基于位移等值面的边坡点安全系数分析
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摘要
为了计算坡体局部稳定性并定量分析边坡滑动机理,本文提出一种新的点安全系数计算方法。假定边坡体内任一点的潜在滑动面与通过该点的合位移等值面具有位置一致性,选用Bezier双三次曲面对通过节点的位移等值面进行拟合,曲面上点的位移梯度即为曲面在该点的法向量,节点位移矢量在位移等值面上的投影为该点的滑动方向,据此计算破坏面上的正应力和滑动方向的剪应力。定义边坡点安全系数为该点抗剪强度与滑动方向上剪应力的比值。与基于应力状态的点安全系数不同,本文方法在位移等值面上定义点安全系数,考虑了边坡体的实际滑动方向,更符合边坡的破坏特征。通过ACADS边坡考题验证本文方法的正确性,本文方法能够为边坡工程三维稳定性分析和滑动机理研究提供思路。
In this paper,a new slope point safety factor calculation method was proposed in order to calculate the local stability of slope body and quantify the slope sliding mechanism.Assuming that the potential sliding surface at any point in the slope has a positional consistency with the combined displacement isosurface passing through this point,a Bezier bicubic curved surface was used to fit the displacement isosurface passing the point.The gradient of the surface point was the normal vector of the surface at that point and the projection of the point displacement vector on the displacement isosurface was the sliding direction of this point,whereby the normal stress on the failure surface and the shear stress in the sliding direction were calculated,to define the slope point safety factor as the ratio between the shear strength at the point and the shear stress in the sliding direction.Different from the traditional definition based on the stress state,the new definition in this paper,which is based on the displacement isosurface and considers the actual sliding direction of the slope body,is more consistent with the slope failure characteristics.The correctness of the proposed method has been verified by using the ACADS examination questions.In addition,the proposed method provides a guidance for the three dimensional stability analysis and sliding mechanism study of slope engineering.
In this paper,a new slope point safety factor calculation method was proposed in order to calculate the local stability of slope body and quantify the slope sliding mechanism.Assuming that the potential sliding surface at any point in the slope has a positional consistency with the combined displacement isosurface passing through this point,a Bezier bicubic curved surface was used to fit the displacement isosurface passing the point.The gradient of the surface point was the normal vector of the surface at that point and the projection of the point displacement vector on the displacement isosurface was the sliding direction of this point,whereby the normal stress on the failure surface and the shear stress in the sliding direction were calculated,to define the slope point safety factor as the ratio between the shear strength at the point and the shear stress in the sliding direction.Different from the traditional definition based on the stress state,the new definition in this paper,which is based on the displacement isosurface and considers the actual sliding direction of the slope body,is more consistent with the slope failure characteristics.The correctness of the proposed method has been verified by using the ACADS examination questions.In addition,the proposed method provides a guidance for the three dimensional stability analysis and sliding mechanism study of slope engineering.
引文
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[2]栾茂田,金崇磐,林皋.土体稳定分析极限平衡法改进及其应用[J].岩土工程学报,1992,14(S1):20-29.LUAN Maotian,JIN Chongpan,LIN Gao.Improved Limit Equilibrium Method and Its Applications to Stability Analysis of Soil Masses[J].Chinese Journal of Geotechnical Engineering,1992,14(S1):20-29.
[3]宋二祥.土工结构安全系数的有限元计算[J].岩土工程学报,1997,19(2):1-7.SONG Erxiang.Finte Element Analysis of Safety Factor for Soil Structures[J].Chinese Journal of Geotechnical Engineering,1997,19(2):1-7.
[4]郑颖人,赵尚毅.有限元强度折减法在土坡与岩坡中的应用[J].岩石力学与工程学报,2004,23(19):3381-3388.ZHENG Yingren,ZHAO Shangyi.Application of Strength Reduction FEM in Soil and Rock Slope[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(19):3381-3388.
[5]王庚荪.边坡的渐进破坏及稳定性分析[J].岩石力学与工程学报,2000,19(1):29-33.WANG Gengsun.The Progressive Failure of Slope and the Stability Analysis[J].Chinese Journal of Rock Mechanics and Engineering,2000,19(1):29-33.
[6]凌道盛,涂福彬,卜令方.基于黏聚区域模型的边坡渐进破坏过程强化有限元分析[J].岩土工程学报,2012,34(8):1387-1393.LING Daosheng,TU Fubin,BU Lingfang.Enhanced Finite Element Analysis of Progressive Failure of Slopes Based on Cohesive Zone Model[J].Chinese Journal of Geotechnical Engineering,2012,34(8):1387-1393.
[7]余飞,陈善雄,余和平.顺层岩质边坡渐进破坏及失稳机理的数值模拟研究[J].岩土力学,2005,26(S):36-40.YU Fei,CHEN Shanxiong,YU Heping.Numerical Simulation Study on Progressive Destruction and Failure Mechanism of Bedding Rock Slopes[J].Rock and Soil Mechanics,2005,26(S):36-40.
[8]王毓泰,周维垣.拱坝坝肩岩体稳定分析[M].贵阳:贵州人民出版社,1982:139-143.
[9]吴家冠,段亚辉.江坪河水电站溢洪洞围岩稳定性仿真分析[J].岩土力学,2009,30(8):2431-2435.WU Jiaguan,DUAN Yahui.Simulation Analysis of Stability of Spillway Tunnels of Jiangping River Hydropower Station[J].Rock and Soil Mechanics,2009,30(8):2431-2435.
[10]樊赟赟,王思敬,王恩志,等.岩土材料剪切破坏点安全系数的研究[J].岩土力学,2009,30(S2):200-203.FAN Yunyun,WANG Sijing,WANG Enzhi,et al.Research on Point Safety Factor of Shear Failure Geomaterials[J].Rock and Soil Mechanics,2009,30(S2):200-203.
[11]周华,王国进,傅少君,等.小湾拱坝坝基开挖卸荷松弛效应的有限元分析[J].岩土力学,2009,30(4):1175-1180.ZHOU Hua,WANG Guojin,FU Shaojun,et al.Finite Element Analysis of Foundation Unloading and Relaxation Effects of Xiaowan Arch Dam[J].Rock and Soil Mechanics,2009,30(4):1175-1180.
[12]杨涛,周德培,马惠民,等.滑坡稳定性分析的点安全系数法[J].岩土力学,2010,31(3):971-975.YANG Tao,ZHOU Depei,MA Huimin,et al.Point Safety Factor Method for Stability Analysis of Landslide[J].Rock and Soil Mechanics,2010,31(3):971-975.
[13]徐芝纶.弹性力学[M].北京:高等教育出版社,1990:247-251.