Nonlinear rheological consolidation analysis of soil around tunnel based on fractional order model

doi:10.3785/j.issn.1008-973X.2023.11.010

Journal of ZheJiang University (Engineering Science)

2023, Vol. 57

Issue (11): 2227-2234 DOI: 10.3785/j.issn.1008-973X.2023.11.010

Nonlinear rheological consolidation analysis of soil around tunnel based on fractional order model

An-feng HU1,2(

),Hao JIANG1,3,Zhi-rong XIAO4,*(

),Sen-lin XIE1,Zhao-qi GONG5,Wen-qian LI6

1. Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China
2. Center for Balance Architecture, Zhejiang University, Hangzhou 310058, China
3. The Architectural Design and Research Institute of Zhejiang University Co. Ltd, Hangzhou 310028, China
4. School of Civil Engineering and Architecture, Zhejiang University of Science and Technology, Hangzhou 310023, China
5. Zhejiang Province Architectural Design and Research Institute, Hangzhou 310006, China
6. Urban Rail Traffic Engineering Branch of China Railway No.10 Engineering Group, Guangzhou 511400, China

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Abstract

The two-dimensional nonlinear consolidation control equation was established, considering the nonlinear changes of compressibility and permeability of the saturated soft soil around the tunnel. The fractional-order Merchant model was introduced to consider the influence of soil rheological properties, and the alternating implicit difference method in Douglas-Jone format was used to solve the equation. The correctness of the solutions was verified by the comparison with the existing analytical solutions. The nonlinear rheological consolidation characteristics of the saturated soft soil around the tunnel were investigated by using the obtained difference decomposition for parametric analysis. Results show that the tunnel leakage pattern, initial permeability coefficient, and permeability index have a large influence on the consolidation rate of the soil, and the more the permeable channels, the larger the initial permeability coefficient, and the smaller the permeability index, the faster the consolidation rate of the soil, while the compression index has a smaller influence on the consolidation rate. The coefficient of permeability anisotropy has a significant effect on the rate of consolidation, and the difference in permeability coefficients in different directions of the soil should be fully considered in the analysis of consolidation properties. When considering the rheological properties of the soil, the consolidation rate of the soil slows down significantly, but when the initial permeability coefficient increases to a certain degree, the effect of the rheological properties of the soil on the consolidation rate of the soil layer can be ignored.

Key words： tunnel saturated soft soil nonlinear rheological consolidation finite difference method fractional order model

Received: 29 December 2022 Published: 11 December 2023

CLC:

TU 43

Fund: 国家自然科学基金资助项目(52378419, 51978612)

Corresponding Authors: Zhi-rong XIAO E-mail: anfenghu@zju.edu.cn;100106@zust.edu.cn

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Cite this article:

An-feng HU,Hao JIANG,Zhi-rong XIAO,Sen-lin XIE,Zhao-qi GONG,Wen-qian LI. Nonlinear rheological consolidation analysis of soil around tunnel based on fractional order model. Journal of ZheJiang University (Engineering Science), 2023, 57(11): 2227-2234.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.11.010 OR https://www.zjujournals.com/eng/Y2023/V57/I11/2227

基于分数阶模型的隧道周围土体非线性流变固结分析

考虑隧道周围饱和软土压缩性和渗透性非线性变化，建立二维非线性固结控制方程，引入分数阶Merchant模型考虑土体流变特性影响，采用Douglas-Jone格式的交替隐式差分法对方程进行求解. 通过与现有解析解进行对比，验证了本研究解的正确性. 利用得到的差分解进行参数分析，研究隧道周围饱和软土的非线性流变固结特性. 结果表明，隧道渗漏模式、初始渗透系数和渗透指数对土体固结速率影响较大，透水通道越多、初始渗透系数越大、渗透指数越小，土体固结速率越快，而压缩指数对固结速率的影响较小；渗透各向异性系数对固结速率有较大影响，在进行固结性状分析时，应当充分考虑土体不同方向渗透系数的差异；当考虑土体流变特性时，土体固结速率显著减小，但当初始渗透系数增大到一定程度时，土体流变特性对土层固结速率的影响可以忽略.

