Introduction

Southwestern China is located at the southeastern margin of the Tibetan Plateau and corresponds to a region of high seismic activity (Chen et al. 2012). Historical records show that strong earthquakes have triggered many landslides and caused significant damage (Weidinger et al. 2002; Dai et al. 2005; Cui et al. 2009; Yin et al. 2009). At 14:28 (Beijing time) on 12 May 2008, the Wenchuan earthquake (M s = 8.0) struck in the Longmenshan fault zone, Sichuan, China. This region is characterized by high relief with a deeply incised valley. Long-duration seismic shaking triggered a number of landslides within the epicentral and surrounding regions (Yin et al. 2009; Chigira et al. 2010; Dai et al. 2011; Gorum et al. 2011; Huang and Fan 2013; Xu et al. 2014). The large volume of landslide material deposited on the slopes in the region enabled the occurrence of numerous post-seismic debris flows, resulting in the further loss of lives and extensive damage to many newly constructed towns and facilities (Parker et al. 2011; Tang et al. 2012; Zhang et al. 2014a). These geohazards killed more than 20,000 people, nearly a quarter of the total of 87,000 deaths resulting from the earthquake (Yin et al. 2009).

However, catastrophic rock avalanches are amongst the most destructive landslides triggered by the Wenchuan earthquake, and remote sensing interpretation showed that the earthquake triggered more than 100 rock avalanches with volumes greater than 10 million cubic metres (Huang et al. 2011). There has been much research on the rock avalanches triggered by this seismic event (e.g. Wang et al. 2009, 2013, 2015; Qi et al. 2011; Yin et al. 2011; Huang et al. 2012a; Yin 2014; Tang et al. 2015; Zhang et al. 2015). Several numerical simulations have analysed the runout behaviours of the rock avalanches triggered by the earthquake (Huang et al. 2012b; Li et al. 2012; Zhang et al. 2013; Zhou et al. 2013; Zhu et al. 2013; Dai et al. 2014; Yuan et al. 2014; Xing et al. 2015; Yin et al. 2015). These simulations have investigated the sliding process of landslide materials originating from the source area. Nevertheless, some rock avalanches involved not only the movement of debris originating from the landslide source area but also the movement of runout path materials and, in some cases, entrainment of material along the runout path which, in some cases, greatly enlarged the landslide volume and elevated the mobility of the displaced landslide material (Chigira et al. 2010; Wang et al. 2013). For example, a large rock avalanche (located at latitude 31°33′04.7″ Ν and longitude 104°06′58.5″ Ε) was triggered by the Wenchuan earthquake in the village of Yanjing, Mianzhu City, Sichuan Province, southwestern China (hereinafter called Wenjia valley rock avalanche). The displaced material travelled about 4,170 m with an elevation descent of about 1,360 m, equivalent to a fahrböschung of 16.9°, less than other landslides with this volume (Huang et al. 2011), and covered an area of 1.5 million square metres, with the final deposited volume of approximately 49 million cubic metres. The displaced landslide material destroyed Yanjing, killed 48 people and buried some houses at the mouth of the Wenjia valley (Fig. 1).

Fig. 1
figure 1

Pre-event image in Google Earth from 12 April 2006 (left) and post-event aerial image taken on 18 May 2008 (right) of the Wenjia valley rock avalanche

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Much research has focused on the rainfall-induced secondary debris flows of the catastrophic event (Tang et al. 2009; Ni et al. 2012; Xu et al. 2012; Zhang et al. 2013, 2014b; Van Asch et al. 2014; Zhou and Tang 2014). Five main debris flows occurred in the Wenjia valley from 24 September 2008 to 18 September 2010. However, little attention has been paid to the post-failure behaviour and debris characteristics of the landslide. Zhang et al. (2016) examined the dynamics of the Wenjia valley rock avalanche through field and laboratory investigations and remote sensing. The results show that shear resistance between grains decreased as the grains became finer due to pervasive fragmentation, which is one of the possible mechanisms by which the granular debris was able to travel a long distance at a high speed. Understanding the characteristics and also the possible movement of this kind of landslide is important to future landslide hazard mitigation. Therefore, a detailed field investigation of the Wenjia valley rock avalanche was performed to allow discussion of the geological and climatic setting and examination of the main characteristics of the landslide.

