Rock avalanches are extremely rapid, massive flow-like movements of
fragmented rock. The travel path of the rock avalanches may be confined by
channels in some cases, which are referred to as channelized rock avalanches.
Channelized rock avalanches are potentially dangerous due to their difficult-to-predict travel distance. In this study, we constructed a dataset with
detailed characteristic parameters of 38 channelized rock avalanches
triggered by the 2008 Wenchuan earthquake using the visual interpretation of
remote sensing imagery, field investigation and literature review. Based on
this dataset, we assessed the influence of different factors on the runout
distance and developed prediction models of the channelized rock avalanches
using the multivariate regression method. The results suggested that the
movement of channelized rock avalanche was dominated by the landslide volume,
total relief and channel gradient. The performance of both models was then
tested with an independent validation dataset of eight rock avalanches that
were
induced by the 2008 Wenchuan earthquake, the

Rock avalanches are extremely rapid, massive flow-like movements of
fragmented rock from a very large rockslide or rockfall (Hungr et al.,
2014). Hundreds of rapid and long runout rock avalanches were triggered by
the
2008 Wenchuan earthquake in Sichuan Province (Zhang et al., 2013), with
catastrophic consequences for residents in the affected areas. For instance,
the 15

Distribution map of large rock avalanches triggered by the Wenchuan earthquake.

Methods for determining the travel distance of landslides can be divided into two categories: dynamic modeling (Heim, 1932; Sassa, 1988; Hungr and McDougall, 2009; Pastor et al., 2009; Lo et al., 2011) and empirical modeling (Scheidegger, 1973; Lied and Bakkehøi, 1980; Corominas, 1996; Finlay et al., 1999; Van Westen et al., 2006; Guo et al., 2014). The dynamic models are able to provide information on landslide intensity, such as velocity, affected area and deposition depth, in addition to travel distance. Nonetheless, dynamic models with a variety of physical bases require accurately quantified input parameters that are difficult to obtain before the events, and many simplified assumptions that are not applicable to the actual situation. Recently Mergili et al. (2015) developed the multi-functional open-source tool r.randomwalk for conceptual modeling of the propagation of mass movements, which can combine the empirical model with the numerical model. Empirical models considering the correlations between observational data provide an effective technique to aid in understanding mechanisms of rock avalanche motion and to develop practical models for predicting rock avalanche travel distance. However, the empirical-statistical models set up from samples with different geomorphological and geological surroundings, trigger conditions or failure modes are not very sufficient to be applied to the Wenchuan earthquake area.

In this study, we compiled a dataset of 38 rock avalanches with flow paths confined by channels (this kind of landslide is hereinafter termed channelized rock avalanche) from interpretation of remote sensing, field investigations and literature review (see Sect. 3.1). Statistical correlations were used to determine the principle factors affecting the mobility of the channelized rock avalanches. Then a stepwise multivariate regression model was developed to build a best-fit empirical model for the travel-distance prediction of this kind of rock avalanches in the Wenchuan earthquake area. A derivative multivariate regression model was also constructed. The performance of both models was then tested with an independent validation dataset of eight rock avalanches in the same area.

The study area (see Fig. 1) is on the northeast-trending Longmenshan thrust fault zone between the Sichuan basin and the Tibetan plateau. Three major sub-parallel faults are the Wenchuan–Maowen fault, the Yingxiu–Beichuan fault and the Pengguan fault (Fan et al., 2014). With long-term endogenic and exogenic geological process, this region is characterized by high mountains and deep gorges with extreme rates of erosion (Qi et al., 2011).

This study selected 38 channelized rock avalanches induced by the Wenchuan
earthquake to study the relations between travel distance and influential
factors. These rock avalanches occurred along the seismogenic
Yingxiu–Beichuan fault; the distance to the fault ranged from 0 m

Summarization of statistical relationships indicating landslide mobility in the literature.

Note: C0, C1, C2, C3 are the constants.

Remote sensing images of two channelized rock avalanches triggered
by the Wenchuan earthquake.