关键词： 隧道, 饱和软土, 非线性流变固结, 有限差分法, 分数阶模型

Fig.1 Nonlinear rheological consolidation calculation model for saturated soft soil around tunnels

Fig.2 Schematic of model mesh at each time step

Tab.1 Geometric and physical parameters of model

Fig.3 Comparison of solutions of proposed method and existing analytical solutions

Fig.4 Schematic diagram of shield segment leakage

Fig.5 Comparison of consolidation rates under influence of tunnel leakage modes

Fig.6 Comparison of consolidation rates under influence of permeability anisotropy

Fig.7 Comparison of consolidation rates under influence of permeability coefficient

Fig.8 Comparison of consolidation rates under influence of permeability index

Fig.9 Comparison of consolidation rates under influence of compression index


[1]	YI X, ROWE R K, LEE K M Observed and calculated pore pressures and deformations induced by an earth balance shield[J]. Canadian Geotechnical Journal, 1993, 30 (3): 476490

[2]	SHIRLAW J N Observed and calculated pore pressures and deformations induced by an earth balance shield: discussion[J]. Canadian Geotechnical Journal, 1995, 32 (1): 181- 189 doi: 10.1139/t95-017

[3]	张冬梅, 黄宏伟, 王箭明软土隧道地表长期沉降的粘弹性流变与固结耦合分析[J]. 岩石力学与工程学报, 2003, (Suppl.1): 2359- 2362 ZHANG Dong-mei, HUANG Hong-wei, WANG Jian-ming Analysis of long-term settlements over tunnels using visco-elastic constitutive model coupled with consolidation theory[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, (Suppl.1): 2359- 2362

[4]	詹美礼, 钱家欢, 陈绪禄粘弹塑性有限单元法及其在隧道分析中的应用[J]. 土木工程学报, 1993, 26 (3): 13- 21 ZHAN Mei-li, QIAN Jia-huan, CHEN Xu-lu Visco-elastic-plastic F. E. M. and its application in tunnel analysis[J]. China Civil Engineering Journal, 1993, 26 (3): 13- 21 doi: 10.15951/j.tmgcxb.1993.03.002

[5]	童磊. 软土浅埋隧道变形、渗流及固结性状研究[D]. 杭州: 浙江大学, 2010. TONG Lei. Studies on land subsidence, seepage field and consolidation behavior of soft soil around a shallow circular tunnel [D]. Hangzhou: Zhejiang University, 2010

[6]	包鹤立. 衬砌局部渗漏条件下软土盾构隧道的长期性态研究[D]. 上海: 同济大学. 2008. BAO He-li. Research on the long-term behavior of sheild tunnel with partially sealed linings in soft soil[D]. Shanghai: Tongji University, 2008.

[7]	LI X Stress and displacement fields around a deep circular tunnel with partial sealing[J]. Computers and Geotechnics, 1999, 24 (2): 125- 140 doi: 10.1016/S0266-352X(98)00035-4

[8]	刘干斌, 谢康和, 施祖元, 等横观各向同性土中深埋圆形隧道的应力和位移分析[J]. 岩土工程学报, 2003, 25 (6): 727- 731 LIU Gan-bin, XIE Kang-he, SHI Zu-yuan, et al. Analysis of stress and displacement around a deep circular tunnel in transversely isotropic soil[J]. Chinese Journal of Geotechnical Engineering, 2003, 25 (6): 727- 731 doi: 10.3321/j.issn:1000-4548.2003.06.018

[9]	曹奕. 软土中盾构隧道的长期非线性固结变形研究[D]. 杭州: 浙江大学, 2014. CAO Yi. Research on long-term nonlinear consolidation deformation of shield tunnel in soft soil[D]. Hangzhou: Zhejiang University, 2014

[10]	李传勋, 谢康和, 胡安峰, 等基于指数形式渗流下的软土一维非线性固结分析[J]. 中南大学学报: 自然科学版, 2012, 43 (7): 2789- 2795 LI Chuan-xun, XIE Kang-he, HU An-feng, et al Analysis of one-dimensional non-linear consolidation with exponential flow[J]. Journal of Central South University: Science and Technology, 2012, 43 (7): 2789- 2795

[11]	ZHANG C Y. Viscoelastic fracture mechanics[M]. Beijing: Science Press, 2006.

