抽降水引发的弱透水层非线性固结解析解

Analytical Solutions for Nonlinear Consolidation of Aquitard Induced by the Dropping of Groundwater Table

抽降水会引发含水层下卧的弱透水层的固结沉降,同时,土体非线性压缩、渗透特性对固结变形的影响也较为明显。故抽降水引发的弱透水层的固结模型中有必要考虑土体的非线性固结特性,但考虑非线性固结特性后弱透水层固结模型的解析求解存在着困难。本文在分析现有非线性固结模型的基础上,获得了弱透水层非线性固结的近似解析解。具体过程为:引入描述土体的非线性压缩、渗透特性的经典非线性关系,在弱透水层初始有效应力为恒值的假定下,采用分离变量法推导了压缩指数C_(c)与渗透指数C_(k)比值不等于1时,潜水层大面积抽水引发的弱透水层1维非线性固结近似解析解。当C_(c)/C_(k)→1时,本文解可退化为相同条件下已有的C_(c)/C_(k)=1时1维非线性固结解,初步地验证了其解答的正确性。将本文解答应用于实际工程的沉降分析中,通过理论计算结果与实测结果的对比分析,进一步表明该弱透水层非线性固结解答应用于实际工程的可靠性。最后,以水位单级等速下降为例,利用本文解计算不同影响因素下弱透水层的固结曲线,分析其非线性固结性状。结果表明:C_(k)值不变时,C_(c)值越大(C_(c)/C_(k)越大),固结速率越缓慢,但相同时间因子下土层沉降量及最终沉降量均越大;C_(c)值不变时,C_(k)值越小(C_(c)/C_(k)越大),固结速率越慢,相同时间因子下土层沉降量越小,但其并不影响最终沉降量。水位下降速率越快,弱透水层固结速率越快,但最终沉降量相同。水位下降终值h_c越大,沉降速率越快,此时C_(c)/C_(k)对固结速率的影响越明显。砂土层自然重度γ越大,相同时间因子下,土层沉降量越大,同时超静孔压消散速率越缓慢,但其并不影响土层内的最终超静孔压。

The dropping of groundwater table by pumping may cause consolidation settlement of aquitard underlying aquifer,and the nonlinear compressibility and permeability of soils have evident influences on the consolidation deformation.Therefore,the nonlinear compressibility and permeability of soils have to be considered in the nonlinear consolidation model of aquitard caused by groundwater pumping,while difficulties exist in solving this consolidation model.Based on the analysis of the existing nonlinear consolidation models,an approximate analytical solution for the nonlinear consolidation of aquitard was derived,in which by adopting the classical nonlinear relationships and assuming a constant initial effective stress at different depths,an approximate analytical solution for one-dimensional nonlinear consolidation of soils caused by large area pumping of phreatic water layer were obtained using the method of separation of variables when the ratio of compressibility index C_(c) to permeability index C_(k) was not equal to 1.When C_(c)/C_(k)→1,the solution can be reduced to the existing one-dimensional nonlinear consolidation solution for the case of C_(c)/C_(k)=1.The solution was applied to the settlement analysis of engineering case,and the comparisons between theoretical and actualmeasurement results further showed that the solution is reliable for actual problems.Finally,taking the single-stage and constant-rate dropping of groundwater table as an example,the consolidation settlement curves of aquitard under different factors were calculated by using the above solution and the non-linear consolidation behaviors were analyzed.The results showed that when the value of C_(k) is constant,the larger C_(c) is(resulting in larger C_(c)/C_(k)),the slower the consolidation rate is,but the greater both the settlement at the same time and the final settlement are.When the value of C_(c) remains constant,the smaller C_(k) is(resulting in larger C_(c)/C_(k)),the slower the consolidation rate is,and the smaller the settlement at the same time during the consolidation process is,however it does not affect the final settlement of aquitard.The faster the dropping rate of groundwater table is,the faster the consolidation rate of aquitard is,while the final settlements under different dropping rate are same.The settlement rate grows with the increase in the final value of groundwater table(hc),whereas the influence of C_(c)/C_(k) on the consolidation rate becomes more evident.The larger the specific weight of soils(γ)is,the larger the settlement at the same time factor is,and the slower the dissipation rate of the excess pore pressure is,which indicates thatγhas no influence on the final value of the excess pore pressure.