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UJIAN AKHIR SEMESTER Desen Pengampuh : La Ode Jonas Tugo, S.T., M.T.



GEOTEKNIK TAMBANG “REVIEW JURNAL INTERNASIONAL”



OLEH: KELOMPOK 5 ANGGOTA: 1. 2. 3. 4. 5.



ALDE RIKA SRI BUNGA HALIM NUR AISA ANDRIANUS DASA MIKDARUL ALFAN



R1D117031 R1D117025 R1D117065 R1D117033 R1D117041



JURUSAN TEKNIK PERTAMBANGAN FAKULTAS ILMU DAN TEKNOLOGI KEBUMIAN UNIVERSITAS HALU OLEO KENDARI 2021



REVIEW JURNAL



Judul Jurnal



: Analisis Stabilitas Lereng Batuan di Himalaya



Volume



: Vol. 2, No. 2 (2010) 000-000 1



Tahun



: 2010



Penulis



: Gali Madhavi Latha dan Arunakumari Garaga



Publikasi



: Departemen Teknik Sipil, Institut Sains India, Bangalore, India



Reviewer



: Kelompok 5



Latar Belakang : Analisis stabilitas lereng batuan menjadi penting untuk desain yang aman dari lereng yang digali seperti tambang terbuka, pemotongan jalan, jembatan kereta api dan juga untuk memeriksa kondisi keseimbangan lereng alami. Meskipun pengetahuan tentang analisis stabilitas dan pemantauan pergerakan lereng serta teknik stabilisasi meningkat secara substansial dalam beberapa tahun terakhir, ketidakstabilan lereng batuan masih menimbulkan kerugian sosial, ekonomi dan lingkungan yang berat di daerah pegunungan. Hal ini terutama disebabkan oleh kompleksitas proses yang mendorong kegagalan lereng dan pengetahuan kami yang tidak memadai tentang mekanisme yang mendasarinya. Semakin banyak, para ahli dipanggil untuk menganalisis dan memprediksi stabilitas lereng tertentu, menilai risikonya, potensi mode kegagalan dan kemungkinan tindakan pencegahan atau perbaikan. Oleh karena itu, penilaian stabilitas



lereng



batuan



dengan



mempertimbangkan



pengaruh



semua



diskontinuitas (sambungan, patahan, lipatan, bidang alas, dll.) Merupakan tugas yang menantang bagi para insinyur. Meskipun kekuatan batuan memainkan peran penting dalam stabilitas lereng, struktur geologi batuan sering mengatur stabilitas lereng pada massa batuan yang bersendi. Karakteristik geologi massa batuan meliputi lokasi dan



jumlah set sambungan, jarak sambungan, orientasi sambungan, material sambungan dan tekanan rembesan. Analisis kinematik umumnya digunakan untuk mengevaluasi kemungkinan balok atau massa batuan bergerak di sepanjang struktur geologi dan meluncur keluar dari permukaan lereng. Langkah pertama dalam analisis kinematik adalah identifikasi fitur diskontinuitas yang akurat. Ini biasanya dilakukan dengan foto udara, pemetaan permukaan dan pemeriksaan inti lubang bor. Setelah diskontinuitas



dipetakan, analisis



kinematik biasanya



dilakukan



dengan



menggunakan pendekatan proyeksi stereografik grafis yang dijelaskan oleh Goodman (2000) dan Philips (1971). Penerapan analisis kinematik untuk penilaian stabilitas lereng batuan juga didokumentasikan dengan baik dalam literatur.



Tujuan



:



Untuk menganalisis stabilitas lereng



dan mengetahui kinematika



kemiringan abutmen kanan untuk analisis kegagalan baji berdasarkan proyeksi stereografik.



Metode



:



Stabilitas lereng statis dari lereng batuan dipelajari dengan menggunakan pendekatan kontinum ekuivalen melalui alat numerik komersial yang paling umum digunakan seperti FLAC dan LERENG / W GEOSTUDIO.



Hasil



: Hasil review menjelaskan mengenai analisis stabilitas lereng dan kinematika



kemiringan untuk analisis kegagalan baji.



1. Analisis Stabilitas Lereng Statis dan Semu Statis dari Lereng a. Analisis Stabilitas Lereng Statis dengan FLAC



Gambar 4. Kisi-kisi FLAC yang digunakan untuk kalkulas stabilitas kalkulasi Gambar 4 menunjukkan grid beda hingga yang dihasilkan dalam FLAC untuk digunakan dalam kalkulasi stabilitas. Hasil yang diperoleh dari analisis stabilitas pada profil potongan ditunjukkan pada Gambar 5 berupa plot FOS (Factor of Safety). Nilai FOS yang diperoleh dari analisis statik adalah 1,88 yang berarti lereng stabil secara global. Gbr. 6 menunjukkan zona plastis untuk profil potongan dengan beban dermaga. Jelas dari Gambar 6 bahwa tegangan terjadi di puncak yang menunjukkan hasil. Analisis kestabilan juga dilakukan pada profil potongan tanpa beban dermaga dan terlihat bahwa nilai faktor keselamatan



tidak



banyak



berubah



dengan



beban



dermaga,



menunjukkan bahwa pengaruh beban dermaga tidak signifikan terhadap stabilitas lereng secara keseluruhan. Alasannya adalah besarnya beban dermaga sangat kecil jika dibandingkan dengan berat lereng secara keseluruhan.



