Start-Up Mechanism and Dynamic Process of Landslides in the Full High Waste Dump

Abstract

Landslides often occur in the open-pit mine dump, which is harmful to the safety operation of mines and slopes. In this work, the landslides that occurred in 2014 at Nanfen open-pit mine of China are studied to understand the triggering mechanism and dynamic process of landslides in the full high waste dump. Field investigation, hydrogeological data analysis, satellite map data, and numerical simulation are combined to analyze and evaluate the landslides. The study shows that the continuous and intensive dumping can lead to shear failure under the action of self-weight. The shear strength of loose dump bodies significantly relies on the water content, freeze-thaw cycle, pore pressure, and gradation of the dump soils. These factors result in the occurrence of landslides in the dump slope. The predictions by the smoothed particle hydrodynamics method show that the shape, influence range, and slip distance of landslides are consistent with that of the field investigation. The present study shows that the SPH method is a powerful numerical technique to describe landslides’ problems.

1. Introduction

Landslides are natural disasters, in which the soils or rock masses on the slope slide down the slope along a specific weak plane or weak zone [1,2]. Because of their high speed, huge energy, and strong impact destructive force, landslides usually lead to a severe loss of personal and property [3,4,5,6]. Currently, the failure mechanism of landslides cannot be completely explained by a perfect theory so that the development of landslides’ models is really appreciated in the geotechnical engineering community.

A series of studies from the perspective of the landslides’ start-up mechanism and the dynamic processes have been reported [7,8,9,10,11,12,13,14]. It is believed that rainfall and snow are the most common causes of landslides [15,16,17,18,19,20]. Earthquakes and other human activities may also lead to landslides [21,22,23,24,25,26]. Thus, it is necessary to analyze the landslides’ initiation mechanism by combining field surveys, satellite data, and numerical methods. One of the advantages of the numerical methods is that the whole process of landslides can be vividly covered. The prevention and control measures for landslides can also be evaluated by such numerical modeling. Moreover, the smoothed particle hydrodynamics (SPH) method, which is referred to as the meshless method [27,28], has many advantages in dealing with large deformation problems, particularly being suitable for simulating landslides and debris flow in the geotechnical engineering [29,30,31,32,33,34].

On 10 April 2014, a large-scale landslide occurred in the full high waste dump of Nanfen open-pit mine in Benxi, China, which resulted in the burial of one sheepfold and several cottages. The field investigation showed that the water retention capacity of the soil was enhanced due to the good gradation of particles, and the high-water content in the waste dump led to the decrease of the soil shear strength. Further, continuous and intensive dumping made the self-weight of the high bench dump slope larger. In April, the atmospheric temperature rose, and the thawing of the frozen layer led to the increase of water pressure and the decrease of shear strength of soil, which eventually led to the occurrence of the landslide.

In this work, we studied the start-up mechanism and dynamic process of the open-pit dump landslide by means of the field investigation, satellite data, and SPH simulation. The SPH simulation helped to understand the fundamental failure mechanism and sliding process of the dump slope. Through the detailed field observation, the topographic and hydrogeological characteristics analysis, and the SPH simulation, we evaluated the influence range, deposition depth, sliding distance, and speed of the landslides.

2. Background and Method

The full high waste dump is located in Nanfen District, Benxi City, Liaoning Province, China (123°46′24″–123°51′03″ E, 41°04′17″–41°06′54″ N, indicated in Figure 1). The project is located in the U-shaped valley of the hanging wall of the open-pit mine, where the dump soils are transported and discharged by belt, which form a single bench waste dump with a vertical drop of about 300 m (shown in Figure 2).

2.1. Geology and Geomorphology

Nanfen mining area is located at the intersection of the second uplift of the Neocathaysian system and the East–West Tianshan–Yinshan structural belt. The landform is a monoclinic structure composed of metamorphic rock strata, belonging to erosion structure of middle and high mountain geomorphology. The elevation of the bottom of the waste dump is 280–420 m, showing a high-to-low trend along the East-West direction. The elevation of the top of the dump slope is about 600 m. The slope angle of the waste dump is about 33°. The underlying bedrock of waste dump is mainly marl, and some are quartz sandstone. Above the bedrock is the Quaternary slope soil with a thickness of about 0–6 m, and some weeds grow on it. The valley slope and foundation soil are relatively stable, and there is no weak stratum, so that the dump soils are directly discharged on it.

