Zhu et al. Journal of Infrastructure Preservation and Resilience
https://doi.org/10.1186/s43065-021-00034-1(2021) 2:20

Journal of Infrastructure
Preservation and Resilience

RESEARCH

Open Access

Probability assessment of slope instability
in seasonally cold regions under climatechangeYulong Zhu1, Tatsuya Ishikawa2*, Tomohito J. Yamada3 and Srikrishnan Siva Subramanian4

Abstract
To semi-quantitatively assess the effects of climate change on the slope failures, this paper proposes an effective
approach for evaluating the influences of climate change on slope stability in seasonally cold regions. To discuss
climate change, this study firstly analyzes the trend of the two main climate factors (precipitation and airtemperature) based on the regression analysis results of the meteorological monitoring data during the past 120
years in different scales (e.g., world, country (Japan), and city (Sapporo)), and the downscaled outputs of threedifferent regional atmospheric models (RAMs) with lateral boundary conditions from three different generalcirculation models (GCMs). Next, to discuss the effects of different climate factors (air temperature, precipitation,etc.) and to determine the key climate factors on the slope instability, a slope stability assessment approach forevaluating the effects of climate changes on slope instability is proposed through the water content simulation andslope stability analysis with considering freeze-thaw action. Finally, to check the effectiveness of the above
assessment approach, assessment of instability of an actual highway embankment slope with the local layer
geometry is done by applying the past and predicted future climate data. The results indicate that affected by
global warming, the air temperature rise in some cold cities is more serious. The climate changes (especially theincrease in precipitation) in the future will increase the infiltration during the Spring season. It will lengthen thetime that the highway slope is in an unstable state due to high volumetric water content, causing the occurrenceof slope failures will be more concentrated in April. While during the Ssummer-Autumn period, the time domain of
its occurrence will become wider.
Keywords: Climate change, Slope instability, Seasonally cold regions, Probability assessment, Freeze-thaw action

Highlights

3. Future climate change is estimated by using the
hybrid-downscaling method.

1. A slope stability assessment approach is proposed
through the water content simulation and slope
stability analysis with considering freeze-thaw action.
2. An effective assessment approach is proposed forsemi-quantitatively evaluating the influences ofclimate change on slope stability in seasonally cold
regions.
* Correspondence: t-ishika@eng.hokudai.ac.jp
2
Laboratory of Analytical Geomechanics, Faculty of Engineering, Hokkaido
University, Kita 13, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan
Full list of author information is available at the end of the article

Introduction
In the coldest month of the year, areas where the groundtemperature is usually below 0 °C, are defined as cold regions [1, 2], such as some high latitude regions, like
Hokkaido, Japan. In the cold regions, the climate factors(e.g., precipitation and air temperature) and their variations are considered as the significant causes of slope
failures or landslides [3, 4]. Therefore, many studies havebeen done to discuss the failure mechanisms and trigger
factors of slope failures in the cold regions [5, 6].

© The Author(s). 2021 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
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Zhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

Ishikawa et al. [7] described that there is a difference inthe failure mechanism of slopes between cold regions
and warm-temperate regions due to additional factors,i.e., freeze-thaw action. Accordingly, Ishikawa et al. [8]divided slope failures in cold regions into two main classes: slope failures occur during the snow-melting season(March–April-May) and slope failures occur during
heavy rainfall season (August–September). Therefore, itis necessary to investigate the influences of climatechange on the slope stability in seasonally cold regions.
During the heavy rainfall season, the frequency of severe rainfall events is expected to increase in many
mountain areas as a consequence of the influence of global warming [9]. The rainfall infiltration caused decreasein matrix suction is considered as a main cause of slope
failures or landslides [10–12]. For example, according to
the statistical data surveyed by Japan Meteorological
Agency [13] for 1000 locations in Japan, the annual average number of rainfall intensity greater than 50 mm/h
increased from 195 times (1987 ~ 1998) to 226 times(1999 ~ 2010). On the other hand, with the intensification of global warming in the past few decades, during
the snow-melting season, the occurrences of slope failures in seasonally cold regions are more frequently reported. For example, surveyed by the Ministry of Land,
Infrastructure, Transport, and Tourism (MLIT), in April,
the average number of slope failures in Japan increased
from about 50 times (2008 ~ 2012) to near 100 times(2013 ~ 2017), almost doubled. While in August, thisnumber increased from about 120 times (2008 ~ 2012)
to near 240 times (2013 ~ 2017), also doubled. Therefore, the influences of climate change on slope stability
are intensifying. However, little attention is paid on theinfluences of climate changes on slope failures in cold
regions [11, 14, 15].
From the view of climate changes, many attempts werealso made to assess the influences of climate change on
slope failures by exploiting downscaled synthetic futureclimate scenarios obtained from the GCMs as an input ofslope stability [9, 16, 17]. Chiang and Chang [9] pointed
out that the average annual maximum rainfall will have a
15.2% increase in 2010–2099 compared with that in
1960–2008, and the average total unstable area will have a
12.8% increase in Taiwan, China. Ciabatta et al. [17]employed the PRESSCA system (an operational early
warning system) for evaluating the influences of climatechange on landslide hazard in the Umbria territory, Italy
for three different periods (1990–2013 (baseline), 2040–
2069, and 2070–2099). They found that in the future
period, mainly during the winter season, a general increase(up to more than 40%) in landslides occurrence is expected for the Umbria territory, Italy.
Accordingly, the objectives of this study are (1) tosemi-quantitatively assess the effects of climate changes

