半渗透边界下非饱和土砂井地基固结特性
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摘要
以往的非饱和土砂井地基研究中未考虑砂井的涂抹作用,均按理想砂井进行研究。然而在实际工程中,施工的扰动会导致砂井内壁附近的土体渗透性减弱,从而影响地基的固结。针对这种情况,本文以均布荷载作用下非饱和土砂井地基为模型,考虑涂抹作用,并将其形成的边界假设为半渗透边界;引入Bessel函数,根据超孔隙压力的耦合控制方程推导了半渗透边界条件下非饱和土砂井地基在Laplace变换域内的固结半解析解,并且采用Crump方法进行Laplace逆变换,得到了时间域内的解;将该砂井地基模型退化为理想砂井模型,与现有文献结果对比,验证了本文研究方法的可靠性。最后通过算例来考察半渗透系数对非饱和土砂井地基固结特性的影响。研究表明,半渗透系数对砂井地基的固结有着重要的影响,且半渗透系数越大,超孔隙压力消散越快。
Former researches of unsaturated drainage well foundations always treated the foundations with ideal radial boundaries,but did not consider the smearing effect. The construction disturbance can affect the speed of consolidation by decreasing the soil permeability near the inside of a drainage well foundation. In this case,the smearing effect is illustrated with the semi-permeable boundary and is included in a new modeling of drainage well foundation in unsaturated soils. By introducing Bessel functions,analytical solutions with respect to excess pore pressures are achieved in the Laplace domain according to the governing equations. Secondly,by utilizing the Crump's method,the inverse Laplace transform to obtain semi-analytical solutions to excess pore pressures in the time domain is performed. It is shown that the present solutions are in good agreement with the previous solutions in the literature and more reliable. Finally,parametric studies are conducted by the variations of excess pore pressures at different ratios of air-water permeability coefficient and the radius. Results indicate that the semi-permeability coefficients have significant influence on the consolidation,and excess pore pressures dissipate faster with the increase of semi-permeability coefficient.
Former researches of unsaturated drainage well foundations always treated the foundations with ideal radial boundaries,but did not consider the smearing effect. The construction disturbance can affect the speed of consolidation by decreasing the soil permeability near the inside of a drainage well foundation. In this case,the smearing effect is illustrated with the semi-permeable boundary and is included in a new modeling of drainage well foundation in unsaturated soils. By introducing Bessel functions,analytical solutions with respect to excess pore pressures are achieved in the Laplace domain according to the governing equations. Secondly,by utilizing the Crump's method,the inverse Laplace transform to obtain semi-analytical solutions to excess pore pressures in the time domain is performed. It is shown that the present solutions are in good agreement with the previous solutions in the literature and more reliable. Finally,parametric studies are conducted by the variations of excess pore pressures at different ratios of air-water permeability coefficient and the radius. Results indicate that the semi-permeability coefficients have significant influence on the consolidation,and excess pore pressures dissipate faster with the increase of semi-permeability coefficient.
引文
Barron R A.1948.Consolidation of fine-grained soils by drain wells[J]Transactions of the American Society of Civil Engineers,113(1):718-742.
Biot M A.1941.General theory of three-dimensional consolidation[J]Journal of Applied Physics,12(2):155-164.
Cai Y Q,Liang X,Zheng Z F,et al.2003.One-dimensional consolidation of viscoelastic soil layer with semi-permeable boundaries under cyclic loadings[J].China Civil Engineering Journal,36(8):86-90.
Gray H.1945.Simultaneous consolidation of contiguous layers of unlike compressible soils[J].Trans.ASCE,110:1327-1356.
Guo B,Gong X N,Lu M M,et al.2009.Theoretical Analysis of partially penetrated sand drains foundation in consideration of smear effect[J].Chinese Journal of Rock Mechanics and Engineering,28(12):2561-2568.
Liem H,Fatahi,B,Khabbaz H.2016.Analytical solution to axisymmetric consolidation in unsaturated soils with linearly depth-dependen initial conditions[J].Computers and Geotechnics,74:102-121.
Liu B,Zhang G,Jiang Y H,et al.2014.Settlement research on single pumping well of foundation pit using changeable permeability coefficient model[J].Journal of Engineering Geology,22(6):1123-1127.
Liu J C.2004.Consolidation analysis for layered-ground improved by sand wells and its engineering application[D].Nanjing:Hoha University.
Liu X W,Xie K H,Pan Q Y,et al.1998.Viscoelastic consolidation theories of soils with vertical darin wells[J].China Civi Engineering Journal,31(1):10-19.
Qin A F,Sun D A,Yang L P,et al.2010.A semi-analytical solution to consolidation of unsaturated soils with the free drainage well[J].Computers and Geotechnics,37(7):867-875.
Qin A F,Yu J F,Ge H.2017.Analysis of consolidation of free drainage well in unsaturated soil with variable permeability coefficient within smear zone[J].Journal of Engineering Geology,25(3):605-611.
Schiffman R L,Stein J R.1970.One-dimensional consolidation of layered systems[J].Journal of Soil Mechanics and Foundation Engineering,ASCE,96(4):1499-1504.
Terzaghi K.1925.Erdbaumechanik auf bodenphysikalischgrundlage[M].Vienna:Leipzig Deuticke.
Wang R C,Xie K H.2001.Viscoelastic consolidation analysis of vertical drainage foundation in semi-permeable boundary[J].Journal of Yangtze River Scientific Research Institute,18(6):33-36.
Xie K H.1996.One-dimensional consolidation analysis of layered soil under semi-permeable boundary[J].Journal of Zhejiang University(Engineering Science),(5):567-575.
