Deformation and Volumetric Change in a Typical Retrogressive Thaw Slump in Permafrost Regions of the Central Tibetan Plateau, China

Abstract

Ice-rich permafrost in the Qinghai–Tibet Plateau (QTP), China, is becoming susceptible to thermokarst landforms, and the most dramatic among these terrain-altering landforms is retrogressive thaw slump (RTS). Concurrently, RTS development can in turn affect the eco-environment, and especially soil erosion and carbon emission, during their evolution. However, there are still a lack of quantitative methods and comprehensive studies on the deformation and volumetric change in RTS. The purpose of this study is to quantitatively assess the RTS evolution through a novel and feasible simulation framework of the GPU-based discrete element method (DEM) coupled with the finite difference method (FDM). Additionally, the simulation results were calibrated using the time series observation results from September 2021 to August 2022, using the combined methods of terrestrial laser scanning (TLS) and unmanned aerial vehicle (UAV). The results reveal that, over this time, thaw slump mobilized a total volume of 1335 m3 and approximately 1050 m3 moved to a displaced area. Additionally, the estimated soil erosion was about 211 m3. Meanwhile, the corresponding maximum ground subsidence and headwall retrogression were 1.9 m and 3.2 m, respectively. We also found that the amount of mass wasting in RTS development is highly related to the ground ice content. When the volumetric ice content exceeds 10%, there will be obvious mass wasting in the thaw slump development area. Furthermore, this work proposed that the coupled DEM-FDM method and field survey method of TLS-UAV can provide an effective pathway to simulate thaw-induced slope failure problems and complement the research limitations of small-scale RTSs using remote sensing methods. The results are meaningful for assessing the eco-environmental impacts on the QTP.

Full text

Citation: Jiao, C.; Niu, F.; He, P.; Ren,
L.; Luo, J.; Shan, Y. Deformation and
Volumetric Change in a Typical
Retrogressive Thaw Slump in
Permafrost Regions of the Central
Tibetan Plateau, China. Remote Sens.
2022,14, 5592. https://doi.org/
10.3390/rs14215592
Academic Editor: Ulrich Kamp
Received: 9 October 2022
Accepted: 2 November 2022
Published: 6 November 2022
Publisher’s Note: MDPI stays neutral
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Copyright: © 2022 by the authors.
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4.0/).
remote sensing
Article
Deformation and Volumetric Change in a Typical Retrogressive
Thaw Slump in Permafrost Regions of the Central Tibetan
Plateau, China
Chenglong Jiao 1,2 , Fujun Niu 1,2,3,* , Peifeng He 1,2, Lu Ren 1,2, Jing Luo 3and Yi Shan 4
1South China Institution of Geotechnical Engineering, School of Civil Engineering and Transportation,
South China University of Tehnology, Guangzhou 510640, China
2State Key Laboratory of Subtropical Building Science, South China University of Technology,
Guangzhou 510640, China
3State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-Environment and Resources,
Chinese Academy of Sciences, Lanzhou 730000, China
4School of Civil Engineering, Guangzhou University, Guangzhou 510006, China
*Correspondence: niufj@scut.edu.cn
Abstract:
Ice-rich permafrost in the Qinghai–Tibet Plateau (QTP), China, is becoming susceptible to
thermokarst landforms, and the most dramatic among these terrain-altering landforms is retrogressive
thaw slump (RTS). Concurrently, RTS development can in turn affect the eco-environment, and
especially soil erosion and carbon emission, during their evolution. However, there are still a lack of
quantitative methods and comprehensive studies on the deformation and volumetric change in RTS.
The purpose of this study is to quantitatively assess the RTS evolution through a novel and feasible
simulation framework of the GPU-based discrete element method (DEM) coupled with the finite
difference method (FDM). Additionally, the simulation results were calibrated using the time series
observation results from September 2021 to August 2022, using the combined methods of terrestrial
laser scanning (TLS) and unmanned aerial vehicle (UAV). The results reveal that, over this time, thaw
slump mobilized a total volume of 1335 m
3
and approximately 1050 m
3
moved to a displaced area.
Additionally, the estimated soil erosion was about 211 m
3
. Meanwhile, the corresponding maximum
ground subsidence and headwall retrogression were 1.9 m and 3.2 m, respectively. We also found
that the amount of mass wasting in RTS development is highly related to the ground ice content.
When the volumetric ice content exceeds 10%, there will be obvious mass wasting in the thaw slump
development area. Furthermore, this work proposed that the coupled DEM-FDM method and field
survey method of TLS-UAV can provide an effective pathway to simulate thaw-induced slope failure
problems and complement the research limitations of small-scale RTSs using remote sensing methods.
The results are meaningful for assessing the eco-environmental impacts on the QTP.
Keywords:
permafrost; thermokarst; retrogressive thaw slump; mass wasting; DEM-FDM; TLS-UAV;
Qinghai–Tibet Plateau
1. Introduction
In the context of the climatic warming of previous decades [
1
–
3
], the ice-rich per-
mafrost in the Arctic Region and Qinghai–Tibet Plateau (QTP) is becoming susceptible to
thermokarst activities, and the most dramatic among these terrain-altering landforms is
retrogressive thaw slump (RTS) [
4
–
7
]. The initiation of thermokarst landslides is mainly
due to the underlain ice-rich permafrost thawing or massive ground ice ablation [
8
–
10
].
Furthermore, the shear strength in the basal zone of the active layer decreases. As a result
of the thawed materials undertaking free fall or semi-circular movement, a headwall (the
steep frozen back scarp) forms on the trailing edge of a slope. Additionally, the solifluction,
derived from the headwall and the sediment inclusions contained in ground ice, flow
downslope to the slump floor.
Remote Sens. 2022,14, 5592. https://doi.org/10.3390/rs14215592 https://www.mdpi.com/journal/remotesensing

Remote Sens. 2022,14, 5592 2 of 18
Thermokarst landslides, including active layer detachment, retrogressive thaw slump,
and multiple retrogressive slides, have major impacts on the hydrological environment
and ecosystem equilibria [4,10,11], and they affect global climate change by activating the
organic carbon stored in permafrost [
12
–
14
]. Consequently, the frozen carbon “buried” in
the permafrost thaws and emits greenhouse gas into the atmosphere, such as carbon dioxide
and methane. This “mutual feedback mechanism” further aggravates global warming.
Concurrently, nearby linear engineering projects are vulnerable to mass wasting induced by
RTSs [
15
], and RTS development can adversely cause the deformation of infrastructure [
16
].
Quantitative estimation of the deformation and volumetric change in RTS development
and evolution can provide more valuable references for the risk and influence assessment
of the permafrost engineering and environment in the QTP.
Being the main permafrost distribution terrain of China, the QTP (Figure 1a) is char-
acterized by relatively thin permafrost thickness. It is ice-rich and near 0
◦
C (warm per-
mafrost) [
17
], and is becoming a hot spot of climatic warming and wetting, and thus related
studies. The formation and development of RTS in the past 10 years (from 2008 to 2017) [
10
]
has accelerated under a warming and wetting climate [
18
]. Especially for the mountain per-
mafrost regions, such as the Hoh Xil region in the hinterland of the QTP, this situation has
accelerated the degradation of the eco-environment of the QTP. Based on remote sensing
interpretations, field surveys, and authors’ previous studies [
10
,
19
], more than 400 RTSs
were observed in the hills and mountainous areas around the Beiluhe River Basin from
2013 to 2022 (Figure 1b). This trend can mobilize vast quantities of mass wasting on a
large time scale. How to quantify the mass wasting of these RTSs has become the key to
assessing the environmental impact.
Most studies have reported distribution characteristics and evolution processes of
RTS across the Arctic Region and the QTP. In the field of remote sensing and evolving
imaging, refs. [
15
,
20
] reported the area of RTSs’ notable expansion, retrogression, and
characteristics from 2017 to 2019 in the north-central QTP. Moreover, ref. [
21
] employed a
space-borne interferometric synthetic aperture radar (InSAR) to map the ground surface
subsidence in a thermokarst terrain in Alaska. Their results quantitatively estimate the
rate of vertical deformation between 2006 and 2010. In the field of light detection and
ranging (LiDAR) and terrestrial laser scanning (TLS), ref. [
22
] used repeat airborne LiDAR
to reveal the accompanying mass wasting processes of permafrost coastal erosion between
2012 and 2013. Additionally, ref. [
23
] utilized TLS to monitor the seasonal deformation
in a thermokarst gully in the northeastern QTP between 2016 and 2018. They found that
the surface subsidence and headwall retreat of the thermokarst gully reached 3.364 m
and 10.66 m during this period. Furthermore, their study can prove the TLS to be a
suitable method to monitor the deformation of RTS. However, these findings, owing to
the absence of high-resolution digital elevation model data cannot quantify the volumetric
changes in RTS development, especially for small-scale RTSs. Most importantly, to the best
of our knowledge, there are few models or technology that can forecast the volumetric
changes and deformation in RTS development areas. Therefore, the fast GPU-based discrete
element method (DEM) and finite difference method (FDM) were employed to quantify
the deformation and volumetric changes in RTSs. The DEM was utilized to solve the large
deformation problems of the ground ice melting and mass wasting in RTSs, and the FDM
was employed to realize the heat conduction considering the phase transition in the ice-rich
permafrost degradation.
Here, we discuss a typical case developed on the northeastern slope of Gu Hill (Ger-
rama, 34
◦
50
0
49
00
N, 92
◦
54
0
12
00
E) in the Beiluhe River Region of the QTP. The straight distance
is about 300 m between the west side of K1129 mileage of the Qinghai–Tibet Railway (QTR,
34
◦
59
0
N, 92
◦
58
0
E) and this thaw slump. Thus, it was named the K1129W thaw slump
(Figure 1). To address the scientific issue of quantifying mass wasting, showing as soil
erosion in the K1129W thaw slump, borehole logging data from 2022, an in situ direct shear
test, unmanned aerial vehicle (UAV) and TLS survey results between 2021 and 2022, and nu-
merical simulations were combined to investigate the volumetric change and deformation