2.2. Hydrometeorological Conditions

The regional hydrological network is not developed. In winter, there is little stream water on the surface, and most of it is stored in the Quaternary slope soil. In summer, rainfall increases, and the river water becomes more abundant. Atmospheric precipitation is the primary recharge source of surface water and groundwater. The average, maximum, and minimum rainfalls are 848–856, 1259.8, and 518.5 mm annually, respectively. The rainfall in flood season accounts for 70% of the annual rainfall. The rainfall in August accounts for 50% of the annual rainfall; the maximum rainfall is 487.0 mm monthly, and the maximum daily storm rainfall is 83.0 mm, locally.

This area is located in the north temperate monsoon climate zone, with four distinct seasons. The annual average temperature is 7.7–8.2 °C; the minimum temperature is −24 °C; the extremely low temperature is −32.3 °C, and the extremely high temperature in summer is 37.3 °C. The frost period (snowfall period) is generally from late November to March of the following year, and the maximum frozen depth is 1.49 m.

2.3. Composition and Gradation of the Waste Dump Soil

The gravel soils that contained block stone, gravel, sand gravel, fine sand, and clay particles in the process of open-pit mining were discharged into the valley and formed a full high waste dump. The soils in the waste dump are the three-phase mixtures of loose soil, air, and water. The composition and gradation of the dump soils seriously affect the stability of the waste dump. The gradation of the waste dump soils is shown in

Table 1. Content of each grade of grains in the dump soils.

	Grain Group Classification	Grain Size Range (d/mm)	Content (%)
Big grain	Boulder (rock)	d > 200	5.50
	Pebble (gravel)	200 > d > 60	17.72
Coarse grain	Coarse gravel	60 > d > 20	27.15
	Medium gravel	20 > d > 5	27.55
	Fine gravel	5 > d > 2	10.90
	Coarse sand	2 > d > 0.5	4.49
	Medium sand	0.5 > d > 0.25	2.89
	Fine sand	0.25 > d > 0.075	2.00
Fine grain	Silt grain	0.075 > d > 0.005	1.00
	Clay grain	0.005 > d	0.80

Note: By courtesy of Nanfen Open-pit Mine Group and Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.

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2.4. Method

Geological survey includes a collection of the geological structure, stratum, lithology data, and slope shape of the area, drawing a representative calculation section map (original ridgeline, maximum section line of dump slope, trench bottom line, etc.) [35]. The height and range of waste dump are determined by the original and current topographic mapping. Through in-situ excavation, extensive use of trench, pilot pit, and field geological survey, the structural characteristics of bulk material in different depth and position of dump profiles are obtained to determine the lithologic composition of the dump soils. A series of field and laboratory tests were conducted. The gradation of the dump soils was determined by the direct measurement method combined with photogrammetry for the block stone (>150 mm), the particle screening method for the small and medium block (2–150 mm), and the national standard soil sieve combined with a hydrometer for the fine particles (<2 mm). The mechanical properties under natural and landslide conditions were obtained by the triaxial tests and direct shear tests.

The information regarding precipitation and temperature from July 2013 to December 2014 was obtained from the data from China National Meteorological Information Center and Nanfen meteorological station. Combined with aerial photography technology and satellite data [36,37,38], the 3D terrain of waste dump was obtained, which was used to construct the 3D geometry model of the problem. The SPH method was employed to model the dynamic process of the dump landslides.

3. The SPH Model

Large deformation is involved in the waste dump landslides. When landslides occur, the speed, density, and other physical quantities at different positions change with time. The governing equations to describe the particle motion and mass conservation of landslides are given as follows:

$$\rho \frac{D{v}_{\alpha }}{Dt}=\frac{\partial {\sigma }_{\alpha \beta }}{\partial x_{\beta }}+f_{\alpha }$$

(1)

$$\frac{D\rho }{Dt}=-\rho \frac{\partial v_{\alpha }}{\partial x_{\alpha }}$$

(2)

where $v_{\alpha }$, $t$, $x_{\beta }$, ${\sigma }_{\alpha \beta }$, $f_{\alpha },$ and $\rho$ are the velocity, time, position, stress tensor, body force, and density, respectively, and $\alpha ,\beta$ denote the coordinate directions.

