Volume 18 Issue 1
. 
Turn off MathJax
Article Contents
Article Navigation >  Journal of Traffic and Transportation Engineering  > 2018  >  18(1): 51-60
ZHAO Jun-hai, ZHANG Lei, ZHANG Chang-guang, CAO Xue-ye. Elastic-plastic solutions of bilinear strain-hardening tunnel and pile cavity based on tri-shear failure criterion[J]. Journal of Traffic and Transportation Engineering, 2018, 18(1): 51-60. doi: 10.19818/j.cnki.1671-1637.2018.01.005
Citation: ZHAO Jun-hai, ZHANG Lei, ZHANG Chang-guang, CAO Xue-ye. Elastic-plastic solutions of bilinear strain-hardening tunnel and pile cavity based on tri-shear failure criterion[J]. Journal of Traffic and Transportation Engineering, 2018, 18(1): 51-60. doi: 10.19818/j.cnki.1671-1637.2018.01.005
shu

Elastic-plastic solutions of bilinear strain-hardening tunnel and pile cavity based on tri-shear failure criterion

doi: 10.19818/j.cnki.1671-1637.2018.01.005

  • School of Civil Engineering, Chang'an University, Xi'an 710061, Shaanxi, China

More Information
  • Author Bio:

    ZHAO Jun-hai(1960-), male, professor, PhD, zhaojh@chd.edu.cn

  • Received Date: 2017-08-05
  • Publish Date: 2018-02-25
    Abstract
  • Tunnel and pile cavity were simplified as thick-walled cylinders, the effects of strain hardening and intermediate principal stress were considered, the elastic-plastic limit solution of thick-walled cylinder under uniform internal and external pressures was deduced based on the trishear failure criterion and the bilinear strain-hardening model, the relationship of internal pressure and elastic-plastic radius under constant external pressure was given, and the effects of many parameters on the limit solution of thick-walled cylinder were discussed, including strengthening modulus, radius ratio, intermediate principal stress and material strength heterogeneity of tension and compression.Research result shows that the proposed solution can overcome the deficiencies of material strength heterogeneity of tension and compression ignored by Tresca and Mises yield criteria, the intermediate principal stress ignored by Tresca and MohrCoulomb yield criteria, as well as the abrupt changing phenomenon of slip plane in twin shearstrength theory.The limit solution increases with the radius ratio and the intermediate principal stress coefficient, but decreases with the tension-compression strength ratio.The effect of external pressure on the limit internal pressure decreases with the tension-compression strength ratio.Compared with no considering strengthening modulus, when the strengthening modulus is0.1 and the radius ratio is 2, the plastic limit internal pressure increases by more than 10%.When the radius ratio increases to 4, the plastic limit internal pressure increases by more than38%, so the strengthening effect is more obvious.Obviously, for the material with strain hardening effect, the result analyzed by the bilinear strain-hardening model is closer to the engineering practices.When the intermediate principal stress and the strain hardening are not considered, the differences of limit expansion soil pressures calculated by the proposed solution are within 0.02% compared with the values calculated by the Vesic theory.However, when the intermediate principal stress and the strain hardening are considered and the ratio of the plastic zone radius to the inner radius is 10, the limit solutions are respectively 1.06 times and1.81 times the values calculated by the Vesic theory.As a result, the limit expansion pressure based on the Vesic theory is too conservative.

     

    • FullText(HTML)
  • loading
    • References(30)
  • [1]
    PANKAJ T. Elastic-plastic transition stresses in a transversely isotropic thick-walled cylinder subjected to internal pressure and steady-state temperature[J]. Thermal Science, 2009, 13 (4): 107-118. doi: 10.2298/TSCI0904107P
    [2]
    SHARMA R, AGGARWAL A K, SHARMA S, et al. Thermo creep transition in functionally graded thick-walled circular cylinder under external pressure[J]. ANNALS of Faculty Engineering Hunedoara—International Journal of Engineering, 2014, 12 (4): 335-342.
    [3]
    LVOV G, KOSTROMITSKAYA O. Effect of material damage on autofrettage of thick-walled cylinder[J]. Universal Journal of Mechanical Engineering, 2014, 2 (2): 44-48. doi: 10.13189/ujme.2014.020202
    [4]
    KAMAL S M, BORSAIKIA A C, DIXIT U S. Experimental assessment of residual stresses induced by the thermal autofrettage of thick-walled cylinders[J]. Journal of Strain Analysis for Engineering Design, 2016, 51 (2): 144-160. doi: 10.1177/0309324715616005
    [5]
    ZHAO Jun-hai, ZHAI Yue, JI Lin, et al. Unified solutions to the limit load of thick-walled vessels[J]. Journal of Pressure Vessel Technology, 2007, 129 (4): 670-675. doi: 10.1115/1.2767356
    [6]
    殷有泉, 陈朝伟. 软化材料厚壁筒的解析解及其稳定性分析[J]. 力学学报, 2010, 42 (1): 56-64. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201001011.htm

