Analytical solution of one-dimensional electroosmotic consolidation considering the thermal effect
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摘要:
近年来，电渗法是疏浚淤泥最有效的地基处理方法之一，但较少学者考虑温度对电渗固结的影响。为探究温度场对电渗固结特性的影响，基于热弹性理论和Esrig电渗固结理论，建立了耦合热平衡和渗流特性的控制方程，利用变量代换和分离变量法，推导了超静孔隙水压力和固结度的解析解，验证了不考虑热效应的电渗固结解为Esrig解，并与模型试验对比，验证了所得解析解的合理性。基于所提解析解与Esrig解的对比，讨论了不同深度、温度、电压对土体电渗固结性状的影响，结果表明：相同电压和温度作用下，在土体不同深度，考虑热效应的电渗固结（简称“TE”）产生的超静孔压消散速度比Esrig电渗固结（简称“E”）产生的孔压更快，且产生的最终孔压值越大。相同深度和电压作用下，温度的上升，TE孔压相比于E孔压，从73%上升至155%；相同深度和温度作用下，电压增加，TE孔压与E孔压增加幅度几乎一致；不同温度与电压下，TE和E固结度的变化较小。热电耦合固结的试验与理论分析为实际工程应用提供了理论指导。
Abstract:In recent years, electro-osmotic method is an effective foundation treatment method for dredged silt; however, few studies have focused on the influence of temperature on the electro-osmotic consolidation. To explore the influence of temperature field on electroosmotic consolidation characteristics, based on the thermos-elasticity theory and the Esrig’s electro-osmotic consolidation theory, the governing equations of coupled heat balance and seepage characteristics were established, and the analytical solutions of excess pore water pressure and the degree of consolidation were derived by using the methods of algebraic transformation and variable separation. The correctness of the proposed solutions was verified by comparing the degenerative analytical solutions with the Esrig’s theory, combined with the model test. Then the effects of the different depths, the temperature, and the voltage on the electroosmotic consolidation behavior of soil were analyzed. Under the same voltage and temperature, the dissipation rate of excess pore pressure generated by electroosmotic consolidation (TE) considering thermal effect is faster than that generated by Esrig electroosmotic consolidation (E), and the final pore pressure of the former is larger than that of latter. Under the same depth and voltage, with the temperature increase, the TE pore pressure increases from 73% to 155% compared with the E pore pressure. Under the same depth and temperature, with the voltage increase, the increase of TE pore pressure is similar to E pore pressure. Under different temperatures and voltages, the degree of consolidation of TE and E changes little. The experimental and theoretical analysis of thermoelectric coupling consolidation can provide theoretical guidance for practical engineering applications.
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Key words:
- electroosmosis /
- thermal effect /
- consolidation /
- analytical solution
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表 1 电渗透系数参数统计
Table 1. Electrical permeability coefficient parameters
温度/°C 电渗透系数/（cm2·s−1·V−1） 最大值 最小值 平均值 式（16）计算值 45 2.76×10−5 1.70×10−5 2.29×10−5 2.38×10−5 55 4.90×10−5 3.04×10−5 3.57×10−5 3.44×10−5 65 6.27×10−5 3.11×10−5 4.79×10−5 4.50×10−5 
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表 2 土体物性参数
Table 2. Soil physical parameters
参数 取值 土体高度/m 1 水力渗透系数/（m·s−1） 2.0×10−9 土的压缩系数/kPa−1 2.5×10−4 泊松比 0.4 热传导系数/（W·m−1·°C−1） 1.5 土颗粒热膨胀系数/°C−1 3×10−5 水热膨胀系数/°C−1 2×10−4 孔隙率/% 0.5 土颗粒比热/（J·g−1·°C−1） 1.5 水的比热/（J·g−1·°C−1） 4.2 水的密度/（g·m−3） 1.0×106 土颗粒密度/（g·m−3） 2.8×106
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