Numerical Evaluation of Tunnel Portal Slope Stability at Bagong Dam Site, East Java, Indonesia

Journal of Applied Geology, vol. 5(1), 2020, pp. 40–52 DOI: http://dx.doi.org/10.22146/jag.57044

Irien Akinina Fatkhiandari, I Gde Budi Indrawan,* and Dwikorita Karnawati

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

ABSTRACT. Geometries of excavated tunnel portal slopes at Bagong Dam site was initially designed without taking into account the earthquake load. The excavated slope designs also assumed that the rocks comprising the slopes were homogenous. The purpose of this research was to evaluate the stability of the excavated tunnel inlet and outlet slopes at the Bagong Dam site under static and earthquake loads using the finite element method. The stability of the natural slopes was also analyzed for comparison. The numerical static and pseudostatic analyses of slope stability were carried out using RS2 software (Rocscience, Inc.). Input data used in the numerical analyses were obtained from engineering geological mapping, rock core analyses, and laboratory tests. The seismic coefficient applied in the pseudo-static slope stability analyses was determined following guideline described in Indonesian National Standard. The engineering geological mapping and evaluation of rock cores indicated that the inlet tunnel slope consisted of four types of materials, namely residual soil, poor quality of volcanic breccia, very poor quality of volcanic breccia, and good quality of volcanic breccia. The outlet portal slope consisted of six types of materials, namely residual soil, very poor quality of limestone, poor quality of limestone, very poor quality of volcanic breccia, poor quality breccia, and good quality breccia. Based on the secondary elastic wave velocity (Vs) values, the rock masses in the research area were classified as hard rock (SA). Seismic analyses based on the earthquake hazard source map with a 10 % probability of exceedance in 50 years provided by the National Earthquake Center (2017) indicated that the PGA and the corresponding amplification factor FPGA in the research area were 0.3 and 0.8, respectively. The calculated seismic coefficient for the pseudostatic slope stability analyses was 0.12. The numerical analysis results showed that, in general, earthquake load reduced critical Strength Reduction Factor (SRF) values of the slopes. However, the natural and excavated tunnel portal slopes were relatively stable under static and earthquake loads. The natural slope at the tunnel inlet with a 40° inclination had a critical SRF value of 4.0, while that of at the tunnel outlet with a 51° inclination had a critical SRF value of 2.6. Under static load, the excavated slopes at the tunnel inlet and outlet having a 45° inclination had critical SRF values of 2.4 and 5.0, respectively. Under earthquake load, the excavated slopes at the tunnel inlet and outlet had critical SRF values of 2.3 and 3.5, respectively. Keywords: Bagong dam · Finite element method · GSI · RS2 · Slope stability.

1I NTRODUCTION The Bagong Dam site is located at Sumurup and Sengon Villages, Bendungan District, Treng- *Corresponding author: I G. B. INDRAWAN, De- galek Regency, East Java Province (Figure 1). partment of Geological Engineering, Universitas Gadjah For the construction of the earth-ﬁll dam, the Mada. Jl. Graﬁka 2 Yogyakarta, Indonesia. E-mail: [email protected] river water was planned to be diverted using a