    YIN You-quan, CHEN Zhao-wei. The analytical solutions of thick-walled cylinder of softening material and its stability[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42 (1): 56-64. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201001011.htm
    [7]
    LEU S Y. Analytical and numerical investigation of strain-hardeningviscoplastic thick-walled cylinders under internal pressure by using sequential limit analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(25-28): 2713-2722. doi: 10.1016/j.cma.2007.02.001
    [8]
    张黎明, 王在泉, 孙辉, 等. 岩石卸荷破坏的变形特征及本构模型[J]. 煤炭学报, 2009, 34 (12): 1626-1631. doi: 10.3321/j.issn:0253-9993.2009.12.008

    ZHANG Li-ming, WANG Zai-quan, SUN Hui, et al. Failure characteristics and constitutive model of rock under unloading condition[J]. Journal of China Coal Society, 2009, 34 (12): 1626-1631. (in Chinese). doi: 10.3321/j.issn:0253-9993.2009.12.008
    [9]
    薛钢, 宫旭辉, 王涛, 等. 10Ni5CrMoV钢循环塑性变形的力学本构关系[J]. 材料开发与应用, 2015, 30 (4): 5-11. https://www.cnki.com.cn/Article/CJFDTOTAL-CLKY201504002.htm

    XUE Gang, GONG Xu-hui, WANG Tao, et al. Mechanical constitutive relation under cyclic loading of 10Ni5CrMoV steel[J]. Development and Application of Materials, 2015, 30 (4): 5-11. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-CLKY201504002.htm
    [10]
    BARTON P, ROMENSKI E. On computational modelling of strain-hardening material dynamics[J]. Communications in Computational Physics, 2012, 11 (5): 1525-1546. doi: 10.4208/cicp.171210.270511a
    [11]
    黄晓莹, 陶俊林. 三种建筑钢筋材料高应变率下拉伸力学性能研究[J]. 工程力学, 2016, 33 (7): 184-189. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201607025.htm

    HUANG Xiao-ying, TAO Jun-lin. Tensile mechanical properties research of three construction steel bars in high strain rate[J]. Engineering Mechanics, 2016, 33 (7): 184-189. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201607025.htm
    [12]
    TABESH M, LIU B, BOYD J G, et al. Analytical solution for the pseudoelastic response of a shape memory alloy thickwalled cylinder under internal pressure[J]. Smart Materials and Structures, 2013, 22 (9): 1-46.
    [13]
    钱凌云, 刘全坤, 王成勇, 等. 厚壁圆筒自增强压力的优化分析[J]. 中国机械工程, 2012, 23 (4): 474-479. doi: 10.3969/j.issn.1004-132X.2012.04.024

    QIAN Ling-yun, LIU Quan-kun, WANG Cheng-yong, et al. Qptimization analysis of autofrettage pressure for thick walled cylinders[J]. China Mechanical Engineering, 2012, 23 (4): 474-479. (in Chinese). doi: 10.3969/j.issn.1004-132X.2012.04.024
    [14]
    赵均海, 张永强, 廖红建, 等. 用统一强度理论求厚壁圆筒和厚壁球壳的极限解[J]. 应用力学学报, 2000, 17 (1): 157-161. doi: 10.3969/j.issn.1000-4939.2000.01.028

    ZHAO Jun-hai, ZHANG Yong-qiang. LIAO Hong-jian, et al. Unified limit solutions of thick wall cylinder and thick wall spherical shell with unified strength theory[J]. Chinese Journal of Applied Mechanics, 2000, 17 (1): 157-161. (in Chinese). doi: 10.3969/j.issn.1000-4939.2000.01.028
    [15]
    常列珍, 潘玉田, 李魁武, 等. 理想弹塑性线性强化模型的身管残余应力分析[J]. 兵工学报, 2013, 34 (4): 385-391. https://www.cnki.com.cn/Article/CJFDTOTAL-BIGO201304002.htm