Page 2 of 15

on the uncertainty of climate factors, and (2) to discuss
the influences of climate changes on the occurrence ofslope failure and its probability distribution. For these
purposes, firstly, this study analyzes the trend of the twomain climate factors (precipitation and air temperature)in the past 120 years and in the future based on the regression analysis and hybrid-downscaling method. Next,
the effects of climate changes on slope instability aresemi-quantitatively assessed by using a proposed slope
stability assessment approach through the water content
simulation and slope stability analysis using a 2dimensional (2D) FEM homogeneous slope model withconsidering freeze-thaw action. Finally, to check the effectiveness of the above assessment approach, assessment of instability of an actual highway embankment
slope with the local layer geometry is done by applying
the past and predicted future climate data.
Slope stability assessment approach
Modelling freeze-thaw action and long-term moisturefluctuation

Slope failures in cold regions are usually subjected tofreeze-thaw actions and rainfall and/or snowmelt water
infiltration. Siva Subramanian et al. [18] proposed aslope stability assessment approach to simulate the longterm fluctuation of the moisture and factor of safety(FOS) for cold region slopes based on non-isothermal
seepage flow and limit equilibrium method (LEM) as
shown in Fig. 1. In this assessment approach, the influences of freeze-thaw action and long-term moisture fluctuation on the slope stability are taken into
consideration. Moreover, the rainfall and/or snowmelt
water infiltration can be simulated. However, runoff isignored as this assessment approach is established byusing the 2D GeoStudio software [19].
Modelling atmosphere-ground interactions

In order to simulate the influences of climate change on
slope stability, the interactions between atmosphere andground (heat exchange, water transfer, etc.) need to bemodeled. The mass balance equation could be used for
calculating the water flux on the ground surface [19]:ðP þ SM Þcosα þ R ¼ I

ð1Þ

where, P indicates precipitation (mm/h); SM indicatessnowmelt water (mm/h); I indicates infiltration (mm/h);
R indicates runoff (mm/h) and α is the slope angle (°).
Snow accumulation models often use average airtemperature to distinguish the precipitation as rainfall orsnowfall [20, 21]. The threshold value of air temperature
to differentiate rainfall and snowfall is 0 °C and snowmelt is assumed to occur when snowpack is present on
the ground with the positive air temperature. The

Zhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

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Fig. 1 Slope stability assessment approach (adapted from [18])snowfall is equal to the precipitation under negative airtemperature [19].
SF ¼ P  f s  SCF

ð2Þ

where, SF is snowfall (mm/h); fs is snow fraction, and
SCF is snow correction factor with the value of 1 [22].
The snow fraction, fs is defined as,
f s ¼ 0 if T a > T f and f s ¼ 1 if T a ≤ T f

ð3Þ

where, Ta is average air temperature (°C) and Tf is freezing point temperature (0 °C).
When air temperature is negative, snow will accumulate on the surface of the soil. Once the air temperature
is positive, the snow will melt into water then penetrate
into soil. The amount of melted water is calculated in
the form of the snow water equivalent.
ΔSWE ¼ SF−SMð4Þ

where, ΔSWE is difference in snow water equivalent(mm/h).






∂
∂ψ
∂
∂ψ
þ
k x ðψ Þ
k y ðψ Þ
þ1
∂x
∂x
∂y
∂y
∂ψ
¼ cðψ Þ∂t

ð5Þwhere, kx(ψ) and ky(ψ) indicate unsaturated hydraulicconductivities in x-direction and y-direction (m/s), respectively; ψ indicates pore water pressure head (m);c(ψ) indicates specific moisture capacity (1/m).
The 2D thermal flow is governed by the equation
given by Kim and Heydinger [24].


