考虑侧面摩擦的侧限压缩模型的数值解法
|
摘要
海上箱筒型基础结构下沉到位后,舱内土体的受力变形可以看作是侧限压缩模型问题,上部荷载引起的侧壁摩擦力与土体应力之间的关系较为复杂。本文通过简化模型,列出了侧限压缩模型的平衡微分方程,分析了方程解析计算时存在的难点,结合摩擦应力边界条件的特点,构造函数迭代法对该方程进行数值求解,展示了计算的收敛过程,得到接触侧面上水平应力和土体表面位移的非线性分布规律,并将其结果与ABAQUS数值模拟结果进行了对比。结果表明,函数迭代法收敛速度较快,计算过程稳定,对其他存在变量耦合边界条件的微分方程数值求解有一定的参考价值。
When a box-type foundation is sunk in place,the deformation calculation of the soil in bulkhead can be regarded as the confined compression model problem.The relationship between the lateral friction caused by the upper load and the soil stress is quite complicated.The differential equations of the confined compression model are listed by simplifying the model,and the difficulties in analytic calculation of the equations are analyzed.According to the characteristics of the frictional stress boundary condition,an iteration method is used to solve the equation numerically.Subsequently,the convergence process is demonstrated,and the nonlinear distribution law of horizontal stress on contact surface and displacement on soil surface is obtained.In addition,these calculated values are compared with the numerical simulation results of ABAQUS.The results show that the iteration method has a high convergence speed and a stable calculation process.It has a certain reference value for the numerical solution of other differential equations with variable coupling boundary condition.
When a box-type foundation is sunk in place,the deformation calculation of the soil in bulkhead can be regarded as the confined compression model problem.The relationship between the lateral friction caused by the upper load and the soil stress is quite complicated.The differential equations of the confined compression model are listed by simplifying the model,and the difficulties in analytic calculation of the equations are analyzed.According to the characteristics of the frictional stress boundary condition,an iteration method is used to solve the equation numerically.Subsequently,the convergence process is demonstrated,and the nonlinear distribution law of horizontal stress on contact surface and displacement on soil surface is obtained.In addition,these calculated values are compared with the numerical simulation results of ABAQUS.The results show that the iteration method has a high convergence speed and a stable calculation process.It has a certain reference value for the numerical solution of other differential equations with variable coupling boundary condition.
引文
[1]孟伟超,罗强,蒋良潍,等.环壁摩擦力对固结试验压缩变形的影响分析[J].武汉理工大学学报,2014,36(8):104-109.(MENG Wei-chao,LUO Qiang,JIANG Liang-wei,et al.Analysis of ring-wall friction effect of consolidation container on the compression deformation in consolidation test[J].Journal of Wuhan University of Technology,2014,36(8):104-109.(in Chinese))
[2]蔡正银,徐光明,顾行文,等.波浪荷载作用下箱筒型基础防波堤性状试验研究[J].中国港湾建设,2010,69(s1):90-94,99.(CAI Zheng-yin,XU Guang-ming,GU Xing-wen,et al.Behavior investigation on a cylindrical breakwater during wave loading[J].China Harbour Engineering,2010,69(s1):90-94,99.(in Chinese))
