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圆孔扩张理论作为一种相对成熟的理论工具已经广泛运用于岩土工程中的各类问题,但是对于初始孔为椭圆孔的扩孔问题,圆孔扩张理论并不适用.基于保角变换的方法将原物理平面上初始椭圆孔洞的外部映射到像平面上的单位圆外部,将原物理平面上由于椭圆孔洞扩张所产生的位移边界条件转换到像平面上,利用平面复变弹性理论,得到初始椭圆形孔洞孔扩张的弹性解.将论文椭圆孔扩张的退化解与传统圆孔扩张的弹性解进行对比分析,验证椭圆孔扩张弹性解的正确性.续而,针对一算例详细分析了椭圆孔扩张的弹性力学特性.研究结果表明,椭圆孔的退化解与传统的圆孔扩张弹性解完全一致,椭圆孔在弹性扩张过程中长轴方向比短轴方向较难扩张,长轴方向需要的扩张压力比短轴方向的要大.此外,当扩张率a2/a1=0.11/0.1=1.1时,扩张的影响半径为10倍的孔径左右.
As a relatively mature theoretical tool, the theory of circular hole expansion has been widely used in geotechnical engineering, but the theory of circular hole expansion is not suitable for the problem of hole expansion whose initial hole is elliptical. Based on the conformal transformation The method maps the exterior of the initial elliptical hole on the original physical plane to the outside of the unit circle on the image plane and transforms the displacement boundary condition on the original physical plane due to the expansion of the elliptical hole into the image plane. Elastic Solution of Initial Elliptical Hole Expansion. Comparing the elastic solution of the expansion of the elliptical hole with the elastic solution of the traditional circular hole expansion, The results show that the degenerate solution of elliptic hole is completely consistent with the traditional elastic expansion of circular hole, the long axis of elliptical hole is more difficult to expand in the process of elastic expansion than the short axis, and the long axis needs The expansion pressure is larger than that of the short axis, and when the expansion ratio a2 / a1 = 0.11 / 0.1 = 1.1, the influence radius of the expansion is about 10 times the aperture.