Understanding the triggering mechanism and post-failure behaviour of such rock avalanches is a challenge in geosciences and a prerequisite for the future prevention or mitigation of disasters. Many numerical studies have been performed to better understand the landslide runout behaviour, and some rational approaches have been proposed for predicting the motion of landslide masses (e.g. Sassa 1988; Hungr 1995; Chen and Lee 2003; Crosta et al. 2003; Denlinger and Iverson 2004; Hungr and Evans 2004; McDougall and Hungr 2004; Poisel et al. 2008; Pirulli and Mangeney 2008; Huang et al. 2012b; Pudasaini and Miller 2013; Pastor et al. 2014; Delaney and Evans 2015). Although the effectiveness of these approaches has been validated by back-analyses of many landslides, the successful forecasting of landslide movement has been rarely reported because different models or parameters of these approaches should be used for different types of landslides. However, back-analyses of case histories are essential because successful back-analyses may be used to calibrate the models, improve forecasting accuracy and provide parameters specific to similar types of rapid landslides for use in the predictive modelling of potential landslides. The present project numerically analysed the post-failure behaviour of the Wenjia valley rock avalanche using the dynamic model DAN3D, which was developed by Hungr and his colleagues (McDougall and Hungr 2004). This model is based on the numerical solutions of depth-averaged shallow-water equations, which have been modified for the flow of earth materials. This model relates to a meshless numerical method, based on smoothed particle hydrodynamics, and allows the simulation of motion across real three-dimensional topography without the mesh distortion problem, and it is thus suitable for the back-analysis of fluidized landslides. Smoothed particle hydrodynamics models combined with depth-integrated equations have been developed and extended to simulate the propagation stage of flow-like landslides, debris flows, lahars and avalanches (McDougall and Hungr 2004; Pastor et al. 2009; Haddad et al. 2010; Huang and Dai 2014). DAN3D allows the simulation of a catastrophic event through systematic iteration of the parameters that govern the basal resistance until the characteristics of the simulated landslide (i.e. velocity, extent and depth of deposits) approximately match those of the real event (McDougall and Hungr 2005). Through the numerical analysis of the Wenjia valley rock avalanche, the most suitable rheological models and parameters were calibrated and validated according to the results of the field investigation. It is expected that these models and parameters will help clarify the propagation process of similar landslides and improve the accuracy of landslide hazard mapping in the region.

Geological and geographical setting

The Wenjia valley is situated near the town of Qingping in the Mianzhu county, in Sichuan. The valley is located on the left bank of the Mianyuan River, about 80 km northeast of the epicentre of the Wenchuan earthquake (Tang et al. 2012). The Wenjia valley landslide occurred in a region of low-mid relief with a moderately incised valley. The elevations range from 2,402 m at the summit of Mount Jiudingshan to 883 m at the mouth of the Wenjia valley (Fig. 2). The depth of the valley incision ranges from 30 to 50 m, the longitudinal gradient of the valley bottom ranges from 150 to 180 ‰, and the angle of the side slope ranges from 35° to 55°.

Fig. 2
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Detailed topography of the Wenjia valley rock avalanche. a Landslide boundary. b Source area. c Hanjia platform (zone I). d Zone II. e Zone III. f Cross-section line. Red arrows express the sliding direction of the sliding mass

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The exposed rocks in the study area include the Guanwushan Group limestone of the Upper Devonian and the Qingping Group siltstone of the Upper Cambrian. The Guanwushan Group overlaps on the Qingping Group and there is nonconformity between them. The landslide is a dip slope failure that occurred in the Guanwushan Group. According to a pre-event Google Earth image and eyewitness reports, the source rock mass was stable before the earthquake.

The study area has a humid subtropical monsoon climate. The average annual temperature is about 14.4 °C and the annual rainfall ranges from 1500 to 1700 mm in Qingping. The maximum daily rainfall recorded was 496.5 mm on 15 August 1995, according to the historical record of this area for the last several decades. There are many streams and well-developed water systems, all of which belong to the Tuo River. The Mianyuan River, a tributary of the Tuo River, has a length of 63.5 km and an average yearly discharge of 15.7 m3/s. The Wenjia valley is located on the left bank of the Mianyuan River. The valley has a length of 3 km and a drainage area of 7.8 km2.