The lithology of outcropping rock in source areas can be divided to four types: carbonate rock, phyllite, igneous rock and sandstone. The deposit of the rock avalanches in the study area was usually debris with mean particle size as tens of centimeters, which suggests that the sliding masses were intensively fragmented during their movement.

The influence of the local geomorphology on the topography of the rock avalanche depositions can be recognized from remote sensing images after the earthquake. The source area and the transition area of channelized rock avalanches in the study area were somehow easy to be differentiated, as the source area are normally located at the top or upper part of slope, while the flow path (flow or transition area) is partially or fully confined by channels (Fig. 2).

Various statistical methods have been applied to predict travel distance of
landslides, and some popular relationships are summarized in Table 1. The
most prevalent one is the equivalent friction coefficient model, which only
takes account of landslide volume (

Moreover, the shape and mobility of rock avalanches are controlled by the local topography. Heim (1932) firstly mentioned the influence of local morphology: the debris masses will undergo different effects with the angle of reach changing, and rock avalanches have to conform to the local morphology regardless of their scale. Abele (1974) summarized four different possibilities of adaptation of the rock avalanche to local morphology. Hsu (1975) noted that a sinuous pathway can reduce runout distance of rock avalanches. Nicoletti and Sorriso-Valvo (1991) inferred that local morphology impacts landslide motion by changing the rate of total energy dissipation along the travel path. To determine the influence of specific channels on the travel distances of rock avalanches, we consider the impacts of the gradient of the upper slopes and lower channels.

Data of various factors for establishment of prediction model of rock avalanche travel distance.

Sketch map of a channelized rock avalanche defining geometric parameters. The red-dashed ellipse indicates the topographic transition dividing the initiated slope, channel and valley floor. The red arrow represents sliding direction of source mass.

Rock avalanches triggered by the Wenchuan earthquake usually initiated from
the
top or the higher part of slopes possibly due to the altitude amplification
effect of earthquake acceleration; therefore the toes of the rupture surface
were commonly found in the source area at the upstream of the pre-existing
channel (See Fig. 3). When the slope failed, the failed mass traveled a
long distance down the channel. The 38 rock avalanches in this study are
selected with the criterion that the flow path is partially or fully
confined by channels. The volumes of these rock avalanches ranged from
0.4 to 50

The terms and notations of a typical channelized rock avalanche are shown in
Fig. 3. The local morphology of a rock avalanche can be divided to three
sections: initiated slope (source area), channel (main travel path or flow
area) and valley floor (deposition area). When the mass moves over the
initiated slope section, it is free from lateral constraints, and the moving
mass is able to spread laterally. After entering the channel, the flowing
mass is constrained by the two lateral slopes. Finally, the mass may reach
a wide valley floor, where it spreads laterally and deposits. The average
inclination of the source area and travel path is obtained,
while the gradient of valley floor (deposition area) is neglected as it has
very little variation. Slope angle (

Travel distance is the most important prediction parameter in rock avalanche hazard evaluation in mountainous areas. Travel-distance prediction of rock avalanche is a complicated issue as it is determined by many different properties of the materials (i.e., grain size distribution and water content), topographical factors, mobility mechanics of failed mass, the confinement attributes of travel path, etc. (Guo et al., 2014). Empirical-statistical methods have long been used as tools to study the mobility of rock avalanche since they are easy to develop and apply, and they are not dependent on knowing the complex physical processes involved in the hypermobility of rock avalanches. Channelized rock avalanches have unique movement paths involving complex, and possibly little-known, physical processes such as grain collisions, fragmentation and entrainment of bed material from the channel sides and bottom. Existing empirical models have not produced a favorable prediction. The forecasting index system and the prediction model of channelized rock avalanches should be discussed first.

In this paper, we first selected controlling factors on rock avalanche
travel distance through correlation analysis. Then we fitted a stepwise
multivariate regression model using all significant correlation variables to
obtain a best-fit empirical model for landslide travel distance and
explored which factors were statistically significant at the same time, as
expressed in Eq. (1).