∂
∂T
λT
∂x
∂x


∂
∂T
∂ð T Þ
∂ð T ÞþλT−vx C w
−vy C w
∂y
∂y
∂x
∂y
∂T
¼C
ð6Þ
∂t
where, T is temperature (°C); λT is thermal conductivity(kJ/(Day∙m∙°C)); vx and vy are the velocities of the waterflow in x and y directions (m/s); Cw is the heat capacityof water (kJ/(m3∙°C)); C is the volumetric heat capacity(kJ/(m3∙°C)).
Governing equation for unsaturated soil shear strength

Governing equations for non-isothermal seepage flow

The 2D seepage flow is governed by the equation given
by Richards [23] and Kim and Heydinger [24].

The shear strength of an unsaturated is expressed basedon Bishop’s effective stress principle by Vanapalli et al.
[25] as given by.

Zhu et al. Journal of Infrastructure Preservation and Resilience00(2021) 2:20

0

τ ¼ c þ ðσn −ua Þ tanϕ þ χðua −uw Þ tanϕ ; χθw −θr¼
θs −θrð7Þ

where, τ is shear strength of unsaturated soil (kPa), σn is
net total stress (kPa), ua is pore air pressure (kPa), uw ispore water pressure (kPa), c’ is effective cohesion (kPa),
ϕ’ is effective angle of internal friction (°) and χ is thematrix suction coefficient which varies from 0 to 1 depending on the volumetric water content (θw), saturated
volumetric water content (θs) and the residual volumetric water content (θr).
Meteorological monitoring data analysis and futureclimate prediction
Meteorological monitoring data analysis

To semi-quantitatively assess the influences of climatechanges on the uncertainty of climate factors in different
scales (e.g. world, country (Japan), and city (Sapporo, aPage 4 of 15city located in the seasonally cold region of northern
Japan)), this study analyzes the trend of the annual average air temperature deviation (Fig. 2(a)), annual cumulative precipitation deviation (Fig. 2(b)), magnification of
precipitation (Fig. 2(c)), and the number of days with airtemperature below zero (Fig. 2(d)) by the regression analysis of the meteorological monitoring data of the past
120 years (1900–2020) of the world, Japan, and Sapporo
referred from JMA. The benchmark of deviation is theaverage value of 30 years (1981–2010). The annually
average air temperature deviation shown in Fig. 2(a) andannually cumulative precipitation deviation shown in
Fig. 2(b) are the difference between them of each year
and this benchmark. Figure 2(a) shows that the world
annually average air temperature increases approximately 0.8 °C per 100 years, while the values of Japanand Sapporo are 1.27 °C per 100 years and 2.46 °C per
100 years, respectively. It means that global warming has
a significant impact on Japan, especially on high latitudeFig. 2 Meteorological monitoring data of the world, Japan, and Sapporo referred from JMA. a. annually average air temperature deviation; (b)annually cumulative precipitation deviation; (c) magnification of precipitation, and (d) number of days with air temperature below zeroZhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

area or seasonal snowy cold regions in Japan like Sapporo. Figure 2(b) plots the annually cumulative precipitation deviation. Six intervals of 20 years are divided
over the past 120 years to analyze the change of the annual cumulative precipitation deviation. It can be seenthat the number of positive values on the three scales
are 12, 14, and 15, respectively, in the past 20 years(2000–2020), which are all the maximum values since1920. It means from 1920, the number of years withheavy rainfall is increasing. Figure 2(c) and Fig. 2(d)shows the magnification of precipitation (the ratio of annually cumulative precipitation of each year to thebenchmark) and the number of days with airtemperature below zero in Sapporo, respectively. The results of fitting curves display that the magnification of
precipitation increases by 0.094 per 100 years, and thenumber of days with air temperature below zero decreases 16.8 days per 100 years in Sapporo. It means thatthe precipitation is increasing and winter is getting
shorter in Sapporo.

Page 5 of 15

To investigate whether climate change has different
effects on air temperature in different seasons, the airtemperature change in four seasons, i.e., December–
January-February (DJF), March–April-May (MAM),
June–July-August (JJA), and September–October-November (SON), in the world, Japan, and Sapporo are
analyzed separately as shown in Fig. 3. It is recognizedthat in all seasons, the influences of climate change on
the air temperature of Sapporo are very significant,followed by Japan, compared with the world. It isnoted that in Sapporo, climate change has the mostobvious effect on the air temperature in the Winterseason (DJF, increases by 2.89 °C per 100 years),followed by Spring season (MAM, increases by 2.63 °C
per 100 years), and then Autumn season (SON, increases by 2.30 °C per 100 years), and finally Summer
season (JJA, increases by 2.03 °C per 100 years). The
increase in average air temperature in Autumn season
and Winter season will cause the thickness of frozen
soil to decrease, and in Spring season will cause theFig. 3 Temperature of the world, Japan, and Sapporo change in different seasons, (a) DJF; (b) MAM; (c) JJA, and (d) SON

Zhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

increase of snowmelt water, which can be consideredas the main reason of the increase in the slope failuresin the cold regions in Japan.
Future climate prediction based on dynamical downscaling
techniques

To further analyze the future climate change, the futureclimate data (2090–2091), i.e., meteorological simulation
data at Nakayama Pass, Sapporo, Hokkaido, Japan is estimated by using another dynamical downscaling technique, the hybrid-downscaling method proposed by
Yamada et al. [26]. The meteorological simulation data
is obtained by downscaling the outputs of 3 different
RAMs with lateral boundary conditions from 3 different
GCMs. Figure 4 shows past meteorological monitoringdata (2012–2013) and future meteorological simulation
data (2090–2091) at Nakayama Pass. It shows that the
average maximum air temperature increases 0.6 °C, andthe average minimum air temperature increases by
3.29 °C in 2090–2091. Therefore, the average airtemperature increases by about 1.945 °C in the next 80
years at Nakayama Pass, which is consistent with an increase of 2.46 °C per 100 years in Sapporo obtained fromthe regression analysis results of the meteorologicalmonitoring data (Fig. 2(a)). Besides, the annual cumulative precipitation increases from 1882 mm (2012–2013)
to 2131 mm (2090–2091). The magnitude of the precipitation increases by about 0.13, which is slightly larger
than the value of the meteorological analysis data (0.094
per 100 years) in Sapporo shown in Fig. 2(c).
Instability assessment of homogeneous conceptual slope
under climate change

According to meteorological analysis data obtained fromthe regression analysis and the meteorological simulation data obtained from hybrid-downscaling method, climate change is gradually increasing the precipitation
and air temperature in Japan (especially in cold regions).
To assess the influences of climate change on the occurrence of slope failure and its probability distribution,water content simulation and slope stability analysis
were performed using a 2D homogeneous conceptual
slope model with the consideration of freeze-thaw actions using the slope stability assessment approach. The
applicability and reliability of the slope stability assessment approach in the analysis of slope stability during
the snow-melting season and heavy rainfall season incold regions has been clearly validated by Siva Subramanian et al. [18].

Page 6 of 15

numerical model used in this study and the appliedboundary conditions. The numerical models are simulatedwith different slope heights (5 m, 10 m, 15 m, and 20 m)
and different slope angles (30°, 35°, 40°, and 45°) to reflectvarious in situ conditions of homogeneous conceptual
slopes. During the simulation, climate data is applied on
the soil surface (ab, bc, cd in Fig. 5). Adiabatic boundary
conditions are set at the right side (de in Fig. 5), the bottom side (ef in Fig. 5), and the left side (af in Fig. 5). Dueto the left side of the model is assumed to adjacent to the
bedrock, no flow boundary is applied on the left side (af inFig. 5) and free drainage boundary is applied on the rightside (de in Fig. 5) and bottom side (ef in Fig. 5).
Figure 6 shows the original climate data at Nakayama
Pass during 2012–2013, which were obtained from theAMeDAS. According to the regression analysis results of
the historical meteorological monitoring data of Sapporo,
the assumption for precipitation is 1.2 times increased andfor air temperature is 2 °C increased in the 80 years later.
Therefore, 4 kinds of assumed climate boundary conditions as listed in Table 1 are applied to 16 kinds of numerical models (4 slope heights × 4 slope angles). A total of 64
numerical simulations are conducted for Nakayama Pass.
Table 2 lists the soil material properties. Dry density (ρd),
porosity (n), effective cohesion (c’), effective internal friction angle (ϕ’), and saturated hydraulic conductivity (ks),were measured by Hokkaido Regional Development Bureau [27]. The SWCC and unfrozen volumetric water content function of soil at Nakayama Pass is plotted in Fig. 7.
As shown in Fig. 7(b), the unfrozen volumetric water content is related to only temperature. In other words, thecondensation and dissipation of ice in the soil over timeand moisture migration are not considered, which is oneof the limitations of this study. Therefore, the influence ofthe time effect and moisture migration on unfrozen volumetric water content in the soil still needs to be further
investigated. The soil water characteristic curve (SWCC)
of the slope is estimated from the grain size distribution
curve by referring to Fredlund et al. [28]. The rest parameters are estimated based on the grain size curve of soil
[29]. The unfrozen water content of the soil is estimatedusing the relationships given by Black and Tice [30].
θuw ðT Þ ¼ θ C f ð−1110ÞT

ð8Þ

where, θuw(T) is unfrozen volumetric water content at
temperature T, θ is function of volumetric water content
against matric suction as, Cf is parameter ranges between 1 to 2.2 for fine to coarse grained soils.