Gambar 5. Faktor safety plot untuk stabilitas statik lereng batuan



Gambar 6. Plastic zone for cut profile with pier loads (kH=0.31 g, kv=0.2 g) (SLOPE/W)



b. Analisis Stabilitas GEOSTUDIO



Lereng



Statis



dengan



LERENG



/



B



Gambar 7. Percobaan permukaan yang gagal dan faktor keselamatan yang sesuai Tegangan yang dihitung dengan analisis tegangan elemen hingga dapat digunakan sebagai tambahan untuk perhitungan kesetimbangan batas untuk analisis stabilitas lereng terlengkap yang tersedia. Dengan berbagai fitur yang komprehensif ini, SLOPE / W dapat digunakan untuk menganalisis hampir semua masalah stabilitas lereng dalam proyek-proyek geoteknik, sipil, dan teknik pertambangan. Untuk kemiringan abutmen yang tepat, analisis kemiringan / W telah dilakukan dengan menggunakan metode irisan biasa untuk mendapatkan faktor keamanan minimum pada permukaan slip kritis berdasarkan teknik iteratif. Nilai FOS yang dihitung dari SLOPE / W digunakan untuk memeriksa silang nilai faktor keamanan yang diperoleh dari FLAC.



c. Periksa Stabilitas Lokal Lereng di Lokasi Dermaga Untuk memeriksa stabilitas terhadap kerusakan lokal, berbagai permukaan slip dipertimbangkan untuk lereng yang melewati berbagai



lokasi dermaga dan faktor keamanan minimum untuk permukaan slip ini diperoleh dengan menggunakan SLOPE / W dengan metode irisan biasa. Gambar 7 menunjukkan permukaan slip ini dan faktor keselamatan yang sesuai yang diperoleh dari analisis kesetimbangan batas. Seperti yang diantisipasi, diamati bahwa dengan berkurangnya ukuran permukaan slip, faktor keamanan bertambah dan faktor keamanan minimum diperoleh untuk permukaan slip yang melewati ujung kaki. d. Analisis Stabilitas Lereng Statis Semu Keruntuhan Lereng



Gambar 8. Faktor Plot Keamanan Untuk Lereng Dengan Dermaga Banyak Dan Banyak Seismik Yang Diperoleh Dari LERENG / W (Kh Dan Kv Diterapkan)



Hasil yang diperoleh dari SLOPE / W ditunjukkan pada Gambar 8 bersama dengan nilai FOS. Gambar menunjukkan nilai FOS mempertimbangkan komponen gempa baik horizontal maupun vertikal. Nilai FOS yang diperoleh sebesar 1,128.



Gambar 9. FOS plot untuk lereng menggunakan pendekatan pseudostatis diperoleh dengan menggunakan FLAC (kH saja diterapkan)



Gambar 10. FOS plot untuk profil potong menggunakan pendekatan pseudo-statis ('kH' dan 'kV' diterapkan) FLAC ditunjukkan pada Gambar 9 menunjukkan plot FOS untuk lereng hanya dengan mempertimbangkan komponen gaya gempa horizontal. Faktor keamanan yang diperoleh untuk kasus ini adalah 1,11. Gambar 10 memberikan plot FOS untuk lereng dengan komponen gaya



gempa horizontal dan vertikal. Nilai FOS untuk kasus ini dikurangi menjadi 1,02.



2. Kinematika Stabilitas Lereng untuk Analisis Kegagalan Baji a. Proyeksi Stereografik Sambungan untuk Abutment Kanan Data geologi mengenai arah kemiringan dan kemiringan berbagai set sambungan di dermaga berbeda



Gambar 11. Proyeksi Stereografik Sambungan di Bagian Lembah



Gambar 12. Proyeksi Stereografik Sambungan di S70 Sudut rata-rata kemiringan abutmen kanan jembatan adalah 50o dan arah kemiringan yang sesuai adalah 123o. Proyeksi stereografik dari kumpulan sambungan pada bagian lembah, P70, P60 dan P50 ditunjukkan pada Gambar. 11, 12, 13 dan 14 masing-masing.



