基于强度折减法的均质土坡稳定性研究
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摘要
在边坡稳定性分析中,相比于传统的极限平衡法、极限分析法等,强度折减有限元法具有明显的优势。这主要体现在其无须事先假定滑动面的形状和位置,只需通过不断降低边坡岩土体强度参数,进而使边坡岩土体因抗剪强度不能抵抗剪切应力而发生破坏,并最终得到边坡的最危险滑动面及相应的安全系数。但此法还存在诸多问题需解决,基于此,本文以均质土坡为例,采用强度折减有限元法对其进行稳定性分析,提出了一些改进方法,得到了一些结论,具体内容如下:
①本文根据各D-P屈服准则在π平面上投影圆的半径表达式,提出了一种各D-P屈服准则相互转化的新的关系式:不同的D-P屈服准则在π平面上投影圆的半径之比即为对应的D-P屈服准则所得安全系数的比值,由于此值只与土体的内摩擦角有关,为便于应用ANSYS程序采用不同D-P屈服准则求解边坡安全系数时查用,本文列出了常用内摩擦角值对应的各种D-P屈服准则所得均质土坡安全系数的转化表格。
②本文结合工程实例比较了三种计算工况下各D-P屈服准则的计算结果,结论表明采用平面应变条件下和非关联流动法则(ψ=0)下的摩尔匹配D-P准则作为均质土坡的屈服准则最为合适。
③采用强度折减有限元法分析边坡稳定性的一个关键问题是如何根据有限元计算结果判定边坡是否处于失稳破坏状态。本文就边坡常用的三类判据(计算的收敛性、塑性区的贯通和特征部位位移的突变性)展开了讨论并基于边坡特征位移的突变判据提出了一种改进的判定方法:以土坡中最大水平位移为研究对象,提出了以最大水平位移增量、折减系数增量比值△S/△F s与折减系数Fs之间的关系曲线取代最大水平位移Smax与折减系数Fs的关系曲线来确定土坡安全系数的方法。新的曲线更能体现强度折减法的本质,更重要的是求解操作上准确方便,并最终通过工程实例验证了它的可行性。
④不同计算参数对边坡稳定性计算精度的影响:强度参数粘聚力C和内摩擦角φ对边坡的影响较大;刚度参数E和ν对边坡安全系数的影响较小,其影响甚至可以忽略不计,条件是土体弹性模量取值不能过小,若很小,很有可能导致部分土体变形过大而使有限元计算不收敛,最终对安全系数产生很大影响。工程经验表明若没有实际的测量数值,弹性模量E不宜小于1MPa。
Compared with the conventional limit equilibrium method and the limit analytical method, the finite element method based on shear strength reduction (SSR) technique has many evident advantages in analyzing the stability of slope. The primary advantage of the SSR is that it can obtain the most dangerous slip surface and the corresponding safety factors of the slope without predetermining the shape and location of the slip surface , but only by reducing the shear strength parameters of the rock and soil of the slope continuously until the shear stress exceeds the shear strength and consequently result in the failure of the slope. However, there are also many problems of the SSR. In order to solve above problems and deeply investigate the SSR, this thesis mainly takes the homogeneous soil slope as case studies , and analyzes their stabilities by making use of the SSR. Some useful conclusions and improved measures are as follows:
①This paper proposes a new transform formula between any different yield criterions based on Drucker-Prager(D-P) criterions according to their semidiameter of projection circles on theπPlane. The ratio of the semidiameter of the projection circles on theπPlane of different D-P yield criterions is equal to the ratio of their corresponding safety factors. Because the ratio is only relative to the friction angle of the soil, this paper lists the transform tables about the frequently used friction angles and their corresponding safety factors under different D-P yield criterions, so that the safety factors of the slope can be found conveniently through the tables when different D-P yield criterions are employed in analyzing the stability of the slope in ANSYS.
②This paper compares the results of different D-P yield criterions under three diffirent calculated conditions, and the conclusions indicate that it is more appropriate to take the D-P yield criterion which is matched by the Mohr-Coulomb criterion under the plane strain condition as the yield criterion of the homogeneous soil slope.
