Analytical solution for one-dimensional electroosmosis consolidation considering threshold potential gradient under time-dependent loading
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摘要: 将起始电势梯度的概念引入电渗固结理论，基于相关假定建立了外荷载随时间变化下考虑有效电势衰减的一维电渗固结控制方程，利用变量代换和分离变量法获得了电渗固结通解，并给出了常见加荷形式下解析解的表达式。将退化解与已有解析解进行比较，并将所提解与有限差分解展开对比，验证了所提解答正确性。基于所提解析解，分析了相关参数对软土地基电渗固结特性的影响。结果表明：起始电势梯度的存在降低了超孔隙水压力绝对值和沉降量；水力渗透系数的减小有利电渗排水固结过程的进行，且电渗透系数与水力渗透系数比值越大，沉降量越大、电渗排水固结效果越好；当采用电渗联合堆载预压法加固时，电渗作用可降低因外荷载引起的正超孔隙水压力的最大值，提高固结排水时土体的稳定性。Abstract: The concept of the threshold potential gradient is introduced into the electroosmosis consolidation theory. The governing equation for one-dimensional electroosmosis consolidation considering the effective potential attenuation with time-dependent loading is established based on the corresponding assumptions. The general analytical solutions for electroosmosis consolidation are obtained by the algebraic transformation and variable separation methods. Meanwhile, the expressions for the analytical solutions of electroosmosis consolidation under common loading patterns are given. The correctness of the proposed solutions is verified by comparing the degenerative analytical solutions in this study with the existing analytical solutions, combined with the comparison between the calculated results of the proposed solutions and the finite difference solutions. Based on the proposed analytical solutions, the effects of the related parameters on the electroosmosis consolidation characteristics of soft soils are analyzed. The results show that the existence of the threshold potential gradient reduces the absolute value of the excess pore water pressure and the settlement of soft soils. The decrease in hydraulic permeability coefficient is conducive to electroosmosis consolidation. The settlement of soft soils increases with the increasing ratio of electroosmosis permeability coefficient to hydraulic permeability coefficient, which leads to a better drainage and consolidation effect. When the soft soils are strengthened by the combined electroosmosis and surcharge preloading, the electroosmosis reduces the maximum value of the positive excess pore water pressure caused by time-dependent loading, which is helpful in improving the stability of soft soils during the consolidation process.
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图 3 本文解析解与有限差分解比较
Figure 3. Comparison between proposed analytical and finite difference solutions
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图 4 起始电势梯度对超孔隙水压力的影响
Figure 4. Effects of threshold potential gradient on excess pore water pressure
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图 5 起始电势梯度对固结度的影响
Figure 5. Effects of threshold potential gradient on degree of consolidation
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图 6 电渗透系数和水力渗透系数比值对超孔隙水压力的影响
Figure 6. Effects of ratio of electric permeability coefficient to hydraulic permeability coefficient on excess pore water pressure
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图 7 电渗透系数和水力渗透系数比值对固结度的影响
Figure 7. Effects of ratio of electric permeability coefficient to hydraulic permeability coefficient on degree of consolidation
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图 8 残余电压对超孔隙水压力的影响
Figure 8. Effects of residual voltage on excess pore water pressure
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图 10 变荷载对超孔隙水压力的影响
Figure 10. Effects of time-dependent loading on excess pore water pressure
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图 11 变荷载对固结度的影响
Figure 11. Effects of time-dependent loading on degree of consolidation
表 1 软土地基的计算参数
Table 1 Parameters of soft soils
参数 取值 参数 取值 土体厚度H/m 1.0 固结系数Cv/(m2·s-1) 9.68×10-7 初始电渗透系数
ke0/(m2·s-1·V-1)1.2×10-9 起始电势梯度
ieo/(V·m-1)5.0 初始水力渗透系数kv0/(m·s-1) 9.5×10-9 q0/kPa 0 有效电压随时间衰减系数b/h-1 2.0×10-5 qu/kPa 100 初始有效电压ϕa/V 100.0 tc/h 100 残余有效电压ϕr/V 50.0 
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