## Probabilistic and Sensitivity Investigation for the Hill Slopes in Uttarakhand, Lesser Himalaya, India

**Ashutosh kainthola**^{1,}, **Dhananjai verma**^{2}, **T N Singh**^{1}

^{1}Department of Earth Sciences, Indian Institute of Technology Bombay, Mumbai, India

^{2}Geological Survey of India, Su: Gujarat, Gandhinagar, India

### Abstract

Himalayas is one of most seismically active mountain chain in the world. Landsides and the mass wasting are a prevalent phenomenon in this region. There are a considerable number of human populations living in the hilly regions which are under a constant threat of hill slope collapse. The stability assessment of these hills is one of the vital steps to mitigate the danger to this natural calamity. The deterministic factor of safety calculations have been traditionally used for the hazard evaluation of the hill slopes. For the present study, two hill slopes, Chandaak and Chhera, have been selected for probabilistic and sensitivity analysis. These areas were analyzed using limit equilibrium method for calculation of factor of safety and probability of failure. The factors of safety were calculated using Bishop's method of slice. The analysis was done for both dry and saturated conditions. At the same time the sensitivity of each parameter on the factor of safety was analyzed. The probability analysis of these areas was done using Monte-Carlo simulation which uses randomly selected discrete values of each variable from their probability distribution. In both the hill slopes the rock mass has varied weathering grade, ranging from highly weathered to moderately weathered. Seasonal variation in the rock mass strength was accounted for in the study. Chhera hill were quantified to have high FOS in both cases (dry and saturated) as compared to the Chahdaak hill, making than more vulnerable.

### At a glance: Figures

**Keywords:** ** **Himalayan, Rock Mechanics, slope stability, numerical simulation, sensitivity analysis

*American Journal of Numerical Analysis*, 2013 1 (1),
pp 8-14.

DOI: 10.12691/ajna-1-1-2

Received September 23, 2013; Revised November 06, 2013; Accepted November 08, 2013

**Copyright:**© 2013 Science and Education Publishing. All Rights Reserved.

### Cite this article:

- kainthola, Ashutosh, Dhananjai verma, and T N Singh. "Probabilistic and Sensitivity Investigation for the Hill Slopes in Uttarakhand, Lesser Himalaya, India."
*American Journal of Numerical Analysis*1.1 (2013): 8-14.

- kainthola, A. , verma, D. , & Singh, T. N. (2013). Probabilistic and Sensitivity Investigation for the Hill Slopes in Uttarakhand, Lesser Himalaya, India.
*American Journal of Numerical Analysis*,*1*(1), 8-14.

- kainthola, Ashutosh, Dhananjai verma, and T N Singh. "Probabilistic and Sensitivity Investigation for the Hill Slopes in Uttarakhand, Lesser Himalaya, India."
*American Journal of Numerical Analysis*1, no. 1 (2013): 8-14.

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### 1. Introduction

Himalayas are a seismically active young mountain belt. The occurrence of landsides and other types of mass wasting are quite a widespread phenomenon in this region. A large number of populations living in the hilly region are under the constant threat of the landslides. The swift growth in population and the small scale miming activities further up the risk to the life of people in these areas. The stability assessment of these hills is one of the steps to mitigate the danger to this natural calamity. The deterministic factor of safety calculations have been traditionally used for the threat evaluation of the hill slopes. The chief demerit of these calculations is that they use a single value for the whole rock mass other than the fact that the rock mass by nature are inherently heterogeneous and can have different physic-mechanical properties in a span of few meters (Singh et al., ^{[1]}; Sarkar et al., ^{[2]}; and Verma et al., ^{[3]}). It is now widely accepted that deterministic methods for analyzing slope stability do not allow for the uncertainty and variability of the strength parameters of soil and rock masses, often noted in the literature, slope failures may occur even though the calculated factor of safety is greater than unity (Verma et al., ^{[4]}; Kainthola et al., ^{[5, 6]}). The variation and uncertainty in the geotechnical data for slope stability appraisal may occur as scattered values for discontinuity orientations and geometries such as discontinuity trace length and spacing, and in laboratory or in situ test results (Park et al., ^{[7]}). Previously, work has been done to overcome bound this uncertainty (Baecher ^{[8]}; Einstein and Baecher ^{[9]}).

