工程力学 ›› 2019, Vol. 36 ›› Issue (9): 79-88.doi: 10.6052/j.issn.1000-4750.2018.06.0349

• 土木工程学科 • 上一篇    下一篇

连续排水边界条件下土体一维流变固结解析解

宗梦繁1, 吴文兵1,2,3, 梅国雄1,2,3, 梁荣柱1, 田乙1   

  1. 1. 中国地质大学工程学院, 湖北, 武汉 430074;
    2. 广西大学土木建筑工程学院, 广西, 南宁 530004;
    3. 广西大学工程防灾与结构安全教育部重点实验室, 广西, 南宁 530004
  • 收稿日期:2018-06-20 修回日期:2019-05-24 出版日期:2019-09-25 发布日期:2019-09-09
  • 通讯作者: 吴文兵(1988-),男,江西鄱阳人,教授,博士,博导,从事岩土工程研究(E-mail:zjuwwb1126@163.com). E-mail:zjuwwb1126@163.com
  • 作者简介:宗梦繁(1992-),男,江西抚州人,博士生,从事固结理论研究(E-mail:zongmengf@163.com);梅国雄(1975-),男,湖北黄梅人,教授,博士,博导,从事固结理论和土体基本性质等方面的研究(E-mail:meigx@163.com);梁荣柱(1988-),男,广东阳江人,副研究员,博士,从事盾构隧道保护相关研究(E-mail:liangcug@163.com);田乙(1995-),男,云南曲靖人,硕士生,从事岩土工程研究(E-mail:tianyibox@163.com).
  • 基金资助:
    国家自然科学基金面上项目(51578164,51678547,51878634,51878185);中国博士后科学基金面上项目(2016M600711);广西防灾减灾与工程安全重点实验室开放基金项目(2016ZDK015)

ANALYTICAL SOLUTION FOR ONE-DIMENSIONAL RHEOLOGICAL CONSOLIDATION OF SOIL BASED ON CONTINUOUS DRAINAGE BOUNDARY

ZONG Meng-fan1, WU Wen-bing1,2,3, MEI Guo-xiong1,2,3, LIANG Rong-zhu1, TIAN Yi1   

  1. 1. Faculty of Engineering, China University of Geosciences, Wuhan, Hubei 430074, China;
    2. College of Civil Engineering and Architecture, Guangxi University, Nanning, Guangxi 530004, China;
    3. Key Laboratory of Disaster Prevention and Structural Safety, Ministry of Education, Guangxi University, Nanning, Guangxi 530004, China
  • Received:2018-06-20 Revised:2019-05-24 Online:2019-09-25 Published:2019-09-09

摘要: 基于四元件流变模型,通过引入连续排水边界条件研究了单级加载下的土体一维流变固结问题。利用分离变量法和Laplace变换技术得到瞬时荷载下的解析解,进而通过积分的方法得到单级加载下的解析解。随后对排水边界和流变模型进行了退化,得到Terzaghi边界下及三元件流变模型下的一维流变固结解答,通过与现有解答对比初步验证了该文解答的正确性。最后,对不同界面参数、流变参数以及加载速率对土体固结特性的影响进行了分析。结果表明:基于连续排水边界得到的固结解答与基于Terzaghi双面排水得到的固结解答的差异主要在固结前期,且两者的差异随界面参数α、β取值变大而减小。流变固结与线弹性固结差异主要在固结后期,流变固结需要更长时间土体才能完全固结。此外,土体固结速率随加载速率增大而增大。

关键词: 一维流变固结, 连续排水边界, 单级加载, 固结度, 界面参数

Abstract: Based on a four-element rheological model, the one-dimensional rheological consolidation problem of soil under one-step loading was studied by introducing continuous drainage boundary conditions. The analytical solution under constant loading is obtained by the separation variable method and the Laplace transform technique, and the analytical solution under one-step loading is obtained by the integral method. Then, by degrading the drainage boundary and rheological model, the solution of one-dimensional rheological consolidation under the Terzaghi's boundary and the three-element rheological model is obtained, and the correctness of the present solution is verified by the comparison with existing solutions. Finally, the consolidation behavior of soil is analyzed for different interface parameters, rheological parameters or loading rate. The results show that:the difference between the consolidation solution based on continuous drainage boundary conditions and that based on Terzaghi's drainage is mainly in the early stage of consolidation, and the difference decreases with the increase of interface parameters α and β. The difference between rheological consolidation and linear elastic consolidation is mainly in the late stage of consolidation, and rheological consolidation requires a longer time for soil to be fully consolidated. In addition, the consolidation rate of soil increases with the increase of loading rate.

