Document Type : Original Research Paper


1 School of Mining Engineering, College of Engineering, University of Tehran, Tehran, Iran

2 Department of Urban Management, Kyoto University, Kyoto, Japan



One of the most important tasks in designing the undercut slopes is to determine the maximum stable undercut span to which various parameters such as the shear strength of the soil and the geometrical properties of the slope are related. Based on the arching phenomenon, by undercutting a slope, the weight load of the slope is transferred to the adjacent parts, leading to an increase in the stability of the slope. However, it may also lead to a ploughing failure on the adjacent parts. The application of counterweight on the adjacent parts of an undercut slope is a useful technique to prevent the ploughing failure. In other words, the slopes become stronger as an additional weight is put to the legs; hence, the excavated area can be increased to a wider span before the failure of the slope. This technique could be applied in order to stabilize the temporary slopes. In this work, determination of the maximum width of an undercut span is evaluated under both the static and pseudo-static conditions using numerical analyses. A series of tests are conducted with 120 numerical models using various values for the slope angles, the pseudo-static seismic loads, and the counterweight widths. The numerical results obtained are examined with a statistical method using the response surface methodology. An analysis of variance is carried out in order to investigate the influence of each input variable on the response parameter, and a new equation is derived for computation of the maximum stable undercut span in terms of the input parameters.


[1]. Handy, R.L. (1985). The Arch in Soil Arching, J. Geotech. Eng., 111 (3): 302–318

[2]. Janssen, H.A. (1895). Versuche uber getreidedruck in Silozellen, Zeitschrift des Vereins Dtsch. Ingenieure, 35:1045–1049.

[3]. Terzaghi, K. (1943). Theoretical soil mechanics. John Wiley & Sons, New York., Theor. soil Mech. John Wiley Sons, New York.

[4]. Wang, W.L. and Yen, B.C. (1974). Soil arching in slopes, J. Geotech. Eng.

[5]. Bosscher, P.J. and Gray, D.H. (1986). Soil Arching in Sandy Slopes, J. Geotech. Eng., 112 (6): 626–645.

[6]. Pipatpongsa, T., Khosravi, M.H., and Takemura, J. (2013). Physical modeling of arch action in undercut slopes with actual engineering practice to Mae Moh open-pit mine of Thailand, in Proceedings of the 18th International Conference on Soil Mechanics and Geotechnical Engineering (ICSMGE18), 1: 943–946.

[7]. Zhou, J., Qin, C., Pan, Q., and Wang, C. (2019). Kinematic analysis of geosynthetics-reinforced steep slopes with curved sloping surfaces and under earthquake regions, J. Cent. South Univ., 26 (7): 1755–1768.

[8]. Zhang, R., Long, M., Lan, T., Zheng, J., and Geoff, C. (2020). Stability analysis method of geogrid reinforced expansive soil slopes and its engineering application, J. Cent. South Univ., 27 (7): 1965–1980.

[9]. Hedayat, A., Haeri, H., Hinton, J., Masoumi, H., and Spagnoli, G. (2018). Geophysical signatures of shear-induced damage and frictional processes on rock joints, J. Geophys. Res. Solid Earth, 123 (2): 1143-1160.

[10]. Sarfarazi, V., Haeri, H., and Khaloo, A. (2016). The effect of non-persistent joints on sliding direction of rock slopes, Comput. Concr., 17 (6): 723–737.

[11]. Sun, S.W., Zhu, B.Z., and Wang, J.C. (2013). Design method for stabilization of earth slopes with micropiles, Soils Found., 53 (4): 487–497.

[12]. Chen, C.Y. and Martin, G.R. (2002). Soil-Structure interaction for landslide stabilizing piles, Comput. Geotech., 29 (5): 363–386.

[13]. Hosseinian, S. and Seifabad, M.C. (2013). Optimization the Distance between Piles in Supporting Structure Using Soil Arching Effect, 3 (6): 386–391.

[14]. Li, C., Wu, J., Tang, H., Wang, J., Chen, F., and Liang, D. (2015). A novel optimal plane arrangement of stabilizing piles based on soil arching effect and stability limit for 3D colluvial landslides, Eng. Geol., 195: 236–247.

[15]. Ausilio, E., Conte, E., and Dente, G. (2001). Stability analysis of slopes reinforced with piles, Comput. Geotech., 28 (8): 591–611.

[16]. Kourkoulis, R., Gelagoti, F., Anastasopoulos, I., and Gazetas, G. (2011). Slope Stabilizing Piles and Pile-Groups: Parametric Study and Design Insights, J. Geotech. Geoenvironmental Eng., 137 (7): 663–677.

[17]. Kourkoulis, R., Gelagoti, F., Anastasopoulos, I., and Gazetas, G. (2011). Hybrid method for analysis and design of slope stabilizing piles, J. Geotech. Geoenvironmental Eng., 138 (1): 1–14.

[18]. Pipatpongsa, T., Khosravi, M.H., Doncommul, P., and Mavong, N. (2009). Excavation problems in Mae Moh lignite open-pit mine of Thailand, in Proceedings of Geo-Kanto2009, 12: 459–464.

[19]. Khosravi, M.H., Pipatpongsa, T., Takahashi, A., and Takemura, J. (2011). Arch action over an excavated pit on a stable scarp investigated by physical model tests, Soils Found., 51 (4): 723–735.

[20]. Khosravi, M.H., Takemura, J., Pipatpongsa, T., and Amini, M. (2016). In-flight excavation of slopes with potential failure planes, J. Geotech. Geoenvironmental Eng., 142 (5): 601-611.

[21]. Khosravi, M.H., Tang, L., Pipatpongsa, T., Takemura, J., and Doncommul, P. (2012). Performance of counterweight balance on stability of undercut slope evaluated by physical modeling, Int. J. Geotech. Eng., 6 (2): 193–205.

[22]. Sarfaraz, H., Khosravi, M.H., Pipatpongsa, T., and Bakhshandeh Amnieh, H. (2020). Application of Artificial Neural Network for Stability Analysis of Undercut Slopes, Int. J. Min. Geo-Engineering, In-press.

[23]. Terzaghi, K. (1950). Mechanism of landslides, Appl. Geol. to Eng. Pract. Geol. Soc., 83–123.

[24]. Khosravi, M.H., Sarfaraz, H., Esmailvandi, M., and Pipatpongsa, T. (2017). A Numerical Analysis on the Performance of Counterweight Balance on the Stability of Undercut Slopes, Int. J. Min. Geo-Engineering, 51 (1): 63–69.

[25]. Inc, I.G. (2015). FLAC3D: Fast Lagrangian Analysis of Continua in 3 Dimension.

[26]. Myer, R.H. and Montgomery, D.C. (2002). Response surface methodology: process and product optimization using designed experiment. Taylor & Francis.

[27]. Montgomery, D.C. (2017). Design and analysis of experiments. John wiley & sons.

[28]. Anderson, M.J. and Whitcomb P.J. (2004). Optimizing processes using response surface methods for design of experiments., CRC Pres.