
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

71732
10.1038/s41598-024-71732-5
Article
The influence of erosion on the dynamic process of landslide in Xinmo Village, Maoxian
Wang Zhong Fu 12
Zhang Xu Sheng xushenghhu@163.com

1
Shi Feng Ge 1
Tian Ye 1
Wu Ming Tang 3
1 https://ror.org/03acrzv41 grid.412224.3 0000 0004 1759 6955 North China University of Water Resources and Electric Power, Zhengzhou, 450046 China
2 Hunan Provincial Key Laboratory of Hydropower Development Key Technology, Changsha, 410014 China
3 grid.488225.1 Huadong Engineering Corporation Limited, Hangzhou, 311122 China
13 9 2024
13 9 2024
2024
14 2142218 3 2024
30 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
A large-scale, high-speed, long-runout landslide occurred in Xinmo Village, Maoxian, Sichuan Province, China, on June 24, 2017. It was characterized by fast sliding speed, rapid volume growth, and large impact area. The dynamic process of such landslides and the influence of erosion on the dynamic process are studied by field investigation, numerical inversion and simulation. The results showed that entrainment erosion was a major factor of landslide volumetric change and a salient feature of the landslide process. An exponential equation relating the erosion rate and the deposition volume was established. Moreover, the study found that a slight change of the erosion rate (1e-4) also had a significant impact on the lateral spreading, longitudinal runout, and vertical erosion. As the erosion rate increased, the lateral spreading, longitudinal runout, and vertical erosion of this type of landslide became more obvious. By using the coefficient of variation method, it was obtained that the erosion rate had a greater influence on the vertical erosion than on the lateral spreading and longitudinal runout. In the study of the velocity of the rock avalanche under different erosion conditions, it was found that the erosion amount and the landslide velocity were not strictly linearly related. This study has important significance for understanding the dynamic process and erosion effect of rock avalanche, and provides useful references and insights for future research in related fields.

Keywords

Xinmo landslide
Erosion
Rock avalanches
Dynamic process
Subject terms

Natural hazards
Engineering
the National Natural Foundation of ChinaGrant U1704243 Wang Zhong Fu Foundation of Hunan Provincial Key Laboratory of Hydropower Development Key TechnologyPKLHD202203 Wang Zhong Fu the National Key Research and Development ProgramGrant No.2019YFC1509704 Wang Zhong Fu issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Rock avalanches, characterized by fast motion, long sliding distance, and wide disaster range, are one of the most destructive landslide types1–3. Such landslides frequently occur in southwest China, at the southeast edge of the Tibetan Plateau, creating a serious safety hazard for the local area4–6.

On June 24, 2017, a catastrophic landslide occurred in Xinmo Village, Sichuan Province, China, burying 40 houses and causing 83 casualties. The Xinmo landslide is a unique and representative post-earthquake giant landslide with high-speed and long-runout characteristics. Many experts and scholars have studied the dynamic process and disaster impact of this type of landslide in depth7–13. Rock avalanches often occur in alpine and gorge areas, accompanied by erosion effects. Therefore, erosion effect research has become a crucial issue of concern14–16.

Numerical simulations, bolstered by the evolution of computer technology and numerical theory, have emerged as pivotal for examining the dynamics and erosion associated with high-velocity long-runout landslides8,17,18. Diverse simulation approaches, ranging from discrete element to continuum-based models, provide a comprehensive view of landslide behavior9,19–24. However, existing research predominantly addresses macroscopic dynamics, with limited analysis of the micro-mechanisms influenced by erosion rates, such as lateral expansion, longitudinal movement, and vertical erosion. The correlation between erosion volume and landslide velocity also lacks precise definition.

This research utilizes the DAN3D for numerical simulations, recognizing its proven effectiveness in modeling debris flow dynamics. The software's flexibility in adjusting rheological models to align with the specific attributes of debris flow throughout its various motion stages, combined with its capacity to factor in the intricacies of three-dimensional gorge morphology, positions DAN3D as an ideal tool for simulating rock avalanches25–27.

