用有限元算出的应力直接计算土坡安全系数

andy77

这个课题我研究过,问题很大
1、原文说 从数学上讲，用上述方法最终都能搜索得到最危险滑裂面并求得最小安全系数。

每个高斯点有2的3次方＝8种不同的应力组合，假如滑弧很大，经过100个高斯点，那就有2的300次方＝2.0370359763344860862684456884094e+90
个应力组合，计算量惊人

2、原文中说 某一点来说出现这样那样的应力方向是可能的，但以往大量的确定性地震反应分析表明，边坡破坏时沿破坏面的应力分布具有一定规律性

由于这些内力的方向都是假定的，即使搜索出来最小可靠度的一个滑弧面，在真正情况中有可能并不能满足应力平衡条件，因此有可能压根不会出现这种情况

因此我在计算中把这种方法否定了，可行性几乎为零

lotus wrote:
1.2 随机地震作用下边坡的稳定性分析 应用有限元边坡稳定分析方法[4，5]，取土体的抗剪强度为莫尔-库仑强度准则，那么曲面上任一点土体的抗剪强度为

τf=σntgφ+c
(4)


式中σn为法向应力，φ和c分别是土体的内摩擦角和粘滞力。边坡稳定分析的目的是要在计算区域内找到这样一个曲面(平面问题为一条曲线)，沿这个面的抗滑稳定安全系数为最小。用有限元方法计算出坝体区域的应力场，并将平面问题的曲线离散后，问题的求解可以表示为

(5)

e为离散后曲线上的一个单元。上式可进一步写成  

(6)

式中|J|为雅可比行列式。上式可以用高斯数值积分计算。在静力条件下，一点沿曲线方向的法向应力和切向应力用下式计算

(7)

式中  

(8)


其中y n'是沿曲线方向的法线斜率。

    在随机地震作用下，式(7)中的各应力分量应为静应力与随机动应力分量之和。由于动应力是由随机动力反应分析得到的，只能得到动应力的平均幅值与平均最大值的大小，而方向是不确定的，所以不能简单地迭加上随机动应力后进行最危险滑裂面的搜索。

    如前所述，本文所考虑的边坡稳定分析方法是一种在有限元应力分析基础之上的、假定初始滑裂面、采用虎克 捷夫(Hooke-Jeeves)方法逐点、逐步搜索求解的数学规划方法。为了迭加上随机动应力又不至于增加太多的计算量，在每一计算点考虑3个动应力(σdx、σdy、σdxy)的随机组合，则法向应力和切向应力可表示为

(9)


其中m=±1,n=±1,l=±1,它们的取值实际上代表了动应力的方向。当m、n、l分别取值时，在每一高斯点形成8种不同的应力组合。由每组算得的σn、τ代入目标函数，取其中对目标函数值贡献最小的应力组合作为此点的计算应力。

    从数学上讲，用上述方法最终都能搜索得到最危险滑裂面并求得最小安全系数。用于最后计算对目标函数值贡献的是其中最不利组合的一种，那么，此时的动应力方向能否代表实际边坡在地震作用下破坏时真实的动应力方向是一个要考虑的问题。因为这里所考虑的地震作用是随机的，对某一点来说出现这样那样的应力方向是可能的，但以往大量的确定性地震反应分析表明，边坡破坏时沿破坏面的应力分布具有一定规律性，这里考虑地震动的随机性来分析边坡的稳定性也应符合这种规律。在后面对模型坝的计算分析中将进一步对这一问题加以说明。

http://www.cws.net.cn/Journal/slxb/199911/12.html

andy77

更有问题就是, 即使圆弧经过10个高斯点, 就有2的30次方=1073741824次圆弧搜索, 看起来计算的算例里面根本不止10个高斯点, 显然这个圆弧搜索是吃力得要命, 我个人甚至怀疑计算的可行性, 根本不大可能做出来

andy77 wrote:
这个课题我研究过,问题很大
1、原文说 从数学上讲，用上述方法最终都能搜索得到最危险滑裂面并求得最小安全系数。

每个高斯点有2的3次方＝8种不同的应力组合，假如滑弧很大，经过100个高斯点，那就有2的300次方＝2.0370359763344860862684456884094e+90
个应力组合，计算量惊人

2、原文中说 某一点来说出现这样那样的应力方向是可能的，但以往大量的确定性地震反应分析表明，边坡破坏时沿破坏面的应力分布具有一定规律性

由于这些内力的方向都是假定的，即使搜索出来最小可靠度的一个滑弧面，在真正情况中有可能并不能满足应力平衡条件，因此有可能压根不会出现这种情况

因此我在计算中把这种方法否定了，可行性几乎为零

mygeotech

sunxiaosan wrote:
mygeotech ：你的有限元模型偏小。有限元计算时模型的底厚至少应该是坡高的2倍。如果你改变模型后，计算结果差别就较大。不妨试试。
我认为：有限元法比条分法进步主要反应在内力的计算方面，两种方法的计算结果相同，不一定就是好事。反过来问：两者计算结果相同，我们为什么还有讨论有限元计算边坡稳定呢？不当请大家批评。计算结果的准确如否主要靠实践检验。