Remote Sens. 2022,14, 5592 3 of 18
law of RTS development during the ice-rich permafrost thawing. We developed a system-
atic method that combined the DEM and FDM to simulate coupled thermo-mechanical
behavior in the mass wasting and “melting” of granular media. To verify the 3D modeling,
the comparative analysis of the UAV and TLS results present the annual deformation and
headwall retreat between 2021 and 2022. This work aims to (i) gain insight into the shear
strength in the basal zone of the active layer; (ii) quantitatively access the mass wasting in
thaw slump development; and (iii) reveal the impact of the volumetric ground ice content
on RTS. This study can help to better show the mutual feedback mechanism between
thermokarst landforms and ecological systems, and provide a more valuable reference for
the assessment of eco-environment impacts in the QTP.
Remote Sens. 2022, 14, 5592 3 of 19
Railway (QTR, 34°59′N, 92°58′E) and this thaw slump. Thus, it was named the K1129W
thaw slump (Figure 1). To address the scientific issue of quantifying mass wasting,
showing as soil erosion in the K1129W thaw slump, borehole logging data from 2022, an
in situ direct shear test, unmanned aerial vehicle (UAV) and TLS survey results between
2021 and 2022, and numerical simulations were combined to investigate the volumetric
change and deformation law of RTS development during the ice-rich permafrost thaw-
ing. We developed a systematic method that combined the DEM and FDM to simulate
coupled thermo-mechanical behavior in the mass wasting and “melting” of granular
media. To verify the 3D modeling, the comparative analysis of the UAV and TLS results
present the annual deformation and headwall retreat between 2021 and 2022. This work
aims to (i) gain insight into the shear strength in the basal zone of the active layer; (ii)
quantitatively access the mass wasting in thaw slump development; and (iii) reveal the
impact of the volumetric ground ice content on RTS. This study can help to better show
the mutual feedback mechanism between thermokarst landforms and ecological sys-
tems, and provide a more valuable reference for the assessment of eco-environment im-
pacts in the QTP.
Figure 1. Location of the study area on the Qinghai–Tibet Plateau (QTP). (a) The distribution of
permafrost on the QTP; the data [24] are from the Qinghai–Tibet Plateau Science Data Centre for
China, National Science and Technology Infrastructure (https://data.tpdc.ac.cn, accessed on 20
April 2021); (b) the topographic map of the study area (modified from [10]); (c) the details of the
studied thaw slump; and (d) the K1129W thaw slump developed on the northeast slope of the
Gerlama Hill in the Beiluhe River Basin. Note that the thaw slump development direction and
borehole location information are shown in Figure 1d.
2. Materials and Methodology
2.1. Study Site Description
The studied thaw slump developed on the west side of the K1129 mileage of the
QTR, which is in the Beiluhe River Region—the hinterland of the QTP. The elevation is
from 4418 m a.s.l to 5320 m a.s.l, with a mean of 4673 m a.s.l [10]. The mean annual air
temperature (MAAT) in this region is −3.8 °C and the mean annual precipitation is more
than 300 mm over the period from 1957 to 2020, falling mainly in summer [9,10,25].
Figure 1.
Location of the study area on the Qinghai–Tibet Plateau (QTP). (
a
) The distribution of
permafrost on the QTP; the data [
24
] are from the Qinghai–Tibet Plateau Science Data Centre for
China, National Science and Technology Infrastructure (https://data.tpdc.ac.cn, accessed on 20 April
2021); (
b
) the topographic map of the study area (modified from [
10
]); (
c
) the details of the studied
thaw slump; and (
d
) the K1129W thaw slump developed on the northeast slope of the Gerlama Hill
in the Beiluhe River Basin. Note that the thaw slump development direction and borehole location
information are shown in Figure 1d.
2. Materials and Methodology
2.1. Study Site Description
The studied thaw slump developed on the west side of the K1129 mileage of the QTR,
which is in the Beiluhe River Region—the hinterland of the QTP. The elevation is from 4418
m a.s.l to 5320 m a.s.l, with a mean of 4673 m a.s.l [
10
]. The mean annual air temperature
(MAAT) in this region is
−
3.8
◦
C and the mean annual precipitation is more than 300 mm
over the period from 1957 to 2020, falling mainly in summer [9,10,25].
Figure 2shows a two-dimensional sketch of the longitudinal section of the K1129W
thaw slump. The present ground surface elevations were investigated through the TLS
survey in August 2022, and the original ground surface data were from the ALOS PALSAR
in 2010 (https://search.asf.alaska.edu/, accessed on 4 October 2010). The thaw slump
development area, with a gentle slope, is between 6.8
◦
and 10
◦
. The current dimensions
of the K1129W thaw slump were approximately 155 m in length from the headwall to the

Remote Sens. 2022,14, 5592 4 of 18
compressed area, and 95 m wide in the middle position (the widest position was 112 m). It
involved the displaced materials with a volume of 12,160 m
3
, and the total disturbed area
was about 11,268 m
2
. A 1.4 m to 2.4 m high headwall formed in the west of this thaw slump,
and about 8% to 15% of the scar area was mainly covered by alpine meadow (Figure 1).
Remote Sens. 2022, 14, 5592 4 of 19
Figure 2 shows a two-dimensional sketch of the longitudinal section of the K1129W
thaw slump. The present ground surface elevations were investigated through the TLS
survey in August 2022, and the original ground surface data were from the ALOS PAL-
SAR in 2010 (https://search.asf.alaska.edu/, accessed on 4 October 2010). The thaw slump
development area, with a gentle slope, is between 6.8° and 10°. The current dimensions
of the K1129W thaw slump were approximately 155 m in length from the headwall to
the compressed area, and 95 m wide in the middle position (the widest position was 112
m). It involved the displaced materials with a volume of 12,160 m3, and the total dis-
turbed area was about 11,268 m2. A 1.4 m to 2.4 m high headwall formed in the west of
this thaw slump, and about 8% to 15% of the scar area was mainly covered by alpine
meadow (Figure 1).
Figure 2. Longitudinal profile of the K1129W thaw slump.
Based on the core logging information for drilling near the thaw slump develop-
ment area in 2022, the main formation conditions are shown in Figure 3a. The superficial
layer (0.5 m to 1 m in thickness) is fine sands and gravels, with a small amount of root
system. The underlying strata are mainly silty clay (the most thickness is up to 8 m) and
the substratum is mudstone with sandstone interlayers [26]. The soil in this area is rela-
tively dry and the gravimetric moisture content (ground ice content) was tested in situ.
As illustrated in Figure 3b, the moisture content curves can reflect the ground ice content
in this area. The permafrost table is 1.95 m deep. The depth of the ground ice layer is ap-
proximately 2.2 m to 3.5 m (the natural area), as estimated from the borehole drilling at
the southwest of the back scarp. The ice content, near the permafrost table, is 68% to 88%
at the depth of 2.2 m to 4 m from the ground surface. Additionally, the mean annual
ground temperature (MAGT), at the depth of 10 m, is about −1.52 °С.
Present ground surface
Original ground surface
Permafrost table
Headwall
Ground ice
Silt and clay
ice crystal
Scar area Displaced mass Slope bottomSlope top
Source area
2 m
Borehole position (2022)
Figure 2. Longitudinal profile of the K1129W thaw slump.
Based on the core logging information for drilling near the thaw slump development
area in 2022, the main formation conditions are shown in Figure 3a. The superficial layer
(0.5 m to 1 m in thickness) is fine sands and gravels, with a small amount of root system. The
underlying strata are mainly silty clay (the most thickness is up to 8 m) and the substratum
is mudstone with sandstone interlayers [
26
]. The soil in this area is relatively dry and
the gravimetric moisture content (ground ice content) was tested in situ. As illustrated in
Figure 3b, the moisture content curves can reflect the ground ice content in this area. The
permafrost table is 1.95 m deep. The depth of the ground ice layer is approximately 2.2 m
to 3.5 m (the natural area), as estimated from the borehole drilling at the southwest of the
back scarp. The ice content, near the permafrost table, is 68% to 88% at the depth of 2.2 m to
4 m from the ground surface. Additionally, the mean annual ground temperature (MAGT),
at the depth of 10 m, is about −1.52 ◦C.
Remote Sens. 2022, 14, 5592 5 of 19
Figure 3. Drilling borehole information of the K1129W thaw slump. (a) Borehole logging and (b)
gravimetric moisture content.
2.2. Computation Module Description
The 3D discrete element thaw slump model was developed in the basic discrete el-
ement model frame, and the heat conduction equation and the ground ice ablation com-
putation module were coupled to simulate heat transfer, latent heat, and ground ice
melting.
2.2.1. Basic Discrete Element Module
The discrete element method was originally developed for the behavior of the kinds
of granular assemblies [27]. Moreover, researchers employed the bonded discrete ele-
ment model to simulate the behavior of cohesive materials, for instance, clay and rock
glacier [28–30]. A close-packed lattice solid model was applied to the landslides [30–34].
In this paper, the model is composed of a series of uniform and close-packed ele-
ments to represent active layer soil, ground ice, and permafrost (Figure 4). Based on the
most basic linear elastic model, the interaction between the elements and their neighbors
was bonded or broken by the normal spring force. The inter-element normal spring force
(F
n
) is defined as the product of relative normal displacement (X
n
) and normal contact
stiffness (k
n
). The equation of the normal spring is:
(1)
where X
b
is the breaking displacement.
Similarly, the tangential spring force (F
s
) is defined as the product of the shear rela-
tive displacement (X
s
) and shear stiffness (k
s
). The equation of the tangential spring is:
(2)
An intact bond may fail in a tangential direction when the inter-element shear force
exceeds the maximum shear force (F
smax
) allowed by the Mohr–Coulomb criterion
[28,35].
(3)
Figure 3.
Drilling borehole information of the K1129W thaw slump. (
a
) Borehole logging and
(b) gravimetric moisture content.