This research seeks to clarify the precise effects of erosion rates on the kinematic properties of rock avalanches and to establish a quantitative link between erosion volume and landslide velocity. Concentrating on the landslide in Xinmo Village, Mao County, Sichuan Province, the research utilizes numerical simulation to thoroughly investigate how erosion rate influence the dynamics of these landslides. Importantly, examining the correlation between erosion volume and velocity offers innovative approaches and insights for the management and mitigation of landslide hazards.

Study area

Introduction to the Xinmo landslide

The Xinmo landslide occurred on the back mountain of Xinmo village, Diexi town, Maoxian, Sichuan province, with the center coordinates of the landslide front edge being 103°39′03.4″E, 32°04′09.4″N. It was a high-elevation long-runout rock avalanche, with bedding attitude of N80°W/SW<47°. It was located in the hinterland of the Hengduan Mountains, a high-altitude area, on the left bank of the Songping gully, a first-level tributary of the Min River. The top elevation of the mountain was about 3400 m, and the foot elevation was about 2200 m. The original slope was steep at the top and gentle at the bottom, with the upper section being a bedrock slope mass with a slope angle greater than 50°, and the lower section being an old landslide accumulation mass triggered by the Diexi earthquake. The Xinmo landslide was located at the intersection of the north–south Minjiang fault seismic belt and the northwest Songping gully fault seismic belt, which was a frequent area of historical earthquakes, and many historical strong earthquakes occurred in or near this area (as shown in Fig. 1). According to seismic statistics, since the tenth century AD, the study area has experienced 20 earthquakes with Ms6 or above, among which the most destructive ones were the Ms7.5 (surface wave magnitude) Diexi earthquake in 1933 and the Ms8.0 Wenchuan earthquake in 2008.Fig. 1 Geological map of the study area indicating the location of the Xinmo landslide, old landslide deposits, barrier lakes and active faults4.

The three regions of landslide

According to the field investigation and the comparison of the DEM before and after the landslide, about 3 million m3 of mountain mass slid out from the high-elevation source area and scraped the loose deposits on the slope along the way. Due to the huge gravitational potential energy, the landslide kept moving until it was stopped by the mountain on the opposite bank of the river, with a horizontal travel distance of more than 2500 m. Figure 2a shows the overall view and the position of the profile line. The geological longitudinal profile is shown in Fig. 37,17.Fig. 2 Landslide overall view and site photos (a) Overall view28 (b) Source region (c) Erosion scarper region (d) Deposit region (e) Boulders (f) Loose deposits (g) Sharp edge.

Fig. 3 The geological longitudinal profile of the Xinmo landslide4.

Source region

The source region is located at the top of the slope, and its planar shape is approximately “U”-shaped, as shown in Fig. 2b. The elevation of the rear edge of the source area is about 3400 m, and the elevation of the front end is about 3100 m, with a height difference of about 300 m and a slope of about 50°. The exposed strata in the source area are mainly quartz sandstone interbedded with slate of the Zagunao Formation.

Erosion scarper region

The erosion scarper region is large, showing a “pipe” shape, as shown in Fig. 2c. The rear edge elevation is 3100 m, the front edge elevation is 2400 m, and the height difference is 700 m. After the landslide source area became unstable and collapsed, it moved at high speed to the gully and collided and scraped with the old slope deposits, changing its movement direction from azimuth 202° to along-gully azimuth 220°. Then the landslide mass carried rock debris and moved rapidly along the gully channel, continuing to scrape and accumulate on both sides, while the debris with smaller kinetic energy and the locally collapsed rocks were directly deposited at the bottom of the transport and erosion zone.

Deposit region

As shown in Fig. 2g, a bedrock step with a slope exceeding 40° is at the end of the erosion scarper region. The landslide mass was blocked by the old landslide deposits (Fig. 2f) after accelerating over the step, resulting in a rapid decrease in velocity. The landslide traveled beyond the Songping gully and continued to move southward for a distance before stopping at the foot of the opposite slope, blocking the river and forming a dammed lake, as shown in Fig. 2d. The deposits have a planar shape resembling a trumpet-shaped new debris flow deposits, with elevations mainly between 2200 and 2400 m, fan-shaped, mainly deposited on the Songping gully terrace, reaching the foot of the opposite mountain at the farthest point, with deposit slopes ranging from 5 to 13°, deposit rear edge elevation of 2420 m, front edge elevation of 2310 m, and height difference of 110 m. Many slate and phyllite rock fragments and small branches carried by rock scraping can be seen in the area, with no rounding or sorting of the rocks, and large boulders deposited as shown in Fig. 2e.

