考虑起始水力坡降的软黏土流变固结解析解
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摘要
软黏土中渗流存在的起始水力坡降会对固结性状有重要影响已逐渐被认识。但能同时考虑起始水力坡降及软黏土流变特性的固结理论仍鲜见报道,对其解析解的研究更为罕见。针对现有理论的不足,考虑软黏土中渗流存在的起始水力坡降及黏性土的流变特性,基于太沙基1维固结理论建立其控制方程,应用拉普拉斯变换获得其解析解。目前存在的考虑起始水力坡降的线性固结解析解和达西定律下考虑流变模型的固结解析解均是本文解的特例,且本文所得解析解与相应差分解的计算结果十分相近。基于该解析解着重分析了起始水力坡降和不同流变模型对固结性状的影响。结果表明:考虑软黏土流变特性后,起始水力坡降(i0)、土层厚度(H)与外荷载(q0)的比值(R)对固结性状的影响并未发生明显改变;R值越大,移动边界到达土层底面所需时间越长,相同时刻土中残留的超静孔压值越大,土层平均固结度越小。考虑流变特性后,移动边界到达土层底面的条件发生改变。如果流变模型参数取值相同,不同流变模型下软黏土固结初期超静孔压消散曲线基本重合,移动边界随时间的下移曲线亦基本重合;固结后期超静孔压消散曲线虽略有差异,但其对计算结果影响甚微,可忽略。
The influence of a threshold gradient of water flow in soft clays on consolidation behavior has been gradually recognized. However, the consolidation theory with consideration of a threshold hydraulic gradient and rheological characteristics has rarely been reported in the literature so far, and especially the analytical solution for this problem has never been studied. In view of the deficiency in consolidation theories, the governing equation for one-dimensional consolidation of the clay with consideration of the threshold gradient and rheological characteristics is developed on the basis of Terzaghi's theory for one-dimensional consolidation. An analytical solution for the governing equation is obtained by the method of Laplace transform. The analytical solutions for one-dimensional consolidation derived so far considering either a threshold gradient or a rheological model are all special cases of the solution derived herein. Based on the solution proposed in this study, the influences of the threshold hydraulic gradient and different rheological models on consolidation behavior are investigated. The results show that the influences of the ratio of the threshold gradient(i0) and the thickness of clay layer(H) to the load(q0) on consolidation behavior with consideration of rheological characteristic do not evidently change comparing to that under consideration of linear elastic model. The larger R is, the longer it takes for the moving boundary to reach the bottom of the layer, and the larger the ultimate value of excess pore water pressure is, and the smaller the ultimate average degree of consolidation is. Moreover, the condition that the moving boundary reaches the bottom of the layer differs with that with no consideration of rheological characteristic. If the same parameters of different rheology models are adopted, the dissipation curves of excess pore water pressure and the variation of moving boundary with time under different rheology models are almost same at the early stage of consolidation. At the late stage of consolidation, the difference between dissipation curves of excess pore water pressure different rheological models is so little that the influence of different rheological models on the result can be ignored.
The influence of a threshold gradient of water flow in soft clays on consolidation behavior has been gradually recognized. However, the consolidation theory with consideration of a threshold hydraulic gradient and rheological characteristics has rarely been reported in the literature so far, and especially the analytical solution for this problem has never been studied. In view of the deficiency in consolidation theories, the governing equation for one-dimensional consolidation of the clay with consideration of the threshold gradient and rheological characteristics is developed on the basis of Terzaghi's theory for one-dimensional consolidation. An analytical solution for the governing equation is obtained by the method of Laplace transform. The analytical solutions for one-dimensional consolidation derived so far considering either a threshold gradient or a rheological model are all special cases of the solution derived herein. Based on the solution proposed in this study, the influences of the threshold hydraulic gradient and different rheological models on consolidation behavior are investigated. The results show that the influences of the ratio of the threshold gradient(i0) and the thickness of clay layer(H) to the load(q0) on consolidation behavior with consideration of rheological characteristic do not evidently change comparing to that under consideration of linear elastic model. The larger R is, the longer it takes for the moving boundary to reach the bottom of the layer, and the larger the ultimate value of excess pore water pressure is, and the smaller the ultimate average degree of consolidation is. Moreover, the condition that the moving boundary reaches the bottom of the layer differs with that with no consideration of rheological characteristic. If the same parameters of different rheology models are adopted, the dissipation curves of excess pore water pressure and the variation of moving boundary with time under different rheology models are almost same at the early stage of consolidation. At the late stage of consolidation, the difference between dissipation curves of excess pore water pressure different rheological models is so little that the influence of different rheological models on the result can be ignored.
引文
[1]Miller R J,Low P F.Threshold gradient for water flow in clay systems[J].Soil Science Society of America Journal,1963,27(6):605-609.
