9【Memoirs of Construction Engineering Research Institute Vol.65(papers)Nov.2023】

EVALUATION OF UNSATURATED SLOPE STABILITY UNDER RAINFALLINFILTRATION
Depu  Hu,  Shoji  Kato  and  Byeong-­Su  Kim

ＡＢＳＴＲＡＣＴ
Rainwater  infiltration  is  a  primary  cause  of  slope  failure  and  studying  the  behavior  of  unsaturated  slopes  subjected  to  wet-­dry  cycles  is  of  paramount  importance.  In  this  study,  the  stability  of  infinite  slopes  subjected  to  hydraulic  hysteresis  during  wet-­dry  cycles  using  three  typical  soils:  Toyoura  sand,  Hiroshimado  soil,  and  DL  clay   is  evaluated.   Initially,  the  soil  water  characteristic  curves  (SWCC)  as  well  as  the   suction  stress  characteristic  curves  (SSCC)  of  these  soils  were  analyzed.  The  study  then  factored  in  the  role  of  suction  stress  as  confining  pressure  to  assess  the  factor  of  safety  (FOS)  under  both  wet  and  dry  conditions.  The  results  suggest  that  the  effect  of  suction  stress  acting  as  confining  pressure  exhibits  the  peak  when  the  suction  matches  the  air-­entry  value  (AEV).  However,  as  one  moves  deeper  from  the  slope  surface,  the  difference  between  the  wetting  FOS  and  drying  FOS  diminishes  rapidly.  In  contrast,  for  soils  with  high  cohesion,  the  influence  of  hydraulic  hysteresis  is  minimal.  Consequently,  using  only  the  drying  process  performance  to  assess  the  entire  wet-­dry  cycle  may  underestimate  the  risk  for  failure,  especially  in  the  case  of  shallow  failures.

１． ＩＮＴＲＯＤＵＣＴＩＯＮ
Japan, an island nation, consists of four main islands. Approximately three-quarters of its land area is mountainous,
and storms are one of the most common disasters. According to the Ministry of Land1), soil disasters surpass 1,000 cases
annually. In 2019, this number spiked to a staggering 2,000 cases. The majority of these disasters occur between Juneand October, a period marked by highly unstable climatic conditions. Given the prevalence of high-intensity storms, it
is essential to assess the influence of rainwater infiltration on unsaturated slope disasters. This study focuses on three
representative soils: Toyoura sand, Hiroshima decomposed granite soil (Masado soil), and DL clay. It aims to explore
soil stability under varying rainfall conditions.
The soil-water characteristic curve (SWCC) stands as a pivotal property for unsaturated soils, denoting therelationship between soil moisture and matric suction. Typically, soil moisture increase will cause the decrease in soil
suction. Yet, even under similar conditions, the same soil might exhibit variations in soil moisture for identical suctionlevels (Fig.1)2). This is evident when comparing the SWCC during the wetting process to that of the drying process,where the former consistently presents lower values, a phenomenon termed as the SWCC hysteresis. Tao et al.3) delved
into the effects of hysteresis on the SWCC across cyclic drying and wetting cycles through the vantage points of porosity
and the internal friction angle. While theoretical frameworks suggest that hysteresis would invariably influence SWCC
and subsequent computations, its exploration remains scant. This oversight is often attributed to constraints incomputational models 4-6) and measurement methodology.
In parallel, recent studies have broached the hysteresis effect of SWCC on slope stability7,8). However, theseinvestigations primarily centered around singular soil types, rendering their findings potentially skewed by specific soil

10properties and thus not universally applicable. A salient factor in these studies is hydraulic conductivity (𝜅𝜅). For a given
soil, the drying process usually exhibits a higher 𝜅𝜅 value than that for the wetting process. Given consistent rainfall andtime duration, the resulting soil moisture derived from drying and wetting 𝜅𝜅 curves will differ, and this discrepancy isfurther nuanced by the soil type in question. Therefore, the simulated factor of safety (FOS) might be inaccurately gauged.
This paper seeks to dissect the variations between drying FOS and wetting FOS corresponding to identical saturationlevels, sidestepping the confounding factor of hydraulic conductivity.

