Introduction

For the safe operation of transportation routes particularly in the hilly terrain, stability assessment of natural slopes as well as landslide affected slopes is important. Indeed, the instability in a rock slope often governed by the in situ geological features such as discontinuity orientations, foliation/bedding planes, or faults/thrusts. And depending on their contribution, different failure type(s) including planar, wedge, and/or toppling can be observed [1]. Although circular failures can also be possible, if the rock mass is highly fractured and/or weathered [1, 2]. Therefore, investigation of failure mode(s) in jointed rock mass becomes relevant to determine the stability of slopes.

In order to determine the failure mode, researchers often considered the kinematic analysis [3]. In general, kinematic analysis determines the geometrically possible movement direction of rock blocks and/or masses with respect to the structural orientation, i.e. dip and direction of considered slope with the present joint set(s). It is important to note that, here the forces responsible for mass movement are ignored and interpretations are made only considering the structural orientations. Followed by kinematic analysis, limit equilibrium method (LEM) and finite element method (FEM)-based approaches are also used in slope stability assessment [4,5,6,7,8,9]. The LEM approach is more convenient for soil slopes or highly weathered disintegrated rock mass, and the main objective in this approach is to optimize the critical slip surface. In contrast, mass movement for rock slopes are mostly governed by the joints. Hence, FEM or discrete element modelling (DEM)-based approaches offer more flexibility to model them and also reduces the related assumptions considered in LEM analysis [10]. To determine the stability of rock slopes using the FEM approach, continuum and discontinuum-based generalization schemes are often practiced. In continuum approach, the characteristics of the rock mass is evaluated and based on that a rock mass property is assigned for the considered section. To assign the rock mass property, generalized Hoek–Brown (GHB) criterion is commonly used [10,11,12,13]. The geological strength index (GSI) is one of the most popular and widely used method for the rock mass characterization. In the GSI method, rock mass characteristics vary from disintegrated to intact categories with numerical scoring of 0–100. A GSI value 0 indicates the rock mass is highly disintegrated and it can be considered as soil, while a GSI value of 100 represents the rock mass have less joints, high roughness, no weathering, with no infilling. Using this GSI method, one can easily determine rock mass characteristics and further used in FEM/DEM-based continuum stability assessment. Although determination of the GSI value is itself a subjective process and the involved ratings can vary depending on expert interpretation. Similarly, researchers argued that this approach is more suitable for disintegrated rock mass as the role of joint sets in the slope stability is ignored [1]. In contrast to soil or say disintegrated rock slopes, stability of rock slopes mainly depends on the joint characteristics. As discussed earlier, joint spacing, orientation, volumetric concentration can significantly affect the slope stability condition. The discontinuum approach allows to incorporate the joint set(s) in the FEM modelling. Universal Distinguished Element Code (UDEC) developed by Cundall [14] has been frequently employed by researchers to model discontinuum rock mass stability [15,16,17,18,19,20]. Pal et al. [21] used UDEC to analyse the stability of the Surabhi landslide in Dehradun, India, taking into account the strength and deformability qualities of the joints and intact rock.

In the present study, the Gangtok–Lachung–Lachen National Highway (NH-510) in Sikkim state of India is considered (Fig. 1). Based on the strategic location, it is one of the most important NH in India. During the Indian summer monsoon (ISM) period (i.e. May to September) frequent landslides have occurred at different stretches of this road and thereby, blocked the traffic and often caused fatalities. So, it is imperative to identify the slope vulnerable to failure. To classify the rock mass, two different rock mass characterization indexes were calculated based on the field parameters. Kinematic analysis performed in DIPS helped to identify potential failure modes. To further investigate, three slopes exhibiting tendency of planar failure were considered based on the site observation to perform detailed numerical modelling using Universal Distinct Element Code (UDEC). Effect of saturation on the joint surface was considered by reducing the basic friction angle in the Barton–Bandis joint model [1, 5]. SurfaceWedge software was utilized to assess the factor of safety against wedge failure for the three identified slopes undergoing wedge failure. It is envisaged that the present attempt will be useful for the locals and government authorities to mitigate and manage slope instability problems. Along with this, wide array of methodological as well as numerical approaches are considered in this attempt, which can be helpful for other practitioners working in the field of slope stability.

