含圆柱形弹性夹杂地基沉降量的解析解
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摘要
研究各向同性地基中含一个圆柱形弹性夹杂的地基沉陷问题。考虑全场的应力、变形特征,运用复变函数的罗朗级数展开技术,构造合适的应力函数,结合夹杂的边界条件和无穷远的性态,获得了全场复势的解析表达。数值结果显示:由于两相材料剪切模量之比的不同,在某个范围内沉陷量大于基底中点沉陷;在这个范围之外,则小于基底中点沉陷。当夹杂埋深为夹杂半径的5倍以上时,就可以运用所得结果,而不致引起太大误差;含圆形隧洞和刚性夹杂的问题可作为特殊情况得到。
The settlement of foundation with a cylindrically elastic inhomogeneity is researched.By considering the stress-deformation characteristic of the total field and applying the technique of series expansion,the appropriate stress functions are constructed;and accordingly the complex potentials of the rock mass are obtained.The numerical results indicate that to the different ratios of the shear moduli between the matrix and the inhomogeneity the settlement value of foundation boundary in some scope is greater than in the middle point of foundation base;and the value in other scope is less than in the middle point of foundation base.The results of the paper are enough accurate when the buried depth of the inhomogeneity is greater than 5 times of the radius of the inhomogeneity.As two special cases,the solutions for a circular tunnel and a rigid inhomogeneity in foundation are recovered.
The settlement of foundation with a cylindrically elastic inhomogeneity is researched.By considering the stress-deformation characteristic of the total field and applying the technique of series expansion,the appropriate stress functions are constructed;and accordingly the complex potentials of the rock mass are obtained.The numerical results indicate that to the different ratios of the shear moduli between the matrix and the inhomogeneity the settlement value of foundation boundary in some scope is greater than in the middle point of foundation base;and the value in other scope is less than in the middle point of foundation base.The results of the paper are enough accurate when the buried depth of the inhomogeneity is greater than 5 times of the radius of the inhomogeneity.As two special cases,the solutions for a circular tunnel and a rigid inhomogeneity in foundation are recovered.
引文
[1]李术才,朱维申,陈卫忠,等.弹塑性大位移有限元方法在软岩隧道变形预估系统研究中的应用[J].岩石力学与工程学报,2002,21(4):466-470.LI Shu-cai,ZHU Wei-shen,CHEN Wei-zhong,et al.Application of elasto-plastic large displacement finite element method to the study of deformation prediction of soft rock tunnel[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(4):466-470.
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[14]郭文复.多层半无限弹性体在圆形荷载作用下的解析解[J].力学学报,1984,16(3):102-106.GUO Wen-fu.Analytical solution of multi-layered elastic body under circular loading[J].Acta Mechanica Sinica,1984,16(3):102-106.
[15]郭广礼,邓喀中,常江.采空区上方建大型建筑物的地基沉降研究[J].中国矿业大学学报,1996,25(2):54-57.GUO Guang-li,DENG Ka-zhong,CHANG Jiang.Study on the foundation settlement of heavy buildings above mine goafs[J].Journal of China University of Mining&Technology,1996,25(2):54-57.
[16]刘福顺,于广明,王卫英,等.土结相互作用的地基沉降和结构内力计算方法[J].青岛理工大学学报,2005,26(6):20-22.LIU Fu-shun,YU Guang-ming,WANG Wei-ying,et al.Calculation of foundation settlement and internal force of structure considering soil structure interaction[J].Journal of Qingdao Technological University,2005,26(6):20-22.
[17]MUSKHELISHVILI N L.Some basic problems of mathema-tical theory of elasticity[M].Leyden:Noordhoff,1975.
[18]TIMOSHENKO S,J N GOODIER.Theory of Elasticity[M].New York:McGraw-Hill,1951.
[19]王文星.岩体力学[M].长沙:中南大学出版社,2004.
[2]刘希亮,李术才,朱维申.恒载作用下底部含水层疏水沉降均匀试验研究[J].岩石力学与工程学报,2004,23(22):3 877-3 883.LIU Xi-liang,LI Shu-cai,ZHU We-shen.Uniform experimental study on subsidence caused by dewatering of bottom aquifer under external fixed load[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(22):3 877-3 883.
[3]曹国强,张仪萍,张土乔,等.地基沉降速率与沉降的关系研究及其应用[J].岩土力学,2003,24(3):467-470.CAO Guo-qiang,ZHANG Yi-ping,ZHANG Tu-qiao,et al.Relationship between settlement-velocity and settlement of ground and its applications[J].Rock and Soil Mechanics,2003,24(3):467-470.