[12]	袁静, 龚晓南, 益德清岩土流变模型的比较研究[J]. 岩石力学与工程学报, 2001, (6): 772- 779 YUAN Jing, GONG Xiao-nan, YI De-qing Comparison study on rheological constitutive models[J]. Chinese Journal of Rock Mechanics and Engineering, 2001, (6): 772- 779 doi: 10.3321/j.issn:1000-6915.2001.06.004

[13]	BLAIR G W S The role of psychophysics in rheology[J]. Journal of Colloid Science, 1947, 2 (1): 21- 32 doi: 10.1016/0095-8522(47)90007-X

[14]	GERASIMOV A N A generalization of linear laws of deformation and its application to inner friction problems[J]. Journal of Applied Mathematics and Mechanics, 1948, 12: 251- 259

[15]	PODLUBNY I. Fractional differential equations[M]. San Diego: Academic Press, 1999.

[16]	YIN D S, WU H, CHENG C, et al Fractional order constitutive model of geomaterials under the condition of triaxial test[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37 (8): 961972

[17]	CAPUTO M. Elasticità dissipazione[M]. Bologna: Zanichelli, 1969.

[18]	BAGLEY R L, TORVIK P J A theoretical basis for the application of fractional calculus to viscoelasticity[J]. Journal of Rheology, 1983, 27 (3): 201- 230 doi: 10.1122/1.549724

[19]	KOELLER R C Applications of fractional calculus to the theory of viscoelasticity[J]. Journal of Applied Mechanics, 1984, 51 (2): 299- 307 doi: 10.1115/1.3167616

[20]	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 doi: 10.3969/j.issn.1000-7598.2007.09.041

[21]	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 (Suppl.1): 239- 249 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 (Suppl.1): 239- 249 doi: 10.16285/j.rsm.2011.s2.022

[22]	YIN D S, LI Y Q, WU H, et al Fractional description of mechanical property evolution of soft soils during creep[J]. Water Science and Engineering, 2013, 6 (4): 446- 455

[23]	罗庆姿, 陈晓平, 王盛, 等软黏土变形时效性的试验及经验模型研究[J]. 岩土力学, 2016, 37 (1): 66- 75 LUO Qing-zi, CHEN Xiao-ping, WANG Sheng, et al An experimental study of time-dependent deformation behavior of soft soil and its empirical model[J]. Rock and Soil Mechanics, 2016, 37 (1): 66- 75 doi: 10.16285/j.rsm.2016.01.008

[24]	解益, 李培超, 汪磊, 等分数阶导数黏弹性饱和土体一维固结半解析解[J]. 岩土力学, 2017, 38 (11): 3240- 3246 XIE Yi, LI Pei-chao, WANG Lei, et al Semi-analytical solution for one-dimensional consolidation of viscoelastic saturated soil with fractional order derivative[J]. Rock and Soil Mechanics, 2017, 38 (11): 3240- 3246 doi: 10.16285/j.rsm.2017.11.020

[25]	刘忠玉, 杨强基于分数阶Kelvin模型的饱和黏土一维流变固结分析[J]. 岩土力学, 2017, 38 (12): 3680- 3687 LIU Zhong-yu, YANG Qiang One-dimensional rheological consolidation analysis of saturated clay using fractional order Kelvin's model[J]. Rock and Soil Mechanics, 2017, 38 (12): 3680- 3687 doi: 10.16285/j.rsm.2017.12.036

