基于稀疏网格配点法的边坡稳定可靠度分析
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摘要
提出了基于稀疏网格配点法的边坡可靠度分析方法;利用有限元强度折减法计算了边坡安全系数,再通过稀疏网格配点法构造代理模型,将隐式功能函数转为显式功能函数,从而降低了有限元计算次数。在此基础上结合蒙特卡罗方法计算边坡失效概率,给出了计算流程,并编写了相应的MATLAB程序。最后以一显式功能函数问题为例验证了稀疏网格配点法的有效性,并以两个边坡问题为例研究了所提方法在边坡可靠度中的应用。结果表明,虽然1阶Smolyak配点法相比2阶Smolyak配点法计算量小,但后者更适用于边坡可靠度分析。所提方法能够对考虑土体参数空间变异性的边坡可靠度进行分析,计算结果与拉丁超立方抽样方法保持一致,计算精度较高,为进行复杂的边坡可靠度分析提供了一条有效的途径。
A new methodology is proposed for reliability analysis of slope stability based on the sparse grid stochastic collocation method. The factor of safety is calculated by using the strength reduction method. Theproposed method can well fit the actual performance function for slope reliability analysis using a surrogate model, which has an excellent modeling capability. The probability of slope failure is then estimated using Monte-Carlo simulation based on this explicit performance function. A computer program is developed. An explicit limit-state function example is provided to validate the accuracy and efficiency of this method. Moreover, taking the two soil slope problems as examples, the application of the proposed method in slope reliability is studied. Results indicate that although the first-order Smolyak collocation method is less computationally intensive than the second-order Smolyak collocation method, the latter is more suitable for slope reliability analysis. The proposed method can analyze the slope reliability by considering the spatial variability of soil parameters, and the calculated results are consistent with the Latin hypercube sampling method, which has high calculation accuracy and provides an effective way to perform complex slope reliability analysis.
A new methodology is proposed for reliability analysis of slope stability based on the sparse grid stochastic collocation method. The factor of safety is calculated by using the strength reduction method. Theproposed method can well fit the actual performance function for slope reliability analysis using a surrogate model, which has an excellent modeling capability. The probability of slope failure is then estimated using Monte-Carlo simulation based on this explicit performance function. A computer program is developed. An explicit limit-state function example is provided to validate the accuracy and efficiency of this method. Moreover, taking the two soil slope problems as examples, the application of the proposed method in slope reliability is studied. Results indicate that although the first-order Smolyak collocation method is less computationally intensive than the second-order Smolyak collocation method, the latter is more suitable for slope reliability analysis. The proposed method can analyze the slope reliability by considering the spatial variability of soil parameters, and the calculated results are consistent with the Latin hypercube sampling method, which has high calculation accuracy and provides an effective way to perform complex slope reliability analysis.
引文
[1]DUNCAN J M.Factors of safety and reliability in geotechnical engineering[J].Journal of geotechnical and geoenvironmental engineering(ASCE),2000,126(4):307-316.
[2]JIANG S H,LI D Q,ZHANG L M,et al.Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method[J].Engineering geology,2014,168(1):120-128.
[3]祝玉学.边坡可靠性分析[M].北京:冶金工业出版社,1993.(ZHUYuxue.Reliability analysis for slope engineering[M].Beijing:Metallurgical Industry Press,1993(in Chinese)).
[4]BHATTACHARYA G,JANA D,OJHA S,et al.Direct search for minimum reliability index of earth slopes[J].Computers and geotechnics,2003,30(6):455-462.
[5]CHO S E.Effects of spatial variability of soil properties on slope stability[J].Engineering geology,2007,92(3/4):97-109.
[6]SRIVASTAVA A,BABU G L S,HALDAR S.Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis[J].Engineering geology,2010,110(3/4):93-101.
[7]GRIFFITHS D,HUANG J,FENTON G A.Influence of spatial variability on slope reliability using 2-D random fields[J].Journal of geotechnical and geoenvironmental engineering(ASCE),2009,10(135):1367-1378.
[8]TANG X S,LI D Q,CHEN Y F,et al.Improved knowledge-based clustered partitioning approach and its application to slope reliability analysis[J].Computers&geotechnics,2012,45(1):34-43.
[9]罗正东,董辉,陈铖,等.基于克里金模型的边坡稳定可靠度分析方法[J].岩土力学,2015(S1):439-444.(LUO Zhengdong,DONGHui,CHEN Cheng,et al.An analytic method for slope stability reliability based on Kriging model[J].Rock and soil mechanics,2015(S1):439-444(in Chinese)).
