Introduction

Landslides are one of the common geohazard worldwide. Some can cause huge economic losses and secondary disasters, under special conditions, because of their volume or mobility (Legros 2002; Pudasaini and Miller 2013). In recent years, global climate change and geological activities such as glacial recession and earthquakes have provided favorable conditions for the occurrence of catastrophic landslides (Yin et al. 2009; Allen et al. 2011; Tsou et al. 2011; Gariano and Guzzetti 2016). Therefore, it is necessary to improve risk assessment to prevent or mitigate the adverse impact of landslides.

To reduce the damage caused by catastrophic landslides, it is necessary to understand their mechanisms, including failure and movement. The former, for most of catastrophic landslides, is the result of the comprehensive functions of long- and short-term factors. Long-term factor, such as climate (Bovis and Jakob 1999), rock weathering (Regmi et al. 2013), and freeze–thaw cycles (Mateos et al. 2012), can slowly change the properties of a slope body. For example, the formation of the Sangrumba landslide that occurred in Nepal Himalaya was mainly influenced by rock weathering that drastically decreased the strength of the rock (Regmi et al. 2013). Compared to this, short-term factors such as earthquakes (Cui et al. 2009), heavy rainfall (Kim et al. 2012), and groundwater (Chigira et al. 2003) destroy the structure of slope body more quickly. For example, the Tsaoling landslide that occurred in Southwestern Taiwan was triggered by the 1999 Chi–Chi earthquake that resulted in several cracks being spread from the shear plane to ground surface (Chigira et al. 2003). Thus, triggering factors should be comprehensively considered to study the failure mechanism of a landslide. The latter, for most of catastrophic landslides, always has some remarkable characteristics such as high volume or mobility. High mobility of the catastrophic landslides could be caused by terrain conditions such as large differences in elevation or special conditions such as entrainment (Hungr and Evans 2004) and dynamic fragmentation of rock (Davies and McSaveney 2009). Therefore, the movement mechanisms should be studied carefully when conditions are different.

Recently, with the development of the computer technique, the prediction or back analysis of the dynamic processes of landslides even more important for risk assessment, as it provides data on characteristics such as sliding velocity and impact area. Several numerical models and computation methods have been proposed for the dynamic prediction and risk evaluation of landslides, based on their failure and movement mechanisms (Lourenço et al. 2006; Pastor et al. 2014; Savage and Hutter 1989). Each model and method has its own characteristics that reflect landslide processes by taking different factors into consideration, and has also reproduced the dynamic processes of landslides successfully by comparing numerical results with experimental data and field measurements. Most numerical models focus mainly on the properties of the landslide body and its influence on mobility by assuming a constant volume for the duration of motion. However, landslide paths are typically covered by loose surficial deposits such as colluvium, residual soil, and organics (McDougall and Hungr 2005). Entrained path material can influence the mobility or increase the volume of the landslide significantly (McDougall and Hungr 2005; Zhou et al. 2016). For example, the 1999 rock avalanche that occurred in Nomash River increased in volume from about 3.7 × 105 to 7.7 × 105 m3 before reaching the valley floor by entrainment (Pirulli and Pastor 2012). Thus, the effect of entrainment that occurs during the sliding process is needed to be further considered.

In this paper, the geological conditions, causes, and main characteristics of the landslide that occurred at Xinmo village on June 24, 2017, in Sichuan, China, are summarized. According to the field investigation, the volume of landslide had a remarkable increase over the sliding process, and entrainment was considered to be the primary cause of it. To better understand how entrainment affects the behavior of the landslide runout, a depth-averaged continuum model taking entrainment into consideration and using the Coulomb friction law is applied. In addition, some influencing factors concerning entrainment are analyzed.