这是因为,对于某些土坡稳定问题,即使使用morgenstern-price这么严格的方法,当采用不同条间力假设的时候,会得出不同的安全系数.有限元法就没有这个问题. 另外对于这个分析所采用的均质土坡,由于最危险滑弧主要限制于土坡内,基础的厚度对最小安全系数没有什么影响.

135135lsy

我想请教一下mygeotech ,我的Plaxis7.2不能改变loadA和loadB的数值，但其他都能实现，不知是什么原因，按手册上的步聚也不行，不知是什么原因，是软件本身短少了什么吗，能帮我解决一下问题吗，多谢！

mygeotech

这里有一些,不是很全.

1.  Slope stability analysis using Monte Carlo technique with FEM
Li, Yu-Chao (Institute of Geotechnical Engineering, Zhejiang University); Ling, Dao-Sheng; Chen, Yun-Min; Zhang, Wen-Jie Source: Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, v 24, n 11, Jun 1, 2005, p 1933-1941 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


2.  Locating critical slip surfaces by a method combining Monte Carlo technique and FEM
Chen, Yun-Min (Inst. of Geotechnical Eng., Zhejiang Univ.); Li, Yu-Chao; Ling, Dao-Sheng Source: Yantu Lixue/Rock and Soil Mechanics, v 25, n SUPPL. 2, November, 2004, p 75-80 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


3.  Finite element method for solving safety factor of slope stability
Zhang, Pei-Wen (China Inst. of Hydropower Res.); Chen, Zu-Yu Source: Yantu Lixue/Rock and Soil Mechanics, v 25, n 11, November, 2004, p 1757-1760 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


4.  Improved search strategy for the critical slip surface using finite element stress fields
Kim, J.Y. (Korea Advanced Inst of Science and Technology); Lee, S.R. Source: Computers and Geotechnics, v 21, n 4, 1997, p 295-313
Database: Compendex
Abstract  |  Detailed Record  |     


5.  On kinematic method in shakedown theory: II. Modified kinematic method
Kamenjarzh, J. (Lomonosov Moscow State Univ); Merzljakov, A. Source: International Journal of Plasticity, v 10, n 4, 1994, p 381-392
Database: Compendex
Abstract  |  Detailed Record  |     


6.  Plastic limit analysis of slope stability using finite element
Wang, Han-Hui (Water Resources and Hydropower Sch., Wuhan Univ.); Wang, Jun-Xing; Wang, Kai-Zhi Source: Yantu Lixue/Rock and Soil Mechanics, v 24, n 5, October, 2003, p 733-738 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


7.  Stability analysis of soil slope by finite element method with plastic limit upper bound
Wang, Junxing (Sch. of Water Resources, Wuhan Univ.); Wang, Hanhui; Wu, Yafeng Source: Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, v 23, n 11, Jun 1, 2004, p 1867-1873 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


8.  Layer thickness optimization in a laminated composite
Conti, P. (Univ of Palermo); Luparello, S.; Pasta, A. Source: Composites Part B:Engineering, v 28, n 3, 1997, p 309-317
Database: Compendex
Abstract  |  Detailed Record  |     


9.  Earth pressure on cantilever walls at design retained heights
Day, Robert A. (The University of Queensland) Source: Proceedings of the Institution of Civil Engineers: Geotechnical Engineering, v 149, n 3, July, 2001, p 167-176
Database: Compendex
Abstract  |  Detailed Record  |     


10.  Geotechnical engineering limit analysis using finite element method
Zheng, Ying-Ren (Dept. of Civil Eng., Logistical Eng. Univ.); Zhao, Shang-Yi; Kong, Wei-Xue; Deng, Chu-Jian Source: Yantu Lixue/Rock and Soil Mechanics, v 26, n 1, January, 2005, p 163-168 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


11.  Determination of critical slip surface using finite element method
Ahn, T.B. (Korea Inst of Construction Technology) Source: Proceedings of the International Offshore and Polar Engineering Conference, v 1, 1999, p 472-479
Database: Compendex
Abstract  |  Detailed Record   


12.  Dynamic safety evaluation of slopes or dam foundations using rigid body-spring element method
Zhang, Jianhai (Sichuan Univ); Fan, Jingwei; He, Jiangda Source: Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, v 18, n 4, Aug, 1999, p 387-391 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


