考虑有效电势衰减的一维电渗固结多态继承计算方法

doi:10.13722/j.cnki.jrme.2019.1177

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摘要有效电势的衰减在电渗排水过程中客观存在，经典一维电渗固结理论不能考虑电势的变化，其结果高估了电渗法的加固效果。针对该问题，依据黎曼积分求和的思路，对有效电势衰减函数进行多态处理，将连续函数转化为离散的状态段，并考虑有效电势衰减与孔压在时间维度上的统一性，利用前、后状态段初始条件继承的方式，将有效电势衰减下的一维电渗固结计算转化为了对单一状态段的反复迭代求解。采用Crank-Nicolson形式对控制方程进行了离散，利用Python进行了该方法的编程实现，进行了3，6，20状态段数下的计算，并与经典理论结果进行了对比分析，结果表明：(1) 考虑电势衰减的孔压幅值要明显低于经典一维固结理论，多态继承的计算方法能够有效地反映出电势衰减带来的影响；(2) 孔压曲线会在分段处发生幅值的突变，并且随着状态段数量的增加，突变现象逐渐降低；(3) 在阳极处，电势衰减的影响最明显，孔压的降低幅度最大。该方法的求解思路清晰、简洁，能够为电渗排水法的实际应用提供良好的理论支持。

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关键词 ：土力学, 一维电渗固结理论, 有效电势衰减, Crank-Nicolson法, Python数值计算

Abstract：The classical one-dimensional electro-osmosis consolidation theory cannot consider the attenuation of the effective potential，which exists objectively in the electro-osmotic process，and hence, overestimates the result of electro-osmosis. Aiming at this problem，theoretical and numerical studies are carried out. According to the idea of Riemann integral summation，the effective potential decay function is reduced to polymorphic form. Considering the uniformity of effective potential decay and pore pressure dissipation in the time dimension，one-dimensional electro-osmotic consolidation calculation under effective potential decay is transformed into iterative solution for a single state segment by inheritance of initial conditions. The governing equation is discretized by using the Crank-Nicolson form，and programming is implemented by using Python. The calculations under the three-segment numbers of 3，6，and 20 were carried out and compared with the classical theoretical results. The results show that the pore pressure amplitude considering the potential decay is significantly lower than that from the classical one-dimensional consolidation theory，and the developed method of polymorphic inheritance can effectively reflect the influence of the potential decay. The pore pressure curve will have a sudden change in amplitude at the segment points，while the mutation phenomenon gradually weakens gradually as the number of state segments increases. At the anode，the effect of the potential decay is most pronounced，and the reduction of the pore pressure is greatest. The method is clear and concise，and can provide good theoretical support for practical application of electro-osmotic drainage method.

Key words： soil mechanics one-dimensional electroosmosis consolidation theory effective potential decay Crank-Nicolson method python numerical calculation

引用本文:

杨晓宇1，2，董建华1，2. 考虑有效电势衰减的一维电渗固结多态继承计算方法[J]. 岩石力学与工程学报, 2020, 39(12): 2530-2539.
YANG Xiaoyu1，2，DONG Jianhua1，2. A polymorphic inheritance calculation method of one-dimensional electro-osmotic consolidation considering effective potential attenuation. , 2020, 39(12): 2530-2539.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2019.1177 或 http://rockmech.whrsm.ac.cn/CN/Y2020/V39/I12/2530

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