Gambar 13. Proyeksi stereografik sambungan pada S60



Gambar 14. Proyeksi stereografik sambungan pada S50



b. Analisis untuk Kegagalan Baji Kerusakanterjadi



karena



tergelincir



di



sepanjang



kombinasi



diskontinuitas. Kondisi untuk longsor mengharuskan sudut gesekan massa batuan dan perpotongan diskontinuitas pada permukaan lereng diatasi.



Gambar 15. Kondisi untuk kegagalan baji



Gambar 16. Diamati dalam Penyimpangan Eksplorasi di P50 Pada stereonet plot, kondisi ini ditunjukkan oleh perpotongan dua lingkaran besar diskontinuitas dalam bulan sabit yang diarsir yang dibentuk oleh gesekan sudut dan lingkaran besar lereng seperti pada Gambar 15. Berdasarkan proyeksi stereografik dengan sudut kemiringan 50o, terlihat bahwa keruntuhan baji mungkin terjadi pada lokasi lembah, P60 dan P50 sebagai garis perpotongan himpunan sambungan 'J1'dan' J3'jatuh pada bulan sabit yang dibentuk oleh sudut kemiringan dan sudut gesekan.



Kegagalan



baji



sebenarnya



terjadi



selama



penggalian



penyimpangan eksplorasi di P50 seperti yang ditunjukkan pada Gambar. 16,



mendukung



interpretasi



stereografik



bahwa



kegagalan



baji



dimungkinkan di zona ini. Melalui percobaan, diamati bahwa nilai maksimum yang diizinkan untuk lereng adalah 43o untuk menghindari kegagalan baji di semua lokasi dan hasilnya disajikan secara lengkap pada Gambar 17.



Gambar 17. Proyeksi Stereografik Sambungan di Lokasi Berbeda untuk Kemiringan Rata 43o



Kekurangan



:



Kekurangan dari penelitian ini adalah tidak dijelaskannya tahapan yang dilakukan untuk memperoleh hasil dalam menganalisis baik analisis stabilitas lereng maupun analisis kegagalan baji.



Kelebihan



:



Kelebihan dari penelitian ini adalah isi pembahasan yang detail beserta dilengkapi dengan gambar sehingga mudah untuk dipahami.



Kesimpulan



:



Kesimpulan dari penelitian ini adalah studi kasus kemiringan besar di wilayah Himalaya di India dilakukan dengan menggunakan pendekatan kontinum yang setara. Kemiringan dianalisa untuk stabilitas di bawah kondisi pembebanan statis dan seismik. Perhitungan Faktor keamanan lereng dalam kondisi statis dan



pseudo-statis memastikan stabilitas global lereng dalam kondisi statis dan pseudostatis. Faktor keamanan lereng dalam kondisi statis adalah 1,88 dan dengan menerapkan gaya gempa horizontal saja, FOS berkurang sebesar 40%. Dengan penerapan gaya gempa vertikal, gaya gempa vertikal berkurang 6% lagi. Probabilitas kegagalan baji dinilai melalui analisis kinematik lereng dengan menggambar proyeksi stereografik bidang sambungan yang berlaku di lokasi jembatan dan lereng. Berdasarkan kinematika, disarankan untuk meratakan kemiringan dari 50o sampai 43o untuk menghindari kegagalan baji di semua lokasi dermaga.



Daftar Pustaka



:



Latha, G. M. Garaga, Arunakumari. 2010. Stability analysis of a rock slope in Himalayas. Department of Civil Engineering, Indian Institute of Science, Bangalore,



India.



Vol.



2,



No.



2



(2010)



000-000.



LAMPIRAN



See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/264178016



Stability analysis of a rock slope in Himalayas Article  in  Geomechanics and Engineering · June 2010 DOI: 10.12989/gae.2010.2.2.125



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Geomechanics and Engineering, Vol. 2, No. 2 (2010) 000-000



1



Technical Note



Stability analysis of a rock slope in Himalayas *Gali Madhavi Latha and Arunakumari Garaga Department of Civil Engineering, Indian Institute of Science, Bangalore, India



(Received April 15, 2010, Accepted May 20, 2010) Abstract. Slope stability analysis of the right abutment of a railway bridge proposed at about 350 m above the ground level, crossing a river and connecting two huge hillocks in the Himalayas, India is presented in this paper. The site is located in a highly active seismic zone. The rock slopes are intensely jointed and the joint spacing and orientation are varying at different locations. Static slope stability of the rock slope is studied using equivalent continuum approach through the most commonly used commercial numerical tools like FLAC and SLOPE/W of GEOSTUDIO. The factor of safety for the slope under static conditions was 1.88 and it was reduced by 46% with the application of earthquake loads in pseudostatic analysis. The results obtained from the slope stability analyses confirmed the global stability of the slope. However, it is very likely that there could be possibility of wedge failures at some of the pier locations. This paper also presents the results from kinematics of right abutment slope for the wedge failure analysis based on stereographic projections. Based on the kinematics, it is recommended to flatten the slope from 50o to 43o to avoid wedge failures at all pier locations. Keywords: jointed rock mass; static slope stability; pseudo-static analysis; kinematic analysis and wedge failure.