The Xinmo village landslide

On June 24, 2017, a catastrophic landslide (located at 32°04′9.4″N and 103°39′3.4″E) occurred at Xinmo village, Diexi town, in Sichuan province, southwest China (Fig. 1), causing 10 fatalities, leaving 73 missing, and burying 46 buildings. The landslide runout extended 2800 m horizontally and 1200 m vertically. This was equivalent to an effective friction angle of 24° and covered an area of ≈ 143.1 × 104 m2. Based on a comparison of pre- and post-event digital elevation models (DEMs), the landslide initially involved displaced material from the source area of 3 × 106 m3 (Bai et al. 2019); however, with the effects of entrainment and rock fragmentation during transport, its final volume became ≈ 6.3 × 106 m3 (Fan et al. 2017a, b). The duration of the landslide was about 100 s, according to records from Sichuan Seismic stations. Based on high-performance unmanned aerial vehicle (UAV) aerial photogrammetry, the sliding range of landslide was divided into three areas (see Fig. 2):

Fig. 1
figure 1

Locations of the Xinmo village landslide and the distribution of the fracture zone

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Fig. 2
figure 2

Images showing catastrophic landslide at Xinmo village, Diexi town, Sichuan province, in southwest China. a Mountain slope before the landslide. b Same area after the landslide

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  1. (a)

    Source area: the landslide source area contained steep terrain with a slope ≈ 53°. The main body consisted of quartz sandstone. The rear and toe elevations of the landslide source area were 3428 m and 3328 m, respectively, giving a height difference of 100 m; the source area was an irregular trapezoid in profile, with a longitudinal length of 440 m and lateral width of 350 m. The slip direction of the landslide was mainly towards the southwest.

  2. (b)

    Middle impact-shoveling area: this area, located between the leading edge of the source area and the old landslide accumulation area, has a longitudinal length of 1210 m and a lateral width of 367 m and a slope of 27°. Subjected to the narrow and straight terrain of the valley, the landslide slip direction was still mainly towards the southwest.

  3. (c)

    Accumulation area: the terrain of this area was flat and wide, which made the landslide spread out during transport; the accumulation area had a lateral width of 1200 m and an area of ≈ 72 × 104 m2. The average thickness of the deposit was approximately 8 m, although the local maximum thickness could exceed 30 m. The landslide destroyed houses, and impacted and blocked the Songpinggou River, a tributary of Minjiang River, and formed a 2000 m long dammed lake. A 2100 m section of the Township Road No. 104 was also buried, and the broken rock mass was observed clearly in this area. Moreover, the mud that splashed onto the other side of Songpinggou river, and areas, where the trees and shrubs collapsed on the outside edge of the accumulation area, were also seen clearly (Fig. 3). It indicates that the landslide moved at a high velocity.

    Fig. 3
    figure 3

    Photos from the site: a close-up of the source and middle impact-shoveling areas; b fallen trees; c stone and mud; and d broken rock

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Apart from these areas that were direct influenced by the landslide, there was an unstable slope at the west of the source and middle impact-shoveling areas (Fig. 2b). The rear of the unstable slope was 3350 m high. This potential hazard area was caused by the traction of the landslide, and divided into two parts by a 35 m wide tension crack (Fan et al. 2017a, b; Ouyang et al. 2017a, b). The leading edge of the unstable slope was wedge-shaped in profile and covered an area of ≈ 18.4 × 104 m2. The rear edge of the unstable slope was an irregular diamond in profile, covered an area of ≈ 7 × 104 m2, and consisted mainly of quartz sandstone bedrock.