Remote Sens. 2022,14, 5592 5 of 18
2.2. Computation Module Description
The 3D discrete element thaw slump model was developed in the basic discrete
element model frame, and the heat conduction equation and the ground ice ablation
computation module were coupled to simulate heat transfer, latent heat, and ground
ice melting.
2.2.1. Basic Discrete Element Module
The discrete element method was originally developed for the behavior of the kinds
of granular assemblies [
27
]. Moreover, researchers employed the bonded discrete ele-
ment model to simulate the behavior of cohesive materials, for instance, clay and rock
glacier [28–30]. A close-packed lattice solid model was applied to the landslides [30–34].
In this paper, the model is composed of a series of uniform and close-packed elements
to represent active layer soil, ground ice, and permafrost (Figure 4). Based on the most
basic linear elastic model, the interaction between the elements and their neighbors was
bonded or broken by the normal spring force. The inter-element normal spring force (F
n
) is
defined as the product of relative normal displacement (X
n
) and normal contact stiffness
(kn). The equation of the normal spring is:
Fn=




knXn,Xn<Xb,intact bond
knXn,Xn<0, broken bond
0, Xn>0, broken bond
(1)
where Xbis the breaking displacement.
Similarly, the tangential spring force (F
s
) is defined as the product of the shear relative
displacement (Xs) and shear stiffness (ks). The equation of the tangential spring is:
Fs=ksXs(2)
An intact bond may fail in a tangential direction when the inter-element shear force
exceeds the maximum shear force (F
smax
) allowed by the Mohr–Coulomb criterion [
28
,
35
].
Fsmax =Fs0−µpFn(3)
Remote Sens. 2022, 14, 5592 6 of 19
Figure 4. Diagrammatic draft of the linear elastic model. (a) Two particles interact through a
spring force (Fn). (b) Two particles are also bonded by a spring along the tangential direction to
simulate the shear force (Fs). (c) A close-packed discrete element model [36].
2.2.2. Heat Conduction Module
Under climatic warming and wetting, the rise in the permafrost temperature causes
exposed ground ice ablation. A heat transfer module was developed herein for the calcu-
lation of the particle temperature in the discrete element model which represents the
ground temperature. Due to the downward ground temperature, the heat (energy) flux
QA of element A in the heat conduction can be calculated by Fourier’s law, which is writ-
ten as:
(4)
where λ is the thermal conductivity (W/m°C = J/m/s/°C); A is the cross-sectional area
(m2) of the heat flow which is defined as the contact area between element A and its
neighboring elements; |R1R2| is the distance between element A and its neighboring el-
ements; and ΔT is the temperature difference between element A and its neighboring el-
ements. As the heat conduction is performed in a porous medium, the thermal retarda-
tion R was introduced into this process. The relationship between the thermal retarda-
tion R and the temperature difference ΔT is represented by the following equation:
(5)
where ni is the direction vector; l is the distance of the heat transport; and qi is the heat
flux on the unit length.
Based on the apparent heat capacity method [37], the ice–water phase transition la-
tent heat was considered in the model. The latent heat QH in the porous medium is ap-
proximated by Equation (6). Additionally, it can change the element temperature, which
is defined by Equation (7)
(6)
(7)
(8)
where θ is the porosity; ρi is the density of ground ice (kg/m3); L is the latent heat of
thawing (J/kg); δT is the temperature difference of the element; m is the mass of an ele-
ment (kg); c is the specific heat of an element (J/kg/K); and Wu(T) is the temperature-
dependent function of unfrozen water content (see Equation (8)), which relates the un-
frozen soil moisture to the soil temperature. The experimental constants p and q are re-
lated to soil properties [38].
(a)
(b)
(c)
Figure 4.
Diagrammatic draft of the linear elastic model. (
a
) Two particles interact through a spring
force (F
n
). (
b
) Two particles are also bonded by a spring along the tangential direction to simulate the
shear force (Fs). (c) A close-packed discrete element model [36].
2.2.2. Heat Conduction Module
Under climatic warming and wetting, the rise in the permafrost temperature causes
exposed ground ice ablation. A heat transfer module was developed herein for the cal-
culation of the particle temperature in the discrete element model which represents the

Remote Sens. 2022,14, 5592 6 of 18
ground temperature. Due to the downward ground temperature, the heat (energy) flux Q
A
of element A in the heat conduction can be calculated by Fourier’s law, which is written as:
QA=−λA|R1R2|∆T(4)
where
λ
is the thermal conductivity (W/m
◦
C = J/m/s/
◦
C); Ais the cross-sectional area (m
2
)
of the heat flow which is defined as the contact area between element A and its neighboring
elements; |R
1
R
2
| is the distance between element A and its neighboring elements; and
∆
T
is the temperature difference between element A and its neighboring elements. As the heat
conduction is performed in a porous medium, the thermal retardation Rwas introduced
into this process. The relationship between the thermal retardation Rand the temperature
difference ∆Tis represented by the following equation:
∆T→
ni=Rlqi(5)
where n
i
is the direction vector; lis the distance of the heat transport; and q
i
is the heat flux
on the unit length.
Based on the apparent heat capacity method [
37
], the ice–water phase transition
latent heat was considered in the model. The latent heat Q
H
in the porous medium is
approximated by Equation (6). Additionally, it can change the element temperature, which
is defined by Equation (7)
QH=θρiL∆Wu(T)(6)
δT=QH/mc (7)
Wu(T) = (1−p)e−(T/q)2+p(8)
where
θ
is the porosity;
ρi
is the density of ground ice (kg/m
3
); Lis the latent heat of
thawing (J/kg);
δ
Tis the temperature difference of the element; mis the mass of an element
(kg); cis the specific heat of an element (J/kg/K); and W
u
(T) is the temperature-dependent
function of unfrozen water content (see Equation (8)), which relates the unfrozen soil
moisture to the soil temperature. The experimental constants pand qare related to soil
properties [38].
2.2.3. Ground Ice Ablation Module
Thaw settlement is the process of soil skeleton compression and drainage consolidation.
It is mainly reflected in the ground surface settlement caused by permafrost thawing or
ground ice ablation, consisting of the ice–water phase-change deformation and compression
deformation under an external load [
39
]. In terms of the retrogressive thaw slump (RTS)
development area, there was no external load on the slope surface of our study site.
Moreover, the consolidation process due to the rearrangement of elements and changes
in pore structure can be considered in the discrete element model. The thaw settlement is
calculated at each step according to the volumetric change in the moisture content of the
elements. The governing equation of vertical deformation (frost heave/thaw settlement)
can be defined as [40,41]:
S=θSw·∆Wuρw−ρi
ρi(H2−H1)(9)
where Sis the vertical deformation (m) over the computing time step;
θ
is the porosity; S
w
is
the water saturation;
∆
W
u
is the volumetric change in the unfrozen water content over the
computing time step;
ρ
is the density (kg/m
3
); and the subscripts w, and irepresent water
and ice, respectively. Additionally, H
1
and H
2
are the original thicknesses of the permafrost
before and after thawing or freezing. Simultaneously, the dimension of elements will be