Method

Numerical simulation method

Introduction to DAN3D

DAN3D is a windows-based program that simulates the motion of landslides by treating them as equivalent fluids with rheological properties, based on the continuum mechanics model. Different rheological models can be chosen, and the parameters of the sliding path of the landslide can be set, to achieve the simulation of the landslide’s velocity, time, distance, and deposit characteristics21. It can dynamically simulate rock avalanches, debris flows, and collapses, and estimate the numerical simulation of landslide motion behavior.

DAN3D is based on the equivalent fluid assumption, and uses a meshless interpolation method based on smoothed particle hydrodynamics (SPH) in the Lagrangian coordinate system, to solve the Saint–Venant equation combined with fluid depth, and applies the continuity dynamic equation, to realize the accurate simulation of the landslide’s motion process and deposition range on complex three-dimensional terrain29. The DAN method is capable of simulating the debris flow motion process well. Depending on the different motion stages of the debris flow, different rheological models can be set. Moreover, the DAN method takes into account the influence of the three-dimensional valley morphology, which enhances its applicability. The advantage of SPH lies in its nature as a pure Lagrange method, which avoids the interface problem between the Euler grid and the material in the Euler description. Therefore, SPH is particularly suitable for solving dynamic large deformation problems such as high-speed collision.

In the DAN analysis, the basal resistance is obtained by the rheological characteristics of the landslide material, so the choice of the rheological relationship is very important, which affects to a large extent whether the simulated landslide motion can show the same behavior as the real landslide. The main rheological models used by the software are: Frictional model, Voellmy model, Plastic model, Newtonian model, Bingham model. Many simulation examples show that the Frictional and Voellmy rheological models can better reflect the landslide motion behavior8,26,27,30–32.

The Frictional model assumes that the shear stress is controlled by the effective normal stress, and its expression is:1 τ=σ(1-γμ)tanφ

where τ is the basal shear stress (Pa);σ is the total stress (Pa); γμ is the pore-pressure ratio;φ is the dynamic basal friction angle (°).

In formula (1), the pore-pressure ratio γμ and the dynamic basal friction angle φ have the following relationship with the comprehensive friction angle φb:2 φb=arctan1-γμtanφ

The Voellmy model assumes that the shear stress on the sliding mass is the sum of the friction force and the additional resistance generated by turbulent flow:3 τ=σf+ρgv2/ξ

where f is the friction coefficient; ξ is the turbulence coefficient; g is the gravitational acceleration (m/s2); ν is the average velocity of the sliding mass (m/s); ρ the density of the sliding mass (kg/m3).

SPH numerical calculation

When interpolating the depth and distribution of landslide, the whole landslide is divided into N particles, each of which contains a limited volume, and the volume can only increase under the condition of erosion and entrainment. And keep the position of each particle at the bottom of the moving reference cylinder, so that each cylinder and particle have the same position. Since the density of the material is assumed to be constant, the flow depth of each reference column position is proportional to the material volume in the region, which is determined by the proximity of nearby particles. Thus, the flow depth at reference column i can be estimated using the summation interpolant33,34hi=∑j=1NVjWij

where j = 1 to N are neighbouring particles located within a local radius of influence, V is the volume of each particle, and W is the interpolating kernel.

Likewise, the local depth gradient can be estimated by∇hi=∑j=1NVj∇Wij

Model calibration

In the DAN3D numerical simulation, the material source file, representing the sliding source area, is derived from the subtraction of the 5m DEM before and after the landslide of Xinmo using surfer.

Accurately determining the values of input parameters that are crucial for the numerical simulation with DAN3D, to enhance the prediction accuracy and reliability of the model, is also a challenge in the current research35.

