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A GIS-based three-dimensional landslide generated waves height calculation method

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Combined with the spatial data processing capability of geographic information systems (GIS), a three-dimensional (3D) landslide surge height calculation method is proposed based on grid column units. First, the data related to the landslide are rasterized to form grid columns, and a force analysis model of 3D landslides is established. Combining the vertical strip method with Newton's laws of motion, dynamic equilibrium equations are established to solve for the surge height. Moreover, a 3D landslide surge height calculation expansion module is developed in the GIS environment, and the results are compared with those of the two-dimensional Pan Jiazheng method. Comparisons show that the maximum surge height obtained by the proposed method is 24.6 % larger than that based on the Pan Jiazheng method. Compared with the traditional two-dimensional method, the 3D method proposed in this paper better represents the actual spatial state of the landslide and is more suitable for risk assessment.
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1
A GIS-based three-dimensional landslide generated waves height calculation
1
method
2
3
Guo Yu1, Mowen Xie 1,*, Lei Bu1, Asim Farooq2
4
1 School of Civil and Resource Engineering, University of Science & Technology
5
Beijing, Beijing 100083, China
6
2 CECOS University, Peshawar Pakistan
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* Corresponding author: Mowen Xie (mowenxie123@163.com)
8
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Abstract: Combined with the spatial data processing capability of geographic
10
information systems (GIS), a three-dimensional (3D) landslide surge height calculation
11
method is proposed based on grid column units. First, the data related to the landslide
12
are rasterized to form grid columns, and a force analysis model of 3D landslides is
13
established. Combining the vertical strip method with Newton's laws of motion,
14
dynamic equilibrium equations are established to solve for the surge height. Moreover,
15
a 3D landslide surge height calculation expansion module is developed in the GIS
16
environment, and the results are compared with those of the two-dimensional Pan
17
Jiazheng method. Comparisons show that the maximum surge height obtained by the
18
proposed method is 24.6% larger than that based on the Pan Jiazheng method.
19
Compared with the traditional two-dimensional method, the 3D method proposed in
20
this paper better represents the actual spatial state of the landslide and is more suitable
21
for risk assessment.
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Key words: landslide; waves height; grid column; GIS
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1. Introduction
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When a reservoir bank landslide body slides into the water, it will cause a waves
25
that can not only endanger the safety of passing ships and surrounding buildings but
26
also threaten the safety of the dam. Therefore, calculating the waves height is important
27
for evaluating the risks of landslides (Xu and Zhou, 2015).
28
The methods of calculating the landslide generated waves height can mainly be
29
divided into analytical method (Noda, 1970; Pan, 1980; Huang et al., 2012; Miao et al., 2011;
30
Di et al., 2008), numerical simulation method (Silvia and Marco, 2011; Montagna et al.,
31
2011), and physical modelling method (Ataie-Ashtiani and Nik-Khah, 2008; Cui and Zhu,
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2011). Analytical method is widely used in engineering applications because of its
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simple modelling processes, which has few requirements for engineers and high
34
precision.
35
The analytical method originated from Node (1970). Node proposed the waves
36
height calculation method on the basis of hydraulics. Since then, many scholars have
37
conducted more in-depth research. For example, Academician Pan Jiazheng of China
38
divided the landslide body into many two-dimensional (2D) vertical strips and
39
calculated the waves height by considering the horizontal and vertical movement of the
40
landslide. This method is called the Pan Jiazheng method (Pan, 1980). Huang et al. (2012)
41
improved the Pan Jiazheng method by considering the resistance of water and the
42
change in the friction coefficient. Miao et al. (2011) proposed a sliding block model
43
based on the 2D vertical strip method to predict the maximum waves height. The
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American Civil Engineering Society recommends a prediction method of the waves
45
height (Di et al., 2008) that assumes the landslide results in the particle motion with a
46
centre of gravity, and Newton's law of motion is used to calculate the waves height.
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The above methods are all 2D analysis methods. In the vertical strip method, the
48
calculation results will differ with the selection of the 2D section. The 2D analysis
49
methods cannot effectively simulate the actual spatial state of three-dimensional (3D)
50
landslide. Hu (Hu, 1995) proposed that the value obtained by 2D analysis method is
51
approximately 70% of the value based on 3D analysis method. To date, analytical
52
method based on the 3D landslide body model has not been studied by scholars.