Remote Sens. 2022,14, 5592 7 of 18
smaller when considering ground ice ablation. A simple thawing- or freezing-induced
variation in particles can be expressed as:
Rk+1=αtRk(10)
where Ris the radius (m) of the element and the subscripts kand k+ 1 represent the
computing time step. Additionally, the deformation coefficient
αt
is calculated by the
above-mentioned process. Equation (10) can be used to solve the thaw settlement problem.
Because the whole process of thermokarst subsidence cannot be completed in the RTS
development area, thawed materials slide down to the slump floor. It is necessary to
improve the contact model for the research of RTS development.
2.2.4. Thaw-Induced Bond Contact Model
For cemented granular materials, such as icy permafrost, elements are bonded together
through the cementation of the pore ice or segregated ice in the soil. Such intergranular
cementation is susceptible to thaw-induced change. Especially for ice-rich permafrost,
ground ice ablation can cause the shrinkage of icy particles and a reduction in shear
strength-related parameters. Such an “ice-melting” process can be realized via an apt
definition of contact models [
42
–
44
]. For feasibility and generalization, we introduce
a “weakening or melting” coefficient
αw
into the basic contact model that governs the
thawing-induced cementation breakage. The normal and tangential force of the weakening
contact model is calculated by:
Fn>αwknXn,Xn>|R1R2|broken bond (11)
Fs>µwFnb,Fnb =αwkn|R1R2|(12)
where
αw
represents the “weakening or melting” coefficient in connection with the normal
contact stiffness k
n
; |R
1
R
2
| represents the center distance of the two contacting elements;
and
µw
represents a threshold of
µp
, which is the coefficient of maximum shear force
corresponding to the normal broken force in a thawing state and assumed independent of
temperature. The normal spring force is becoming weak and cannot sustain enough tension.
The “weakening or melting” coefficient
αw
is affected by several parameters including
temperature, soil type, and water chemistry. The weakening coefficient
αw
is defined as a
function of the unfrozen moisture equation, which is a temperature-dependent coefficient.
Note that the function of the weakening coefficient is used for the thawing phase.
αw=A(Wu(T)−Wu(Tt)),T<Tt
0 , T>Tt(13)
A=θSw(ρw−ρi)/ρi(14)
where Ais the soil texture-related coefficient, which can be estimated by Equation (14);
T
t
is the melting temperature of permafrost. Both Aand T
t
in this study are assumed to
be constant.
2.3. Setup of Model and Parameters
Ground ice ablation induces permafrost thaw-related consolidation problems widely
found on the QTP, such as thermokarst subsidence, thermal erosion, thermokarst lake,
and thermokarst landslide. To solve this kind of large deformation problem, a discrete
element method software MatDEM [
45
] was employed in this study. Through the secondary
development, an improved bond contact model considering heat transport, ice–water phase
change, and thaw settlement consolidation was used in the simulation. The numerical
simulation is mainly carried out from the following two parts: (1) the shear behavior
in the basal zone of the active layer; (2) deformation and volumetric change in thaw
slump development.

Remote Sens. 2022,14, 5592 8 of 18
2.3.1. Basal Zone Shear Test Model
To understand the shear behavior in the basal zone of the active layer, especially for
the permafrost thaw state, a DEM simulation of a direct shear test was first conducted in
this work concerning the in situ shear tests [
9
] near this study area (the specific direct shear
test apparatus is shown in Figure 5). Two sets of in situ shear tests were executed at a gentle
slope site near the previously studied landslides on the Beiluhe River Basin [
9
]. Each set of
experiments loaded four groups of vertical pressure from 1 to 1.6 times of gravity pressure
on the top plate because excessive vertical pressure causes a change in strength parameters
between the sample and ground ice.
Figure 5shows the experiment setups of the simulation and in situ tests. The specimen
was discretized into 23,500 elements in the model and the radius of each particle was from
1 to 1.414 mm. A 50 mm by 50 mm by 30 mm specimen was placed in the same inside
size shear box (generated by the cluster elements in MatDEM), and the vertical stresses of
31.00, 37.54, 44.08, and 50.61 kPa were applied to the top plate. The simulation adopted the
horizontal displacement load to the sample. The total displacement was 5 mm, which was
decomposed into several loading steps (each step was 0.25 mm), and each cyclic step was
broken into 2500 steps. In addition, the volumetric ice content at the active layer–ground
ice interface was assumed to be 46%, which was from the borehole data.
Moreover, three weakening coefficients
αw
were used to prepare the different thawing
states of ice-rich permafrost. To reveal a preliminary law on the shear strength parameter
“weakening” in the interface between the active layer and the ground ice, three scenarios of
the inter-granular cementation weakening coefficient
αw
were executed with 0.03, 0.01, 0,
where the selected vertical pressures were consistent with the aforemetioned direct shear
test. The geotechnical parameters of each material are listed in Table 1.
Remote Sens. 2022, 14, 5592 9 of 19
Figure 5. Diagrams of numerical and in situ shear strength tests. (a) The active layer and ground
ice interface; (b) a cross-section of the discrete element model; (c) in situ shear strength test setup
[9]; (d) a cutting soil sample on the surface of the massive ground ice [9].
Table 1. Geotechnical properties at the K1129W thaw slump site.
Depth (m) 0.5 1.5 1.9 Ground Ice Layer
Young modulus, E (MPa) 11.68 4.36 8.66 830
Poisson’s ratio 0.12 0.19 0.16 0.14
Uniaxial tensile strength, σ
t
(kPa) - 0.65 2 15.4
Uniaxial compressive strength, σ
c
(kPa) - 11 20 66.5
Intergranular friction coefficient, μ 0.68 0.55 0.62 0.2
Element density, ρ (kg/m
3
) 1850 1950 2150 917
2.3.2. Thaw-Induced Slope Failure Model
To quantitatively assess the deformation and volumetric change in RTS, a simula-
tion of a typical thaw slump development process was performed, and the dynamic of
the sliding particles from the source area was recorded. The massive ground ice ablation
contributed to the reduction in the shear strength in the basal zone and the active layer
particle instability. The moving elements represented the solifluction materials that slid
and flowed. Concurrently, a steep back scarp was formed on this gentle slope. Based on
this kind of thermokarst landslide’s typical characteristics, a three-dimensional discrete
element model of the K1129W thaw slump was used, as shown in Figure 6. The deposit-
ed elements were molded according to the digital elevation model and placed in a rec-
tangular simulation box [36] (integrated into the MatDEM). The numerical model con-
sisted of 5 layers from the ground surface to the bedrock and was 350 m on the X-axis,
220 m on the Y-axis, and 0 to 48 m on the Z-axis (Figure 6). We built this thaw slump
model with 224,388 active elements and 252,003 wall elements using discrete particles
with an average radius of 1 m. The physical properties are listed in Table 2.
Figure 5.
Diagrams of numerical and in situ shear strength tests. (
a
) The active layer and ground ice
interface; (
b
) a cross-section of the discrete element model; (
c
) in situ shear strength test setup [
9
];
(d) a cutting soil sample on the surface of the massive ground ice [9].