1. Introduction Stability analysis of rock slopes becomes essential for the safe design of excavated slopes like open pit mines, road cuts, railway bridges and also to check the equilibrium conditions of a natural slope. Though the knowledge regarding stability analyses and monitoring the slope movement and also the stabilization techniques improved substantially in recent years, rock slope instabilities still extract a heavy social, economic and environmental toll in mountainous regions. This is mainly due to the complexity of the processes driving slope failure and our inadequate knowledge of the underlying mechanisms. Ever increasingly, experts are called upon to analyse and predict the stability of a given slope, assessing its risk, potential mode of failure and possible preventive or remedial measures. Hence the stability assessment of rock slopes considering the influence of all the discontinuities (joints, faults, folds, bedding planes etc.) is a challenging task for engineers. Though the strength of the rock plays an important role in the slope stability, geological structure of the rock often govern the stability of slopes in jointed rock masses. Geological characteristics of rock mass include location and number of joint sets, joint spacing, joint orientations, joint material and seepage pressure. A rock slope can fail due to one or the combination of these following four *Corresponding author, Associate Professor, E-mail: [email protected]



2



Gali Madhavi Latha and Arunakumari Garaga



mechanisms; circular sliding, plane sliding, wedge sliding and toppling. Circular failure occurs in rock mass which can be justified as homogeneous medium. When the instability is dictated by the presence of pre-existing discontinuities, the failure will be in the form of plane sliding, wedge sliding or toppling, Hoek and Bray (2004). In continuum analysis using graphical or computer methods, the planar failure can be identified. Wedge failure can be identified through stereographic projections of joint planes. To assess the stability of a rock slope, all these possible failure modes need to be checked carefully. There are several tools available at present to carry out slope stability analyses of jointed rocks and these are well documented by several researchers. Limit equilibrium method used in conjunction with numerical modelling still remains the most commonly adopted method in rock slope engineering, even though most failures involve complex internal deformation and fracturing which bears little resemblance to the rigid block assumptions required by most limit equilibrium back-analyses. Some of the numerical techniques proposed by the earlier researchers include: the shear strength reduction technique developed by Matsui and San (1992), Universal Discrete Element Code (UDEC) developed by Cundall and Strack (1979), Pseudo-static analysis of slope stability proposed by Mononobe and Matsuo (1929) and Okabe (1926). Ling and Cheng (1997) proposed a pseudo-static procedure that determines the seismic factor of safety of a rock mass which slides along a joint plane or along the line of intersection of the joint planes, as a result of earthquake excitation or blasting. These numerical techniques were used by several earlier researchers for various rock engineering applications. Sjoberg (1999) performed numerical analyses of jointed rock masses using UDEC and finite difference program Fast Lagrangian Analysis of Continua (FLAC). Bhasin and Kaynia (2004) performed static and dynamic rock slope stability analyses for a 700-m high rock slope in western Norway using numerical discontinuum modelling technique. Choi and Chung (2004) analysed the stability of jointed rock slopes using Barton-Bandis constitutive model in Discrete Element Code. Chuhan et al. (1997) used Distinct Element Method for the dynamic analysis of high rock slopes and block structures. Kinematic analysis is generally used to evaluate the possibility of blocks or masses of rock moving along geologic structures and sliding out of the face of a slope. The first step in the kinematic analysis is the accurate identification of the features of discontinuities. This is normally done by aerial photographs, surface mapping and examination of borehole cores. Once the discontinuities are mapped, kinematic analysis is usually carried out using graphical stereographic projection approach explained by Goodman (2000) and Philips (1971). Application of kinematic analysis for rock slope stability assessment is also documented well in literature. Some of the applications include Goodman (1995), Leung and Kheok (1987), Yoon et al. (2002), Haswanto and Abd-Ghani (2008).



2. Description of the rock slope A railway line is being laid in the state of Jammu and Kashmir, India and this line is crossing the river Chenab at a height of about 359 m. A bridge is being constructed with a total of 18 piers at this place connecting two big hillocks. Among these piers, 4 piers (P10-P40) are resting on the left abutment and the other 14 piers (P50-P180) are resting on the right abutment. Slope stability analysis of the right abutment is taken up in the present study. The section of the bridge and abutments along with the foundations that could affect the stability of the slope are shown in Fig. 1.