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Geographic information systems (GIS) is widely used in geotechnical engineering.
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The most notable feature of GIS is that they can transform vector data into grid data
55
sets based on a grid column unit model (Xie et al., 2006a). Because of the high 3D spatial
56
data processing capability of GIS, many scholars have added geotechnical professional
57
models to their respective systems. For example, our research team established a 3D
58
limit equilibrium method based on GIS, and developed a slope stability analysis module
59
called 3Dslope (Xie et al., 2003a; 2003b; 2006b). Jia et al. (2015) proposed a slope stability
60
analysis method by coupling a rainfall infiltration model and 3D limit equilibrium
61
method within the GIS environment. Mergili (2014) combined GRASS GIS and the 3D
62
Hovland model to implement a 3D slope stability model capable of considering shallow
63
and deep-seated slope failures. Therefore, to develop a waves height calculation module
64
in GIS, it is necessary to first establish a force analysis model of the 3D landslide in
65
GIS.
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Based on the spatial data processing capability of GIS, this paper applies the grid
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column unit model to establish a 3D landslide model, and proposes a method for
68
calculating the waves height. Compared with 2D analysis methods, the 3D method
69
proposed in this paper better represents the actual spatial state of landslides.
70
Simultaneously, the resistance of the water is considered to improve the accuracy of the
71
calculation result. To make the calculation more convenient, an expansion module is
72
developed to calculate the waves height in GIS, and the feasibility of the module is
73
verified by a case study.
74
2. GIS-based method of calculating the waves height
75
2.1. Grid column unit model
76
For a slope, the representation of data is mainly in the form of vectors. These data
77
include but are not limited to slip surface, strata, groundwater, fault, slip, and other
78
types of data. These vector data layers can be converted to raster data layers using the
79
spatial analysis capabilities of GIS to form a grid data set. The grid data structure
80
consists of rectangular units. Each rectangular unit has a corresponding row and column
81
number and is assigned an attribute value that represents the grid unit (Xie et al., 2004).
82
Therefore, the slope can be divided into square columns based on the grid units to form
83
a grid column unit model, as shown in Fig. 1.
84
85
Fig. 1. Grid column unit model ((a) 3D view of landslide, (b) 3D view of one column).
86
2.1. Force analysis
87
First, we arbitrarily selected a grid column in a 3D landslide body, as shown in
88
Fig. 2. We can specify the forces acting on the grid column as follows.
89
(1) The weight of one grid column is W; the direction is the Z-axis; and the weight
90
acts at the centroid of the grid column.
91
(2) The resultant horizontal seismic force is kW, where k is the “seismic
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coefficient”; the direction of kW is the sliding direction of the landslide; and the
93
resultant horizontal force acts at the centroid of the grid column.
94
95
Fig. 2. Force analysis of one grid column.
96
(3) The external loads on the ground surface are represented by P; the direction of
97
P is the Z-axis, and these external loads act at the centre of the top of the grid column.
98
(4) The normal and shear stresses on the slip surface are represented by σ and τ,
99
respectively. The normal stress is perpendicular to the slip surface, and the shear stress
100
is in the sliding direction of the landslide. The normal and shear stresses act at the
101
centroid of the bottom of the grid column.
102
(5) The pore water pressure on the slip surface is u.
103
(6) The horizontal tangential forces on the left and right sides of a grid column are
104
T and T+T, respectively; the vertical tangential forces on the left and right sides of a
105
grid column are R and R+R, respectively; the normal forces on the left and right sides
106
of a grid column are F and F+F, respectively; the horizontal tangential forces on the
107
front and rear sides of a grid column are E and EE, respectively; the vertical
108
tangential forces on the front and rear sides of a grid column are V and V+V,
109
respectively; and the normal forces on the front and rear sides of a grid column are H
110
and H+H, respectively. For convenience, the resultant force between columns in the
111
sliding direction of the landslide is defined as ΔD.
112
2.3. The spatial relationships among parameters
113
Fig. 3 shows the 3D spatial relationships among parameters on the slip surface. θ
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is the dip of the grid column at the slip surface; α is the dip direction of the grid column
115
at the slip surface; β is the sliding direction of the landslide; θr is the apparent dip of the
116
main inclination direction of the landslide; αx is the apparent dip of the X-axis; and αy
117
is the apparent dip of the Y-axis.
118
119
Fig. 3. 3D spatial relationships among parameters at the slip surface. ((a)
120
and (b) are the spatial relationships for 3D views of one grid column and
121
the coordinate system, respectively).
122
As shown in Fig. 3, the apparent dips of the X-axis and Y-axis are as follows.
123
tan cos tan , tan sin tanxy
   
