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

TL;DR: Wang et al. as discussed by the authors proposed a 3D landslide surge height calculation method based on grid column units, and the results showed that the maximum surge height obtained by the proposed method is 24.6% larger than that based on the Pan Jiazheng method.
Abstract: . 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.

Summary (1 min read)

1. Introduction

  • The most notable feature of GIS is that they can transform vector data into grid data sets based on a grid column unit model (Xie et al., 2006a) .
  • Because of the high 3D spatial data processing capability of GIS, many scholars have added geotechnical professional models to their respective systems.
  • Their research team established a 3D limit equilibrium method based on GIS, and developed a slope stability analysis module called 3Dslope (Xie et al., 2003a; 2003b; 2006b) .
  • Mergili (2014) combined GRASS GIS and the 3D Hovland model to implement a 3D slope stability model capable of considering shallow and deep-seated slope failures.

GIS.

  • Column unit model to establish a 3D landslide model, and proposes a method for calculating the waves height.
  • Compared with 2D analysis methods, the 3D method proposed in this paper better represents the actual spatial state of landslides.
  • Simultaneously, the resistance of the water is considered to improve the accuracy of the calculation result.

2.3. The spatial relationships among parameters

  • To facilitate subsequent calculations, the XOY coordinate system was converted to an X ´CY ´ coordinate system.
  • The X ´-axis direction was defined as the sliding direction of the landslide.
  • The right-hand rule determined the positive directions of the Y ´-and Z-axes.

2.5. Dynamic equation based on grid column units

  • When the obtained horizontal acceleration is negative, the maximum velocity can be obtained.
  • Finally, ax and vx in the calculation process can be plotted as respective curves versus the sliding time.

4.3. Waves analysis

  • The calculations indicate that the results of the 2D method are smaller than those of the 3D method.
  • Compared that of the 2D method, the computational model of the 3D method better represents the actual spatial state of the landslide.

5. Conclusions

  • Because the Pan Jiazheng method is based on a 2D section, the calculation results will vary with the selected section.
  • The 3D landslide body model based on grid column units is used to overcome the above shortcomings, and the calculation model better represents the actual spatial state of the landslide body.
  • Therefore, the proposed method is more suitable for practical risk assessment.

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1
A GIS-based three-dimensional landslide generated waves height calculation
1
method
2
3
Guo Yu
1
, Mowen Xie
1,*
, Lei Bu
1
, Asim Farooq
2
4
1
School of Civil and Resource Engineering, University of Science & Technology
5
Beijing, Beijing 100083, China
6
2
CECOS University, Peshawar Pakistan
7
*
Corresponding author: Mowen Xie (mowenxie123@163.com)
8
9
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.
22
Key words: landslide; waves height; grid column; GIS
23
1. Introduction
24
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,
32
2011). Analytical method is widely used in engineering applications because of its
33
https://doi.org/10.5194/nhess-2019-230
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Author(s) 2019. CC BY 4.0 License.

2
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
44
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.
47
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.
53
Geographic information systems (GIS) is widely used in geotechnical engineering.
54
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.
66
Based on the spatial data processing capability of GIS, this paper applies the grid
67
https://doi.org/10.5194/nhess-2019-230
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c
Author(s) 2019. CC BY 4.0 License.

3
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.
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2. GIS-based method of calculating the waves height
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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).
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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
92
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4
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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5
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; θ
r
is the apparent dip of the
116
main inclination direction of the landslide;
α
x
is the apparent dip of the X-axis; and
α
y
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
2
1 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, h
m
is the height of each stratum, and
r
m
is the unit
133
weight of each stratum. For the grid column units above the water,
r
m
is calculated from
134
the natural unit weight. For grid column units under water,
r
m
is calculated from the
135
https://doi.org/10.5194/nhess-2019-230
Preprint. Discussion started: 10 September 2019
c
Author(s) 2019. CC BY 4.0 License.

