In geo-engineering, mechanical problems of surcharge loads acting on ground surface and shallow tunnel excavation are often encountered. When the complex variable method is applied, such problems turn to non-zero resultant issues and generally result in infinite displacement singularity in geomaterial at infinity, which violates the fact that displacement components at infinity should be zero in field observations. The displacement singularity at infinity caused by non-zero resultants corresponds non-zero coefficients of logarithmic items in complex potentials. To eliminate the singularity at infinity, the symmetrical method is adopted so that the far-field displacement obtained from the modified displacement solution conducted by the complex variable method would be logically identical to the reality. Two fundamental cases of single surcharge load acting on ground surface and single tunnel excavation are presented to verify the modified displacement solution, and good agreements are observed. The main advantage that the proposed solution eliminates displacement singularity at infinity and makes far-field displacement logically accord with field observation is presented by comparing to the original solution. The drawback that the proposed solution is dependent on modified depth is discussed as well.

中文翻译：

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超载荷载与浅埋隧道开挖位移的修正复变量法

在地质工程中，经常会遇到超载荷载作用于地表和浅层隧道开挖等力学问题。当应用复变量法时，这类问题会转为非零结果问题，一般会导致地材在无穷远处出现无限位移奇异性，这违背了野外观测中无穷远位移分量应为零的事实。由非零合力引起的无穷远位移奇点对应复势中对数项的非零系数。为了消除无穷远奇点，采用对称法，使复变量法修正位移解得到的远场位移在逻辑上与实际一致。提出了单一超载荷载作用于地表和单一隧道开挖的两个基本情况，以验证修改后的位移解，并观察到良好的一致性。与原解相比，该解的主要优点是消除了无穷远位移奇异性，使远场位移在逻辑上符合现场观测。还讨论了所提出的解决方案依赖于修改后的深度的缺点。与原解相比，该解的主要优点是消除了无穷远位移奇异性，使远场位移在逻辑上符合现场观测。还讨论了所提出的解决方案依赖于修改后的深度的缺点。与原解相比，该解的主要优点是消除了无穷远位移奇异性，使远场位移在逻辑上符合现场观测。还讨论了所提出的解决方案依赖于修改后的深度的缺点。