On the contrary, wp is

identical to w, and wc is zero while the groundwater

pressure head is positive, that is, the soil is saturated.

The factor of safety FS defining as the ratio of resisting

stress to sliding stress can be written as

FS ¼ tan /0

tan aþ

c0 � cwwcv tan /0 � cwwp tan /0

cZ sin a cos að18Þ

Examinations

Three designed scenarios are first used to examine the

influences of the main drying and wetting curves on rain-

fall-induced shallow landslides. The bottom of shallow soil

is connected with a highly pervious and stiff stratum. The

hillslope conditions and the soil parameters of three

designed scenarios are adopted as shown in Table 1.

The simulated results of groundwater pressure heads with

respect to time from scenarios 1 and 2 are depicted in Fig. 1.

Figure 1 indicates that the main drying curve has a larger

propagation speed of wetting front than the main wetting

curve. This is because that with the same groundwater

pressure head at the initial state, the hydraulic conductivity

and the volumetric water content of the main drying curve

0 20 40 60 8013000

14000

15000

16000

17000

18000

resisting stress (main drying curve)sliding stress (main drying curve)resisting stress (main wetting curve)sliding stress (main wetting curve)

Time (hrs)

Stre

ss (

N/m

2 )

Fig. 4 The simulated results of sliding and resisting stress at depth of

185 cm for scenario 2

15500

16000

16500

17000

17500

18000

18500

19000

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

0 20 40 60 80 100

0 20 40 60 80 100

0 20 40 60 80 100

0.5

0.6

0.7

0.8

0.9

1.0

1.1


Time (hrs)

Eff

ectiv

e st

ress

par

amet

er

Dep

th-a

vera

ged

unit

wei

ght (

N/m

3 ) Fa

ctor

of

safe

ty

Fig. 5 The simulated results of effective stress parameter, depth-

averaged unit weight of soil, and factor of safety at depth of 185 cm

for scenario 2


123

are greater than those of the main wetting curve. In addition,

in comparison with the main wetting curve, the main drying

wetting curve also causes a fast redistribution of ground-

water pressure head after the end of rainfall. To further

investigate the hysteresis effect, the simulated results of

groundwater pressure heads with respect to time, respec-

tively, at depth of 200 cm for scenario 1 and at depth of

185 cm for scenario 2 are displayed in Fig. 2. It should be

-300 -250 -200 -150 -100 -50 0 50

0

50

100

150

200

250


-300 -250 -200 -150 -100 -50 0

0

50

100

150

200

250

t = 0t = 4 hrst = 10.3 hrst = 16 hrst = 24 hrst = 48 hrs

1.0 1.1 1.2 1.3 1.4 1.5 1.6

0

50

100

150

200

250

t = 0t = 4 hrst = 12 hrst = 21.5 hrs ( failure )SF = 1

1.0 1.1 1.2 1.3 1.4 1.5 1.6

0

50

100

150

200

250

t = 0t = 4 hrst = 10.3 hrs ( failure )SF = 1

Factors of safety

Dep

ths

(cm

) D

epth

s (c

m)


Drying

Drying

Wetting

Wetting

Z = 235 cm Z = 280 cm


groundwater pressure heads and

factors of safety from the main

drying and wetting curves for

scenarios 3

-100

-80

-60

-40

-20

0


14000

14500

15000

15500

16000

16500

17000

17500

18000

0 20 40 60 80 100 0 20 40 60 80 100

0 20 40 60 80 1000 20 40 60 80 100

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.98

1.00

1.02

1.04

1.06

1.08

1.10

1.12

Time (hrs)

Gro

undw

ater

pre

ssur

e he

ad (

cm)

Eff

ectiv

e st

ress

par

amet

er

Dep

th-a

vera

ged

unit

wei

ght (

N/m

3 ) Fa

ctor

of

safe

ty


groundwater pressure heads,

effective stress parameters,

depth-averaged unit weights of

soil, and factors of safety at

depth of 235 cm for scenario 3


123

first mentioned that, as shown below, the landslides are

triggered at depths of 200 and 185 cm for scenarios 1 and 2.

Figure 2 reveals that for scenario 1 the main wetting curve

has a larger maximum dissipation of matric suction than the

main drying curve, but scenario 2 yields a contrary outcome.

Therefore, the significance of the hysteresis effect to shallow

landslides induced by rainfall is expected.