Analysis of the cause of the landslide

Landslides generally occurred under certain conditions, such as great differences in elevation, heavy rainfall, and cracked geological structures (Khan et al. 2011; Rahman et al. 2014). From this point of view, the cause of the Xinmo village landslide is analyzed using a combination of these impact factors, a field investigation, and the three additional aspects. The first aspect is landform and topography. The landslide developed at the top of a sharp ridge line located at the left bank of the Songping river that belongs to a first-order tributary of the Minjiang river. This area has a rugged alpine terrain under the effect of strong tectonic erosion, and its strata outcropping belong to the Weiguanqun formation of the Devonian, Carboniferous and Lower Permian periods, and to the Zagunao and the Bocigou formations of thee Triassic (Fan et al. 2017a, b). Marbleized limestone, metamorphic sandstone, and phyllite are the main components of this area. For the Xinmo landslide, it developed within the Zagunao formation that consists of metamorphic sandstone interacted with slate. The mountainous region in which the Xinmo village landslide occurred is located in an NE–SW transition belt from the Chengdu Plain to the Qinghai–Tibet Plateau (Gao et al. 2017). The v-shaped valley has an elevation difference of over 1600 m. The geological cross section along profile line A–A (Fig. 2) was drawn based on field investigation, geological analysis, and interpretation of aerial images. Both sides of the mountain are steep and the slopes of the upper and middle parts of the mountain are greater than 50° (Fan et al. 2017a, b). These provide favorable energy conditions for the formation of landslides. The second additional aspect is the geological structure of the land. The landslide region is in the middle of the Longmenshan fault zone, where fold and fault structures are very developed. There are existed four arcuate faults, including Jiaochanggou Fault, Chahuagou Fault, Guancaigou Fault, and Shidaguan Fault. These arcuate faults are crossed slantwise by a North–West-trending fault (named Songpinggou Fault) that develops nearly along the Songping river. The Songpinggou Fault is originating from Moshi village and ending at Guanyinya near Jiaochang village, which plays a key role in triggering and controlling the development of geological hazards in this area (Wang et al. 2008). In this area, the rock stratum has an occurrence of 184°/53°, and its trend is close to the main slip direction of the landslide. Moreover, this area is near the epicenter of the 7.5 M Diexi earthquake that occurred on March 25, 1933 (Chai et al. 1995); several landslides were induced afterwards (Wang et al. 2008). The combined effects of repeated earthquakes on this area after 1933, including the 2008 Wenchuan earthquake, exacerbated the slope and damage to the rock mass. The seismic intensity in the earthquake reached Level X, causing the mountain to crack (Chai et al. 1995). These are favorable geological structural conditions for landslide formation. The abundantly developed tension cracks and lateral fissures caused by historical earthquakes made the slope unstable. According to a Google Earth image from August 8, 2003, three macroscopic cracks can be found in the source area along the sliding direction of the landslide (Fig. 4). It suggests that the slope had been already gravitationally deformed and was prone to future failure long time ago (Fan et al. 2017a, b; Su et al. 2017). The third additional aspect is rainfall infiltration. The local climate is controlled by the monsoon climate of the East Tibetan Plateau, with a maximum recorded daily rainfall of 104.2 mm and an average annual precipitation of 716.5 mm (Wang et al. 2008). There was more rainfall in Maoxian province during the 2017 flood season than in the previous years. According to records from two rainfall observation stations near Diexi, the cumulative rainfall exceeded 200 mm from May 1 to June 23 (Fig. 5). After continuous rainfall from June 8 to 14, there was a 42% increase in monthly rainfall compared to the same period in the previous years. The stability of the rock slope was thus reduced gradually with the continuous rainwater seepage, adding further to the conditions that resulted in the landslide (Ouyang et al. 2017a, b).

Fig. 4
figure 4

Google Earth image from August 8, 2003, showing that macroscopic cracks existed in the source area before the Xinmo village landslide

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Fig. 5
figure 5

Daily and cumulative rainfall from May 1 to June 23, 2017, recorded at rainfall observation stations near Xinmo village

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Analysis of the entrainment process of the landslide

Entrainment, as a remarkable feature of the Xinmo landslide, is a continuous process along with the movement of the landslide. Meanwhile, its influence to the landslide is dynamic. Thus, having the knowledge of the evolution of entrainment is necessary, for analyzing the effect of entrainment on the landslide. In this study, based on the field investigations and remote-sensing techniques, three stages of the entrainment process were presented as follows (Fig. 6):

Fig. 6
figure 6

Sketches of the entrainment processes of the landslide

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  1. (a)

    The main block with a volume of 3 × 106 m3 ruptured suddenly at the source area, and impacted the surface of valley (Fig. 3a). Then, the block transformed into relatively small particles and then shoveled some of the surface materials, which makes the sliding mass having some fluidization characteristics (Su et al. 2017). This change is more conductive to the occurrence of entrainment. However, the entrainment-induced change on the velocity and volume of landslide is small at this stage.