The SPH’s essence is to discretize the problem domain into a series of particles. Each particle carries information such as density, mass, position, and velocity. Using integral interpolation method, we approximate an arbitrary field function $f\left(x\right)$ [39]:

$$f\left(x\right)\approx \underset{\Omega }{{\displaystyle \int }}f\left(x^{\prime }\right)W\left(x-x^{\prime },h\right)\mathrm{d}{x}^{\prime }$$

(3)

where, $W$ is the smoothing kernel function, and $h$ is the smoothing length. The cubic spline function [40] was chosen as the interpolation polynomial in this study.

The landslide body is composed by a series of three-phase mixtures composed of rock and soil particles, water, and air. In order to simplify the problem we study, the dump body is treated as a homogeneous material, and the Mohr-Coulomb model is used to characterize the dump landslides. The general stress state of waste dump materials [41] can be expressed as follows:

$$f\left({\sigma }_{\alpha \beta }\right)=f\left(I_1,J_2,J_3\right)=R_{mc}q-ptan\varphi -c=0$$

(4)

where

$$R_{mc}\left(\mathsf{\Theta },\varphi \right)=\frac{1}{\sqrt{3}cos\varphi }sin\left(\mathsf{\Theta }+\frac{\pi }{3}\right)+\frac{1}{3}cos\left(\mathsf{\Theta }+\frac{\pi }{3}\right)tan\varphi$$

(5)

$I_1$ is the first invariant of stress; $J_2$ and $J_3$ are the second and third invariant of deviatoric stress, respectively; $q$ is the von Mises equivalent stress; $p$ and $c$ are the equivalent pressure stress and cohesion, respectively; $\varphi$ and $\mathsf{\Theta }$ are the friction angle and deviatoric polar angle, respectively.

We choose the flow potential $g$ as the smooth elliptic function in the deviatoric stress plane [42]:

$$g\left({\sigma }_{\alpha \beta }\right)=g\left(I_1,J_2,J_3\right)=\sqrt{{(ϵc_{0}tan\psi )}^2+{(R_{mw}q)}^2}-ptan\psi$$

(6)

where

$$R_{mw}\left(\mathsf{\Theta },e\right)=\frac{4\left(1-e^2\right)co{s}^2\mathsf{\Theta }+{(2e-1)}^2}{2\left(1-e^2\right)cos\mathsf{\Theta }+\left(2e-1\right)\sqrt{4\left(1-e^2\right)co{s}^2\mathsf{\Theta }+5e^2-4e}}\frac{3-sin\psi }{6cos\psi }$$

(7)

and

$$e=\frac{3-sin\varphi }{3+sin\varphi }$$

(8)

where $ϵ$ is the meridional eccentricity, $c_0$ represents the initial cohesion yield stress, $\psi$ is the dilation angle, and $e$ represents the deviatoric eccentricity.

The stress is composed of deviatoric stress and hydrostatic pressure:

$${\sigma }_{\alpha \beta }=S_{\alpha \beta }+\frac{1}{3}{I}_1{\delta }_{\alpha \beta }$$

(9)

where $S$ represents the deviatoric stress tensor, and $I$ is a unit matrix. The bulk materials in the dump here are generally considered to be elastoplastic materials, the strain rate tensor can be divided into two parts, the elastic strain rate tensor ${\dot{\epsilon }}_{\alpha \beta }^e$ and the plastic strain rate tensor ${\dot{\epsilon }}_{\alpha \beta }^p$:

$${\dot{\epsilon }}_{\alpha \beta }={\dot{\epsilon }}_{\alpha \beta }^e+{\dot{\epsilon }}_{\alpha \beta }^p$$

(10)

where α and β denote the Einstein’s notation. The landslide process involves large deformation, so we introduce the Jaumann rate of the Cauchy stress here:

$${\sigma }_{\alpha \beta }^{\nabla }={\dot{\sigma }}_{\alpha \beta }-{\dot{\omega }}_{\alpha r}{\sigma }_{\beta r}+{\sigma }_{\alpha r}{\dot{\omega }}_{\beta r}$$

