AN EVALUATION OF ROCK SLOPE STABILITY USING LIMIT ...

J. SE Asian Appl. Geol., Jul–Dec 2014, Vol. 6(2), pp. 79–88

AN EVALUATION OF ROCK SLOPE STABILITYUSING LIMIT EQUILIBRIUM ANALYSES

Faridha Aprilia and I Gde Budi Indrawan*

Department of Geological Engineering, Faculty of Engineering, Universitas Gadjah Mada, Indonesia

Abstract

The stability of rock slopes is controlled by severalfactors, such as the intact rock strength, disconti-nuity characteristics, groundwater condition, andslope geometry. Limit equilibrium (LE) analyseshave been commonly used in geotechnical practiceto evaluate the stability of rock slopes. A number ofmethods of LE analyses, ranging from simple to so-phisticated methods, have been developed. This pa-per presents stability analyses of rock slopes at theBatu Hijau open mine in Sumbawa Barat using var-ious methods of LE analyses. The LE analyses wereconducted at three cross sections of the northern wallof the open mine using the Bishop Simplified, JanbuSimplified, Janbu Generalised, and General LimitEquilibrium (GLE) methods in Slide slope stabilitypackage. In addition, a Plane Failure (PF) analysiswas performed manually. Shear strength data of thediscontinuity planes used in the LE analyses wereobtained from back analyses of previous rock slopefailures. The LE analysis results showed that therock slopes were likely to have shallow non-circularcritical failure surfaces. The factor of safety (Fs) val-ues obtained from the Bishop Simplified, Janbu Sim-plified, Janbu Generalised, and GLE methods werefound to be similar, while the Fs values obtained fromthe PF method were higher than those obtained fromthe more rigorous methods.Keywords: Batu Hijau mine, Bishop Simplified,Janbu Simplified, Janbu Generalised, limit equilib-rium analyses, general limit equilibrium, rock slopestability, plane failure.

*Corresponding author: IG.B. INDRAWAN, Depart-ment of Geological Engineering, Faculty of Engineer-ing, Universitas Gadjah Mada, Indonesia. E-mail: [email protected]

1 Introduction

Rock slopes may fail in various modes, suchas plane, wedge, toppling, or circular failure(Hoek and Bray, 1981). Stability of rock slopescan be analysed by manual calculation employ-ing simple equations and charts, spreadsheetsoftware, and computer programs. LE meth-ods have been commonly used in stability as-sessment of soil and rock slopes. The meth-ods were developed based on the principles ofstatic equilibrium (Ching and Fredlund, 1984).For rock slope stability analyses, the methodsanalyse the equilibrium of a potentially unsta-ble rock mass by comparing the forces leadingthe rock mass to fail (i.e., driving forces, Df)along the failure surface and the forces resist-ing the movement of the rock mass (i.e., resist-ing forces (R f ) (Figure 1). The ratio of R f to D fis called the factor of safety against sliding (Fs),as formulated in Equation (1). A slope is con-sidered to be in the state of equilibrium if the Fsequals to 1.

Fs =R f

D f=

Rc + Rφ

W sin ψ=

cA + W cos ψ tan φ

W sin ψ(1)

where: Rc = cohesion force; c = cohesionof failure surface; R = friction force; φ = an-gle of internal friction of failure surface; A =rock mass area; W = rock mass weight; ψ =rock slope angle. A number of methods ofLE analyses have been developed. The meth-ods vary with respect to slope failure modes(plane, wedge, toppling, or circular failure)and the assumptions and equilibrium condi-tions adopted in order to achieve a determi-nate solution. Some methods consider only

79

APRILIA and INDRAWAN

Figure 1: Forces acting on a failure surfaceof rock slope (Gonzalez de Vallejo and Ferrer,2011).

normal force, while the other methods con-sider both normal and shear forces acting onthe slices. Furthermore, some methods con-sider only force or moment equilibrium con-dition, while the other methods satisfy bothequilibrium conditions. The Bishop Simplified,Janbu Simplified, Janbu Generalised, and GLEmethods have been commonly used in the LEanalyses (e.g., Fredlund et al., 1981; Ching andFredlund, 1984). Bishop’s Simplified methodis based on the moment equilibrium condi-tion, while the Janbu Simplified and Gener-alised methods are based on the force equilib-rium condition. The GLE method satisfies bothforce and moment equilibrium conditions inthe formulation (Krahn, 2004). The Batu Hijauopen mine is one of the largest gold and coppermines in Indonesia operated by PT. NewmontNusa Tenggara. A number of rock slope fail-ures due to weak rock mass condition associ-ated with high degree of rock fractures has beenoccurred since the beginning of the mine oper-ation in early 2000 (Adriansyah, 2012). Evalu-ation of rock slope stability is performed rou-tinely to ensure the safety and optimum of min-ing activities. This paper presents stability anal-yses of rock slopes at the Batu Hijau open minein Sumbawa Barat using the Bishop Simplified,Janbu Simplified, Janbu Generalised, and GLE