==
(1)
124
The slip surface area of one grid column is calculated by
125
( )
22
21 sin sin
cos cos
xy
xy
A cellsize




=

(2)
126
where cellsize represents the size of each grid column.
127
The apparent dip in the main inclination direction of the landslide is calculated as
128
follows.
129
( )
tan tan cos
r
 
=−
(3)
130
The weight W of the grid column is expressed as
131
2
1
n
mm
m
W cellsize h r
=
=
(4)
132
where m is the number of strata, hm is the height of each stratum, and rm is the unit
133
weight of each stratum. For the grid column units above the water, rm is calculated from
134
the natural unit weight. For grid column units under water, rm is calculated from the
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buoyant unit weight.
136
The pore water pressure is obtained as follows (Zhang, 2016).
137
cos
D
u
=
(5)
138
where D is the distance from the centre bottom of the grid column to the water surface.
139
When the sliding body enters the water, the resistance of the water is calculated as
140
follows (Chow, 1979).
141
2
1
=2wf
G c v S
(6)
142
where G is the resultant force of the resistance of the water to the sliding body; cw is the
143
viscous resistance coefficient, which is 0.18; ρf is the buoyant density (g/m3), taking the
144
average of all stratum; v is the velocity of the landslide (m/s); and S is the surface area
145
of the grid column in the water (m2).
146
2.4. Coordinate system conversion
147
148
Fig. 4. Coordinate system conversion.
149
To facilitate subsequent calculations, the XOY coordinate system was converted to
150
an X´CY´ coordinate system. The X´-axis direction was defined as the sliding direction
151
of the landslide. The right-hand rule determined the positive directions of the Y´- and
152
Z-axes. In addition, point O, i.e., the origin of the XOY coordinate system, was
153
translated to point C in the X ´CY´ coordinate system, as shown in Fig. 4. The
154
transformation of the coordinates can be expressed as follows:
155
(7)
156
where x´ and y ´ are the coordinate values of the centre bottom of each grid column
157
in the X ´CY´ coordinate system. x and y are the coordinate values of the centre
158
bottom of each grid column in the XOY coordinate system; and x 0 and y0 are the
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coordinate values of point C in the XOY coordinate system.
160
2.5. Dynamic equation based on grid column units
161
We assume that all of the grid column units move continuously, do not separate in
162
the macroscopic dimension and remain vertical after sliding, as also assumed by Pan
163
Jiazheng (Pan, 1980). The force analysis of one grid column and the spatial relationships
164
among parameters at the slip surface are shown in Fig. 2 and Fig. 3, respectively.
165
166
Fig. 5. Force analysis in the vertical direction and sliding direction of the landslide.
167
We arbitrarily selected a grid column unit (the grid column unit in row i and
168
column j). According to Newtons laws of motion, dynamic equilibrium equations are
169
established in the sliding direction of the landslide and the vertical direction. The force
170
analyses in the sliding direction of the landslide and vertical direction are shown in
171
Fig. 5.
172
( )
,
, , , , , , , , , ,
cos sin cos ij
r
i j i j i j i j i j i j i j i j i j i j x
W
A A kW D G a
g
 