  2. (b)

    After that, the mass slid along the high slope, and its characteristics change in the aspect of velocity and volume. A large volume of unconsolidated substrate materials was scraped in the middle area and mixed with the sliding mass, which have a strong effect on the flow characteristics of the landslide. In this stage, the velocity and volume of the landslide increased significantly under the combined effect of continuous entrainment and gravity (Fan et al. 2017a, b; Ouyang et al. 2017a, b). Meanwhile, the shear force from landslide on eroded bed surface also became larger, which means that the erosion ability of the landslide reached maximum. According to the thickness distribution obtained from the difference between the DEM pre- and post-events, a mass of about 3.3 × 106 m3 was eroded by the sliding mass, whereas the averaged thickness of the eroded layer was about 10 m.

  3. (c)

    Finally, the sliding mass with large volume and high velocity entered the flat area, and spread not only to downstream, but also to either side. Then, its velocity decreased quickly due to the increase of frictional resistance, which leads to little surface materials scraped. The thickness of deposits at the Xinmo village was about 5–10 m, with a maximum value of 15 m. For the deposits along the river, its averaged thickness was 10–15 m with a local maximum value of over 20 m.

Description of models

To investigate the behavior of the runout of the Xinmo village landslide, a depth-averaged model was used to study its dynamics (Hungr and McDougall 2009; Gray and Edwards 2014). This model reduces the complicated three-dimensional Navier–Stokes equations into a simple two-dimensional continuum problem by neglecting the changes in the vertical motion characteristics of the landslide, which depends on its large aspect ratio; in other words, if its lateral extension was large compared to the thickness of the layer (Pitman et al. 2003; Savage and Hutter 1989). This greatly decreases the computation cost while preserving information on the fundamental behavior of landslide, and has been validated by a series of experimental benchmarks and real hazards (Liu et al. 2016; Ouyang et al. 2015, 2017a, b). Besides, this model also assumes that the landslide consists of homogeneous material and has a large deformation by neglecting its complex material component. This hypothesize could capture the flow characteristics of landslide well while considering the effect of material properties on landslide motion, e.g., anisotropy. Moreover, entrainment was considered as one of the main factors that increased the volume of the Xinmo village landslide, and the effect of entrainment is considered in the applied model. It is assumed that the eroded materials could mix well with the landslide and its properties are the same with that of the landslide, which is helpful for highlight the effect of entrainment on landslide motion while neglecting some extra special phenomena, e.g., dilatancy. A traditional Cartesian coordinate system, O-xyz, is introduced; the x-axis is along the horizontal direction, the y-axis lies in the cross direction, and the z-axis is parallel to the direction of the gravitational acceleration (Chen and Lee 2003). Using this coordinate system, detailed topographic effects can be included in the gradients of the basal topography in the x- and y-directions (Fischer et al. 2012). According to Pitman et al. (2003), the governing equations, based on the conservation of mass and momentum, can be expressed as

$$\partial_{t} h + \partial_{x} (hu )+ \partial_{y} (hv )= E ,$$
(1)
$$\partial_{t} (hu )+ \partial_{x} \left( {hu^{2} + \frac{1}{2}k_{x} g_{x} h^{2} } \right) + \partial_{y} (huv )= u_{b} E + g_{x} h - \frac{u}{{\left| {\mathbf{u}} \right|}}\mu g_{z} h ,$$
(2)
$$\partial_{t} (hv )+ \partial_{x} (huv )+ \partial_{y} \left( {hv^{2} + \frac{1}{2}k_{y} g_{y} h^{2} } \right) = v_{b} E + g_{y} h - \frac{v}{{\left| {\mathbf{u}} \right|}}\mu g_{z} h,$$
(3)

