Evaluation of slope stability through rock mass classification and kinematic analysis of some major slopes along NH-1A from Ramban to Banihal,North Western Himalayas

Amit Jaiswal,A.K.Verma,T.N.Singh

Department of Civil and Environmental Engineering,Indian Institute of Technology Patna,Patna,801106,India

Keywords: Rock mass classification Kinematic analysis Slope stability Himalayan road Static and dynamic conditions

ABSTRACT The network of Himalayan roadways and highways connects some remote regions of valleys or hill slopes,which is vital for India’s socio-economic growth.Due to natural and artificial factors,frequency of slope instabilities along the networks has been increasing over last few decades.Assessment of stability of natural and artificial slopes due to construction of these connecting road networks is significant in safely executing these roads throughout the year.Several rock mass classification methods are generally used to assess the strength and deformability of rock mass.This study assesses slope stability along the NH-1A of Ramban district of North Western Himalayas.Various structurally and non-structurally controlled rock mass classification systems have been applied to assess the stability conditions of 14 slopes.For evaluating the stability of these slopes,kinematic analysis was performed along with geological strength index (GSI),rock mass rating (RMR),continuous slope mass rating (CoSMR),slope mass rating(SMR),and Q-slope in the present study.The SMR gives three slopes as completely unstable while CoSMR suggests four slopes as completely unstable.The stability of all slopes was also analyzed using a design chart under dynamic and static conditions by slope stability rating (SSR) for the factor of safety (FoS) of 1.2 and 1 respectively.Q-slope with probability of failure (PoF) 1% gives two slopes as stable slopes.Stable slope angle has been determined based on the Q-slope safe angle equation and SSR design chart based on the FoS.The value ranges given by different empirical classifications were RMR(37-74),GSI(27.3-58.5),SMR(11-59),and CoSMR(3.39-74.56).Good relationship was found among RMR&SSR and RMR &GSI with correlation coefficient (R2) value of 0.815 and 0.6866,respectively.Lastly,a comparative stability of all these slopes based on the above classification has been performed to identify the most critical slope along this road.

1.Introduction

Slope failure is one of the major global catastrophes.It is a challenging issue in the Himalayan region,causing environmental damage and human casualties (Panikkar and Subramanyan,1997).The continuous tectonic activities in Himalayas combined with huge rainfall induce massive slope failure in the area (Paul and Mahajan,1999).Due to the complex geology,active fold-thrustbelt (FTB),steep mountainous slopes and high relief,rockslides are frequently reported in this region (Ghosh et al.,2012).The losses in Himalayan region account for an estimated 30% of global losses because of landslides and associated devastation (Li,1990;Dahal et al.,2009).According to study of Varnes (1984),the accurate measure of losses due to landslides is not monetary units but rather the disturbance and suffering of human lives.According to 2010-2020 reports of the national crime record bureau (NCRB) of India,about 3985 death cases were caused by landslides across India.

Determining safe cut slope angles and appropriate excavation techniques are important for buildings in the highway (Avc? et al.,1999).Removing the natural earth material affects the stability of the naturally slope(Avs?ar et al.,2014).However,slope instabilities along the roads in hilly terrains often cause inconvenience in movement.The trend of the existing discontinuities in rocks plays an important role in slope stability (Sardana et al.,2019a,b).Slope failure along the road section occurs because of these randomly aligned discontinuities in the rock.Thus,it is critical to determine the unfavorable orientation of the discontinuity(Park et al.,2016).Depending on the relationship between these discontinuities,slope failure can be either planar,wedge,toppling or a combination of these with a dominance of one mode.To evaluate these failure types,several rock mass classification methods have been developed.Geotechnical assessment of rocks through empirical classification utilizes geological inputs for stability analyses of natural slopes and engineering designs(Azarafza et al.,2017).Some of the most commonly utilized empirical methods are rock quality designation (RQD) (Deere,1963),Q-system (Barton et al.,1974;Barton and Bar,2015;Bar and Barton,2017),rock mass rating(RMR)(Bieniawski,1979,1989),slope mass rating (SMR) (Romana,1985,1993),and geological strength index(GSI)(Hoek et al.,1995;Hoek and Brown,1997;Marinos and Carter,2018),continuous slope mass rating (CoSMR) (Tomás et al.,2007),Chinese slope mass rating(CSMR)(Chen,1995),slope stability rating(SSR)(Taheri et al.,2006)and Q-slope(Barton and Bar,2015).Q-slope and SMR classifications can be used to quickly assess the stability of natural slopes(Azarafza et al.,2020a,b).Numerous modifications have been made to all these methods when analyzing the stability of slopes(Azarafza et al.,2021).Several scholars assess slope stability using these rock mass classifications(e.g.Sarkar et al.,2012;Vishal et al.,2017;Verma et al.,2018;Sardana et al.,2019a,b).Some studies have been conducted for critical slope to identify slope failure mode using kinematic analysis (e.g.Ghosh et al.,2014;Sah et al.,2018;Sardana et al.,2019a,b;Khanna and Dubey,2021).Instability evaluation of rock slopes by numerical modelling techniques has also been performed (e.g.Verma and Singh 2010;Verma et al.,2016,2019;Kumar et al.,2017;Pradhan et al.,2018).