Wenjia valley rock avalanche

Post-failure behaviour of the rock avalanche

On the basis of a detailed field investigation, a geological map and longitudinal profile of the Wenjia valley rock avalanche are presented in Figs. 2 and 3, respectively. The landslide initiated as a rock slide in the limestone rock mass. After detaching from its source area under strong earthquake ground motions, the sliding mass on the left side ran down rapidly towards the direction of 283° and then transformed into debris flow as it impacted the Hanjia platform. After passing a scarp with a height of about 280 m at an elevation of 1599 m, the debris ran up the opposite slope on the right bank of the valley at location A in Fig. 2. After colliding with the right bank of the valley (Fig. 4a), the debris flow changed its direction and entered the platform at an elevation of 1300 m at a direction of 123°. The debris flow superelevated at the valley bend (Fig. 4b, c) at location B in Fig. 2. The debris changed direction again and travelled down along the valley at a direction of 278° and then ran up the ridge with a trend of 070° at location C in Fig. 2. After colliding with the right bank of the valley (Fig. 4d), the debris continued to move along the valley at a direction 278° west of south and finally came to rest at the mouth of the valley. The displaced materials created an air blast so powerful that it downed trees along its sides and front margin, indicating the rapid movement of the rock avalanche (Fig. 5).

Fig. 3
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Longitudinal profile of the Wenjia valley rock avalanche along line 1-1′ shown in Fig. 2

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Fig. 4
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Dynamic characteristics of the Wenjia valley rock avalanche. a Displaced materials ran up the opposite slope on the right bank of the valley at location A in Fig. 2 (view towards NWW). b, c Superelevation in the valley bend at location B in Fig. 2 (view towards 205° and 188°, respectively). d Run-up on the ridge with a trend 070° at location C in Fig. 2 (view towards 100°)

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Fig. 5
figure 5

Air blast downed trees along its sides and front margin. a On the left side of the valley (view towards 290°). b On the right side of the valley (view towards 290°). c On the right bank of the Mianyuan River (view towards 265°)

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Detailed description of the rock avalanche

The source area is located on the eastern slope of the Wenjia valley, 3.6 km from the Yingxiu-Beichuan Fault, which caused the Wenchuan earthquake. The head scarp and toe of the rupture surface are at elevations of 2268 and 1780 m, respectively. This area has a length of 960 m along the main slide direction, a width of 500–1080 m and an area of 0.69 km2 (Fig. 6a). The sliding mass mainly consisted of Upper Devonian Guanwushan limestone with a thickness of 20–30 m and an initial volume of 28.5 million cubic metres. Three major joint sets are present at 315°/70° (J1), 135°/38° (J2) and 237°/78° (J3) and the bedding plane is 320°/32° (Fig. 6b). The sliding surface developed along the bedding plane (Fig. 6c).

Fig. 6
figure 6

a Source area of the Wenjia valley rock avalanche (view towards NEE). b Stereonet of the main discontinuity sets present in the source area, J1:315°/70°, J2:135°/38°, J3:237°/78°; the bedding plane is 320°/32°. c Cliff in the middle part of the source area

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The displaced materials were mainly deposited at elevations ranging from 908 to 1780 m. The area of transportation and deposition can be divided into three zones according to the elevation, direction of the landslide motion and longitudinal gradient of the deposits (Fig. 2). The grain size distribution of the deposits is shown in Table 1.

Table 1 Grain size distribution of the deposits in the different zones
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Zone I is located at the Hanjia platform between the toe of the source area and the scarp and has elevations ranging from 1599 to 1780 m (Fig. 7a). This subzone has a volume of 22.6 million cubic metres (Xu et al. 2012) and a longitudinal channel gradient of 10–30°. The slide mass entrained the original Quaternary deposit on the Hanjia platform and damaged part of a fir tree forest on the left side of the zone (Fig. 7b). The landslide deposits in this zone consist of poorly sorted debris and its parent rock is limestone. The rock avalanche debris contains 30 % particles larger than 100 cm, 40 % particles ranging in size from 20 to 100 cm, 20 % particles ranging in size from 1 to 20 cm and 10 % particles smaller than 1 cm in diameter.