Remote Sens. 2022,14, 5592 9 of 18
Table 1. Geotechnical properties at the K1129W thaw slump site.
Depth (m) 0.5 1.5 1.9 Ground Ice Layer
Young modulus, E(MPa) 11.68 4.36 8.66 830
Poisson’s ratio 0.12 0.19 0.16 0.14
Uniaxial tensile strength, σt(kPa) - 0.65 2 15.4
Uniaxial compressive strength, σc(kPa) - 11 20 66.5
Intergranular friction coefficient, µ0.68 0.55 0.62 0.2
Element density, ρ(kg/m3)1850 1950 2150 917
2.3.2. Thaw-Induced Slope Failure Model
To quantitatively assess the deformation and volumetric change in RTS, a simulation
of a typical thaw slump development process was performed, and the dynamic of the
sliding particles from the source area was recorded. The massive ground ice ablation
contributed to the reduction in the shear strength in the basal zone and the active layer
particle instability. The moving elements represented the solifluction materials that slid
and flowed. Concurrently, a steep back scarp was formed on this gentle slope. Based on
this kind of thermokarst landslide’s typical characteristics, a three-dimensional discrete
element model of the K1129W thaw slump was used, as shown in Figure 6. The deposited
elements were molded according to the digital elevation model and placed in a rectangular
simulation box [
36
] (integrated into the MatDEM). The numerical model consisted of
5 layers from the ground surface to the bedrock and was 350 m on the X-axis, 220 m on the
Y-axis, and 0 to 48 m on the Z-axis (Figure 6). We built this thaw slump model with 224,388
active elements and 252,003 wall elements using discrete particles with an average radius
of 1 m. The physical properties are listed in Table 2.
Remote Sens. 2022, 14, 5592 10 of 19
Figure 6. Basic discrete element model (a), details of the headwall (b), and the three-dimensional
point cloud model (c) of the K1129W thaw slump.
The flow chart (Figure 7) illustrates the specific implementation processes of cou-
pling the aforementioned computation modules in this discrete element model. The de-
tailed simulation procedure is described in the following steps. Firstly, based on the fi-
nite difference method (FDM), we generated the temperature differences matrix of the
thermal disturbance elements and their neighboring elements. Additionally, the heat
flux was then calculated for these elements. Concurrently, the element temperature was
recorded in the “d.mo.SET. aT” matrix. Secondly, the unfrozen moisture function was
used to calculate the change in unfrozen water content under the temperature condition
in this step. Furthermore, the dimension of the particles was adjusted by integrating
their equations of thawing vertical deformation when the element temperature was
greater than 0 °C. Simultaneously, the program calculated the elements’ temperature re-
duction due to the release of phase change latent heat and recorded the final tempera-
ture of an iterative calculation step. At the same time, the shear strength in the basal
zone was detected and the friction-related parameters of the interface between ground
ice and the basal zone were adjusted in the thaw-induced bond contact model. Lastly,
the particles were advanced to new positions under gravity conditions in the Newtonian
physics system. The simulation was run for 1000 steps until the neighbor elements be-
came positive.
Figure 7. Flow chart and framework of DEM-FDM in the K1129W thaw slump.
Heat Conduction
Module
Ground ice
Ablation Module
Basic Discrete
Element Model
For totalcircle circle
Discretize the domain in simulation box and set initial temperature
For node i (center of particles) circle
Call ‘Heat Conduction Module’
Compute temperature difference matrix
Compute heat flux transfer to neighbor elements
Compute temperature decreasing matrix
unfrozen moisture content matrix
if T < freezing temperature in ice domain then
Call ‘Ground Ice Ablation Module’
Compute thaw settlement coefficient
Run the one-time iterative computation
Compute position, velocity, and force
Save the result of each compute step
Deformation and volumetric change in thaw slump
development area
FDM
Thaw-induced Bond
Contact Model
DEM
Figure 6.
Basic discrete element model (
a
), details of the headwall (
b
), and the three-dimensional
point cloud model (c) of the K1129W thaw slump.
The flow chart (Figure 7) illustrates the specific implementation processes of coupling
the aforementioned computation modules in this discrete element model. The detailed
simulation procedure is described in the following steps. Firstly, based on the finite
difference method (FDM), we generated the temperature differences matrix of the thermal
disturbance elements and their neighboring elements. Additionally, the heat flux was
then calculated for these elements. Concurrently, the element temperature was recorded
in the “d.mo.SET. aT” matrix. Secondly, the unfrozen moisture function was used to
calculate the change in unfrozen water content under the temperature condition in this step.
Furthermore, the dimension of the particles was adjusted by integrating their equations
of thawing vertical deformation when the element temperature was greater than 0
◦
C.

Remote Sens. 2022,14, 5592 10 of 18
Simultaneously, the program calculated the elements’ temperature reduction due to the
release of phase change latent heat and recorded the final temperature of an iterative
calculation step. At the same time, the shear strength in the basal zone was detected and
the friction-related parameters of the interface between ground ice and the basal zone were
adjusted in the thaw-induced bond contact model. Lastly, the particles were advanced to
new positions under gravity conditions in the Newtonian physics system. The simulation
was run for 1000 steps until the neighbor elements became positive.
Remote Sens. 2022, 14, 5592 10 of 19
Figure 6. Basic discrete element model (a), details of the headwall (b), and the three-dimensional
point cloud model (c) of the K1129W thaw slump.
The flow chart (Figure 7) illustrates the specific implementation processes of cou-
pling the aforementioned computation modules in this discrete element model. The de-
tailed simulation procedure is described in the following steps. Firstly, based on the fi-
nite difference method (FDM), we generated the temperature differences matrix of the
thermal disturbance elements and their neighboring elements. Additionally, the heat
flux was then calculated for these elements. Concurrently, the element temperature was
recorded in the “d.mo.SET. aT” matrix. Secondly, the unfrozen moisture function was
used to calculate the change in unfrozen water content under the temperature condition
in this step. Furthermore, the dimension of the particles was adjusted by integrating
their equations of thawing vertical deformation when the element temperature was
greater than 0 °C. Simultaneously, the program calculated the elements’ temperature re-
duction due to the release of phase change latent heat and recorded the final tempera-
ture of an iterative calculation step. At the same time, the shear strength in the basal
zone was detected and the friction-related parameters of the interface between ground
ice and the basal zone were adjusted in the thaw-induced bond contact model. Lastly,
the particles were advanced to new positions under gravity conditions in the Newtonian
physics system. The simulation was run for 1000 steps until the neighbor elements be-
came positive.
Figure 7. Flow chart and framework of DEM-FDM in the K1129W thaw slump.
Heat Conduction
Module
Ground ice
Ablation Module
Basic Discrete
Element Model
For totalcircle circle
Discretize the domain in simulation box and set initial temperature
For node i (center of particles) circle
Call ‘Heat Conduction Module’
Compute temperature difference matrix
Compute heat flux transfer to neighbor elements
Compute temperature decreasing matrix
unfrozen moisture content matrix
if T < freezing temperature in ice domain then
Call ‘Ground Ice Ablation Module’
Compute thaw settlement coefficient
Run the one-time iterative computation
Compute position, velocity, and force
Save the result of each compute step
Deformation and volumetric change in thaw slump
development area
FDM
Thaw-induced Bond
Contact Model
DEM
Figure 7. Flow chart and framework of DEM-FDM in the K1129W thaw slump.
Table 2. Physical and thermal parameters of the K1129W thaw slump model.
Properties and Parameters Values
Soil
Density of solid grains 2350 kg/m3
Thermal conductivity of soil (λw) 1.48 W/m/K
Specific heat of soil (cw) 1041.5 J/kg/K
Permafrost
Density of ice (ρi)910 kg/m3
Density of ice-rich permafrost (50–80%) 1700 kg/m3
Thermal conductivity of ice (λi) 2.14 W/m/K
Thermal conductivity of ice-rich permafrost (50–80%) 1.87 W/m/K
Specific heat of ice (ci) 2108 J/kg/K
Specific heat of ice-rich permafrost (50–80%) 1860 J/kg/K
Latent heat (Lw)3.34 ×105J/kg
Others
Shape factor for unfrozen water content q3.0
Terminal fraction of moisture unfrozen p0.165
2.4. TLS-UAV Method
To calibrate the simulation results, a combined method of terrestrial laser scanning
(TLS) and unmanned aerial vehicle (UAV) was put forward. The details of the data
acquisition and processing are as follows.
2.4.1. Terrestrial Laser Scanner Survey
To obtain a high-resolution point cloud of the K1129W thaw slump development area,
the Leica P50 terrestrial laser scanner was employed in our study. The picture acquisition
speed is up to 976 k points/s, and the maximum scanning distance is 120 m. The scanning
scope was set from
−
55
◦
to 90
◦
in the vertical direction and 0
◦
to 360
◦
in the horizontal
direction, and the scanning accuracy was set as 1.6 mm of a 10 m scan radius. To measure
the total volumetric change and deformation in the thaw slump development area, two