The present paper focuses on comprehensive approach of various rock mass classifications with integration of the kinematic analysis to evaluate slope instability observed along the National Highway (NH 1-A),especially for steep slopes presented between Seri to Ramsoo in the Ramban district in North Western Himalayas.Geological investigations were carried to determine the distribution of geological discontinuity to calculate the rock mass characteristics to analyze the slope stability by RMR (Bieniawski,1979),SMR (Romana et al.,2003),CoSMR(Tomás et al.,2007),GSI (Hoek and Brown,1997) and SSR (Taheri et al.,2006) and Q-slope(Barton and Bar,2015)along with kinematic analysis performed on Dips 6.0.

The methods applied for evaluating the critical slope conditions along the studied road section is provided in Table 1,in addition to the advantages and limitations of each method.

Table 1Applied rock mass classification system with advantages and limitations.

Unfortunately,none of the existing classifications considers all the important slope stability parameters when evaluating the conditions of the existing slope.Very few studies are available based on SSR and Q-slope for the Himalayan region because of its complicated geological conditions.In this context,the effect of almost all the critical parameters that cause slope instability is considered with the aid of different classifications.Some good correlations have also been developed among RMR-SSR and RMR-GSI for the first time in Himalayan region.

2.Study area

The study area is located between Seri and Ramsoo in Ramban district in North Western Himalayas.Study location lies between 33°14.5′N to 33°20.62′N and 75°12′E to 75°13.65′E with a stretch of approximately 21 km along the road(Fig.1).The stretch lies along the left bank of the Bichleri River(a tributary of Chenab)along the National Highway NH-1A.During the monsoon season,NH-1A regularly gets blocked due to slope failure at several locations affecting busy traffic.Ramban-Banihal section of the NH-1A is the worst portion in this part of the Himalayan Road.This area is one of the world’s most affected regions due to frequent landslides(Chingkhei et al.,2013).

Fig.1.Map showing location of critical slopes along NH 1-A from Seri to Ramsoo.

Geologically,some area consists of agglomeratic shale of lesser Himalayan sequence confined by main boundary thrust (MBT) in the south.It is further divided from the Salkhala group and Piparan granitic intrusion of central crystalline sequence in the north with main central thrust (MCT).Stratigraphically,the area lies between the two regional scale thrust zones of Himalaya(MBT to MCT)and some part of central crystalline.The rock type in this study area consists mainly of limestone,quartzite,slate,phyllite,and granitic gneiss(Shanker et al.,1989;Bhat et al.,1999).The regional strike of area varies from NW-SE to WNW-ESE,with dip variation from very steep to steep towards N or S.Rocks in the area are marked by two to three steeply dipping joint sets with one bedding or foliation plane.

3.Methodology

The method adopted in the present study is shown in flowchart as in Fig.2.Field investigations were carried out to determine the most critical slopes on the road section of NH-1A from Seri to Ramsoo.Lithological details of all 14 slopes along the road are shown in Table 2.The slope height varies from 70 m to 205m,with width from 60 m to 175 m,and the slope angle varies from 48°to 75°.Orientation and discontinuity of slopes measured along with other properties of discontinuities are presented in Table 3.Different rocks observed during field investigation of these slopes were very fragile with multiple joint sets.Field datasets collected from field include important joint characteristics like joint spacing,aperture,roughness,infilling and groundwater conditions associated with each critical slope.These characteristics were required to calculate RMRbasic,SMR,CoSMR,basic and modified GSI,SSR,Qslope,and kinematic analysis for stability assessment.Fig.3 shows field image of major joint sets exhibited on or near the surface of the slopes.Uniaxial compressive strength(UCS)and internal angle of friction (φ) of the collected samples from the slopes were determined in the laboratory as per ASTM standard: D-5731-95(Table 4).Fig.4 shows the UCS determination from core samples in the laboratory.

Fig.2.Flowchart showing different slope classification techniques used in the study.

Table 2Detailed slope location with its rock type.

Table 3Joint and slope properties dataset exposed on slope surface.

Table 4Laboratory determined values of UCS,RQD and internal friction angle of the samples collected from each slope.