Citations
More filters
Journal Article
TL;DR: Based on the Pan Jiazheng vertical slice method formula and considering the water resistance and the decrease of friction coefficient after the water influence, this paper proposed an improved formula of vertical slice algorithm that is feasible to analyze the sliding velocity of landslides near reservoir.
Abstract: Based on the Pan Jiazheng vertical slice method formula and considering the water resistance and the decrease of friction coefficient after the water influence,this paper proposes an improved formula of vertical slice method that is feasible to analyze the sliding velocity of landslides near reservoirWith this formula,this paper analyzes the sliding velocity of Egongdai ancient landslide under unstable situation,and compares the difference of those two methodsThe results shows that after water storage,the maximum horizontal velocity of Egongdai ancient landslide is about 8 m/s when it is sliding,and the results by the two methods are some differentHaving considered the water influence during sliding,the results by the improved formula of vertical slice method is more close to the reality,which can enhance the accuracy of the sliding velocity calculation for reservoir landslidesThis research has some important reference values to the sliding velocity analysis of reservoir landslides

1 citations

References
More filters
Journal ArticleDOI
TL;DR: In this paper, a new Geographic Information Systems (GIS) grid-based three-dimensional deterministic model and taking the slope unit as the mapping unit were used to map landslide hazard using the 3-D safety factor index and failure probability.
Abstract: Based on a new Geographic Information Systems (GIS) grid-based three-dimensional (3-D) deterministic model and taking the slope unit as the mapping unit, this study maps landslide hazard using the 3-D safety factor index and failure probability. Assuming the initial slip to be the lower part of an ellipsoid, the 3-D critical slip surface in the 3-D slope stability analysis is located by minimizing the 3-D safety factor using the Monte Carlo random simulation. The failure probability of the landslide is calculated using an approximate method in which the distributions of c, φ and the 3-D safety factor are assumed to be in normal distribution. The method has been applied to a case study on three-dimensionally and probabilistically mapping landslide hazard.

135 citations


"A GIS-based three-dimensional lands..." refers background in this paper

  • ...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)....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a modified version of the revised Hovland method is used to evaluate the slope stability over a large number of randomly selected slip surfaces, ellipsoidal or truncated in shape.

98 citations

Journal ArticleDOI
TL;DR: In this article, a grid-based 3D deterministic model has been developed for slope stability analysis by combining the geographic information systems (GIS) spatial analysis function and a hydrologic analysis and modeling tool with a column-based three-dimensional (3D) slope stability model.
Abstract: In this paper, by combining the geographic information systems (GIS) spatial analysis function and a hydrologic analysis and modeling tool with a column-based three-dimensional (3D) slope stability analysis model, a new GIS grid-based 3D deterministic model has been developed for slope stability analysis. Assuming the initial slip as the lower half of an ellipsoid, the identification of the 3D critical slip surface in the 3D slope stability analysis is performed by means of a minimization of the 3D safety factor using Monte Carlo random simulation. By using this hydrologic analysis and modeling tool, dividing the whole study area into slope units, and taking each slope unit as a study object, the minimum 3D safety factor for each slope unit can be obtained, and the landslide hazard can then be mapped for the whole study area.

88 citations


"A GIS-based three-dimensional lands..." refers methods in this paper

  • ...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)....

    [...]

Journal ArticleDOI
TL;DR: A horizontal bi-dimensional finite volume model is proposed in order to study the wave generated by the Vajont landslide and a moving wall is introduced reproducing the effects of the landslide.
Abstract: On October 9th 1963 a huge landslide fell into the Vajont artificial reservoir in Northern Italy, and displaced the water which overtopped the dam and produced a destructive wave that inundated the valley causing about 2000 casualties and complete devastation. The landslide has been the subject of many geological studies, and is one of the largest ever documented in literature. Nevertheless, only a small number of hydraulic analyses have been conducted relating the sliding motion to the consequent water waves and describing the formation of different waves and how they interfered with each other. A numerical model, capable of doing so, has not yet been presented.In this paper, a horizontal bi-dimensional finite volume model is proposed in order to study the wave generated by the Vajont landslide. We hereby introduce a moving wall reproducing the effects of the landslide.

78 citations


"A GIS-based three-dimensional lands..." refers methods in this paper

  • ...…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, 32 2011)....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the authors presented numerical computations of tsunamis generated by landslides falling along the flank of a conical island, based on the VOF technique for the treatment of the free surface.
Abstract: This paper presents numerical computations of tsunamis generated by landslides falling along the flank of a conical island. The model used is the fully three-dimensional commercial code FLOW-3D, based on the VOF technique for the treatment of the free surface. The model results are compared against available experimental data that allow validation of the model, evaluation of its accuracy, and estimation of the computational costs. The main conclusion of this research is that the model is applicable at reasonable costs for a few accurate simulations that may be used for preparing precomputed inundation maps of coasts prone to the risk of tsunamis inundation.

54 citations

Frequently Asked Questions (1)
Q1. What are the contributions in this paper?

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.