考虑土体抗拉强度的边坡永久位移极限分析
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摘要
通过野外观测与室内试验发现,边坡后缘往往存在拉应力区。拉应力区的存在会影响边坡的稳定性,而地震荷载的存在会放大这种影响。分析拉应力区对边坡稳定性的影响,当前主要采用的方式为:对强度准则中抗拉强度进行折减(即张拉截断)。文章通过极限分析上限原理和拟静力法,推导出边坡临界加速度计算方程。以边坡在不同参数组合下的位移系数为基础,输入实测地震波,采用改进的Newmark法对边坡进行位移分析。文章算例的结果表明:拉应力区的存在会大大降低边坡临界加速度,土体在完全张拉截断下的临界加速度对边坡可能会产生超过50%的折减。拉应力区的存在也可以使永久位移达到传统的摩尔库伦理论计算值的2倍之多。文中所有的结果皆以图表形式展示,非常便于理解以及读取数据。
Through field observation and laboratory experiment, it is found that the stability of the slope is influenced by the existence of tensile stress zone in the back edge of the slope, while the influence is amplified by the existence of seismic load. To analyze the impact of tensile stress zone on the stability of slope, the main method used at present is to reduce the tensile strength in the strength criterion(i.e., tension cut-off). According to the upper limit principle of limit analysis and the quasi-static method, the calculation equation of the critical acceleration of the slope is derived. Based on the displacement coefficients of the slope under different parameter combinations, the measured seismic wave was input and the improved Newmark method was used to analyze the displacement of the slope. The results show that the critical acceleration of the slope can be greatly reduced by the existence of the tensile stress area, and the critical acceleration of the soil mass under the complete tension cut-off may produce more than 50% reduction of the slope. The existence of the tensile stress zone can also make the permanent displacement as much as twice the value calculated by the traditional Mohr-Coulomb yield criterion. All of the results in this article are presented in graphical form, which is very easy to understand and read.
Through field observation and laboratory experiment, it is found that the stability of the slope is influenced by the existence of tensile stress zone in the back edge of the slope, while the influence is amplified by the existence of seismic load. To analyze the impact of tensile stress zone on the stability of slope, the main method used at present is to reduce the tensile strength in the strength criterion(i.e., tension cut-off). According to the upper limit principle of limit analysis and the quasi-static method, the calculation equation of the critical acceleration of the slope is derived. Based on the displacement coefficients of the slope under different parameter combinations, the measured seismic wave was input and the improved Newmark method was used to analyze the displacement of the slope. The results show that the critical acceleration of the slope can be greatly reduced by the existence of the tensile stress area, and the critical acceleration of the soil mass under the complete tension cut-off may produce more than 50% reduction of the slope. The existence of the tensile stress zone can also make the permanent displacement as much as twice the value calculated by the traditional Mohr-Coulomb yield criterion. All of the results in this article are presented in graphical form, which is very easy to understand and read.
引文
[1] Keefer D K. Statistical analysis of an earthquake-induced landslide distribution - The 1989 Loma Prieta, California event[J]. Engineering Geology, 2000, 58(3～4): 231～249.
[2] Meehan C L, Vahedifard F. Evaluation of simplified methods for predicting earthquake-induced slope displacements in earth dams and embankments[J]. Engineering Geology, 2013, 152(1): 180～193.
[3] Baker R, Shukha R, Operstein V, et al. Stability charts for pseudo-static slope stability analysis[J]. Soil Dynamics and Earthquake Engineering, 2006, 26(9): 813～823.
[4] Zhang K, Cao P. Slope seismic stability analysis on kinematical element method and its application[J]. Soil Dynamics and Earthquake Engineering, 2013, 50: 62～71.
[5] Zhao L H, Cheng X, Zhang Y B, et al. Stability analysis of seismic slopes with cracks[J]. Computers and Geotechnics, 2016, 77: 77～90.
[6] Yang C W, Zhang J J, Fu X, et al. Improvement of pseudo-static method for slope stability analysis[J]. Journal of Mountain Science, 2014, 11(3): 625～633.
[7] Newmark N M. Effects of earthquakes on dams and embankments[J]. Géotechnique, 1965, 15(2): 139～160.
[8] Rathje E M, Bray J D. Nonlinear coupled seismic sliding analysis of earth structures[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2015, 126(11): 1002～1014.