The probabilistic analys is one of the techniques which are being employed to overcome the uncertainties in the stability assessments of both rock and soil slopes. The probabilistic analysis considers the ambiguity in geotechnical parameters and results (Kainthola et al., ^{[5, 6, 10, 11]}). In the probabilistic method, the analysis carries out the analysis of random properties of the rock mass. Random properties of input parameters used for probabilistic analysis and are obtained by statistical evaluation of available geological and geotechnical data. Subsequently, using random properties of input parameters determined previously, probability of failure is evaluated (Park et al., ^{[1, 7]}). Limited or uncertain data can be utilized in analysis and judgments can be quantified (Whittlestone et al., ^{[12]}). Probabilistic risk analysis is used in an effort to overcome the subjective judgment of slope stability parameters and resultant, single value, factor of safety. The subjectivity and uncertainties are due to the spatial variability of the material properties and their measurements, as well as uncertainties in reliability of the hypothesis carried out to approximate the mechanical behavior of the geo-material. Monte Carlo simulation is used to generate random numbers from which each of the variable values is assigned. It is required that the distribution of all the input variables is either known or assumed. The factor of safety can be assessed to determine the probability of failure. The hill slopes were also analyzed for sensitivity for each of the input parameters to see the change of which geo-mechanical factor has the most influence in the factor of safety of the hill slopes. The analyses were done using Limit equilibrium method. In limit analysis, the objective is generally to determine the collapse load; whereas the factor of safety is calculated in method of slices. The methods of slices are based on the limit equilibrium theory. Various methods of slices were proposed in the 1950s and 1960s. These methods were proposed with different assumptions on the shape of slip surfaces and the interslice forces. The most commonly used methods of slices comprised the Fellenius method, the methods of Bishop ^{[13]}, Janbu ^{[14]}, Morgenstern & Price ^{[15]} and Spencer ^{[16]}. Other efforts (Chen & Morgenstern ^{[17]}; Chen & Shao ^{[18]}; Chen ^{[19]}) were made in the 1980s to develop efficient and accurate optimizing techniques for the solution of the critical slip surface and the minimum factor of safety.

In the present investigation two 500m high hill slopes, Chandaak and Chhera in Pithoragarh, lesser Himalaya, India where small scale mining of magnesite is also taking place, were analyzed for the probability of failure through probabilistic and sensitivity analysis using limit equilibrium method. The Chandaak hill slope is composed of magnesite veins containing dolostone while the Chhera hill slope is predominantly made up of phyllites. In both the hill slopes the rock mass has varied weathering grade, ranging from highly weathered to moderately weathered. The two hills slopes were chosen due to their proximity to human settlements and mining activities. Previously, during the rainy season, some minor slope failure activities had taken place in the area which were reported in the local media. The analysis was carried out for both dry and saturated condition accounting for the seasonal variation in the rock mass strength.

### 2. Geology of the Area

The present investigation was undertaken to study the instability of hill slopes in and around Pithoragarh District, Uttarkhand, India in the lesser Himalaya. The area around Pithoragarh exposes the rocks of Gangolihat formation and the Berinag quartzite. The rocks exhibit a variation in its strike from NNE-SSW to NE-SW direction with low to moderate amount of dip mainly towards northern direction. The Pithoragarh Formation present in the study area consist of five members namely – the Thalkedar Limestone, Sor Slate, Unnamed member, Gangolihat Dolomite and lastely the Karlani Slates in the Pithoragarh-Bageshwar area while in the Tejam-Kapkot area the five members are Tejam Dolomite, Dewalchaura Slate, Balgad Dolomite, Kapkot Dolomite and finally Saline Slate. The Pithoragarh / Tejam Formation of Upper Precambrian to Lower Palaeozoic age represent a calcareous facies. The uppermost Berinag Formation in the area consists of a single member, Berinag Quartzite representing an arenaceousfacies of Devonian to Lower Carboniferous age (Valdiya ^{[20]}).

**2.1. Field Investigation**

The hill slopes of Chandaak and Chhera were visited for collection for field data and sampling (Figure A&B). The hill slopes were investigated for average slope angle, slope height 502m & 32° for Chandaak area and 500m & 38° for Chhera area. The discontinuity orientation, persistence, and spacing in the rock mass were also measured which were used in the estimation of the Geological strength Index (GSI) of the hill slopes (Hoek et al. ^{[21]}). 10 to 20 GSI readings were taken for each hill slope.