Fig.1 Hysteresis of the SWCC

2． CALCULATION MODEL
2.1 EFFECT OF SUCTION STRESS AS THE CONFINING PRESSURE
The general equations for the shear strength of unsaturated soil can be derived as the extension of effective stress(i.e., skeleton stress) equation proposed by Bishop9):
𝜎𝜎 � = (𝜎𝜎 − 𝑢𝑢� ) + (𝑢𝑢� − 𝑢𝑢� )𝜒𝜒

(1)

where 𝜎𝜎 is the total normal stress; 𝑢𝑢� is the pore-air pressure; 𝑢𝑢� is the pore-water pressure; (𝑢𝑢� − 𝑢𝑢� ) is suction;(𝜎𝜎 − 𝑢𝑢� ) is the net stress perpendicular to the contact surface; 𝜒𝜒 is parameter related to soil saturation. On this basis,the  shear  strength  of  unsaturated  soil  is  given  through  Mohr’s  failure  criterion:�𝜏𝜏 = 𝑐𝑐 � + (𝜎𝜎 − 𝑢𝑢� ) tan 𝜑𝜑 � + (𝑢𝑢� − 𝑢𝑢� )𝜒𝜒
�where 𝑐𝑐 is the effective cohesion of soil; 𝜑𝜑 is the effective angle of internal friction angle.

(2)

As  mentioned  above,  various  prediction  models  can  be  used  to  compute  the  "effective  stress  parameter  χ"  defined  by  Bishop9), and the structures of formulas are generally similar. The main difference lies in the way to calculate thecontribution of suction to the shear strength of unsaturated soil. This study will use the model of Vanapalli et al. 10) to
calculate the shear strength of unsaturated soils:𝜏𝜏� = 𝑐𝑐 � + (𝜎𝜎 − 𝑢𝑢� ) tan 𝜑𝜑 � + (𝑢𝑢� − 𝑢𝑢� ) × �(tan 𝜑𝜑 � ) �𝜃𝜃� − 𝜃𝜃���𝜃𝜃� − 𝜃𝜃�

(3)

where 𝜃𝜃� is the current volumetric water content; 𝜃𝜃� is the residual volumetric water content. 𝜃𝜃� is the saturated

volumetric water content.

This model can well capture the altering characteristics of the shear strength when the volumetric water content or

saturation varies. However, it cannot simulate the altering state of shear stress well when the water content exceeds theresidual zone (𝜃𝜃� <𝜃𝜃� ). For this study, the key point is the impact of changes in soil water moisture on shear strength,
and the SWCC hysteresis effect does not involve the situation where the soil reaches the residual state and continues tolose water. Therefore, the model is available to predict the soil performance with the moisture changes. On this basis,
Karube and Kato11) summarized the contribution of suction to shear strength as suction stress. As shown:11𝑝𝑝� = 𝑆𝑆� ∗ 𝑠𝑠 =𝜃𝜃� − 𝜃𝜃�𝑆𝑆 − 𝑆𝑆𝑆𝑆∗ 𝑠𝑠 =∗ 𝑠𝑠𝜃𝜃� − 𝜃𝜃�100 − 𝑆𝑆𝑆𝑆

(4)

where 𝑝𝑝� is the suction stress; 𝑆𝑆� is the effective saturation; 𝑠𝑠 = 𝑢𝑢� − 𝑢𝑢� is the suction. 𝑆𝑆 is the current degree ofsaturation; 𝑆𝑆𝑆𝑆 is the residual degree of saturation.

On this basis, Kato et al.12) experimentally concluded that the suction stress (𝑝𝑝� ) in unsaturated soil can also be

considered as the part of the confining pressure to further increase the shear strength rather than only acting as thecohesion component (𝑐𝑐 � ).

In detailly, if the calculation is conducted according to Eq. (3), the suction stress will be only considered as a part ofthe cohesion. In this case, when performing the unconfined compression test on the unsaturated soil, the Mohr's circle
should be tangent to the Y axis (like unconfined compression test for saturated soil in Fig.2a). However, according to
Kato et al.12) experiment results of the unconfined compression test on unsaturated soil, the distance appears between theexperimentally obtained Mohr's circle and the Y axis (Fig.2b). And Kim et al.13) proved that this distance is exactly equal
to the suction stress (𝑝𝑝� ) through geometric methods.

Therefore, it can be considered that the 𝑝𝑝� in unsaturated soil effects not only on a part of the cohesion, but also

contributes to the shear strength as a part of the confining pressure, which is recognized under low confining pressure
condition. Then the formula can be modified as:𝜏𝜏� = 𝑐𝑐 � + (𝜎𝜎 − 𝑢𝑢� + 𝑝𝑝� ) tan 𝜑𝜑 � + (𝑢𝑢� − 𝑢𝑢� ) �(tan 𝜑𝜑 � ) �𝑆𝑆 − 𝑆𝑆���
100 − 𝑆𝑆�(5)

However, the contribution of suction stress to the FOS has rarely been studied. Therefore, under the condition of 𝑝𝑝�

acting as confining pressure, the influence of wet-dry cycle on FOS deserves further discussion.
τ

τ

𝑐𝑐 �

𝑐𝑐(�����)