[4]周志芳,朱宏高,陈静,等.深基坑降水与沉降的非线性耦合计算[J].岩土力学,2004,25(12):1 984-1 988.ZHOU Zhi-fang,ZHU Hong-gao,CHEN Jing,et al.Nonlinear coupling calculation between dewatering and settlement of deep foundation pits[J].Rock and Soil Mechanics,2004,25(12):1 984-1 988.
[5]姚成焕,石宜生.三峡机场高填方土基沉降观测与计算研究[J].岩土力学,2001,22(4):513-518.YAO Cheng-huan,SHI Yi-sheng.The settlement observation and calculation for deep fill soil in the three gorges airport[J].Rock and Soil Mechanics,2001,22(4):513-518.
[6]HASSEN G,DE BUHAN P.A two-phase model and related numerical tool for the design of soil structures reinforced by stiff linear inclusions[J].European Journal of Mechanics A/Solids,2005,24:987-1 001.
[7]GHOSH C,MADHAV M R.Settlement response of a reinforced shallow earth bed[J].Geotextiles&Geomembranes,1994,13(10):643-656.
[8]孔德志,王慎堂,张庆贺.非均匀地基上弹性地基板的变形特征[J].河南大学学报,2002,32(1):91-94.KONG De-zhi,WANG Shen-tang,ZHANG Qing-he.Deformation feature of the elastic foundation board on non-uniform ground[J].Journal of Henan University(Natural Science),2002,32(1):91-94.
[9]袁凡凡,栾茂田,闫澍旺,等.倾斜荷载作用下层状非均质地基的极限承载力[J].岩土力学,2004,25(增刊):564-573.YUAN Fan-fan,LUAN Mao-tian,YAN Shu-wang,et al.Ultimate bearing capacity of layered inhomogeneous foundations under inclined loads[J].Rock and Soil Mechanics,2004,25(Supp.2):564-573.
[10]郑永来,潘杰,韩文星.软土地铁隧道沉降分析[J].地下空间与工程学报,2005,1(1):67-74.ZHENG Yong-lai,PAN Jie,HAN Wen-xing.Analysis on the settlements of metro tunnels in soft soil[J].Chinese Journal of Underground Space and Engineering,2005,1(1):67-74.
[11]李晓红,靳晓光,王宏图,等.采动下卧煤层对深埋隧道结构稳定性的影响[J].岩土力学,2005,26(9):1 448-1 455.LI Xiao-hong,JIN Xiao-guang,WANG Hong-tu.Study on structural stability of deep buried highway tunnel with underlying coal bed exploiting[J].Rock and Soil Mechanics,2005,26(9):1 448-1 455.
[12]郭毅之,金先龙,丁峻宏,等.沉管隧道地震响应分析的并行计算[J].岩石力学与工程学报,2005,24(15):2 723-2 727.GUO Yi-zhi,JIN Xian-long,DING Jun-hong,et al.Parallel processing of seismic response analysis for immersed tunnel[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(15):2 723-2 727.
[13]徐汉忠.ψ函数在成层地基沉陷计算中的应用[J].河海大学学报,1994,22(2):102-106.XU Han-zhong.Application of function ofψin calculation of settlement for layered foundations[J].Journal of Hohai University,1994,22(2):102-106.
[14]郭文复.多层半无限弹性体在圆形荷载作用下的解析解[J].力学学报,1984,16(3):102-106.GUO Wen-fu.Analytical solution of multi-layered elastic body under circular loading[J].Acta Mechanica Sinica,1984,16(3):102-106.
[15]郭广礼,邓喀中,常江.采空区上方建大型建筑物的地基沉降研究[J].中国矿业大学学报,1996,25(2):54-57.GUO Guang-li,DENG Ka-zhong,CHANG Jiang.Study on the foundation settlement of heavy buildings above mine goafs[J].Journal of China University of Mining&Technology,1996,25(2):54-57.
[16]刘福顺,于广明,王卫英,等.土结相互作用的地基沉降和结构内力计算方法[J].青岛理工大学学报,2005,26(6):20-22.LIU Fu-shun,YU Guang-ming,WANG Wei-ying,et al.Calculation of foundation settlement and internal force of structure considering soil structure interaction[J].Journal of Qingdao Technological University,2005,26(6):20-22.
[17]MUSKHELISHVILI N L.Some basic problems of mathema-tical theory of elasticity[M].Leyden:Noordhoff,1975.
[18]TIMOSHENKO S,J N GOODIER.Theory of Elasticity[M].New York:McGraw-Hill,1951.
[19]王文星.岩体力学[M].长沙:中南大学出版社,2004.
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