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。
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.
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