2502-2822/© 2020 The Authors. Open Access and published under the CC-BY license. NUMERICAL EVALUATION OF TUNNEL PORTAL SLOPE STABILITY AT BAGONG DAM SITE diversion tunnel. Geometries of the inlet and main types of lithologies, namely volcanic brec- outlet tunnel portal slopes were designed by cia and limestone, existed in the Bagong Dam BBWS Brantas (2017) using a numerical soft- site were likely members of the Mandalika and ware Plaxis developed by Bentley Systems, Inc. Wonosari Formations, respectively. In addition, However, earthquake load was not considered faults and joints observed in the Bagong Dam into the slope designs. In addition, the rocks site and the surrounding had a consistent ori- comprising the slopes were assumed to be ho- entation to the regional Meratus structural pat- mogenous, and the shear strength parameters tern (NE–SW), as described by Pulunggono dan for the slope stability analyses were obtained Martodjodjo (1994). from laboratory direct shear strength tests. As located in an active seismic region, the stability 3M ETHOD of the tunnel portal slopes may be affected by Engineering geological mapping around the earthquakes. As discontinuities tend to reduce tunnel portals, evaluation of rock cores at four rock mass strength, ignoring rock mass quality boreholes drilled by BBWS Brantas (2014) near controlled by rock fractures may lead to over- the inlet and outlet tunnel portals (Figure 1), estimated slope factor of safety. Therefore, sta- and laboratory testing of soil and rock samples bility evaluation of the designed inlet and por- were carried out to obtain data of rock mass tal slopes by taking into account the earthquake layers and the engineering properties. Rock load and rock fracturing degree is necessary. mass quality was determined by the Geological The finite element method has been increas- Strength Index (GSI) of the rock cores following ingly used in slope stability analyses (Hammah equation proposed by Hoek et al. (2013) as fol- et al., 2004). Excellent reviews of finite element lows: analyses of slope stability are provided in nu- merous textbooks (e.g., Duncan et al., 2014; Wyl- RQD GSI = 1.4Jcond + (1) lie, 2018). One of the advantages of the finite el- 2 ement method over the traditional limit equilib- where Jcond = joint conditions of rock cores rium method is that no assumption needs to be as described in Bieniawski (1989); RQD = rock made in advance about the shape or location of quality designation. the failure surface (e.g., Griffith and Lane, 1999; The pseudostatic slope stability analyses Rocscience Inc., 2001). were carried out to estimate the stability of This paper presents results of engineering ge- the tunnel portal slopes under an earthquake ology study carried out to evaluate the stability load. Following procedures described in SNI of designed tunnel portal slopes at The Bagong 8460 (BSN, 2017), the seismic coefficient used Dam site under static and earthquake loads us- in pseudostatic slope stability analyses were ing the finite element method. Results of the calculated as 0.5 of the peak ground accelera- engineering geological mapping and rock core tion (PGA) determined by considering the site evaluations are presented, and results of static class and amplification factor (FPGA). In addi- and pseudostatic slope stability analyses are tion, the SNI 8460 (BSN, 2017) adopts ground highlighted. motions with a 10 % probability of exceedance in 50 years (corresponding approximately to 2G EOLOGICAL SETTING a 500-year return period) for seismic slope The Regional Geological Map of Madiun Sheet design. The peak ground acceleration at par- prepared by Hartono et al. (1992) shows that ticular sites can be obtained from earthquake the Bagong Dam site and the surrounding con- hazard source maps produced by the National sist of the Mandalika and Wonosari Formations Earthquake Center (2017). (Figure 2). The Mandalika Formation was es- The static and pseudostatic slope stability timated to form in Oligocene to Early Miocene, analyses were carried out using a finite element while the Wonosari Formation was estimated to based RS2 software developed by Rocscience, form in Early to Late Miocene. Based on sur- Inc. The input parameters in the slope stability face geological mapping and evaluation of drill analyses are shown in Table 1. Figure 3 shows cores, Fatkhiandari (2020) indicated that two the geometries of the natural slopes with the

Journal of Applied Geology 41 FATKHIANDARI et al.

FIGURE 1. Research area at the Bagong Dam site.

42 Journal of Applied Geology NUMERICAL EVALUATION OF TUNNEL PORTAL SLOPE STABILITY AT BAGONG DAM SITE

FIGURE 2. Regional geological map of the Madiun sheet (Hartono et al.,1992). rock masses applied in the slope stability anal- sisted of six types of materials, namely residual yses. The natural slope at the tunnel inlet had a soil, very poor quality of limestone, poor qual- 40° inclination, while that of at the tunnel outlet ity of limestone, very poor quality of volcanic had a 51° inclination. The groundwater levels breccia, poor quality breccia, and good quality in both slopes were inferred from drilling data. breccia. Typical cores of rock masses compris- Following the best practice of excavated slope ing the slopes are shown in Figure 4. The ma- design, the excavated slopes at the tunnel in- terial properties from the laboratory tests (Ta- let and outlet were designed to have a 1:1 slope ble 4) then used as input parameters in the slope ratio (or 45° inclination). The SNI 8460 (BSN, stability analyses. Intact rock constant (mi) of 2017) required a minimum factor of safety val- each rock mass quality was estimated based on ues of 1.5 and 1.1 for permanent slopes under the range of mi value for each rock type pro- static and earthquake loads, respectively. In vided in the RS2 database by considering the the numerical finite element analyses, the fac- weathering degree of the intact rock. Distur- tor of safety values was represented by critical bance factor (D) values were all set into zero by Strength Reduction Factor (SRF) values. assuming that the excavation processes caused minimum disturbance to the surrounding rock 4R ESULTS AND DISCUSSION masses. 4.1 Rock mass types and properties 4.2 Earthquake load Types and qualities of the rock masses comprising the inlet and outlet tunnel portal slopes are Measurement data of the previous study shown in Table 2. Those characteristics of the (BBWS Brantas, 2014) indicated that the re- rock masses were determined from the engi- search area had more than 1500 m/s secondary neering geological mapping and evaluation of elastic wave velocity (Vs) values. Therefore, the rock cores at Borehole BT3 and BBT 3 (Ta- the rock masses are classified as a hard rock ble 1). The inlet tunnel slope consisted of four (SA) class. The earthquake hazard source map types of materials, namely residual soil, poor with a 10 % probability of exceedance in 50 quality of volcanic breccia, very poor quality of years provided by the National Earthquake volcanic breccia, and good quality of volcanic Center (2017) indicated that the PGA and the breccia. Meanwhile, the outlet portal slope con- corresponding amplification factor FPGA in