4.Kinematic analysis

Kinematic analysis can identify the possible failure modes of rock slope.It has been extensively applied to analyze the stability of rock slopes.Discontinuities in rock masses are randomly oriented,resulting in three major types of failures: toppling,plane,and wedge.Discontinuities like foliation,bedding planes,joints,shear zones and faults are potential failure planes when their orientation is compared to slope orientation.Markland’s test is the basis for kinematic analysis (Hoek and Bray,1981).During kinematic analysis,the stereographic projection is utilized,in which the dip,dip direction,and internal friction angle of discontinuities are depicted through stereonet,and the failure type is investigated in relation to slope orientation (Park et al.,2016).

The planar failure mode occurs when a continuous discontinuity dips towards the slope with the strike almost parallel to that of the slope.Wedge failure takes place when the intersection of two discontinuities forms wedge shape blocks of rock,and the line of intersection dips in the slope direction.During kinematic analysis,planar failure is depicted by the region confined inside the daylight region and outside of the friction pole circle,while wedge failure mode is characterized by the intersection of discontinuity planes plotted inside the critical zone.Critical zone is the region outside the plane of slope but inside the cone of friction plane(Wyllie and Mah,2004).

Toppling failure mode is common where discontinuity planes are in sub-vertical to vertical cases.In this failure type,the rock blocks or columns rotate along a fixed base.Failures in topple are of two types,flexural topple and block topple.In the case of block toppling,rock columns are generated on single set of steeply dipping discontinuities along the slope face.The height of individual column is determined by the spacing of discontinuities,while in the case of flexural toppling,rock columns disjointed by discontinuities get bend in the forward direction prior to failure(Wyllie and Mah,2004).In toppling,planes of discontinuity slide with respect to each other.Slide limiting plane in the stereoplot of flexural toppling is designated as the critical zone.The dip of slip limit plane is determined by subtracting the friction angle from the slope angle,and for direction it follows the slope face’s direction.

The orientations of different discontinuity planes were mapped during the field investigation to determine its failure mode through kinematic analysis with Rocscience Inc.,2015.Discontinuities orientation,slope orientation and angle of internal friction (φ) are provided in Tables 2 and 3.The discontinuity data are plotted on the stereonet as poles,and the concentration of poles on an individual discontinuity plane is generated.On the stereonet,the plane representing the slope face is shown,and the great circle in the center represents the angle of internal friction.The relationship between friction cone,joint planes and slope plane has been used to identify the failure mode.Six slopes (L-6,L-8,L-9,L-10,L-11,L-12) out of fourteen show wedge failure type,while seven slopes(L-1,L-2,L-3,L-5,L-7,L-13,L-14) show planar failure and last one slope (L-4)corresponds to topple failure (Fig.5a-c).Although slopes L-1,L-2,and L-3 were determined to be planar failure during kinematic analysis,it was observed in the field that failure modes of these slopes were of mixed type with a dominance of planar failure mode.In general,it is observed that southwest dipping joints are mostly responsible for planar failure in slope because most of the slopes in the study area also dip in south to southwest direction.Fig.6 shows the distribution of slopes along the road and their failure modes.It was observed that 42.85% of slopes have given wedge,50% have given planar and 7.15% have given toppling failure mode.These failure modes for individual slopes along with critical plane or intersection of planes were further utilized for detailed investigation through SMR and CoSMR.

Fig.5.(a)Kinematic analysis depicting possible planar failure for seven slopes(L-1,L-2,L-3,L-5,L-7,L-13,L-14)along a particular plane;(b)Kinematic analyses depicting possible topple failure for L-4 slope along a plane;and(c)Kinematic analysis depicting possible wedge failure for six slopes(L-6,L-8,L-9,L-10,L-11,L-12)along with line of intersection of two wedge generating planes.

4.1.Slope stability analysis based on rock mass classification

In the present study,empirical rock mass classification and kinematic analysis have been used to evaluate the stability of rock slopes.Rock mass classification is an important technique to analyze the stability of road-cut slopes,and it has been proven quite effective for design and construction over the last few decades(Goel and Singh,2011).It assesses the condition of slope based on existing geological structures and characteristics properties of rock.Most empirical rock mass classifications have been modified over time for tunnels,slopes and mines (Pantelidis,2009).

4.2.Rock mass rating (RMR)

Bieniawski (1974) proposed the rock mass rating (RMR) classification and it has been revised over time(Bieniawski,1979,1989).The RMR have been extensively used in various engineering fields dealing with rocks,such as mining and civil constructions of tunneling,the road in hill terrains,bridges,dams and hydropower projects.Five input factors are required to determine the basic RMR value (RMRbasic).The ratings for all these five factors are based on their field conditions: (i) uniaxial compressive strength (UCS);(ii)Rock quality designation (RQD);(iii) condition of discontinuities;(iv)Spacing of discontinuities;and(v)groundwater condition.The value of RMRbasicranges from 0 to 100,estimated by adding the ratings for these five characteristics given by Bieniawski(1989).