Numerical model and boundary conditions of 2D numericalhomogeneous slope model

Simulation results of 2D numerical homogeneous slopemodel

A 2D numerical model is established to simulate slope
stability under climate change. Figure 5 shows the

To assess the influences of climate change on the occurrence of slope failures, water content simulation andZhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

Page 7 of 15

Fig. 4 Climate in the past and future at Nakayama Pass: (a) max. Air temperature; (b) min. Air temperature; (c) precipitation during 2012–2013; (d)precipitation during 2090–2091; (e) wind speed

slope stability analysis were performed. The calculated
snow depth, daily snowmelt, daily infiltration, and daily
rainfall under the four climate conditions are shown in
Fig. 8. Figure 8(a) displays the calculated and measured
snow depth. Seeing Fig. 8(a), the results suggest that thecalculated snow depth under case 1 is consistent withthe measurement data, meaning that the simulation results are reliable. It is recognized that when the airtemperature is increased by 2 °C, the time when thesnow disappears is advanced from June 1st (case 1) toMay 23rd (case 2), and the maximum snow depth isdecreased from 2.79 m (case 1) to 2.66 m (case 2). Whenthe precipitation is increased by 1.2 times, the maximum
snow depth is increased from 2.79 m (case 1) to 3.42 m(case 3). Figure 8(b) and Fig. 8(c) show that the increasein the air temperature increases snowmelt and infiltration during the Spring season and the end of the Autumn season. The main reason is that on one hand airtemperature controls snowmelt during those periods
and the snowmelt water is the main water supply of theinfiltration. On the other hand, when the average airtemperature is increased by 2 °C, during Spring season

Zhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

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Fig. 5 2D numerical homogeneous slope model with applied boundary conditions

and Autumn season, some negative air temperatures become positive, which causes some snowfalls are converted into the rainfalls as shown in Fig. 8(d). At thesame time, more snow on the ground surface melt into
water and infiltrate into the soil reducing the slope
stability.
To assess the influences of climate change on slope
stability subjected to snowmelt and heavy rainfall respectively, a year is divided into two different intervals
according to the different causes of slope failures:
Winter-Spring period (the key factor of slope failure issnowmelt water) and Summer-Autumn period (the key
factor of slope failure is heavy rainfall). The probability

Fig. 6 Original climate data obtained from the AMeDAS at Nakayama Pass

distribution is described by probability density function,
which is a function that can be used to describe theprobability of the slope failures in a time interval (1month in this study).
!
1ðx−μÞ2f ðxÞ ¼ pﬃﬃﬃﬃﬃﬃﬃﬃ
ð9Þ
exp −2 σ2π=2  σwhere, f(x) is the normal density at x, which is parameterized in terms of the mean and the variance, denotedby σ and μ2, respectively.
Figure 9 (a) and Fig. 9 (b) show the total number ofdays with slope failure (FOS < 1) and the fitting normal

Zhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

Table 1 Study cases under various weather conditions
Case name

Precipitation condition

Temperature condition

Case 1

Original Precip. (AMeDAS)

Original Temp. (AMeDAS)

Case 2

Original Precip. (AMeDAS)

Original Temp. + 2 °C

Case 3

Original Precip. × 1.2

Original Temp. (AMeDAS)

Case 4

Original Precip. × 1.2

Original Temp. + 2 °C

density curve (NDC) of numerical results during theWinter-Spring period and the Summer-Autumn period,
respectively. Figure 9 suggests that when air temperature
increases 2 °C (case 2) compared with the original climate conditions (case 1), during the Winter-Spring
period, the μ will decrease and the σ will increase. The
NDC becomes chunky and moves to March. It meansthat the increased air temperature causes more slope
failures to occur earlier and broadens the time domainof slope failures in the Spring season. The main reason
is that the increased air temperature leads to the shortening of Winter season and the advancement of thesnow-melting season. However, during the SummerAutumn period, it is the exact opposite that the increased air temperature increases the value of μ and decreases the value of σ. The NDC becomes thin and tall,and moves to September. It means that the increased airtemperature causes more slope failures to occur laterand narrows the time domain of slope failures in the Autumn season. When precipitation increases 1.2 times(case 3) compared with the original climate conditions(case 1), during the Winter-Spring period, the μ will increase and the σ will decrease, and during the SummerAutumn period, μ will decrease and the σ will increase.
It means that the increased precipitation causes more
slope failures to occur later and narrows the time domain of slope failures in the Spring season, and more
slope failures to occur earlier and broadens the time domain of slope failures in the Summer season.
Table 2 Soil properties used for the simulation
Soil properties