    CHANG Lie-zhen, PAN Yu-tian, LI Kui-wu, et al. Residual stress analysis of gun barrel with bi-linear material model[J]. Acta Armamentarii, 2013, 34 (4): 385-391. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-BIGO201304002.htm
    [16]
    吴昊, 方秦, 张亚栋, 等. 深部巷道块系围岩分析模型及稳定性探讨[J]. 岩土工程学报, 2009, 31 (8): 1229-1235. doi: 10.3321/j.issn:1000-4548.2009.08.012

    WU Hao, FANG Qin, ZHANG Ya-dong, et al. Analytical model and stability of surrounding block rock mass around deep tunnels[J]. Chinese Journal of Geotechnical Engineering, 2009, 31 (8): 1229-1235. (in Chinese). doi: 10.3321/j.issn:1000-4548.2009.08.012
    [17]
    曹黎娟, 赵均海, 魏雪英. 基于统一强度理论的灰土挤密桩应力分析[J]. 岩土力学, 2006, 27 (10): 1786-1790. doi: 10.3969/j.issn.1000-7598.2006.10.029

    CAO Li-juan, ZHAO Jun-hai, WEI Xue-ying. Stress analysis of lime-soil compacted pile based on the unified strength theory[J]. Rock and Soil Mechanics, 2006, 27 (10): 1786-1790. (in Chinese). doi: 10.3969/j.issn.1000-7598.2006.10.029
    [18]
    曹雪叶, 赵均海, 张常光. 基于三剪统一强度准则的厚壁圆筒自增强分析[J]. 中国机械工程, 2017, 28 (1): 75-81. doi: 10.3969/j.issn.1004-132X.2017.01.013

    CAO Xue-ye, ZHAO Jun-hai, ZHANG Chang-guang. Autofrettage analysis of thick-walled cylinder based on triple-shear unified strength criterion[J]. China Mechanical Engineering, 2017, 28 (1): 75-81. (in Chinese). doi: 10.3969/j.issn.1004-132X.2017.01.013
    [19]
    董陇军, 李夕兵. 岩石试验抗压、抗拉区间强度及代表值可信度研究[J]. 岩土工程学报, 2010, 32 (12): 1969-1974. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201012030.htm

    DONG Long-jun, LI Xi-bing. Interval parameters and credibility of representative values of tensile and compression strength tests on rock[J]. Chinese Journal of Geotechnical Engineering, 2010, 32 (12): 1969-1974. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201012030.htm
    [20]
    张常光, 赵均海, 杜文超. 岩石中间主应力效应及强度理论研究进展[J]. 建筑科学与工程学报, 2014, 31 (2): 6-19. doi: 10.3969/j.issn.1673-2049.2014.02.003

    ZHANG Chang-guang, ZHAO Jun-hai, DU Wen-chao. Advances in rock for intermediate principal stress effect and strength theory[J]. Journal of Architecture and Civil Engineering, 2014, 31 (2): 6-19. (in Chinese). doi: 10.3969/j.issn.1673-2049.2014.02.003
    [21]
    侯公羽, 李晶晶, 杨悦, 等. 基于幂强化本构模型的轴对称圆巷弹塑性解[J]. 岩土力学, 2014, 35 (1): 134-142. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201401021.htm

    HOU Gong-yu, LI Jing-jing, YANG Yue, et al. Elastoplastic solution of axisymmetric circular tunnel based on power-hardening model[J]. Rock and Soil Mechanics, 2014, 35 (1): 134-142. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201401021.htm
    [22]
    胡小荣, 林太清. 三剪屈服准则及其在极限内压计算中的应用[J]. 中国有色金属学报, 2007, 17 (2): 207-215. doi: 10.3321/j.issn:1004-0609.2007.02.005

    HU Xiao-rong, LIN Tai-qing. Triple-shear yield criterion and its applications to limit pressures for thin and thick wall cylinders and thick wall spherical shells[J]. The Chinese Journal of Nonferrous Metals, 2007, 17 (2): 207-215. (in Chinese). doi: 10.3321/j.issn:1004-0609.2007.02.005
    [23]
    朱倩, 赵均海, 张常光, 等. 双层组合厚壁圆筒弹脆塑性极限内压统一解[J]. 工程力学, 2015, 32 (9): 68-75. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201509011.htm