During the field survey,the geotechnical information is determined to calculate RMRbasic,which includes compressive strength,RQD,joint spacing,joint condition,and hydrological conditions.All these were analyzed for the 14 slopes.The slope surfaces exhibited dry groundwater conditions when the field survey was conducted,which aided in comparing the RMRbasicresults with GSI values.The RMRbasicfor each slope was calculated by adding rating of each parameter,and the obtained RMRbasicvalues range from 37 to 74(see Table 5).It is observed from the field RMRbasicdataset that granitic gneiss has generally higher RMRbasicvalue than slate and phyllite.Calculated RMRbasicvalues show that majority of the slate and phyllite locations falls in fair rock type (class III) and granitic gneiss locations falls in good rock type (class IV) of RMR classification.Two locations(L-1 and L-13)have slate but their conditions fall in poor rock type (class II) according to RMR classification.

Table 5RMRbasic values along with rating assigned to each factor for 14 slopes.

4.3.Geological strength index (GSI)

Hoek and Brown(1997)proposed the geological strength index(GSI),and several scholars have modified it (Marinos and Hoek,2000;Sonmez and Ulusay,2002).It assesses the peak strength for the rocks which are heavily jointed.It is extensively utilized to evaluate the strength of jointed rocks on the basis blockiness and discontinuities surface conditions.This approach is handy for assessing characteristics of rock mass quickly and is a straightforward method.It has the advantage of overcoming the difficulties associated with evaluating RMR for very poor rock mass and double-counting the influence of groundwater and joint orientation.

The earliest approach utilized in describing the rock mass conditions with the aid of GSI was based on the Hoek-Brown failure criterion (Hoek et al.,1995),where the GSI value was calculated from RMR(Bieniawski,1989) with an empirical equation:

whereRMRbasicis the basic RMR value proposed by Bieniawski(1979,1989).

The RMRbasicis the rating for rock mass with the groundwater condition rating value (15),and the adjustment rating for joint orientation is zero (Goel and Singh,2011).Hoek and Marinos(2000) proposed GSI chart which can estimate the range of GSI value based on two axes representing blockiness and joint surface quality.

The quantified GSI chart proposed by Sonmez and Ulusay(2002)is defined based on two parameters:surface condition rating(SCR)based on roughness,infilling and weathering and structure rating(SR) calculated through volumetric joint count (Jv):

whereRf,Rr,andRware the rating values,which are the same as in the RMR rating scheme.

Based on the horizontal and vertical scales that represent surface discontinuity condition represented as joint condition(Jcond89)and blockiness as given by RQD (Deere,1963) respectively,Hoek et al.,2013 have quantified the GSI charts of Hoek and Marinos(2000).GSI expression sums these two scales:

The range of GSI values of 14 slopes considered during this study was determined by field assessment of the discontinuity surface conditions and rock mass structure.In this study,GSI values were calculated according to previous studies (e.g.Hoek et al.,2013;Sonmez and Ulusay,2002;Hoek and Marinos,2000),and their graphical plot is given in Fig.7.The range of GSI values was the classification outcome of Marinos and Hoek (2000).When these slopes were projected on the GSI chart of Sonmez and Ulusay(2002),all 14 slopes showed blocky structural ratings with SCR variation from good to poor.The brown dot in Fig.8 represents SR and SCR-based quantified values of GSI for the slopes under evaluation.GSI values obtained from Sonmez and Ulusay (2002) have been utilized to estimate SSR values of slopes.Table 6 presents the value of GSI calculated from the above applied GSI classification.

Fig.7.Comparison plot for quantified GSI values GSI (2002) and GSI (2013) and GSI range GSI (2000).

Fig.8.Quantified value of GSI projected on modified chart of GSI (Sonmez and Ulusay,2002) (Red arrows indicates the location number).

Table 6GSI range value from (2000) and quantified GSI values from GSI (2002) and GSI(2013) classification.

4.4.Slope mass rating (SMR)

Slope mass rating (SMR) is used to assess the stability of rock slopes (Romana,1985,1993).SMR is calculated through the RMRbasicand four adjustment factors (F1,F2,F3andF4in Eq.(5)).Three of the adjustment factors(F1,F2andF3)depend on the mutual relationship between the geometer of topography and vulnerability of discontinuity along with the addition of one more correction factor(F4in Eq.(5))which is based on excavation method(Goel and Singh 2011):

In this context,F1denotes the parallel relationship among slope strike and discontinuity strike direction.It varies from 1.00 (when both strike direction is almost parallel) to 0.15 (when the angle is more than 30°between both strike direction and the chance of failure is less).F1is represented as

whereArepresents the angle between slope and discontinuity dip direction.