0

𝑞𝑞�

𝜎𝜎

𝑝𝑝�

0

𝑝𝑝�

𝑝𝑝� + 𝑞𝑞�𝝈𝝈Fig.2a Unconfined compression test for saturated

Fig.2b Unconfined compression test for unsaturated

soil

soil

α

Fig.3 Diagram of an infinite slope

2.2 FACTOR OF SAFETY OF UNSATURATED INFINITE SLOPE
This paper will analyze the assumed homogeneous infinite unsaturated slope (Fig. 3). When the sliding surface is in
the soil layer with depth H, its FOS can be expressed as14):

12

𝐹𝐹� =

𝑐𝑐� + (𝜎𝜎 − 𝑢𝑢� ) tan 𝜑𝜑 �𝛾𝛾� 𝐻𝐻 sin 𝛼𝛼(6)where 𝐹𝐹� is the safety factor; 𝑐𝑐� is the total cohesion of soil, including cohesion of saturated part 𝑐𝑐 � and thecontribution of suction stress to cohesion (𝑝𝑝� tan 𝜑𝜑 � ) in the unsaturated part; 𝛾𝛾� is the volumetric weight of the soil;

𝐻𝐻 is the depth of sliding surface below the ground surface; 𝛼𝛼 is the angle of the slope. Then, as described in Eq. (3),since there is another suction stress as an additional confining pressure, the formula is transformed into:𝐹𝐹� =𝑐𝑐� + (𝜎𝜎 − 𝑢𝑢� + 𝑝𝑝� ) tan 𝜑𝜑 �𝛾𝛾� 𝐻𝐻 sin 𝛼𝛼(7)𝜎𝜎 − 𝑢𝑢� = 𝛾𝛾� 𝐻𝐻 cos 𝛼𝛼(8)And for the theoretically infinite slope, the mutual forces between the slices can be ignored, and the normal stressperpendicular to the slope all comes from the component of gravity, that is:
Therefore, Eq. (7) can be rewritten as:
𝐹𝐹� =

𝑐𝑐�
tan 𝜑𝜑 � 𝑝𝑝� tan 𝜑𝜑 �++𝛾𝛾� 𝐻𝐻 sin 𝛼𝛼 tan 𝛼𝛼 𝛾𝛾� 𝐻𝐻 sin 𝛼𝛼(9)2.3 ANALYSIS OF LIMIT EQUILIBRIUM STATE

For the conduction of the theoretical evaluation on general finite slope, the force analysis in the limit equilibrium
state is the popular methods, and the corresponding safety factor can be computed according to the force equilibrium or
moment equilibrium. Compared with the formula calculation method of Cho and Lee14), it has a higher degree of
flexibility. Since the limit equilibrium analysis method is not an assumed infinite slope, the required number of soil slices
can be adjusted according to the actual slope size. However, due to its complex calculation, computer software is usuallyused for the process.
Traditionally, flow net was one of the most commonly approach to solve seepage problems. However, theconstruction of flow net is not a trivial task. This study will use SEEP/W and SLOPE/W in Geostudio to perform accurate
seepage numerical analyzes15,16). For analysis of rainfall penetration problems through SEEP/W, slope geometry,boundary conditions, and parameters for SWCC, soil material, and hydraulic conductivity are required. In the simulationof slope behavior under rainwater infiltration, as an input boundary condition, flux could be controlled on the slope
surface. When rainfall occurs, runoff is simulated with the provision of zero constant water pressures to slope surface.
And SEEP/ W outputs the distribution of pore-water pressure at different position points and time points. Further, Limit
equilibrium method is used in SLOPE/W to determine the FOS, then find the critical slip surface and the minimum FOS
with time. The basic calculation logic is as follows:
According to the definition of FOS: 𝐹𝐹 = 𝜏𝜏� ⁄𝜏𝜏, the reduced shear strength of soil slice (mobilized shear force) canbe given as:𝜏𝜏� =𝛽𝛽𝜏𝜏� 𝛽𝛽= [𝑐𝑐� + (𝜎𝜎 − 𝑢𝑢� + 𝑝𝑝� ) tan 𝜑𝜑 � ]
𝐹𝐹
𝐹𝐹

(10)

where, 𝜏𝜏� is the mobilized shear stress; 𝜏𝜏� is the shear strength; 𝜏𝜏 is the shear stress; 𝐹𝐹 is the factor of safety; 𝛽𝛽 is
the projection of the width of the soil slice on the bottom of the slip surface. 𝜎𝜎� =��is the average normal stressperpendicular to the sliding surface. Therefore, the equilibrium equation of each soil slice can be written according to

the moment equilibrium and force equilibrium respectively:
Taking the circle center of the sliding surface as the reference for moment equilibrium:
𝑊𝑊𝑥𝑥� + 𝐸𝐸� 𝑥𝑥�� − 𝐸𝐸� 𝑥𝑥�� + 𝑋𝑋� 𝑥𝑥�� − 𝑋𝑋� 𝑥𝑥�� − 𝜏𝜏� 𝑥𝑥�� − 𝑁𝑁𝑥𝑥� = 0