13.  Slope stability analysis using strength reduction technique
Chang, Yuan-Liang (Department of Civil Engineering, National Chung-Hsing University); Huang, Tien-Kuen Source: Journal of the Chinese Institute of Engineers, Transactions of the Chinese Institute of Engineers,Series A/Chung-kuo Kung Ch'eng Hsuch K'an, v 28, n 2, March, 2005, p 231-240
Database: Compendex
Abstract  |  Detailed Record   


14.  Reinforcing mechanism of anchors in slopes: A numerical comparison of results of LEM and FEM
Cai, Fei (Department of Civil Engineering, Gunma University); Ugai, Keizo Source: International Journal for Numerical and Analytical Methods in Geomechanics, v 27, n 7, June, 2003, p 549-564
Database: Compendex
Abstract  |  Detailed Record  |     


15.  Discussion on criteria for evaluating stability of slope in elastoplastic FEM based on shear strength reduction technique
Liu, Jin-Long (Institute of Rock and Soil Mechanics, Chinese Academy of Sciences); Luan, Mao-Tian; Zhao, Shao-Fei; Yuan, Fan-Fan; Wang, Ji-Li Source: Yantu Lixue/Rock and Soil Mechanics, v 26, n 8, August, 2005, p 1345-1348 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


16.  Genetic algorithm for searching for critical slip surface in soil slopes based on stress fields
Wang, Chenghua (Dept. of Hydraulic Eng., Sch. of Civil and Hydraulic Eng., Tsinghua Univ.); Xia, Xuyong; Li, Guangxin Source: Qinghua Daxue Xuebao/Journal of Tsinghua University, v 44, n 3, March, 2004, p 425-428 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


17.  Analyzing of two dimensional slope stability and foundation problems considering soil-structure interaction effect
He, Stanley Z. (Haley & Aldrich, Inc) Source: Congress on Computing in Civil Engineering, Proceedings, 1996, p 832-837
Database: Compendex
Abstract  |  Detailed Record   


18.  Definitions of safety factor of slope stability analysis with finite element method
Zheng, Hong (Institute of Rock and Soil Mechanics, Chinese Academy of Sciences); Tian, Bin; Liu, De-Fu; Feng, Qiang Source: Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, v 24, n 13, Jul 1, 2005, p 2225-2230 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


19.  Study on optimum design of landslide stabilization by parallel evolutionary neural network method
Yin, Shunde (Lab. of Rock and Soil Mech., Inst. of Rock and Soil Mech., Chinese Acad. of Sci.); Feng, Xiating; Zhang, Youliang; Zhou, Hui; Zhao, Hongbo Source: Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, v 23, n 16, Aug 15, 2004, p 2698-2702 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


20.  3D stability analysis of landslides based on strength reduction (II): Evaluation of reinforcing factor of safety
Deng, Jian-Hui (Lab. of Rock and Soil Mech., Inst. of Rock and Soil Mech., Chinese Acad. of Sci.); Zhang, Jia-Xiang; Min, Hong; Mei, Song-Hua Source: Yantu Lixue/Rock and Soil Mechanics, v 25, n 6, June, 2004, p 871-875 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


21.  Prediction method of slope stability due to permeation of rainwater
Chen, Shan-Xiong (Inst. of Rock and Soil Mech., Chinese Acad. of Sci.); Tan, Xin; Liu, Zhi-Guo Source: Rock and Soil Mechanics, v 23, n SUPPL., October, 2002, p 31-36 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


22.  Determination of slip surface in slope based on theory of slip line field
Zhu, Yi-Wen (School of Civil and Architecture Engineering, Wuhan University); Wu, Chun-Qiu; Cai, Yuan-Qi Source: Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, v 24, n 15, Aug 1, 2005, p 2609-2616 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


23.  Adaptive elasto-visco-plastic finite element analysis of the stability of Dayantang slope
Chen, Shangfa (Sch. of Hydraulic and Elec. Eng., Wuhan Univ.); She, Chengxue; Chen, Shenghong Source: Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, v 21, n 2, February, 2002, p 169-175 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record   


24.  Finite element modelling of embankment stability
Toufigh, Mohammad M. (Univ of Kennan) Source: International Journal for Engineering Modelling, v 10, n 1-4, 1997, p 57-62
Database: Compendex
Abstract  |  Detailed Record   


25.  Numerical simulation on failure mechanism of rock slope by strength reduction FEM
Zheng, Yingren (Logistical Eng. Univ.); Zhao, Shangyi; Deng, Weidong Source: Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering, v 22, n 12, December, 2003, p 1943-1952 Language: Chinese
Database: Compendex
Abstract  |  Detailed Record