1 Introduction

The Himalayan mountain belt comprises seismically active mountains having many unstable slopes due to adverse geological, meteorological and geotechnical conditions (Vishal et al. 2015a; Pradhan et al. 2015). The population residing in the Himalayan region are under constant threat of landslides. Increased anthropogenic activities in recent times appear to be an additional factor leading to instability in the Himalayan region. The disaster following the Gorkha earthquake of Nepal Himalaya in 2015 and that of the Kedarnath tragedy of Uttarakhand Himalaya in 2013 have reminded the need for implementation of risk-mitigation strategies and techniques in the hazard-prone regions of the Himalaya. The rockfall studies as well as slope stability investigations have earlier been carried out using different rating, numerical simulations and analysis techniques (Ahmad et al. 2013; Ansari et al. 2014; Singh et al. 2013; Vishal et al. 2010; Gupte et al. 2013; Trivedi et al. 2012). When a rockmass detaches itself from a slope face, it falls down the slope with flight trajectories that are hazardous. Rockfalls occur frequently in steep mountainous regions, quarries and mines and are much less studied and analysed than landslides. Rockfalls are generally initiated by meteorological conditions majorly rainfall, biological factors such as trees and animals and vibrations due to earthquake and blasting (Ahmad et al. 2013). Therefore, it is important to check and arrest rockfall in populated areas, especially along road cut slopes that experience dynamic loading. To minimize the effects, slope failure analysis and stabilization of slopes require in-depth understanding of the processes that govern the stability behaviour of the slopes (Monjezi and Singh 2000; Sarkar et al. 2012; Verma and Singh 2010; Singh et al. 2008; Pradhan et al. 2011, 2014; Vishal et al. 2015b).

For rockfall studies, a mathematical model coded for simulation applications and called as CADMA was designed by Azzoni et al. (1995) to predict fall trajectories and other relevant parameters (kinetic energy, bounce height, run-out distance of falling blocks). This model relies on the rigid body mechanics and applied mathematics which analyse rockfall in two-dimensional space. In the present investigation, the trajectories and kinetic energies of falling rockmass were chiefly analysed at a slope scale by simulator RocFall 4.0 by RocScience. After detachment, the key factors that dominate the flight of the rockmass are geometry and material of the slope. These factors outline the motion of the rockfall which may be classified into four types—free fall, sliding, rolling and bouncing (Ritchie 1963). According to Ritchie (1963), if the slope face is vertical or near-vertical, an easy free fall occurs (if the gradient of slope below potential falling rocks exceeds 76°). If the mean gradient decreases, the falling rock blocks collide with slope surface and cause bouncing of detached rock blocks. If the slope material is soil or talus cones, then straightforward rolling or slipping of the rockmass will be more pronounced. If the slope consists of hard rock terrain, bouncing of rockmass can be observed. Further, if the mean slope gradient is less than approximately 45°, bouncing of the rocks will gradually transform to rolling. The key property of the slope which gives rise to the present differentiation among the type of motion of the rock blocks is the restitution of the slope material. Bedrock surface has higher restitution values, whereas soil or talus cones have lower values. Rockfall mainly occurs when the downward forces acting on the rockmass changes, and that change may occur due to change in slope face geometry or morphology caused by natural or anthropogenic factors (Ahmad et al. 2013). Ansari et al. (2013) proposed the Rockfall Hazard Rating System for India (RHRSI) as a modified scheme of rockfall rating for the Indian subcontinent. In this study, the Colorado Rockfall Hazard Rating System (CRHRS) and the Rockfall Hazard Rating System for India (RHRSI) were applied and the results were correlated. The results from simulation estimating the run-out distances of the detached blocks were analysed to predict risk.

2 An overview of rockfall investigations

Roads through the mountainous regions are often hit by rockfall hazards that can cause injuries and even fatalities (Ferlisi et al. 2012). During rockfall, the rocks get detached from the cliff face and fall freely under the influence of gravity (Youssef et al. 2014). Rockfall susceptibility could be defined as a quantitative and/or qualitative assessment of the category, volume and spatial distribution of rockfall which may potentially occur in an area (Fell et al. 2008). To assess rockfall hazards, different approaches including heuristic, deterministic and statistical techniques have been applied (Dai and Lee 2002; Guzzetti et al. 2006). Rockfall hazard studies have been carried out for protection of historic sites and monuments (Topal et al. 2007; Wang et al. 2012), effects on forests (Dorren et al. 2006; Perret et al. 2004) and along road cut slopes (Budetta 2004; Ansari et al. 2016; Palma et al. 2012; Alejano et al. 2007).