Stability analysis of a rock slope in Himalayas



3



Fig. 1 Section of the gorge with pier foundations along the slope



Fig. 2 Photograph showing the proposed bridge site



Fig. 2 shows the photograph taken at the site of proposed bridge. The rocks present at the bridge site are heavily jointed. The subsurface at the extent of the bridge site considered for slope stability analysis essentially consists of Dolomitic limestone with different degrees of weathering and fracturing. The main discontinuities at the site are one sub-horizontal foliation joint dipping at about 20~30 degrees in north-east (NE) direction and two sub-vertical joints. The summary of structural features present in the area is given in Table 1. Properties of intact rocks obtained through laboratory testing of cores collected from boreholes at the site are given in Table 2. The original slope has to be cut and benches need to be provided to facilitate the



4



Gali Madhavi Latha and Arunakumari Garaga



Table 1 Summary of the structural features at the site Feature



Strike



Railway line alignment Foliation joint Sub-vertical joint -1 Sub-vertical joint -2



o



o



N 120 - N 300 N 140o - N 320o N 150o - N 330o N 75o - N 255o



Dip



Dip direction



− 27o 65o 80o



− N 50o N 240o N 165o



Table 2 Properties of intact rock at the site Property



Value 3



Density (kg/m ) Young’s modulus (GPa) Poisson’s ratio UCS (Mpa) ‘c’ (Mpa) for intact rock ‘φ’ degrees Hoek and Brown parameters ‘m’ and ‘s’



2762 65 0.15 115 44.44 35 23.52, 1.0



Fig. 3 Profile selected for the stability analysis



construction of foundations along the slope. The outline of benching profile selected for the right abutment is shown in Fig. 3.



Stability analysis of a rock slope in Himalayas



5



Table 3 Rock mass properties used in the stability calculations Property



Value 3



Density (kg/m ) Young’s modulus (GPa) Poisson’s Ratio Hoek and Brown Parameter ‘m’ Hoek and Brown Parameter ‘s’ Cohesion ‘c’ (kPa) Friction angle ‘ϕ’ (degrees)



2762 4.34 0.15 0.59 0.00127 1785 23



3. Static and pseudo-static slope stability analysis of the slope 3.1 Static slope stability analysis by FLAC The slope is simulated using FLAC (Fast Lagrangian Analysis of Continua) version 5.0 developed by Itasca consulting group (1995). FLAC is a widely used commercial, explicit finite difference code for applications in soils and rocks. It is impossible to incorporate and model all the discontinuities in large slope in a numerical model as the joints are spaced very close (joint spacing varying between 5 mm to 10 mm). Hence the slope is represented by an equivalent continuum in which the effect of discontinuities has been considered by reducing the properties and strength of intact rock to those of the rock mass. The slope is analysed for plane-strain condition in small-strain mode. A relatively finer discretization of 100 × 80 grid size is chosen for modelling the slope. At the base of the model boundary, both horizontal (x) and vertical (y) displacements are arrested by fixing the nodes. Along left and right of the boundary horizontal displacements are arrested. Initial stresses of magnitude σxx = σyy = σzz = 8 MPa are applied to all the zones. Stability analysis is carried out using Hoek-Brown failure criterion in FLAC. FLAC calculates the factor of safety automatically using the shear strength reduction technique through bracketing (Matsui and San 1992). In this technique, the values of shear strength parameters ‘c’ and ‘φ’ are updated in every trial until the difference between lower and upper brackets is minimal according to the following equations. 1 ctrial = ----------- × c Ftrial φ trial = tan



–1



1---------tan φ Ftrial



(1) (2)



The value of ‘Ftrial’ at which slope will have instability i.e. failure is calculated by FLAC using the bracketing technique. Initially upper and lower brackets are established. The initial lower bracket is any ‘Ftrial’ for which a simulation converges. The initial upper bracket is any ‘Ftrial’ for which the simulation does not converge. Next, a point midway between the upper and lower brackets is tested. If the simulation converges, lower bracket is replaced by this new value. If the simulation does not converge, the upper bracket is replaced. The process is repeated until the difference between the upper and lower brackets is less than a specific tolerance. The analysis is carried out with and without pier loads. Properties of the rock mass used in the



6



Gali Madhavi Latha and Arunakumari Garaga



Table 4 Details of the footing pressures Property



P50



P60



P70



P80



P90



Chainage (km) Original ground level (m) Ground level after benching (m) Depth of foundation (m) Foundation size (m × m) Footing Pressure (kPa)



51.065 747.829 724 3 28 × 36 374.86



51.13 807.421 784 3 11 × 9.5 588.00



51.1865 838.657 832 3 11 × 6.5 409.00



51.2265 841.476 832 3 11 × 6.5 415.00



51.2765 832.750 832 7 11 × 6.5 317.00



Fig. 4 FLAC grid used for the stability calculations



stability calculations are shown in Table 3. These are the average values obtained by laboratory tests on jointed rock mass collected at different pier locations. Table 4 presents the values of pier loads applied on the slope at respective pier locations. Fig. 4 shows the finite difference grid generated in FLAC for using in the stability calculations. The results obtained from the stability analysis on the cut profile are shown in Fig. 5 in the form of FOS (Factor of Safety) plot. The value of FOS obtained from the static analysis is 1.88 which means that the slope is globally stable. Fig. 6 shows the plastic zone for the cut profile with pier loads. It is clear from Fig. 6 that tension is occurring at the crest indicating yielding. Stability analysis was also carried out on cut profile without pier loads and it was noticed that the value of factor of safety is not altered greatly with the pier loads, showing that the effect of pier loads is insignificant on the overall stability of the slope. The reason for this is that the magnitude of the pier loads is very less when compared to the overall weight of the slope.