Ye W M,Wang C S,Wang Q,et al.2009.Laboratory tests on the characteristics of air-permeation in unsaturated Shanghai soft soil[J].Journal of Engineering Geology,17(2):244-248.
蔡袁强,梁旭,郑灶锋,等.2003.半透水边界的黏弹性土层在循环荷载下的一维固结[J].土木工程学报,36(8):86-90.
郭彪,龚晓南,卢萌盟,等.2009.考虑涂抹作用的未打穿砂井地基固结理论分析[J].岩石力学与工程学报,28(12):2561-2568.
刘波,张功,江永华,等.2014.基于变渗透系数的深基坑单井抽水沉降研究[J].工程地质学报,22(6):1123-1127.
刘加才.2004.层状砂井地基固结分析及其工程应用[D].南京:河海大学.
刘兴旺,谢康和,潘秋元,等.1998.竖向排水井地基黏弹性固结解析理论[J].土木工程学报,31(1):10-19.
秦爱芳,余继放,葛航.2017.考虑涂抹区渗透系数变化的非饱和土砂井地基固结特性分析[J].工程地质学报,25(3):605-611.
王瑞春,谢康和.2001.半透水边界的竖向排水井地基黏弹性固结分析[J].长江科学院院报,18(6):33-36.
谢康和.1996.层状土半透水边界一维固结分析[J].浙江大学学报(工学版),(5):567-575.
叶为民,王初生,王琼,等.2009.非饱和黏性土中气体渗透特征[J].工程地质学报,17(2):244-248.
Biot M A.1941.General theory of three-dimensional consolidation[J]Journal of Applied Physics,12(2):155-164.
Cai Y Q,Liang X,Zheng Z F,et al.2003.One-dimensional consolidation of viscoelastic soil layer with semi-permeable boundaries under cyclic loadings[J].China Civil Engineering Journal,36(8):86-90.
Gray H.1945.Simultaneous consolidation of contiguous layers of unlike compressible soils[J].Trans.ASCE,110:1327-1356.
Guo B,Gong X N,Lu M M,et al.2009.Theoretical Analysis of partially penetrated sand drains foundation in consideration of smear effect[J].Chinese Journal of Rock Mechanics and Engineering,28(12):2561-2568.
Liem H,Fatahi,B,Khabbaz H.2016.Analytical solution to axisymmetric consolidation in unsaturated soils with linearly depth-dependen initial conditions[J].Computers and Geotechnics,74:102-121.
Liu B,Zhang G,Jiang Y H,et al.2014.Settlement research on single pumping well of foundation pit using changeable permeability coefficient model[J].Journal of Engineering Geology,22(6):1123-1127.
Liu J C.2004.Consolidation analysis for layered-ground improved by sand wells and its engineering application[D].Nanjing:Hoha University.
Liu X W,Xie K H,Pan Q Y,et al.1998.Viscoelastic consolidation theories of soils with vertical darin wells[J].China Civi Engineering Journal,31(1):10-19.
Qin A F,Sun D A,Yang L P,et al.2010.A semi-analytical solution to consolidation of unsaturated soils with the free drainage well[J].Computers and Geotechnics,37(7):867-875.
Qin A F,Yu J F,Ge H.2017.Analysis of consolidation of free drainage well in unsaturated soil with variable permeability coefficient within smear zone[J].Journal of Engineering Geology,25(3):605-611.
Schiffman R L,Stein J R.1970.One-dimensional consolidation of layered systems[J].Journal of Soil Mechanics and Foundation Engineering,ASCE,96(4):1499-1504.
Terzaghi K.1925.Erdbaumechanik auf bodenphysikalischgrundlage[M].Vienna:Leipzig Deuticke.
Wang R C,Xie K H.2001.Viscoelastic consolidation analysis of vertical drainage foundation in semi-permeable boundary[J].Journal of Yangtze River Scientific Research Institute,18(6):33-36.
Xie K H.1996.One-dimensional consolidation analysis of layered soil under semi-permeable boundary[J].Journal of Zhejiang University(Engineering Science),(5):567-575.
Ye W M,Wang C S,Wang Q,et al.2009.Laboratory tests on the characteristics of air-permeation in unsaturated Shanghai soft soil[J].Journal of Engineering Geology,17(2):244-248.
蔡袁强,梁旭,郑灶锋,等.2003.半透水边界的黏弹性土层在循环荷载下的一维固结[J].土木工程学报,36(8):86-90.
郭彪,龚晓南,卢萌盟,等.2009.考虑涂抹作用的未打穿砂井地基固结理论分析[J].岩石力学与工程学报,28(12):2561-2568.
刘波,张功,江永华,等.2014.基于变渗透系数的深基坑单井抽水沉降研究[J].工程地质学报,22(6):1123-1127.
刘加才.2004.层状砂井地基固结分析及其工程应用[D].南京:河海大学.
刘兴旺,谢康和,潘秋元,等.1998.竖向排水井地基黏弹性固结解析理论[J].土木工程学报,31(1):10-19.
秦爱芳,余继放,葛航.2017.考虑涂抹区渗透系数变化的非饱和土砂井地基固结特性分析[J].工程地质学报,25(3):605-611.
王瑞春,谢康和.2001.半透水边界的竖向排水井地基黏弹性固结分析[J].长江科学院院报,18(6):33-36.
谢康和.1996.层状土半透水边界一维固结分析[J].浙江大学学报(工学版),(5):567-575.
叶为民,王初生,王琼,等.2009.非饱和黏性土中气体渗透特征[J].工程地质学报,17(2):244-248.