Rockfall involves detachment of rock fragments and their free fall, subsequent rolling, sliding, bouncing and deposition near the foot of the slopes (Hutchinson 1988; Varnes 1978). Rapp (1960) and Whalley (1984) have classified the rockfall on the basis of size or volume. Rockfall may occur on natural or excavated slopes and the sizes of blocks may range from small pebbles to big boulders of few metres. The degree of rockfall depends upon the type of bedrock, and physical and chemical weathering (Day 1997; Schumm and Chorley 1964). Slope morphometry and potential falling rock characteristics are the most important factors determining whether a rock could fall (Dorren 2003). Frost and thaw process is one of the well-known causative factors of rockfall initiation (Coutard and Francou 1989; Grove 1972; Matsuoka and Sakai 1999; McCarroll et al. 1998). Wieczorek et al. (1995, 2000) concluded that the factors like earthquakes, rain storms, rapid snow melt, freezing and thawing cycles of water in joints and root penetration are very common in facilitating rockfall and rockslides. Anthropogenic factors also contribute in slope instability in hard rocks, although it is relatively minor as compared to the geological and other natural factors (Selby 1982). In general, coupling of topographical, geological, climatological, time and anthropogenic factors controls the occurrence and intensity of rockfall in any area.

The detached rock blocks can follow different modes of motion, viz. freefall, bouncing or rolling depending on the mean slope gradient. During free fall, the movement can be translation of centre of rock or rotation of block around its centre (Azzoni et al. 1995). The velocity of the free falling rock blocks is affected by air friction, but it has less significant effect on the motion (Bozzolo and Pamini 1986). Bouncing of falling blocks occurs as the mean slope gradient decreases, when free falling rock collides with the surface and the blocks, particularly the competent rocks, tend to break just after the first bounce (Bozzolo and Pamini 1986). As the total kinetic energy is directly proportional to the mass of the object, smaller blocks have lower kinetic energy. So, obstacles in the path such as plantation can retain smaller blocks more easily (Dorren 2003). On the basis of some quantitative studies, Jahn (1988) suggested that forest cover in rockfall-prone areas reduces probable rockfall events by three to ten times compared to slope having no forest cover. Zinggeler et al. (1991) determined the importance of trees in stopping falling rocks. They suggested that topography is important and the falling rocks loose energy by colliding with the stems of the trees. Several rockfall studies on varying geological and geomorphological conditions have been conducted in past (Caine 1976; Douglas 1980; Fahey and Lefebure 1988; Matsuoka 1990; Nyberg 1991; Rapp 1960; Sass 1998; Sommerhoff 1977). From the last couple of years, considerable progress has been made in estimating the run-out tracks of rockfall of known magnitude (Dorren 2003). However, the mechanism that determines temporal and spatial occurrence of small rockfall is not well known and still limited particularly for locations where exposure of rockfall hazard is inevitable (Krautblatter and Moser 2009).

The concept of rockfall hazard rating was introduced for the Canadian pacific railways by Brawner and Wyllie (1976). The first state wide exponential rating system for rockfall hazard rating was published by Wyllie (1987) which was later modified by Oregon Department of Transportation (DOT) and classified on the basis of the parameters: slope height, ditch catchment, average vehicle risk, decision site distance, roadway width, geological characteristics controlling rockfall, block size, quantity of rockfall, climatic conditions, role of water and rockfall history. Later the scores of these parameters were interpolated (Pierson et al. 1990; Pierson and Van Vickle 1993). Colorado’s RHRS was modified from the original Oregon DOT’s RHRS (Andrew 1994). Over time many modifications have been made by incorporating more precise, specific nature from several categories in CDOT’s current RHRS (Santi et al. 2009). Colorado RHRS includes factors such as slope height, segment length, slope inclination, slope continuity, geological factors influencing rockfall, block size, climatic conditions rockfall history and the number of accidents caused due to rockfall. CDOT again modified the rating system by including the ditch catchment, decision site distance and average daily traffic. Many RHRS systems have been developed with time by considering different parameters and variable scores: Ohio RHRS, Mussouri’s RHRS, Tennessee’s RHRS, New York’s RHRS, Idaho’s RHRS and RHRS for Indian rockmass. The differences in parameters and scores are due to applicability to the local conditions. In the Indian context, the studies on rockfall are limited. More so in the Uttarakhand Himalaya, the rockfall phenomenon is recurrent as much as the landslides, but is understood only in little details. This study was conducted by focusing on problems of rockfall in morpho-dynamic Uttarakhand Himalayas using rockfall hazard rating and simulation technique.