    ZHU Qian, ZHAO Jun-hai, ZHANG Chang-guang, et al. Elastic-brittle-plastic unified solutions of limit internal pressure for double-layered combined thick-walled cylinder[J]. Engineering Mechanics, 2015, 32 (9): 68-75. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201509011.htm
    [24]
    李艳, 赵均海, 张常光. 非饱和土条形地基太沙基极限承载力三剪统一解[J]. 岩土力学, 2015, 36 (11): 3128-3134. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201511012.htm

    LI Yan, ZHAO Jun-hai, ZHANG Chang-guang. Tripleshear unified solution of Terzaghi's ultimate bearing capacity for unsaturated soil foundation[J]. Rock and Soil Mechanics, 2015, 36 (11): 3128-3134. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201511012.htm
    [25]
    赵均海, 朱倩, 张常光, 等. 基于统一强度理论的组合厚壁圆筒弹塑性统一解[J]. 固体力学学报, 2014, 35 (1): 63-70. https://www.cnki.com.cn/Article/CJFDTOTAL-GTLX201401009.htm

    ZHAO Jun-hai, ZHU Qian, ZHANG Chang-guang, et al. Elastic-plastic unified solutions for combined thick wall cylinder based on unified strength theory[J]. Chinese Journal of Solid Mechanics, 2014, 35 (1): 63-70. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-GTLX201401009.htm
    [26]
    林太清, 胡小荣. 基于三剪统一强度准则的厚壁圆筒极限承压分析[J]. 福州大学学报: 自然科学版, 2006, 34 (5): 727-731. doi: 10.3969/j.issn.1000-2243.2006.05.024

    LIN Tai-qing, HU Xiao-rong. Limit pressures for thick wall cylinders based on the triple shear unified failure criterion[J]. Journal of Fuzhou University: Natural Science, 2006, 34 (5): 727-731. (in Chinese). doi: 10.3969/j.issn.1000-2243.2006.05.024
    [27]
    HUANG X P. A generalautofrettage model of a thick-walled cylinder based on tensile-compressive stress-strain curve of a material[J]. Journal of Strain Analysis for Engineering Design, 2005, 40 (6): 599-607. doi: 10.1243/030932405X16070
    [28]
    李铀, 李锶, 白世伟. 理想弹塑性厚壁圆筒弹塑性应力场再研究[J]. 岩石力学与工程学报, 2002, 21 (6): 897-899. doi: 10.3321/j.issn:1000-6915.2002.06.027

    LI You, LI Si, BAI Shi-wei. Re-research on the stress field of perfect elasto-plastic thick-wall tube[J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 21 (6): 897-899. (in Chinese). doi: 10.3321/j.issn:1000-6915.2002.06.027
    [29]
    VESI'C A S. Expansion of cavities in infinite soil mass[J]. Journal of the Soil Mechanics and Foundations Division, 1972 (3): 265-290.
    [30]
    胡小荣, 俞茂宏. 三剪强度准则及其在巷道围岩弹塑性分析中的应用[J]. 煤炭学报, 2003, 28 (4): 389-393. doi: 10.3321/j.issn:0253-9993.2003.04.012

    HU Xiao-rong, YU Mao-hong. New tri-shear failure criterion and its application in elasto-plastic analysis for the wall rock of tunnel[J]. Journal of China Coal Society, 2003, 28 (4): 389-393. (in Chinese). doi: 10.3321/j.issn:0253-9993.2003.04.012
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Get Citation
    PDF
    XML

    Article Metrics

    Article views (470) PDF downloads(360) Cited by()
    Proportional views
    Related

    Copyright《Journal of Traffic and Transportation Engineering》编辑部陕ICP备05001904号-1

    Address ：Editorial Department of Journal of Traffic and Transportation Engineering, Chang 'an University, Middle Section of South Second Ring Road, Xi 'an, Shaanxi（710064） Tel：029-82334388 Email：jygc@chd.edu.cn

    All visit:Today's visit:

    Supported by: Beijing Renhe Information Technology Co. Ltd    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return