In previous numerical simulation studies of rock avalanche using DAN3D, researchers usually adopted the friction model to characterize the source region, while for the erosion scraper region and deposit region, they adopted the Voellmy model, which has been demonstrated by previous studies to effectively simulate the behavior of rock avalanches8,26,27,30–32. The present study also chose this model as the research model based on the field investigation and comparative analysis of the Xinmo landslide.

Based on the laboratory tests of the Xinmo landslide mass by the researchers36, the Unit Weight of the sliding source area is 25 kN/m3. As described in Sect. "Numerical simulation method", the basal friction angle parameter in the friction model governs both the basal resistance and the pore pressure, and the friction angle can be derived from the equivalent apparent friction angle. In the Voellmy model, the friction coefficient and the turbulence coefficient are the controlling factors. This paper uses the numerical inversion method, which can determine the values of the simulation parameters in the model. Based on the data of the total duration and the distribution of the accumulation mass of the Xinmo landslide obtained from the field investigation, this paper verifies the consistency of the simulated landslide duration and the accumulation distribution with the actual situation through multiple calculations and error analysis. After multiple calibrations, the numerical simulation results are highly consistent with the field investigation results. The internal friction angle controlling the longitudinal stress in the flowing landslide mass was taken as 35°. This factor has rather limited influence on the results provided it is kept within a realistic range. To reduce the number of adjustable parameters, the authors use the same value in most analyses, carried out using DAN or DAN3D37,38. Finally, this study uses 2000 particles and simulates according to the parameters shown in Table 1. Table 1 DAN3D numerical simulation parameters of Xinmo landslide.

	Unit weight (kN/m3)	Friction angle (deg.)	Pore-pressure coefficient	Friction coefficient	Turbulence coefficient (m/s2)	Internal friction angle (deg.)	
Source region	25	25	0.16	/	/	35	
Erosion scarper region	23	/	/	0.05	1000	35	
Deposit region	22	/	/	0.10	800	35	

Erosion rate

The erosion of path material is an important feature of rock avalanches21. The landslide path is usually covered by loose deposits that differ from the landslide material. The high-speed moving landslide mass may cause the destruction and displacement of the deposits, resulting in entrainment and erosion. The entrained and erosion material along the path, which increases the landslide volume, alters the landslide composition, modifies the rheology of the landslide interior and the base, and thus influences the landslide motion and accumulation. However, the erosion and entrainment of landslides are complex, and laboratory tests and numerical simulations cannot fully reveal their entire mechanisms. This paper mainly examines the influence of varying the erosion amount on both the dynamic process and the accumulation range of rock avalanches. Using DAN3D numerical simulation—the erosion amount is controlled by adjusting its built-in parameter erosion rate E¯. It is worth noting that the definition of erosion rate E¯ in the DAN3D numerical simulation differs from the traditional meaning of Entrainment Ratio (ER)37, and the calculation formula is as follows:4 E¯=lnVfV0S¯

where V0 is the total volume of the landslide entering the entrainment area, Vf is the total volume of the sliding mass exiting the entrainment area, and S¯ is the estimated average path length of the entrainment area.

According to formula (4), the erosion amount increases with the increase of erosion rate E¯. Based on this, this paper examines the influence of the erosion amount variation on the dynamic process and the accumulation morphology of the study area, which is a simple but feasible study. By varying erosion rate E¯, the effects of different erosion amounts on the landslide motion and the accumulation morphology can be observed, which can help to better understand and predict the dynamics and the possible consequences of rock avalanches.