Fig. 7
figure 7

Transportation and deposition area. a View of the Hanjia platform towards the source area (view towards 75°). b Damaged part of a fir tree forest on the left side of zone I (view towards NEE). c First run-up zone and longitudinal ridge (view towards NWW). d Longitudinal ridge on the left side of the valley resulting from the superelevation (view towards E). e First platform (view towards E). f Second platform (view towards 270°)

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Zone II is located between the cliff (Fig. 7a) and the mouth of the right branch of the Wenjia valley and has elevations ranging from 988 to 1400 m (Fig. 2). The zone includes two subzones (zones IIa and IIb), according to the direction of the landslide motion.

Zone IIa is located at the 1300-m platform along the direction of 123° and has elevations ranging from 1225 to 1400 m (Fig. 7a). This subzone has an average longitudinal gradient of about 5° and a thickness greater than 100 m. Three longitudinal ridges can be found in this subzone. The first ridge is on the left side of the valley and has a trend of 203°, a length of 270 m and a width of 34 m (Fig. 8). The rock avalanche debris deposited on the ridge contains 5 % particles larger than 20 cm, 20 % particles ranging in size from 1 to 20 cm and 75 % particles smaller than 1 cm in diameter. The second ridge is also on the right side of the valley resulting from the run-up at location A in Fig. 2 and has a trend of 220°, a length of 550 m and a maximum width of 160 m (Figs. 7c and 8). The rock avalanche debris deposited on the ridge contains 10 % particles larger than 20 cm, 60 % particles ranging in size from 1 to 20 cm and 30 % particles smaller than 1 cm in diameter; the largest boulder is more than 160 cm in diameter. The third ridge is on the left side of the valley and results from the superelevation at location B in Fig. 2 and has a strike of 240°, a length of 340 m and a width of 65 m (Fig. 7d). The rock avalanche debris deposited on the ridge contains 30 % particles larger than 100 cm, 25 % particles ranging in size from 20 to 100 cm, 30 % particles ranging in size from 1 to 20 cm and 15 % particles smaller than 1 cm in diameter.

Fig. 8
figure 8

Cross sections taken along lines 2-2′ (a) and 3-3′ (b) shown in Fig. 2

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Zone IIb is located at elevations ranging from 988 to 1225 m a.m.s.l. This subzone has an average longitudinal gradient of 18–25° and a thickness of 45–120 m. The rock avalanche debris deposited on the right side of the subzone contains 5 % particles larger than 100 cm, 25 % particles ranging in size from 20 to 100 cm, 40 % particles ranging in size from 1 to 20 cm and 30 % particles smaller than 1 cm in diameter. The rock avalanche debris deposited on the left side of the subzone contains less than 5 % particles larger than 100 cm, 10 % particles ranging in size from 20 to 100 cm, 35 % particles ranging from 1 to 20 cm and 40 % particles smaller than 1 cm in diameter.

Zone III is located at elevations ranging from 908 to 1016 m. Two platforms are found in this zone. The first platform is located at elevations of 988–1016 m and has an average longitudinal gradient of 5°, a length of 118 m and a width of 71 m (Fig. 7e). The rock avalanche debris deposited on the first platform contains 30 % particles ranging in size from 1 to 20 cm and 70 % particles smaller than 1 cm in diameter. The second platform is located at elevations of 908–988 m and has an average longitudinal channel gradient of about 6°, a length of 167 m and a width of 94 m (Fig. 7f). The platform has been covered by a secondary debris flow.

Numerical runout modelling of the rock avalanche

Dynamic model

Dynamic back-analysis can be empirical, using historical data such as those of the volume, fall height and runout (e.g. Scheidegger 1973; Corominas 1996), and/or numerical modelling to analyse the runout behaviour of the rock avalanche (Hungr et al. 2005). To investigate the runout behaviour of the Wenjia valley rock avalanche and provide parameters specific to the same type of landslides for use in predictive modelling of potential landslides, the rock avalanche was numerically modelled using the dynamic model DAN3D developed by Hungr and his colleagues (McDougall and Hungr 2004).