③One of the most important problems to analyse the stability of slope with the finite element method based on SSR technique is how to evaluate whether the slope is steady or not according to the result of FEM. This paper discusses three common criterias(the convergence of numerical computaions, the connectivity of plactic zone and the abruptness of the displacement or deformation at a certain characteristic location) and proposes an improved method based on the abruptness of the displacement or deformation at a certain characteristic location: this paper makes research on the maximal horizontal displacement, and obtains the safety factor of soil slope with the new curve of the ratio of the maximal horizontal displacement increment△S and strength reduction coefficient incremen△Fs and strength reduction coefficient Fs instead of the curve of the maximal horizontal displacement Smax and strength reduction coefficient Fs. The new curve can show the essence of SSR technique more clearly, and also can make the solution more exact and easy, and finally prove it feasible with some examples of application.
④Different calculating parameters have various influences on the analysis accuracy of slope stability: First, the variation of cohesion C and friction angleφaffects the analysis results evidently, and the the variation of E andνaffects the analysis slighty ,which can nearly be igored.However,the value of E can’t be too little, or it will cause too large value of deformation of the slope, which results in the divergence of numerical analysis and affects the safety factor accurately.In case of no practical data, it’s better for the Young’s modulus E to be greater than equal to 1.0Mpa.
①本文根据各D-P屈服准则在π平面上投影圆的半径表达式,提出了一种各D-P屈服准则相互转化的新的关系式:不同的D-P屈服准则在π平面上投影圆的半径之比即为对应的D-P屈服准则所得安全系数的比值,由于此值只与土体的内摩擦角有关,为便于应用ANSYS程序采用不同D-P屈服准则求解边坡安全系数时查用,本文列出了常用内摩擦角值对应的各种D-P屈服准则所得均质土坡安全系数的转化表格。
②本文结合工程实例比较了三种计算工况下各D-P屈服准则的计算结果,结论表明采用平面应变条件下和非关联流动法则(ψ=0)下的摩尔匹配D-P准则作为均质土坡的屈服准则最为合适。
③采用强度折减有限元法分析边坡稳定性的一个关键问题是如何根据有限元计算结果判定边坡是否处于失稳破坏状态。本文就边坡常用的三类判据(计算的收敛性、塑性区的贯通和特征部位位移的突变性)展开了讨论并基于边坡特征位移的突变判据提出了一种改进的判定方法:以土坡中最大水平位移为研究对象,提出了以最大水平位移增量、折减系数增量比值△S/△F s与折减系数Fs之间的关系曲线取代最大水平位移Smax与折减系数Fs的关系曲线来确定土坡安全系数的方法。新的曲线更能体现强度折减法的本质,更重要的是求解操作上准确方便,并最终通过工程实例验证了它的可行性。
④不同计算参数对边坡稳定性计算精度的影响:强度参数粘聚力C和内摩擦角φ对边坡的影响较大;刚度参数E和ν对边坡安全系数的影响较小,其影响甚至可以忽略不计,条件是土体弹性模量取值不能过小,若很小,很有可能导致部分土体变形过大而使有限元计算不收敛,最终对安全系数产生很大影响。工程经验表明若没有实际的测量数值,弹性模量E不宜小于1MPa。
Compared with the conventional limit equilibrium method and the limit analytical method, the finite element method based on shear strength reduction (SSR) technique has many evident advantages in analyzing the stability of slope. The primary advantage of the SSR is that it can obtain the most dangerous slip surface and the corresponding safety factors of the slope without predetermining the shape and location of the slip surface , but only by reducing the shear strength parameters of the rock and soil of the slope continuously until the shear stress exceeds the shear strength and consequently result in the failure of the slope. However, there are also many problems of the SSR. In order to solve above problems and deeply investigate the SSR, this thesis mainly takes the homogeneous soil slope as case studies , and analyzes their stabilities by making use of the SSR. Some useful conclusions and improved measures are as follows:
①This paper proposes a new transform formula between any different yield criterions based on Drucker-Prager(D-P) criterions according to their semidiameter of projection circles on theπPlane. The ratio of the semidiameter of the projection circles on theπPlane of different D-P yield criterions is equal to the ratio of their corresponding safety factors. Because the ratio is only relative to the friction angle of the soil, this paper lists the transform tables about the frequently used friction angles and their corresponding safety factors under different D-P yield criterions, so that the safety factors of the slope can be found conveniently through the tables when different D-P yield criterions are employed in analyzing the stability of the slope in ANSYS.