where t is time; h is the thickness of the landslide; g = (gx, gy, gz) is gravitational acceleration; u = (u, v) denotes the velocity components in the x- and y-directions, and ub= (ub, vb) is the velocity at the lower boundary corresponding to each velocity component (Pitman et al. 2003; Iverson and Ouyang 2015); µ = tanφbed represents the friction coefficient of the rock avalanches in contact with the bed, where φbed is the basal friction angle; E is the basal entrainment rate; and k  = (kx, ky) represents the lateral stress coefficient in the x- and y-directions. Depending on whether the material being studied is expanding or contracting, k(x,y) can be defined using a function of the internal and basal angles. From a Mohr diagram, the formula for k(x,y) can be derived as follows (Savage and Hutter 1989):

$$k_{x} = \left\{ {\begin{array}{*{20}c} {k_{{x_{\text{act}} }} } & \quad{\partial u/\partial x > 0} \\ {k_{{x_{\text{pas}} }} } & \quad{\partial u/\partial x < 0} \\ \end{array} } \right.;\quad k_{y} = \left\{ {\begin{array}{*{20}c} {k_{{y_{\text{act}} }}^{{x_{\text{act}} }} } & \quad{\partial u/\partial x > 0,} & {\partial v/\partial y > 0} \\ {k_{{y_{\text{act}} }}^{{x_{\text{pas}} }} } & \quad{\partial u/\partial x < 0,} & {\partial v/\partial y > 0} \\ {k_{{y_{\text{pas}} }}^{{x_{\text{act}} }} } & \quad{\partial u/\partial x > 0,} & {\partial v/\partial y < 0} \\ {k_{{y_{\text{pas}} }}^{{x_{\text{pas}} }} } & \quad{\partial u/\partial x < 0,} & {\partial v/\partial y < 0} \\ \end{array} } \right.,$$
(4)

where \(k_{{x_{\text{act/pas}} }}\) and \(k_{{y_{\text{act/pas}} }}\) denote the lateral stress state in the x- and y-directions, respectively, and can be defined as a function of the internal and basal angles of friction:

$$\left\{ \begin{aligned} k_{{x_{\text{act/pas}} }} = 2\sec^{2} \varphi_{\text{int}} \left( {1 \mp \left\{ {1 - \cos^{2} \varphi_{\text{int}} \sec^{2} \varphi_{\text{bed}} } \right\}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} } \right) - 1 \hfill \\ k_{{y_{\text{act/pas}} }} = \frac{1}{2}\left( {k_{x} + 1 \mp \left\{ {\left( {k_{x} - 1} \right)^{2} + 4\tan^{2} \varphi_{\text{bed}} } \right\}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} } \right) \hfill \\ \end{aligned} \right.,$$
(5)

where “−” and “+” correspond to an active state and a passive state, respectively; φint is the internal friction angle of the landslide.

Entrainment, a phenomenon that frequently occurs on landslides in fields, may have a remarkable impact on the landslide mobility (Pirulli and Pastor 2012; Cuomo et al. 2016). Erosion action can also increase the volume of a landslide, and the volume of deposited material may increase several times with respect to the initial sliding mass (McDougall and Hungr 2005). This study investigates the effect of entrainment on landslide mobility while ignoring rock fragmentation. Since the importance of entrainment was realized, many formulas for entrainment rate have been proposed in the literature and greatly improved our understanding of this phenomenon (Blanc et al. 2011; Iverson and Ouyang 2015; Pudasaini and Fischer 2016). For entrainment, its extent relates to landslide movement, material properties and topographic feature (Cuomo et al. 2016; Hungr and Evans 2004). To consider these factors comprehensively and simply, the entrainment law proposed by Blanc et al. (2011), based on the analysis of data from experiments, is applied here as follows:

$$E = h \cdot \left| {\mathbf{u}} \right| \cdot K \cdot \left( {{ \tan }\theta } \right)^{2.5} ,$$
(6)

where θ is the slope angle; |u| is the modulus of vector u, |u| = (u2 + v2)0.5; and K is an empirical parameter to be calibrated, and relates to the properties of landslide and bed materials.