Remote Sens. 2022,14, 5592 11 of 18
TLS investigations were performed in September 2021 and August 2022. Each scanning
contained 8 stations.
The post-processing software Leica Cyclone 9.2.0 (https://leica-geosystems.com) was
used for the massive point cloud data splicing of adjacent station data and the coordinate
system conversion. After basic preprocessing, spatial sampling was conducted and the
unrelated points were removed. Additionally, the 0.1 m spacing points were then extracted
and were meshed to the time series triangular irregular networks (TINs). Furthermore, the
TIN comparison work was executed in Matlab 2019b.
2.4.2. Unmanned Aerial Vehicle Survey
To supplementarily quantify the thaw slump deformation and volumetric change,
the UAV-based orthoimages and digital elevation model of the investigated thaw slump
were utilized to reconstruct the 3D model and digitalize the K1129W thaw slump area. DJI
Matrice M300 RTK, equipped with a Zenmuse P1 visible light camera lens, was employed
to take aerial photos of the K1129W thaw slump and the surrounding area. DJI Pilot
2 software was used to plan the flight route and control the aircraft. The flight height was
set to 60 m higher than the headwall, and the overlap rate was set at 75% in the heading
direction and 85% in the sidewise direction. Two UAV fights were conducted in September
2021 and August 2022. Eventually, the aerial images of every fight were imported into the
post-processing software DJI Terra to conduct aero-triangulation and model reconstruction.
Additionally, high-resolution (<10 mm) orthoimages and the 3D model presented detailed
information on the K1129W thaw slump. The comparative analysis can replenish the TLS
investigation. Figure 8shows the overall analysis flow chart of the TLS-UAV method.
Remote Sens. 2022, 14, 5592 12 of 19
model presented detailed information on the K1129W thaw slump. The comparative
analysis can replenish the TLS investigation. Figure 8 shows the overall analysis flow
chart of the TLS-UAV method.
Figure 8. Data acquisition and processing flowchart of terrestrial laser scanning and unmanned
aerial vehicle.
3. Results
3.1. Shear Strength of the Ground Ice and Active Layer
This study first obtained the shear stress–displacement relationship of the basal
zone in the detachment failure process between the active layer and the ground ice layer
(Figure 9). It is evident that an obvious stress-softening process is presented in the shear
stress–displacement curves. Concurrently, the shear stress and horizontal displacement
curves of the discrete element model were demonstrated by the authors’ previous in situ
test [9]. Figure 9 also illustrates a good consistency between the model and the field ex-
periment.
Point Cloud
Data Collection
TLS Sites
Layout
UAV Flight
Planning
Data Splicing
and Alignment
3D Thaw
Slump Model
Ground
Control points
(GCPs)
Resampling and
Meshing
Multi-Temporal
Changes Comparison
Aerial Images
Capture
Aero
triangulation
2D Maps
Orthoimage
Digital
elevation model
Thaw slump
Boundary
Identification
Vertical
Deformation
Prick GCPs
Headwall
Retrogression
Figure 8.
Data acquisition and processing flowchart of terrestrial laser scanning and unmanned
aerial vehicle.
3. Results
3.1. Shear Strength of the Ground Ice and Active Layer
This study first obtained the shear stress–displacement relationship of the basal zone in
the detachment failure process between the active layer and the ground ice layer (Figure 9).
It is evident that an obvious stress-softening process is presented in the shear stress–
displacement curves. Concurrently, the shear stress and horizontal displacement curves
of the discrete element model were demonstrated by the authors’ previous in situ test [
9
].
Figure 9also illustrates a good consistency between the model and the field experiment.

Remote Sens. 2022,14, 5592 12 of 18
Remote Sens. 2022, 14, 5592 12 of 19
model presented detailed information on the K1129W thaw slump. The comparative
analysis can replenish the TLS investigation. Figure 8 shows the overall analysis flow
chart of the TLS-UAV method.
Figure 8. Data acquisition and processing flowchart of terrestrial laser scanning and unmanned
aerial vehicle.
3. Results
3.1. Shear Strength of the Ground Ice and Active Layer
This study first obtained the shear stress–displacement relationship of the basal
zone in the detachment failure process between the active layer and the ground ice layer
(Figure 9). It is evident that an obvious stress-softening process is presented in the shear
stress–displacement curves. Concurrently, the shear stress and horizontal displacement
curves of the discrete element model were demonstrated by the authors’ previous in situ
test [9]. Figure 9 also illustrates a good consistency between the model and the field ex-
periment.
Point Cloud
Data Collection
TLS Sites
Layout
UAV Flight
Planning
Data Splicing
and Alignment
3D Thaw
Slump Model
Ground
Control points
(GCPs)
Resampling and
Meshing
Multi-Temporal
Changes Comparison
Aerial Images
Capture
Aero
triangulation
2D Maps
Orthoimage
Digital
elevation model
Thaw slump
Boundary
Identification
Vertical
Deformation
Prick GCPs
Headwall
Retrogression
Figure 9.
Comparison between the in situ tests and DEM simulations of horizontal stress–
displacement curves. (
a
) Horizontal stress–displacement curves and samples after shear failure
of (b) in situ test [9] and (c) discrete element test.
Figure 10 shows the evolution of the shear stress displacement with different interface
strength parameters of the weakening coefficient
αw
for the specified loading plate. It
is clear that both the peak and residual shear stresses decrease with the cementation
weakening coefficient
αw
for one given vertical pressure. With the decline in the granular
cementation weakening coefficient
αw
, the appearance of stress softening was not obvious.
Moreover, with the peak shear stress decline due to the friction coefficient decrease, granular
cementation is more liable to break. Thereby, the critical stress was approaching the low-
cementation weakening coefficient scenario. In addition to determining the strength
parameters in the basal zone of the active layer, the direct shear test simulation can, in turn,
demonstrate granular cementation “weakening or breaking” due to the ground ice ablation
module described in Section 2.3.2.
Remote Sens. 2022, 14, 5592 13 of 19
Figure 9. Comparison between the in situ tests and DEM simulations of horizontal stress–
displacement curves. (a) Horizontal stress–displacement curves and samples after shear failure of
(b) in situ test [9] and (c) discrete element test.
Figure 10 shows the evolution of the shear stress displacement with different inter-
face strength parameters of the weakening coefficient α
w
for the specified loading plate.
It is clear that both the peak and residual shear stresses decrease with the cementation
weakening coefficient α
w
for one given vertical pressure. With the decline in the granular
cementation weakening coefficient α
w
, the appearance of stress softening was not obvi-
ous. Moreover, with the peak shear stress decline due to the friction coefficient decrease,
granular cementation is more liable to break. Thereby, the critical stress was approach-
ing the low-cementation weakening coefficient scenario. In addition to determining the
strength parameters in the basal zone of the active layer, the direct shear test simulation
can, in turn, demonstrate granular cementation “weakening or breaking” due to the
ground ice ablation module described in Section 2.3.2.
Figure 10. Comparison of the shear stress with loading horizontal displacement with different
weakening coefficients α
w
at vertical stresses of (a) 30.00 kPa, (b) 44.08 kPa, and (c) 50.61 kPa.
3.2. Deformation and Volumetric Change Analysis
Heat conduction in ice-rich permafrost can impact the granular structure, shown as
shear strength decreases through the thaw-induced contraction of particles and weaken-
ing of the cementation between the particles. It is, therefore, indispensable to demon-
strate the deformation characteristics of RTS under climatic warming. Due to climatic
warming and wetting, the exposed ground ice at the lower part of the headwall was be-
ginning to melt. Furthermore, the cementation of thawing elements was gradually
weakening.
Figure 11 shows the deformation simulation results of the K1129W thaw slump to
elucidate and present concise results, and the resultant displacement of particles with
more than 0.5 m is extracted from the model. For conciseness, these extracted elements
are superimposed on the image of the K1129W thaw slump area. The white boundary
line represents the thaw slump development area outlined from the orthoimage of the
UAV survey in September 2021 (Figure 11). Concurrently, the subsidence and headwall
retrogression (Figure 11a) and sliding direction velocity component (Figure 11b) in the
thaw slump development area were also calculated in the model. During the one-time
thaw slump process, the overall vertical deformation varied dramatically in the lower
part of the headwall, with subtle variations in collapsed scar area; following the active
layer detachment failure at the headwall, the thawed particles slid down the sliding sur-
face and flowed to the front edge of the slope. The ground subsidence reached 2.3 m at
the lower part of the headwall. Figure 11a shows the headwall retreat of the K1129W
thaw slump. The total displacement of headwall retrogression was approximately 2.2 m
to 3.5 m during a one-time thaw slump process. Especially for the northwestern part, the
retreat distance reached 3.5 m, and this is the location where the maximum ground sub-
sidence occurred. Figure 11b shows the velocity evolution of melting or sliding mass. At
Figure 10.
Comparison of the shear stress with loading horizontal displacement with different
weakening coefficients αwat vertical stresses of (a) 30.00 kPa, (b) 44.08 kPa, and (c) 50.61 kPa.
3.2. Deformation and Volumetric Change Analysis
Heat conduction in ice-rich permafrost can impact the granular structure, shown as
shear strength decreases through the thaw-induced contraction of particles and weakening
of the cementation between the particles. It is, therefore, indispensable to demonstrate the
deformation characteristics of RTS under climatic warming. Due to climatic warming and
wetting, the exposed ground ice at the lower part of the headwall was beginning to melt.
Furthermore, the cementation of thawing elements was gradually weakening.