Result

Numerical simulation result of the Xinmo landslide

Figure 4 shows the distribution of the accumulation thickness at different times of the Xinmo landslide. In the initial stage, the landslide material with a volume of about 3.06 × 106 m3 detached from the source region and moved rapidly along the NE-SW direction. In the 0–20 s stage, the material source in the sliding source region started to slide, the accumulation thickness decreased rapidly, and gradually entered the erosion scraper region. In the 20–60 s stage, the landslide passed through the erosion region and entered the deposit region, and the landslide mass reached the landslide front edge at 100 s. In the 100–120 s stage, the landslide crept in the deposit region. The reason for the decrease of the accumulation thickness in the 0–20 s stage is that the original material source started to slide quickly downward, and the initial material source thickness decreased. After entering the erosion scraper region, the accumulation thickness and volume of the landslide increased rapidly with the increase of the erosion amount. After the landslide mass reached the landslide front edge at 100 s, the landslide accumulated and expanded laterally in the deposit region. The final accumulation morphology of the landslide was roughly consistent with the field investigation (Fig. 2a).Fig. 4 The accumulation thickness distribution map of the Xinmo landslide. (a) t = 10s, (b) t = 20s, (c) t = 30s, (d) t = 40s, (e) t = 50s, (f) t = 60s, (g) t = 70s, (h) t = 80s, (i) t = 90s, (j) t = 100s, (k) t = 110s, (l) t = 110s

Figure 5 shows the maximum velocity distribution map of the Xinmo landslide. The maximum velocity accumulation map of the landslide output by DAN3D is the maximum velocity of the smooth sample passing through the area during the sliding. Therefore, the velocity distribution map area is larger than the accumulation thickness area. As shown in the figure, in the numerical simulation of the Xinmo landslide, the maximum velocity of the Xinmo landslide was in the erosion area. The reason is that the velocity increased rapidly when the landslide mass detached from the bedrock and started to slide. In the initial erosion area stage, the landslide mass collided with the scraping, and the velocity was generally at a high level. When colliding with the original loose deposits on the slope surface, the velocity gradually decreased. With the increase of erosion, the landslide slowed down in the continuous movement, the landslide mass reached the landslide front edge, and the landslide velocity was almost zero.Fig. 5 The maximum velocity distribution map of the Xinmo landslide.

Figure 6 shows the final erosion thickness distribution map of the Xinmo landslide. As shown in the figure, the erosion degree of the Xinmo landslide in the source region and the deposit region was weaker than that in the erosion scraper region. The main erosion range was in the avalanches channel formed by the erosion scraper region, which was consistent with the kinematic mechanism and field investigation results of the rock avalanches erosion scraping.Fig. 6 The final erosion thickness distribution map of the Xinmo landslide.

Result analysis of the influence of erosion rate on the dynamic process of landslides

Erosion rate is an important influencing parameter in rock avalanches, which affects the accumulation volume, velocity, lateral spreading, longitudinal displacement and other issues of the landslide. This section mainly focuses on the Xinmo landslide, using the calibrated rheological parameters, to study the lateral spreading, longitudinal displacement and vertical erosion of the landslide under different erosion rate conditions.

Figure 7 shows the accumulation thickness map of the Xinmo landslide under different erosion rate conditions. Table 2 shows the accumulation volume, lateral spreading, longitudinal displacement and maximum erosion thickness under different erosion rate conditions. As shown in the Table 2, the larger the erosion rate, the larger the overall accumulation volume, and the more obvious the lateral spreading and longitudinal displacement of the landslide, and the greater the erosion thickness. Based on the relationship between the accumulation volume and the erosion rate in Table 2, an exponential equation with a range of independent variable values of (0, 0.001] is fitted according to the exponential function model, as shown in Fig. 8. The values are compared with the actual simulation values, and the relative error is small—and the accumulation volume at E¯ = 0.0009 is predicted, and the predicted value is 13.6369 × 106m3. Then, numerical simulation is performed at E¯ = 0.0009, and the simulation value is 13.7042 × 106m3, and the relative error is also small. The coefficient of variation method, which is a statistical method for measuring the degree of data variation, is used to analyze which one of the lateral spreading, longitudinal displacement and vertical erosion has a greater influence by erosion rate.Fig. 7 The accumulation thickness map of the Xinmo landslide under different erosion rate. (a) E¯ = 0.0004 (b) E¯ = 0.0005 (c) E¯ = 0.0006 (d) E¯ = 0.0007 (e) E¯ = 0.0004 (f) E¯ = 0.0005.

Table 2 Simulation results of the Xinmo landslide under different erosion rate conditions.

