软土地基固结Neumann随机有限元分析
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摘要
基于Biot固结理论和Neumann随机有限元理论,提出了沉降固结理论的Neumann随机有限元分析方法,并开发了相应的有限元计算程序.以某工程为例,对软土地基固结沉降进行随机有限元分析,探讨了地基沉降与超静孔压随机性状随时间的变化规律以及在空间上的分布特征.计算结果表明:不同随机有限元法沉降标准差的空间分布形式都比较类似,沉降标准差随着深度的增加而减小,并在坡脚附近出现局部减小现象;相同深度时,加固区的沉降标准差要大于非加固区.
The Neumann stochastic finite element method for predicting the consolidation settlement of a foundation was developed based on the Biot's consolidation theory,and a finite element program was designed to analyze the road embankment.Through an example of the practical project,the consolidation settlement of a soft soil foundation was analyzed using the Neumann stochastic finite element method,and the change over time and spatial distribution of the foundation settlement and excess pore water pressure were discussed.The calculated results show that the spatial distribution of the standard deviation of settlement obtained by different stochastic finite element methods is similar.The standard deviation of settlement decreases with the increase of depth,and has a local minimum near the slope foot.The standard deviation of settlement in the reinforced area is larger than that in the unreinforced area under the same depth.
The Neumann stochastic finite element method for predicting the consolidation settlement of a foundation was developed based on the Biot's consolidation theory,and a finite element program was designed to analyze the road embankment.Through an example of the practical project,the consolidation settlement of a soft soil foundation was analyzed using the Neumann stochastic finite element method,and the change over time and spatial distribution of the foundation settlement and excess pore water pressure were discussed.The calculated results show that the spatial distribution of the standard deviation of settlement obtained by different stochastic finite element methods is similar.The standard deviation of settlement decreases with the increase of depth,and has a local minimum near the slope foot.The standard deviation of settlement in the reinforced area is larger than that in the unreinforced area under the same depth.
引文
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[16]陈晓平,黄国怡,梁志松.珠江三角洲软土特性研究[J].岩石力学与工程学报,2003,22(1):137-141.(CHEN Xiao-ping,HUANG Guo-yi,LIANG Zhi-song.Study on soft soil properties of the pearl river delta[J].Chinese Journal of Rock Mechanics andEngineering,2003,22(1):137-141.(in Chinese))
[17]刘春原,阎澍旺.岩土参数随机场特性及线性预测[J].岩土工程学报,2002,24(5):588-591.(LIU Chun-yuan,YAN Shu-wang.Characteristic of the random field of geotechnical parameters and linear prediction[J].Chinese Jounal of Geotechnical Engineering,2002,24(5):588-591.(in Chinese))
[18]包承纲.地基工程可靠度分析方法研究[M].武汉:武汉测绘科技大学出版社,1997:1-18.
[19]李涛.软土路基大变形固结随机有限元分析[D].杭州:浙江大学,2006.
[2]刘宁.三维可分向量随机场局部平均的三维随机有限元及可靠度计算[J].水利学报,1995(6):75-82.(LIU Ning.3-Dstochastic FEM and reliability calculation based on vector seperatable field local average[J].Journal of Hydraulic Engineering,1995(6):75-82.(in Chinese))
[3]CAMBOU B.Application of first order uncertainty analysis in the finite element method in linear elasticity[C]//Proceedings of the SecondInternational Conference on Applications of Statistics and Probabilisy in Soils and Structural Engineering.Aachen:[s.n.],1975:67-88.
[4]DENDROU B A,HOUSTIS E N.An inference finite element method for field application,applied mathematical modeling[M].Guildford:[s.n.],1978:49-55.
[5]BAECHER G B,INGRA T S.Stochastic FEM in settlement prediction[J].Journal of Geotech Engineering,1981,107(2):449-463.
[6]HANDA K,ANDERSON K.Application of finite element methods in statistical analysis ofstructures[C]//Proceedings of the ThirdInternational Conference on Struct Safety and Reliability.Trondheim:[s.n.],1981:409-417.
[7]HISADA T,NAKAGIRI S.Stochastic finite element method developed for struct.safety and reliability[C]//Proceedings of the ThirdInternational Conference on Struct Safety and Reliability.Trondheim:[s.n.],1981:395-408.
[8]SHINOZUKA M,DEODATIS G.Response variability of stochastic finite element systems[J].Journal of Engineering Mechanics ASCE,1988,114(3):499-519.
[9]YAMAZAKI F,SHINOZUKA M,DASUPTA G.Neumann expansion for stochastic finite element analysis[J].Journal of EngineeringMechanics ASCE,1988,114(8):1335-1354.
[10]赵雷.随机参数结构动力分析方法及地震可靠度研究[D].成都:西南交通大学,1996.
[11]傅旭东,茜平一,刘祖德.浅基础沉降可靠性的Neumann随机有限元分析[J].岩土力学,2001,22(3):285-290.(FU Xu-dong,QIAN Ping-yi,LIU Zhu-de.Neumann stochastic finite element analysis for reliability of settlement of the shallow foundation[J].Rock andSoil Mechanics,2001,22(3):285-290.(in Chinese))
[12]NISHIMURA S,FUJII H,SHIMADA K.FEM consolidation analysis considering variability of soil parameters[C]//Applications ofStatistics and Probability.Rotterdam:Balkema,1995:85-92.
[13]郭志川,刘宁.地基固结沉降随机有限元计算和可靠度分析[J].岩土力学,2001,22(4):481-485.(GUO Zhi-chuan,LIU Ning.The SFEM analysis and reliability assessment of consolidation settlement based on Biot consolidation theory[J].Rock and Soil Mechanics,2001,22(4):481-485.(in Chinese))
[14]龚晓南.高等土力学[M].杭州:浙江大学出版社,1996.
[15]陈虬,戴志敏.等参局部平均随机场和Neumann随机有限元法[J].计算结构力学及其应用,1991,8(4):397-402.(CHENQiu,DAI Zhi-min.The isoparametric local average random field and Neumann stochastic finite element method[J].ComputationalStructural Mechanics and Applications,1991,8(4):397-402.(in Chinese))
[16]陈晓平,黄国怡,梁志松.珠江三角洲软土特性研究[J].岩石力学与工程学报,2003,22(1):137-141.(CHEN Xiao-ping,HUANG Guo-yi,LIANG Zhi-song.Study on soft soil properties of the pearl river delta[J].Chinese Journal of Rock Mechanics andEngineering,2003,22(1):137-141.(in Chinese))
[17]刘春原,阎澍旺.岩土参数随机场特性及线性预测[J].岩土工程学报,2002,24(5):588-591.(LIU Chun-yuan,YAN Shu-wang.Characteristic of the random field of geotechnical parameters and linear prediction[J].Chinese Jounal of Geotechnical Engineering,2002,24(5):588-591.(in Chinese))
[18]包承纲.地基工程可靠度分析方法研究[M].武汉:武汉测绘科技大学出版社,1997:1-18.
[19]李涛.软土路基大变形固结随机有限元分析[D].杭州:浙江大学,2006.
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