Force equilibrium in the horizontal direction:

𝐸𝐸� − 𝐸𝐸� − 𝜏𝜏� cos 𝛼𝛼 − 𝑁𝑁 sin 𝛼𝛼 = 0

(11)

(12)

13

where: 𝑊𝑊 is the self-weight of each soil slice; 𝑁𝑁 is the normal force on the base of the slice; 𝑥𝑥� is the distance fromeach force to the circle center of the slip surface; 𝐸𝐸� ，𝐸𝐸� ，𝑋𝑋� ，𝑋𝑋� are the horizontal compression force and vertical

shear force caused by the soil slices adjacent to the selected soil slice, noting that the mark "L" and "R" stand for left andright, respectively. However, this is only the force situation of one soil slice. Since all soil slices need to be summed insubsequent calculations, the forces E and X between slices can be considered as the state of mutual cancellation
respectively under the condition of no external force.
Substituting Eq. (11) and Eq. (12) into Eq. (10), the two expressions of moment equilibrium and force equilibriumof safety factor can be written in the form of Eq. (13) and Eq. (14):
𝐹𝐹� =

𝐹𝐹� =

∑ 𝛽𝛽𝛽𝛽[𝑐𝑐� + (𝜎𝜎 − 𝑢𝑢� + 𝑝𝑝� ) tan 𝜑𝜑 � ]∑ 𝑊𝑊𝑥𝑥� − ∑ 𝑁𝑁𝑥𝑥�

∑ 𝛽𝛽 cos 𝛼𝛼 [𝑐𝑐� + (𝜎𝜎 − 𝑢𝑢� + 𝑝𝑝� ) tan 𝜑𝜑 � ]∑ 𝑁𝑁 sin 𝛼𝛼

(13)
(14)

In actual cases, the shear forces X and normal stress E applied to the selected soil slice are hard to be solved, and itis necessary to adopt some other methods to indirectly calculate the average normal stress perpendicular to the contact
surface (𝑁𝑁), such as through the force balance in the vertical direction for further analysis. This research will adopt thesimplified Bishop method to obtain the factor of safety. And the normal stress E and shear force X between soil slices
can be ignored. Therefore, the normal stress can be considered as 𝑁𝑁 = 𝑊𝑊 cos 𝛼𝛼.

It is worth noting that if the moment equilibrium equation and force equilibrium equation are applied to the infinite

slope: for Eq. (13) and Eq. (14), the "circle center" of the slip surface on an infinitely slope can be considered as a point
located at infinity perpendicular to the contact surface. Therefore 𝑥𝑥� = 0, and Eq. (13) and Eq. (14) are consistent with
Eq. (9).

Note that Eq. (3) is used to analyze the slope stability in SEEP/W and SLOPE/W without considering the contributionthat suction stress acts as the confining pressure. That, 𝐹𝐹� = 𝐹𝐹(𝑠𝑠) + 𝐹𝐹(𝑝𝑝� ) can be used to modify the FOS:
𝐹𝐹(𝑠𝑠) =tan 𝜑𝜑 �𝑐𝑐�
+𝛾𝛾� 𝐻𝐻 sin 𝛼𝛼 tan 𝛼𝛼𝐹𝐹(𝑝𝑝� ) =𝑝𝑝� tan 𝜑𝜑 �𝛾𝛾� 𝐻𝐻 sin 𝛼𝛼

(15)
(16)

where 𝐹𝐹� is the FOS considering 𝑝𝑝� as the confining pressure; 𝐹𝐹(𝑠𝑠) is the FOS calculated by geotechnical simulation
software, Geostudio; and 𝐹𝐹(𝑝𝑝� )  is the correction value of FOS that needs to be calculated additionally.