Fig. 1
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Location of Outcrops on Gangtok–Lachung–Lachen National Highway (NH-510), Sikkim, India

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Study Area and Field Investigation

The elevation of Sikkim Himalaya ranges from ~ 280 to more than 8500 m. The climatic condition of this area varies significantly from the southern to the northern part. The climate of the southern lowlands is mainly subtropical and as elevation increases towards the north, alpine type clod climate is observed. The area received annual precipitation of more than 4000 mm, of which ~ 80% is showered during the monsoon period (May to September). The high variation in climatic and rainfall conditions significantly affects the vegetation type as well as the physical weathering processes in this area. Apart from high intensity rainfall, frequent earthquakes are also observed in this area, e.g. in 2011 an earthquake of Mw 6.9 is recorded in this area and triggered many landslides, causing extensive damage. Similarly, earthquake caused slope instabilities increase the size and count of rainfall-induced slope failures during the post-earthquake monsoon periods. All these situations make this area vulnerable to landslides and can be marked as a landslide hotspot in the Indian Himalayan terrain.

The Himalayan sequence of Sikkim consists of different lithostratigraphic units ranging from lower to higher metamorphic grades [22]. The study area comes under the Central Crystalline Gneissic Complex Group (CCGC). The main geological formations belonging to the Darjeeling and Chungthang formations are mainly comprised of gneiss, schist, and quartzite type of rocks (Fig. 2).

Fig. 2
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Geological map of the study area along the Gangtok–Lachung–Lachen National Highway

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Joint's attitude was recorded during the field investigation. These data of joints were used to perform kinematics of slopes and find out the type of slope failure (planar or wedge). Other data like spacing between the joints, joint roughness coefficient (JRC), unconfined compressive strength (UCS) (determined by using Schmidt hammer), and hydrological conditions have been noted to calculate the rock mass rating (RMR) and geological strength index (GSI). During the field investigation, predominant joint sets mostly three in numbers were considered to interpret the rock mass. Generally, slope cutting-induced mechanical breakages increase the appearance to joint counts. To decrease the uncertainty level, the current option is found to be suitable for all investigated slopes. Using measured data and literature information, characteristics such as joint normal stiffness, joint shear stiffness, friction angle of the joint, and cohesive strength of the joint have been estimated [23].

Hoek and Brown [24] introduced the geological strength index (GSI) to characterize the rock mass. The geological features, together with a visual assessment of the rock mass, are used as direct input for the selection of appropriate parameters to estimate rock-mass strength and deformability. GSI also helps in characterizing difficult-to-describe rock masses in the field. Several researchers have adapted and modified the GSI [25,26,27,28]. Sonmez and Ulusay [29] proposed new metrics and ratings, such as structural rating (SR) based on volumetric joint count (Jv, the sum of the number of joints in unit volume rock mass) and surface condition rating (SCR) based on input characteristics such as roughness, weathering, and infilling. Instead of a range of GSI values, one can generate a specific GSI value based on structural rating and surface condition rating.

Bieniawski [30, 31] proposed the rock mass rating (RMR) system, which is based on the values of five discontinuity parameters: (i) uniaxial compressive strength (UCS), (ii) rock quality designation (RQD), (iii) discontinuity spacing, (iv) discontinuity condition, and (v) groundwater condition. Bieniawski [31] assigned ratings to these variables. RMRbasic, which goes from 0 to 100, is calculated by adding these ratings. The UCS is determined in this work using an N-type Schmidt hammer since it is less sensitive to surface flaws, and it is also preferred by ISRM [23]. Palmstorn's equation (RQD = 115–3.3 Jv) was used to estimate the RQD value. The volumetric joint is calculated by counting the number of joints in one cubic metre of a rock mass (Jv). The JRC value is calculated by comparing the appearance of a discontinuity surface to standard profiles given by Barton and Choubey [32]. Table 1 summarizes the attributes of joints and slope for all the 16 locations and in Fig. 3, the pictorial representation of all the sixteen slopes are shown along with the field observations. Table 2 shows the details regarding the calculation of RMRbasic and the range of GSI for all the 16 slopes.

Table 1 Joint and slope attributes recorded in the field
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Fig. 3
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Photographs of slopes used in the study: a outcrop 1 with planar failure, b outcrop 2 with planar failure, c outcrop 3 with wedge failure, d outcrop 4 with planar failure, e outcrop 5 with planar failure, f outcrop 6 with no failure, g outcrop 7 with planar failure, h outcrop 8 with wedge failure, i outcrop 9 with wedge failure, j outcrop 10 with no failure, k outcrop 11 with no failure, l outcrop 12 with planar failure, m outcrop 13 with planar failure, n outcrop 14 with planar failure, o outcrop 15 with planar sliding, p outcrop 16 with planar sliding