[3]肖忠,王元战,及春宁.基于极限平衡法的箱筒型基础防波堤稳定性分析[J].岩土工程学报,2013,35(5):828-833.(XIAO Zhong,WANG Yuan-zhan,JI Chun-ning.Stability analysis of bucket foundation breakwaters based on limit equilibrium method[J].Chinese Journal of Geotechnical Engineering,2013,35(5):828-833.(in Chinese))
[4]闫澍旺,霍知亮,孙立强,等.海上风电机组筒型基础工作及承载特性研究[J].岩土力学,2013,34(7):2036-2042.(YAN Shu-wang,HUO Zhi-liang,SUN Li-qiang,et al.Study of working mechanism and bearing capacity behavior of bucket foundation for offshore wind turbine[J].Rock and Soil Mechanics,2013,34(7):2036-2042.(in Chinese))
[5]刘永刚.海上风力发电复合筒型基础承载特性研究[D].天津大学,2014.(LIU Yong-gang.Bearing Characteristics of Composite Bucket Foundation for Offshore Wind Turbine[D].Tianjin University,2014.(in Chinese))
[6]练继建,贺蔚,吴慕丹,等.带分舱板海上风电筒型基础承载特性试验研究[J].岩土力学,2016,37(10):2746-2752.(LIAN Ji-jian,HE Wei,WU Mu-dan,et al.Experimental study of bearing characteristic of bucket foundation of offshore wind turbine with bulkheads[J].Rock and Soil Mechanics,2016,37(10):2746-2752.(in Chinese))
[7]王元战,肖忠,迟丽华,等.筒型基础防波堤稳定性简化计算方法[J].岩土力学,2009,30(5):1367-1372.(WANG Yuan-zhan,XIAO Zhong,CHI Lihua,et al.A simplified calculation method for stability of bucket foundation breakwater[J].Rock and Soil Mechanics,2009,30(5):1367-1372.(in Chinese))
[8]梅国雄,宰金珉,赵维炳.土体侧限压缩模量简易计算方法及其应用[J].岩土力学,2003,24(6):1057-1059,1064.(MEI Guo-xiong,ZAI Jin-min,ZHAO Wei-bing.A simplified calculation method of oedometric modulus of soil and its application[J].Rock and Soil Mechanics,2003,24(6):1057-1059,1064.(in Chinese))
[9]Potyondy J G.Skin friction between various soils and construction materials[J].Géotechnique,1961,11(4):339-353.
[10]梁越,储昊,卢孝志,等.钢-土界面剪切规律时效性室内试验研究[J].水利水运工程学报,2015(1):28-32.(LIANG Yue,CHU Hao,LU Xiao-zhi,et al.Experimental studies on time effect of shearing characteristics of steel-soil interface[J].Hydro-Science and Engineering,2015(1):28-32.(in Chinese))
[11]吕亚茹,丁选明,孙甲,等.刚性荷载下现浇X形桩复合地基极限承载力特性研究[J].岩土力学,2012,33(9):2691-2696,2703.(LYa-ru,DING Xuanming,SUN Jia,et al.Analysis of ultimate bearing capacity of X-section cast-in-place concrete pile composite foundation under rigid load[J].Rock and Soil Mechanics,2012,33(9):2691-2696,2703.(in Chinese))
[12]徐芝纶.弹性力学(第五版)[M].北京:高等教育出版社,2016.(XU Zhi-lun.Elasticity(5th Edition)[M].Beijing:Higher Education Press,2016.(in Chinese))
[13]罗晓明,齐朝晖,孔宪超.平面棱柱铰内考虑摩擦效应的接触分析[J].计算力学学报,2012,29(3):387-392.(LUO Xiao-ming,QI Zhao-hui,Kong Xian-chao.Non-colliding contact analysis with friction in the planar prismatic joint[J].Chinese Journal of Computational Mechanics,2012,29(3):387-392.(in Chinese))
[14]Lehane B M,White D J.Lateral stress changes and shaft friction for model displacement piles in sand[J].Canadian Geotechnical Journal,2005,42(4):1039-1052.
[15]张晓军,杨树生,李珊珊,等.耦合边界条件下SturmLiouville问题的渐近展开[J].内蒙古师范大学学报(自然科学汉文版),2016,45(6):749-752,756.(ZHANG Xiao-jun,YANG Shu-sheng,LI Shan-shan,et al.The asymptotic expansion of Sturm-Liouville problem with coupled boundary condition[J].Journal of Inner Mongolia Normal University(Natural Science Edition),2016,45(6):749-752,756.(in Chinese))
[16]Sauer T.Numerical Analysis(2nd)[M].New Jersey:Addison-Wesley,2012.
