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任意荷载下分数阶导数黏弹性饱和土体一维固结

汪磊, 孙德安, 解益, 李培超

汪磊, 孙德安, 解益, 李培超. 任意荷载下分数阶导数黏弹性饱和土体一维固结[J]. 岩土工程学报, 2017, 39(10): 1823-1831. DOI: 10.11779/CJGE201710010
引用本文: 汪磊, 孙德安, 解益, 李培超. 任意荷载下分数阶导数黏弹性饱和土体一维固结[J]. 岩土工程学报, 2017, 39(10): 1823-1831. DOI: 10.11779/CJGE201710010
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WANG Lei, SUN De-an, XIE Yi, LI Pei-chao. One-dimensional consolidation of fractional order derivative viscoelastic saturated soils under arbitrary loading[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(10): 1823-1831. DOI: 10.11779/CJGE201710010
Citation: WANG Lei, SUN De-an, XIE Yi, LI Pei-chao. One-dimensional consolidation of fractional order derivative viscoelastic saturated soils under arbitrary loading[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(10): 1823-1831. DOI: 10.11779/CJGE201710010
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任意荷载下分数阶导数黏弹性饱和土体一维固结  English Version

  • 1. 上海大学土木工程系,上海 200444;
    2. 上海工程技术大学城市轨道交通学院,上海 201620;
    3. 上海工程技术大学机械工程学院,上海 201620

基金项目: 国家自然科学基金项目（11672172）
详细信息
    作者简介:

    汪 磊(1985- ),男,讲师,主要从事土的固结研究。E-mail: wangleiwangjiang@163.com。

    通讯作者:

    孙德安，E-mail：sundean@shu.edu.cn

  • 中图分类号: TU447

One-dimensional consolidation of fractional order derivative viscoelastic saturated soils under arbitrary loading

  • 1. Department of Civil Engineering, Shanghai University, Shanghai 200444, China;
    2. School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620, China;
    3. School of Mechanical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China