Journal of Applied Geology 43 FATKHIANDARI et al.

TABLE 1. Input parameters for slope stability analyses.

Analysis type Plane strain Stress analysis Tensile failure reduce shear strength; Joint tension reduce joint stiffness Effective stress analyses (static load); total stress analyses (earthquake load) Mesh Graded, 3-noded triangle Field stress Gravity, actual ground surface Displacement Top: Free Side: Restrain XY Bottom: Restrain XY Material properties Initial element loading: Field stress & body force Failure criteria: Mohr-Coulomb (soil); Generalized Hoek-Brown (rock) Material type: Plastic

TABLE 2. Rock masses at borehole BT3 (inlet slope).

Depth (m) Material Weathering degree Jcond RQD GSI Rock mass quality Completely 0–3 Residual soil 0 0 - - weathered Moderately Poor quality of volcanic 3.5–30 Volcanic breccia 15 7 26 weathered breccia Very poor quality of 30–40 Volcanic breccia Highly weathered 10 0 15 volcanic breccia Good quality of 40–70 Volcanic breccia Slightly weathered 25 44 59.5 volcanic breccia

TABLE 3. Rock masses at borehole BBT3 (outlet slope).

Depth (m) Material Weathering degree Jcond RQD GSI Rock mass quality Completely 0–3 Residual soil 0 0 - - weathered Very poor quality of 3–17 Limestone Highly weathered 10 0 15 limestone Moderately Moderate quality of 17–20.8 Volcanic breccia 15 7 26 weathered volcanic breccia Very highly Very poor quality of 20.8–35.2 Limestone 10 6 18 weathered limestone Good quality of 35.2–50 Volcanic breccia Slightly weathered 25 70 72.5 volcanic breccia

44 Journal of Applied Geology NUMERICAL EVALUATION OF TUNNEL PORTAL SLOPE STABILITY AT BAGONG DAM SITE 60

Residual soil

40 Poor quality breccia

1 Very poor quality breccia

Good quality breccia 20 0

0 10 20 30 40 50 60 70 80 90 100 110 120 130 Project Project2

Analysis Description

Drawn By Scale 1:509 Company Date File Name PHASE2 8.014 3/10/2020, 12:55:54 PM inlet alami coba 1.fez 125

100 Residual soil

Poor quality of limestone

1 75 Poor quality of volcanic breccia Very poor quality of limestone1 Very poor quality of volcanic breccia 50 Good quality of volcanic breccia 25 0 -25

0 25 50 75 100 125 150 175 200 225 250 275 Project Project4

Analysis Description

Drawn By Scale 1:1104 Company Date File Name PHASE2 8.014 3/8/2020, 11:34:07 PM outlet lereng alami rev.fez

FIGURE 3. Geometries of natural slopes: (a) inlet; (b) outlet.

Journal of Applied Geology 45 FATKHIANDARI et al.