[26]	汪磊, 李林忠, 徐永福, 等半透水边界下分数阶黏弹性饱和土一维固结特性分析[J]. 岩土力学, 2018, 39 (11): 4142- 4148 WANG Lei, LI Lin-zhong, XU Yong-fu, et al Analysis of one-dimensional consolidation of fractional viscoelastic saturated soils with semi-permeable boundary[J]. Rock and Soil Mechanics, 2018, 39 (11): 4142- 4148 doi: 10.16285/j.rsm.2017.0659

[27]	刘忠玉, 崔鹏陆, 郑占垒, 等基于非牛顿指数渗流和分数阶Merchant模型的一维流变固结分析[J]. 岩土力学, 2019, 40 (6): 2029- 2038 LIU Zhong-yu, CUI Peng-lu, ZHENG Zhan-lei, et al. Analysis of one-dimensional rheological consolidation with flow described by non-Newtonian index and fractional-order Merchant's model[J]. Rock and Soil Mechanics, 2019, 40 (6): 2029- 2038 doi: 10.16285/j.rsm.2018.1085

[28]	黄明华, 胡可馨, 赵明华分数阶黏弹性地基中洞周超孔隙水压力消散特性分析[J]. 岩土工程学报, 2020, 42 (8): 1446- 1455 HUANG Ming-hua, HU Ke-xin, ZHAO Ming-hua Dissipation characteristics of excess pore-water pressure around tunnels in viscoelastic foundation using a fractional-derivative model[J]. Chinese Journal of Geotechnical Engineering, 2020, 42 (8): 1446- 1455 doi: 10.11779/CJGE202008009

[29]	刘忠玉, 张家超, 郑占垒, 等考虑Hansbo渗流的二维Biot固结有限元分析[J]. 岩土力学, 2018, 39 (12): 4617- 4626 LIU Zhong-yu, ZHANG Jia-chao, ZHENG Zhan-lei, et al Finite element analysis of two-dimensional Biot’s consolidation with Hansbo’s flow[J]. Rock and Soil Mechanics, 2018, 39 (12): 4617- 4626 doi: 10.16285/j.rsm.2017.0892

[30]	蒋洪胜, 侯学渊盾构掘进对隧道周围土层扰动的理论与实测分析[J]. 岩石力学与工程学报, 2003, 22 (9): 1514- 1520 JIANG Hong-sheng, HOU Xue-yuan Theoretical study and analysis of site observation on the influence of shield excavation on soft clays around tunnel[J]. Chinese Journal of Geotechnical Engineering, 2003, 22 (9): 1514- 1520 doi: 10.3321/j.issn:1000-6915.2003.09.022

[31]	DAVIS E H, RAYMOND G P A nonlinear theory of consolidation[J]. Géotechnique, 1965, 15 (2): 161- 173

[32]	MESRI G, ROKHSAR A Theory of consolidation for clays[J]. Journal of the Geotechnical Engineering Division, ASCE, 1974, 100 (8): 889- 903 doi: 10.1061/AJGEB6.0000075

[33]	李锐铎, 乐金朝基于分数阶导数的软土非线性流变本构模型[J]. 应用基础与工程科学学报, 2014, 22 (5): 856- 863 LI Rui-duo, YUE Jin-chao Nonlinear rheological constitute of soft soil based on fractional order derivative theory[J]. Journal of Basic Science and Engineering, 2014, 22 (5): 856- 863

[34]	NASH D F T, RYDE S J Modelling consolidation accelerated by vertical drains in soils subject to creep[J]. Géotechnique, 2001, 51 (3): 257- 273

[35]	孙钧. 岩土材料流变及其工程应用[M]. 北京: 中国建筑工业出版社, 1999.

[36]	胡浩, 周建, 张晓, 等软土渗透各向异性特性及其微观机理研究[J]. 低温建筑技术, 2021, 43 (6): 101- 105 HU Hao, ZHOU Jian, ZHANG Xiao, et al Study on the permeability anisotropy and microscopic mechanism of soft soil[J]. Low Temperature Architecture Technology, 2021, 43 (6): 101- 105 doi: 10.13905/j.cnki.dwjz.2021.06.024

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