The dynamic model is governed by internal and basal rheological relationships. The rheologies that have been found to represent recorded events most accurately are the frictional and Voellmy rheologies (Boultbee 2005). The frictional rheology assumes the resisting shear force (τ) to depend only on the effective normal stress (σ). The frictional equation is expressed as

$$ \tau =\sigma \left(1-{r}_u\right) \tan \phi $$
(1)

where the pore pressure ratio, r u , and the dynamic friction angle, φ, are the rheological parameters to be introduced in the model. The pore pressure ratio is derived from the pore pressure, u, normalized by the total bed normal stress at the base, σ. The pore pressure ratio and the dynamic friction angle can be alternatively expressed by a single variable referred to as the bulk basal friction angle, φ b:

$$ {\phi}_b= \arctan \left(1-{r}_u\right) \tan \phi $$
(2)

The Voellmy rheology describes total resistance as a sum of a frictional term and a turbulent term:

$$ \tau =\sigma f+\rho g{v}^2/\xi $$
(3)

The frictional term relates the shear stress to the normal stress through a friction coefficient, f, which is analogous to tanφ b. The turbulent term summarizes all velocity-dependent factors of flow resistance and is expressed by the square of the velocity and the density of the debris through a turbulence coefficient, ξ (Table 2).

Table 2 Back-calculated values of the rheological parameters and models for the Wenjia valley rock avalanche
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Simulations of velocity were compared to the estimation of velocity from run-up and superelevation. The run-up velocity was obtained as (Evans et al. 2001)

$$ {V}_{\min }={(2gh)}^{0.5} $$
(4)

where V min (in metres per second) is the minimum velocity, g is the gravitational constant and h is the run-up height.

The superelevation velocity was estimated as (Evans et al. 2001)

$$ {V}_{\min }={\left(gdr/b\right)}^{0.5} $$
(5)

where d is the superelevation, r is the radius of curvature of the bend and b is the width of the path.

Input data

The pre- and post-DEMs (digital elevation models) were created by superimposing the 1:50,000-scale pre-event topographic map on the post-event aerial image (Fig. 9). The input sliding surface and source thickness files were created using pre- and post-event DEMs at a scale of 1:50,000. The source depths were approximated by subtracting the post-event DEM from the pre-event DEM and isolating the probable main failure zone. Data outside of this zone were filtered, leaving a displaced volume of approximately 28.5 million cubic metres. The isolated source depths were then subtracted from the pre-event DEM to estimate the initial sliding surface elevations. Assuming a volume of 25 % volume bulking, as suggested by Hungr and Evans (2004), the initial volume of displaced materials was estimated to be 35.6 million cubic metres for DAN3D simulation. Data spacing was set to 20 m for input into the model.

Fig. 9
figure 9

Pre-event (a) and post-event (b) DEMS

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The model has several parameters, including both control and rheological parameters (McDougall and Hungr 2004). The control parameters are the number of particles, N; the particle smoothing coefficient, B; the velocity smoothing coefficient, C; and the stiffness coefficient, D. The rheological parameters are the internal friction angle, φ i, the basal rheological parameters (which depend on the selected basal rheology) and, if applicable, the entrainment growth rate, E s.

Continuum simulation is performed through discretization of the governing equations, but a sufficiently large number of computational elements (particles) are required to capture the behaviour at each important location within the sliding mass. Increasing the number of particles (N) can increase the resolution of the continuum method. The particle smoothing coefficient (B) affects the smoothness of the interpolated flow depth, and it can be adjusted by the user until the initial depth interpolation appears smooth. The velocity smoothing coefficient (C) determines how much the velocities of neighbouring particles affect the central particle. Velocity smoothing introduces some numerical diffusion, which appears to smooth out strong shocks, increase stability and reduce the tendency for particles to line up in the downstream direction in channelized reaches of the path. The dimensionless stiffness coefficient (D) controls the strain-dependent rate of the transition between the active and passive internal stress states. On the basis of the parametric analyses presented in this paper, the control parameters N = 2000, B = 4, C = 0.45 and D = 460 are recommended for the duration of motion.