Key words: one-dimensional rheological consolidation, continuous drainage boundary, one-step loading, consolidation degree, interface parameter

中图分类号: 

  • TU43
[1] Gray H. Simultaneous consolidation of contiguous layers of unlike compressible soils[J]. Transactions of the American Society of Civil Engineering, 1945, 110:1327-1356.
[2] Schiffman R L, STEIN J R. One-dimensional consolidation of layered systems[J]. Journal of Soil Mechanics and Foundations Division, ASCE, 1970, 96(4):1499-1504.
[3] 梅国雄, 夏君, 梅岭. 基于不对称连续排水边界的太沙基一维固结方程及其解答[J]. 岩土工程学报, 2011, 33(1):28-31. Mei Guoxiong, Xia Jun, Mei Ling. Terzaghi's one-dimensional consolidation equation and its solution based on asymmetric continuous drainage boundary[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(1):28-31. (in Chinese)
[4] Liu J C, Lei G H. One-dimensional consolidation of layered soils with exponentially time-growing drainage boundaries[J]. Computers and Geotechnics, 2013, 54(10):202-209.
[5] 何利军, 吴立松, 张涛, 等. 基于连续边界条件的土层厚度随时间变化的平均固结度研究[J]. 工程力学, 2016, 33(增刊1):11-17. He Lijun, Wu Lisong, Zhang Tao, et al. The average degree of consolidation about soil layer thickness changing with time based on continuous drainage boundary[J]. Engineering Mechanics, 2016, 33(Suppl 1):11-17. (in Chinese)
[6] Wu W B, Zong M F, El Naggar M H, et al. Analytical solution for one-dimensional consolidation of double-layered soil with exponentially time-growing drainage boundary[J]. International Journal of Distributed Sensor Networks, 2018, 14(10):1-11.
[7] 宗梦繁, 吴文兵, 梅国雄, 等. 连续排水边界条件下土体一维非线性固结解析解[J]. 岩石力学与工程学报, 2018, 37(12):2829-2838. Zong Mengfan, Wu Wenbing, Mei Guoxiong, et al. An analytical solution for one-dimensional nonlinear consolidation of soils with continuous drainage boundary[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(12):2829-2838. (in Chinese)
[8] 李勇义, 冯健雪, 梅国雄. 连续排水边界下梯形循环荷载作用的一维固结解析解[J]. 工程力学, 2019, 36(2):134-140. Li Yongyi, Feng Jianxue, Mei Guoxiong. One-dimensional consolidation analysis of the trapezoidal cyclic loading under continuous drainage boundary[J]. Engineering Mechanics, 2019, 36(2):134-140. (in Chinese)
[9] Schiffman R L. Consolidation of soil under timedependent loading and varying permeability[J]. Proceedings Highway Research Board, 1958, 37:584-617.
[10] Wilson N E, Elgohary M M. Consolidation of soils under cyclic loading[J]. Canadian Geotechnical Journal, 1974, 11(3):420-423.
[11] Alonso E E, Krizek R J. Randomness of settlement rate under stochastic load[J]. Journal of the Geotechnical Engineering Division, ASCE, 1974, 100(6):1211-1226.
[12] Favaretti M, Soranzo M. A simplified consolidation theory in cyclic loading conditions[C]. Proceedings of International Symposium on Compression and Consolidation of Clayey Soils. Japan:Hiroshima, 1995, 1:405-409.
[13] 关山海, 谢康和, 胡安峰. 低频循环荷载下地基一维固结性状分析[J]. 岩土力学, 2003, 24(5):849-853. Guan Shanhai, Xie Kanghe, Hu Anfeng. Analysis of one-dimensional consolidation behavior of soil under low-frequency cyclic loading[J]. Rock and Soil Mechanics, 2003, 24(5):849-853. (in Chinese)
[14] 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.
[15] Lo K Y. Secondary compression of clays[J]. Journal of Soil Mechanics and Foundation Engineering Division, ASCE, 1961, 87(4):61-87.