+  =
(8)
173
,
, , , , , , , , , , ,
sin cos ij
ry
i j i j i j i j i j i j i j i j i j i j i j
W
A A W P V R a
g
 
+ +  −  =
(9)
174
where
175
( )
, , , , ,
tan
i j i j i j i j i j
cu
 
= +
(10)
176
where ax and ayi, j are the horizontal acceleration and vertical acceleration of the grid
177
column, respectively; φi, j is the effective friction angle of the grid column at the slip
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surface; g is gravitational acceleration; ci, j is the effective cohesion of the grid column
179
at the slip surface; and Gi, j is the resistance of water to the grid column. For grid column
180
units above water, ui, j is calculated by Eq. (5), and Wi, j is calculated by taking the
181
natural unit weight. For grid column units under water, ui, j is 0, and Wi, j is calculated
182
based on the buoyant unit weight.
183
According to this assumption, the horizontal acceleration ax of each grid column
184
unit is the same, and the vertical acceleration ayi
j of each grid column unit varies. Pan
185
Jiazheng suggested that (Pan, 1980) there is a certain proportional relationship between
186
ax and ayi
j, that is, ayi
j/ax=tanδi
j. δi
j is the horizontal inclination angle of the line
187
connecting the centre bottom of the grid column to the centre bottom of the next grid
188
column in the sliding direction of the landslide. The effect of vertical tangential forces
189
is ignored, namely, ΔVi, j-ΔRi, j=0; therefore, Eq. (9) can be transformed as follows.
190
,
, , , , , , , , ,
sin cos tan
ij
rx
i j i j i j i j i j i j i j i j i j
W
A A W P a
g
 
+ − =
(11)
191
The simultaneous Eqs. (10) and (11) can be obtained as follows.
192
( )
( )
,
, , , , , , , ,
,
, , , ,
sin tan tan
sin tan cos
ij
rx
i j i j i j i j i j i j i j i j
ij r
i j i j i j i j
W
A u c W P a
g
A
 
 
+ + +
=+
(12)
193
For the entire sliding body, the forces between the grid columns are internal forces,
194
that is, the resultant force is 0, yielding Eq. (13).
195
,0
ij
IJ
D=

(13)
196
By summing all the grid column units, the horizontal acceleration ax can be
197
determined by Eq. (8).
198
( )
, , , , , , , , ,
,
cos sin cos -r
i j i j i j i j i j i j i j i j i j
x
IJ ij
A A kW G
ag
W
 

− −
=



(14)
199
Substituting Eqs. (10) and (12) into Eq. (14) yields the following equation.
200
, , , , , , , ,
, , , ,
( tan )
tan
i j i j i j i j i j i j i j i j
x
IJ i j i j i j i j
B E F G H kW L
ag
W H Q

+ − −
=



(15)
201
where
202
( )
2
, , , , , ,
cos tanr
i j i j i j i j i j i j
B A u c c

=−
(16)
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( ) ( )
, , , , , , , ,
cos sin sin tanr
i j i j i j i j i j i j i j i j
E A u c
 
= −
(17)
204
( ) ( )
, , , , , , ,
cos tan sin cosr
i j i j i j i j i j i j i j
F W P
 