In accordance with the equivalent fluid concept, a frictional model rheology was adopted to simulate the internal rheology of the slide mass. The yield criterion is governed by the internal friction angle (φ i) and the effect of pore pressure can be accounted for implicitly with the internal friction angle. In this paper, an internal friction angle of 35° is set for the moving mass, without pore pressure in all simulations.

The frictional model can be used in the source area and zone I and the Voellmy rheology in zones II and III. The basal rheological parameters were adjusted by trial and error to achieve the best fit with the observed extension of the landslide deposit, considering also published values for comparable case studies (Hungr and Evans 1996; McDougall et al. 2006; Evans et al. 2007; Sosio et al. 2008). The transition between the frictional and Voellmy models was placed at an elevation of 1400 m. To the Donghekou rock avalanche triggered by the 2008 Wenchuan earthquake, Wang et al. (2013) found that the sliding liquefaction phenomenon can occur on the landslide material in the source area during the main shock of the earthquake as a result of undrained shearing in a saturated sliding zone. Wang et al. (2014a, b) also performed the undrained cyclic shear tests and found that the monitored excess pore water pressure showed a delayed response—it reached a constant pore water pressure of 280 kPa under an estimated normal stress of 300 kPa—resulting in an effective normal stress of 20 kPa, indicating that this runout path material is highly liquefiable. Based on the above results, in order to simulate the frictional loss along the sliding surface resulting from the undrained loading, we examined excess pore water pressure acting on the potential sliding surface in the source area because soil in the sliding zone was fully saturated (equivalent to a range of the pore pressure ratio (r u ) of 0.5–0.8). A dynamic friction angle of 30° was adopted for the frictional model at zone I without buildup of pore pressure. A Voellmy rheology was selected to characterize the runout behaviour of the landslide below an elevation of 1400 m in zones II and III. For the simulation of this part of the path, values for the friction coefficient (f) in the range of 0.05–0.25 together with values for the turbulence coefficient (ξ) in the range of 100–2000 m/s2 were used. It is noted that these values for the Voellmy parameters are within the range of those found to best simulate the runout and velocity of the majority of rockslide debris avalanche case histories analysed by Hungr and Evans (1996). These values were then used in a series of simulation runs to obtain the best fit for the observed characteristics of the Wenjia valley rock avalanche.

Mass and momentum transfer during the entrainment of the path material can affect landslide dynamics. A useful preliminary estimate of the average volume growth rate (\( \overline{E_s} \)) for a specific entrainment zone can be obtained using the natural exponential growth equation (McDougall and Hungr 2005):

$$ {V}_f={V}_0 \exp \left(\overline{E_{\mathrm{s}}}\overline{S}\right) $$
(6)

where V f is the estimated total volume of the landslide exiting the zone, V 0 is the estimated total volume of the landslide entering the zone and \( \overline{S} \) is the approximate average path length of the zone. Given the initial and final volumes, as observed, and the approximate length of the entrainment zone, the appropriate rate to use in a simulation can be back-calculated using Eq. 6, which ensures that the required volume is entrained from the known length of the entrainment zone (cf. McDougall and Hungr 2005). To simulate entrainment, volume growth rates of 3.4 × 10−4 and 7.6 × 10−5 m−1 were specified at zones I, II and III, respectively.

Results and discussion

A series of back-analyses were performed to determine the best rheological parameters for the simulation (Table 1). The results of the DAN3D simulation are presented in Fig. 10. The runout is precisely duplicated with a dynamic friction angle (φ) of 30° and a pore pressure ratio (r u ) of 0.62 for the materials in the source area, with a dynamic friction angle of 30° in zone I and with Vollemy parameters of friction coefficient f = 0.09 (dimensionless) and turbulent coefficient ξ = 2,000 m/s2 in zones II and III. The results show that the duration of the movement is estimated at 240 s for an average velocity of 17.4 m/s. The simulated run-ups and superelevations in the three major impact zones match the measured trimline, suggesting that the flow velocities are accurately simulated.