**Figure 1.**A) Debris flow near Chandaak area, B) A planar rock failure near Chhera area

The representative rock blocks collected from different vulnerable locations were brought and specimens of different geometrical shapes were prepared for performing the different test to evaluate instability. The tests were carried out as per International Society of Rock Mechanics (ISRM) suggesting methods (ISRM, ^{[22]}). The 10 samples were tested for their uniaxial compressive strength and unit weight. The laboratory tests were conducted for both dry and saturated conditions. The samples were kept under water for 72 hours to measure the reduction in their strength after the saturation.

**2.2. Random Variables**

As input parameters for the model, uniaxial compressive strength (UCS), GSI and unit weight of the rock mass don’t have a single value but are rather scattered, they were used as random variable for the probability and sensitivity analysis (Table 1). The normal probability distribution function was used for the variables. The normal PDF was used as the maximum number of data was within three times the standard deviation. The analysis was done using Limit equilibrium method using GSI, intact rock constant (m_{i}), UCS, disturbance factor (D) (Hoek ^{[21]}). As small scale mining is taking place in the area, a disturbance factor of 0.7 was taken for both the areas studied. The intact rock constant (m_{i}) value of 9 for Dolostone and 7 for Phyllite was used for the analysis as suggested by (Hoek ^{[21]}). The GSI readings were taken at the most critical sites and were averaged out. The mean, standard deviation, and relative maximum and minimum values were calculated for the scattered input parameters. The relative minimum and maximum values indicates the maximum and minimum distance from the mean value.

**Figure 2.**

**A) LEM simulation for Chandaakarea (Dry). B) FOS (Bishop simplified) v/s Relative frequency Chandaak area (Dry)**

**Figure 3.**Sensitivity plot chandaak dry

**Figure 4.**

**A) LEM simulation for Chandaak area (saturated), B) FOS (Bishop simplified) v/s Relative frequency Chandaak area (Saturated)**

**Figure 5.**Sensitivity plot Chandaak (Saturated)

**Figure 6.**A) LEM simulation for Chhera area (dry), B) FOS (Bishop simplified) v/s Relative frequency Chhera area (Dry)

**2.3. Limit Equilibrium Analysis**

The two hill slopes, Chandaak and Chhera were analyzed using limit equilibrium method for calculation of factor of safety and probability of failure. At the same time the sensitivity of each parameter on the factor of safety was analyzed. The probability analysis was done using Monte-Carlo simulation which uses randomly selected discrete values of each variable from their probability distribution. A sensitivity analysis indicates which input parameters may be critical tothe assessment of slope stability, and which input parameters are less important (Singh et al., ^{[1]} and Kainthola ^{[5, 6]}). A Sensitivity analysis involves the variation of individual variables between minimum and maximum values and a sensitivity analysis is performed on only one variable at a time while probabilistic analysis uses the values of all the random variables. The factor of safety was calculated using Bishop's method of slice. The analysis was done for both dry and saturated conditions. During the field visit few wet patches and water springs were observed which were used to infer information regarding the ground water condition of the area. The water table was also raised by 2-3 meters for saturated conditions with subsequent reduction in their UCS values (Table 1).

**Figure 7.**Sensitivity plot Chhera (Dry)

**Figure 8.**

**A) LEM simulation for Chhera area (saturated), B) FOS (Bishop simplified) vs Relative frequency Chhera area (saturated)**

**Figure 9**

**.**Sensitivity plot Chhera (Saturated)

### 3. Results and Discussion

The probabilistic analysis is one of the techniques which are being employed to overcome the uncertainties in the stability assessments of both rock and soil slopes. In the probabilistic method, the analysis is carried out on the random properties of the rock mass. Random properties as input parameters have been used for probabilistic analysis and are obtained by statistical evaluation of available geological and geotechnical data from laboratory as well as field. The results have taken into account the uncertainties of the rock mass. The chandaak hills composed of dolostone had relatively lower strength compared to phylliticchhera hill. There was a significant reduction in strength parameters under the saturated conditions. For all the test results, GSI values were shown to have been most sensitive with respect to the FOS. While the unit weigh of the rock material was least sensitive towards the FOS. The mean FOS yielded was lower as compared to the deterministic values. The hill slopes of Chandaak area become quite critical under the saturated state (Table 2). The chief attribute for the lowering in strength and factor of safety for the Chandaak area is due to the high porosity of the dolostones which are rock composed of magnesian and calcium carbonates of sedimentary origin. On the other hand, the reduction in safety factor for Chhera is considerable less as the porosity of phyllites is quite less as compared to dolostones.