摘要

    摘要
  • 摘要: 将分数阶导数理论引入Kelvin-Voigt模型,来描述黏弹性饱和土体的力学行为。对饱和土体一维固结方程和分数阶导数Kelvin-Voigt本构方程实施Laplace变换,联立求解得到变换域内有效应力和沉降的解析解。采用Crump方法实现Laplace数值反演,获得了任意荷载情况下物理空间内一维固结问题的半解析解。并将指数荷载情况下分数阶导数模型退化到黏弹性情形,结果与已有文献解析解相同,验证了本研究提出任意荷载情况下分数阶导数黏弹性解的可靠性。最后,分析了相关参数对固结沉降的影响。研究表明,任意荷载情形下分数阶导数黏弹性饱和土体一维固结发展过程与黏滞系数和分数阶次有关,分数阶次越大,固结沉降发展越快;黏滞系数越大,固结沉降变化越慢;荷载变化趋势与由荷载参数变化引起的沉降变化规律是一致的,且最终沉降量一致。本研究有助于深入认识分数阶黏弹性饱和土体的固结行为。
    Abstract: The theory of fractional calculus is introduced into the Kelvin-Voigt constitutive model to describe the mechanical behavior of viscoelastic saturated soils. Applying the Laplace transform upon one-dimensional consolidation equation of saturated soils and the fractional order derivative Kelvin-Voigt constitutive equation, the analytical solutions of the effective stress and the settlement are derived in the Laplace domain. Then the semi-analytical solutions to one-dimensional consolidation problem under arbitrary loadings in physical space are obtained after implementing the Laplace numerical inverse transform using the Crump’s method. As the case of viscoelasticity, the simplified semi-analytical solutions under exponential loading in this study are the same as the available analytical solutions in literatures. It is indicated that the proposed solutions under arbitrary loading are reliable. Finally, parametric studies are conducted to analyze the effects of the related parameters on the consolidation settlement. The results show that the process of one-dimensional consolidation of viscoelastic saturated soils with fractional order derivative is related to viscosity coefficient and fractional order. The larger the fractional order is, the more quickly the consolidation settlement occurs; and the higher the viscosity coefficient is, the slower the consolidation settlement takes place. The trend of loadings is consistent with the variation pattern of soil settlement caused by the change of the load parameters, and the final settlement is identical. The present study can be of help to further understand the consolidation behavior of viscoelastic saturated soils.
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    • 参考文献(22)
  • [1] 刘忠玉, 闫富有, 王喜军. 基于非达西渗流的饱和黏土一维流变固结分析[J]. 岩石力学与工程学报, 2013, 32(9): 1937-1944. (LIU Zhong-yu, YAN Fu-you, WANG Xi-jun. One-dimensional rheological consolidation analysis of saturated clay considering on non-Darcy flow[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(9): 1937-1944. (in Chinese))
    [2] 刘林超, 闫启方. 分数导数模型描述的黏弹性土层中桩基水平振动研究[J]. 工程力学, 2011, 28(12): 139-145. (LIU Lin-chao, YAN Qi-fang. Lateral vibration of single pile in viscoelastic soil described by fractional derivative model[J]. Engineering Mechanics, 2011, 28(12): 139-145. (in Chinese))
    [3] 陈宗基. 固结及次时间效应的单向问题[J]. 土木工程学报, 1958, 5(1): 1-10. (CHEN Zong-ji. Unidirectional issue several time consolidation effect[J]. China Civil Engineering Journal, 1958, 5(1): 1-10. (in Chinese))
    [4] 赵维炳. 广义Voigt模型模拟的饱水土体一维固结理论及其应用[J]. 岩土工程学报, 1989, 11(5): 78-85. (ZHAO Wei-bing. Generalized Voigt model to simulate the saturated soil and water body one-dimensional consolidation theory and its application[J]. Chinese Journal of Geotechnical Engineering, 1989, 11(5): 78-85. (in Chinese))
    [5] 蔡袁强, 徐长节, 袁海明. 任意荷载下成层黏弹性地基的一维固结[J]. 应用力学和数学, 2001, 22(3): 307-313. (CAI Yuan-qiang, XU Chang-jie, YUAN Hai-ming. Under arbitrary loading viscoelastic foundation layer of one-dimensional consolidation[J]. Applied Mathematics and Mechanics, 2001, 22(3): 307-313. (in Chinese))
    [6] XIE K H, XIE X Y, LI X B. Analytical theory for one-dimensional consolidation of clayey soils exhibiting rheological characteristics under time-dependent loading[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 2008, 32(14): 1833-1855.
