1 Introduction

The mass movement is a significant phenomenon of mountainous areas that involves movement of earth masses from small rockfalls to big rock avalanches and very often produces catastrophic affects. The uncertainty of the frequency and magnitude of the mass movement events has strong impact on human society in terms of life losses and infrastructure damages (Dorren 2003; Holm and Jakob 2009). Unfortunately, the rockfall events are often ignored by the local population due to their relatively low magnitude as compared to the other mass movement process (Holm and Jakob 2009). However, they still pose significant hazard to lives and blockage of the roads. The reason for this impact is primarily human related that includes settlement of human population in mountainous areas at very steep slopes. On the other hand, the major damages occur due to the mass movement volume and long distance travelled from the source point (Corominas 1996). A common problem is to assess the factors and impact of mass movement volume on travel distance.

Previous investigations have analyzed mass movement events and travel distance, using two empirical models: the “Fahrböschung angle” (Heim 1932; Shreve 1968; Scheidegger 1973; Hsü 1975; Corominas 1996; Erismann and Abele 2001) and the “shadow angle” (Lied 1977; Hungr and Evans 1988; Evans and Hungr 1993). Different theories have been proposed to explain the phenomena of long travel distance for the large mass movements (Van Gassen and Cruden 1989; Melosh 1986; Nicoletti and Sorriso-Valvo 1991; Davies et al. 1999). The volume dependence of the Fahrböschung angle has been questioned by many authors for large- (Hsü 1975; Hungr 1990) and small-scale mass movements (Hunter and Fell 2003). There is a lack of agreement between researchers about findings of volume and travel distance relationships. Consequently, different conclusions have been derived from these simple relations.

In Pakistan, like other developing countries, the risk posed by the mass movement before the earthquake of October 8, 2005, was underestimated, and no scientific investigation was carried out. As a result, the people and government had to pay high price in term of human life, property, relocation and reconstruction of settlements. For instance, the Muzaffarabad (the capital of Pakistan-administered Kashmir) and many other important towns and valleys (Jhelum and Neelum valleys) were left isolated due to the disruption of the communication links. Thousands of mass movements were triggered during this earthquake in Muzaffarabad and surrounding areas (Basharat et al. 2014). These were mainly rockfalls, debris falls, rock slides and rock avalanches, ranging in volumes from few hundred cubic meters to hundreds of million cubic meters. The number of fatalities associated directly and indirectly with these mass movements was about 26,500 people (Petley et al. 2006).

Large-volume events with long travel distances occurring during the earthquake were rare but potentially highly destructive. For example, the Hattian Bala rock avalanche having volume more than hundreds of million cubic meters destroyed everything in its travel path through burial and resulted in 595 casualties (Basharat et al. 2012). In addition, this catastrophic event blocked the way of Karli and Tung streams, creating two landslide dams. In contrast, small-volume rockfall events were the most common phenomena during this earthquake (Owen et al. 2008). However, the rockfall events have caused less fatality as compared to large-volume events.

After the devastating effect produced by the mass movements during the earthquake, the efforts are being made to identify and characterize the mass movement event to improve the knowledge about the mass movements through a systematic collection of field data. The information gathered from field data was used to describe the characteristics and behavior of mass movements such as volume, Fahrböschung angle, fall height, travel path and surface area.

The present study describes the empirical analysis for statistically significant set of data derived from geometric parameters, in Muzaffarabad, Jhelum and Neelum valleys (Fig. 1). The data were analyzed and presented in the form of empirical relationship among the volume, Fahrböschung angle, fall height, travel path and surface area. The consistency of our data was tested by comparing it with data from different parts of the world, published in earlier studies. The analysis indicates the differences in the observed run-out distance and mobility among different types of mass movements. The results may be used to assess and mitigate the risk posed by the mass movements in different part of the world with similar conditions.

Fig. 1
figure 1

Location of the mass movement events, identified for empirical analysis of geometrical parameters of mass movements, triggered by the 2005 Kashmir earthquake in the vicinity of Jhelum Valley, Neelum Valley and Muzaffarabad, in the Northeast Himalayas of Pakistan

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1.1 Geographical and geological setting

The 2005 Kashmir earthquake affected area is characterized by young mountains, active tectonics, fragile lithology and steep topography. The area is rugged terrain and mountainous with many old mass movements. The ridges and valleys generally trend southeast–northwest parallel to the regional geological structures of the area. Generally, the relief of the area is high in the northeastern part as compared to southern part (Fig. 1). The weathering of rock depends upon the topography, climatic conditions, geology, structure, vegetation and slopes of the area. Heavy rainfall, high relief, steep slopes and highly sheared and fractured rock units made mass wasting an important degradation process. The degraded talus accumulated on the low foot hills.

