成层未打穿砂井地基固结Lagrange插值解法  

LAGRANGE INTERPOLATION FOR MULTI-LAYER GROUND IN CONSOLIDATION OF PARTIALLY PENETRATED VERTICAL DRAINS

作　　者：闫富有[1] 

机构地区：[1]郑州大学土木工程学院,河南郑州450002

出　　处：《岩石力学与工程学报》2007年第9期1932-1939,共8页Chinese Journal of Rock Mechanics and Engineering

摘　　要：考虑井阻和涂抹区的影响,建立成层未打穿砂井地基固结的数值模型和算法。将未打穿砂井底面下的软土层视为虚拟排水井,同时将未打穿砂井转化为打穿的多段砂井,使得土层边界条件和数值计算过程简单化。对超孔隙水压力用Lagrange插值多项式等结点插值近似,把砂井打设区固结方程转化为结点的超孔隙水压力的简单微分方程组,砂井固结方程转化为一线性代数方程组,以4层土为例,导出详细的计算公式。如增加土层数,仅需改变边界结点系数公式。最后,把该解法与相关近似方法的计算结果进行分析比较,并给出一个多层软土路基预压加固工程案例。结果表明,将下卧层简化为一维固结与考虑其三维固结对计算结果影响很小。Considering the well resistance and the smear effects, the numerical modeling and the solution method for multi-layered clays consolidation by partially penetrated vertical drains under time-dependent loading are presented. Assuming a virtual drain penetrating the soft strata at the bottom of the actual drain, the partially penetrated vertical drain is transformed into a fully penetrated vertical drain, thus the boundary conditions for consolidation equations and the numerical process are simplified. The excess pore water pressure of each stratum is interpolated and approximated by Lagrange interpolation polynomials; and the algebraic equations of excess pore water pressure at boundary nodal points are obtained with inner nodal points. Thus the consolidation equations of the section with vertical drains are transformed into simple differential equations describing the values of excess pore water pressure in the nodes, and linear algebraic simultaneous equations of vertical drains consolidation in the nodes are obtained simultaneously. For the four-layer soils, the calculating formulas are presented in detail. If the number of soil layers is added, the boundary nodal coefficient formulas are changed only. The presented numerical results are compared with those using the relevant approximate methods： and an example of roadbed composed of four soft soil layers under preloading is analyzed. It is shown that there are no much differences between the one-dimensional model and the three-dimensional model adopted in the underlying undrained zone.

关 键 词：土力学 固结 成层地基 数值算法 未打穿砂井 LAGRANGE插值 

分 类 号：TU472.3[建筑科学—结构工程]