= − +

(18)
205
, , , ,
sin tanr
i j i j i j i j
Lc

=+
(19)
206
( )
, , , , ,
cos tan sin cosr
i j i j i j i j i j
H
 
= − −
(20)
207
, , , ,
sin tanr
i j i j i j i j
Qc

=+
(21)
208
2.6. Calculation of the sliding velocity
209
210
Fig. 6. Rasterization and partitioning of landslides.
211
The steps in calculating the landslide sliding velocity are as follows.
212
(1) Using the spatial analysis capability of GIS, the landslide body is rasterized,
213
and the size of the grid column unit (i, j) can be set to an arbitrary square. A partitioning
214
line is drawn from the bottom to the top of the landslide every ΔL in the sliding direction
215
of the landslide, and the resulting regions are numbered zone 1, zone 2, zone 3, ..., zone
216
(n-1), zone n. Each partition includes a number of grid column units, and the length of
217
zone n is less than or equal to ΔL, as shown in Fig. 6. For a grid column unit that is not
218
completely contained within a partition, if the area within the partition is greater than
219
half of the total area, the unit is divided into that partition; otherwise, the unit is divided
220
into the next partition.
221
(2) For each grid column unit, the parameters required in Eq. (15) are calculated.
222
(3) t0 is the starting point of when the landslide body begins to slide, and t0=0.
223
When the landslide body moves distance ΔL sequentially in the sliding direction of the
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landslide, the corresponding time is recorded as t1t2t3tn, and the corresponding
225
velocity is expressed as vx1, vx2, vx3vxn.
226
4The horizontal acceleration at t0 can be calculated by Eq. (15) and is denoted
227
as ax0, and the velocity at time t0 is zero. After sliding distance ΔL is reached, the
228
following equations can be obtained.
229
10
2
xx
v a L=
(22)
230
10
0
2
x
L
tt a
=+
(23)
231
(5) At t=t1, the landslide body has horizontally moved by a distance ΔL in the
232
sliding direction of the landslide, zone 1 has slipped form the sliding surface. The
233
horizontal acceleration ax1 at t1 is still calculated by Eq. (15). Unlike t0, the weight for
234
zone (n-1) changes to the weight for zone n, and the weight for zone (n-2) becomes the
235
weight for zone (n-1), and so on (at this time, there is no grid column for zone n). After
236
ax1 is calculated, the following can be established.
237
2
2 1 1
2
x x x
v a L v=  +
(24)
238
21
21
1
xx
x
vv
tt a
=+
(25)
239
(6) The calculation is continued in turn. When the obtained horizontal acceleration
240
is negative, the maximum velocity can be obtained. Finally, ax and vx in the calculation
241
process can be plotted as respective curves versus the sliding time.
242
2.7 Calculation of the waves height
243
The China Institute of Water Resources and Hydropower Research proposed an
244
empirical formula for waves height calculation (Zhong et al., 2007). In the formula, the
245
main factors that affect the waves height are the sliding velocity and volume of the
246
landslide. The formula for calculating the maximum waves height is as follows.
247
1.85
0.5
max 2
m
v
dV
g
=
(26)
248
where
max is the maximum waves height (m); d is the comprehensive influence
249
coefficient, with an average value of 0.12; vm is the maximum sliding velocity (m/s); V
250
is the volume of the landslide body in the water (m3); and g is gravitational acceleration,
251
which equals 9.8 m/s2.
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The formula for calculating the waves height at different distances from the
253
landslide body is as follows.
254
0.5
12
n
m
v
dV
g
=
(27)
255
where
is the waves height at a distance of L metres from the landslide body (m); n is
256
the calculation coefficient, which is 1.4; and d1 is the influence coefficient related to
257
distance L, which is determined by the following formula.
258
( )
( )
10.5945
0.5 , 35
6.1274 , 35
L
dLL
=
(28)
259
3. Program implementation
260
Combined with the waves height calculation method, an expansion module was
261
developed based on component object model (COM) technology in the ArcGIS
262
environment. Fig. 7 illustrates the computational process.
263
Rasterization
