基于连续排水边界条件的砂井地基固结解析解
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摘要
为弥补瞬时恒定荷载下传统砂井固结理论中边界条件存在的缺陷,首先,通过引入连续排水边界条件,采用特征函数法对砂井地基3维固结方程进行解答,得到考虑涂抹及井阻效应的解析解。然后,通过对解析解的退化,与既有的研究结果对比,验证所得解的正确性。最后,根据所得解析解对砂井地基在连续排水边界条件下的超孔隙水压力及平均固结度进行分析。分析结果表明:连续排水边界条件可以通过改变界面参数b值的大小,实现从完全不排水到完全排水整个过程的表达,从而对传统砂井固结理论进行补充。在超孔隙水压力方面,随着b值的减小,地基表面排水能力降低,在地基顶面处,也逐渐出现一定的超孔隙水压力,且b越小,顶面处的超孔隙水压力越大;在同一水平面处,距离砂井越远,孔压越大。在固结度方面,随着b的减小,地基平均固结度显著降低,故传统固结理论中的顶面完全排水条件,可能会高估地基的实际固结速度。涂抹区以及砂井中渗透系数的降低均会显著降低地基固结速度,所以,施工中应减小对井壁土体的扰动,增加竖井的渗流能力,以减弱涂抹和井阻效应。尽管砂井地基以径向渗流为主,但竖向渗流对地基的固结也有较大影响,忽略其作用可能会导致地基的固结沉降预测速度被低估。
For the limitations of the boundary condition under instantaneous constant load in traditional sand-drained consolidation theory, the three-dimensional consolidation equation of sand-drained ground was solved based on the continuous drainage boundary. And the analytical solution considering the effects of smear and well resistance was obtained. Then, the rationality of the solution was verified by degenerating and comparing the analytic solution with the existing research results. Finally, the excess pore water pressure and average consolidation degree of sanddrained ground under continuous drainage boundary conditions were analyzed according to the analytical solution. The results showed that the continuous drainage boundary condition realizes the whole process from impermeable to completely permeable by changing the value of interface parameter b, which compensates for the shortcoming of traditional boundary. In terms of the excess pore water pressure, the drainage capacity of ground surface is reduced with the decrease of the value of b. Therefore, the excess pore water pressure exists at the top surface of the ground, and the smaller the b is, the greater the excess pore water pressure is. Meanwhile, the pore pressure increases with the enhancing distance from the sand-drained at the same plane. As for the consolidation degree, the average consolidation degree of the ground decreases with the decrease of b.So, the consolidation rate of the ground may be overestimated under the complete drainage condition of the traditional consolidation theory.Moreover, the consolidation rate of the foundation would be significantly reduced with the decrease of the permeability coefficient in the smear area and the sand well. Therefore, the disturbance to the soil of the well wall should be reduced and the seepage capacity of the vertical drainage should be increased to weaken the smear effect and the well resistance. In addition, the rates of settlements and consolidation will be underestimated if the vertical seepage is ignored, although the radial seepage is dominant in sand-drain.
For the limitations of the boundary condition under instantaneous constant load in traditional sand-drained consolidation theory, the three-dimensional consolidation equation of sand-drained ground was solved based on the continuous drainage boundary. And the analytical solution considering the effects of smear and well resistance was obtained. Then, the rationality of the solution was verified by degenerating and comparing the analytic solution with the existing research results. Finally, the excess pore water pressure and average consolidation degree of sanddrained ground under continuous drainage boundary conditions were analyzed according to the analytical solution. The results showed that the continuous drainage boundary condition realizes the whole process from impermeable to completely permeable by changing the value of interface parameter b, which compensates for the shortcoming of traditional boundary. In terms of the excess pore water pressure, the drainage capacity of ground surface is reduced with the decrease of the value of b. Therefore, the excess pore water pressure exists at the top surface of the ground, and the smaller the b is, the greater the excess pore water pressure is. Meanwhile, the pore pressure increases with the enhancing distance from the sand-drained at the same plane. As for the consolidation degree, the average consolidation degree of the ground decreases with the decrease of b.So, the consolidation rate of the ground may be overestimated under the complete drainage condition of the traditional consolidation theory.Moreover, the consolidation rate of the foundation would be significantly reduced with the decrease of the permeability coefficient in the smear area and the sand well. Therefore, the disturbance to the soil of the well wall should be reduced and the seepage capacity of the vertical drainage should be increased to weaken the smear effect and the well resistance. In addition, the rates of settlements and consolidation will be underestimated if the vertical seepage is ignored, although the radial seepage is dominant in sand-drain.