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Table 2 RMR, GSI, and failure mode of the studied outcrop
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Kinematic Analysis

Kinematic analysis is used to determine potential failure modes in a jointed rock mass. The analysis is made based on the slope geometry, material properties, and angular relations between discontinuities and the surfaces of the slopes. Analysis of all the sixteen slopes was performed using Rocscience DIPS. For unfavourable jointed rock slopes, the probable failure modes and failure zones are indicated. The kinematic analysis is based on the relationship between joint and slope orientations [33], which is detailed by Hoek and Bray [3]. When a discontinuity dips in the same direction (± 20°) to the slope and the amount of dip is less than the amount of slope dip but larger than the internal friction angle, a planar failure in the slope can occur. The line of intersection of two discontinuities (plunge line), which follow in the same direction (± 20°) as the slope and the angle of plunge become less than the angle of a slope but larger than the friction angle, can favour the formation of wedge failure. To establish the orientation of discontinuities and the slope face of the locations chosen for the current investigation, the structural data of joints and slope faces were plotted in stereographic projections. The stereographic plots depict the various modes of failure and zones of failure for the slopes under consideration (Fig. 4). The failures may be seen in Fig. 4 by the shaded areas in the stereographic plots. The kinematic analysis highlighted that ten out of the sixteen slopes have the joint setting favourable for the planar sliding, three have a probability of wedge sliding, and the remaining three are found to be stable.

Fig. 4
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Stereographic projection of the studied outcrops using kinematic analysis in Rocscience DIPS

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Numerical Modelling Using Universal Distinct Element Code (UDEC)

UDEC is numerical modelling software that is commonly used to simulate the behaviour of rock masses and other geological materials by discretizing them into distinct elements. UDEC is a two-dimensional numerical programme for continuum and dis-continuum modelling that uses the distinct element approach [34]. It should be noted that more computational effort is needed to simulate assemblies of separate blocks that are mechanically integrated with their surfaces and corners [35]. The construction of the numerical model in UDEC, generally follows the following steps, as illustrated in Fig. 5.

Fig. 5
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Methodology used in UDEC to carry out the stability analysis of the rock slopes

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Detailed numerical analysis of three slopes is performed using UDEC. The slopes showing large planar failure in the presence of other joint sets are selected for detailed numerical analysis in UDEC. The other slopes which had partial or localized failure may be due to the road widening activity were discarded. In UDEC, the continuum and the dis-continuum approach is used depending on the field conditions. UDEC has the capability of incorporating the strength and deformability properties of the joints and intact rock for stability analysis. As reported in Pal et al. [21], the joint shear strength parameters were assumed based on the type of rock that exists in the study area. It was attempted to incorporate the persistent joint sets observed in the field in the numerical model. The non-persistent joint sets or the surfaces due to the mechanical road widening activity were discarded. The spacing of the joint sets in the numerical was altered due the non-convergence issues in UDEC, details are mentioned in the subsequent sections. The input parameters for this approach were determined using field data and available literature. The most often used criterion for calculating the factor of safety (FOS) is the generalized Hoek–Brown (GHB) criterion [26]

Model Configuration

Material property is the utmost important input parameter for any numerical analysis. Hence, care has been taken to decide the material properties. UCS, GSI, Hoek–Brown constant (mi), disturbance factor (D), and elastic modulus of intact rock (Ei) are the main input parameters for the present study. Two modelling techniques are used based on slope geometry and rock mass condition. In case of continuum analysis, the shear strength parameters such as equivalent friction angle, cohesive strength, and tensile strength for the rock masses are estimated using RocLab software from Rocscience library. These values are obtained by a fitting straight line over the generalized Hoek–Brown (GHB) failure envelope [26]. The procedure of fitting entails balancing the areas above and below the Mohr–Coulomb plot. Gercek’s [36] quoted value of Poisson's ratio for quartzite is presumed to be on the upper side.

The bottom of the slope is fixed in both the vertical and horizontal directions. The slope’s vertical boundaries are fixed in the horizontal direction. Both field stress and body force are used in UDEC. The field stress characterizes the in situ stress conditions, while the body force represents the elements’ self-weight. In UDEC, there is no direct option for defining the element size. There is an input parameter termed as aspect ratio. The aspect ratio is defined as the ratio of the longest dimension of an element to the shortest dimension. And for a defined aspect ratio, the mess generation is automatic. For all the three slopes, multiple simulations were run with different aspect ratios, and the variation in the FoS was recorded to arrive at an appropriate aspect ratio for the analysis. If aspect ratio is large then the mess generated is course and it takes less time for the convergence. By comparing model results with the field observation, the aspect ratio is refined to achieve better agreement between the simulated and observed behaviours. Aspect ratio of 1–2 is used in this analysis to ensure numerical stability and to achieve suitable FoS resembling the field condition. The generalized Hoek–Brown (GHB) criterion was used to estimate representative shear strength parameters for rock mass of varying slopes in this scenario.