A B

C D

FIGURE 4. Photographs of rock cores: (A) very poor quality of limestone; (B) very poor quality of volcanic breccia; (C) moderate quality of volcanic breccia; (D) good quality of volcanic breccia. the research area were 0.3 and 0.8, respectively. (i.e., 40° for natural inlet slope and 45° for exca- The calculated seismic coefficient for the pseu- vated inlet slope). Meanwhile, the critical SRF dostatic slope stability analyses was, therefore, value of the outlet slope increased as the slope 0.12. inclination reduced due to excavation (i.e., 51° for natural outlet slope and 45° for excavated 4.3 Portal slope stability outlet slope). The trends of decreased and in- Contours of maximum shear strains resulted creased critical SRF values of the inlet and out- from the slope stability analyses for the natu- let slopes, respectively, under static load, were ral and excavated slopes under static and earth- consistent with those under earthquake load quake loads are shown in Figure 5 to Figure 8. (Table 5). At the same time, the critical SRF values are summarized in Table 5. In general, the natural 5C ONCLUSIONS and designed excavated slopes met the stability The engineering geological mapping and eval- requirements specified in SNI 8460 (BSN, 2017), uation of rock cores indicated that the inlet tun- where the slopes under static and earthquake nel slope consisted of four types of materials, loads had critical SRF (or factor safety) of more namely residual soil, poor quality of volcanic than 1.5 and 1.1, respectively. Figure 6 and Fig- breccia, very poor quality of volcanic breccia, ure 8 show that maximum shear strains devel- and good quality of volcanic breccia. The out- oped at the toes of the inlet and outlet excavated let portal slope consisted of six types of mate- slopes above the tunnel portal. The maximum rials, namely residual soil, very poor quality of shear strain values were relatively insignificant limestone, poor quality of limestone, very poor (i.e., less than 5 %), and the critical SRF values quality of volcanic breccia, poor quality brec- were relatively high. cia, and good quality breccia. Based on the The simulation results imply that the earth- secondary elastic wave velocity (Vs) values, the quake load reduces the critical SRF values of rock masses in the research area were classi- all the slopes. Under the static load, the criti- fied as hard rock (SA). Seismic analyses based cal SRF value of the inlet slope decreased as the on the earthquake hazard source map with a slope inclination increased due to excavation 10 % probability of exceedance in 50 years pro-

46 Journal of Applied Geology NUMERICAL EVALUATION OF TUNNEL PORTAL SLOPE STABILITY AT BAGONG DAM SITE

Critical SRF: 3.99 Maximum Shear Strain 0.00

0.08 60 0.16

0.24

0.32

0.40 1 0.48

0.56 40 0.64

0.72 1 0.80 20 0

0 20 40 60 80 100 120 140 Project Project2

Analysis Description

Drawn By Scale 1:531 Company Date File Name INTERPRET 8.014 3/10/2020, 12:55:54 PM inlet alami coba 2.fez

Critical SRF: 2.71 Maximum Shear Strain 0.00

0.30 60 0.60 0.12 0.90

1.20

1.50 1 1.80

2.10

40 2.40

2.70

3.00 1 20 0

0 10 20 30 40 50 60 70 80 90 100 110 120 130 Project Project2

Analysis Description

Drawn By Scale 1:497 Company Date File Name INTERPRET 8.014 3/10/2020, 12:55:54 PM inlet alami coba 2_gempa012.fez

FIGURE 5. Contours of maximum shear strains developed in natural inlet slopes resulted from (a) static; (b) pseudostatic analyses.

Journal of Applied Geology 47 FATKHIANDARI et al.

Critical SRF: 2.4 Maximum Shear Strain 0.00

60 0.01

0.01

0.02

0.03

0.04

0.04 1

0.05 40 0.06

0.06

0.07 1 20 0

0 10 20 30 40 50 60 70 80 90 100 110 120 130 Project Project1

Analysis Description

Drawn By Scale 1:482 Company Date File Name INTERPRET 8.014 3/11/2020, 9:11:53 AM inlet desain coba 2.fez

60 Critical SRF: 2.31 Maximum Shear Strain 0.00

0.08 50 0.16 0.12

0.24 1 0.32

40 0.40

0.48

0.56

0.64 1 30 0.72

0.80 20 10 0

0 10 20 30 40 50 60 70 80 90 100 110 Project Project1

Analysis Description

Drawn By Scale 1:437 Company Date File Name INTERPRET 8.014 3/11/2020, 9:11:53 AM inlet desain coba 2_gempa 012.fez

FIGURE 6. Contours of maximum shear strains developed in excavated inlet slopes resulted from (a) static; (b) pseudostatic analyses.