The simulated results of factors of safety with respect to

time from scenarios 1 and 2 are shown in Fig. 3. It can be

observed from Fig. 3 that for scenario 1 the main wetting

curve triggers shallow landslide with a depth of 200 cm,

whereas the slope instability is not caused by the main drying

curve. On the contrary, for scenario 2 the main drying curve

rather than the main wetting curve induces shallow landslide,

and the failure depth is 185 cm. This consequence shows that

the main drying and wetting curves affect the prediction of

shallow landslide occurrence. The sliding and resisting

stresses with respect to time at depth of 185 cm for scenario 2

as shown in Fig. 4 together with the effective stress param-

eter, the depth-averaged unit weight, and the factor of safety

displayed in Fig. 5 are applied to analyze in detail the hys-

teresis effect on shallow landslide. Figure 4 indicates that the

main drying curve has larger resisting and sliding stresses

than the main wetting curve at the initial state due to a larger

depth-averaged unit weight of soil and effective stress

parameter as shown in Fig. 5. Before the wetting front

arrives, the resisting and sliding stresses increase with the

increase in depth-averaged unit weight of soil resulting from

rainfall infiltration. The resisting stress rapidly decreases

with the arrival of wetting front and then gradually increases

with the recovery of matric suction. The largest decrease in

resisting stress takes place while the maximum dissipation of

matric suction is reached. It must be noted that despite having

a larger maximum dissipation of matric suction than the

wetting curve, the main drying curve still causes a larger

resisting stress, but it triggers slope instability. This is due to

the fact that, in comparison with the main wetting curve, the

main drying curve simultaneously has a larger sliding stress

resulting from a larger depth-averaged unit weight of soil as

shown in Fig. 5.

Figure 6 depicts the simulated results of groundwater

pressure heads and factors of safety with respect to time from

scenario 3. Figure 6 indicates that the main drying and

wetting curves all induce shallow landslide, but their failure

depths and times to failure are quite different. The main

drying curve triggers slope failure at the depth of 235 cm at

21.3 h after the rainfall. The simulated results of ground-

water pressure head, depth-averaged unit weight of soil,

effective stress parameter, and factor of safety with respect to

time at depth of 235 cm from scenario 3 are depicted in

Fig. 7. Figure 7 shows that the main wetting curve causes a

larger maximum dissipation of matric suction together with a

less factor of safety than the main drying curve, but it does

not trigger slope failure at this depth. This is because that the

main wetting curve had already induced shallow landslide at

bottom boundary about 11 h earlier than the main drying

curve as shown in Fig. 6. The simulated results of ground-

water pressure head, depth-averaged unit weight of soil,

-52.5

-52.0

-51.5

-51.0

-50.5

-50.0

14500

15000

15500

16000

16500

17000

17500


0 20 40 60 80 100

0 20 40 60 80 100 0 20 40 60 80 100

0 20 40 60 80 1000.40

0.45

0.50

0.55

0.60

0.65

0.98

0.99

1.00

1.01

1.02

1.03

1.04

Time (hrs)

Fact

or o

f sa

fety

Eff

ectiv

e st

ress

par

amet

er

Dep

th-a

vera

ged

unit

wei

ght (

N/m

3 )

Gro

undw

ater

pre

ssur

e he

ad (

cm) Fig. 8 The simulated results of

groundwater pressure heads,

effective stress parameters,

depth-averaged unit weights of

soil, and factors of safety at

bottom boundary for scenario 3


123

effective stress parameter, and factor of safety with respect to

time at bottom boundary from scenario 3 are depicted in

Fig. 8. Figure 8 displays that with the pervious boundary

condition as shown in Eq. 5, the groundwater pressure head

and the effective stress parameter at the bottom of shallow

soil remain unchanged. Hence, as shown in Eq. 18 the var-

iation of factor of safety depends only on the depth-averaged

unit weight of soil.

It can be concluded from the discussion above that the

main drying and wetting curves not only influence the

shallow landslide occurrence but also affect the failure

depth and the time to failure. The rainfall thresholds (Tsai

2008) of three designed scenarios shown in Fig. 9 are

further applied to investigate hysteresis effect on shallow

landslide occurrence. Figure 9 reveals that contrary to

scenario 2, the minimum landslide-triggering rainfall

amounts of the main drying curve for scenarios 1 and 3 are

greater than those of the main wetting curve. In addition,

for scenarios 1 and 2 the main drying curve has less rainfall

duration thresholds for landslide occurrence than the main

wetting curve, whereas scenario 3 reaches a contrary out-

come. It is clear that for safety consideration, the com-

monly used main drying curve may underestimate the

occurrence of shallow landslides.