3． SOIL PARAMETERS AND DATA PROCESSING

In this study, the selected soil objects are Toyoura sand, Masado soil, and DL clay. Hatakeyama et al.17) carried out
continuous pressurization method on the three kinds of soils to obtain the experimental soil-water characteristic curves
and the soil physical parameters are shown in Table 1.
These three kinds of soil are three representative sand, clayey soil and silt respectively. The particles of Toyoura sandare relatively large in size, and the average diameter is generally around 0.2mm, which can be considered as a soil withpoor water retention performance; DL clay is just the opposite that average particle size distribution (PSD) is nearly
0.01mm, and the water retention performance is much stronger than that of Toyoura sand; Masado soil is a fine-grainedmaterial with a wide PSD.
Therefore, the infinite slope composed of these three soils will be assumed and conduct the theoretically analysis to
explore the influence of the wet-dry cycle on slopes constituted by different material.
The fitting parameter for SWCCs of the wetting process and drying process are calculated by extracting the result
obtained by Hatakeyama17) and using the SWCC model of Van Genuchten4):

14

�

��
�
1
𝑆𝑆� = ��
�
1 + [𝑎𝑎(𝑢𝑢� − 𝑢𝑢� )](17)

where: 𝑎𝑎 and 𝑛𝑛 are fitting parameters; 𝑎𝑎 is approximately the reciprocal of the air entry value; 𝑛𝑛 is related to thevoid distribution. Combined with Eq. (3), the relationship between suction and volumetric water content can be obtained:
�

��
�
1
𝜃𝜃� = ��∗ (𝜃𝜃� − 𝜃𝜃� ) + 𝜃𝜃��[𝑎𝑎(𝑢𝑢)]1+
� − 𝑢𝑢�(18)

The fitting result of SWCC are shown in Fig.4. The suction stress characteristic curve (SSCC), that is, the relationshipbetween suction stress (𝑝𝑝� ) and suction18,19) are shown in Fig.5. The fitted parameters results are shown in Table 1.
Table 1 parameters of soils

Testedsoils

Particles

Uniformity

Mean Grain

Density

Coefficient

Diameter�Toyourasand
Masadosoil
DL clay𝜌𝜌�   (𝑔𝑔⁄𝑐𝑐𝑐𝑐� )𝑎𝑎�   (𝑘𝑘𝑘𝑘𝑘𝑘)

𝑎𝑎�   (𝑘𝑘𝑘𝑘𝑘𝑘)

𝑛𝑛�

𝑛𝑛�

(𝑔𝑔⁄𝑐𝑐𝑐𝑐 )
2.641

𝑈𝑈�

1.49

𝐷𝐷�� (𝑚𝑚𝑚𝑚)
0.172

1.5

0.25

0.44

5

4.1

2.614

46.1

0.484

1.08

2.6

5.12

1.8

1.6

2.651

4.58

0.0171

1.5

0.03

0.04

2.33

2.36

Note: 𝑎𝑎� , 𝑛𝑛� , 𝑎𝑎� , 𝑛𝑛�   𝑎𝑎𝑎𝑎𝑎𝑎  𝑡𝑡ℎ𝑒𝑒  𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓  𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝  𝑜𝑜𝑜𝑜  𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑  𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝  𝑎𝑎𝑎𝑎𝑎𝑎  𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤  𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝, 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟.
40

50

Degree of saturation

Degree of saturation

35
30
25
20
15
10
5
0
0.01

Fitted drying SWCC
Fitted wetting SWCC
Experiment drying data
Experiment wetting data
0.1

1

40

30

20

10

Fitted drying SWCC
Fitted wetting SWCC
Experiment drying data
Experiment wetting data

0

10

100

1000

Suction (kPa)

0.1

1

10

100

1000

Suction (kPa)

Fig.4a  Fitting  SWCC  for  Toyoura  sandFig.4c  Fitting  SWCC  for  DL  clay

4． RESULT AND DISCUSSION
Degree of saturation

70

The  manual  calculation  for  the  factor  of  safety  of  the  60homogeneous   two-­dimensional  infinite  slope  will  be  50

conducted  firstly. Set  the  distance  between  the  selected  slip  surface  and  the  ground  surface  denoted  as  H.  And  the  40soil  parameters  of  the  slope  are  the  same  as  mentioned  

30

20

10
0.01

above.  Then  compare  the  results  of  the  four  cases  in  Table  2:  Case  1:  consider  suction  stress  𝑝𝑝�    only  acts  as  cohesion  in  Fitted drying SWCC
Fitted wetting SWCC
Experiment drying data
Experiment wetting data
0.1

1

10

Suction (kPa)

Fig.4b  Fitting  SWCC  for  Masado  soil

100

1000

drying  process;;  Case  2:  consider  suction  stress  𝑝𝑝�      only  acts  as  cohesion  in  wetting  process;;  Case  3:  consider   𝑝𝑝�   contributing  to  both  cohesion  and  confining  pressure  in  drying  process;;  Case  4:  consider   𝑝𝑝�    contributing  to  both  cohesion  and  confining  pressure  in  wetting  process.