Value

Dry density of soil (ρd)

1400 kg/m3

Porosity (n)0.47

Unfrozen thermal conductivity (λu)

127.04 kJ/(Day∙m∙°C)

Frozen thermal conductivity (λf)

132.24 kJ/(Day∙m∙°C)

Hydraulic conductivity of saturated soil (ks)5.62 × 10−7 m/s

Unfrozen volumetric heat capacity (ζu)

2237 kJ/(m3∙°C)

Frozen volumetric heat capacity (ζf)

1624 kJ/(m3∙°C)

Volumetric water content of saturated soil (θs)

0.47 m3/m3

Residual Volumetric water content of soil (θr)

0.12 m3/m3

Undrained shear strength (qu)52 kPaEffective cohesion (c’)

9.75 kPa

Effective angle of internal friction (ϕ’)

35°Page 9 of 15

When considering changes in air temperature and precipitation together, it can be seen that during theWinter-Spring period both μ and σ decrease, while during the Summer-Autumn period both μ and σ increase.
This is consistent with the trend of slope failures inJapan investigated by the MLIT from 2008 to 2017 asshown in Fig. 10. It indicates that during the WinterSpring period the occurrence of slope failures will be
more concentrated in April, while during the SummerAutumn period, the time domain of its occurrence will
become wider. Therefore, the numerical results are believable through the verification of the investigation results. It indicates that the meteorological analysis data
are reliable and the proposed assessment approach isavailable for evaluating the effects of climate changes onslope instability.
Assessment of actual highway slope instability underclimate change

In previous chapter, an assessment approach for evaluating the effects of climate changes on slope instability is
proposed using the 2D homogeneous conceptual slopemodel with considering different slope heights and different slope angles. To check the effectiveness of theabove assessment approach, assessment of instability ofan actual highway embankment slope with the local
layer geometry is done by applying the past (meteorological monitoring data during 2012–2013) and predicted future climate data by dynamical downscaling
techniques (meteorological simulation data during
2090–2091). Along the national highway route 230 in
Hokkaido, Japan, at Nakayama Pass, the slope failure occurred successively on May 4th, 2012, and April 7th,
2013 as shown in Fig. 11. On May 4th, 2012, within therange of about 40 m in length and up to 110 m in transverse width, approximately 13,000 m3 of soil collapsed
and caused 20 days road closure. On April 7th, 2013, another slope failure occurred with more than 11,000 m3of sediment collapsed [31]. The increase in the snowmelt
water due to climate change was considered as the maincauses of the slope failures.
Numerical model and boundary conditions of the highway
slope at Nakayama passThe 2D numerical model with the slope stratigraphy for
highway slope at Nakayama Pass is established, which
consists of three layers of embankment filling, talus, andbedrock as shown in Fig. 12. The parametric analysis ofslope failures at Nakayama Pass is performed by inputting meteorological monitoring data during 2012–2013(measured by AMeDAS) and meteorological simulation
data during 2090–2091 (simulated by GCMs) as shownin Fig. 4. The measured groundwater table is given in
Fig. 12. Table 3 lists the five kinds of boundaryZhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

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Fig. 7 Soil water characteristic curve (SWCC) and unfrozen volumetric water content function of soil at Nakayama Pass (a) SWCC, (b) unfrozen
volumetric water content vs. temperature

Fig. 8 Simulation results vs. time (a) snow depth, (b) daily snowmelt, (c) daily infiltration, and (d) daily rainfallZhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

Page 11 of 15

Fig. 9 Total number of days with slope failure and the fitting normal density curve (NDC) of 64 numerical models. a during the Winter-Spring
period; and (b) during the Summer-Autumn period

conditions for parametric studies. The soil properties are
given in Table 4. The bedrock is modeled as an impenetrable material.
Simulation results of the highway slope at Nakayama pass