3 Area of investigation

The study region is located in Uttarakhand, India, along National Highway (NH)-58 between Rishikesh and Devprayag, near the village Saknidhar. The coordinates of the village are N 30°5′9.5″ and E 78°32′52.1″. The roadways in this region allow movement of pilgrims to the important Hindu pilgrimage circuit ‘Char Dham’. The high density movement season is late spring to summers, during March to June that leads to heavy vehicular and pedestrian traffic. The road also leads to the Mana Pass that is close to the Indo-Tibetan border. A major part of the route runs along the hill cut slopes and several zones of rockfall and large scale slope failures may be encountered. The rockfall-prone slopes are on the upstream to Saknidhar and are comprised of jointed sandstone of Chakrata formation, having many blocks on slope facet that can cause damage to downstream side locality (Fig. 1). The slopes are very steep and have multiple cracks and fractures traversing through them. Nearly half of the studied slope was made of weathered bedrock. The bedrock is also massively jointed. This 5–6-km zone is marked as rockfall- and landslide-prone region (Figs. 2, 3). Some previous studies were conducted for slope mass rating and kinematic analysis by Siddique et al. (2015) along NH-58 at Rishikesh.

Fig. 1
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Satellite imagery of study area just upstream side of Saknidhar township

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Fig. 2
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An overview of the cliffs, hills and roads in Uttarakhand along NH-58

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Fig. 3
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Investigated slope along NH-58, near Saknidhar, Uttarakhand

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4 Methodology

While landslide hazards have been studied well in the past, the focus on rockfall has not been as much and there exists the need to apply modern techniques to understand rockfall in the mountainous regions. Over the past two decades, several 2D and 3D programs such as CRSP by Pfeiffer and Bowen (1989) and Pfeiffer et al. (1991); RocFall by Stevens (1998); Mobyrock by Paronuzzi and Artini (1999); Eboul by Descoeudres and Zimmermann (1987) were developed using different rockfall models (Azzoni et al. 1995; Bozzolo et al. 1988; Hungr and Evans 1988; Spang and Rautenstrauch 1988). RocFall 4.0 has been designed to develop 2D slopes for studying rockfall phenomenon and its alternative attributes. Rockfall trajectories can be simulated using rigorous and lumped model. Rigorous models are given by rolling the rocks deliberately down a given slope, and the rockfall trajectory can be established. The lump model simulates rockfall trajectories in which different types of motion of a rock can be traced throughout its fall. The coefficient of restitution can be estimated from field tests (Evans and Hungr 1993; Robotham et al. 1995), by back analysis (Evans and Hungr 1993; Fornaro et al. 1990; Pfeiffer and Bowen 1989; Kobayashi et al. 1990; Paronuzzi 1989; Descoeudres and Zimmermann 1987; Budetta and Santo 1994) or by theoretical estimation (Kobayashi et al. 1990; Bozzolo and Pamini 1986). The motion of rockmass depends on the slope face, i.e. vertical or nearly vertical and on slope material such as soil, vegetation, talus cones or hard bedrock. Further, optimization of slope by numerical methods provides better understanding of slope stability as well as rockfall pattern.

In this study, detailed field work was performed on NH-58 and based on the field inputs, the two rockfall hazard rating systems were implemented and the results analysed. Due to the differences in the weightage of parameters in each system, different rating scores were achieved (discussed in Sect. 5). During field work, the rock samples were collected and transported to the laboratory. The samples were tested to obtain the required geomechanical characteristics. The parameters were together used to develop efficient numerical models using RocFall 4.0. For simplifying the study, the slope roughness was reduced during simulation. Further, certain parameters like the shape of the blocks, mechanical characteristics of the overall slope and local slope angles at impacts are not uniquely defined and can assume random values, in accordance with Azzoni et al. (1995). Suitably, the statistical analysis was performed by taking the obtained values. The numerical study was extended to optimize various parameters such as slope angle, ditch angle and ditch width.