Stability analysis of a rock slope in Himalayas



7



Fig. 5 Factor of safety plot for the static stability of rock slope



Fig. 6 Plastic zone for cut profile with pier loads (kH=0.31 g, kv=0.2 g) (SLOPE/W)



3.2 Static slope stability analysis by SLOPE/W of GEOSTUDIO The same slope is modelled in SLOPE/W of GEOSTUDIO. SLOPE/W is a popular software for



8



Gali Madhavi Latha and Arunakumari Garaga



Fig. 7 Trial failure surfaces and corresponding factors of safety



computing the factor of safety of earth and rock slopes. Using limit equilibrium approach, SLOPE/ W can model heterogeneous soil types, complex stratigraphic and slip surface geometry, and variable pore-water pressure conditions using a large selection of soil models. Stresses computed by a finite element stress analysis may be used in addition to the limit equilibrium computations for the most complete slope stability analysis available. With this comprehensive range of features, SLOPE/ W can be used to analyze almost any slope stability problems in geotechnical, civil, and mining engineering projects. For the right abutment slope, SLOPE/W analyses have been carried out using ordinary method of slices to obtain minimum factors of safety for the critical slip surfaces based on iterative techniques. The FOS values computed from SLOPE/W are used to cross check the values of factors of safety obtained from FLAC. 3.3 Check for local stability of slope at pier locations In order to check the stability against local failures, various slip surfaces were considered for the slope passing through various pier locations and the minimum factors of safety for these slip surfaces are obtained using SLOPE/W with ordinary method of slices. Fig. 7 shows these slip surfaces and corresponding factors of safety obtained from the limit equilibrium analysis. As anticipated, it is observed that as the size of the slip surface is reduced, the factor of safety is increased and the minimum factor of safety was obtained for the slip surface passing through the toe. 3.4 Pseudo static slope stability analyses Slope failure and landslides are mainly caused due to the earthquake induced ground shaking and associated inertial forces. Earthquakes with even a very small magnitude may trigger failure in slopes which are perfectly stable otherwise. As the slope under consideration is situated in seismic zone V of India, where severe earthquakes are expected, it is mandatory to assess the stability of the



Stability analysis of a rock slope in Himalayas



9



Fig. 8 Factor of safety plot for the slope with pier loads and seismic loads obtained from SLOPE/W (kH and kV are applied)



slope under seismic conditions. The seismic slope stability is estimated using pseudo-static approach (Mononobe and Matsuo 1929, Okabe 1926). Pseudo-static analysis involves simulating the ground motion as constant static horizontal force acting in a direction out of the face. The analysis represents the effects of earthquake shaking by pseudo-static accelerations that produce inertial forces, ‘FH’ and ‘FV’ which act through the centroid of the failure mass. The magnitude of the pseudo-static force is the product of seismic coefficient ‘kH’ and the weight of the sliding block ‘W’. The value of ‘kH’ may be taken as equal to the design PGA (Peak Ground Acceleration) which is expressed as a fraction of the gravity acceleration. The horizontal pseudo-static force decreases the factor of safety by reducing the resisting force (for φ > 0) and increases the driving force. The vertical pseudo-static force typically has less influence on the factor of safety since it reduces (or increases, depending upon the direction) both the driving force and the resisting force, as a result the effect of vertical accelerations are usually neglected in pseudo-static analyses. However the effect of vertical acceleration is also considered in the present study. The horizontal pseudo-static forces are assumed to act in directions that produce positive driving moments. Results of the pseudo-static analysis critically depend upon the horizontal seismic coefficient (kH). Therefore selection of appropriate pseudo-static coefficient is very important. Usually this value is selected based on the Most Credible Earthquake (MCE) for the specific seismic zone in which the slope is situated. In the present study, the horizontal seismic coefficient ‘kH’ is selected as 0.31 g based on the previous earthquake history of the region and MCE scenario. The value of the vertical seismic coefficient ‘kV’ is taken as 2/3rd of ‘kH’ as per the Indian Standard Code IS 1893 (2002). The analysis is carried out for two different cases i.e. considering the horizontal seismic force component (kH) alone in the first case and by applying both vertical and horizontal components (kH and kV) in the second case. Pseudo-static analysis of the slope is carried out using both SLOPE/W and FLAC. The result obtained from SLOPE/W is shown in Fig. 8 along with the FOS value. Figure shows the FOS value considering both horizontal as well as vertical components of earthquake. The value of FOS obtained is 1.128. Similarly the results obtained from pseudo-static analysis of the slope in