[16] 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. Tan T K. One dimensional problems of consolidation and secondary time effects[J]. China Civil Engineering Journal, 1958, 5(1):1-10. (in Chinese)
[17] 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 Weibing. Theory of 1-D consolidation of saturated clay modeled with the generalized Voigt model and its application[J]. Chinese Journal of Geotechnical Engineering, 1989, 11(5):78-85. (in Chinese)
[18] 王奎华, 谢康和, 曾国熙. 双面半透水边界的一维粘弹性固结理论[J]. 岩土工程学报, 1998, 20(2):34-36. Wang Kuihua, Xie Kanghe, Zeng Guoxi. A study on 1-D consolidation of soils exhibiting rheological characteristics with impeded boundaries[J]. Chinese Journal of Geotechnical Engineering, 1998, 20(2):34-36. (in Chinese)
[19] 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.
[20] 李西斌, 谢康和, 王奎华, 等. 双面半透水边界饱和土层在循环荷载作用下一维粘弹性固结解析解[J]. 工程力学, 2004, 21(5):103-108. Li Xibin, Xie Kanghe, Wang Kuihua, et al. Analytical solution of 1-D visco-elastic consolidation of soils with impeded boundaries under cyclic loadings[J]. Engineering Mechanics, 2004, 21(5):103-108. (in Chinese)
[21] 高彦斌. 饱和软粘土一维非线性流变——固结耦合分析[J]. 工程力学, 2006, 23(8):116-121. Gao Yanbin. One-dimensional nonlinear creepConsolidation analysis of saturated clay[J]. Engineering Mechanics, 2006, 23(8):116-121. (in Chinese)
[22] 李传勋, 马浩天, 金丹丹. 考虑起始水力坡降的软黏土流变固结解析解[J]. 工程科学与技术, 2019, 51(2):53-60. Li Chuanxun, Ma Haotian, Jin Dandan. Analytical solution for rheological consolidation of soft clay with threshold hydraulic gradient[J]. Advanced Engineering Sciences, 2019, 51(2):53-60. (in Chinese)
[23] 李西斌. 软土流变固结理论与试验研究[D]. 杭州:浙江大学, 2005:126-130. Li Xibin. Theoretical and experimental studies on rheological consolidation of soft soil[D]. Hangzhou:Zhejiang University, 2005:126-130. (in Chinese)
[1] 冯健雪, 陈征, 李勇义, 梅国雄. 连续排水边界条件下线性加载地基一维固结解析解[J]. 工程力学, 2019, 36(6): 219-226.
[2] 冯健雪, 陈征, 李勇义, 梅国雄. 连续排水边界条件下考虑自重的地基一维固结分析[J]. 工程力学, 2019, 36(5): 184-191.
[3] 李勇义, 冯健雪, 梅国雄. 连续排水边界下梯形循环荷载作用的一维固结解析解[J]. 工程力学, 2019, 36(2): 134-140.
[4] 何利军, 吴立松, 张涛, 梅国雄. 基于连续边界条件的土层厚度随时间变化的平均固结度研究[J]. 工程力学, 2016, 33(增刊): 11-17.
[5] 谢新宇, 王龙, 刘开富. 层状地基一维固结电阻网法解答[J]. 工程力学, 2012, 29(6): 98-104.
[6] 赵海峰. 微米厚度金属薄膜/陶瓷基体界面力学性能的实验测量与数值模拟[J]. 工程力学, 2009, 26(4): 68-072,.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] 王小兵;刘扬;崔海清;韩洪升. 螺旋流抑制杆管偏磨的PIV实验研究[J]. 工程力学, 2011, 28(11): 225 -230 .
[2] 潘旦光;楼梦麟;董聪. P、SV波作用下层状土层随机波动分析[J]. 工程力学, 2006, 23(2): 66 -71 .
[3] 李宏男;杨浩. 基于多分支BP神经网络的结构系统辨识[J]. 工程力学, 2006, 23(2): 23 -28,4 .
[4] 杨璞;刘应华;袁鸿雁;岑章志. 计算结构极限载荷的修正弹性补偿法[J]. 工程力学, 2006, 23(3): 21 -26 .
[5] 张伟伟;夏巍;叶正寅. 一种高超音速热气动弹性数值研究方法[J]. 工程力学, 2006, 23(2): 41 -46 .
[6] 纵智育;辛克贵;王珊. 张力膜结构初始形态分析的曲面四边形单元[J]. 工程力学, 2006, 23(3): 32 -36,2 .
[7] 李雷;谢水生;黄国杰. 应变梯度塑性理论下超薄梁弯曲中尺度效应的数值研究[J]. 工程力学, 2006, 23(3): 44 -48 .
[8] 裴星洙;张立. 点焊箱型截面薄壁构件的翘曲扭转研究[J]. 工程力学, 2006, 23(3): 56 -62 .
[9] 王元清;武延民;石永久;江见鲸. 温度对结构钢材裂纹尖端张开位移(CTOD)的影响分析[J]. 工程力学, 2006, 23(4): 74 -78 .
[10] 郭薇薇;夏禾;徐幼麟. 风荷载作用下大跨度悬索桥的动力响应及列车运行安全分析[J]. 工程力学, 2006, 23(2): 103 -110 .
X

近日,本刊多次接到来电,称有不法网站冒充《工程力学》杂志官网,并向投稿人收取高额费用。在此,我们郑重申明:

1.《工程力学》官方网站是本刊唯一的投稿渠道(原网站已停用),《工程力学》所有刊载论文必须经本刊官方网站的在线投稿审稿系统完成评审。我们不接受邮件投稿,也不通过任何中介或编辑收费组稿。

2.《工程力学》在稿件符合投稿条件并接收后会发出接收通知,请作者在接到版面费或审稿费通知时,仔细检查收款人是否为“《工程力学》杂志社”,千万不要汇款给任何的个人账号。请广大读者、作者相互转告,广为宣传!如有疑问,请来电咨询:010-62788648。

感谢大家多年来对《工程力学》的支持与厚爱,欢迎继续关注我们!

《工程力学》杂志社

2018年11月15日