48 Journal of Applied Geology NUMERICAL EVALUATION OF TUNNEL PORTAL SLOPE STABILITY AT BAGONG DAM SITE

Critical SRF: 2.63 150

Maximum

125 Shear Strain 0.00

0.00

100 0.00

0.00

0.01

1 0.01 75 0.01

1 0.01 0.01

50 0.01 25 0

0 25 50 75 100 125 150 175 200 225 250 275 Project Project4

Analysis Description

Drawn By Scale 1:1103 Company Date File Name INTERPRET 8.014 3/8/2020, 11:34:07 PM outlet lereng alami rev.fez

150 Critical SRF: 2.01

125 0.12

Maximum Shear Strain 100 0.00

0.00

0.00 1

75 0.00

0.00

1 0.01

0.01 50 0.01

0.01

0.01 25 0

0 25 50 75 100 125 150 175 200 225 250 275 Project Project4

Analysis Description

Drawn By Scale 1:1083 Company Date File Name INTERPRET 8.014 3/8/2020, 11:34:07 PM outlet lereng alami +gempa rev 012.fez

FIGURE 7. Contours of maximum shear strains developed in natural outlet slopes resulted from (a) static; (b) pseudostatic analyses.

Journal of Applied Geology 49 FATKHIANDARI et al.

Critical SRF: 4.97 125

Maximum Shear Strain 0.00

0.01 100 0.01

0.02

0.03 1

75 0.04

0.04 1 0.05

0.06

50 0.06

0.07 25 0

0 25 50 75 100 125 150 175 200 225 250 275 Project Project1

Analysis Description

Drawn By Scale 1:1050 Company Date File Name INTERPRET 8.014 3/4/2020, 10:21:22 AM outlet lereng desain rev.fez

Critical SRF: 3.49 175

0.12 150

Maximum 125 Shear Strain 0.00

0.01

100 0.01

0.02

0.03 1 0.03 75 0.03 1 0.04

0.05

50 0.05 25 0

0 25 50 75 100 125 150 175 200 225 250 275

FIGURE 8. Contours of maximum shear strains developed in excavated outlet slopes resulted from (a) static; (b) pseudostatic analyses.

50 Journal of Applied Geology NUMERICAL EVALUATION OF TUNNEL PORTAL SLOPE STABILITY AT BAGONG DAM SITE

TABLE 5. Summary of slope stability analysis re-

i sults. = i m Critical SRF Slope

GSI m Natural slope Excavated slope Earth- Earth- Static Static quake load quake load (kPa) load

c load σ Inlet 4.0 2.7 2.4 2.3 3.5

(°) Outlet 2.6 2.0 5.0 φ

vided by the National Earthquake Center (2017) (kPa) indicated that the PGA and the corresponding ampliﬁcation factor FPGA in the research area

v c were 0.3 and 0.8, respectively. The calculated seismic coefﬁcient for the pseudostatic slope stability analyses was 0.12. The numerical anal- = uniaxial compressive strength (UCS) of intact rock;

c ysis results showed that the earthquake load σ

(kPa) reduced the critical Strength Reduction Factor E (SRF) values of the slopes. However, the natural and excavated tunnel portal slopes were rela- ) 3 tively stable under static and earthquake loads. The natural slope at the tunnel inlet with a 40°

(kN/m inclination had a critical SRF value of 4.0, while γ that of at the tunnel outlet with a 51° inclina- = internal friction angle; tion had a critical SRF value of 2.6. Under static φ

4. Material properties. load, the excavated slopes at the tunnel inlet and outlet having a 45° inclination had criti-

ABLE cal SRF values of 2.4 and 5.0, respectively. Un- T = cohesion;

c der earthquake load, the excavated slopes at the tunnel inlet and outlet had critical SRF values of 2.3 and 3.5, respectively. In summary, the natural and excavated inlet and outlet portal slopes met the requirements speciﬁed in SNI 8460 (BSN, 2017) for seismic slope designs. = Poisson’s ratio; v ACKNOWLEDGEMENTS The authors would like to thank Balai Besar Wilayah Sungai (BBWS) Brantas, the Ministry of Public Works and Housing of Indonesia, for permission conducting this research. The ﬁrst

= Young’s modulus; author would like to thank the Ministry of Pub- E = disturbance factor.