10



Gali Madhavi Latha and Arunakumari Garaga



Fig. 9 FOS plot for the slope using pseudo-static approach obtained using FLAC (kH alone is applied)



Fig. 10 FOS plot for the cut profile using pseudo-static approach (‘kH’ and ‘kV’ are applied)



FLAC are shown in Figs. 9 to 11. Fig. 9 gives the FOS plot for the slope considering only horizontal seismic force component. The factor of safety obtained for this case was 1.11. Fig. 10 gives the FOS plot for the slope with both horizontal and vertical seismic force components. The value of FOS for this case was reduced to 1.02. Factor of safety for the slope without considering earthquake loads was 1.89. By applying the horizontal earthquake force alone, the FOS is reduced to 1.11 and with the application of vertical



Stability analysis of a rock slope in Himalayas



11



Table 5 Factors of safety values obtained from slope stability analysis Without earthquake loading



Profile Original Slope Benched profile



With earthquake loading (kh = 0.31 g)



With earthquake. loading (kh = 0.31 g, kv = 0.2 g)



SLOPE/W



FLAC



SLOPE/W



FLAC



SLOPE/W



FLAC



1.920 1.829



1.880 1.900



− 1.128



− 1.110



− 1.128



− 1.023



Table 6 Details of joints at different locations along the slope Location Valley P70 P60 P50



Joint set J1 Dip o



42 67o 40o 40o



Joint set J2



Dip Direction o



049 047o 049o 054o



Dip o



52 47o 56o 48o



Joint set J3



Dip Direction o



238 244o 240o 234o



Dip



Joint set J4



Dip Direction



o



72 70o 69o 71o



o



151 131o 153o 153o



Dip o



15 51o 39o 08o



Dip Direction 336o 263o 308o 032o



earthquake force it is further reduced to 1.02. Earthquake loads reduced the FOS by 46%. The minimum FOS required for rock slopes considering the earthquake loads is 1.2. But the factor of safety obtained from pseudo-static analysis considering both horizontal and vertical loads is falling below the required FOS value. However it is noteworthy to mention that the pseudo-static analysis is a highly conservative method because it is performed with continually applied seismic forces in horizontal and vertical directions, which is not realistic. For this analysis, as FOS value of 1.0 is acceptable as per NEHRP guidelines for land sliding hazards. Hence the slope can be considered as globally stable under seismic loading conditions as well. The factors of safety obtained from static and pseudo-static slope stability analyses using both FLAC and SLOPE/W are summarised in Table 5.



4. Kinematics of slope stability for wedge failure analysis In the previous section of this paper, global stability of the slope is examined through static and pseudo-static slope stability analysis and it was found that the slope is stable in both static and probable seismic conditions. However, the global failure is a rare possibility for this slope under consideration. Though the overall stability is understood, it is very much essential to investigate the possibility of local wedge failures which might occur due to the intersection of joint sets daylighting on to the slope. The possibility of wedge failure at different pier locations is examined in this section by plotting stereographic projections for the prevailing joint sets in the bridge site. The geological data of joint sets for the stereographic projections is obtained from the joint mapping done by the geologists from the exposed slope surface at different pier locations. 4.1 Stereographic projection of joints for the right abutment The geological data regarding the dip and dip direction of various joint sets at different pier



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Gali Madhavi Latha and Arunakumari Garaga



Fig. 11 Stereographic projections of joints at valley portion



Fig. 12 Stereographic projections of joints at S70



locations obtained form the geological mapping at the slope site is presented in Table 6. Using the data in Table 6, stereographic projections of joint sets are plotted for various locations. The average angle of slope for the right abutment of the bridge is 50o and the corresponding dip direction is 123o. Stereographic projections of joint sets at valley portion, P70, P60 and P50 are shown in Figs. 11, 12, 13 and 14 respectively.