[10]蒋水华,李典庆,周创兵.基于拉丁超立方抽样的边坡可靠度分析非侵入式随机有限元法[J].岩土工程学报,2013,35(S2):70-76.(JIANG Shuihua,LI Dianqing,ZHOU Chuangbing.Non-intrusive stochastic finite element method for slope reliability analysis based on Latin hypercube sampling[J].Chinese journal of geotechnical engineering,2013,35(S2):70-76(in Chinese)).
[11]李典庆,蒋水华,周创兵,等.考虑参数空间变异性的边坡可靠度分析非侵入式随机有限元法[J].岩土工程学报,2013,35(8):1413-1422.(LI Dianqing,JIANG Shuihua,ZHOU Chuangbing,et al.Reliability analysis of slopes considering spatial variability of soil parameters using non-intrusive stochastic finite element method[J].Chinese journal of geotechnical engineering,2013,35(8):1413-1422(in Chinese)).
[12]吴振君,王水林,汤华,等.一种新的边坡稳定性因素敏感性分析方法-可靠度分析方法[J].岩石力学与工程学报,2010,29(10):2050-2055.(WU Zhenjun,WANG Shuilin,TANG Hua,et al.A new sensitivity analysis approach for slope stability-reliability analysis method[J].Chinese journal of rock mechanics and engineering,2010,29(10):2050-2055(in Chinese)).
[13]邓志平,李典庆,曹子君,等.考虑地层变异性和土体参数变异性的边坡可靠度分析[J].岩土工程学报,2017(6):986-995.(DENGZhiping,LI Dianqing,CAO Zijun,et al.Slope reliability analysis considering geological uncertainty and spatial variability of soil parameters[J].Chinese journal of geotechnical engineering,2017(6):986-995(in Chinese)).
[14]DITLEVSEN O,MADSEN H O.Structural reliability methods[M].New York:Wiley,1996.
[15]赵国藩.工程结构可靠性理论与应用[M].大连:大连理工大学出版社,1996.(ZHAO Guofan.Reliability theory and its applications for engineering structures[M].Dalian:Dalian University of Technology Press,1996(in Chinese)).
[16]XU B,LOW B K.Probabilistic stability analyses of embankments based on finite element method[J].Journal of geotechnical and geoenvironmental engineering,2006,132(11):1444-1454.
[17]CHO S E.Probabilistic stability analyses of slopes using the ANN-based response surface[J].Computers and geotechnics,2009,36(5):787-797.
[18]XIU D,HESTHAVEN J S.High-order collocation methods for differential equations with random inputs[J].Society for industrial and applied mathematics,2005,27(3):1118-1139.
[19]GANAPATHYSUBRAMANIAN B,ZABARAS N.Sparse grid collocation schemes for stochastic natural convection problems[J].Journal of computational physics,2007,225(1):652-685.
[20]FOO J,YOSIBASH Z,KARNIADAKIS G E.Stochastic simulation of riser-sections with uncertain measured pressure loads and/or uncertain material properties[J].Computer methods in applied mechanics and engineering,2007,196(41):4250-4271.
[21]HE J,GAO S,GONG J.A sparse grid stochastic collocation method for structural reliability analysis[J].Structural safety,2014,51:29-34.
[22]WASILKOWSKI G W,WOZNIAKOWSKI H.Explicit cost bounds of algorithms for multivariate tensor product problems[J].Journal of complexity,1995(11):1-56.
[23]LUO X,LI X,ZHOU J,et al.A Kriging-based hybrid optimization algorithm for slope reliability analysis[J].Structural safety,2012,34(1):401-406.
[24]KIM S H,NA S W.Response surface method using vector projected sampling points[J].Structural safety,1997,19(1):3-19.
[25]JIANG S H,LI D Q,ZHANG L M,et al.Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method[J].Engineering geology,2014,168(1):120-128.
[2]JIANG S H,LI D Q,ZHANG L M,et al.Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method[J].Engineering geology,2014,168(1):120-128.
[3]祝玉学.边坡可靠性分析[M].北京:冶金工业出版社,1993.(ZHUYuxue.Reliability analysis for slope engineering[M].Beijing:Metallurgical Industry Press,1993(in Chinese)).
[4]BHATTACHARYA G,JANA D,OJHA S,et al.Direct search for minimum reliability index of earth slopes[J].Computers and geotechnics,2003,30(6):455-462.
[5]CHO S E.Effects of spatial variability of soil properties on slope stability[J].Engineering geology,2007,92(3/4):97-109.
[6]SRIVASTAVA A,BABU G L S,HALDAR S.Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis[J].Engineering geology,2010,110(3/4):93-101.