methods. In addition, a simple LE analysis,as described in Eq.(1), called herein Plane Fail-ure (PF) analysis, was also performed to verifywhether or not a simpler LE method could re-sult in a factor of safety as realistic as the morerigorous LE methods, which satisfied the New-tonian force principles at the interslices (Fred-lund and Krahn, 1977). Results of the rock slopestability analyses using the LE methods are pre-sented and compared and the differences be-tween the analysis results are highlighted.

2 Geology and rock engineering proper-ties

The research area is mainly composed ofhighly fractured grey volcanic lithic breccia andquartzdiorite (Figure 2). The volcanic brecciasand quartz diorite have unit weights of 27 and26 kN/m3, respectively (PT. Newmont NusaTenggara, 2013). The geological structures de-veloped in the rock mass in the research areaare mainly northwest-southeast and northeast-southwest oriented joints and faults, whichare products of tectonic and magma intrusion(Figure 3 and Figure 4). The rock mass rating(RMR) values of the rock slopes range from 20to 70 and are dominated by 30 to 40 (PT. New-mont Nusa Tenggara, 2013), indicating a poorrock mass quality (Bieniawski, 1989).

3 Methodology

The LE analyses using the Bishop Simplified,Janbu Simplified, Janbu Generalised, and GLEmethods were performed in Slide slope stabil-ity package (Rocscience, Inc.). In the LE analy-ses, the strength of joints- and faults-filled ma-terials, which were relatively homogenous, wasmodeled by Mohr-Coulomb criterion, and thestrength of rock masses was modeled by theanisotropic strength function. A non-circulartype of failure surfaces was assigned in allmethods as kinematic analyses of discontinu-ity measurements in the field indicated that therock slopes would likely not fail in a circularmode (Aprilia, 2014). The rock masses con-sisting the slopes were grouped into domains,where each domain represented a rock mass

80 © 2014 Department of Geological Engineering, Gadjah Mada University

AN EVALUATION OF ROCK SLOPE STABILITY USING LIMIT EQUILIBRIUM ANALYSES

Figure 2: Geological map of research area (PT. Newmont Nusa Tenggara, 2013).

Figure 3: Major geological structures in research area (PT. Newmont Nusa Tenggara, 2013).

© 2014 Department of Geological Engineering, Gadjah Mada University 81


Figure 4: Joints and faults observed in research area.

having similar lithology, strength, and geologicstructure. Disturbance factor (D) due to blast-ing effects was applied to the rock masses basedon the depth from the ground surface. D val-ues equal to 1, 0.7, and 0.5 were assigned forthe rock masses at 0-30 m, 30-50 m, and morethan 50 m depths, respectively.

The LE analyses using PF method was per-formed manually. The Fs was calculated bycomparing the resisting forces and drivingforces acting on the failure surfaces, as de-scribed in Equation (1). To facilitate the com-putation, the potentially unstable rock massesabove the assumed failure surfaces at the allcross sections, including the rock masses aboveand below the ramps at the cross sections B andC, were divided into several blocks of slicesfollowing the angles of the failure surfaces. Thedriving and resisting forces from rock massblocks upslope were taken into account in thecalculation of driving and resisting forces ofrock mass blocks downslope. The critical fail-ure surfaces of rock masses for LE analysesusing the PF method were drawn based onthose obtained from the LE analyses usingthe GLE method. The critical failure surfacesobtained from the Bishop Simplified, JanbuSimplified, Janbu Generalised, and GLE meth-ods appeared to be relatively similar to eachother, as presented below.