Remote Sens. 2022,14, 5592 13 of 18
Figure 11 shows the deformation simulation results of the K1129W thaw slump to
elucidate and present concise results, and the resultant displacement of particles with
more than 0.5 m is extracted from the model. For conciseness, these extracted elements
are superimposed on the image of the K1129W thaw slump area. The white boundary
line represents the thaw slump development area outlined from the orthoimage of the
UAV survey in September 2021 (Figure 11). Concurrently, the subsidence and headwall
retrogression (Figure 11a) and sliding direction velocity component (Figure 11b) in the
thaw slump development area were also calculated in the model. During the one-time
thaw slump process, the overall vertical deformation varied dramatically in the lower part
of the headwall, with subtle variations in collapsed scar area; following the active layer
detachment failure at the headwall, the thawed particles slid down the sliding surface
and flowed to the front edge of the slope. The ground subsidence reached 2.3 m at the
lower part of the headwall. Figure 11a shows the headwall retreat of the K1129W thaw
slump. The total displacement of headwall retrogression was approximately 2.2 m to 3.5 m
during a one-time thaw slump process. Especially for the northwestern part, the retreat
distance reached 3.5 m, and this is the location where the maximum ground subsidence
occurred. Figure 11b shows the velocity evolution of melting or sliding mass. At the active
layer detachment failure stage, the velocity of the thawed materials increased dramatically.
Additionally, the maximum velocity of particles was 3.1 m/s. After the detachment failure,
the velocity of most elements declined and gradually stopped at the front edge of the thaw
slump development area. Most particles at the front edge of the sliding mass did not have
an evident velocity at the end of the computation time. The potential energy of RTS caused
by the ground ice ablation at the lower part of the headwall may have dissipated. Note
that the simulated headwall retrogression retreated evenly due to the ground ice content,
and distribution was assumed to obey uniform distribution. However, we could not obtain
the ground ice distribution of the entire thaw slump development area, which was limited
by geological data and field harsh conditions. The comparison between the annual change
in the thaw slump boundary lines and the simulation results is introduced in Section 3.3.
Remote Sens. 2022, 14, 5592 14 of 19
the active layer detachment failure stage, the velocity of the thawed materials increased
dramatically. Additionally, the maximum velocity of particles was 3.1 m/s. After the de-
tachment failure, the velocity of most elements declined and gradually stopped at the
front edge of the thaw slump development area. Most particles at the front edge of the
sliding mass did not have an evident velocity at the end of the computation time. The
potential energy of RTS caused by the ground ice ablation at the lower part of the head-
wall may have dissipated. Note that the simulated headwall retrogression retreated
evenly due to the ground ice content, and distribution was assumed to obey uniform
distribution. However, we could not obtain the ground ice distribution of the entire
thaw slump development area, which was limited by geological data and field harsh
conditions. The comparison between the annual change in the thaw slump boundary
lines and the simulation results is introduced in Section 3.3.
To quantitatively estimate the volumetric change in the K1129W thaw slump, the
dynamic of the sliding particles from the source area was recorded. As illustrated in
Figure 11, about 437 elements slid from the source area to the collapsed scar area. Less
than 125 particles slid out of the trailing edge of the landslide, which presented the soil
erosion or mass wasting of the RTS. During this one-time thaw slump process, the mass
wasting that occurred in the lower part of the headwall was approximately 1335 m
3
, the
volumetric change in displaced mass in the thaw slump development area was approx-
imately 1050 m
3
, and the volume of the soil erosion was approximately 211 m
3
.
Figure 11. Simulated evolution of the K1129W thaw slump. (a) Displacement evolution of related
elements. (b) Velocity evolution of related elements. Note that the white solid line represents the
thaw slump boundary in September 2021.
3.3. Comparisons between Geophysical Survey and Simulation
To quantify the deformation and volumetric change in the K1129W thaw slump
and verify the simulation results, this research delineated the thaw slump development
area margin using a high-resolution digital elevation model and a TIN model for 2021
and 2022. The blue and light yellow lines represented the boundary of the K1129W thaw
Figure 11.
Simulated evolution of the K1129W thaw slump. (
a
) Displacement evolution of related
elements. (
b
) Velocity evolution of related elements. Note that the white solid line represents the
thaw slump boundary in September 2021.

Remote Sens. 2022,14, 5592 14 of 18
To quantitatively estimate the volumetric change in the K1129W thaw slump, the
dynamic of the sliding particles from the source area was recorded. As illustrated in
Figure 11, about 437 elements slid from the source area to the collapsed scar area. Less than
125 particles slid out of the trailing edge of the landslide, which presented the soil erosion
or mass wasting of the RTS. During this one-time thaw slump process, the mass wasting
that occurred in the lower part of the headwall was approximately 1335 m
3
, the volumetric
change in displaced mass in the thaw slump development area was approximately 1050
m3, and the volume of the soil erosion was approximately 211 m3.
3.3. Comparisons between Geophysical Survey and Simulation
To quantify the deformation and volumetric change in the K1129W thaw slump and
verify the simulation results, this research delineated the thaw slump development area
margin using a high-resolution digital elevation model and a TIN model for 2021 and
2022. The blue and light yellow lines represented the boundary of the K1129W thaw slump
in September 2021 and August 2022, respectively (Figure 12b). The negative values in
Figure 12a indicated the erosion or thaw settlement zone of the thaw slump development
area, representing the ground subsidence due to the melted or collapsed materials sliding
to the deposition zones. On the contrary, the positive values indicated the displaced area,
denoting the accumulation of deposited materials from the thawed headwall. Through
the superposition analysis of these data, the calculated vertical deformation and headwall
retreat results were shown in Figure 12 between 2021 and 2022. The significant deformation
of the headwall retrogression and surface subsidence appeared in the northwest of the
thaw slump development area. During this period, the headwall retreat values in the south-
western and northwestern “lobe” parts were approximately 2.8 m and 3.2 m, respectively.
Additionally, the vertical deformation was
−
1.9 m at the lower part of the headwall. The
geophysical investigation and simulation results were in good agreement. In addition to
the good consistency of the deformation, the TLS and UAV survey results can display the
deformation characteristic more delicately. Especially for the thaw slump retrogression, the
results can indirectly reflect the ground ice ablation.
Remote Sens. 2022, 14, 5592 15 of 19
slump in September 2021 and August 2022, respectively (Figure 12b). The negative val-
ues in Figure 12a indicated the erosion or thaw settlement zone of the thaw slump de-
velopment area, representing the ground subsidence due to the melted or collapsed ma-
terials sliding to the deposition zones. On the contrary, the positive values indicated the
displaced area, denoting the accumulation of deposited materials from the thawed
headwall. Through the superposition analysis of these data, the calculated vertical de-
formation and headwall retreat results were shown in Figure 12 between 2021 and 2022.
The significant deformation of the headwall retrogression and surface subsidence ap-
peared in the northwest of the thaw slump development area. During this period, the
headwall retreat values in the southwestern and northwestern “lobe” parts were ap-
proximately 2.8 m and 3.2 m, respectively. Additionally, the vertical deformation was
−1.9 m at the lower part of the headwall. The geophysical investigation and simulation
results were in good agreement. In addition to the good consistency of the deformation,
the TLS and UAV survey results can display the deformation characteristic more deli-
cately. Especially for the thaw slump retrogression, the results can indirectly reflect the
ground ice ablation.
To calculate the volumetric change in the thaw slump development area, the time
series of the high-density point cloud from the TLS survey was conducted for compari-
son. The retreat of the headwall caused an increment in the collapsed scar area. With the
thawed materials sliding down the face of the headwall, most of the materials were left
in the displaced area and the others flowed away. The total volumetric change was
about 1412 m
3
in the thaw slump development area. Among them, about 1124 m
3
was
added to the displaced area. Thus, the estimated amount of mass wasting was about 288
m
3
.
Figure 12. Surface deformation (a) and headwall retrogression (b) of the K1129W thaw slump de-
velopment area using terrestrial laser scanning (TLS) and unmanned aerial vehicle (UAV).
4. Discussion
4.1. Impact of the Ground Ice Content
Ice-rich permafrost thawing, or massive ground ice ablation, are the most signifi-
cant prerequisites for RTS development. Ice-rich permafrost in the study area comprises
pore ice, segregated ice, soil mass, unfrozen water, and gas-filled voids[46]. In a natural
state, during the one-sided thawing of the active layer in a warm period, unfrozen water
migrates downward toward the thawing front descending from the ground surface
when there are a negative ground temperature gradient conditions [47]. However, in the
RTS development area, the headwall of RTS showed exposed ground ice, especially in
our study site. Under high air temperature and heavy rain conditions, the rate of ground
ice ablation increased, and the meltwater seeped or drained to the sliding face. Due to
the ground ice melt, the shear strength of soil near the permafrost table would decrease
and the pore water pressure would increase simultaneously.
Figure 12.
Surface deformation (
a
) and headwall retrogression (
b
) of the K1129W thaw slump
development area using terrestrial laser scanning (TLS) and unmanned aerial vehicle (UAV).
To calculate the volumetric change in the thaw slump development area, the time
series of the high-density point cloud from the TLS survey was conducted for comparison.
The retreat of the headwall caused an increment in the collapsed scar area. With the thawed
materials sliding down the face of the headwall, most of the materials were left in the
displaced area and the others flowed away. The total volumetric change was about 1412 m
3
in the thaw slump development area. Among them, about 1124 m
3
was added to the
displaced area. Thus, the estimated amount of mass wasting was about 288 m3.