The parameterF2denotes the dip angle of the discontinuity in planar failure mode,i.e.the probability of joint shear strength.For joints dipping more than 45°,its value is 1,while for joint dipping less than 20°,it is 0.F2can be calculated as

whereBjsymbolizes joint dip angle.F2always remains 1 for toppling failure.

The parameterF3represents joint dip and slope dip relation.When the dip of joints and slope are parallel,conditions are fairly well;while an unfavorable condition is encountered when the dip of slope is 10°more than that of joint.

4.5.Continuous slope mass rating (CoSMR)

Continuous slope mass rating(CoSMR)is the modified approach for SMR with the integration of continuous function to improve the estimation for the stability classes.It reduces the uncertainty that results from the border values (Tomás et al.,2007).Its value is calculated using the same mathematical formula as SMR,with the variation in calculating the adjustment factor(F1,F2,andF3),whileF4is same as defined in SMR.CoSMR is continuous,whereas SMR is discrete in nature.F1,F2andF3can be expressed by

whereA,BandCare the auxiliary angles,which can be calculated with the given expression based on their failure mode (Romana,1985).F3is computed using Eq (10) for wedge and planar failure;while Eq.(11) is used if toppling failure type occurs (Tomás et al.,2007).

The failure modes for all 14 slopes were determined using the kinematic analysis.Seven slopes (L-1,L-2,L-3,L-5,L-7,L-13,L-14)were of planar failure,six (L-6,L-8,L-9,L-10,L-11,L-12) of wedge failure,and one(L-4)of topple failure.SMR and CoSMR values were also evaluated for 14 vulnerable slopes.It has been observed that for the majority of the slopes,the SMR values have a higher value than the CoSMR values except for the case of toppling slope (L-4)where the value of CoSMR is much more than the SMR value (see Fig.9).Based on SMR values,stability class along with the failure mode and probability of failure can be defined(Romana,1985),and accordingly for all the studied slopes,the results are tabulated in Table 7.Lowest value of SMR gives a completely unstable condition in SMR classification.It was observed that SMR value ranges from 11 to 59,with the majority of rock condition as bad(class IV)as per the classification of Romana (1985).While,CoSMR values range between 3.39 and 74.56,with the majority rock condition falling in bad (class IV) as per the classification of Romana (1985).Above classification assesses effectively the slopes stability for structurally controlled failure surfaces.Kinematic analysis is helpful in determining the plane and different failure modes.The possible planes and wedges determined from the above analysis were later validated on-site,and it was found that these were not the only surfaces of failure,but the majority of the failure had happened along the above predetermined planes.

Fig.9.Variation of SMR and CoSMR for 14 slopes.

Table 7SMR and CoSMR values for the slopes along with other parameters.

4.6.Slope stability rating (SSR)

In evaluating slope stability,SMR can assess the structural influence on slope stability.This technique,however,has its limits when used for large-scale rock slopes and closely joined rock masses.SMR system is intrinsically dependent on the orientation of discontinuities,which are difficult to be determined in the crushed rock masses having several joint sets or rock masses with random joints with low persistence and unclear orientation.

Taheri et al.(2006) developed the SSR on the basis of several case studies of Iran,which was later amended by Taheri and Tani(2007) to attain the requirements of stability assessment of closely spaced and heavily joined and large-scale slopes.This rating scheme utilizes modified GSI value of Sonmez and Ulusay(2002).In the SSR method,five additional parameters are considered in addition to GSI,including rock type,UCS,groundwater,seismic forces,and slope excavation method.For different factors of safety(FoS),basic design chart defining the relationship between the SSR value and slope height for the safe slope angle has been proposed.These design charts can evaluate the safe slope angles along with the stability of existing cut slopes.

An empirical formula for SSR includes the addition of modified GSI and five additional parameters that are important for slope stability identification.The formula is as follows:

whereP1,P2,P3,P4andP5are the rating values specified by Taheri et al.(2006).For 14 slopes,the values of GSI were obtained from the chart (Sonmez and Ulusay,2002).