Structurally, the region encloses the Hazara-Kashmir syntaxis (HKS). The HKS is a NNW trending regional scale antiform structure that folds the lesser- and sub-Himalayas (Fig. 2). Except for the Himalayan Frontal Thrust, all the major thrusts including Main Boundary Thrust (MBT) and Panjal Thrust (PT) are refolded by this structure. Unlike the usual anticlines, where the younger rocks lie in the limb and older rocks comprises successively in the core, the HKS exposes the youngest rocks in the core and successively older rocks in the limbs (Fig. 2). This explains crustal stacking due to thrusting prior to the formation of the Hazara-Kashmir syntaxial structure (Calkins et al. 1975). Thus, the limbs of the HKS comprise folded PT and MBT. In the HKS, the MBT, PT, Jhelum Fault and Muzaffarabad Fault are the important active tectonic features (Fig. 2; Wadia 1931; Armbruster et al. 1978; Baig and Lawrence 1987; Baig 2006).

Fig. 2
figure 2

Geological map of Hazara-Kashmir syntaxis (compiled and modified after Wadia 1931; Calkins et al. 1975; Greco 1989; Baig and Lawrence 1987; Hussain et al. 2004)

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The regional geology of the earthquake affected area shows sedimentary, metasedimentary, metavolcanics and metaigneous rock units. These lithostratigraphic units have different geological control on the mass movements of the area. The Precambrian to Tertiary rocks are exposed in the HKS around Muzaffarabad, Jhelum and Neelum valleys areas. The rock sequence includes the Precambrian Hazara and Tanol Formations, the Cambrian Muzaffarabad Formation and Mansehra Granite, the Carboniferous-Triassic Panjal Formation, the Paleocene–Eocene sequence, the Early Miocene Murree Formation, the Late Miocene Kamlial Formation and Quaternary sediments (Fig. 2; Calkins et al. 1975; Greco 1989; Hussain et al. 2004).

The geological units of tertiary sediments comprise of a wide variety of rocks, including alternating nodular limestone, calcareous and carbonaceous shale, sandstone, siltstone, marl, claystone and local conglomerates. The Precambrian Tanol Formation consists of chlorite quartz mica schist, chlorite, biotite quartzofeldspathic schist, metaquartzite, garnet mica schist, graphitic schist and local marble (Shah 1977). The sequence is intruded by early Paleozoic granite gneisses. The rock sequence is multiply deformed and metamorphosed (Greco 1989; Khan 1994). These rocks are jointed and fractured. The Precambrian rocks of Hazara Formation comprise of fractured and cleaved slate, phyllite and shale with minor limestone.

The Carboniferous-Triassic Panjal Formation includes basic metavolcanics, quartzofeldspathic schist and graphitic schist (Khan 1994). The sequence along MBT is highly fractured, jointed and sheared. These lithologies, brittle structures and steep slopes controlled the mass movements locally along MBT during earthquake ground shaking. Most of the mass movements occurred in interbedded sandstone, siltstone, shale and claystone of Murree Formation and highly fractured carbonate rocks of Cambrian Muzaffarabad Formation, which are well known for their susceptibility to mass movement occurrences in many part of the world (;Khazai and Sitar 2003; Chigira et al. 2010). The dolomites of Muzaffarabad Formation along fault are deformed into joints, fractures, breccia and gouge. The sedimentary rocks of sandstone, mudstone, siltstone, shale and claystone are most susceptible to produce shallow mass movements. These are weakly cemented and consequently broken by fractures and joints.

2 Data source and methodology

Systematic field investigations were carried out to identify mass movement events. A total of 103 mass movement events were identified, and detailed surveys were carried out to gather field data for analysis (Fig. 1). These mass movements were mapped during field investigations in November 2010–2011. A mass movement inventory, containing the geometric parameters including volume, length, height, surface area, deposit area and Fahrböschung angle, was prepared for statistical analysis (Table 1). This inventory also indicates the locations and types of 103 mass movement events (Fig. 3).