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Table  2  Marks  for  different  cases
Drying  SWCC  Wetting  SWCC

𝑝𝑝� only acts as cohesion (Eq.3)
CASE  1
CASE  2𝑝𝑝� contributes to confining pressure (Eq.5)
CASE  3

CASE  4

4.1 EFFECT OF SUCTION STRESS ON FOS
2.4

infinite  slope  under  the  influence  of  different  factors.  
Here,  to  explore  the  behavior  of  shallow  slopes  firstly,  the  2.2

surface   was  set  to  1  meter;;  The  angle  of  inclination  of  

2.5

2.0

FOS

distance  between  the  selected  slip  surface  and  the  ground  3.0

Drying SSCC
Wetting SSCC
Case 1Case 2
Case 3
Case 41.5
2.0

slope  is  set  to  26°;;  Eq.  (6)  and  Eq.  (7)  are  used  to  calculate  1.0the  FOSs   in   the  case  1,2  and  case  3,4  in  Table   2,  

0.5

1.8

respectively.  The  plotted  profiles  are  shown  in  Fig.5.
The  trend  of  the  relationship  curves  between  FOS  and  Suction stress (kPa)The  example  (Fig.3)   is  to  examine  the  theoretical  

0.0
0

2

4

6

8

10

12

14

Suction (kPa)suction  is  almost  identical  to  SSCCs  for  all  3  soils,  indicating  that  the  suction  stress  plays  a  crucial  role  in  the  Fig.5a  Relationship  between  FOS  and  suction  for  FOS.  For  the  soils  with  narrow  PSD  such  as  Toyoura  sand  Toyoura  sand

2.95

𝐹𝐹𝑂𝑂𝑂𝑂�����      will  increase  with  an  increase  in  suction  initially,  then  followed  by  a  decrease  after  the  suction  0.3

adding  another  suction  stress  as  the  confining  pressure  

2.85
0.2
2.80

based  on  the  Eq.  (6),  the  gap  caused  by  hysteresis  Drying SSCC
Wetting SSCC
Case 1Case 2
Case 3
Case 42.75(between   𝐹𝐹𝑂𝑂𝑂𝑂�����    and   𝐹𝐹𝑂𝑂𝑂𝑂����� )  will  further  increase  with  the  consideration  of   𝑝𝑝� acting as confining pressure.  

0.4

2.90

FOS

being  greater  than  AEV.  Moreover,  since  the  Eq.  (7)  

0.5

3.00

confining  pressure,  the  gap  between   𝐹𝐹𝑂𝑂𝑂𝑂�����      and  Suction stress (kPa)and  DL  clay,  without  considering  suction  stress  as  

0.1

2.70

0.0
0.0

0.5

1.0

1.5

2.0

Suction (kPa)The  stress  corresponding  to  AEV  can  be  considered  as  the  critical  value  where  the  impact  of  hysteresis  peaks.  For  Fig.5b  Relationship  between  FOS  and  suction  for  the  clay  such  as  Masado  soil,  on  the  other  hand,  FOSs  of  Masado  soil
7than  AEV,  and  the  critical  value  of  FOS  or  suction  stress  6could  be  determined  when  suction  is  greater  than  AEV.
Specifically,  without  considering  suction  stress  as  and   𝐹𝐹𝑂𝑂𝑂𝑂�����    for  Toyoura  sand  and  DL  clay  are  0.1  and  1.1,   respectively.  As  adds   the   suction  stress  as  the  confining  pressure,  the  gaps  (between   𝐹𝐹𝑂𝑂𝑂𝑂����� and𝐹𝐹𝑂𝑂𝑂𝑂����� )  will  increase  to  0.3  and  1.6  respectively.  For  Masado  soil,  however,  even  the  maximum  gap  between  𝐹𝐹𝑂𝑂𝑂𝑂�����    and   𝐹𝐹𝑂𝑂𝑂𝑂�����    is  less  than  0.1.  

5FOS

confining  pressure,  the  peak  of  gap  between   𝐹𝐹𝑂𝑂𝑂𝑂�����   100

Drying SSCC
Wetting SSCC
Case 1Case 2
Case 3
Case 4

10

4

3

1

Suction stress (kPa)each  case  will  remain  constant  as  the  suction  is  greater  

2

1
0.1

1

10

100

0.1
1000

Suction (kPa)Fig.5c  Relationship  between  FOS  and  suction  for  DL  clay

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55m

5m

Ground surface

Slip surfaces
110m

5m

5m

Fig.6  The  model  used  for  the  simulation
Among  several  factors,  soil  properties  can  be  considered  as  one  of  the  most  important  factors.  Due  to  low  AEV  of  the  selected  Masado  soil,  which  is  only  0.68kPa,  the  suction  stress  of  Masado  soil  is  limited  (maximum  value  of  suction  stress  is  only  0.4kPa).  Furthermore,  the  cohesion  (𝑐𝑐 � )  of  masado  soil  is  set  to  5kPa  in  the  calculation  of  shear  strength.  