Erosion rate	Accumulation volume (× 106m3)	Maximum erosion thickness (m)	Lateral spreading (m)	Longitudinal displacement (m)	
0.0004	6.1422	31.7738	1318	1195	
0.0005	7.2946	33.7680	1342	1245	
0.0006	8.6364	35.2394	1394	1303	
0.0007	10.2154	38.3826	1430	1351	
0.0008	12.0125	40.2761	1479	1384	
0.0010	15.4307	45.6647	1527	1438	

Fig. 8 Fitting equation of erosion rate and Accumulation Volume.

The coefficient of variation is a statistic that measures the degree of variation of the observed values, reflecting the degree of dispersion on the unit mean39,40. Based on the coefficient of variation, the lateral spreading, longitudinal displacement and vertical erosion under different erosion rate influences are compared, and the results are shown in Table 3. It is concluded that compared with vertical erosion, the erosion rate has a relatively small influence on the lateral spreading and longitudinal displacement. It can be seen that, due to the influence of erosion rate, both the vertical erosion has a greater influence than the lateral spreading and longitudinal displacement during the process of landslide volume increase and the increase of erosion amount has the same influence on the lateral spreading and longitudinal displacement. In the future flume test research, the influence of lateral spreading also needs to be considered. Table 3 Differences of erosion rate on lateral spreading, longitudinal displacement and vertical erosion.

	Sample size	Maximum value	Minimum value	Normalized standard deviation	Coefficient of variation (%)	
Lateral spreading	6	1527	1318	0.010	5.71	
Longitudinal displacement	6	1438	1195	0.011	6.79	
Vertical erosion	6	45.6647	31.7738	0.022	13.45	

Figure 9 shows the comparison diagram of the maximum velocity change with the simulation time under different erosion rate conditions. The velocity change trend under different erosion rate has a high consistency, and the difference is the magnitude of the change trend. When all the particles of the landslide mass have not entered the erosion scarper region, the velocity change is completely consistent. When some particles enter the erosion scarper region, the maximum velocity changes according to the erosion amount. As shown in Fig. 9, after entering the erosion area, the velocity of erosion rate below 0.0006 (including 0.0006) enters a peak value first, while the velocity of 0.0007 (including 0.0007) and above lags behind by 1-2 s. In this stage, the maximum velocity is the case of erosion rate of 0.0007. In the stage of erosion rate of 0.0004 ~ 0.0007, the larger the erosion rate, the larger the maximum velocity; in the stage of erosion rate of 0.0007 ~ 0.001, the larger the erosion rate, the smaller the maximum velocity. This indicates that in this stage, when the gravitational potential energy is converted into kinetic energy, the erosion amount increases within a certain range, which has a positive effect on the velocity; and when the erosion rate reaches a certain level, increasing the erosion amount will hinder the velocity. When the landslide mass entrains the erosion material into the accumulation, the larger the erosion amount, the smaller the velocity. This indicates that when the slope becomes gentle, the larger the erosion amount, the easier it is to form accumulation, which has a reverse effect on the velocity.Fig. 9 Maxvelocity-Time relationship diagram under different erosion rate.

Discussion

Erosion rate action analysis

In this study, we used DAN3D software, a widely used tool for numerical simulation of rapid long-distance landslides, to invert the dynamic process of the Xinmo Village landslide. DAN3D has good applicability in the numerical simulation of rock avalanches8,38. Using the built-in parameter erosion rate in DAN3D, the influence mechanism of erosion rate on the dynamic process of the landslide is discussed, and the corresponding conclusions are obtained. At present, few researchers use erosion rate to control the erosion amount to study the influence of erosion effect.

Previous field observations and experiments on the runout path of rock avalanches have shown that the deposited material on the runout path of rock avalanches has a profound impact on its behavior and runout. Dufresne et al. obtained the conclusion of the influence of the material on the runout path on the landslide motion through field investigation and experiment: when encountering the path material, mobilizing the path material requires energy consumption. After erosion entrainment, the influence of entrained material on the landslide motion depends on the erosion efficiency41. Based on the DAN3D numerical simulation, this paper studies the influence of path material by adjusting the erosion amount. When the avalanches enters the erosion scarper region, energy is consumed when mobilizing the path material, which is manifested as a decrease in velocity in the numerical simulation results. With the erosion of path material, in this simulation, the landslide has a longer runout distance with the increase of erosion amount. This indicates that the erosion efficiency is high in the simulation process of the Xinmo landslide. The numerical simulation quantitatively supplements the previous field observation results and experimental results. Therefore, in general, the numerical simulation results are in good agreement with the laboratory and field characteristics.