Parameters
(θ, α, W, P, u, A, θr )
Partitioning the
landslide
β
Calculation of
sliding velocity
Continue to count
twice
ax<0
No
Yes
Input parameters
(k, c, φ)
The maximum velocity
Calculation of maximum
surge height
End
264
Fig. 7. The computational process.
265
4. Case study
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4.1. Overview of the project
267
The Kaiding landslide is approximately 14.5 km away from the dam of the
268
Houziyan hydropower station in Sichuan, China. The length of the landslide along the
269
river is approximately 490 m, the top elevation is 2080 m, the bottom elevation is 1754
270
m, and the volume is approximately 4.5 million cubic metres. Plan and section views
271
are shown in Fig. 8 and Fig. 9, respectively.
272
273
Fig.8. The plan view of the Kaiding landslide.
274
275
Fig. 9. The section view of the Kaiding landslide.
276
4.2. Calculation of the sliding velocity
277
The unit size of a grid column is 5 m×5 m, and ΔL = 10 m. The internal friction
278
angle φ at the slip surface is 22.8°, the natural unit weight is 18.84 kN/m3, the buoyant
279
unit weight is 19.43 kN/m3, the buoyant density is 2.11×106 g/m3, and the elevation of
280
the reservoir water level is 1810.3 m. When the landslide body slides, the effective
281
cohesion c at the slip surface will decrease to 0, that is, c=0 (Pan, 1980). Using this
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method and Pan Jiazheng's 2D method, the acceleration and velocity curves with the
283
sliding time can be obtained, as shown in Fig. 10 and Fig. 11, respectively. The
284
calculation results are shown in Table 1.
285
Table 1 Calculation results
286
The Pan Jiazheng method
The proposed method
t(s)
ax(m/s²)
vx (m/s)
t(s)
ax(m/s²)
vx (m/s)
0
0.84
0
0
1.25
0
3.65
1.52
5.48
3.30
1.84
6.07
5.21
1.21
7.35
4.70
1.50
8.17
6.47
0.94
8.49
5.83
1.19
9.52
7.61
0.66
9.17
6.84
0.88
10.40
8.68
0.34
9.49
7.78
0.60
10.96
9.73
0.02
9.51
8.67
0.28
11.21
10.81
-0.35
9.13
9.57
-0.08
11.14
11.95
-0.71
8.33
10.48
-0.45
10.73
13.28
-1.27
6.74
11.45
-0.90
9.86
The calculation results indicate that the maximum velocity obtained by the
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proposed method is 11.21 m/s, the starting acceleration is 1.25 m/s2, and the sliding
288
time required to reach the maximum velocity is 8.67 s. In comparison, the maximum
289
velocity obtained by the Pan Jiazheng method is 9.51 m/s, the starting acceleration is
290
0.84 m/s2, and the sliding time required to reach the maximum velocity is 9.73 s.
291
Comparing the results of the proposed method with those of the Pan Jiazheng
292
method, the maximum velocity of the proposed method is 15.2% higher than that
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calculated by the Pan Jiazheng method, the starting acceleration is 32.8% higher, and
294
the sliding time required to reach the maximum velocity is 1.06 s short.
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0246810 12 14
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
The proposed method
The Pan Jiazheng method
Acceleration (m/s2)
Sliding time (s)
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Fig. 10. Horizontal acceleration curve with the sliding time.
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0246810 12 14
0
3
6
9
12
15
The proposed method
The Pan Jiazheng method
Velocity (m/s)
Sliding time (s)
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Fig. 11. Sliding velocity curve with the sliding time.
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4.3. Waves analysis
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According to the most dangerous working conditions, it is assumed that the
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landslide body all slips into the water. The volume V of the landslide body under water
302
is 340×104 m3. According to Eqs. (26) and (27), the maximum waves height obtained
303
by the proposed method is 9.66 m, and the waves height at the dam site is 0.56 m. The
304
maximum waves height obtained by the Pan Jiazheng method is 7.28 m and the waves
305
height at the dam site is 0.44 m.
306