D lic Works and Housing of Indonesia for the master’s degree scholarship. The assistance of Ms. Elisabeth Cary Cesaria in conducting ﬁeld

Layer 2Layer 3 Poor quality breccia unsaturatedLayer Poor 4 quality breccia saturatedLayer 5 Very poor quality breccia unsaturatedLayer 6 Very poor quality breccia saturated Good quality breccia saturatedLayer 5–14 24–30 2Layer 3 Poor quality limestone unsaturated 14–24Layer 24–36 Very 4 poor quality limestone 19.7 unsaturatedLayer 19.7 5 Poor quality breccia unsaturatedLayer 6 Poor quality breccia 36–70 20.82 saturated 20.82Layer 4–16 7 Very poor 4–21.5 quality breccia saturated Good 2902753.6 quality 728978.6 breccia saturated 0.3 21.73 2902753.6 0.3 24.4 728978.6 24.4 0.3 4–37.5 0.3and 37.5–47 3314766.0 - - 36–39 41900000.0 19633300.0 19.1 0.3laboratory - 0.18 0.09 20.82 - 47–50 - - 20.49 - - - 2902753.6 - 25363.2 - 23.65 728978.6 0.3 1498.0 25363.2works 2902753.6 0.3 25.9 - 1498.0 - 15 0.3 - 25.9 4334517.2 18 - 14222.21 15 23090.0 0.307 29460.0 18 -is 18 59.5 - gratefully 18 27 18 - - 20 - 12 12 25363.2 - - 1498.0 26 25363.2 acknowl- 18469.16 15 26 72.5 18 18 20 18

= unit weight; edged. γ

REFERENCES Bor IDInlet Layer 1 Residual soil Material (breccia)Outlet Layer 1 Residual soil (limestone) 0–5Note: 10.16 Depth (m) 0–4 10350.0 0.2 11.52 72.24 0.33 10350.0 0.3 - 63.93 8.52 - - - - - intact rock constant; BBWS Brantas (2014) SID Bendungan Bagong

Journal of Applied Geology 51 FATKHIANDARI et al.

Kabupaten Trenggalek termasuk Model Test. Hammah, R.E, Curran, J.H., Yacoub, T., and Surabaya. Corkum, B. (2004) Stability Analysis of Rock BBWS Brantas (2017) Survey Investigasi Tambahan Slopes using the Finite Element Method. In: EU- Geologi Bendungan Bagong di Kabupaten Treng- ROCK 2004 & 53rd Geomechanics Colloquium, galek. Surabaya. Schubert (ed.). Bieniawski, Z.T. (1989) Engineering Rock Mass Clas- Hoek, E., Carter, T.G., Diederichs, M.S. (2013) Quan- sifications. John Wiley and Sons. tification of the Geological Strength Index Chart. BSN (2017) SNI (Standar Nasional Indonesia) 8460: Geomechanics Symposium, USA. Persyaratan Perancangan Geoteknik. Jakarta. National Earthquake Research Centre (2017) Peta Duncan, J.M., Wright, S.G., and Brandon, T.L. (2014) Sumber Bahaya dan Gempa Indonesia, Jakarta. Soil Strength and Slope Stability. John Wiley & Kementerian Pekerjaan Umum dan Perumahan Sons, Inc. Rakyat. Fatkhiandari, I.A. (2020) Analisis Kestabilan dan Pulunggono, A. dan Martodjojo, S. (1994) Peruba- Sistem Penyangga Terowongan Saluran Penge- han Tektonik Paleogen-Neogen di Jawa. In: Proc. lak Bendungan Bagong Kabupaten Trenggalek Seminar Geologi dan Geotektonik Pulau Jawa. Provinsi Jawa Timur. Master Thesis. Departe- Yogyakarta. Geological Engineering Department ment of Geological Engineering Universitas Gad- Gadjah Mada University. jah Mada. Unpublished. Rocscience Inc. (2001) Application of the finite Griffith, D. V. and P. A. Lane (1999) Slope Stability element method to slope stability, Toronto, 2001– Analysis by Finite Elements. Geotechnique 49, 2004. URL: https://www.rocscience.com/assets/ No. 3., p 387–403 resources/learning/papers/Application-of-the- Hartono, U., Baharuddin, dan Brata, K. (1992) Peta Finite-Element-Method-to-Slope-Stability.pdf geologi regional lembar Madiun. Pusat Penelitian Wyllie, D.C. (2018) Rock Slope Engineering–Civil dan Pengembangan Geologi. Applications. Taylor & Francis Group, LLC.

52 Journal of Applied Geology