Table 1 Geometrical data of 103 mass movement events triggered by the 2005 Kashmir earthquake in the vicinity of Jhelum Valley, Neelum Valley and Muzaffarabad in the Northeast Himalayas of Pakistan
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Fig. 3
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Photographs show the types, locations and parameters of mass movement (a) deep-seated large rockfall (Hattian Bala), (b) Dunga Kuss rockfall (road in Neelum Valley), (c) small rockfall (Panjgran, Neelum Valley)

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The longitudinal profiles that describe the geometrical parameters of each mass movement event were prepared. Length (travel distance) and height (fall height) were measured from the longitudinal profiles. In addition, Fahrböschung angle was measured directly in the field and later on verified from the longitudinal profiles. ArcGIS 9.3 software was used to measure the surface area of polygons that represent the mass movement and include source, path and deposit. In order to calculate the volume of mass movements, the average thickness was estimated for the deposit volume. The best way to estimate mass movement volume is analysis of change in elevation using pre- and post-earthquake digital elevation models (DEMs; Kerle 2002; Martha et al. 2010). However, due to the scarcity of pre- and post-earthquake DEMs, our measurement of volume is mainly based on the field assessment (e.g., Legros 2002; Devoli et al. 2009). For this study, the volumes of the mass movements were estimated by multiplying the deposit area with an estimated average thickness (estimated on the basis of field observation). In some cases, the volumes of the mass movement events that occurred along the Jhelum River and the Neelum River were smaller than the actual rock mass displaced from the scarp. This difference in volume is attributed to erosion of the deposited material by the river, especially during flooding. However, these differences are more likely to have minor effect on the validity and reliability of the data. For mass movements with small volumes, it is sometimes difficult to estimate the accurate volume due to hindrances like dense vegetation and subsequent transportation of the material. In these cases, the minimum estimate for the volume was taken into account (e.g., Legros 2002).

3 Types of investigated mass movements

A classification based on a volumetric nomenclature (Varnes 1978; Fell 1994) for rockfall was followed to describe all types of mass movement data, collected during field surveys, because our primary concern of rockfall classification involves travel distance and Fahrböschung angle to explain the manner of progression of movement. The present rockfall size classification based on a volumetric nomenclature was used for the empirical analysis (Table 2).

Table 2 Mass movement classification based on a volumetric nomenclature (modified after Varnes 1978; Fell 1994)
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The term rockfall is characterized by the failure of relatively steep rock slopes or cliffs along a surface where little or no shear displacement takes place (Varnes 1978). In general, rockfalls involve a direct downward movement and large to small detachments (102–108 m3), although there is no well-defined volume limit (Evans and Hungr 1993). The low-magnitude rockfall (<104 m3) termed as small rockfall or debris fall (Varnes 1978) is distinguished from a medium rockfall (104–106 m3). Subsequently, medium rockfall is distinguished from large rockfall (>106 m3). Large rockfalls (>106 m3) are termed as mountain fall or sturzstrom (Heim 1932) or rock avalanche (Varnes 1978).

4 Geometrical parameters considered for empirical analysis

In this study, the geometrical parameters considered for the empirical analysis are related to the mass movement failure as shown in Fig. 4. One empirical parameter is the Fahrböschung angle (Heim 1932) or travel angle. The Fahrböschung is the angle between the horizontal and line connecting from the highest point of the mass movement scarp to the distal margin of the displaced mass. Various scientists have referred to this line by other names such as: angle of the equivalent coefficient of friction (Shreve 1968), travel angle (Hungr 1990; Cruden and Varnes 1996), reach angle (Corominas 1996) and travel distance angle (Hunter and Fell 2003).

Fig. 4
figure 4

Sketch of mass movement source point, falling mass and deposit. Definitions of parameters used in the present analysis are explained in text. Sketch is modified from Evans and Hungr (1993) and Copons et al. (2009)

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The term L refers to the travel distance or corresponding horizontal distance which is the horizontal projection of the line connected from the source point of the mass movement and the farthest block. The term H is the fall height or elevation difference between the highest point and the lowest point of the mass movement.

5 Data analysis

5.1 Relationship between volume and Fahrböschung angle for mass movements

The plot of the Fahrböschung angle versus mass movement volume in Fig. 5 shows inverse correlation between the tangent of the Fahrböschung values and mass movement volumes. A regression equation has been obtained, Log tanα = −0.066 log V − 0.210, with a squared correlation (R 2 = 0.29), which estimates the maximum travel distance of mass movement events from their volume. The relationship between mass movement volume and Fahrböschung angle suggests that the values of the Fahrböschung angle decrease with the increase in volume of the mass movement events. However, in some cases, small-volume mass movements have Fahrböschung angles as low as the large-volume mass movements (Table 1; Fig. 5). The non-uniformity of mass movements is apparent in scattered diagram where data points corresponding to landslide volume and travelled distance are widely dispersed along regression line (Fig. 5).