引文
[1]Terzaghi K.Theoretical soil mechanics[M].New York:John Wiley and Sons Inc.,1943.
[2]Biot M A.General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941(12):155-167.
[3]Carrillo N.Simple two and three dimensional cases in the theory of consolidation of soils[J].Math and Physics,1942(21):1-5.
[4]Barron R A.Consolidation of fine-grained soils by drain wells[J].Transactions of American Society of Civil Engineers,1948,74(6):718-742.
[5]Hansbo S,Jamiolkowski M,Kok L.Consolidation by vertical drains[J].Geotechnique,1981,31(1):45-66.
[6]Yu Chunliang,Zhang Aijun,Zhao Qingyu,et al.Analytical analysis for consolidation of composite foundation reinforced by permeable and im-permeable piles[J].Rock and Soil Mechanics,2017,38(11):3255-3260.[于春亮,张爱军,赵庆玉,等.透水桩与不透水桩组合型复合地基固结解析分析[J].岩土力学,2017,38(11):3255-3260.]
[7]Lu Mengmeng,Zhang Qiang,Jing Hongwen,et al.Consolidation of band-shaped drain based on equivalent annular drain[J].Chinese Journal of Rock Mechanics and Engineering,2017,37(2):513-520.[卢萌盟,张强,靖洪文,等.基于环形等效的排水板地基固结[J].岩石力学与工程学报,2017,37(2):513-520.]
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[9]Basack S,Nimbalkar S.Free strain analysis of the performance of vertical drains for soft soil improvement[J].Geomechanics and Engineering,2017,13(6):963-975.
[10]Xie Kanghe,Zeng Guoxi.Consolidation theories for drain wells under equal strain condition[J].Journal of Geotechnical Engineering,1989,1(2):3-17.[谢康和,曾国熙.等应变条件下的砂井地基固结解析理论[J].岩土工程学报,1989,1(2):3-17.]
[11]Walker R,Indraratna B.Vertical drain consolidation with parabolic distribution of permeability in smear zone[J].Journal of Geotechnical Engineering,2006,132(7):937-941.
[12]Cai Yuanqiang,Liang Xu,Zheng Zaofeng,et al.One-dimensional consolidation of viscoelastic soil layer with semi-permeable boundaries under cycle loadings[J].China Civil Engineering Journal,2003,36(8):86-90.[蔡袁强,梁旭,郑灶锋,等.半透水边界的粘弹性土层在循环荷载下的一维固结[J].土木工程学报,2003,36(8):86-90.]
[13]Liu Jiacai,Shi Jianyong,Zhao Weibing,et al.Consolidation analysis of double-layered ground with impeded boundaries using vertical drains for soil improvement[J].Rock and Soil Mechanics,2007,28(1):116-122.[刘加才,施建勇,赵维炳,等.双层竖井地基半透水边界固结分析[J].岩土力学,2007,28(1):116-122.]
[14]Wang Lei,Sun Dean,Li Linzhong,et al.Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with symmetric semi-permeable drainage boundary[J].Computers and Geotechnics,2017,89:71-80.
[15]Sun Ju,Xie Xinyu,Xie Kanghe.Analytical theory for consolidation of double-layered composite round under impeded boundaries[J].Journal of Zhejiang University(Engineering Science),2007,41(9):1467-1471.[孙举,谢新宇,谢康和.半透水边界双层复合地基固结解析理论[J].浙江大学学报(工学版),2007,41(9):1467-1471.]
[16]Xie Kanghe.One dimensional consolidation analysis of layered soils with impeded boundaries[J].Journal of Zhejiang University(Natural Science Edition),1996,30(5):567-575.[谢康和.层状土半透水边界一维固结分析[J].浙江大学学报(自然科学版),1996,30(5):567-575.]
[17]Hu Yayuan.Consolidation solution for sand-drained ground with impeded boundaries under vacuum preloading[J].Advanced Engineering Sciences,2018,50(2):32-41.[胡亚元.半透水边界砂井地基的真空预压固结解[J].工程科学与技术,2018,50(2):32-41.]
[18]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.[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.]
[19]卢萌盟,谢康和.复合地基固结理论[M].北京:科学出版社,2016:108-121.
[20]Zhang Y G,Xie K H,Wang Z.Consolidation analysis of composite ground improve by ranular columns considering variation of permeability coefficient of soil[C].ASCE GeoShanghai International Conference Special Publication,Ground Modification and Seismic Mitgation(GSP152),2006:135-142.