Fig. 10
figure 10figure 10figure 10

a–i Time-lapse images of the DAN3D simulation. The contours of deposit depth are at 10-m intervala. The elevation contours are at 20-m intervals

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A plot of the maximum simulated flow velocities recorded along the runout path is shown in Fig. 11. The maximum velocity, 56 m/s, was recorded near the toe of the rupture surface. As mentioned above, the possible velocities were also calibrated by means of run-ups and superelevations. After passing the cliff at an elevation of 1599 m, the debris ran up the opposite slope on the right bank of the valley at location A in Fig. 2, and Eq. 4 yields a velocity estimate of 45 m/s for a measured run-up of h = 100 m. The debris flow superelevated at the valley bend at location B in Fig. 2. For this bend, Eq. 5 yields a velocity of 38 m/s for the parameters of d = 180 m, r = 600 m and b = 750 m. The debris ran up the ridge at location C in Fig. 2, and Eq. 4 yields a velocity estimate of 22.4 m/s for a measured run-up of h = 25 m. Figure 10 shows that the simulated velocities are lower than the velocities from the results of the run-up and superelevation analysis. The differences in the velocities can be attributed to measurement errors associated with Eqs. 4 and 5, and determining the run-up height and radius of a curve from an aerial view is subject to limitations. It was thus difficult to match the DAN3D-simulated velocity values with the field velocities inferred from debris behaviour.

Fig. 11
figure 11

Plot of the maximum simulated flow velocities recorded along the runout path. The maximum velocity contours are at 5-m/s intervals and the elevation contours are at 20-m intervals

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The final distribution of the debris obtained in the simulation is shown in Fig. 12. The figure gives an average depth of about 43 m and a maximum depth of over 112 m at the Hanjia platform; these results are roughly consistent with the range of the depth obtained from the DEMs constructed from 1:50,000-scale topographic maps. The final deposit volume was estimated to be 49.0 million cubic metres due to entrainment along the runout path.

Fig. 12
figure 12

Final distribution of the debris at 10-m intervals

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Using the DAN3D model, many case studies of rapidly moving landslides in North America have been analysed and a valuable database of calibrated parameters has been created (cf. Hungr et al. 2005). We numerically modelled the Niumian valley rock avalanche triggered by the Wenchuan earthquake using the DAN3D model (Xing et al. 2015). The simulated results show that the duration of the Niumian valley rock avalanche is about 120 s with an average velocity of 22 m/s, and the Wenjiagou valley rock avalanche has a duration of about 240 s with an average velocity of 17.4 m/s. The travel angle, fahrböschung, value of the Wenjia valley rock avalanche is less than that of the Niumian valley rock avalanche. Further case studies will be investigated using the DAN model to obtain rheological parameters for landslide hazard assessment in the mountainous areas of southwestern China.

Summary and conclusions

On 12 May 2008, the Wenjia valley rock avalanche was triggered by the Wenchuan earthquake in Mianzhu, Sichuan, China. On the basis of the field investigation, this paper introduced the general setting and main characteristics of the landslide and analysed the runout behaviour with the DAN3D model. The following summarizes the study.

  1. 1.

    The Wenjia valley rock avalanche was a rapid and long-runout catastrophic landslide triggered by the Wenchuan earthquake. This catastrophic event destroyed the village of Yanjing, killed 48 people and buried some houses at the mouth of the Wenjia valley. The displaced materials travelled about 4170 m, with a descent of about 1360 m.

  2. 2.

    A field investigation showed that the displaced materials created an air blast so powerful that it downed trees along its sides and front margin, indicating the rapid movement of the rock avalanche.

  3. 3.

    A recently developed dynamic model (DAN3D), which accounts for material entrainment along the runout path, was used to simulate the runout behaviour of this event. The sliding velocity and depositing area were modelled using a combined (Frictional–Frictional–Vollemy) model that well simulates the landslide.

  4. 4.

    The simulation results show that the rock avalanche had a duration of about 240 s and an average velocity of 17.4 m/s. The simulation velocities were lower than those obtained from the run-up and superelevation analysis. However, the simulation predicted the shape of the deposit well. Good agreement between the observation and simulation results was achieved, suggesting that this model with the parameters obtained through back-analyses is useful for the prediction of landslides in the same area and similar types of landslide hazard.