#### Table 2. Results of the probabilistic analysis for the two areas using both Bishop's method and Fellenius method

The analysis was carried out to get the FOS (deterministic), probability of failure (PF) and reliability index (normal and lognormal) of the hill slope. The probability of failure is described as equal to the number of analyses with safety factor less than 1, divided by the total Number of Samples. Reliability index is also used as a parameter to assess the stability of slopes. The Reliability Index (RI)indicates of the number of standard deviations which separate the Mean Safety Factor from the critical safety factor of 1 (Rocscience ^{[23]}). Table 2 depicts the investigation results for the hill slopes under both dry and saturated conditions. It is clearly visible that the FOS, OF and RI values using Fellenius method were lower as compared to the Bishop’s method. The lower results may be attributed to the assumptions in the Bishops method. As can be see from Table 2, the probability of failure (PF) inceases by 80.5 and 72.8 percentage from dry to Saturated method using Bishop’s and fellenius method , respectively. While for the Chhera area the PF shows an exceptional increase of 200 to 148 percentage percentage from dry to Saturated method using Bishop’s and fellenius method , respectively, although the hill slope is relatively stable as compared to the Chandaak hill slope. The study also demonstrates that the factor of safety for any analysis yielded by Bishop’s methods is higher as compared to the FOS achieved by Fellenius method (Table 2). The values achieved using limit equilibrium method are conservative as compared to finite element methods ( Kainthola et al., 2012), hence though the FOS values deem them relatively stable, the slopes are relatively higher probability of failure.

### 4. Conclusion

In the present investigation two 500m high hill slopes, Chandaak and Chhera in Pithoragarh, lesser Himalaya, India where small scale mining of magnesite is also taking place, were analyzed for the probability of failure through probabilistic and sensitivity analysis using limit equilibrium method. The Chandaak hill slope is composed of magnesite veins containing dolostone while the Chhera hill slope is predominantly made up of phyllites. In both the hill slopes the rock mass has varied weathering grade, ranging from highly weathered to moderately weathered. The analysis was carried out for both dry and saturated condition accounting for the seasonal variation in the rock mass strength. In the both case i.e in dry as well as saturated, Chhera hill were computed to have higherFOS as compared to the Chahdaak hill (Table 2). Also the probability of failure of Chhera hill is very less as compared to Chandaak, which becomes wuite critical under saturated conditions. Though the PF of total hill slope collapse is low but the occurrence of local failures can’t be denied which have been reported from the area.

### References

[1] | Rajesh Singh, R. K. Umrao and T.N. Singh, 2012, Probabilistic analysis of slope in Amiyan landslide area, Uttarakhand. Geomatics, Natural Hazards and Risk. | ||

In article | |||

[2] | K. Sarkar, T.N.Singh and A.K. Verma,2012, A numerical simulation of landslide-prone slope in Himalayan region - a case study, International Journal of Arabian Geosciences, 5, 73-81. | ||

In article | CrossRef | ||

[3] | D. Verma, D.Choudhury, P. G. Ranjith and T. N. Singh, 2012, Scale effect on strength and failure modes of open pit cut slope of Wardha Valley coalfield in India, In Geo-Congress 2012: State of the Art and Practice in Geotechnical Engineering, Geotechnical Special Publication, No. 225, ASCE, Edited by R. D. Hryciw, A. A. Zekkos and N. Yesiller, Reston, VA, USA, 576-585. | ||

In article | |||

[4] | D. Verma, R. Thareja, A. Kainthola, and T. N. Singh, 2011, Evaluation of open pit mine slope stability analysis, International Journal of Earth Sciences and Engineering, 4(4), 590-600. | ||