[2]蔡正银,徐光明,顾行文,等.波浪荷载作用下箱筒型基础防波堤性状试验研究[J].中国港湾建设,2010,69(s1):90-94,99.(CAI Zheng-yin,XU Guang-ming,GU Xing-wen,et al.Behavior investigation on a cylindrical breakwater during wave loading[J].China Harbour Engineering,2010,69(s1):90-94,99.(in Chinese))
[3]肖忠,王元战,及春宁.基于极限平衡法的箱筒型基础防波堤稳定性分析[J].岩土工程学报,2013,35(5):828-833.(XIAO Zhong,WANG Yuan-zhan,JI Chun-ning.Stability analysis of bucket foundation breakwaters based on limit equilibrium method[J].Chinese Journal of Geotechnical Engineering,2013,35(5):828-833.(in Chinese))
[4]闫澍旺,霍知亮,孙立强,等.海上风电机组筒型基础工作及承载特性研究[J].岩土力学,2013,34(7):2036-2042.(YAN Shu-wang,HUO Zhi-liang,SUN Li-qiang,et al.Study of working mechanism and bearing capacity behavior of bucket foundation for offshore wind turbine[J].Rock and Soil Mechanics,2013,34(7):2036-2042.(in Chinese))
[5]刘永刚.海上风力发电复合筒型基础承载特性研究[D].天津大学,2014.(LIU Yong-gang.Bearing Characteristics of Composite Bucket Foundation for Offshore Wind Turbine[D].Tianjin University,2014.(in Chinese))
[6]练继建,贺蔚,吴慕丹,等.带分舱板海上风电筒型基础承载特性试验研究[J].岩土力学,2016,37(10):2746-2752.(LIAN Ji-jian,HE Wei,WU Mu-dan,et al.Experimental study of bearing characteristic of bucket foundation of offshore wind turbine with bulkheads[J].Rock and Soil Mechanics,2016,37(10):2746-2752.(in Chinese))
[7]王元战,肖忠,迟丽华,等.筒型基础防波堤稳定性简化计算方法[J].岩土力学,2009,30(5):1367-1372.(WANG Yuan-zhan,XIAO Zhong,CHI Lihua,et al.A simplified calculation method for stability of bucket foundation breakwater[J].Rock and Soil Mechanics,2009,30(5):1367-1372.(in Chinese))
[8]梅国雄,宰金珉,赵维炳.土体侧限压缩模量简易计算方法及其应用[J].岩土力学,2003,24(6):1057-1059,1064.(MEI Guo-xiong,ZAI Jin-min,ZHAO Wei-bing.A simplified calculation method of oedometric modulus of soil and its application[J].Rock and Soil Mechanics,2003,24(6):1057-1059,1064.(in Chinese))
[9]Potyondy J G.Skin friction between various soils and construction materials[J].Géotechnique,1961,11(4):339-353.
[10]梁越,储昊,卢孝志,等.钢-土界面剪切规律时效性室内试验研究[J].水利水运工程学报,2015(1):28-32.(LIANG Yue,CHU Hao,LU Xiao-zhi,et al.Experimental studies on time effect of shearing characteristics of steel-soil interface[J].Hydro-Science and Engineering,2015(1):28-32.(in Chinese))
[11]吕亚茹,丁选明,孙甲,等.刚性荷载下现浇X形桩复合地基极限承载力特性研究[J].岩土力学,2012,33(9):2691-2696,2703.(LYa-ru,DING Xuanming,SUN Jia,et al.Analysis of ultimate bearing capacity of X-section cast-in-place concrete pile composite foundation under rigid load[J].Rock and Soil Mechanics,2012,33(9):2691-2696,2703.(in Chinese))
[12]徐芝纶.弹性力学(第五版)[M].北京:高等教育出版社,2016.(XU Zhi-lun.Elasticity(5th Edition)[M].Beijing:Higher Education Press,2016.(in Chinese))
[13]罗晓明,齐朝晖,孔宪超.平面棱柱铰内考虑摩擦效应的接触分析[J].计算力学学报,2012,29(3):387-392.(LUO Xiao-ming,QI Zhao-hui,Kong Xian-chao.Non-colliding contact analysis with friction in the planar prismatic joint[J].Chinese Journal of Computational Mechanics,2012,29(3):387-392.(in Chinese))
[14]Lehane B M,White D J.Lateral stress changes and shaft friction for model displacement piles in sand[J].Canadian Geotechnical Journal,2005,42(4):1039-1052.
[15]张晓军,杨树生,李珊珊,等.耦合边界条件下SturmLiouville问题的渐近展开[J].内蒙古师范大学学报(自然科学汉文版),2016,45(6):749-752,756.(ZHANG Xiao-jun,YANG Shu-sheng,LI Shan-shan,et al.The asymptotic expansion of Sturm-Liouville problem with coupled boundary condition[J].Journal of Inner Mongolia Normal University(Natural Science Edition),2016,45(6):749-752,756.(in Chinese))
[16]Sauer T.Numerical Analysis(2nd)[M].New Jersey:Addison-Wesley,2012.