To check the effectiveness of the above assessment approach, assessment of instability of an actual highway
embankment slope with the local layer geometry is done
by applying the past and predicted future climate data.
The simulation results of the variation in the FOS,
ground surface temperature, volumetric (vol.) water content and infiltration are given in Fig. 13. Figure 13(a) displays that during snow-melting season, the FOS has arapidly decrease due to the snowmelt water infiltration
increases the vol. water content as shown in Fig. 13(d),which causes the slope to be in an unstable state (FOS <1). After the snow-melting season, the FOS graduallyrises to the normal level. It is noted that there is a much
longer (more than doubled) unstable state of the highway slope at Nakayama Pass under B3 (53 days) and B5(64 days) boundary conditions compared with the B1(22 days) boundary condition. However, the unstablestate of the highway slope at Nakayama Pass has almost
no significant increase under B2 (23 days) and B4 (25days) boundary conditions. It means that climate change(especially the increase in precipitation) in the future will
enhance the instability of the slopes and lead to more
slope failures occur. Figure 13(b) displays that the cumulative infiltration between March 1st and July 1st (surrounded by the red dash box) is 1142.1 mm, 1283.7 mm,
and 1173.3 mm under B1, B2, and B4 boundary condition, respectively. The difference in infiltration is almost
negligible. However, the cumulative infiltration between
March 1st and July 1st is 1930.4 mm and 2055.2 mm

Fig. 10 Annual average number of slope failures in each month and the fitting normal density curve (NDC) of investigation results. a during
2008–2012; and (b) during 2013–2017

Zhu et al. Journal of Infrastructure Preservation and ResilienceFig. 11 Slope failures at Nakayama Pass on Route 230

Fig. 12 2D numerical highway slope model at Nakayama Pass

(2021) 2:20

Page 12 of 15

Zhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

Page 13 of 15

Table 3 Study cases under various weather conditions for parametric studies
Boundary name

Air temp.
(2012/2013)

Precip.
(2012/2013)

Wind speed(2012/2013)

Air temp.
(2090/2091)

Precip.
(2090/2091)

Wind speed(2090/2091)

B1

o

o

o

×

×

×

B2

×

o

o

o

×

×

B3

o

×

o

×

o

×

B4

o

o

×

×

×

o

B5

×

×

×

o

o

o

× − unapplied weather data; o – applied weather data

under B3 and B5 boundary conditions with an increaseof approximately 69% and 80%, respectively. During thisperiod, the ground surface is unfrozen as shown in
Fig. 13(c). Therefore, the infiltration increases the vol.
water content eventually causes slope failure (seeFig. 13(d)). Accordingly, it can be obtained that climatechange (especially the increase in precipitation) in the
future will increase the infiltration and cause more slope
failures during the Spring season.

Discussions
To assess the effects of climate change on the slope stability, this paper proposes an assessment approach for evaluating the effects of different climate factors (precipitation,
air temperature, wind speed, etc.) on slope instability
through the water content simulation and slope stability
analysis with considering freeze-thaw action in seasonallycold regions. The proposed assessment approach canevaluate the effects of the climate change on the slope stability by analyzing the change of the shape and translationof the normal density curve (NDC) of the distribution ofslope failures in 1 year, which provides an effective
method to semi-quantitatively evaluate the impact of climate change on the occurrence time and distribution ofslope failures. During the analysis, three kinds of different
climate data are discussed: meteorological monitoring
data, meteorological analysis data, and meteorologicalsimulation data. The meteorological monitoring data is

the direct monitoring data so it is more reliable. However,this kind of climate data is historical data so it can not be
used in the future. The meteorological analysis data is theassumed future climate data that add the average changes
in precipitation and air temperature from the regression
analysis to the meteorological monitoring data. Therefore,
this kind of climate data can be obtained very easily andquickly, while the differences of climate change in different seasons are not considered. The meteorological simulation data are obtained from GCMs. The differences ofclimate change in different seasons are considered, while
this kind of data is more complex and difficult to obtain.
In addition, the analysis of the slope stability in this study
is based on a 2D FEM model, therefore, extending thesimulation model to 3D is the future assignment of thisstudy.

Conclusions
According to the regression analysis results of the meteorological monitoring data during the past 120 years in
different scales (e.g., world, country (Japan), and city
(Sapporo)), affected by global warming, the airtemperature rise in some cold cities is more serious.
Meanwhile, the precipitation is also increasing andWinter is getting shorter in these cold regions. In different seasons, climate change has the more obvious influences on the increase in the air temperature in theWinter season (DJF) and Spring season (MAM)

Table 4 Soil properties of the actual highway slope at Nakayama Pass
Soil properties

Embankment filling

Talus materials

Dry density of soil (ρd)

1400 kg/m

1200 kg/m3

Porosity (n)

0.47

0.53

Unfrozen thermal conductivity (λu)

127.04 kJ/(Day∙m∙°C)

103.7 kJ/(Day∙m∙°C)