In the case of continuum analysis, the shear strength parameters of the jointed rock mass, which includes the joint element, are used to calculate the GSI for the entire rock mass. When employing joint elements in UDEC, the material properties of the rock between the joints should be used. If the rock between the joints is intact, the material properties of the intact rock must be used. If all the joint sets are included in the numerical model, the rock between the joint sets is considered to be intact in this study. The input parameters for joints are also equally important in this combined method of continuum-interface analysis. In this approach, the discontinuities are represented as an interface element in between the rock wall. The method focuses on the explicit simulation of interfaces between joint walls through joint elements. The method given by Barton [37] is used to compute joint normal stiffness (kn). Normal stiffness (kn) is calculated using Eq. (1).

$$ k_{n} = \frac{{E_{i} E_{m} }}{{L(E_{i} - E_{m} )}} $$
(1)

where Em is the rock mass's deformation modulus, Ei is the intact rock material's deformation modulus, kn is normal stiffness, and L is mean joint spacing.

The ratio of kh/ks generally ranges between 10 and 20 for the problems where low normal stresses are generally encountered. Assuming the value of kh/ks = 10, shear stiffness (ks) is calculated [1]. The input parameters taken into account for the continuum-interface analysis of outcrop-7 are shown in Table 3.

Table 3 Input parameters for continuum-interface analysis of outcrop-7
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Similarly, the required parameters for outcrop-13 and outcrop-15 are obtained. The input parameters for continuum-interface analysis of outcrop-13 and outcrop-15 are tabulated in Table 4 and 5, respectively.

Table 4 Input parameters for continuum-interface analysis of outcrop-13
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Table 5 Input parameters for continuum-interface analysis of outcrop-15
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For outcrop-7, numerical analysis is done first by considering the joint wall as dry and saturated. For the Outcrop 13, the intact rock strength has been reduced to rock mass strength using the GHB criteria. This has been done based on the field observation, as the joint spacing was less than 20 cm in most of the slope. It is not possible to incorporate such closely spaced joints in numerical mode due to the non-convergence of the solution in UDEC. Outcrop-15 has been analysed for two different conditions one with only the most unfavourable joint set and another with two persistent joint sets.

Factor of Safety (FOS) Calculation

The slope stability factor was computed using UDEC software for three outcrops out of sixteen. These three outcrops were selected on the basis of field observations. FOS for outcrop-7 has been calculated by taking into account two different conditions, i.e. with and without the presence of water in the joint sets, in order to better understand the effect of water saturation on factor of safety. The presence of water can significantly affect the stability and behaviour of rock mass. UDEC is flexible in assigning the element without much difficulty. The slope was dry at the time of the site visit. The factor of safety is 1.50 under dry condition. And the FOS is 1.43 while considering the joints with the presence of water. The effect of water is considered by reducing the basic friction angle of the joints [1, 21]. This is happening because the water acts as a lubricant, reducing the resistance between the joint surfaces and making it easier for them to slip or slide past each other [24, 38].

For outcrop-13, joints observed in the field had a spacing of less than 6 cm in major portion of the slope and the material found in slope was disintegrated instead of rock blocks. Due to a convergence problem, it is not possible to take these thinly spaced joints into account in UDEC. Therefore, FOS for outcrop-13 is calculated without taking any joints into the numerical model. Instead the rock mass shear strength properties were reduced from the intact rock properties based on the rock mass characterization done using GSI. This slope's FOS was determined to be 1.13, which is only marginally stable. Additionally, it closely relates to the conditions at the actual site.

FOS for outcrop-15 has been calculated considering the slope as a single-jointed slope and a double-jointed slope. The FOS when we consider the slope as single jointed is 3.04, which is on a very higher side and the FOS is 1.40 when we consider the slope to have two joint sets and represents the actual slope condition observed during the field visit. The parameters like strength, shear, and normal stiffness were used to calculate FOS. Figures 6, 7, 8, 9, and 10 shows the analysis of the slope using UDEC. The present analysis shows the importance of selecting the correct method of analysis and field investigation data. With the help of detailed field investigation data and some assumption regarding the intact rock properties, a comparable factor of safety can be obtained.