The parameterP1denotes the compressive strength of intact rock.It was determined from rock core pieces of field samples in the laboratory.P2is determined from the rating assigned to different rock types.The slopes stability depends on the intrinsic properties of the rock type.Taheri et al.(2006)divided the rock types into six groups based on two properties,i.e.material constant(mi)in Hoek-Brown failure criteria(Hoek and Brown,2019)and dry unit weight of intact rock.P3depends on the type of excavation done along the slope.Different excavation types influence slope stability by creating new discontinuities and weakening the rock strata along previously existing discontinuities.P4defines the groundwater level,reflecting the degree of saturation of rock slope.Saturation is calculated as the amount of groundwater level at the bottom of the slope with respect to slope height.P5discusses the effects of earthquake forces on slope stability.Different earthquake zones have different peak horizontal acceleration values at the slope,and their effect on instability rating scheme have been proposed by Taheri and Tani (2007).

Multiple stability evaluation of slopes has been done using the limit equilibrium method for developing the chart of the SSR system to develop a valuable tool for determining the stability of excavated rock slopes for practicing engineers.The height of rock slope was considered during SSR design chart development,and it varied from 25 m to 400 m with slope angle ranging from 30°to 70°.Compressive strength of rock,rock type,groundwater condition,slope excavation technique,and earthquake were all taken into account to determine the slope stability.As a result,several design charts were developed showing the correlation between safe slope angle (within 30°-70°) and slope height versus SSR values for various FoS(i.e.1.5,1.3,1.2,and 1.0)(Taheri et al.,2006).The stable slope excavation angle for a particular slope height can be estimated from these charts with known SSR values for different FoS values.

Few of the slopes considered in this study have been excavated,while other slopes are being still modified for highway widening.In the seismic zonation map,the study area falls in seismic zone IV.It is crucial to analyze the above slopes through SSR design charts to evaluate the stability by comparing the constructed slope angle with the actual slope angles for two different FoS values of 1.2 and 1.0,as presented in Fig.10.The SSR values were determined for all the 14 cut slopes (Table 8) and were plotted with respect to slope height and superimposed on the design charts of SSR to estimate the safe slope angle.The values of SSR are 47-94.2.It was found that eight slopes (L-1,L-3,L-5,L-6,L-7,L-8,L-13,and L-14) were unstable while six (L-2,L-4,L-9,L-10,L-11,and L-12) slopes were stable with the minimum FoS of 1.2.For the FoS value of 1.0,eight slopes(L-1,L-3,L-5,L-6,L-7,L-8,L-13,L-14)were unstable,one(L-12)partially stable,and five slopes(L-2,L-4,L-9,L-10,L-11)stable.The analysis of slope cuts through SSR suggested that most of the slopes were unstable because of steeper angles compared to the stable slope angle.Therefore,the risk of rock fall and slide is found to be always associated with all the slopes under investigation.

Fig.10.Slope height versus SSR plot overlaid on SSR design chart: (a) FoS=1 and (b) FoS=1.2.

Table 8Estimated SSR for all the vulnerable 14 slopes.

4.7.Q-slope analysis

Q-slope is an empirical classification system for evaluating the stability condition of rock slopes excavated to construct highways,railways and open-pit mining operations (Barton and Bar,2015).This method evolved from the Q-system classification for rock mass assessment (Barton et al.,1974).This approach relies geological field work experience and engineering geological judgments(Azarafza et al.,2020a,b,2022).In Q-slope,the parameters(Jr,Ja,Jn,and RQD)are the same as Q-system.This method evolved from the Q-system of rock mass evaluation (Barton et al.,1974),which has been applied to evaluate rock exposures,drill cores,and tunnels for the past forty years.

In addition,a new element known as the orientation factor is used for orientation correction applied onJr/Jaratio to the planar failure surface and both planes of potential wedges.This orientation factor provides weightage to relative orientation of each plane(O).Jwice(Jw) incorporates the effect of long-term exposure of the rock masses to different environmental and climatic situations.The stress reduction factor (SRF) for slope represents condition of the surface slope and stress-to-strength ratios of major discontinuities.

Q-slope value is evaluated as follows:

whereJnrepresents the joint set number,Jris the joint roughness number,Jais the joint alteration number,Jwiceis an environmental effect,and SRF is slope stress reduction factor.

Barton and Bar (2015) developed an equation which can be applied to all the slope heights to determine the steepest angle of slope (β),which can be stable without reinforcement or support:

Eqs.(14)-(17) determine the steepest stable slope angle(β) for the probability of failure(PoF)at 50%,30%,15%,and 1%,respectively.These expressions have been used in this study to calculate the steepest slope angles (β) for all 14 slopes for the PoF,such as 1%,15%,30% and 50%,without any further reinforcing measures.The value of Q-slope computed through Eq.(16)for all 14 slopes varies from 0.25 to 2.677 and is given in Table 9.These values are plotted in Fig.11 with respect to the actual slope angle on the Q-slope stability chart provided by Barton and Barton (2017).Eight slopes(L-1,L-2,L-3,L-6,L-7,L-11,L-13,L-14) are unstable with present slope angle,four slopes (L-5,L-8,L-9,L-10) are in uncertain condition,and two(L-4,L-12)are in a stable state.From Eqs.(14)-(17),the steepest slope angles(β)for all the 14 slopes were calculated for PoF values 1%,15%,30% and 50% (see Table 10).