Numerical implementation

The proposed numerical schemes employ a finite-volume method to discretize the model equations and a Riemann approximation solver to manage the discontinuous problem at the grid cell interface (Loukili and Soulaïmani 2007). However, there are two challenges to solving this system. First, it is important to preserve a steady state at the discrete level by balancing the flux and source terms. To satisfy this condition, several well-balanced schemes have been proposed (Gosse 2000). We refer to Audusse et al. (2004); this well-balanced scheme can also satisfy some natural properties such as non-negativity of flow depth and discrete entropy inequality. Second, spurious flow is always induced for complex terrain, especially at the wet or dry fronts (Bollermann et al. 2013). To manage this complexity, the local bed slope and variables such as flow depth and velocity need to be modified to prevent a non-physical flux across the grid cell interface. More details of this modification are described in Liang and Borthwick (2009).

Numerical analysis of the catastrophic 2017 landslide at Xinmo village, Diexi, Sichuan province, china

To accurately simulate the movement of a landslide, it is necessary to ensure that the elevation data used are close to that of the actual terrain. To achieve this, pre- and post-event DEMs from 2013 and 2017, respectively, were used to obtain the surface and subsurface geometry of the landslide accumulation. These terrain elevation data were provided by the Sichuan Geomatics Center at a spatial resolution of 5 × 5 m. The total initial volume in the calculation is 3.09 × 106 m3. After the mobility indices for the landslide are quantified, the data can be used to evaluate its behavior and compare the simulated results with measured data. For the Xinmo village landslide, the basal frictional angle φbed is the most important parameter that influences the landslide mobility, and the value of this parameter can be estimated roughly using the ratio of vertical descent H and horizontal extent L (Iverson and George 2015; Ouyang et al. 2017a, b), H/L = 0.42, representing a friction angle of 24°. Another mobility index that affects landslide-spreading behavior is the normal stress coefficient kap. Equation (4) shows that determining this index requires the value of the internal friction angle φint. Field investigation indicated that the material source for the landslide consisted mainly of quartz sandstone; therefore, a common value of 35° is used for φint (Ouyang et al. 2017a, b). This is reasonable, even if it is somewhat greater than the friction angle for soil material. The entrainment parameter K is also a key parameter related to the material properties of the landslide and the eroded surface. Based on some characteristics (such as landslide runout, degree of erosion of the sliding zone, and distribution of accumulation) of the landslide event, the value of K is assumed to be 0.0018 after lots of calibrations. Actually, these characteristics of the event are both influenced by the properties of landslide and bed materials such as saturated unit weight and dry-saturated weight. However, due to the limitation of the used model and the lack of field data, we have to use the value of K to reflect indirectly the effect of these material properties. A refined model for better incorporating the effects of theses material properties is needed to be investigated in future study. The empirical parameter value of g = 9.8 m/s2 is also used to calculate landslide motion. Following Pudasaini and Fischer (2016), this case assumes that ub is approximated by the averaged velocity, ub= 0.5u.

