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| Stability charts for rock slopes based on the method of reduction of Hoek-Brown strength |
| SUN Chaowei1，CHAI Junrui1，2，XU Zengguang2，QIN Yuan2，LI Gang1 |
(1. Shaanxi Key Laboratory of Safety and Durability of Concrete Structures，Xijing University，Xi?an，Shaanxi 710123，China；
2. State Key Laboratory Base of Eco-hydraulic in Northwest Arid Area，Xi?an University of Technology，Xi?an，
Shaanxi 710048，China) |
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Abstract Stability charts provide a simple and effective way to evaluate the preliminary slope stability. Using the Hoek-Brown strength reduction FEM，this paper presents a series of stability charts to determine the safety factor of rock mass slopes satisfying the Hoek-Brown criterion. Firstly，the explicit formula of instantaneous Mohr- Coulomb friction angle and cohesive strength are derived based on the normal and shear stresses relationship of the Hoek-Brown criterion. Then，implementation of the non-linear Hoek-Brown strength reduction method is achieved in slope stability calculations. An example analysis shows that the Hoek-Brown strength reduction method can obtain a reliable safety factor and slip surface，but avoid determining instantaneous friction angle ?i and cohesive strength ci through iteration analysis. On this basis，stability charts for calculating the safety factors with a specified slope angle ? = 45°and disturbance factor D = 0 are proposed. Then，the disturbance weighting factor fD and the slope angle weighting factor f? are established to illustrate the influence of the disturbance factor and slope angle on the stability of rock slopes，respectively，and the charts for determining fD and f? are then provided. Thus，Stability charts for rock mass slopes satisfying the Hoek-Brown criterion are produced. Finally，this method is applied to two real engineering cases，and the results show that the proposed stability charts can be used to determine safety factors of rock mass slopes reliably.
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[1] TAYLOR D W. Stability of earth slopes[J]. Journal of the Boston Society of Civil Engineers，1937，24(3)：197–246.
[2] JANBU N. Slope stability computations[M]. Norway：Trondheim，Technical University of Norway，1968.
[3] GENS A，HUTCHINSON J N，CAVOUNIDIS S. Three-dimensional analysis of slides in cohesive soils[J]. Geotechnique，1988，38(1)：1–23.
[4] BAKER R. A second look at Taylor?s stability chart[J]. Journal of Geotechnical and Geoenvironmental Engineering，2003，129(12)： 1 102–1 108.
[5] MICHALOWSKI R L. Stability charts for uniform slopes[J]. Journal of Geotechnical and Geoenvironmental Engineering，2002，128(4)：351–355.
[6] MICHALOWSKI R L. Limit analysis and stability charts for 3D slope failures[J]. Journal of Geotechnical and Geoenvironmental Engineering，2010，136(4)：583–593.
[7] MICHALOWSKI R L，DRESCHER A. Three-dimensional stability of slopes and excavations[J]. Geotechnique，2009，59(10)：839–850.
[8] MICHALOWSKI R L，MARTEL T. Stability charts for 3D failures of steep slopes subjected to seismic excitation[J]. Journal of Geotechnical and Geoenvironmental Engineering，2011，137(2)：183–189.
[9] LI A J，MERIFIELD R S，LYAMIN A V. Limit analysis solutions for three dimensional undrained slopes[J]. Computers and Geotechnics，2009，36(8)：1 330–1 351.
[10] LI A J，MERIFIELD R S，LYAMIN A V. Three-dimensional stability charts for slopes based on limit analysis methods[J]. Canadian Geotechnical Journal，2010，47(12)：1 316–1 334.
[11] STEWARD T，SIVAKUGAN N，SHUKLA S K，et al. Taylor?s slope stability charts revisited[J]. Journal of Geotechnical and Geoenvironmental Engineering，2011，11(4)：348–352.
[12] SUN J，ZHAO Z. Stability charts for homogenous soil slopes[J]. Journal of Geotechnical and Geoenvironmental Engineering，2013，139(12)：2 212–2 218.
[13] SUN C W，CHAI J R，XU Z G，et. al. 3D stability charts for convex and concave slopes in plan view with homogeneous soil based on the strength-reduction method[J]. International Journal of Geomechanics，2017，17(5)：215–225.
[14] 卢坤林，朱大勇，杨 扬. 均质边坡准三维安全系数实用计算曲线[J]. 岩土力学，2012，33(增2)：111–117.(LU Kunlin，ZHU Dayong，YANG Yang. Calculation charts for estimating safety factors of 3D homogeneous slopes[J]. Chinese Journal of Rock and Soil Mechanics，2012，33(Supp.2)：111–117.(in Chinese))
[15] HOEK E，BROWN E T. Empirical strength criterion for rock masses[J]. Journal of Geotechnical and Geoenvironmental Engineering，1980，106(9)：1 013–1 035.
[16] DAWSON E M，ROTH W H，DRESCHER A. Slope stability analysis by strength reduction[J]. Geotechnique，1999，49(6)：835–840.
[17] DUNCAN J M. Fellow state of art：limit equilibrium and finite element analysis of slopes[J]. Journal of Geotechnical and Geoenvironmental Engineering，1996，122(7)：577–596.