The LE analyses were performed at threecross sections A, B, and C (Figure 5). Eachslope of the cross sections B and C is essen-tially divided into two parts, which are belowand above the ramp. Meanwhile, the slope of

the cross section A is a continuous slope with-out any ramp. Geometries of the rock slopes ofthe cross sections A, B, and C assigned for theLE analyses using the Bishop Simplified, andJanbu Simplified and Generalised, and GLEmethods are shown in Figure 6, while geometryof the cross section A and typical forces actingon rock mass blocks above failure surfaces as-signed in the PF method are shown in Figure 7.The cohesion (c) and internal friction angle (φ)values of potential failure surfaces, which werelikely controlled by existence of joints and faultsin the rock mass, were obtained by performingback analyses to the previous rock slope fail-ures F#X1, F#X2 and F#X3 located near the re-spective cross sections (Figure 5). In the backanalyses, as the faults observed in the field weretypically open, the fault planes were conserva-tively assumed to have c = 0 kPa and as thefaults were typically filled with clay materials,the fault planes were assumed to have φ = 20°,as described in Hoek and Bray (1981). The backanalysis of each slope failure was performed intwo steps. In the first step, the c value for thejoint set was initially set to 0 kPa to search forthe φ value for the maximum φ value for thejoint set when the Fs equals to 1 or close to1, indicating slope failure. In the second stepor once the φ value for the maximum φ valuefor the joint set were obtained, the c value forthe joint set was increased and φ value for thejoint set was decreased until the condition of Fsequals to or close to 1 was attained. The final cand φ values for the planes of the joint sets werethen used in the LE analyses.



Figure 5: Locations of rock slope failures and cross sections for slope stability analyses.

The influence of pore water pressure changesdue to rain water infiltration on the rock slopestability was not considered in all LE analy-ses. As the ground water level was consider-ably deep (Figure 6) and would likely not in-fluence the calculation results, the influence ofpore water pressure was not considered in thePF method. Adopting stability conditions byPriest and Brown (1983), the slopes were con-sidered to be in equilibrium, critical, and safeconditions when Fs = 1, 1 < Fs < 1.2 and Fs ≥1.2, respectively.

4 Results and discussions

Results of the back analyses of the previous rockslope failures F#X1, F#X2 and F#X3 are listed inTable 1. When the slopes failed, the joint planeswere estimated to have c values ranging from57 kPa to 85 kPa and φ values ranging from 25°to 27°. The estimated c values of the joint planesthat were higher than those of the fault planeswere considered to be reasonable as the sepa-ration (aperture) of the joint planes was typi-

Table 1: Back analysis results of slope failures.

cally small or was not as large as that of the faultplanes.

Figure 9 to Figure 11 show LE analysis resultsof cross sections A, B, and C using the BishopSimplified, Janbu Simplified, Janbu Gener-alised, and GLE methods. The non-circularcritical failure surfaces predicted by all meth-ods were relatively shallow (i.e., less than 30m below the slope surface) and located in theuppermost layer of the rock mass domains. Atthe cross sections B and C, the critical failuresurfaces were developed above and below theramps. The Fs values for the critical failuresurfaces analysed using all methods are listedin Table 2. In general, the Bishop Simplified,



Figure 6: Geometries of cross sections A (top), B(middle), and C (bottom) assigned in the BishopSimplified, Janbu Simplified and Generalised,and GLE methods.

Figure 7: Geometry of cross section A andforces acting on rock mass blocks above failuresurfaces assigned in PF method.

Janbu Simplified and General, and GLE meth-ods resulted in similar Fs values. This is inagreement with the slope stability analysis re-sults obtained by Ching and Fredlund (1984),who concluded that the difference between re-sults of slope stability analyses using BishopSimplified, Janbu Simplified and Generalisedmethods were insignificant for shallow failuresurfaces. As each method of the LE analyses isessentially a special case of the GLE (Fredlundet al., 1981), the Fs values obtained from theGLE method are expected to be similar to thoseof the Bishop Simplified, Janbu Simplified andGeneralised methods. Table 2 also shows thatthe PF method results in Fs values higher thanthe other methods of the LE analyses. The dis-crepancy of the analysis results was expectedas, among any others, the side forces at eachslice were not considered in the PF method.The assumed failure surfaces in the PF methodwere likely not the critical failure surfaces (hav-ing the minimum Fs). Although analysis resultsobtained from the PF method are relatively farfrom those from the more rigorous methods,the PF method can be used for a preliminaryassessment of slope stability.

The LE analyses using the Bishop, JanbuSimplified and Generalised, and GLE methodsshow that the slopes at the all cross sectionshad Fs values between 1 and 1.2 and were es-sentially in a critical condition, according to



Table 2: Results of LE analyses.

the slope stability conditions proposed by Priestand Brown (1983). Although the calculation re-sults showed that the slopes were in a criticalcondition, the slopes in the field appeared to bestable. The discrepancy between the analysisresults and the field conditions may be partlydue to the low estimated shear strength param-eters (c and φ) of the discontinuity (fault andjoint) planes. More reasonable shear strengthparameters obtained from direct measurementswill likely result in Fs values that are closer tothe field conditions.