Therefore,  compared  with  cohesion,  the  influence  of  the  changes  in  suction  stress  on  FOS  is  diluted.  For  Toyoura  sand  and  DL  clay,  the  cohesion  is  generally  low,  and  it  can  be  2.4

directly  set  to  0.  Hence  the  influence  of  suction  stress  on  2.2

another   𝑝𝑝�      acting  as  confining  pressure  will  further  amplify  the  impact  of  the  hysteresis,  and  this  amplification  would  be  affected  by  soil  cohesion  (𝑐𝑐 � ).

4.2 EFFECT OF CASES ON FOS AT
DIFFERENT DEPTH
To  further  explore  the  impact  of  SWCC  hysteresis  at  different  depths,  the  geotechnical  simulation  software,  Geostudio,  will  be  used  to  simulate  the  failure  behavior  of  the  infinite  slopes.  The  established  model  is  shown  in  Fig.6.  Where  the  solid  line  in  the  model  is  the  ground  surface,  and  five  dotted  lines  represent  five  cases  of  

1.8

0

6

15

20

Elapsed Time (d)2530Drying FOS
Wetting FOS

5

RainfallNo Rainfall
H=1m

3

and  go  vertically  upwards,  to  simulate  the  sliding  surface  1parallel  to  the  slope  and  close  to  the  bottom.

10

sand

2

influence  on  the  initial  state,  the  water  level  line  is  set  

5

H=15m

Fig.7a Relationship between FOS and time for Toyoura

used  to  make  the  soil  slices  possess  the  same  thickness  days,  then  continuous  drainage  for  20  days.  To  reduce  the  Drying FOS
Wetting FOS

1.2

respectively.  Then,  the  “Fully  specify  slip  surface”  analysis:  the  rainfall  condition  is  set  to  be  50mm/h  for  10  

H=5m
H=10m

1.4

4

of  the  infinite  slope16).   As  hypothesis  for  theoretical  

H=3m

1.6

H=10m  and  H=15m  from  the  ground  surface,  command  and  the  “Tension  crack  line”  command  can  be  

H=1m

2.0

FOS

sliding  surfaces  with  distances  of  H=1m,  H=3m,  H=5m,  No Rainfall

FOS

FOSs  is  obvious.  Thus,  for  all  soils,  consideration  of  Rainfall

H=3m
H=5m
H=10m
H=15m

0
0

5

10

15

20

Elapsed Time (d)2530

Fig.7b  Relationship  between  FOS  and  time  for  Masado  
soil

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Note  that  the  study  is  to  explore  the  difference  of  wet  3.5and  dry  FOS  under  the  same  water  content.  And  for  soils,  3.0

different  soil  moisture  using   𝜅𝜅�    and   𝜅𝜅�    even  under  the  same  rainfall  infiltration.  Therefore,  simulation  with  the  real  soil  parameter  may  cause  greater  interference.   To  mitigate  this  interference,  in  the  simulation,  the   𝜅𝜅�    and  𝜅𝜅�    of  the  same  soil  are  set  to  the  same  constant  value.  

Simultaneously,   𝜅𝜅   is  properly  tuned  to  adjust  the  rate  of  rainwater  infiltration,  so  that  the  difference  of  FOSs  under  FOSgenerally,  hydraulic  conductivity   (𝜅𝜅  )  in  drying  process  (𝜅𝜅� )  and  wetting  process  (𝜅𝜅� )  are  different.  It  may  cause  No Rainfall

Rainfall

H=1m

2.5
2.0

H=3m
H=5m
H=10m

1.5
Drying FOS
Wetting FOS

1.0
0

5

10

H=15m
15

20

Elapsed Time (d)2530

Fig.7c  Relationship  between  FOS  and  time  for  DL  clay

different  cases  can  be  observed  perceptibly.  Under  thesame  rainfall  conditions,  the  relationship  curve  between  FOSs  and  elapsed  time  simulated  through  SWCC  in  drying  process  (drying  SWCC)  and  wetting  process  (wetting  SWCC)  can  be  obtained  (Fig.  7).  Note  that  Eq.  (13)  and  Eq.  (14)  are  adopted  to  modify  the  FOS  value  with  consideration  of   𝑝𝑝�    acting  as  confining  pressure.