Remote Sens. 2022,14, 5592 15 of 18
4. Discussion
4.1. Impact of the Ground Ice Content
Ice-rich permafrost thawing, or massive ground ice ablation, are the most significant
prerequisites for RTS development. Ice-rich permafrost in the study area comprises pore
ice, segregated ice, soil mass, unfrozen water, and gas-filled voids [
46
]. In a natural state,
during the one-sided thawing of the active layer in a warm period, unfrozen water migrates
downward toward the thawing front descending from the ground surface when there are a
negative ground temperature gradient conditions [
47
]. However, in the RTS development
area, the headwall of RTS showed exposed ground ice, especially in our study site. Under
high air temperature and heavy rain conditions, the rate of ground ice ablation increased,
and the meltwater seeped or drained to the sliding face. Due to the ground ice melt, the
shear strength of soil near the permafrost table would decrease and the pore water pressure
would increase simultaneously.
Therefore, the ground ice content can affect the intergranular cementation state in
permafrost. In this study, the thaw slump development process was simulated with
different volumetric ice contents (from 1% to 90%). Due to the headwall retrogression being
highly related to the height of the headwall, the slope angle, and the scale of RTS [
48
],
this study quantitatively estimated the mass wasting and headwall retrogression in a
determined headwall height and thaw slump scale. Thus, the ratio of the retrogression
and height in the frozen back scarp was defined as retrogression ratio r
1
, and the ratio of
the volumetric change and thaw slump development area was defined as mass wasting
ratio r
2
. Figure 13 presents that the mass wasting and headwall retrogression tended to
enlarge with the increase in ground ice content. The minimum volumetric ice content of
active layer detachment failure was about 10% in this thaw slump. The volumetric change
and headwall retrogression increased approximately linearly (r
2
= 0.9729, p< 0.001, n= 70;
r
2
= 0.8597, p< 0.001, n= 70, respectively) with volumetric ice content in this study site.
With a higher ground ice content, the bonds were more susceptible to “weak or breakage”,
and thereby the elements in the active layer group were prone to slide.
4.2. Research Deficiencies
Although the fast GPU-based discrete element method (DEM) is a high-efficiency
means to calculate large deformation problems, the thermokarst landslide is a long-term
evolutionary process that is different from traditional landslides, such as avalanche and
debris flow. The mud-flow materials in the scar area make it difficult to drill in RTS
development areas. We could not obtain the ground ice content in the scar area. Thus, the
model mainly simulated the active layer detachment failure at the steep frozen back scarp
and the thawed materials downslope sliding during the thawing season. Moreover, the
simulation did not consider the solifluction that remained on the scar area after the last
thawing season. The difference between the simulation and TLS-UAV is mainly owing to
this reason. Additionally, the TLS-UAV method can acquire a set of high-density three-
dimensional point cloud coordinates of RTS. Investigation data can be utilized to build
a detailed geomorphological picture and analyze the deformation [
23
]. However, this is
limited by the accessibility of the study area because most RTSs are located in no man’s land.
Concurrently, a high-resolution digital surface (elevation) model is needed for an accurate
real terrain numerical model. Furthermore, there is the limitation that the remoting sensing
method cannot accurately assess the order of mass wasting less than 500 m
2
and elevation
changes less than 1.6 m [8].
To replenish the limitations of the remote sensing and TLS-UAV combined methods, as
well as to meet ordinary computer computing, it is essential to simulate these “small-scale”
thaw slumps in the QTP. Meanwhile, the method presented in this paper can be used to es-
timate the evolution of landslides, especially for mass wasting and headwall retrogression.

Remote Sens. 2022,14, 5592 16 of 18
Remote Sens. 2022, 14, 5592 16 of 19
Therefore, the ground ice content can affect the intergranular cementation state in
permafrost. In this study, the thaw slump development process was simulated with dif-
ferent volumetric ice contents (from 1% to 90%). Due to the headwall retrogression being
highly related to the height of the headwall, the slope angle, and the scale of RTS [48],
this study quantitatively estimated the mass wasting and headwall retrogression in a de-
termined headwall height and thaw slump scale. Thus, the ratio of the retrogression and
height in the frozen back scarp was defined as retrogression ratio r1, and the ratio of the
volumetric change and thaw slump development area was defined as mass wasting ratio
r2. Figure 13 presents that the mass wasting and headwall retrogression tended to en-
large with the increase in ground ice content. The minimum volumetric ice content of ac-
tive layer detachment failure was about 10% in this thaw slump. The volumetric change
and headwall retrogression increased approximately linearly (r2 = 0.9729, p < 0.001, n =
70; r2 = 0.8597, p < 0.001, n = 70, respectively) with volumetric ice content in this study
site. With a higher ground ice content, the bonds were more susceptible to “weak or
breakage”, and thereby the elements in the active layer group were prone to slide.
Figure 13. Mass transport, headwall retrogression, and relation with volumetric ice content. (a)
Box plots of volumetric change in K1129W thaw slump development area of different volumetric
ice contents. (b) Linear relation between mass transport amount and volumetric ice content. (c)
Box plots of headwall retrogression in K1129W thaw slump development area of different volu-
metric ice contents. (d) Linear relation between headwall retrogression and volumetric ice content.
Note that the red short dash is the average value.
4.2. Research Deficiencies
Although the fast GPU-based discrete element method (DEM) is a high-efficiency
means to calculate large deformation problems, the thermokarst landslide is a long-term
evolutionary process that is different from traditional landslides, such as avalanche and
debris flow. The mud-flow materials in the scar area make it difficult to drill in RTS de-
velopment areas. We could not obtain the ground ice content in the scar area. Thus, the
model mainly simulated the active layer detachment failure at the steep frozen back
<10 10–20 21–30 31–40 41–50 51–60 61–70
0
50
100
150
200
250
Mass transport (m
3
)
<10 10–20 21–30 31–40 41–50 51–60 61–70
0
2
4
6
8
Volumetric ice content
(
%
)
Headwall retrogression (m)
0 10203040506070
0
1
2
3
4
5
6
7
8
Headwall retrogression (m)
Volumetric ice content
(
%
)
0 1020304050607080
0
50
100
150
200
250
Mass transport (m
3
)
(a)
y = 3.73664 x – 2.8983
R
2
= 0.97292
(b)
(c)
y = 0.088 x + 1.036
R
2
= 0.85974
(d)
Figure 13. Mass transport, headwall retrogression, and relation with volumetric ice content. (a) Box
plots of volumetric change in K1129W thaw slump development area of different volumetric ice
contents. (
b
) Linear relation between mass transport amount and volumetric ice content. (
c
) Box
plots of headwall retrogression in K1129W thaw slump development area of different volumetric ice
contents. (
d
) Linear relation between headwall retrogression and volumetric ice content. Note that
the red short dash is the average value.
5. Conclusions
In this research, we quantitatively assessed the seasonal deformation and volumetric
change in a typical thaw slump in the permafrost terrain of the QTP with a discrete element
model and geophysical model. We found that the results of ground subsidence, mass
wasting, and headwall retrogression were well described by the simulation. Some valuable
findings were drawn as follows:
(1) We proposed a systematic computation procedure, GPU-based DEM-FDM, for
the effective simulation of the coupled thermo-mechanical thaw-induced slope failure
problem. It is demonstrated that the thaw-induced bond contact model can effectively
present the “weakening” of intergranular cementation, showing the shear strength decrease.
Concurrently, the law of shear strength in the basal zone of the active layer under the
thawing or thawed state was determined by the simulation.
(2) In a thawing season, the total volumetric change was approximately 1335 m
3
.
Headwall retrogression was about 2.2 m to 3.5 m and the surface subsidence reached 2.3 m
in the lower part of the headwall. Approximately 1050 m
3
of thawed materials were moved
to the displaced area, and the amount of soil erosion was about 211 m3.
(3) The minimum volumetric ice content required to trigger active layer detachment
failure is approximately 10%. The relation between volumetric ice content and mass wasting
can be expressed as a linear equation.
TLS-UAV technology and the DEM-FDM method can replenish the limitations of
remote sensing, especially for “small-scale” RTSs. This kind of behavior, especially for the
impact of ground ice content, can provide valuable insights into predicting the future RTS

Remote Sens. 2022,14, 5592 17 of 18
evolution of the QTP and the Arctic. Additionally, quantifying soil erosion has significant
implications for the assessment of the eco-environment of the whole QTP.
Author Contributions:
Conceptualization, F.N., C.J. and J.L.; methodology, C.J.; software, C.J. and
P.H.; validation, L.R., Y.S. and J.L.; formal analysis, C.J.; investigation, F.N., C.J. and P.H.; resources,
F.N. and J.L.; data curation, C.J., L.R., Y.S. and P.H.; writing—original draft preparation, C.J.; writing—
review and editing, F.N., C.J., Y.S. and J.L.; visualization, C.J.; supervision, F.N., J.L. and Y.S.; project
administration, F.N.; funding acquisition, F.N. All authors have read and agreed to the published
version of the manuscript.
Funding:
This work was supported by the Second Tibetan Plateau Scientific Expedition and Research
(STEP) Program (Grant No. 2019QZKK0905), the Strategic Priority Research Program of the Chinese
Academy of Sciences (Grant No. XDA19070504), and the Guangdong Provincial Key Laboratory of
Modern Civil Engineering Technology (2021B1212040003).
Conflicts of Interest: The authors declare no conflict of interest.
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