    [7] 李皓玉, 杨绍普, 刘 进, 等. 移动分布荷载下层状黏弹性体系的动力响应分析[J]. 工程力学, 2015, 32(1): 120-127. (LI Hao-yu, YANG Shao-pu, LIU Jin, et al. Dynamic response in multilayered viscoelastic medium generated by moving distributed loads[J]. Engineering Mechanics, 2015, 32(1): 120-127. (in Chinese))
    [8] GEMANT A. A method of analyzing experimental results obtained from elasto-viscous bodies[J]. Journal of Applied Physics, 1936, 7(1): 311-317.
    [9] TAYLOR D W, MERCHANT W. A theory of clay consolidation accounting for secondary compression[J]. Journal of Mathematics and Physics, 1940, 19(3): 167-185.
    [10] TAN T K. Secondary time effects and consolidation of clays[J]. Scientia Sinica, 1958, 7(11): 1060-1075.
    [11] 李西斌, 贾献林, 谢康和. 变荷载下软土一维流变固结解析理论[J]. 岩土力学, 2006, 27(增刊): 140-146. (LI Xi-bin, JIA Xian-lin, XIE Kang-he. Analytical solution of 1D viscoelastic consolidation of soft soils under time-dependent loadings [J]. Rock and Soil Mechanics, 2006, 27(S0): 140-146. (in Chinese))
    [12] 何利军, 孔令伟, 吴文军, 等. 采用分数阶导数描述软黏土蠕变的模型[J]. 岩土力学, 2011, 32(增刊): 239-244. (HE Li-jun, KONG Ling-wei, WU Wen-jun, et al. A description of creep model for soft soil with fractional derivative[J]. Rock and Soil Mechanics, 2011, 32(S0): 239-244. (in Chinese))
    [13] 尹检务, 旷杜敏, 王智超. 压实土固结蠕变特征及分数阶流变模型参数的分析[J]. 湖南科技大学学报(自然科学版), 2015, 30(3): 46-51. (YIN Jian-wu, KUANG Du-min, WANG Zhi-chao. Consolidation creep characteristics of compacted clay and its parameters analysis of rheological constitutive model based on fractional calculus[J]. Journal of Hunan University of Science ＆ Technology (Natural Science Edition), 2015, 30(3): 46-51. (in Chinese))
    [14] 陈 亮, 陈寿根, 张 恒, 等. 基于分数阶微积分的非线性黏弹塑性蠕变模型[J]. 四川大学学报(工程科学版), 2013, 45(3): 7-11. (CHEN Liang, CHEN Shou-gen, ZHANG Heng, et al. A nonlinear viscoelasto-plastic creep model based on fractional calculus[J]. Journal of Sichuan University (Engineering Science Edition), 2013, 45(3): 7-11. (in Chinese))
    [15] 孙海忠, 张 卫. 一种分析软土黏弹性的分数导数开尔文模型[J]. 岩土力学, 2007, 28(9): 1983-1986. (SUN Hai-zhong, ZHANG Wei. Analysis of soft soil with viscoelastic fractional derivative Kelvin model[J]. Rock and Soil Mechanics. 2007, 28(9): 1983-1986. (in Chinese))
    [16] YIN De-shun, LI Yan-qing, WU Hao, et al. Fractional description of mechanical property evolution of soft soils during creep[J]. Water Science and Engineering, 2013, 6(4): 446-455.
    [17] 殷德顺, 任俊娟, 和成亮, 等. 一种新的岩土流变模型元件[J]. 岩石力学与工程学报, 2007, 26(9): 1899-1903. (YIN De-shun, REN Jun-juan, HE Cheng-liang, et al. A new rheological model element for geomaterials[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(9): 1899-1903. (in Chinese))
    [18] 王智超, 罗迎社, 罗文波, 等. 路基压实土流变变形的力学表征及参数辨识[J]. 岩石力学与工程学报, 2011, 30(1): 208-216. (WANG Zhi-chao, LUO Ying-she, LUO Wen-bo, et al. Mechanical characterization and parameter identification of rheological deformation of subgrade compacted soil[J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(1): 208-216. (in Chinese))
    [19] NONNENMACHER T F, METZLER R. On the Riemann-Liouville fractional calculus and some recent applications[J]. Fractals, 1995, 3(3): 557-566.
    [20] MANDELBORT B B. The fractal geometry of nature[M]. San Fransico: Freeman, 1982.
    [21] 何光渝, 王卫红. 精确的拉普拉斯数值反演方法及其应用[J]. 石油学报, 1995, 16(1): 96-103. (HE Guang-yu, WANG Wei-hong. Accurate numerical Laplace inversion method and its application[J]. Acta Petroleisinaca, 1995, 16(1): 96-103. (in Chinese))
    [22] 张先伟, 王常明. 结构性软土的黏滞系数[J]. 岩土力学, 2011, 32(11): 3276-3282. (ZHANG Xian-wei, WANG Chang-ming. Viscosity coefficient of structural soft clay[J]. Rock and Soil Mechanics, 2011, 32(11): 3276-3282. (in Chinese))
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出版历程
  • 收稿日期:  2016-06-19
  • 发布日期:  2017-10-24

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