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工程地质学报  2018, Vol. 26 Issue (6): 1480-1489    DOI: 10.13544/j.cnki.jeg.2017-480
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任意荷载下双面半透水边界分数阶导数黏弹性饱和土层一维固结
李林忠1, 汪磊2, 李培超1, 孙德安3
1. 上海工程技术大学机械与汽车工程学院 上海 201620;
2. 上海工程技术大学城市轨道交通学院 上海 201620;
3. 上海大学土木工程系 上海 200444
ONE-DIMENSIONAL CONSOLIDATION OF FRACTIONAL DERIVATIVE VISCOELASTIC SATURATED SOIL LAYER WITH SYMMETRIC SEMI-PERMEABLE BOUNDARIES UNDER ARBITRARY LOADING
LI Linzhong1, WANG Lei2, LI Peichao1, SUN Dean3
1. School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620;
2. School of Urban Railway Transportation, Shanghai University of Engineering Science, Shanghai 201620;
3. Department of Civil Engineering, Shanghai University, Shanghai 200444
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摘要 基于Terzaghi一维固结理论,分析了考虑半透水边界条件的分数阶导数黏弹性饱和土层在随时间变化的任意荷载作用下一维固结问题。首先,应用Laplace变换联立求解饱和土层一维固结微分方程和分数阶Kelvin-Voigt黏弹性本构方程,推导出有效应力和沉降在Laplace变换域内的解析解,采用Crump方法进行Laplace逆变换,得到了时间域内的半解析解。然后将本文得到的半解析解分别退化为半透水边界条件下基于黏弹性假设的一维固结半解析解和双面透水边界条件下基于分数阶黏弹性假设的一维固结半解析解,结果与已有文献的半解析解相同,验证了本研究所提出解的可靠性。最后通过算例分别考察了半透水边界参数、分数阶黏弹性模型参数和荷载参数对饱和土层固结沉降的影响。研究表明,半透水边界条件参数、分数阶次与黏滞系数主要影响饱和土层固结的发展快慢,而饱和土层的最终沉降量主要受到土层压缩模量的影响;另外,饱和土层的固结规律与外荷载变化规律一致。
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李林忠
汪磊
李培超
孙德安
关键词半透水边界   任意荷载   分数阶导数   黏弹性   饱和土层   一维固结     
Abstract: Based on one-dimensional consolidation theory of Terzaghi, this paper studies the one-dimensional consolidation problem of saturated soil layer with fractional viscoelastic model under symmetric semi-permeable boundaries subjected to arbitrary loading. By using the Laplace transform upon the one-dimensional consolidation equation of saturated soils and the fractional Kelvin-Voigt viscoelastic constitutive equation, the analytical solutions of effective stress and settlement in the Laplace transform domain are obtained. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi-analytical solutions in the time domain. It is shown that the present solution is reliable and in a good agreement with the existing solutions from literatures by reducing the proposed solution. Last, several numerical examples are provided to investigate the consolidation behavior of saturated soils with the fractional viscoelastic model under symmetric semi-permeable boundaries subjected to arbitrary loading. The results illustrate that, in the case of arbitrary loading, the consolidation rate is affected by the semi-permeable boundary parameters, fractional order, viscosity coefficient and load parameters. The final settlement of saturated soil layer is affected by the modulus of compressibility. In addition, the consolidation behavior of soil layer is consistent with the characteristics of loadings.
Key wordsSemi-permeable boundary   Arbitrary loading   Fractional order derivative   Viscoelasticity   Saturated soil layer   One-dimensional consolidation   
收稿日期: 2017-10-13;
基金资助:国家自然科学基金项目(41807232,11672172)资助
通讯作者: 汪磊(1985-),男,博士,副教授,主要从事土的固结研究.Email:wangleiwangjiang@163.com     E-mail: wangleiwangjiang@163.com
作者简介: 李林忠(1992-),男,硕士生,主要从事饱和土固结方面的研究.Email:heartbeatsllz@163.com
引用本文:   
李林忠,汪磊,李培超等. 任意荷载下双面半透水边界分数阶导数黏弹性饱和土层一维固结[J]. 工程地质学报, 2018, 26(6): 1480-1489.
LI Linzhong,WANG Lei,LI Peichao et al. ONE-DIMENSIONAL CONSOLIDATION OF FRACTIONAL DERIVATIVE VISCOELASTIC SATURATED SOIL LAYER WITH SYMMETRIC SEMI-PERMEABLE BOUNDARIES UNDER ARBITRARY LOADING[J]. Journal of Engineering Geology, 2018, 26(6): 1480-1489.
 
没有本文参考文献
[1] 周凤玺, 贺钇铭, 赖远明. 非均匀地基与均匀地基一维固结解答之间的转换关系[J]. 工程地质学报, 2015, 23(2): 260-264.
[2] 徐珊, 陈有亮, 赵重兴. 单向压缩状态下上海地区软土的蠕变变形与次固结特 性研究[J]. 工程地质学报, 2008, 16(4): 495-501.
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