[2]Biot M A.General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941(12):155-167.
[3]Carrillo N.Simple two and three dimensional cases in the theory of consolidation of soils[J].Math and Physics,1942(21):1-5.
[4]Barron R A.Consolidation of fine-grained soils by drain wells[J].Transactions of American Society of Civil Engineers,1948,74(6):718-742.
[5]Hansbo S,Jamiolkowski M,Kok L.Consolidation by vertical drains[J].Geotechnique,1981,31(1):45-66.
[6]Yu Chunliang,Zhang Aijun,Zhao Qingyu,et al.Analytical analysis for consolidation of composite foundation reinforced by permeable and im-permeable piles[J].Rock and Soil Mechanics,2017,38(11):3255-3260.[于春亮,张爱军,赵庆玉,等.透水桩与不透水桩组合型复合地基固结解析分析[J].岩土力学,2017,38(11):3255-3260.]
[7]Lu Mengmeng,Zhang Qiang,Jing Hongwen,et al.Consolidation of band-shaped drain based on equivalent annular drain[J].Chinese Journal of Rock Mechanics and Engineering,2017,37(2):513-520.[卢萌盟,张强,靖洪文,等.基于环形等效的排水板地基固结[J].岩石力学与工程学报,2017,37(2):513-520.]
[8]Yoshikuni H,Nakanodo H.Consolidation of soils by vertical drain wells with finite permeability[J].Soils and Foundations,1974,14(2):35-46.
[9]Basack S,Nimbalkar S.Free strain analysis of the performance of vertical drains for soft soil improvement[J].Geomechanics and Engineering,2017,13(6):963-975.
[10]Xie Kanghe,Zeng Guoxi.Consolidation theories for drain wells under equal strain condition[J].Journal of Geotechnical Engineering,1989,1(2):3-17.[谢康和,曾国熙.等应变条件下的砂井地基固结解析理论[J].岩土工程学报,1989,1(2):3-17.]
[11]Walker R,Indraratna B.Vertical drain consolidation with parabolic distribution of permeability in smear zone[J].Journal of Geotechnical Engineering,2006,132(7):937-941.
[12]Cai Yuanqiang,Liang Xu,Zheng Zaofeng,et al.One-dimensional consolidation of viscoelastic soil layer with semi-permeable boundaries under cycle loadings[J].China Civil Engineering Journal,2003,36(8):86-90.[蔡袁强,梁旭,郑灶锋,等.半透水边界的粘弹性土层在循环荷载下的一维固结[J].土木工程学报,2003,36(8):86-90.]
[13]Liu Jiacai,Shi Jianyong,Zhao Weibing,et al.Consolidation analysis of double-layered ground with impeded boundaries using vertical drains for soil improvement[J].Rock and Soil Mechanics,2007,28(1):116-122.[刘加才,施建勇,赵维炳,等.双层竖井地基半透水边界固结分析[J].岩土力学,2007,28(1):116-122.]
[14]Wang Lei,Sun Dean,Li Linzhong,et al.Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with symmetric semi-permeable drainage boundary[J].Computers and Geotechnics,2017,89:71-80.
[15]Sun Ju,Xie Xinyu,Xie Kanghe.Analytical theory for consolidation of double-layered composite round under impeded boundaries[J].Journal of Zhejiang University(Engineering Science),2007,41(9):1467-1471.[孙举,谢新宇,谢康和.半透水边界双层复合地基固结解析理论[J].浙江大学学报(工学版),2007,41(9):1467-1471.]
[16]Xie Kanghe.One dimensional consolidation analysis of layered soils with impeded boundaries[J].Journal of Zhejiang University(Natural Science Edition),1996,30(5):567-575.[谢康和.层状土半透水边界一维固结分析[J].浙江大学学报(自然科学版),1996,30(5):567-575.]
[17]Hu Yayuan.Consolidation solution for sand-drained ground with impeded boundaries under vacuum preloading[J].Advanced Engineering Sciences,2018,50(2):32-41.[胡亚元.半透水边界砂井地基的真空预压固结解[J].工程科学与技术,2018,50(2):32-41.]
[18]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.[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.]
[19]卢萌盟,谢康和.复合地基固结理论[M].北京:科学出版社,2016:108-121.
[20]Zhang Y G,Xie K H,Wang Z.Consolidation analysis of composite ground improve by ranular columns considering variation of permeability coefficient of soil[C].ASCE GeoShanghai International Conference Special Publication,Ground Modification and Seismic Mitgation(GSP152),2006:135-142.