[7]GRIFFITHS D,HUANG J,FENTON G A.Influence of spatial variability on slope reliability using 2-D random fields[J].Journal of geotechnical and geoenvironmental engineering(ASCE),2009,10(135):1367-1378.
[8]TANG X S,LI D Q,CHEN Y F,et al.Improved knowledge-based clustered partitioning approach and its application to slope reliability analysis[J].Computers&geotechnics,2012,45(1):34-43.
[9]罗正东,董辉,陈铖,等.基于克里金模型的边坡稳定可靠度分析方法[J].岩土力学,2015(S1):439-444.(LUO Zhengdong,DONGHui,CHEN Cheng,et al.An analytic method for slope stability reliability based on Kriging model[J].Rock and soil mechanics,2015(S1):439-444(in Chinese)).
[10]蒋水华,李典庆,周创兵.基于拉丁超立方抽样的边坡可靠度分析非侵入式随机有限元法[J].岩土工程学报,2013,35(S2):70-76.(JIANG Shuihua,LI Dianqing,ZHOU Chuangbing.Non-intrusive stochastic finite element method for slope reliability analysis based on Latin hypercube sampling[J].Chinese journal of geotechnical engineering,2013,35(S2):70-76(in Chinese)).
[11]李典庆,蒋水华,周创兵,等.考虑参数空间变异性的边坡可靠度分析非侵入式随机有限元法[J].岩土工程学报,2013,35(8):1413-1422.(LI Dianqing,JIANG Shuihua,ZHOU Chuangbing,et al.Reliability analysis of slopes considering spatial variability of soil parameters using non-intrusive stochastic finite element method[J].Chinese journal of geotechnical engineering,2013,35(8):1413-1422(in Chinese)).
[12]吴振君,王水林,汤华,等.一种新的边坡稳定性因素敏感性分析方法-可靠度分析方法[J].岩石力学与工程学报,2010,29(10):2050-2055.(WU Zhenjun,WANG Shuilin,TANG Hua,et al.A new sensitivity analysis approach for slope stability-reliability analysis method[J].Chinese journal of rock mechanics and engineering,2010,29(10):2050-2055(in Chinese)).
[13]邓志平,李典庆,曹子君,等.考虑地层变异性和土体参数变异性的边坡可靠度分析[J].岩土工程学报,2017(6):986-995.(DENGZhiping,LI Dianqing,CAO Zijun,et al.Slope reliability analysis considering geological uncertainty and spatial variability of soil parameters[J].Chinese journal of geotechnical engineering,2017(6):986-995(in Chinese)).
[14]DITLEVSEN O,MADSEN H O.Structural reliability methods[M].New York:Wiley,1996.
[15]赵国藩.工程结构可靠性理论与应用[M].大连:大连理工大学出版社,1996.(ZHAO Guofan.Reliability theory and its applications for engineering structures[M].Dalian:Dalian University of Technology Press,1996(in Chinese)).
[16]XU B,LOW B K.Probabilistic stability analyses of embankments based on finite element method[J].Journal of geotechnical and geoenvironmental engineering,2006,132(11):1444-1454.
[17]CHO S E.Probabilistic stability analyses of slopes using the ANN-based response surface[J].Computers and geotechnics,2009,36(5):787-797.
[18]XIU D,HESTHAVEN J S.High-order collocation methods for differential equations with random inputs[J].Society for industrial and applied mathematics,2005,27(3):1118-1139.
[19]GANAPATHYSUBRAMANIAN B,ZABARAS N.Sparse grid collocation schemes for stochastic natural convection problems[J].Journal of computational physics,2007,225(1):652-685.
[20]FOO J,YOSIBASH Z,KARNIADAKIS G E.Stochastic simulation of riser-sections with uncertain measured pressure loads and/or uncertain material properties[J].Computer methods in applied mechanics and engineering,2007,196(41):4250-4271.
[21]HE J,GAO S,GONG J.A sparse grid stochastic collocation method for structural reliability analysis[J].Structural safety,2014,51:29-34.
[22]WASILKOWSKI G W,WOZNIAKOWSKI H.Explicit cost bounds of algorithms for multivariate tensor product problems[J].Journal of complexity,1995(11):1-56.
[23]LUO X,LI X,ZHOU J,et al.A Kriging-based hybrid optimization algorithm for slope reliability analysis[J].Structural safety,2012,34(1):401-406.
[24]KIM S H,NA S W.Response surface method using vector projected sampling points[J].Structural safety,1997,19(1):3-19.
[25]JIANG S H,LI D Q,ZHANG L M,et al.Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method[J].Engineering geology,2014,168(1):120-128.
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