[2]Pascal F,Pascal H,Murray D W.Consolidation with threshold gradients[J].International Journal for Numerical and Analytical Methods in Geomechanics,1981,5(3):247-261.
[3]Liu Ciqun.Approximate solutions for one-dimensional consolidation with a threshold gradient[J].Chinese Journal of Geotechnical Engineering,1982,4(3):107-109.[刘慈群.有起始比降固结问题的近似解[J].岩土工程学报,1982,4(3):107-109.]
[4]Liu Zhongyu,Zhang Tianhang,Ma Chongwu.Effect of initial hydraulic gradient on one-dimensional consolidation of saturated clays[J].Rock and Soil Mechanics,2007,28(3):467-470.[刘忠玉,张天航,马崇武.起始水力梯度对饱和黏土一维固结的影响[J].岩土力学,2007,28(3):467-470.]
[5]Xie K H,Wang K,Wang Y L,et al.Analytical solution for one-dimensional consolidation of clayey soils with a threshold gradient[J].Computers and Geotechnics,2010,37(4):487-493.
[6]Zhou Y,Bu W K,Lu M M.One-dimensional consolidation with a threshold gradient:A Stefan problem with rate-dependent latent heat[J].International Journal for Numerical and Analytical Methods in Geomechanics,2013,37(16):2825-2832.
[7]Wang Kun,Xie Kanghe,Liu Xingwang,et al.Solution for one-dimensional consolidation with threshold gradient subjected to non-uniformly distributed initial pore water pressure[J].Chinese Journal of Geotechnical Engineering,2011,33(9):1419-1424.[王坤,谢康和,刘兴旺,等.初始孔压非均布考虑起始比降的一维固结解[J].岩土工程学报,2011,33(9):1419-1424.]
[8]Li Chuanxun,Wang Kun.Analysis of one-dimensional nonlinear consolidation for soft soils with threshold gradient[J].Journal of Jiangsu University(Natural Science Edition),2014,35(6):732-737.[李传勋,王坤.考虑起始水力坡降的软土一维非线性固结分析[J].江苏大学学报(自然科学版),2014,35(6):732-737.]
[9]Huang Jieqing,Xie Xinyu,Wang Wenjun,et al.Study on one-dimensional nonlinear consolidation behavior for saturated soils with threshold gradient[J].Chinese Journal ofGeotechnical Engineering,2013,35(2):355-363.[黄杰卿,谢新宇,王文军,等.考虑起始比降的饱和土体一维复杂非线性固结研究[J].岩土工程学报,2013,35(2):355-363.]
[10]Li Chuanxun,Dong Xingquan,Jin Dandan,et al.Nonlinear large-strain consolidation analysis of soft clay considering threshold hydraulic gradient[J].Rock and Soil Mechanics,2017,38(2):377-384.[李传勋,董兴泉,金丹丹,等.考虑起始水力坡降的软土大变形非线性固结分析[J].岩土力学,2017,38(2):377-384.]
[11]Taylor D W,Merchant W.A theory of clay consolidation accounting for secondary compression[J].Journal of Mathematics and Physics,1940,19(1/2/3/4):167-185.
[12]Xia Jun,Mei Guoxiong,Mei Ling,et al.Biot’s consolidation finite layer analysis of viscoelastic soil[J].Chinese Journal of Geotechnical Engineering,2009,31(3):437-441.[夏君,梅国雄,梅岭,等.考虑固结的黏弹性地基的有限层法[J].岩土工程学报,2009,31(3):437-441.]
[13]Chen Xiaoping,Bai Shiwei.Research on creep consolidation characteristics and calculation model of soft soil[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(5):728-734.[陈晓平,白世伟.软土蠕变-固结特性及计算模型研究[J].岩石力学与工程学报,2003,22(5):728-734.]
[14]Yin J H,Graham J.Elastic visco-plastic modelling of onedimensional consolidation[J].Geotechnique,1996,46(3):515-527.
[15]Bjerrum L.Engineering geology of norwegian normallyconsolidated marine clays as related to settlements of buildings[J].Geotechnique,1967,17(2):63-117.
[16]Xie K H,Xie X Y,Li X B.Analytical theory for one-dimensional consolidation of clayey soils exhibiting rheological characteristics under time-dependent loading[J].International Journal for Numerical and Analytical Methods in Geomechanics,2008,32(14):1833-1855.
[17]Li Xibin,Xie Kanghe,Chen Fuquan.One dimensional consolidation and permeability tests considering stress history and rheological characteristic of soft soils[J].Journal of Hydraulic Engineering,2013,44(1):18-25.[李西斌,谢康和,陈福全.考虑软土流变特性和应力历史的一维固结与渗透试验[J].水利学报,2013,44(1):18-25.]