The results of the simulation of the moving flow depth of the Xinmo landslide, and the corresponding erosion depth of the basal surface at different times t = 0, 20, 40, and 100 s, are shown in Figs. 7 and 8, respectively. The landslide and erosion of basal surface are outlined with colors representing different thicknesses. The maximum depth of the initial landslide in the source area is 81.3 m. Initially, the landslide accelerated due to the steep inclination of the slope after it collapsed. When the moving mass passed through the narrow section of the creek, the simulated mass reached a maximum velocity of 55 m/s. The simulation found that the erosion degree of the basal surface is highest in this area and that this was caused by the continuous movement and high velocity of the mass. After the terrain at the lower section of the creek was flattened and broadened, the moving mass decelerated and became a deposit under the effects of friction resistance. With the relatively flat terrain and the decreasing movement velocity, the degree of erosion of the basal surface in this area decreases, even vanishing on the edge of accumulation area, where the moving velocity of mass is close to zero. Finally, the moving mass that destroyed Xinmo village and blocked the Songpinggou river had a maximum thickness of 45 m. The volume of the mass deposited downstream was computed as about 6.21 × 106 m3, compared to the estimated volume of 6.3 × 106 m3. Figure 8b shows that the computed deposit area of the landslide match well with data from the field investigation. The maximum eroded depth of the bed surface was computed as about 11.6 m, which as well as its location also match well with data from the field investigation (Fan et al. 2017a, b). However, there is a difference between computational flow area and measured sliding path at the western edge of the accumulation area. This could be attributed to field observations that show a hump in the middle of the accumulation area (Fig. 9a) (Yin et al. 2017). The moving mass impacted this hump during transport, and the part of this mass with a high velocity and low weight splashed westwards. However, this splashed material is only a small portion of total moving mass, and the average depth of the deposits on the western edge of the accumulation area are only about 2 m (as shown in Fig. 9b). Unfortunately, it is difficult for the depth-averaged continuum model to consider the splash behavior of a moving mass, and this is neglected in the current simulation. Nevertheless, the simulated results can provide a basis for risk evaluation and selecting sites for buildings.

Fig. 7
figure 7

Map views of the simulated behavior of the Xinmo village landslide. The red line is the outline of the landslide path; the background image is pre-event satellite imagery

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Fig. 8
figure 8

Map views of the simulated erosion depth of the basal surface. The red line is the outline of the landslide path; the background image is pre-event satellite imagery

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Fig. 9
figure 9

a Hump located in the middle of the accumulation area. The blue lines indicate the sliding direction of moving mass and the blue line indicates the lower and upper boundaries of hump. b Western edge of the accumulation area

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In addition, the effect of entrainment on landslide mobility was also investigated. The final deposited depths at t = 100 s, with and without entrainment, are shown in Fig. 10. Without entrainment, the travel distance and area influenced by the landslide are smaller, and the deposit is shallower, than when entrainment occurs. To illustrate the difference between the mobility of the landslide in the two cases, the evolutions of the maximum velocity and kinetic energy of the landslide during its run, are shown in Fig. 11. The simulation results show similar characteristics overall. Initially, the maximum velocity and kinetic energy of the landslide in the two cases are the same, because in the detaching area, the entrainment effect is absent. The maximum velocity with entrainment is smaller than without entrainment at an early stage, and becomes larger at a later stage. This is because that the sliding mass mixed with a large volume of unconsolidated substrate materials and the velocity is decreased based on the law of momentum conservation. Nevertheless, the eroded material gained kinetic energy from the sliding mass, and its kinetic energy went up with time under the gravity effect. In addition, because of that the total kinetic energy with entrainment is larger than without entrainment. When the sliding mass entered the flat area, its large kinetic energy resulted in a longer travel distance and larger influenced area. Moreover, it should be noted that the differences between the maximum velocity and kinetic energy of the landslide in the two cases are small when the entrainment is small. These differences become larger, since the effect of entrainment becomes more obvious. All of them show that entrainment can affect not only the volume of a landslide but also its mobility.

Fig. 10
figure 10

Comparison of the simulated results between deposit distributions at t = 100 s, a without entrainment and b with entrainment

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Fig. 11
figure 11

Evolutions of maximum velocity and total kinetic energy of the Xinmo landslide in simulations with and without entrainment