Demonstration

A real case scenario is further used to demonstrate the

influences of the main drying and wetting curves on rainfall-

induced shallow landslides. Typhoon Masa on 22 August

2005 triggered many shallow landslides in Shihmen Reser-

voir watershed, northern Taiwan. The shallow landslide

located near YuFeng elementary school is employed for this

600 800 1000 1200 1400 160010

12

14

16

18

20


300 400 500 600 700 800 9008

10

12

14

16

18

20

22

24

200 400 600 800 1000 12000

2

4

6

8

10

12

14

Rainfall amount (mm)

Rai

nfal

l dur

atio

n (h

rs)

Scenario 1

Scenario 2

Scenario 3

Fig. 9 The simulated results of rainfall thresholds for scenarios 1–3

-400 -300 -200 -100 0

-400 -300 -200 -100 0

0

50

100

150

200

250

300


0

50

100

150

200

250

300


Dep

ths

(cm

)

Drying

Wetting

Fig. 10 The simulated results of groundwater pressure heads from

the main drying and wetting curves for the real case scenario


123

demonstration. Based on rainfall data from stations in the

watershed, the hyetograph of the landslide site during

Typhoon Masa can be obtained using the inverse-distance

method (Yang et al. 2008; Tsai and Chen 2010). The hill-

slope conditions and the soil parameters are adopted from

hydrogeological surveying and soil mechanics laboratory

testing (Chen 2005; Yang et al. 2008) as follows:

dLZ = 313 cm, dZ = 460 cm, a = 348, /0 = 29.38, c0 =

2.46 kPa, Gs = 2.68, cw = 9,800 N/m3, Ks = 2.45 9

10-6 m/s, N = 1.2, nd = 0.03, hs = 0.40, and hr = 0.08.

Due to no information on wetting process, the relationship

nd ¼ nw=2 suggested by Kool and Parker (1987) is used in

this simulation. The simulated results of groundwater pres-

sure heads and factors of safety with respect to time from the

main drying and wetting curves are displayed in Figs. 10 and

11, respectively. It can be observed again from Fig. 10 that in

comparison with the main wetting curve, the main drying

curve has a larger propagation speed of wetting front.

Figure 11 shows that the main drying and wetting curves all

induce slope instability, and their failure depths are 190 and

313 cm, respectively. The measured failure depth is about

300 cm. For the simulation of this real case scenario, the

main wetting curve seems to provide a more reliable esti-

mation of failure depth than the main drying curve. However,

due to lack of data, the comparison of times to failure cannot

be conducted.

Conclusions

Many places around the world are threatened by rainfall-

induced landslides. Shallow landslides can be caused by

the dissipation of matric suction resulting from rainfall

infiltration. The soil water characteristic curve is needed

for modeling rainfall infiltration. The complex nature of the

liquid-phase configuration in an unsaturated porous med-

ium leads to hysteresis effect in soil water characteristic

curve. The rainfall-induced shallow landslides were usually

analyzed using the main drying curve because it is a time-

consuming and costly task to measure the main wetting

curve. However, the soil is in wetting process during

rainfall infiltration as it gains moisture. Neglecting the

main wetting curve may affect the assessment of rainfall-

induced shallow landslides. In this study, three designed

scenarios and a real case scenario are used to examine

hysteresis effect on rainfall-induced shallow landslides.

The outcome shows that the groundwater pressure head is

strongly affected by hysteresis effect, and the prediction of

shallow landslide occurrence depends on the selection of

the main drying and wetting curves. As compared with the

drying wetting curve, a less minimum landslide-triggering

rainfall amount and a less rainfall duration threshold for

landslide occurrence may be produced using the main

wetting curve. This reveals that the commonly used main

drying curve may underestimate shallow landslide occur-

rence. The main drying and wetting curves influence not

only the shallow landslide occurrence, but also the failure

depth and the time to failure. It can be concluded that

evaluating rainfall-induced shallow landslides should take

the hysteresis effect into consideration.

Acknowledgments This study was funded by the National Science

Council of the Republic of China under Grant No. NSC 98-2625-

M-415-001-MY2.

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1.0 1.2 1.4 1.6 1.8

1.0 1.2 1.4 1.6 1.8

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