5 Conclusions

The stability of rock slopes at the Batu Hijaumine was evaluated using the Bishop Simpli-fied, Janbu Simplified, Janbu Geralised, andGLE methods of the LE analyses. The rockslopes were likely to have shallow non-circularcritical failure surfaces located in the upper-most layer of the rock mass domains. The Fsvalues obtained from the Bishop Simplified,Janbu Simplified, Janbu Geralised, and GLEmethods were found to be similar, while theFs values obtained from the PF method werehigher than those obtained from the BishopSimplified, Janbu Simplified, Janbu Gener-alised, and GLE methods.

Acknowledgement

The research was supported by Departmentof Geological Engineering Universitas GadjahMada and PT. Newmont Nusa Tenggara. Thefirst author wishes to thank PT. Newmont NusaTenggara for the opportunity to do the research.The assistance of Mrs. Adriansyah and KhatibSyarbini of Department of Geotechnical and

Hydrogeology of PT. Newmont Nusa Tenggarais gratefully acknowledged.

References

Adriansyah, Y., 2013. Prediksi LongsorBerdasarkan Data Hasil Pemantauan Perg-erakan Lereng di Tambang Batu Hijau – PT.Newmont Nusa Tenggara (Studi Kasus dariBeberapa Longsoran). Seminar Nasional Ge-omekanika II, Peran Geomekanika dalamPembangunan Sektor Pertambangan, Per-minyakan dan Infrastruktur, Aston PrimeraPasteur, Bandung, Indonesia.

Aprilia, F. 2014. Analisis Tipe Longsor danKestabilan Lereng berdasarkan OrientasiStruktur di Dinding Utara Tambang Batu Hi-jau, Sumbawa Barat. Skripsi. Jurusan TeknikGeologi, Fakultas Teknik, Universitas GadjahMada (unpublished).

Bieniawski, Z.T. 1989. Engineering Rock MassClassification. John Wiley & Sons, New York.

Ching, R., K., H. and Fredlund, D.G. 1984.Quantitative Comparison of Limit Equilib-rium Methods of Slices. Proceedings of theFourth International Symposium on Land-slides, Toronto, Canada, pp. 373-379.

Fredlund, D.G. and Krahn, J. 1977. Compari-son of Slope Stability Methods of Analysis.Canadian Geotechnical Journal, Vol. 14, pp.429-439.

Fredlund, D.G., Krahn, J., and Pufahl, D.E.1981. The Relationship between Limit Equi-librium Slope Stability Methods. In Proceed-ings of the 10th Conference of the Interna-tional Society for Soil Mechanics and Founda-tion Engineering (ISSMFE), Stockholm, Swe-den, Vol. 3, pp. 409–416.

Gonzalez de Vallejo, L. I. and Ferrer, M. 2011.



Figure 8: LE analysis results of cross sections A(top), B (middle), and C (bottom) using BishopSimplified method.

Figure 9: LE analysis results of cross sections A(top), B (middle), and C (bottom) using JanbuSimplified method.



Figure 10: LE analysis results of cross sectionsA (top), B (middle), and C (bottom) using JanbuGeneralised method.

Figure 11: LE analysis results of cross sectionsA (top), B (middle), and C (bottom) using GLEmethod.



Geological Engineering. Leiden, Nether-lands: CRC Press/Balkema.

Hoek, E. and Bray, J.W. 1981. Rock Slope En-gineering. 3rd Ed. The Institution of Miningand Metallurgy, London.

Krahn, J. 2004. Stability Modelling withSLOPE/W. GEO-SLOPE/W International,Ltd., Canada.

PT. Newmont Nusa Tenggara. 2013. Laporan

Intern. Departemen Geoteknik dan Hidro-geologi PT. Newmont Nusa Tenggara, Sum-bawa Barat (unpublished).

Priest, S.D. dan Brown, E.T. 1983. Probabilis-tic stability analysis of variable rock slopes.Transactions of Institution of Mining andMetallurgy. (Section A: Mining Industry), pp.A1 - A12.


AN EVALUATION OF ROCK SLOPE STABILITY USING LIMIT ...

Documents

Transcript of AN EVALUATION OF ROCK SLOPE STABILITY USING LIMIT ...