The landslide is approximately 14.5 km from the dam, the crest elevation is
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1847.02 m, and the elevation of the reservoir water level is maintained at 1810.3 m.
308
When the waves height at the dam site is 0.56 m, water will not flow over the dam crest
309
and the safe operation of the dam will not be affected.
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The maximum waves height obtained by the proposed method is 24.6% larger than
311
that based on the Pan Jiazheng method, and the waves height at the dam site obtained
312
by the proposed method is 21.4% larger than that based on the Pan Jiazheng method.
313
The calculations indicate that the results of the 2D method are smaller than those
314
of the 3D method. Compared that of the 2D method, the computational model of the
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3D method better represents the actual spatial state of the landslide. As an analytical
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method, the 3D model in this paper is more suitable than the 2D model.
317
5. Conclusions
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Combined with the powerful spatial analysis ability of GIS, a 3D landslide force
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analysis model based on grid column units was established. The dynamic equilibrium
320
equation for calculating the sliding velocity of a 3D landslide was derived to calculate
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the waves height by combining Newton's laws of motion. To make the calculation more
322
convenient, an expansion module is developed to calculate the waves height in GIS,
323
and the feasibility of the module is verified by a case study.
324
Through calculations based on the case study, the maximum waves height
325
calculated by the 3D method proposed in this paper is 24.6% larger than that based on
326
the 2D Pan Jiazheng method, and the sliding time required to reach the maximum
327
velocity is shorter by 1.06 s. The calculations indicate that the results of the 2D method
328
are smaller than those of the 3D method.
329
Because the Pan Jiazheng method is based on a 2D section, the calculation results
330
will vary with the selected section. In this paper, the 3D landslide body model based on
331
grid column units is used to overcome the above shortcomings, and the calculation
332
model better represents the actual spatial state of the landslide body. Therefore, the
333
proposed method is more suitable for practical risk assessment.
334
335
Data availability: All data generated or analysed during this study are included in this
336
published article.
337
338
Author contributions: G.Y. and M.X. conceived of the presented idea. G.Y.
339
implemented the algorithm, and developed the theory. G.Y., M.X., and A.F. revised the
340
manuscript critically. G.Y. and L.B. finished the programming work. A.F. checked the
341
language.
342
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Competing interests: The authors declare that they have no conflict of interest.
344
345
Acknowledgment: I would like to express my sincere gratitude to Prof. Mowen Xie,
346
Lei Bu, and Asim Farooq for their motivation and for providing me access to their
347
immense knowledge during this research work. This work was supported by the
348
National Natural Science Foundation of China [grant numbers 41372370].
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350
351
352
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References
354
Ataie-Ashtiani, B. and Nik-Khah, A.: Impulsive waves caused by subaerial landslides,
355
Environmental Fluid Mechanics, 8, 263-280, 2008.
356
Cui, P. and Zhu, X. H.: Surge generation in reservoirs by landslides triggered by the wenchuan
357
earthquake, Journal of Earthquake and Tsunami, 5, 461-474, 2011.
358
Chow, C. Y.: An introduction to computational fluid mechanics, John Wiley and Sons, Inc.,
359
New York, 1979.
360
Di, R. M. and Sammarco, P. : Analytical modeling of landslide-generated waves, Journal of
361
Waterway, Port, Coastal, and Ocean Engineering, 134, 53-60, 2008.
362