In article | |||

[5] | Kainthola, A., Verma, D., Singh, T. N. (2011) Computational analysis for the Stability of Black Cotton Soil Bench in an Open Cast Coal Mine in Wardha Valley Coal Field, Maharashtra, Int. Jour. of econ. Env. Geol. 2(1), 11-28. | ||

In article | |||

[6] | Kainthola, A., P. K. Singh, A. B. Wasnik, M. Sazid and T. N. Singh, (2012) Finite Element Analysis of Road Cut Slopes using Hoek & Brown Failure Criterion, International Journal of Earth Sciences and Engineering, 5(5),1100-1109. | ||

In article | |||

[7] | Hyuck-Jin Parka,T, Terry R. Westb, Ik Woo.( 2005). Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40, Western North Carolina, USA, Engineering Geology , 79, 230-250. | ||

In article | CrossRef | ||

[8] | Baecher, G.B.(1983). Statistical analysis of rock mass fracturing.J.Math. Geol. 15 (2), 329-347. | ||

In article | CrossRef | ||

[9] | Einstein, H.H., Baecher, G.B. (1983). Probabilistic and statistical methods in engineering geology; specific methods and examples-Part 1: exploration. Rock Mech. Rock Eng. 16, 39-72. | ||

In article | CrossRef | ||

[10] | Kainthola, A., Verma, D., S S Gupte, T N Singh,2011, A coal mine dump stability analysis-A case study, International journal of Geomaterial, 1:1-13. | ||

In article | |||

[11] | Kainthola, A. Verma, D., S S Gupte, T N Singh,2011, Analysis of failed dump slope using limit equilibrium approach, Mining Engineers’ Journal, 12 (12): 28-32. | ||

In article | |||

[12] | Whittlestone, A.P., Johnson, J.D., Rogers, M.E., and Pine, R.J. (1995). Probabilistic risk analysis of slope stability. Trans. Instn. Min. Metall. ( Scct.A: Mining Industry), 101,149-158. | ||

In article | |||

[13] | Bishop, A.W.(1955). The use of the slip circle in the stability analysis of slopes.Geotechnique 5(1), 7-17. | ||

In article | CrossRef | ||

[14] | Janbu, N. (1957). Earth pressure and bearing capacity calculations by generalized procedure of slices. Proc. 4^{th}Int.Conf. Soil. Mech. FdnEngng, 2, 207-212. London: Butterworths. | ||

In article | |||

[15] | Morgenstern, N.R. & Price, V.E. (1965). The analysis of the stability of general slip surface.Geotechnique 15(1), 79-93. | ||

In article | CrossRef | ||

[16] | Spencer, E. (1967). A method of analysis of the stability of embankments assuming parallel interslices forces. Geotechnique 17(1), 11-26. | ||

In article | CrossRef | ||

[17] | Chen, Z.Y. & Morgenstern, N.R. (1983). Extensions to the generalized method of slices for stability analysis.Can.Geotech.J. 20(1),104-119. | ||

In article | CrossRef | ||

[18] | Chen, Z.Y. & Shao, C.M. (1988). Evaluation of minimum factor of safety in slope stability analysis.Can.Geotech.J. 25 (4), 735-748. | ||

In article | CrossRef | ||

[19] | Chen, Z.Y. (1992). Random trials used in determining global minimum factor of safety. Can.Geotech.J. 29 (1), 225-233. | ||

In article | CrossRef | ||

[20] | Valdiya, K.S. (1980). Geology of Kumaun Lesser Himalaya Wadia Institute of Himalayan Geology, Dehradun, India, 21p. | ||

In article | PubMed | ||

[21] | Hoek, E., Carranza-Torres, C. and Corkum, B. (2002) Hoek–Brown failure criterion-2002 ed. In: Proc. of the 5th North Am. Rock Mech. Symp. and 17th Tunnelling Association of Canada Conference: NARMS-TAC, University of Toronto, 267-271. | ||

In article | |||

[22] | ISRM .(1979). Suggested methods for determining the uniaxial compressive strength and deformability of rock materials, Int J Rock Mech Min Sci. 16 (2), 135-140. | ||

In article | |||

[23] | Rocscience “A new area in slope stability analysis: Shear strength reduction finite element technique.” RocNews. 2004. | ||

In article | |||