In  terms  of  the  relationship  curve,  in  the  rainfall  stage,  as  the  saturation  increases,  the  FOS  simulated  by  the  wetting  SWCC  and  drying  SWCC  of  the  three  types  of  soils  all  show  a  decrease  trend.  In  the  wetting  process,  the  FOS  obtained  from  wetting  SWCC  (wetting  FOS)  is  always  lower  than  FOS  obtained  from  drying  SWCC  (drying  FOS),  and  the  gap  between  wetting  FOS  and  drying  FOS  show  the  decrease  with  an  increase  in  soil  moisture.  Thus,  the  impact  of  SWCC  hysteresis  on  the  FOS  is  declined  as  the  slope  tends  to  be  saturated.  The  results  are  consistent  with  the  conclusion  obtained  from  the  theoretical  calculation.
According  to  Fig.  7,  when  the  sliding  surface  is  closed  to  ground  surface,  the  larger  difference  between  the  drying  FOS  and  the  wetting  FOS  would  be  observed.  Specifically,  when  the  distance  between  the  sliding  surface  and  the  ground  surface  is  1m  (H=1m),  the  maximum  FOS  gaps  of  Toyoura  sand,  Masado  soil  and  DL  clay  are  about  10%,  40%  and  15%,  respectively.  And  when  the  H  reaches  3  meters,  the  gap  will  drastically  reduce  to  3%,  30%  and  8%.  On  this  basis,  however,  if  the  depth  is  further  increased  to  5m,  10m  or  15m,  the  gaps  between  the  drying  FOS  and  the  wetting  FOS  of  the  three  soils  become  much  less  significant.  Therefore,  at  depths  greater  than  5m,  FOSs  appear  to  be  less  sensitive  to  SWCC  hysteresis.

5． CONCLUSIONIn  this  paper,  firstly,  the  influence  of  drying  process  and  wetting  process  on  soil  water  characteristic  curve  (SWCC)  was  analyzed.  Then  cited  the  experimental  data  of  Toyoura  sand,  Masado  soil  and  DL  clay  obtained  by  Hatakeyama  et  al.17),  and  further  examined  the  suction  stress  characteristic  curve  (SSCC)  to  analyze  the  influence  of   𝑝𝑝�      only  as  cohesion  and   𝑝𝑝�    as  a  part  of  confining  pressure  on  the  factor  of  safety  (FOS),  respectively.  On  this  basis,  assume  the  infinite  slopes  composed  of  these  three  soils  respectively,  and  perform  theoretical  calculations.  Then  analyze  the  infinite  slope  stability  through  Geostudio  simulation  to  verify  and  expand  the  results.  The  conclusions  are  as  follow:

1.  By  comparing  SSCCs  and  the  relationship  between  FOS  and  suction  in  the  infinite  slope  with  a  depth  H=1m,  suction  stress  can  be  considered  to  dominate  the  change  of  the  FOS.  Moreover,  the  disparity  between  FOSs  calculated  by  wetting  SWCC  and  by  drying  SWCC  will  further  increase  when   𝑝𝑝�    is  considered  as  an  extra  confining  pressure.

2.  In  addition  to  the  particle  size  of  soil  materials,  the  change  of  FOSs  will  also  be  affected  by  apparent  cohesion.  In  Masado  soil,  since  the   𝑐𝑐 �    is  set  to  5kPa,  the  influence  of  the  change  of  suction  stress  on  FOS  is  diluted.

3.  The  paper  use  Geostudio  to  simulate  the  FOS  changes  of  three  soils  at  various  depths.  Results  show  that  when  the  selected  H  is  less  than  5  m,  slope  stability  will  be  greatly  affected  by  SWCC  hysteresis  and   𝑝𝑝�    acting  as  confining  pressure  or  not.  And  as  the  H  continues  to  increase,  this  affect  will  be  weakened  rapidly.

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Overall,  in  the  previous  slope  stability  analysis,  the  hysteresis  effect  of  SWCC  was  usually  ignored,  and  only  the  SWCC  obtained  from  the  drying  process  was  used  to  estimate  the  soil  performance  in  the  entire  process.  This  study  verified  that  this  method  may  be  suitable  for  deep  slopes.  However,  for  shallow  slopes  or  some  specific  soils,  it  may  seriously  underestimate  the  impact  of  SWCC  hysteresis  and   𝑝𝑝�    acting  as  confining  pressure  or  only  acting  as  apparent  cohesion.

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AUTHORS
Depu  Hu                           Doctoral  student,  Graduate  School  of  Engineering,  Kobe  University,  Japan
Shoji  Kato                      Associate  Prof.,  Dr.  Eng.,  Graduate  School  of  Engineering,  Kobe  University,  Japan
Byeong-­Su  Kim              Associate  Prof.,  Dr.  Eng., Dept.  of  Civil  &  Environmental  Eng.,  Dankook  University,  Korea