5 Results and discussions

5.1 Rockfall hazard rating

Rockfall hazard rating schemes provide qualitative assessment of rockfall hazards which can be applied during preliminary stages of investigations. Major factors considered in RHRS are slope, climate, geology, traffic and rockfall frequency which includes several internal parameters and scores are assigned to each. Different rockfall schemes have been developed under different conditions. An attempt was made to classify the road cut slopes using two different rating schemes and the results were co-related. Rockfall Hazard Rating System for Indian Rockmass and modified Colorado Rockfall Hazard Rating System (CRHRS) were employed, and the results bear good co-relation. Such rating systems provide good initial assessment in rockfall studies. They essentially are qualitative methods for prioritizing the rockfall-prone zones in a given area to address with remedial measures.

The RHRSI method is a modification of Pierson et al. (2005) by Ansari et al. (2013) and includes five major classes (28 parameters). The algebraic sum of score for each parameter gives final hazard rating which enables to determine the hazard potential for rockfall to occur. Each parameter comprises a set of sub-parameters based on the vulnerability of slopes, triggering mechanisms and causes, and frequency of rockfall events to happen. In case of each parameter, the rating criteria points increase exponentially from 3 to 81 points. Once the scores are computed, a comparative chart is drawn and the slopes with maximum total scores are estimated to pose maximum risk and addressed on a priority basis. While the major factors in both classifications systems are similar, the weightage are not of the same values. While in case of RHRSI, vegetation contributes 50 points to the hazard score, it is a mere 27 in case of CRHRS. Similarly, the ditch catchment scores are 60 and 24 in case of RHRSI and CRHRS, respectively, leading to large variations in the cumulative score for the slope factor. However, some parameters provide comparable or same scores too, for instance, the annual precipitation provided 94 and 98 points to the total score in RHRSI and CRHRS, respectively. The cumulative scores were obtained as 539 and 466 in RHRSI and CRHRS, respectively. The score in each category and the final computed scores are given in Tables 1 and 2. The slopes have high values as indicated by both the methods, and it is understood that they need attention to prevent any damage due to rockfall. It is also interesting to note that both the systems do not incorporate or recommend the scores for involvement of mitigation conditions or methods.

Table 1 Rockfall hazard rating system for Indian rockmass
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Table 2 Modified Colorado rockfall hazard rating system
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The results obtained from both the methods were correlated (Fig. 4). Due to variations in slope parameters, small differences exist in the points while climate, geology and traffic scores are almost same due to similar ratings and weightage in both classifications. However, the total score from either scheme is very high indicating that the slope under investigation is under critical situation and needs proper treatment to reduce fatalities and obstruction in traffic along NH-58, Saknidhar.

Fig. 4
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A comparison between the scores of Rockfall Hazard Rating System for Indian rockmass and modified rockfall hazard rating system

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5.2 Numerical simulation

Numerical models using RocFall 4.0 were developed for one of the slopes along which recurrent failures are reported, as well as observed during the fieldwork. The slope geometry was constructed to the best possible approximation to represent the road cut slope. The overall geometry of the slope was created by including the benches on the slope which guide the pattern of rockfall trajectories during simulation (Fig. 5a). Simulations were conducted without considering any barrier in front of the slope as per the field conditions. The slope height, width of ditch and width of road were estimated as 10.02, 2.28 and 7.1 m, respectively (Table 3). The gradient of the cliff was steep—upper part comprised of massively jointed sandstone while the outer lower part of the slope was covered by weathered debris. Due to variable slope angles along the cliff, different types of rockfall motions were observed. The coefficients of normal and tangential restitution for the field lithology were taken as 0.35 and 0.85, respectively. The rock material making the slope was different; thus, the portion of the slope below fresh sandstone was categorized as weathered rockmass, and consequently, the coefficients of normal and tangential restitution were taken as 0.47 and 0.55.

Fig. 5
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a Geometry of slope under investigation; b Rockfall trajectory of 100 blocks of 10 kg falling from top of the slope

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Table 3 Field data collected from the area of investigation
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The rockfall trajectories depend on many factors like slope geometry, friction, roughness of slope face, density and restitution of rock. As observed in this case, as the initial slope from the top is steep, thus, the detached rock block experiences free fall. It bounces on all benches after detachment. The middle part of the slope is weathered rock with very less tangential restitution that inhibits bouncing and the rock blocks undergo rolling or sliding motion. On the lower bench, the blocks bounce up to greater heights, some fall into the valley while some fall on the road. Through simulation, the rockfall trajectories were obtained for 10-kg falling blocks through 100 simulations (Fig. 5b).