Reach angle, also called the apparent coefficient of friction, is a well-known index to express the landslide mobility. It is the angle of the line connecting the crown of the landslide source area to the toe of the displaced mass. This angle is firstly conducted by Heim (1992) in the famous energy-line model as the average coefficient of friction of a sliding mass from initiation to rest. The reach angle is supposed to possess the ability of landslide mobility prediction because of its tendency to decrease with the increase of landslide volume as illustrated by many researchers (Scheidegger, 1973; Corominas, 1996).

In this study, the influence of landslide volume, drop height, slope of the source area and flow path (channel) on the reach angle of the channelized rock avalanches are examined (Figs. 4 and 5). Figure 4a presents log(volume) vs. log(reach angle), showing a weak correlation probably due to the limited volume range in our dataset, constrained movement in channel and local morphology of channels. In order to analyze the effect of potential energy on the reach angle, the effective drop height (defined as the total height minus the height of source area) is used instead of the total height to exclude the effect of the superposition of source height and total height. That is especially useful for landslides with large-size initiation but limited travel distance. A significant positive correlation is observed between the reach angle and effective drop height, apart from the four lower scatters in Fig. 4b. Figure 5a and b indicate obvious positive correlations between the reach angle with both the slope gradient in source area and channel gradient along the flow path. The large scatter in Figs. 4 and 5 suggests that the reach angle of channelized rock avalanches might be controlled by some other factors, such as local topography rather than volume, but this needs to be further studied.

Correlation coefficients of continuous variables listed in Table 2.

Note: the number in italics indicates the two variables are not significantly correlated.

Correlation coefficients between different variables and

Relationship between horizontal travel distance and volume of channelized rock avalanches.

Figure 6 illustrates that the travel distance varies exponentially with

The regression coefficients and results of significance tests of two multivariate regression models.

“Coefficients” of each variable has three kinds: LCI is the lower bound of the coefficients with 95 % confidence; mean is the mean value of the coefficients; UCI is the upper bound of the coefficients with 95 % confidence.

Relationship between horizontal travel distance and total relief of channelized rock avalanches.

According to the matrix of correlation coefficients (Table 3),

Equation (2) can be transformed to Eq. (3):

While

Background parameters and predicted values of eight rock avalanches in the same area used for validation.

“Triggers” is the triggering condition of rock avalanches: WCEQ
represents the 2008 Wenchuan

Residual plots for the two multivariate regression models: Fig. 9a is for Eq. (2) and Fig. 9b is for Eq. (4).

The validity of these two models was evaluated through the significance
test leading to the highest

Figure 9 compares the predicted travel distances estimated by using
Eqs. (2) and (4) with the observed ones. It suggests that the predicted
values of the samples are close to the observed ones. Where

The comparison between observed and predicted travel distance for the two multivariate regression models.

The regression equations were tested using an independent sample validation
dataset of eight rock avalanches in the same area induced by three different
kinds of triggers: 2008

Sketch map of flow capacity of channel affecting on the
travel distance of the Wenjia Gully channelized rock avalanche:

Relationship between the volume and travel distance

The results of our analysis of the dataset indicate that the mobility
(travel distance) of channelized rock avalanche is positively correlated
with landslide volume and total relief but negatively correlated with
channel gradient. As Fig. 6 shows, the travel distance of channelized rock
avalanche would rapidly increase with volume of rock avalanche enlarged.
Such a high correlation between landslide volume and travel distance implies
that the travel distance of channelized rock avalanche is dominated by the
spreading of the slide mass (Davies et al., 1999; Staron and Lajeunesse, 2009). The high positive
correlation between total relief and travel distance is for two reasons: the
larger the total relief is, the more kinetic energy the slide mass could
obtain and the further it could travel (Legros, 2002). The
channel gradient is highly correlated with the

The residual analysis result demonstrates that the projection process in the
early motion stage will significantly enlarge the travel distance of rock
avalanches. The projection phenomenon was observed in the Wenchuan
earthquake region by Huang et al. (2011), defined as the thrown out or
projectile motion of slope material due to site amplification effect of
seismic wave causing the peak ground acceleration to be larger than 9.8