(11)

where $\dot{\omega }$ is the rate-of-rotation tensor. Finally, the SPH formula of rate-of-rotation tensor ${\dot{\omega }}_{\alpha \beta }$ and strain rate tensor ${\dot{\epsilon }}_{\alpha \beta }$ were obtained as follows:

$${\dot{\omega }}_{\alpha \beta }=\frac{1}{2}\left[{\sum }_{j=1}^n\frac{m_j}{{\rho }_j}\left(v_{\alpha }^j-v_{\alpha }^i\right)\frac{\partial W_{ij}}{\partial x_{\beta }^i}-{\sum }_{j=1}^n\frac{m_j}{{\rho }_j}\left(v_{\beta }^j-v_{\beta }^i\right)\frac{\partial W_{ij}}{\partial x_{\alpha }^i}\right]$$

(12)

$${\dot{\epsilon }}_{\alpha \beta }=\frac{1}{2}\left[{\sum }_{j=1}^n\frac{m_j}{{\rho }_j}\left(v_{\alpha }^j-v_{\alpha }^i\right)\frac{\partial W_{ij}}{\partial x_{\beta }^i}+{\sum }_{j=1}^n\frac{m_j}{{\rho }_j}\left(v_{\beta }^j-v_{\beta }^i\right)\frac{\partial W_{ij}}{\partial x_{\alpha }^i}\right]$$

(13)

The stress–strain relationship in SPH form for the model is obtained:

$$\begin{array}{cc}{\dot{\sigma }}_{\alpha \beta }^i=& {\dot{\omega }}_{\alpha r}^i{\sigma }_{\beta r}^i-{\sigma }_{\alpha r}^i{\dot{\omega }}_{\beta r}^i+2G{\dot{e}}_{\alpha \beta }^i+K{\dot{\epsilon }}_{rr}^i{\delta }_{\alpha \beta }-{\dot{\lambda }}^i\{Ktan\psi {\delta }_{\alpha \beta }\\ & +\left[\left(K-\frac{2G}{3}\right)S_{mt}^i{S}_{mt}^i{\delta }_{\alpha \beta }+2G\left(S_{\alpha t}^i{S}_{\beta t}^i-\frac{2}{3}{J}_2{S}_{\alpha \beta }^i\right)\right]\frac{\partial g}{\partial J_3}+2G\frac{\partial g}{\partial J_2}{S}_{\alpha \beta }^i\}\end{array}$$

(14)

where $r$, $m,$ and $t$ are the Einstein’s notation.

4. Results and Discussion

4.1. Description of Landslides in the Full High Waste Dump

Since the full high waste dump of Nanfen open-pit iron mine began to use the dumping machine in 2004, it has been dumping continuously for about ten years, making the overall height of the waste dump up to 300 m. The large rock masses need to be broken, which makes the size of rock masses smaller, resulting in the relatively low stability of the dump. Before the landslide, cracks and collapse often appear at the dump slope top under the action of self-weight, and the maximum collapse height reaches 2 m (Figure 3b,c). As temperatures rise, the permafrost in the waste dump begins to melt, and the internal water pressure increases, which leads to the stability decrease of the waste dump. In the upper part of the slope, the slope bulges due to melting, and the multiple tensile cracks appear under the action of gravity (Figure 3d). When most of the frozen layers melt, the water pressure inside the soil is close to the maximum that reaches to the critical failure stage of landslides. There are many long and wide cracks in the working area of the dumping machine on the west side of the dump (Figure 4a), and collapse occurs in some areas (Figure 4b–d), with the length of about 350 m and the width of 160 m. At the west edge of the dump, the collapse height and length have reached 20 and 80 m, respectively.

The landslides we study can be divided into source area, propagation area and deposition area (Figure 5a). Based on the geological survey, the landslides’ body has a height of 280 m and a width of 133 m. The depth (thickness) from the back edge of the landslides to the original shoulder of the slope is 38 m; the dip angle is 38–40°, and the landslides’ volume V = 65 × 10⁴ m³ is estimated. After the occurrence of landslides, the landslides’ masses accumulated in the valley at the foot of the dump. The length from the original slope toe to the front edge of the accumulated bodies is about 420 m, and the thickness of the accumulated bodies is about 20–30 m. The landslides have destroyed some cottages and led to about 180 sheep in the sheepfold being buried (Figure 5b).