[18] UGAI K，LESHCHINSKY D. Three-dimensional limit equilibrium and finite element analysis：a comparison of results[J]. Soils Found，1995，35(4)：1–7.
[19] HOEK E，CARRANZA-TORRES C，CORKUM B. Hoek-Brown failure criterion-2002 edition[C]// Proceedings of the North American Rock Mechanics Society Meeting. Toronto：University of Toronto Press，2002：267–273.
[20] YANG X L，LI L，YIN J H. Stability analysis of rock slopes with a modified Hoek-Brown failure criterion[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2004，28(2)：181–190.
[21] JOHAN C，LARS D. An exact implementation of the Hoek-Brown criterion for elasto-plastic finite element calculations[J]. International Journal of Rock Mechanics and Mining Sciences，2008，48(6)：831–847.
[22] PRIEST S D. Determination of shear strength and three-dimensional yield strength for the Hoek-Brown yield criterion[J]. Rock Mechanics and Rock Engineering，2005，38(4)：299–327.
[23] 林 杭，曹 平，李江腾，等. 基于广义Hoek-Brown准则的边坡安全系数间接解法[J]. 煤炭学报，2008，33(10)：1 147–1 151.(LIN Hang，CAO Ping，LI Jiangteng，et al. The indirect calculation method for the safety factor of slope based on generalized Hoek-Brown criterion[J]. Journal of China Coal Society，2008，33(10)：1 147– 1 151.(in Chinese))
[24] HAMMAH R E，YACOUB T E，CORKUM B，et al. The shear strength reduction method for the generalized Hoek-Brown criterion[C]// Proceedings of the 40th US Symposium on Rock Mechanics. Anchorage，Alaska：[s. n.]，2005：805–810.
[25] BENZ T，SCHWAB R，KAUTHER R A，et al. A Hoek-Brown criterion with intrinsic material strength factorization[J]. International Journal of Rock Mechanics and Mining Sciences，2008，45(2)：210–222.
[26] 吴顺川，金爱兵，高永涛. 基于广义Hoek-Brown准则的边坡稳定性强度折减法数值分析[J]. 岩土工程学报，2006，28(11)：1 975–1 980.(WU Shunchuan，JIN Aibing，GAO Yongtao. Numerical simulation analysis on strength reduction for slope of jointed rock masses based on gereralized Hoek-Brown failure criterion[J]. Chinese Journal of Rock Mechanics and Engineering，2006，28(11)：1 975–1 980.(in Chinese))
[27] 林 杭，曹 平，赵延林，等. 强度折减法在Hoek-Brown准则中的应用[J]. 中南大学学报：自然科学版，2007，38(6)：1 219–1 224. (LIN Hang，CAO Ping，ZHAO Yanlin，et al. Application of strength reduction method in Hoek-Brown criterion[J]. Journal of Central South University：Science and Technology，2007，38(6)：1 219–1 224.(in Chinese))
[28] 宗全兵，徐卫亚. 基于广义Hoek-Brown强度准则的岩质边坡开挖稳定性分析[J]. 岩土力学，2008，29(11)：3 071–3 076.(ZONG Quanbing，XU Weiya. Stability analysis of excavating rock slope using generalized Hoek-Brown failure criterion[J]. Rock and Soil Mechanics，2008，29(11)：3 071–3 076.(in Chinese))
[29] 宋 琨，晏鄂川，毛 伟，等. 广义Hoek-Brown准则中强度折减系数的确定[J]. 岩石力学与工程学报，2012，31(1)：106–112.(SONG Kun，YAN Echuan，MAO Wei，et al. Determination of shear strength reduction factor for generalized Hoek-Brown criterion[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(1)：106–112.(in Chinese))
[30] 蒋青青. 基于Hoek-Brown准则点安全系数的边坡稳定性分析[J]. 中南大学学报：自然科学版，2009，40(3)：786–790.(JIANG Qingqing. Stability of point safety factor of slope based on Hoek-Brown criterion[J]. Journal of Central South University：Science and Technology，2009，40(3)：786–790.(in Chinese))
[31] FU W X，LIAO Y. Non-linear shear strength reduction technique in slope stability calculation[J]. Computers and Geotechnics，2010，37(3)：288–298.
[32] 廖 异，曾祥国，符文熹，等. Hoek-Brown岩体非线性强度的线性化方法[J]. 中南大学学报：自然科学版，2012，43(12)：4 902–4 911. (LIAO Yi，ZENG Xiangguo，FU Wenxi，et al. Linearization method of non-linear strength of Hoek-Brown rock mass[J]. Journal of Central South University：Science and Technology，2012，43(12)：4 902– 4 911.(in Chinese))
[33] SONMEZ H，ULUSAY R. Modifications to the geological strength index(GSI) and their applicability to stability of slopes[J]. International Journal of Rock Mechanics and Mining Sciences，1999，36(6)：743–760.
[34] LI A J，MERIFIELD R S，LYAMIN A V. Effect of rock mass disturbance on the stability of rock slopes using the Hoek-Brown failure criterion[J]. Computers and Geotechnics，2011，38(4)：546–558.
[35] SHEN J Y，KARAKUS M，XU C S. Chart-based slope stability assessment using the Generalized Hoek-Brown criterion[J]. International Journal of Rock Mechanics and Mining Sciences，2013，64：210–219.
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2018, Vol. 37 