Relationship between the volume and

Relationship between the volume and

The mobility of landslides is influenced by a variety of factors, such as topography, landslide size, material type, landslide type and water content. The important role of topographical constrains on the landslide mobility can be indicated from the high positive correlation of reach angle with effective drop height, slope gradient and channel gradient (see Figs. 4 and 5). Besides, some microtopography like turns (changes of channel flow direction), drop cliff and broad depression along the landslide travel path will influence the motion and deposition of rock avalanches remarkably. The rock avalanches corresponding with the four large bias scatter in Fig. 4b are the Wenjia Gully, Hongshi Gully, Niumian Gully and Donghekou rock avalanche, whose flow paths have cliffs in the upper end of channels with notable drop heights of 260, 150, 60 and 160 m, respectively, according to field investigations. Moreover, fluidization characteristics such as superelevation near curve transitions can be found in the channel section of these four rock avalanches. This steep microtopography will enlarge the mobility of rock avalanches because the sliding mass will undergo the drop, collision and fragmentation effects in the early motion stage, which will facilitate motion-mode transformation from sliding to flowing. This transformation will enhance the mobility of rock avalanches traveling a much longer distance than predicted. Attention also must be paid to the broad depression along the channel, which can contain a large amount of debris mass and therefore curb the travel distance of channelized rock avalanches. For example, in the Wenjia Gully almost half of the total volume of the rock avalanche was deposited at the beginning of the channel (see Fig. 10c), leading to a shorter travel distance than expected.

To investigate the influence of landslide types on the landslide mobility,
we compile our dataset with the dataset created by Guo et al. (2014), as it
contains the data of 32 landslides with other types (debris avalanches, rockslides, soil slides) triggered by the Wenchuan earthquake. We plot the
relationship between

The common triggers of landslides are earthquakes and rainfall. The influence of triggers on landslide distribution has been well studied, but the effect of triggers on the landslide mobility still constitutes a gap in scientific knowledge. Zhang et al. (2013) indicated that rock avalanches triggered by earthquakes have a slightly lower mobility than those not triggered by earthquakes, and rock avalanches close to the seismic fault do not always have a higher mobility even when a rock avalanche near the seismic fault is subjected to higher ground accelerations. Guo et al. (2014) also mentioned that the seismic acceleration has less influence than rock type, sliding volume, slope transition angle and slope height on landslide travel distance. According to Table 5, two rainfall-induced rock avalanches show stronger mobility than earthquake-induced ones. The rock avalanches induced by rainfall express a stronger mobility than the earthquake-induced ones may due to lubrication effect of water. However, a detailed study on the influence of triggers on the landslide mobility is required.

A channelized rock avalanche refers to a rock avalanche with a flow path confined between valley walls. Relevant detailed data on 38 channelized rock avalanches triggered by Wenchuan earthquake were collected by remote sensing, field investigation and literature review. The results of correlation and regression analysis revealed that the movement of channelized rock avalanches is dominated by the spreading of the failed mass. Landslide volume, total relief and channel angle had predominant effects, playing a dominating role in the on travel distance of channelized rock avalanches. Stepwise multivariate regression was used to develop a nonlinear best-fit travel-distance prediction model for the channelized rock avalanches. An alternative multivariate regression model was also built. The reliability of the two models was tested by an independent validation dataset of eight rock avalanches in the same area and produced good results, meeting the requirements for preliminary evaluation of travel distance for channelized rock avalanches in the Wenchuan earthquake area.

Data from Guo et al. (2014) in Fig. 11 are available at

The authors declare that they have no conflict of interest.

This work was supported by the Fund for International Cooperation (NSFC-RCUK_NERC), Resilience to Earthquake-induced landslide risk in China (grant no. 41661134010), the Young Scientists Fund of the National Natural Science Foundation of China (grant no. 41302241), the Fund for Creative Research Groups of China (grant no. 41521002), The authors thank Mauri McSaveney for his constructive comments and editing the English the paper. Edited by: T. Glade Reviewed by: T. W. J. van Asch, H.-B. Havenith, and M. Mergili