基于分数阶微积分理论的软土应力-应变关系
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摘要
利用分数阶微积分理论提出等应变率加载情况下的软土应力–应变关系。关系式显示应力–应变之间呈乘幂函数关系。通过大量的常规(等应变率加载情况下)三轴试验验证基于分数阶微积分理论的软土应力–应变关系,同一种土的分数阶阶数β不随围压变化并能够反映土的"软硬"程度。试验发现,初始弹模与围压呈较好的线性关系。与邓肯–张模型相比,应力–应变的乘幂关系具有明确的理论基础,这一点与邓肯–张模型纯粹基于曲线形状相似的应力–应变双曲线假设形成鲜明的区别。创新点在于将软土看作介于理想固体和理想流体之间的物质进行研究,并用分数阶微积分理论给出应力–应变关系,这在以往的研究中都没有先例。
On the basis of the fractional calculus operator theory,the stress-strain relation of soft soil under the condition of loading with constant strain rate is proposed.The analysis results show that stress–strain of soft soil performs exponent relation,which can be proved by large amounts of triaxial tests(under constant strain rate).It is found that the orderβof fractional calculus keeps constant to the same kind of soil and characterize soft or hard soil.The test results show that there is a linear relationship between confining pressures and initial tangent modulus.Compared with Duncan-Chang model that hypothesizes stress-strain relation is hyperbolic in response to similar shape of experimental curve,the stress-strain relation from the fractional calculus has rigorous theoretical background.The major innovation of our researches is that the soil is considered as the matter whose behaviors are intermediate between that of the ideal solid and fluid,and it also may be the first known application of fractional calculus in soil stress-strain relation.
On the basis of the fractional calculus operator theory,the stress-strain relation of soft soil under the condition of loading with constant strain rate is proposed.The analysis results show that stress–strain of soft soil performs exponent relation,which can be proved by large amounts of triaxial tests(under constant strain rate).It is found that the orderβof fractional calculus keeps constant to the same kind of soil and characterize soft or hard soil.The test results show that there is a linear relationship between confining pressures and initial tangent modulus.Compared with Duncan-Chang model that hypothesizes stress-strain relation is hyperbolic in response to similar shape of experimental curve,the stress-strain relation from the fractional calculus has rigorous theoretical background.The major innovation of our researches is that the soil is considered as the matter whose behaviors are intermediate between that of the ideal solid and fluid,and it also may be the first known application of fractional calculus in soil stress-strain relation.
引文
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[2]缪林昌,张军辉,陈艺南.江苏海相软土压缩特性试验研究[J].岩土工程学报,2007,29(11):1711–1714.(MIAO Linchang,ZHANG Junhui,CHEN Yinan.Study on compressibility of Jiangsu marine clay[J].Chinese Journal of Geotechnical Engineering,2007,29(11):1711–1714.(in Chinese))
[3]栾茂田,范庆来,杨庆.非均质软土地基上吸力式沉箱抗拔承载力数值分析[J].岩土工程学报,2007,29(7):1054–1059.(LUAN Maotian,FAN Qinglai,YANG Qing.Numerical analysis of ultimate pull-out resistance of suction caissons in inhomogeneous soft foundation[J].Chinese Journal of Geotechnical Engineering,2007,29(7):1054–1059.(in Chinese))
[4]周健,张姣,苏燕.软土地下建筑物地震易损性分析[J].武汉理工大学学报(交通科学与工程版),2007,31(3):397–399.(ZHOU Jian,ZHANG Jiao,SU Yan.Seismic risk analysis of underground structures in soft soil-analysis of seismic vulnerability[J].Journal of Wuhan university of technology(Transportation Science and Engineering),2007,31(3):397–399.(in Chinese))
[5]熊玉春,房营光.饱和软黏土地基的损伤模型与震陷计算[J].振动工程学报,2006,19(3):359–363.(XIONG Yuchun,FANG Yingguang.A damage model for saturated clay foundation and its seismic settlement[J].Journal of Vibration Engineering,2006,19(3):359–363.(in Chinese))
[6]MANDELBROT B B.The fractal geometry of nature[M].New York:W.H.Freeman and Company,1982.
[7]OLDHAM K B,SPANIER J.The fractional calculus.London:Academic Press,1974.
[8]ZAYED A I.Handbook of function and generalized function transformations[M].Florida:CRC Press,1996.
[9]GORENFLO R,FRANCESCO M.Essentials of fractional calculus[M].Aarhus:MaPhySto Center,2000.
[10]钱家欢,殷宗泽.土工原理与计算[M].北京:中国水利水电出版社,1996.(QIAN Jiahuan,YIN Zongze.Theory and calculation of soil engineering[M].Beijing:China Water Power Press,1996.(in Chinese))
[11]杨雪强,朱志政,韩高升,等.不同应力路径下土体的变形特性与破坏特性[J].岩土力学,2006,27(12):2181–2185.(YANG Xueqiang,ZHU Zhizheng,HAN Gaosheng,et al.Deformation and failure characteristics of soil mass under different stress paths[J].Rock and Soil Mechanics,2006,27(12):2181–2185.(in Chinese))
[12]周葆春,王靖涛,杨晓东.武汉黏土修正剑桥模型参数研究[J].武汉理工大学学报,2007,29(3):103–107.(ZHOU Baochun,WANG Jingtao,YANG Xiaodong.Research on parameters of modified cam CLAY for Wuhan clay[J].Journal of Wuhan University of Technology,2007,29(3):103–107.(in Chinese))
[13]冯世进,周子范,陈云敏,等.城市固体废弃物剪切强度参数的研究[J].浙江大学学报(工学版),2005,39(7):987–991.(FENG Shijin,ZHOU Zifan,CHEN Yunmin,et al.Study on shear strength parameters of municipal solid waste[J].Journal of Zhejiang University(Engineering Science),2005,39(7):987–991.(in Chinese))
[14]李治.模拟基坑应力路径的真三轴平面应变试验研究[硕士学位论文][D].南京:河海大学,2007.(LI Zhi.Plane strain experiment research of simulating stress path of excavation pit by the true triaxial cell[M.S.Thesis][D].Nanjing:Hohai University,2007.(in Chinese))
[15]中国自然资源学会.资源科学学科发展报告[M].北京:中国科学技术出版社,2007.(China Society of Natural Resources.Report on advances in resources science[M].Beijing:China Science and Technology Press,2007.(in Chinese))
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