Fig. 5
figure 5

Relationship between log tangent of the Fahrböschung and log mass movement volume for all investigated mass movements triggered by the 2005 Kashmir earthquake

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5.2 Relationship between the volume and Fahrböschung angle for individual groups of mass movements

To understand the effect of volume on Fahrböschung angle for each individual group of rockfalls, the data set of 103 mass movement events was split into large, medium and small rockfalls based on the volume of the mass movements (Varnes 1978; Fell 1994; Table 2).

The tangent of the Fahrböschung values was plotted against the volumes of each individual group of large, medium and small rockfalls in a log–log plot (Fig. 6). The coefficient of regression analysis for each individual group (large, medium and small) and their statistical information are presented in Table 3. The analysis shows the linear trend and an existing minor correlation between the tangent of the Fahrböschung values and the volume of the group of all mass movements (Fig. 6; Table 3). For the analysis of the large rockfall group, unfortunately, only four large rockfalls were available which posed limitation in statistical analysis of the group of rockfalls. To analyze the medium rockfall group, 16 rockfalls having volume 104–106 m3 were taken into account for analysis. The analysis shows that there is a significant and a good correlation between the volume and Fahrböschung angle values (Table 3). On the other hand, 83 small rockfalls with smallest volumes (<1 × 104) were considered for the analysis of the small rockfall group. The result indicates that there is a statistically significant but minor correlation between the tangent of the Fahrböschung angle and the small rockfalls (Table 3). The analyses show that mobility increases with increasing volume of mass movement.

Fig. 6
figure 6

Relationship between tangent of the Fahrböschung and volume for large, medium and small rockfalls

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Table 3 Results of the linear regression analysis of tanα versus the mass movement volume of each individual group
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5.3 Relationship between the height of fall (H) and the travel distance (L)

The analysis of 16 medium rockfalls and 83 small rockfalls was performed to determine the relationship between height of fall and travel distance (Tables 1 and 2). The values of height of fall (H) versus travel distance (L) were plotted on a log–log plot (Figs. 7, 8). For the data set of 16 medium rockfall events (Fig. 7), the standard least square regression analysis gives the empirical relationship: Log L = 1.138 log H − 0.219, with squared correlation R 2 = 0.86. For the data set of 83 small rockfall events (Fig. 8), a best fit regression equation is obtained: Log L = 0.953 log H + 0.195, with squared correlation R 2 = 0.83.

Fig. 7
figure 7

Relationship between the log height of the fall (H) and the log travel distance (L) for all 16 types of medium rockfalls triggered by the 2005 Kashmir earthquake

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Fig. 8
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Relationship between the log height of fall (H) and the log travel distance (L) for all 83 types of small rockfalls triggered by the 2005 Kashmir earthquake

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An analysis of the data shows that the travel distance is proportional to the height of fall for both types (medium rockfalls and small rockfalls) of mass movements (Figs. 7, 8). This indicates that there is a significant positive relationship and linear trend between the height of the fall and travel distance for medium rockfalls (R 2 = 0.86) and small rockfalls (R 2 = 0.83). In addition, the fall height does not affect the Fahrböschung angle values in this analysis because different values of the tangent of the Fahrböschung were found for similar fall height (Table 4).

Table 4 Geometrical data of similar height of fall with different Fahrböschung angle
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5.4 Relationship between surface area and volume of mass movements

In general, the larger surface area of a mass movement is likely to have larger volume. An analysis of 103 mass movement events was performed to determine the relationship between the volume and surface area. Figure 9 shows the values of the different surface areas and their respective volumes plotted on a log–log graph. The best fit equation obtained from the least square regression analysis is: Log A = 0.584 log V + 1.0537, with squared correlation R 2 = 0.79.

Fig. 9
figure 9

Relationship between log surface area and log mass movement volume for all types of mass movements triggered by the 2005 Kashmir earthquake

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An analysis of the data reveals that there is statistically significant positive correlation (R 2 = 0.79) between the surface area and the volume of the mass movements. This indicates that the volume of the mass movements is directly proportional to the surface area.

5.5 Relationship between volume and Fahrböschung angle for degree of confinement

The term confined was used for those failure surfaces that travel deep under the original ground and deposited the material at foot in the form of bulging. Conversely, the term unconfined was used when the material deposited below the valley bottom without apparent foot bulging. In order to determine the effect of the degree of confinement on mass movement travel distance, travel path was divided into unconfined, partly confined and confined travel paths. The Fahrböschung angle values versus volume of unconfined, partly confined and confined mass movements were plotted on log–log plot (Fig. 10). The analysis for each degree of confinement (unconfined, partly confined and confined) and their statistical information are presented in Table 5. The results indicate that no correlation was found for confined travel path and minor correlation was found for the unconfined and partly confined travel paths.