Stability analysis of a rock slope in Himalayas



13



Fig. 13 Stereographic projections joints at S60



Fig. 14 Stereographic projections of joints at S50



4.2 Analysis for wedge failure Wedge failure occurs due to sliding along a combination of discontinuities. The conditions for sliding require that the friction angle of the rock mass ‘φ ’ is overcome, and that the intersection of the discontinuities "daylight" on the slope surface. On the stereonet plot, these conditions are



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Gali Madhavi Latha and Arunakumari Garaga



Fig. 15 Condition for wedge failure



Fig. 16 Wedge failure observed in exploratory drift at P50



indicated by the intersection of two discontinuity great circles within the shaded crescent formed by the friction angle and the slope's great circle as shown in Fig. 15. Based on the stereographic projections with slope angle of 50o, it is seen that wedge failure is possible at valley, P60 and P50 locations as the line of intersection of joint sets ‘J1’ and ‘J3’ is falling in the crescent formed by the slope angle and friction angle. Wedge failure is in fact occurred during excavation of exploratory drift at P50 as shown in Fig. 16, supporting the stereographic interpretations that the wedge failures are possible in this zone. It is observed that the friction angle reported from the laboratory tests is very low (about 20ο). However, increase in the value of friction angle will not arrest the wedge failures as it could be seen from the stereographic plots that the line of intersection of joints in the crescent is close to the slope rather than the friction cone. Hence to avoid the wedge failures at the above mentioned locations (Valley, P50 and P60), the slope needs to be flattened. By plotting the stereographs for slope angle of 45o, it was observed that the wedge failure is still possible at P60. By trial, it was observed that the maximum permissible value for slope is 43o to avoid wedge failures at all the locations and the results are presented comprehensively in Fig. 17.



Stability analysis of a rock slope in Himalayas



15



Fig. 17 Stereographic projections of joints at different locations for flattened slope of 43o



5. Conclusions A case study of large slope in Himalayan region of India is taken up in this paper and numerical analysis of the slope is carried out using the equivalent continuum approach. The slope is analyzed for stability under static and seismic loading conditions. Calculation of Factor of safety for the slope in static and pseudo-static conditions confirmed the global stability of the slope in static and pseudo-static conditions. The factor of safety for the slope under static conditions was 1.88 and by applying the horizontal earthquake force alone, the FOS is reduced by 40%. With the application of vertical earthquake force it is further reduced by another 6%. Probability of wedge failure is assessed through kinematic analysis of the slope by drawing stereographic projections of joint planes prevailing in the bridge site and the slope. Based on the kinematics, it is recommended to flatten the slope from 50o to 43o to avoid wedge failures at all pier locations.



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Gali Madhavi Latha and Arunakumari Garaga



norway”, Eng. Geol., 71, 213-226. Choi, S.O. and Chung, S. (2004), “Stability analysis of jointed rock slopes using the Barton-Bandis constitutive model in UDEC”, Int. J. Rock Mech. Min. Sci., 41(1), 581-586. Cundall, P.A. and Strack, O. D. (1979), “A discrete numerical model for granular assemblies”, Geotechnique, 21, 47-65. Goodman, R.E. (1995), “Block Theory and its application”, Geotechnique, 45(3), 383-423. Goodman, R.E. (2000), Introduction to Rock Mechanics, John Wiley & Sons, New Jersey, USA Haswanto, W.A. and Abd-Ghani, R. (2008), “Kinematic and block theory applications to rock slope stability analysis at Fraser’s hill Pahang Malaysia”, Electron. J. Geotech. Eng., 13(D). Hoek, E. and Bray, J. (2004), Rock Slope Engineering, Ed. D.C. Wyllie and C.W. Mah, Taylor and Francis, London, UK. IS 1893 (2002), Criteria for earthquake resistant design of structures, Bureau of Indian Standards, New Delhi, India. Itasca (1995), FLAC Version 5. User's Manuals, Itasca Consulting Group, Minnesota, USA. Leung, C.F. and Kheok, S.C. (1987), “Computer aided analysis of rock slope stability”, Rock Mech. Rock Eng., 20, 111-122. Ling, H.I., Alexander, H. and Cheng, D. (1997), “Rock sliding induced by seismic force”, Int. J. Rock Mech. Min., 34(6), 1021-1029. Matsui, T. and San, K.C. (1992), “Finite element slope stability analysis by shear strength reduction technique”, J. Soils Found., 32(1), 59-70. Mononobe, N. and Matsuo, H. (1929), “On the determination of earth pressures during earthquakes”, Proceedings of World Engineering Conference, Tokyo, Japan, Vol. IX, Paper No. 388, 177-185. Okabe, S. (1926), “General theory of earth pressure”, J. JPN Soc. Civil Eng., 12(1), 311. Phillips, F.C. (1971), The use of Stereographic Projections in Structural Geology, Edward Arnold, London, UK. Sjoberg, S. (1999), Analysis of large scale rock slopes, Doctoral Thesis, Department of Civil and Mining Engineering, Lulea University of Technology, Sweden. Yoon, W.S., Jeong, U.J. and Kim, J.H. (2002), “Kinematic analysis for sliding failure of multi-faced rock slopes”, Eng. Geol., 67, 51-61. Zhang, C. Pekau, O., Jin, F. and Wang, G. (1997), “Application of distinct element method in dynamic analysis of high rock slopes and blocky structures”, Soil Dyn. Earthq. Eng., 16, 385-394.



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