4.2. Start-Up Mechanism of Landslides

Rainfall is generally considered to be the most crucial inducing factor of landslides. However, rainfall is not the most direct factor in the present landslides in the waste dump. When the landslides occurred in the full high waste dump on 10 April 2014, the rainfall amount was the lowest one, only 0.2 mm within one month.

In 2004, the waste dump of Nanfen open-pit mine continuously rose to a vertical height of 300 m (see Figure 6) while the settlement was obvious under the action of self-weight. The uneven settlement at the top of the slope led to multiple cracks (Figure 3b), which facilitated the infiltration of rainfall and snow water. As the height of waste dumping increases, the stability of the slope would gradually decrease.

The waste dump is mainly composed of granite, green mudstone, and quartz-feldspar schist, supplemented by hornblende schist and phyllite. According to the gradation of the dump soils (Table 1), the total amount of particles with size less than 5 mm is as high as 22.08%. These fine particles could decrease in moisture and then produce high viscosity, which probably enhance the water retention capacity of the waste dump. The water in the dump soils could reduce the friction force between particles, and the fine particles would migrate in the skeleton, which could change the original structure. The fine particles could be taken away by the erosion of the slope surface, and the gap between the coarse particles would be potentially increased, which makes the rainfall infiltration easier. When there is precipitation, the water pressure inside the soil continuously increases, which leads to the decrease of shear strength and stability of the waste dump soils.

According to the monitoring data, although the month rainfall was only 0.2 mm (Figure 7a) in April, the accumulated rainfall in the second half of 2013 was 744.8 mm. Further, the rainfall of 673.1 mm from July to October made a full of water in the dump, which could not be drained in time due to the high water retention capacity of fine particles. It immediately experienced the freezing period from October 2013 to February 2014 (Figure 7b), which resulted in the frost of the rainwater and snow water of the dump. The expansion of the frozen layer could make the soil part uplift. However, when the frozen layer melts, it causes the soil shrinkage. This kind of expansion and contraction leads to the growth and propagation of local damage, weak planes, and cracks in the waste dump. Finally, uneven collapse and settlement on the slope surface emerge (Figure 3d). Indeed, from March to April, as the temperature rises, the frozen layer inside the dump melts, and the pore water fills in the weak plane formed by the thawing of the frozen layer. The water pressure in the soil increases, and some loose bodies exhibit shear dilatation. In April, with the further rise of temperature, the internal frozen layer is nearly completely melted, and the water pressure of soil reaches the maximum.

During the cold season from November 2013 to February 2014, snowfall occurred. In the low-temperature environment in winter, the dump was still dumping normally (Figure 8a–c). When there were ice and snow layers on the slope surface, the soils were continuously discharged to form ice and snow interlayers in the slope. When the snow and ice melt in spring, the weak planes would be formed on the melting place of ice snow interlayers. Sometimes, several continuous water belts would form in the soils, dramatically reducing the shear strength and stability of the waste dump, which is probably another important inducing factor of the landslides.

4.3. Dynamic Process of Landslides

The landslides that occurred on 10 April 2014 are a typical geological disaster in Nanfen open-pit mine. In this study, the SPH method is applied to reproduce the dynamic process of landslides as well as help us to understand the mechanism of large-scale landslide disaster in the waste dump.

The computational domain is about 860 × 200 × 300 m, surrounding the potential landslides in the study. The profile of the original valley before dumping generated by SketchUp software is referred to as boundary conditions imposed on the computational domain. It is noted that the general contacts in Abaqus between the dump bodies and the profile should be activated during simulating to delimit the potential sliding bodies from the computational domain. The frictional coefficient of the contacts is 0.6, and the total simulating time is 100 s. The material properties are given in

Table 2. Calculation parameters for the landslide simulation.