②This paper compares the results of different D-P yield criterions under three diffirent calculated conditions, and the conclusions indicate that it is more appropriate to take the D-P yield criterion which is matched by the Mohr-Coulomb criterion under the plane strain condition as the yield criterion of the homogeneous soil slope.
③One of the most important problems to analyse the stability of slope with the finite element method based on SSR technique is how to evaluate whether the slope is steady or not according to the result of FEM. This paper discusses three common criterias(the convergence of numerical computaions, the connectivity of plactic zone and the abruptness of the displacement or deformation at a certain characteristic location) and proposes an improved method based on the abruptness of the displacement or deformation at a certain characteristic location: this paper makes research on the maximal horizontal displacement, and obtains the safety factor of soil slope with the new curve of the ratio of the maximal horizontal displacement increment△S and strength reduction coefficient incremen△Fs and strength reduction coefficient Fs instead of the curve of the maximal horizontal displacement Smax and strength reduction coefficient Fs. The new curve can show the essence of SSR technique more clearly, and also can make the solution more exact and easy, and finally prove it feasible with some examples of application.
④Different calculating parameters have various influences on the analysis accuracy of slope stability: First, the variation of cohesion C and friction angleφaffects the analysis results evidently, and the the variation of E andνaffects the analysis slighty ,which can nearly be igored.However,the value of E can’t be too little, or it will cause too large value of deformation of the slope, which results in the divergence of numerical analysis and affects the safety factor accurately.In case of no practical data, it’s better for the Young’s modulus E to be greater than equal to 1.0Mpa.
引文
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[2] Bishop A W.The use of the slip circle in the stability analysis of slopes [J].Geotechnique, 1955,(5):7~17.
[3] Janbu N.Application of composite slip surface for stability analysis[C].Proceedings of European Conference on Stability of Earth Slopes,Sweden,1954,(3):43~49.
[4] Spencer E.A method of analysis of the stability of embankments assuming parallel interslice forces[J].Geotechnique,1967,17(1):11-26.
[5] Morgenstern N R,Price V E.The Analysis of the Stability of General Slip Surfaces[J]. Geotechniqu,1965,15(1):79~93.
[6] Chen Z,Morgenstern N R.Extensions to the generalized method of slices for stability analysis [J].Canadian Geothechniacal Joural,1983,20(1):104~119.
[7] 杨庚宇.土坡稳定分析中条分法的解析计算[J].力学与实践,1995,(2).
[8] 陆亦庄.土坡稳定性分析瑞典法最危险圆弧圆心位置的探求[J].路基工程,1997,(2).
[9] 张雄.边坡稳定性分析的改进条分法[J].岩土工程学报,1994,16(3):84~92.
[10] 秦鸣.土坡稳定的优化分析[J].华东交通大学学报,1996,(2).
[11] 朱大勇.边坡临界滑动场及其数值模拟[J].岩土工程学报,1997(1):63~68.
[12] 郑颖人,赵尚毅,时卫民.边坡稳定分析的一些进展[J].地下空间,2001,21(5):450~454.
[13] 杨明成,郑颖人.基于极限平衡理论析局部最小安全系数法[J].岩土工程学报,2002,24(3):600~604.
[14] 徐秉业.结构塑性极限分析[M].北京:中国建筑工业出版社,1985.
[15] 郑颖人,龚晓南.岩土塑性力学基础[M].北京:中国建筑工业出版社,1989.
[16] 潘家铮.建筑物的抗滑稳定和滑坡分析[M].北京:中国水利出版社,1980.
[17] 吴世明.土坡稳定的非线性极限分析[J].岩土工程学报,1987,9(6):27~37.
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