Fig. 6
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Slope for outcrop-7 dry condition

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Fig. 7
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Slope for outcrop-7 including water saturation of joint

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Fig. 8
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Slope for outcrop-13

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Fig. 9
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Slope for outcrop-15 single jointed

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Fig. 10
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Slope for outcrop 15 double-jointed

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The factor of safety for above-mentioned slopes is shown in Table 6.

Table 6 Factor of safety for different outcrops under different conditions
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Wedge Stability Analysis

Apart for the detailed two dimensional numerical analyses of three slopes, SWedge software was also used to determine the minimum factor of safety of three other slopes having clear indication of wedge failure from the kinematic analysis and field investigation. It examines the number of discrete joint plane orientations as well as all potential combinations of two joints that create a wedge. The analysis requires a dip amount and direction of the joints showing wedge along with cohesion, friction angle, height, direction, and angle of the slope. The wedge is considered to be rigid body in nature. The input parameters examined for slope stability using SWedge software are shown in Table 7.

Table 7 Input parameters used in wedge analysis
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The factor of safety for outcrop 3 is 1.33, which is nearly stable as observed in the field and FOS for outcrop 8 and 9 is 0.95 and 0.94, respectively, which indicated the instability in the slopes (Fig. 11, Table 8). Furthermore, the observations recorded from the field substantially correlates with the SWedge analysis results. This show the correct selection of the model is essential to replicate the actual site conditions.

Fig. 11
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Slopes for Outcrops-Sikkim

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Table 8 Factor of safety for different Outcrops-Sikkim
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Summary and Conclusions

The research discusses the significance of field observations in the numerical stability analysis of rock slopes. The study focuses on the Gangtok–Lachung–Lachen Highway in Sikkim, India, and aims to assess the stability of sixteen slopes along this highway using different techniques. The study emphasizes the importance of field data in selecting the appropriate numerical modelling approach to ensure meaningful results. Geological and geotechnical parameters obtained from field investigations were used to classify the rock mass based on the geological strength index (GSI) and rock mass rating (RMR) values. By taking into account the structural information of the joints and slope surfaces, kinematic analysis was carried out using the Rocscience DIPS software to assess the failure mode of the slope. The analysis helped in identifying potential failure modes and zones where failures might occur in the studied slopes. The results indicated that out of the sixteen slopes, ten were susceptible to planar failure, three exhibited potentiality of wedge failure, while the remaining three slopes were found as stable. Further to determine the FOS, three critical slopes were selected, and numerical modelling was done in such as numerical analysis (in UDEC) and analytical technique (in SWedge). The research sheds light on the stability of rock slopes along the Gangtok–Lachung–Lachen Highway by combining field investigations, kinematic analysis, and numerical modelling.

The present attempt considers rock slopes for stability assessment. Outcrop no 13 is disintegrated in nature and because of that a continuum analysis could be justified. And the computed FOS is 1.13, which could justify the field observations. But for the outcrop number 7 and 15, this justification is not valid. In the outcrop no 7 and 15, the spacing of the predominant joint sets are in the range of 0.2 to 0.6 m. In the numerical simulation in UDEC, it was attempted to model the joints with spacing of 0.6 m, but due to the non-convergence of the solution, it was not possible. Then, an iterative approach was taken to arrive at a joint spacing with which the solution could converge, and the FOS value was in line with the filed observations. For the outcrop no 7 and 15, a joint spacing of 2 m was finalized. The factor of safety for these two outcrops were 1.5 and 1.4 respectively under dry condition and with both the joint sets, respectively. The effect of water saturation on the FOS was also studied for the outcrop no 7. By reducing the basic friction angle, the FOS was reduced from 1.50 to 1.43 for the outcrop no 7. Though the exact joint spacing could not be modelled in UDEC, the FOS obtained are comparable with the filed observations. The FOS values are slightly on the higher side because of mainly two reasons. The joint spacing considered in the UDEC simulation are on the higher side, and the present slope is stable after the failure of the unstable portion.

Selection of the correct numerical modelling technique for slope stability based on the field observations is very essential. The numerical study on different types of rock slopes in the area clearly reveals that the current methodology is precise since the FOS are comparable with the field observations. In conclusion, it can be said that field observations play a crucial role in numerical stability analysis of rock slopes. The integration of field inputs, kinematic analysis, and numerical modelling provides a comprehensive understanding of stability conditions and failure mechanisms associated with specific slope sections. The findings of this study can contribute to the assessment and management of rock slope stability along the Gangtok–Lachung–Lachen Highway in the Sikkim Himalaya region.