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Discussion

Landslide mobility in alternative scenarios

Since the Xinmo landslide has been widely studied by several scholars that focus on investigating the geometrical feature (Fan et al. 2017a, b; Yin et al. 2017), triggering mechanism (Fan et al. 2017a, b; Su et al. 2017), and motion process (Chen and Wu 2018; Ouyang et al. 2017a, b), its characteristics at each stage were well summarized. These studies also agreed that entrainment is a main factor to influence the geometrical feature and motion process of Xinmo landslide, but the study on how this factor affects the landslide is still missing. Although Ouyang et al. (2017a, b) and Chen and Wu (2018) simulated the Xinmo landslide using different numerical approach, they both treated the eroded substrate materials as part of the initial mass of landslide. Entrainment is an ongoing process, which changes the movement features of landslide gradually. From this point of view, this study is the first discussion about the available motion scenarios using two initial settings and improves the knowledge of the dynamic process of the Xinmo landslide. Initial setting 1 is the same with Fig. 7 (t = 0 s), and initial setting 2 that has a landslide volume of 5.75 × 106 m3 is shown in Fig. 12a. Both of these settings have the same parameters. The evolutions of the maximum velocity and kinetic energy of the landslide for two cases are shown in Fig. 13. The simulation results show that the velocity with setting 2 is smaller than with setting 1 at an early stage, and becomes larger at a later stage. Meanwhile, the maximum value of velocity with setting 2 is larger than with setting 1, and the time of it appearing is later. It is because that the eroded materials and source mass slid at the same time, which makes that the sliding mass has a larger kinetic energy from the start (Fig. 13b) and affects the movement of the landslide. The final shape of the landslide with setting 2 also has a great difference from the field investigation (Fig. 12b). These results indicate that it may be not appropriate to treat the eroded materials as part of the initial mass of landslide when simulating landslide movement.

Fig. 12
figure 12

Initial and final shape of the landslide for the case with setting 2

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Fig. 13
figure 13

Evolutions of maximum velocity and total kinetic energy of the landslide in simulations with two settings

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Landslide velocity profiles for alternative scenarios

As suggested by Pitman et al. (2003) and Pudasaini and Fischer (2016), once the materials at the bottom have just been eroded, its velocities ub are different than the depth-averaged (mean) velocities u that appear in the inertial (or, the convective) part. In addition, the value of ub depends on the type of landslide velocity profile. However, it is difficult to determine the velocity profile within the part of a real landslide case, and the choice of a realistic velocity profile will be driven by several considerations. Here, the values of ub ranging from 0.2u to 0.8u corresponding to different velocity profiles are used for simulation, to study its influence on landslide mobility. Clear trends emerge when mobility indices of landslide are calculated from the results of alternative simulations that use different values of ub (Fig. 14). The velocity and total kinetic energy of the landslide are both enhanced when a larger value of ub is applied. For these three cases (ub = 0.2u, 0.5u, 0.8u), the final volumes of landslide are 5.95 × 106 m3, 6.21 × 106 m3, and 6.43 × 106 m3, respectively. It indicates that the mobility and entrainment ability of the landslide are interacted on each other. Once entrainment occurs, it enhances the landslide mobility and further leads to more eroded substrate materials. However, this behavior will only be experienced on steep terrain which provides favorable conditions for eroded material to gain kinetic energy under the gravity effect. If the sliding mass entry a flat area, the eroded materials cannot gain enough kinetic energy and, therefore, decrease the mobility of sliding mass due to the law of momentum conservation.

Fig. 14
figure 14

Evolutions of maximum velocity and total kinetic energy of the landslide in simulations with different values of ub

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Conclusion

On June 24, 2017, a catastrophic landslide occurred at Xinmo village, Diexi town, in Sichuan province, China. This paper investigated the general setting, causes, and main dynamic characteristics of the landslide. Based on field investigations, entrainment is considered as one of the major causes of the increase in volume of landslide. The dynamic process of the landslide is reproduced and analyzed using a depth-averaged continuum model. The results from the simulation are compared with field observations and measurements; these indicate that the depth-averaged continuum model is able to capture the runout behavior of the landslide well by considering the effect of entrainment. The effects of entrainment on landslide mobility were also investigated, and results show that entrainments enhance the latter. These results suggest that a depth-averaged continuum model that considers special conditions can be used to predict similar types of landslides and assist in risk evaluation and building site selection.