[9] You L Z, Michalowski R L. Displacement charts for slopes subjected to seismic loads[J]. Computers and Geotechnics, 1999, 25(1): 45～55.
[10] Utili S, Abd A H. On the stability of fissured slopes subject to seismic action[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2016, 40(5): 785～806.
[11] Zhao L H, Cheng X, Dan H C, et al. Effect of the vertical earthquake component on permanent seismic displacement of soil slopes based on the nonlinear Mohr-Coulomb failure criterion[J]. Soils and Foundations, 2017, 57(2): 237～251.
[12] Zhao L H, Cheng X, Li L, et al. Seismic displacement along a log-spiral failure surface with crack using rock Hoek-Brown failure criterion[J]. Soil Dynamics and Earthquake Engineering, 2017, 99: 74～85.
[13] 尤明庆. 均质土坡滑动面的变分法分析[J]. 岩石力学与工程学报, 2006, 25(S1): 2735～2745.YOU Mingqing. Study on landslide of homogeneous soil with calculus of variations[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(S1): 2735～2745. (in Chinese with English abstract)
[14] Duncan J M, Wright S G. Soil strength and slope stability[M]. Hoboken: Wiley, 2005.
[15] Utili S. Investigation by limit analysis on the stability of slopes with cracks[J]. Géotechnique, 2013, 63(2): 140～154.
[16] Michalowski R L. Stability of intact slopes with tensile strength cut-off[J]. Géotechnique, 2017, 67(8): 720～727.
[17] Kaniraj S R, Abdullah H. Effect of berms and tension crack on the stability of embankments on soft soils[J]. Soils and Foundations, 1993, 33(4): 99～107.
[18] Baker R. Tensile strength, tension cracks, and stability of slopes[J]. Soils and Foundations, 1981, 21(2): 1～17.
[19] Park D, Wang Z J, Michalowski R L. Consequences of seismic excitation on slopes in soils with a tensile strength cutoff[A]. Geotechnical Frontiers 2017[C]. Orlando, Florida: American Society of Civil Engineers, 2017: 304～313.
[20] Taylor D W. Fundamentals of soil mechanics[J]. Soil Science, 1948, 66(2): 161.
[21] Chen W F. Limit analysis and soil plasticity[M]. Amsterdam: Elsevier, 1975.
[22] Chang C J, Chen W F, Yao J T P. Seismic displacements in slopes by limit analysis[J]. Journal of Geotechnical Engineering, 1984. 110(7): 860～874.
[23] Michalowski R L, You L Z. Displacements of Reinforced Slopes Subjected to Seismic Loads[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2000, 126(8): 685～694.
[24] Li X P, He S M, Wu Y. Seismic displacement of slopes reinforced with piles[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2010, 136(6): 880～884.
[25] Nadukuru S S, Michalowski R L. Three-dimensional displacement analysis of slopes subjected to seismic loads[J]. Canadian Geotechnical Journal, 2013, 50(6): 650～661.
[26] He Y, Hazarika H, Yasufuku N, et al. Three-dimensional limit analysis of seismic displacement of slope reinforced with piles[J]. Soil Dynamics and Earthquake Engineering, 2015, 77: 446～452.
[27] Zhang Y B, Chen G Q, Zheng L, et al. Effects of near-fault seismic loadings on run-out of large-scale landslide: A case study[J]. Engineering Geology, 2013, 166: 216～236.
[28] Zhang Y B, Wang J M, Xu Q, et al. DDA validation of the mobility of earthquake-induced landslides[J]. Engineering Geology, 2015, 194: 38～51.
[29] Zhang Y B, Zhang J, Chen G Q, et al. Effects of vertical seismic force on initiation of the Daguangbao landslide induced by the 2008 Wenchuan earthquake[J]. Soil Dynamics and Earthquake Engineering, 2015, 73: 91～102.
[2] Meehan C L, Vahedifard F. Evaluation of simplified methods for predicting earthquake-induced slope displacements in earth dams and embankments[J]. Engineering Geology, 2013, 152(1): 180～193.
[3] Baker R, Shukha R, Operstein V, et al. Stability charts for pseudo-static slope stability analysis[J]. Soil Dynamics and Earthquake Engineering, 2006, 26(9): 813～823.
[4] Zhang K, Cao P. Slope seismic stability analysis on kinematical element method and its application[J]. Soil Dynamics and Earthquake Engineering, 2013, 50: 62～71.
