为了解决饱和软土地基一维非线性固结微分方程的近似解相对误差大的问题,基于饱和软土地基一维非线性固结理论,考虑软土渗透系数和压缩性在固结过程中的非线性变化的影响, 给出了无量纲化的非线性固结控制方程,引入权重因子λ将非线性偏微分方程简化为线性方程,其中权重因子λ可取小数(0<λ<1),进而结合边界条件给出了考虑权重因子λ变化下的简化解析解。通过MATLAB软件数值编程计算对比可见:Lekha等近似解法是权重因子λ=0.5时的特例;Lekha等近似解与差分法数值解最大相对误差高达19%;采用变权重因子λ法的简化解则精度更高。文中提出的一维非线性固结简化解法便于软土非线性固结理论在工程实际中的应用。
Abstract
The relative error of the approximated solution of differential equation of one-dimensional nonlinear consolidation of saturated soft soil is quite large. In the light of one-dimensional nonlinear consolidation theory of saturated soft soil foundation, a dimensionless nonlinear consolidation control equation is given in consideration of the influences of nonlinear changes of soft soil’s permeability coefficient and compressibility in the consolidation process, and the weighting factor λ is incorporated to simplify the nonlinear partial differential equation to a linear equation, where the weighting factor λ is a fractional number (0 <λ <1), and a simplified analytic solution considering the weighting factor λ is given in conjunction with the boundary condition. Calculation by MatLab reveals that the Lekha approximation method is the special case of the weighting factor λ=0.5 in this paper. The maximum relative error of the approximate solution and the difference method of Lekha is as high as 19%. By using the simplified solution of the variable weight λ, higher accuracy can be achieved. The proposed simplified solution in this paper is convenient to be applied to engineering practice.
关键词
饱和软黏土 /
一维非线性固结理论 /
渗透系数 /
压缩系数 /
权重因子 /
简化解法
Key words
saturated soft clay /
1D nonlinear consolidation theory /
permeability coefficient /
compression factor /
weighting factor /
simplified solution
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参考文献
[1] TERZAGHI K. Theoretical Soil Mechanics[M] . New York: Wiley, 1943.
[2] DAVIS E H, RAYMOND G P. A Nonlinear Theory of Consolidation[J] . Geotechnique, 1965, 15(2): 161-173.
[3] BARDEN L, BERRY P L. Consolidation of Normally Consolidated Clay[J] . Journal of the Soil Mechanics and Foundation Division, ASCE, 1965, 91(SM5): 15-35.
[4] MESRI G, ROKHSAR A. Theory of Consolidation for Clays[J] . Journal of Geotechnical Engineering, ASCE, 1974, 100(8): 889-904.
[5] MIKASA M .The Consolidation of Soft Clay: A New Consolidation Theory and Its Application[J] . Japan Society of Civil Engineers, 1965,16(7): 21-26.
[6] GIBSON R E, ENGLAND G L, HUSSEY M J L. The Theory of One-dimensional Consolidation of Saturated Clays 1. Finite Nonlinear Consolidation of Thin Homogeneous Layers[J] . Geotechnique, 1967, 17(3): 261-273.
[7] HANSBO S, JAMIOLKOWSKI M. Consolidation by Vertical Drains[J] . Géotechnique , 1981 , 31 (1) :45-66.
[8] LEKHA K R, KRISHNASWAMY N R, BASAK P. Consolidation of Clays for Variable Permeability and Compressibility[J] . Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 2003, 129(11):1001-1009.
[9] RUJIKIATKAMJORN C. Radial Consolidation of Clay Using Compressibility Indices and Varying Horizontal Permeability[J] . Canadian Geotechnical Journal, 2005, 42(5): 1330-1341.
[10] HUANG C X,DENG Y B. Consolidation Theory for Prefabricated Vertical Drains with Elliptic Cylindrical Assumption[J] . Computers and Geotechnics,2016,77(1):156-166.
[11] 黄朝煊,邓岳保,胡国杰. 基于排水体椭圆柱假定的井阻非线性竖井地基固结理论[J] . 岩石力学与工程学报, 2017, 36(3): 725-735.
[12] 黄朝煊,王正中,方咏来.考虑漏气及井阻非线性的真空预压地基固结解析解[J] .岩土力学,2017,38(9): 725-735.
[13] 黄朝煊, 邓岳保. 考虑复杂荷载及井阻非线性时竖井地基固结解析解研究[J] . 水文地质工程地质, 2017, 44(1): 57-63.
[14] 黄朝煊,方咏来.线性加载下塑料排水板地基固结理论探讨[J] .工程地质学报, 2017, 25(3): 678-685.
[15] 黄朝煊, 方咏来, 曾 甑. 塑料排水板处理地基固结特性研究[J] . 长江科学院院报, 2017, 34(2): 99-103.
[16] 温介邦, 王跃伟, 谢康和, 等. 软土非线性固结计算若干表格及应用[J] . 岩土力学, 2008, 29(8): 2163-2169.
[17] 吴 健,谢新宇,朱向荣. 饱和土体一维复杂非线性固结特性研究[J] . 岩土力学, 2010,31(1): 81-86.
[18] 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.
[19] 谢康和,温介邦,胡虹宇,等.考虑应力历史影响的饱和土一维非线性固结分析[J] .科技通报,2006,22(1):68-76,83.
[20] 刘忠玉,纠永志,乐金朝,等.基于非Darcy渗流的饱和黏土一维非线性固结分析[J] .岩石力学与工程学报,2010,29(11):2348-2355.
基金
浙江省基础公益研究计划项目(LGF18E090004);浙江省水利厅科技计划项目(RC1701);浙江省水利水电勘测设计院科标业资助项目(B1609,B1803)
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