# Mathematical Model of Landslides with Curved Sliding Plane Using Fracture Criterion of Solid Soil-Rock System

## Abstract

Alluvial cliff with high slope and step has been known to cause curving sliding plane. This phenomenon is adopted as a knowledge, but it has never been studied theoretically. In this paper, mathematics derivation phenomenon is proposed using special model of 11 fracture criterion ????-????. The quantity of ???? is A???? 2 with A is a friction coefficient of stress ???? 2 . The failure model was substituted to the corresponding Mohr circle resulting the expected curve. The curve was used to measure the observed field profile to obtain the friction coefficient A.

## References

Alsubal, S., N. B. Sapari., I. S. Harahap, and M. A. M. Al-Bared (2019). A review on mechanism of rainwater in triggering landslide. In IOP Conference Series: Materials Science and Engineering, 513; 012009

Alvioli, M., F. Guzzetti, and M. Rossi (2014). Scaling properties of rainfall induced landslides predicted by a physically based model. Geomorphology, 213; 38–47

Bin, Z, J., Xue, Y, X., Qi, H, S., tang, Y. J, and Zhun, B (2020). Math- ematical statistical model of horizontal displacement and rainfall of step deformation landslide in three gorges reservoir area. Rock and Soil Mechanics, 41(1); 305–311

Dai, Z., Y. Huang., H. Cheng, and Q. Xu (2014). 3D numerical mod- eling using smoothed particle hydrodynamics of flow-like landslide propagation triggered by the 2008 Wenchuan earthquake. Engi- neering Geology, 180; 21–33

Das, B. M(2002). Principles of Geotechnical Engineering. Fifth edition, USA: Bill Stenquist

Das, B. M.(2016). Principles of Geotechnical Engineering, USA : Cem- cage Learning

De-Blasio, F. V. (2011). Introduction to the physics of landslides: lecture notes on the dynamics of mass wasting. London: Springer Science & Business Media

Duc, D. M. (2013). Rainfall-triggered large landslides on 15 De- cember 2005 in Van Canh district, Binh Dinh province, Vietnam. Landslides, 10; 219–230

Fan, L., P. Lehmann., B. McArdell, and D. Or (2017). Linking rainfall-induced landslides with debris flows runout patterns to- wards catchment scale hazard assessment. Geomorphology, 280; 1–15

Gariano, S. L. and F. Guzzetti (2016). Landslides in a changing climate. Earth-Science Reviews, 162; 227–252

Garry, B(2004). Understanding Soil Risk and Hazards, Nebraska: USDA Greco, R., G. Giorgio., G. Capparelli, and P. Versace (2013). Early warning of rainfall-induced landslides based on empirical mobility
function predictor. Engineering Geology, 153; 68–79

Heckson, A, and Rutter, E(2016). The Mohr–Coulomb criterion for intact rock strength and friction–a re-evaluation and consideration
of failure under polyaxial stresses Solid Earth, 7; 493-508 Helwany, S(2007). Applied Soil Mechanics, USA: John Wiley

Labuz, J. P, and Zhang, A.(2012). Mohr Coulomb Failure Criterion, Rock Mech, 45:975-979

Lelovic, A, and Vasovic, D.(2020). Determination of Mohr-Coulomb Parameters for Modelling of Concrete, Crystals: 10, 808

Li, X., S. He., Y. Luo, and Y. Wu (2012). Simulation of the slid- ing process of Donghekou landslide triggered by the Wenchuan
earthquake using a distinct element method. Environmental Earth
Sciences, 65(4); 1049–1054

Liu, H (2020). Wellbore stability evaluation method based on the
continuous tangent envelope of a Mohr circle. Science Progress,
301(1); 1-12

Murthy, V. N. S(2002). Geotechnical Engineering: Principles and Prac-
tices of Soil Mechanics and Foundation Engineering, Taylor and Francis
Inc

Padmaja, S. B., G.V.N. Reddy, and Reddy, E. S (2021). Landslide
stability analysis using mathematical approach. Material Today
Proceedings, 1; 1–10

Permanasari, Vico, I, and Endi, E(2020). Determination of Slip
Surface Using 2D Geoelectric Resistivity Method and Laboratory Analysis for Landslide Prone Area Pesawaran, Lampung Earth and Environmental Science, 537

Permanasari, Akabar, Handayani, Hendrajaya(2020). Determination of the type of soil using 2d geoelectric method and laboratory anal- ysis for landslide area Cililin west java Journal of Physics: Conference Series, 1127(1); 012041

Permanasari(2017). Mekanisme Runtuhan Tebing dengan Bidang Gelincir Melengkung Sebagai Awal Longsoran Lereng, Studi Kasus Daerah Cililin Kabupaten Bandung Barat. Dissertation: Unpub- lished

Saito, H., W. Murakami., H. Daimaru, and T. Oguchi (2017). Effect of forest clear-cutting on landslide occurrences: Analysis of rainfall thresholds at Mt. Ichifusa, Japan. Geomorphology, 276; 1–7

Shanmugam, G. and Y. Wang (2015). The landslide problem. Journal of Palaeogeography, 4(2); 109–166

Shi, C., Y. An., Q. Wu., Q. Liu, and Z. Cao (2016). Numerical simulation of landslide-generated waves using a soil–water cou- pling smoothed particle hydrodynamics model. Advances In Water Resources, 92; 130–141

Thomson, E, and Huppert, H(2007). Granular column collapses: further experimental results Journal Fluida, 575; 117-186

Wesley,L.D(2013). FundamentalsofSoilMechanicsforSedimentary and Residual Soils, Jhon Wiley Press: Canada

Wu, L., Y. Zhou., P. Sun., J. Shi., G. Liu, and L. Bai (2017). Labora- tory characterization of rainfall-induced loess slope failure. Catena, 150; 1–8

Wu, L. Z., A. P. S. Selvadurai., L. M. Zhang., R. Q. Huang, and J. Huang (2016). Poro-mechanical coupling influences on potential for rainfall-induced shallow landslides in unsaturated soils. Advances In Water Resources, 98; 114–121

Zhang, L., X. Zhao., X. Yan, and X. Yang (2016). A semi-analytical method of stress-strain analysis of buried steel pipelines under submarine landslides. Applied Ocean Research, 59; 38–52

## Authors

Permanasari, I. N. P., Hendrajaya, L., & Handayani, G. (2022). Mathematical Model of Landslides with Curved Sliding Plane Using Fracture Criterion of Solid Soil-Rock System. Science and Technology Indonesia, 7(1), 1–8. https://doi.org/10.26554/sti.2022.7.1.1-8