The results show that the bounce height of rock blocks from the surface of the slope is high at the initial trajectory zone with a value as high as 1.2 m (Fig. 6a). However, the maximum kinetic energy of nearly 380 J was observed at approximately the middle level of the slope (Fig. 6b). This is due to the high velocity of free falling blocks from the head of the cliff. Another peak bounce height was observed at around 8 m and this corresponds to the impact of high kinetic energy of the moving blocks. The translational velocity and the total kinetic energy follows similar pattern on falling rock blocks of 10 kg (Fig. 6c). The input values and the output results of simulation are listed in Table 4.

Fig. 6
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a Plot of bounce height envelope at varying locations; b plot of translational velocity envelope at varying locations; c plot of total kinetic energy envelope at varying locations for 10-kg blocks

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Table 4 Input and output parameters of simulation
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5.3 Optimization

After simulation of the vulnerable cliff, an attempt was made to optimize the slope parameters along with the ditch geometry. It is important to note that while the overall slope angle has a strong influence on the trajectory of the rock block, the ditch geometry (width and slope) controls the final energy of the fallen rock blocks. During optimization studies, the overall slope angle was changed from 40° to 65° with an interval of 5° and the resulting rockfall trajectories were obtained. The angle of the slope when varied from 40° to 50° showed a rise in the number of blocks crossing over to the road. Further, a significant change in the ditch width was observed and that led to the change in the energy configurations of the falling rock blocks. The comparison charts for the number of rock blocks crossing the road and the most probable kinetic energy with respect to the slope angle is shown in Fig. 7.

Fig. 7
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a Number of blocks crossing road and b most probable kinetic energy with varying slope angle

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The most optimum ditch angle was found by varying the cliff slope between 40° and 70° by taking an interval of 5° and testing all the variations in ditch angle. 10,000 possible rock trajectories were taken to estimate the risk. It was found that for each given slope angle, as the ditch angle was increased, the number of rocks stopped by the ditch also increased (Fig. 8). The change in number of rocks is minimum for 40° slope while it is maximum for 70° slope. It was found that for a 70° slope, the risk can be reduced by up to 13 % with a ditch angle of 15° while on a flat ditch; the maximum risk will be at an angle of 65°. With an increase in the ditch angle, the vertical component of the falling blocks becomes more effective.

Fig. 8
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a Percentage rock blocks stopped in the ditch on varying slope angle; b percentage rock blocks that move beyond the ditch on varying slope angle

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6 Conclusions

The rockfall hazard study along NH-58 near Saknidhar, Uttarakhand reveals that the studied slope is under critical threat of rockfall which needs proper attention and protection. Recurrent rockfall leads to loss of property and affect the safety and the lives of people residing in the downstream locality. According to the rock hazard rating systems, slopes having less than 300 score can be assigned as low priority while those having a total score above 500 need urgent remedial action. In this study that implemented different hazard rating schemes, the slopes were found to have total scores of 539 and 466 and need immediate treatment to reduce fatalities along the highway. Special attention must be given to the hanging blocks and the vulnerable slopes along the highway.

The bounce height, maximum kinetic energy and run-out distance of the falling rock blocks were determined using the simulation studies. The maximum kinetic energy was found to be 379.89 J for only 10-kg rock block. The kinetic energy is directly proportional to mass of the falling blocks. A heavier rock block will have a higher kinetic energy during fall and can have serious consequences when hitting a vehicle, human or an establishment. The maximum run-out distance for the rockfall blocks was calculated as 9.21 m and this may be severe to cause obstructions in the transport. The maximum translational velocity was found to be 7.882 m/s and the barrier capacity was 233.18 J for only 10-kg blocks from the height of 10.02 m. To understand these numbers better, optimization studies were conducted to have more scenarios before any implementation works are done. To minimize the hazard risk, the ditch width can be increased or the angle of ditch inclination can be changed to retain falling blocks more efficiently. Initially when the ditch width was increased, the number of rocks retained in ditch reduced. Additionally, with the increase in ditch width, the slope angle was modified giving more energy to the falling rock block. On increasing the ditch angle in the direction opposite to the rock block motion, a reduction in kinetic energy of the moving block was observed. As high ditch angles are not safe enough for traffic, angles up to 15° only were considered and recommended. From these results, it can clearly be inferred that lesser the angle between the slope profile and the ditch, more the number of rocks retained in the ditch. Thus, appropriate slope profiles which minimize the risk hazard may be obtained through detailed field and laboratory investigation.