Fig.11.Slope stability condition for fourteen slopes with aid of Q-slope stability plot.

Table 9Q-slope values of investigated 14 slopes.

Table 10Steepest slope angle obtained from slope angle equation for PoF 1%,15%,30%&50% and actual slope angle.

5.Results and discussion

This study considers fourteen rock slopes in 21 km length of the stretch of NH-1A of Ramban district for detailed investigation.The investigation includes kinematic analysis and different empirical classification studies of all slopes.Majority of the slopes were observed to have very fragile rock types with multiple joint sets.The stability of all these slopes was analyzed for both structurally and non-structurally controlled failures.Rock mass of the investigated slope was classified into several categories based on RMRbasicvalues ranging from 37 to 74.However,majority of the slate and phyllite locations were in the group of fair rock type(class III)while granitic gneiss locations were in the category of good rock type(class II) according to RMR classification.This is due to the lower strength and lower RQD values of slate and phyllite as compared to granitic gneiss.Rock mass classifications of these rocky slopes were also performed through GSI.Particular values of GSI were determined through the quantified GSI method proposed by Marinos and Hoek’s (2002),and GSI equations by Hoek et al.(2013) are found to be well within the GSI range determined by Hoek and Marinos (2000).For the two cases (L-3,L-4),the values of quantitative GSI were near the lower GSI range,and in one case (L-7),it was near the upper GSI range.However,when individual GSI values were plotted,the increasing and decreasing trends for particular slopes for all three GSI classifications were similar.Value of GSI varied between 27.3 and 58.5,with a majority of values less than 47.The GSI values of all the rock slopes fall within the blocky structure with discontinuity surface conditions varying from poor to good.The blocky structure on rock slopes was also observed during field investigation.

SMR was determined after performing kinematic analysis and calculating RMRbasicalong with other adjustment parameters needed for SMR calculation of the slopes considered.For all the slopes considered,discrete and continuous functions were both adopted to determine the slope mass rating.It was observed that the stability of these slopes was influenced mainly by one or two planes.Based on the SMR values,slope stability assessment revealed that three slopes(L-1,L-2,L-14)were completely unstable,the other three (L-5,L-6,L-8) were unstable,and the remaining eight(L-3,L-4,L-7,L-9,L-10,L-11,L-12,L-13)were in partially stable condition.While the CoSMR value revealed that the four slopes(L-1,L-2,L-8,L-14)were completely unstable,five(L-5,L-6,L-7,L-9,L-10) unstable,four (L-3,L-10,L-12,L-13) partially stable and the remaining one (L-4) stable.Most of the unstable slopes lied in theslate and phyllite rock type while partially stable slopes lied in the granitic gneiss rock type.This is because the RMR value of granitic gneiss is generally higher than slate and phyllite,and the instability in granitic gneiss is mainly controlled by structural deformation.The unfavorable orientation of joints is responsible for instability in slopes with higher RMR values.It is worth mentioning that partially stable(granitic gneiss)slopes could be potential failure sites under external factors such as earthquakes,heavy rainfall,or human constructions because of their structural deformation.Comparison of CoSMR and SMR values for all the considered slopes shows that CoSMR values are less than the SMR values for eight slopes(L-1,L-5,L-7,L-8,L-9,L-10,L-11,L-12),while SMR values are less than CoSMR for six slopes(L-2,L-3,L-4,L-6,L-13,L-14).Values of SMR for eight slopes were larger becauseF3value,which depends on the amount of difference of angle between slope dip and discontinuity dip,is larger for CoSMR(dip of the discontinuity is less than the dip of the slope).This results in higher negative values for the product ofF1,F2andF3and hence CoSMR value is found to be lower than SMR value.The lower values of SMR than CoSMR for six slopes were due to the higher value ofF1,which denotes the parallel relationship between slope and discontinuity strike direction (both slope and discontinuity are almost parallel to each other).The value of SMR ranges 11-59 while CoSMR ranges between 3.39 and 74.56.This shows that Romana’s SMR is less conservative than CoSMR.One of the advantages of CoSMR is that it gives distinctive value to each factor of adjustment of SMR,thus reducing subjectivity.Both of these methods (SMR and CoSMR) can describe the condition of structurally controlled slopes,but they could be ineffective for rock slopes having closely spaced discontinuities.