[5] Zhao L H, Cheng X, Zhang Y B, et al. Stability analysis of seismic slopes with cracks[J]. Computers and Geotechnics, 2016, 77: 77～90.
[6] Yang C W, Zhang J J, Fu X, et al. Improvement of pseudo-static method for slope stability analysis[J]. Journal of Mountain Science, 2014, 11(3): 625～633.
[7] Newmark N M. Effects of earthquakes on dams and embankments[J]. Géotechnique, 1965, 15(2): 139～160.
[8] Rathje E M, Bray J D. Nonlinear coupled seismic sliding analysis of earth structures[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2015, 126(11): 1002～1014.
[9] You L Z, Michalowski R L. Displacement charts for slopes subjected to seismic loads[J]. Computers and Geotechnics, 1999, 25(1): 45～55.
[10] Utili S, Abd A H. On the stability of fissured slopes subject to seismic action[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2016, 40(5): 785～806.
[11] Zhao L H, Cheng X, Dan H C, et al. Effect of the vertical earthquake component on permanent seismic displacement of soil slopes based on the nonlinear Mohr-Coulomb failure criterion[J]. Soils and Foundations, 2017, 57(2): 237～251.
[12] Zhao L H, Cheng X, Li L, et al. Seismic displacement along a log-spiral failure surface with crack using rock Hoek-Brown failure criterion[J]. Soil Dynamics and Earthquake Engineering, 2017, 99: 74～85.
[13] 尤明庆. 均质土坡滑动面的变分法分析[J]. 岩石力学与工程学报, 2006, 25(S1): 2735～2745.YOU Mingqing. Study on landslide of homogeneous soil with calculus of variations[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(S1): 2735～2745. (in Chinese with English abstract)
[14] Duncan J M, Wright S G. Soil strength and slope stability[M]. Hoboken: Wiley, 2005.
[15] Utili S. Investigation by limit analysis on the stability of slopes with cracks[J]. Géotechnique, 2013, 63(2): 140～154.
[16] Michalowski R L. Stability of intact slopes with tensile strength cut-off[J]. Géotechnique, 2017, 67(8): 720～727.
[17] Kaniraj S R, Abdullah H. Effect of berms and tension crack on the stability of embankments on soft soils[J]. Soils and Foundations, 1993, 33(4): 99～107.
[18] Baker R. Tensile strength, tension cracks, and stability of slopes[J]. Soils and Foundations, 1981, 21(2): 1～17.
[19] Park D, Wang Z J, Michalowski R L. Consequences of seismic excitation on slopes in soils with a tensile strength cutoff[A]. Geotechnical Frontiers 2017[C]. Orlando, Florida: American Society of Civil Engineers, 2017: 304～313.
[20] Taylor D W. Fundamentals of soil mechanics[J]. Soil Science, 1948, 66(2): 161.
[21] Chen W F. Limit analysis and soil plasticity[M]. Amsterdam: Elsevier, 1975.
[22] Chang C J, Chen W F, Yao J T P. Seismic displacements in slopes by limit analysis[J]. Journal of Geotechnical Engineering, 1984. 110(7): 860～874.
[23] Michalowski R L, You L Z. Displacements of Reinforced Slopes Subjected to Seismic Loads[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2000, 126(8): 685～694.
[24] Li X P, He S M, Wu Y. Seismic displacement of slopes reinforced with piles[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2010, 136(6): 880～884.
[25] Nadukuru S S, Michalowski R L. Three-dimensional displacement analysis of slopes subjected to seismic loads[J]. Canadian Geotechnical Journal, 2013, 50(6): 650～661.
[26] He Y, Hazarika H, Yasufuku N, et al. Three-dimensional limit analysis of seismic displacement of slope reinforced with piles[J]. Soil Dynamics and Earthquake Engineering, 2015, 77: 446～452.
[27] Zhang Y B, Chen G Q, Zheng L, et al. Effects of near-fault seismic loadings on run-out of large-scale landslide: A case study[J]. Engineering Geology, 2013, 166: 216～236.
[28] Zhang Y B, Wang J M, Xu Q, et al. DDA validation of the mobility of earthquake-induced landslides[J]. Engineering Geology, 2015, 194: 38～51.
[29] Zhang Y B, Zhang J, Chen G Q, et al. Effects of vertical seismic force on initiation of the Daguangbao landslide induced by the 2008 Wenchuan earthquake[J]. Soil Dynamics and Earthquake Engineering, 2015, 73: 91～102.