Fig. 10
figure 10

Relationship between tangent of the Fahrböschung and volume for degree of confinement

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Table 5 Results of the linear regression analysis of tanα versus volume for unconfined, partly confined and confined mass movements
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6 Comparison between present and published data

In order to understand the consistency of the 2005 Kashmir earthquake data set with those published in earlier studies in the different parts of the world. The data published in several references were collected and plotted on a log–log graph (Fig. 11). The analysis shows the relationship between the Fahrböschung angle and volume of the mass movements for rock avalanches and rockfalls from the previously published data (Scheidegger 1973; Erismann and Abele 2001; Copons et al. 2009) and the 2005 Kashmir earthquake data set. Despite the diversity of the data set and the differing mechanisms, the results showed a decreasing tendency of Fahrböschung angle (tanα) with increasing mass movement volume. This indicates that the volume of the mass movement has a strong effect on travel distance (Fig. 11).

Fig. 11
figure 11

Relationship between log tangent of the Fahrböschung and log mass movement volume. Comparison between the data of Scheidegger (1973), Erismann and Abele (2001), Copons et al. (2009) and the 2005 Kashmir earthquake data set

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As shown in Fig. 11, most of the scattered data near the left top of the plot belong to the small rockfalls of Copons et al. (2009). The representative points for large rock avalanches (Scheidegger 1973; Erismann and Abele 2001) are concentrated in the lower right part of the plot. Due to larger volumes, these rock avalanches possess low tanα values which significantly reduce scatter in the plot. The 2005 Kashmir earthquake data set involves mass movements with different volumes from small rockfalls to large rockfalls. The points are concentrated in the middle of the plot. This means that mass movements with smaller volumes are on the top left area of the plot and the mass movements with high volumes are in the lower right part of the plot.

The 2005 Kashmir earthquake data set shows the higher values of the Fahrböschung angle similar to Copons et al.’s (2009) data set, while the data set of Scheidegger (1973) and Erismann and Abele (2001) shows the lower values of the Fahrböschung angle. This is due to the smaller volume of the rockfalls of the 2005 Kashmir earthquake data set which have a different dynamic motion than larger rockfalls (>106 m3), as already accepted by many researchers (Nicoletti and Sorriso-Valvo 1991; Corominas 1996; Erismann and Abele 2001).

The analysis of the 2005 Kashmir earthquake data set reveals that there is weak or minor correlation (R 2 = 29) between volume of mass movement and Fahrböschung angle (tanα), while those plotted by Scheidegger (1973) and Copons et al. (2009) have coefficients of correlation (R 2) ranging from 0.73 to 0.49. However, there is not much difference of correlation (R 2 = 0.35) for the data set of Erismann and Abele (2001) and for large scale mass movements. Based on the observation of the different data sets, it can be concluded that the empirical relationship suggested in earlier studies is mainly consistent with the data set of the 2005 Kashmir earthquake. However, the 2005 Kashmir earthquake data set displays higher values of Fahrböschung angle as compared to the previous published data except Copons et al. (2009) data set. The higher values of Fahrböschung angle in the data set belong to the smaller volume of the rockfalls. Moreover, these rockfalls occurred mainly nearby rivers, streams, roads and on high-altitude areas.

7 Conclusions

This study presents empirical relationships for better understanding of mass movement behavior in the vicinity of the Muzaffarabad and surrounding areas, in the Northeast Himalayas of Pakistan. Based on the field data, different types of mass movements with similar mechanisms of failures were considered for this analysis. The relationship between different parameters including volume, Fahrböschung angle, fall height, surface area, travel path and mass movement travel distance was analyzed. The empirical analysis showed that the Fahrböschung angle depends to some extent on the volume. Furthermore, minor correlation was found between the Fahrböschung angle and volumes of small rockfalls. A linear trend with strong correlation exists between height of fall and travel distance for medium rockfalls (R 2 = 0.86) and small rockfalls (R 2 = 0.83). For this data set, height of fall does not affect the Fahrböschung angle values, because for similar height of fall, different values of the Fahrböschung angle were found. Moreover, for the analysis of degree of confinement, minor correlation was found for unconfined and partly confined travel paths, and no correlation was found for confined travel path. The empirical results of the 2005 Kashmir earthquake data set are mainly consistent with the previously published data from other parts of the world.