[2]Pascal F,Pascal H,Murray D W.Consolidation with threshold gradients[J].International Journal for Numerical and Analytical Methods in Geomechanics,1981,5(3):247-261.
[3]Liu Ciqun.Approximate solutions for one-dimensional consolidation with a threshold gradient[J].Chinese Journal of Geotechnical Engineering,1982,4(3):107-109.[刘慈群.有起始比降固结问题的近似解[J].岩土工程学报,1982,4(3):107-109.]
[4]Liu Zhongyu,Zhang Tianhang,Ma Chongwu.Effect of initial hydraulic gradient on one-dimensional consolidation of saturated clays[J].Rock and Soil Mechanics,2007,28(3):467-470.[刘忠玉,张天航,马崇武.起始水力梯度对饱和黏土一维固结的影响[J].岩土力学,2007,28(3):467-470.]
[5]Xie K H,Wang K,Wang Y L,et al.Analytical solution for one-dimensional consolidation of clayey soils with a threshold gradient[J].Computers and Geotechnics,2010,37(4):487-493.
[6]Zhou Y,Bu W K,Lu M M.One-dimensional consolidation with a threshold gradient:A Stefan problem with rate-dependent latent heat[J].International Journal for Numerical and Analytical Methods in Geomechanics,2013,37(16):2825-2832.
[7]Wang Kun,Xie Kanghe,Liu Xingwang,et al.Solution for one-dimensional consolidation with threshold gradient subjected to non-uniformly distributed initial pore water pressure[J].Chinese Journal of Geotechnical Engineering,2011,33(9):1419-1424.[王坤,谢康和,刘兴旺,等.初始孔压非均布考虑起始比降的一维固结解[J].岩土工程学报,2011,33(9):1419-1424.]
[8]Li Chuanxun,Wang Kun.Analysis of one-dimensional nonlinear consolidation for soft soils with threshold gradient[J].Journal of Jiangsu University(Natural Science Edition),2014,35(6):732-737.[李传勋,王坤.考虑起始水力坡降的软土一维非线性固结分析[J].江苏大学学报(自然科学版),2014,35(6):732-737.]
[9]Huang Jieqing,Xie Xinyu,Wang Wenjun,et al.Study on one-dimensional nonlinear consolidation behavior for saturated soils with threshold gradient[J].Chinese Journal ofGeotechnical Engineering,2013,35(2):355-363.[黄杰卿,谢新宇,王文军,等.考虑起始比降的饱和土体一维复杂非线性固结研究[J].岩土工程学报,2013,35(2):355-363.]
[10]Li Chuanxun,Dong Xingquan,Jin Dandan,et al.Nonlinear large-strain consolidation analysis of soft clay considering threshold hydraulic gradient[J].Rock and Soil Mechanics,2017,38(2):377-384.[李传勋,董兴泉,金丹丹,等.考虑起始水力坡降的软土大变形非线性固结分析[J].岩土力学,2017,38(2):377-384.]
[11]Taylor D W,Merchant W.A theory of clay consolidation accounting for secondary compression[J].Journal of Mathematics and Physics,1940,19(1/2/3/4):167-185.
[12]Xia Jun,Mei Guoxiong,Mei Ling,et al.Biot’s consolidation finite layer analysis of viscoelastic soil[J].Chinese Journal of Geotechnical Engineering,2009,31(3):437-441.[夏君,梅国雄,梅岭,等.考虑固结的黏弹性地基的有限层法[J].岩土工程学报,2009,31(3):437-441.]
[13]Chen Xiaoping,Bai Shiwei.Research on creep consolidation characteristics and calculation model of soft soil[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(5):728-734.[陈晓平,白世伟.软土蠕变-固结特性及计算模型研究[J].岩石力学与工程学报,2003,22(5):728-734.]
[14]Yin J H,Graham J.Elastic visco-plastic modelling of onedimensional consolidation[J].Geotechnique,1996,46(3):515-527.
[15]Bjerrum L.Engineering geology of norwegian normallyconsolidated marine clays as related to settlements of buildings[J].Geotechnique,1967,17(2):63-117.
[16]Xie K H,Xie X Y,Li X B.Analytical theory for one-dimensional consolidation of clayey soils exhibiting rheological characteristics under time-dependent loading[J].International Journal for Numerical and Analytical Methods in Geomechanics,2008,32(14):1833-1855.
[17]Li Xibin,Xie Kanghe,Chen Fuquan.One dimensional consolidation and permeability tests considering stress history and rheological characteristic of soft soils[J].Journal of Hydraulic Engineering,2013,44(1):18-25.[李西斌,谢康和,陈福全.考虑软土流变特性和应力历史的一维固结与渗透试验[J].水利学报,2013,44(1):18-25.]