Advanced Search
  • 全国中文核心期刊
  • 中国科技核心期刊
  • 美国工程索引（EI）收录期刊
  • Scopus数据库收录期刊
Volume 39 Issue 10
Turn off MathJax
Article Contents
Abstract
References
Related Articles
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
shu

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

More Information
  • Received Date: June 19, 2016
  • Published Date: October 24, 2017
    Graphical Abstract
    • 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.
    • FullText(HTML)
    • References (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))
    • Related Articles

  • Related Articles

    [1]LIU Hongwei, WANG Mengqi, ZHAN Liangtong, FENG Song, WU Tao. Method and apparatus for measuring in-situ gas diffusion coefficient and permeability coefficient of unsaturated soils[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(5): 948-958. DOI: 10.11779/CJGE20221228
    [2]JI Yong-xin, ZHANG Wen-jie. Experimental study on diffusion of chloride ions in unsaturated soils[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(9): 1755-1760. DOI: 10.11779/CJGE202109022
    [3]XU Fei, CAI Yue-bo, QIAN Wen-xun, WEI Hua, ZHUANG Hua-xia. Mechanism of cemented soil modified by aliphatic ionic soil stabilizer[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(9): 1679-1687. DOI: 10.11779/CJGE201909012
    [4]HUANG Wei, LIU Qing-bing, XIANG Wei, ZHANG Yun-long, WANG Zhen-hua, DAO Minh Huan. Water adsorption characteristics and water retention model for montmorillonite modified by ionic soil stabilizer[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(1): 121-130. DOI: 10.11779/CJGE201901013
    [5]ZHANG Wen-jie, GU Chen, LOU Xiao-hong. Measurement of hydraulic conductivity and diffusion coefficient of backfill for soil-bentonite cutoff wall under low consolidation pressure[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(10): 1915-1921. DOI: 10.11779/CJGE201710021
    [6]HUANG Qing-fu, ZHAN Mei-li, SHENG Jin-chang, LUO Yu-long, ZHANG Xia. Numerical method to generate granular assembly with any desired relative density based on DEM[J]. Chinese Journal of Geotechnical Engineering, 2015, 37(3): 537-543. DOI: 10.11779/CJGE201503019
    [7]LIU Qing-bing, XIANG Wei, CUI De-shan. Effect of ionic soil stabilizer on bound water of expansive soils[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(10): 1887-1895.
    [8]LIU Qing-bing, XIANG Wei, CUI De-shan, CAO Li-jing. Mechanism of expansive soil improved by ionic soil stabilizer[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(4): 648.
    [9]Microcosmic mechanism of ion transport in charged clay soils[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(11): 1794-1799.
    [10]XI Yong, Hui, REN Jie. Laboratory determination of diffusion and distribution coefficients of contaminants in clay soil[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(3): 397-402.
    • Supplements (0)

Catalog

    Get Citation
    PDF
    XML
    Article views PDF downloads Cited by()
    Related
    Copyright © 2010 Editorial By Chinese Journal of Geotechnical Engineering 苏ICP备05007122号-11公安联网备案号：32010602011255
    Editorial Office address：34 Hujuguan,Nanjing 210024,ChinaPostal Code：210024Tel：025-85829534，85829556E-mail: ge@nhri.cn

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return