According to the velocity change curve under different erosion rate conditions, the erosion amount has a significant influence on the velocity of rock avalanches. When the material in the sliding source area enters the erosion region, due to the terrain change, there is a particle splash phenomenon, resulting in two main accelerations when entering the erosion region. However, the peak time of different erosion rate is not exactly the same. When the erosion rate E < 0.0007, the maximum velocity peak appears at the first acceleration position, but when the erosion rate E ≥ 0.0007, the maximum velocity peak appears at the second acceleration position. And when the erosion rate E = 0.0007, the peak value of the maximum velocity is the largest. When the material enters the accumulation area, the velocity trend basically shows a downward trend. Finally, the larger the erosion rate of the working condition, the smaller the maximum velocity. This indicates that the influence of erosion rate on the velocity of rock avalanches is not a simple influence—in different positions, the influence of different erosion rates is different.

Research limitation

However, when using DAN3D to invert the dynamic process, the dynamic friction problem of the rock initial position control sliding structure surface and the initial acceleration condition problem cannot be considered, which may cause the landslide to enter the erosion region in the dynamic process inversion3,12. The time cannot be accurately inverted. And erosion rate is a simplified concept, and further research on how much the erosion amount increases at a specific position for the landslide dynamic process research needs to be further studied. The issue of how erosion at the previous moment affects movement at the next moment has not been studied in depth. In summary, this study is of great significance for understanding the landslide erosion and accumulation process, assessing the landslide disaster risk, and providing a scientific basis for the future landslide disaster prevention and risk management. In the future, further research is needed on the influence of different along-course materials on rock avalanches, in order to study the dynamic process of rock avalanches more finely.

Conclusion

Based on the field investigation of the Xinmo Village landslide, this paper carried out DAN3D numerical simulation inversion and determined the numerical simulation parameters for the Xinmo Village landslide. Through numerical simulation, the dynamic process of the Xinmo Village landslide was deeply analyzed, and the influencing factors of the landslide deposit volume and velocity were deeply explored. Moreover, the paper discussed the impacts of erosion amount on the lateral spreading, longitudinal displacement, vertical erosion and velocity of the Xinmo landslide. The main findings are as follows:Numerical inversion is of great significance in determining the parameters of DAN3D landslide numerical simulation. Numerical inversion is based on the actual landslide data, constantly optimizing the input parameters of the model, thereby improving the accuracy and reliability of the simulation results. In the case of the Xinmo Village landslide, the duration was 120 s, the main erosion occurred in the erosion scarper region, and the overall erosion scarper region velocity was higher.

The landslide mass finally accumulated into a fan shape. The landslide accumulation volume is more responsive to the variation of erosion rate, and an exponential equation relating erosion rate and accumulation volume is derived. erosion rate positively influences the lateral spreading, longitudinal displacement and vertical erosion of the landslide, which further verifies that erosion is a crucial factor causing and aggravating landslide disasters.

Based on the coefficient of variation analysis, we found that the erosion rate has a stronger effect on vertical erosion than on lateral expansion and longitudinal movement. By analyzing the maximum velocity of the landslide mass under different erosion rate conditions, it is revealed that the magnitude of erosion amount has distinct effects on the velocity at different stages of the landslide.

Acknowledgements

The author would like to acknowledge the National Key Research and Development Program (Grant No.2019YFC1509704), the National Natural Foundation of China (Grant U1704243), Foundation of Hunan Provincial Key Laboratory of Hydropower Development Key Technology (PKLHD202203).

Author contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Z.F.W, X.S.Z., F.G.S, Y.T., and M.T.W. The first draft of the manuscript was written by X.S.Z. and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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