Frozen thermal conductivity (λf)

132.24 kJ/(Day∙m∙°C)

135.7 kJ/(Day∙m∙°C)

Volumetric water content of soil at 0 °C (θwf)

3

3

3

0.15 m /m

0.10 m3/m3−7

Hydraulic conductivity of saturated soil (ks)5.62 × 10 m/s

1 × 10−4 m/s

Unfrozen volumetric heat capacity (ζu)

2237 kJ/(m3∙°C)

2398 kJ/(m3∙°C)

Frozen volumetric heat capacity (ζf)

1624 kJ/(m ∙°C)

1392 kJ/(m3∙°C)

Effective cohesion (c’)

9.75 kPa

52 kPaEffective angle of internal friction (ϕ’)

35°

11.36°

3

Zhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

Page 14 of 15

Fig. 13 Simulation results of (a) FOS vs. time, (b) Daily infiltration vs. time, (c) Ground surface temperature vs. time, and (d) Vol. water content vs.
time (the red dash line is saturated vol. water content)

compared with the Autumn season (SON) and Summer
season (JJA). During the Spring season (MAM) and theend of the Autumn season (SON), the increase in the airtemperature causes the increase in the snowmelt andinfiltration.
Climate change (especially the increase in precipitation) in the future will increase the infiltration during
the Spring season. It will lengthen the time that the
highway slope is in an unstable state, thereby enhancing
the instability of the slopes and lead to more slope failures occur in the future. The increased air temperatureleads to the shortening of winter season and the advancement of the snow-melting season. It causes theslope failures occur earlier and broadens the time domain of slope failures in the Spring season, and causes
more slope failures to occur later and narrows the time
domain of slope failures in the Autumn season. The increased precipitation causes more slope failures to occur
later and narrows the time domain of slope failures in

the Spring season, and causes more slope failures tooccur earlier and broadens the time domain of slope failures in the Summer season. When considering changes
in precipitation and air temperature together, during theWinter-Spring period, the occurrence of slope failures
will be more concentrated in April, while during theSummer-Autumn period, the time domain of its occurrence will become wider.
The research findings propose an effective method tosemi-quantitatively evaluate the influences of climatechange on slope stability and the probability distributionof the slope failures by using numerical simulation, regression analysis, and statistical analysis. It can be usedin the adjustment of counter measures of slope failuresat the actual design and maintenance works in the
future.
Abbreviations
RAMs: Regional atmospheric models; GCMs: General circulation models;
NDC: Normal density curve; 2D: 2-Dimensional; FEM: Finite element model;

Zhu et al. Journal of Infrastructure Preservation and Resilience(2021) 2:20

JMA: Japan meteorological agency; MLIT: Ministry of land, infrastructure,transport, and tourism; AMeDAS: Automatic meteorological data acquisition
system; FOS: Factor of safety; LEM: Limit equilibrium method; DJF: December–
january-february; MAM: March–april-may; JJA: June–july-august;
SON: September–october-november; SWCC: Soil water characteristic curve

8.

Acknowledgments
Since the main works of this study were finished in Hokkaido University, theauthors gratefully acknowledge the support of Hokkaido University and
Hokkaido Government.

10.

Authors’ contributions
YZ drafted this manuscript, analyzed climate data and performed the thermal
and mechanical numerical simulations. TI guided the works of this study andthe writing of this manuscript, and interpreted the climate data. TJY conducted
the general circulation modeling and future climate prediction. SSS conducted
the thermal and mechanical modelling and collected the past climate data. The
author(s) read and approved the final manuscript.

9.

11.
12.

13.

14.

Funding
This study is financially supported in part by Grant- in-Aids for Scientific
Research (A) (16H02360) from Japan Society for the Promotion of Science(JSPS) KAKENHI. This study also supported by the Fundamental ResearchFunds for the Central Universities (JB2021043).

15.

Availability of data and materials
The datasets used and/or analyzed during the current study are available
from the corresponding author on reasonable request.

17.

Declarations

18.

Competing interests
The authors declare that they have no competing interests.
Author details
1
School of Water Resources and Hydropower Engineering, North China
Electric Power University, Changping Beinong 2#, Beijing, China. 2Laboratoryof Analytical Geomechanics, Faculty of Engineering, Hokkaido University, Kita
13, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan. 3River & WatershedEngineering Laboratory, Faculty of Engineering, Hokkaido University, Kita 13,
Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan. 4State Key Laboratory ofGeo-hazard Prevention and Geo-environment Protection, Chengdu Universityof Technology, Chengdu, Sichuan, China.
Received: 16 April 2021 Accepted: 29 June 2021

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