The slope stability rating classification (Taheri et al.,2006) was also applied on all the fourteen considered slopes to overcome this closely spaced discontinuity constraint.This method has also developed some graphical relationships for determining the relative stability condition of slopes.The SSR value versus slope height of all the fourteen slopes have been plotted and superimposed on individual graphs of factor of safety values of 1 and 1.2.According to IS 14243-2(1995),the minimum FoS for both natural and cut rock slopes should be 1 and 1.2 under dynamic and static conditions,respectively.Stability of the individual slopes has been assessed in both dynamic and static conditions by comparing the measured slope angle to the safe slope angle determined through a plot between SSR versus slope height superimposed on the FoS values of 1 and 1.2.

Q-slope classification was used to assess the stability conditions of all the fourteen rock slopes considered in this study,along with the steepest stable angle of slopes.The calculated Q-slope values for each slope were plotted on a Q-stability plot for the existing slope angles in order to determine the stability condition of slopes for a PoF of 1%.

Table 11 represents the comparative stability analysis for 14 slopes obtained from different empirical classification methods.SMR and CoSMR classifications categorize the slope stability condition into five classes based on rating and probability of failure,from completely stable to completely unstable conditions.While SSR classification categorizes slope conditions into three classes stable,partially stable and unstable and slope height is plotted with SSR values for FoS values of 1 and 1.2 to determine the stability of the slope.Similarly,Q-slope classification also categorizes slope conditions in three classes when the existing slope angle is plotted against a Q-slope value for (PoF) of 1%.Categories defined by Qslope classification are stable,uncertain and unstable.The comparative stability analysis suggests that the safe slope angles derived from SSR for static and dynamic conditions are conservative compared to Q-slope-derived safe angles.Fig.12 represents the plot of slope angle under actual conditions,stable static slope angle,stable dynamic slope angle and Q-slope stable angle withPoF=1% andPoF=50%,respectively.Thus,field conditions of all the studied slopes must be considered along with these classifications investigation to define the most critical slopes present in the study area.

Fig.12.Comparative slope angles of actual,stable static,stable dynamic and PoF=1% and PoF=50%.

Table 11Comparative slope stability obtained from various rock mass classifications methods.

Based on the various assessments through empirical classifications for the above 14 rock-cut slopes,different relationships have been established between rock mass classification systems (see Fig.13).Six different correlation plots,i.e.RMR-SSR,RMR-GSI,SSR-GSI,Q-slope-GSI,Q-slope-RMR,Q-slope-SSR,have been plotted.Among these six plots,RMR-SSR and RMR-GSI have good correlation coefficient (R2) of 0.815 and 0.6866,respectively.The good correlation between RMR and SSR is that both classifications give maximum rating to the strength of the rock in their definitions.The linear relationship between RMR and GSI has been developed(e.g.Hoek et al.,1995).The empirical equations for these two plots are:

Fig.13.Different rock mass classification system with their R2 values.

The other five correlation plots have not given good correlation coefficient (R2) values.This can be due to the limited dataset generated during this study.

The main limitation of the study is that none of the existing classifications considers all the important slope stability parameters.Hence the developed method provides better and more reliable applicability for evaluating a wider range of slope conditions.Another limitation is that it uses only empirical classifications which mostly have the value of all parameters in a certain range,and it can sometimes provide incorrect interpretations.This study will help in infrastructure and road development in the area by identifying the most critical slopes of the region.Since this study also incorporates the effect of seismicity on the slopes,it provides betters understanding of slopes both under static and dynamic situations as seismicity in the Himalayas.

6.Conclusions

The aim of the study is to assess the stability of 14 major slopes along the NH 1-A in the Ramban district in North Western Himalayas,which is quite dynamic and prone to sliding.Various rock mass classification systems and kinematic analyses were carried out to determine stable zones and their sensitivity to sliding under the current situation.The analysis showed that seven slopes have planar failure,one has toppling failure,and six have wedge failure.Toppling and wedge failures occur mainly in granitic gneiss,and planer failure occurs in slate,phyllite and schist rock types.The slopes stability is mainly influenced by one or two discontinuity planes.The RMRbasicvalues range from 37 to 74,indicating poor to good rock mass quality.Field investigations were carried out to calculate the several modification values of GSI to assess the slopes condition.SMR and CoSMR range from unstable to partially stable condition while SSR values are calculated under dynamic and static conditions.The Q-slope approach also shows that eight slopes are stable,four slopes are uncertain,and two slopes are unstable.An empirical equation between RMR and SSR with good correlation coefficientR2value of 0.815 was established.The results indicate that most slopes in the study area are unstable and are very prone to failure.The findings provide a reliable basis for identifying the critical slopes on which further numerical analysis can be done.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The authors like to acknowledge the National Highway Authority of India,Ramban,for technical discussion and assistance during fieldwork.