Hu, G. T.: Landslide dynamics, Geological Press, Beijing, 1995. (in Chinese)
363
Huang, J. L., Zhong, Z. H., and Zhang, M. F. : Sliding velocity analysis of reservoir bank
364
landslides based on the improved vertical slice method, Journal of Mountain Science, 30,
365
555-560, 2012. (in Chinese)
366
Jia, N., Yang, Z. H., Xie, M. W., Mitani, Y., and Tong, J. X.: GIS-based three-dimensional
367
slope stability analysis considering rainfall infiltration, Bulletin of Engineering Geology
368
and the Environment, 74, 919-931, 2015.
369
Miao, T. D., Liu, Z. Y., Niu, Y. H., and Ma, C. W.: A sliding block model for the runout
370
prediction of high-speed landslides, Canadian Geotechnical Journal, 38, 217-226, 2011.
371
Montagna, F., Bellotti, G., and Risio, M. D.: 3D numerical modeling of landslide-generated
372
tsunamis around a conical island, Natural Hazards, 58, 591-608, 2011.
373
Mergili, M., Marchesini, I., Rossi, M., Guzzetti, F., and Fellin, W.: Spatially distributed three-
374
dimensional slope stability modelling in a raster GIS, Geomorphology, 206, 178-195, 2014.
375
Noda, E.: Water waves generated by landslides, Journal of the Waterways, Harbors and Coastal
376
Engineering Division, 96, 835-855, 1970.
377
Pan, J. Z.: Stability of construction against sliding and landslide analysis, Water Conservancy
378
Press, Beijing, China, 1980. (in Chinese)
379
Silvia, B. and Marco, P.: Shallow water numerical model of the wave generated by the Vajont
380
landslide, Environmental Modelling & Software, 26, 406-418, 2011.
381
Xie, M., Esaki, T., Zhou, G., and Mitani, Y.: Geographic information systems-based three-
382
dimensional critical slope stability analysis and landslide hazard assessment, Journal of
383
Geotechnical and Geoenvironmental Engineering, 129, 1109-1118, 2003.
384
Xie, M., Esaki, T., and Zhou, G.: GIS-based 3D critical slope stability analysis and landslide
385
hazard assessment, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 129,
386
1109-1118, 2003.
387
Xie, M., Esaki, T., and Zhou, G.: GIS-Based Probabilistic Mapping of Landslide Hazard Using
388
a Three-Dimensional Deterministic Model, Natural Hazards, 33, 265-282, 2004.
389
https://doi.org/10.5194/nhess-2019-230
Preprint. Discussion started: 10 September 2019
c
Author(s) 2019. CC BY 4.0 License.
17
Xie, M., Esaki, T., and Cai, M.: GIS-based implementation of three-dimensional limit
390
equilibrium approach of slope stability, Journal of Geotechnical and Geoenvironmental
391
Engineering, 132, 656-660, 2006.
392
Xie, M., Esaki, T., Qiu C., and Wang, C.: Geographical information system-based
393
computational implementation and application of spatial three dimensional slope stability
394
analysis, Computers and Geotechnics, 33, 260-274, 2006.
395
Xu, F., Yang, X., and Zhou, J.: Experimental study of the impact factors of natural dam failure
396
introduced by a landslide surge, Environmental Earth Sciences, 74, 4075-4087, 2015.
397
Zhong, D.H., An, N., and Li, M. C.: 3D dynamic simulation and analysis of slope instability of
398
reservoir banks, Chinese Journal of Rock Mechanics and Engineering, 26, 360-367, 2007.
399
(in Chinese)
400
Zhang, T.: Analysis on the landslide-generated waves of yalong river basin and its impact on
401
reservoir area, Master thesis, Department of Constructional Engineering, Tianjin University,
402
Tianjin, China, 2016. (in Chinese)
403
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Preprint. Discussion started: 10 September 2019
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... Building upon previous research, Yu developed a three-dimensional landslide surge height calculation extension module on the GIS platform, thereby extending existing two-dimensional models to three dimensions. However, the majority of studies have primarily engaged in two-dimensional simulations of landslide motion processes or confined their investigations to localized three-dimensional simulations on GIS platforms [35,36]. There is limited research on conducting real three-dimensional simulations of landslide dynamics throughout the entire process based on DEM on GIS platforms. ...
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