	Property	Value
Dumpling soil	Young’s modulus $E$ (MPa)	26.23
	Poisson’s ratio $\nu$	0.36
	Cohesion $c$ (KPa)	1.0
	Friction angle φ (°)	20
	Density $\rho$ (Kg/m3)	2250

Note: By courtesy of Nanfen Open-pit Mine Group and Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.

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The landslides shown in Figure 9 contain both real and numerical simulations. Among them, Figure 9a,b show the real shape before and after the landslide. In Figure 9a, several cottages can be seen, and most of the cottages were buried or destroyed after the landslide in Figure 9b. Figure 9c,d shows the shape of the landslide before and after the numerical simulation. Figure 9d shows the morphology of the landslide tongue obtained by numerical simulation, and the actual morphology of the landslide tongue is shown in Figure 9e. By comparing the pictures, it is found that the numerical simulation results are consistent with the actual shape.

To observe the process of landslides simulated by SPH, the movement ranges of sliding bodies at different time steps t = 0 s, 10 s, 20 s, 30 s, 40 s, and 100 s are presented in Figure 10, respectively. It is found that at the simulating time t = 30 s, the profile of landslides tends to be almost unchanged. Observing the motion of the slope from t = 0 s to t = 30 s, it is noted that sliding bodies mostly move along the gully, and the movement direction of the landslides is affected by the topography. At the bottom of the dump slope, the movement of the landslide mass is limited by the slope on both sides. The landslide masses partially accumulate at the foot of the slope and partially converge into the middle valley, forming a tongue-like landslide.

The total displacement contours (U-Magnitude) of the full high waste dump at t = 10 s, 20 s, 35 s, and 100 s are indicated in Figure 11. When t = 10 s, the displacement near the dump’s centerline is the largest but gradually decreases to both sides. When t = 20 s, the soils on both sides of the dump are blocked by the hillsides on both sides of the dump, which begin to accumulate. This is why some of them converge into the valley below the dump. When t = 35 s, the maximum displacement of the landslides reaches 594.6 m, which is close to the corresponding movement distance 601.9 m of the sliding bodies at the simulation time t = 100 s. This shows that the landslides tend to cease within 30–40 s.

Next, the velocity contours (V-Magnitude) from t = 1 s to t = 100 s are given in Figure 12. It is shown that the landslides first experience an acceleration process, then decelerate and tend to cease gradually. In fact, it means that the velocity is from zero to maximum (t = 18.0 s) and then gradually decreases to zero (t = 100 s).

To observe the deposition evolution characteristics of landslides, we select two sections perpendicular to the direction of the valley and one section along the direction of the valley from the simulating model of the waste dump. It is found from Figure 13 that the prediction of surface of the slope by the simulation is approximately similar to the surface of the actual landslides.

The sliding process and topography evolution of the landslides simulated by the SPH model is presented in Figure 14. The predicted profile (purple line) of the landslides is in good agreement with the profile (solid red line) of the actual landslides. The distance between the original slope toe and the actual landslides’ front is about 420 m, which is in basic agreement with the real measured data in situ. Generally, the simulations basically describe the evolving characteristics of the landslides, involving sliding distance, slope shape, and deposition depth.

In Figure 15, the dump heights of sliding bodies at Section 2–2 by the SPH simulation clearly change with respect to time, and the depth and width of deposition at t = 27 s, t = 35 s, and t = 100 s are illustrated, respectively. The actual depth and width of deposition are about 24 and 92.3 m, respectively. It can also be demonstrated in Figure 15 that the elevation of predicted profile (t = 100 s) is basically identified with the actual one of the landslides. The final shape of profile by the SPH simulation is almost identified with the actual one of the landslides at this section.

Similarly, Figure 16 presents the dump process of sliding bodies by the SPH simulation at Section 3–3. The depth and width of deposition at t = 20 s, t = 35 s, and t = 100 s are illustrated, respectively. The actual depth and width of deposition are about 48 and 191.7 m, respectively. The average thickness of deposition of the landslides is about 40–45 m. Even though there exists a slightly difference between the elevations by the SPH simulation and the actual landslides at this section, the basic shapes of profile are of good consistency.

