(1. State Key Laboratory of Geomechanics and Geotechnical Engineering，Institute of Rock and Soil Mechanics，Chinese Academy of Sciences，Wuhan，Hubei 430071，China；2. University of Chinese Academy of Sciences，Beijing 100049，China；
3. Yunnan Dayong Highway Co.，Ltd.，Dali，Yunnan 671000，China)
Abstract：Newmark rigid-block analysis is a permanent displacement calculation method which has been widely used in practice. However，the traditional method can only apply to the shallow linear slip surfaces which slip directions are close to the slope angle. In order to extend this method to circle slip surface and deep linear slip surface，the functions to calculate the seismic yield coefficient are improved based on the traditional methods. Then the permanent displacements of different slip surfaces are analyzed and compared with other Newmark methods including slices method and finite element decoupled method and the influences of slope height，angle and the form of slip surface on seismic yield coefficient are studied. Finally the proposed method is compared with large shaking table test. The results show that，when the slip surface is large，the traditional Newmark method is underestimated the permanent displacement of circle and deep linear slip surface. The improved Newmark method shows the great agreement with slicing methods and finite element decoupled method. The yield acceleration is related with stability coefficient，the range of slip surface and slope angle. The relationship between different levels of earthquake intensities and permanent displacement shows a good agreement with large shaking table test，which confirms that the modified Newmark method inherits the traditional method′s advantages and has better precision and wider application.
[1] 李瑞芳. 基于斜条分法边坡地震永久位移分析[硕士学位论文][D]. 长沙：湖南大学，2016.(LI Ruifang. Seismic displacements analysis of slopes with inclined slices[M. S. Thesis][D]. Changsha：Hunan University，2016.(in Chinese))
[2] SEED H B. Closure on landslides during earthquakes due to soil liquefaction[J]. Journal of Soil Mechanics and Foundations Div.，1969，95(SM 4)：1 123.
[3] NEWMARK N M. Effects of earthquakes on dams and embankments[J]. Geotechnique，1965，15(2)：139–160.
[4] MAKDISI F I，SEED H B. A simplified procedure for estimating earthquake-induced deformations in dams and embankments[R]. California：Earthquake Engineering Research Center，College of Engineering，University of California，1977：2–13.
[5] AMBRASEYS N N，MENU J M. Earthquake-induced ground displacements[J]. Earthquake Engineering and Structural Dynamics，1988，16(7)：985–1 006.
[6] JIBSON R W. Predicting earthquake-induced landslide displacements using Newmark's sliding block analysis[J]. Transportation Research Record，1993，1411：9–17.
[7] 王 欢，车爱兰，葛修润，等. 岩质高边坡动力稳定性评价方法与应用[J]. 上海交通大学学报，2011，45(5)：706–710.(WANG Huan，CHE Ailan，GE Xiurun，et al. Application of the method for seismic stability of high rock slope[J]. Journal of Shanghai Jiaotong University，2011，45(5)：706–715.(in Chinese))
[8] 薄景山，徐国栋，景立平. 土边坡地震反应及其动力稳定性分析[J]. 地震工程与工程振动，2001，21(2)：116–120.(BO Jingshan，XU Guodong，JING Liping. Seismic response and dynamic stability analysis of soil slopes[J]. Earthquake Engineering and Engineering Vibration，2001，21(2)：116–120.(in Chinese))
[9] 王 斌，车爱兰，葛修润. 岩质高陡边坡动力响应及失稳机制大型振动台模型试验研究[J]. 上海交通大学学报，2015，49(7)：951–956.(WANG Bin，CHE Ailan，GE Xiurun. Shaking table test on earthquake response of discontinuous medium high and steep rock slope[J]. Journal of Shanghai Jiaotong University，2015，49(7)：951–956.(in Chinese))
[10] 杨国香，叶海林，伍法权，等. 反倾层状结构岩质边坡动力响应特性及破坏机制振动台模型试验研究[J]. 岩石力学与工程学报，2012，31(11)：2 214–2 221.(YANG Guoxiang，YE Hailin，WU Faquan，et al. Shaking table model test on dynamic response characteristics and failure mechanism of anti-dip layered rock slope [J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(11)：2 214–2 221.(in Chinese))
[11] 黄润秋. 灾害性崩滑地质过程的全过程模拟[J]. 中国地质灾害与防治学报，1994，5(增)：11–17.(HUANG Runqiu. Full-course Simulation of Hazardous Rockfalls and Avalanches[J]. The Chineses Journal of Geological Hazard and Control，1994，5(Supp.1)：11–17.(in Chinese))
[12] 刘忠玉，马崇武，苗天德，等. 高速滑坡远程预测的块体运动模型[J]. 岩石力学与工程学报，2000，19(6)：742–746.(LIU Zhongyu，MA Chongwu，MIAO Tiande，et al. Kinematic block model of long run-out prediction[J]. Chinese Journal of Rock Mechanics and Engineering，2000，19(6)：742–746.(in Chinese))
[13] 邬爱清，林绍忠，马贵生，等. 唐家山堰塞坝形成机制DDA模拟研究[J]. 人民长江，2008，39(22)：91–95.(WU Aiqing，LIN Shaozhong，MA Guisheng，et al. Formation mechanism analysis of Tangjiashan barrier dam by DDA software[J]. Yangtze River，2008，39(22)：91–95.(in Chinese))
[14] 曹琰波，戴福初，许 冲，等. 唐家山滑坡变形运动机制的离散元模拟[J]. 岩石力学与工程学报，2011，30(增1)：2 878–2 887.(CAO Yanbo，DAI Fuchu，XU Chong，et al. Discrete element simulation of deformation and movement mechanism for Tangjiashan landslide[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(Supp.1)：2 878–2 887.(in Chinese))
[15] JIBSON R W，HARP E L，MICHAEL J A. A method for producing digital probabilistic seismic landslide hazard maps[J]. Engineering Geology，2000，58(3)：271–289.
[16] JIBSON R W. Regression models for estimating coseismic landslide displacement[J]. Engineering Geology，2007，91(2)：209–218.
[17] 徐光兴，姚令侃，李朝红，等. 基于汶川地震强震动记录的边坡永久位移预测模型[J]. 岩土工程学报，2012，34(6)：1 131–1 136.
(XU Guangxing，YAO Lingkan，LI Chaohong，et al. Predictive models for permanent displacement of slopes based on recorded strong-motion
data of Wenchuan Earthquake[J]. Chinese Journal of Geotechnical Engineering，2012，34(6)：1 131–1 136.(in Chinese))
[18] STRENK P M，WARTMAN J. Uncertainty in seismic slope deformation model predictions[J]. Engineering Geology，2011，122(1)：61–72.
[19] INGLES J，DARROZES J，SOULA J C. Effects of the vertical component of ground shaking on earthquake-induced landslide displacements using generalized Newmark analysis[J]. Engineering Geology，2006，86(2)：134–147.
[20] BIONDI G，CASCONE E，MAUGERI M. Seismic response of submerged cohesionless slopes[C]// International Conferences on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics. [S. l.]：[s. n.]，2001.
[21] DENG J，TSUTSUMI Y，KAMEYA H，et al. A modified procedure to evaluate earthquake-induced displacement of slopes containing a weak layer[J]. Soils and Foundations，2010，50(3)：413–420.
[22] BANDINI V，BIONDI G，CASCONE E，et al. A GLE-based model for seismic displacement analysis of slopes including strength degradation and geometry rearrangement[J]. Soil Dynamics and Earthquake Engineering，2015，71：128–142.
2019, Vol. 38 