Generally speaking, the SPH method is better accommodated to characterize landslides. Especially when describing debris problems, it plays an important role in the optimization of slope design scheme through its availability and computational efficiency. Another advantage is that the SPH method is particularly suitable for describing large deformations of the problem, which is difficult to do with finite element methods. Even though discrete element methods could be employed to simulate landslides and debris problems, currently, the computational efficiency and requirement for computer memory together limit its three-dimensional applications in practice. However, as a good simulation technique, the SPH method does not have such disadvantages. Our case study shows that the characteristics of landslides in Nanfen full high waste dump cover sliding distance, velocity, shape, deposition depth and width, and other information data, all of which could be presented as required.

4.4. Discussion

The full high waste dump easily yields large deformations, and its stability deteriorates under the action of self-weight and environmental factors, which leads to the occurrence of landslides.

Besides, in contrast to the other slopes, the stability of dump slopes is significantly affected by the dumping process. At present, the waste dump slope, the rainfall, and snow in the early stage play an important role in the landslides. The fine particles in the soils significantly reduce the permeability of the waste dump. Of course, the precipitation in the early stage could be stored in the soils, slowly infiltrating afterwards. Due to the possibly uneven distribution of fine particles in the dump, the permeability distribution is also unpredictable so that it is difficult to monitor the change of pore pressure. There may be more fine particles of the soils in some places of the dump where the permeability is very low, and the moisture is easily stored. Consequently, it is difficult to exclude for a long time, which leads to the increase in pore pressure. This situation could be widely extended in the dump soils. Following with the freeze–thaw, the further development of pore pressure and weak planes in the dump would lead to the occurrence of landslides.

The process of dumping is carried out for a long time in the present waste dump. The stability of the dump is not only associated with the gradation of the dump soils but also restricted by the dumping fashion, rainfall, mechanical vibration and other environmental factors. Due to the massive volume of the waste dump, the internal defects cannot be fully described by the numerical model. However, from the viewpoint of statistical physics, it is reasonable to regard the present dump soils as a homogeneous material in the SPH modeling. Though there is some difference between the simulating results and the actual landslides, it is acceptable to the simulation of massive waste dump at the current computational sources.

The valley affects the trend of landslides, and the vegetation coverage in the gully, farmland, and cottage are associated with the scale of landslides. Moreover, the valley terrain where the dump is located restricts the overall stability of the dump partially. Figure 10 shows that the strike of landslides is obviously affected by the topography of gully. The landslide masses in the deposition area are restricted by the slopes on both sides of the valley and move towards the middle of the valley, forming a landslide tongue at the front edge of the landslides. This is consistent with the actual situation. Besides, the behavior of landslides is also related to the volume of landslide masses. In the deposition area, the surface profiles at different sections do not show similar shape. For example, in Figure 15 and Figure 16, the cross-sectional contours of the deposition area are shown as a smooth curve and a wavy line. This could be limited by the local topography. In the process of numerical simulation, the small difference in local topography does not affect the final results. In Figure 15 and Figure 16, the cross-sectional contours of the numerical simulations of the deposition area are all smooth curves, which could be due to the particle number used by the SPH method, resulting in small differences. Nevertheless, this does not affect the final simulating results. It is beneficial to the site selection design of intercepting dam in the following optimization design of the dump slope.

5. Conclusions

We have studied the characteristics of landslides occurred in Nanfen open-pit mine of China by combined field investigation and geological and hydrological data collection, with the SPH method. We have also analyzed the start-up mechanism and the dynamic process characters of the landslides.

Our investigation showed that the rainfall and snow in the early stage, gradation of dump soils, discharged fashion, and freeze-thaw cycle are main causes in the start-up mechanism of landslides in the waste dump slope. The results simulated by the SPH method showed that the movement characteristics of landslides is basically consistent with that of the actual landslides. It is shown that the present landslides can be better characterized using the SPH method to understand their dynamic evolution and basic characters. This point is useful to help us provide an optimal design scheme of the following dump slope in the future.

It was shown by our study that the SPH method is a powerful numerical technique that is very suitable to better describe stability evaluation and large deformation problems such as landslides and debris flows in engineering geology. Further study would be needed to combine different material constitutive models and multi-physics with the SPH method to explore the complicated failure phenomena and process of landslides under coupled field conditions.