莫尔圆极点确定的新方法

莫尔圆在岩土材料的强度理论、应力路径以及地基承载力等方面具有广泛的应用。极点是莫尔应力圆上的一个特殊点，具有惟一性，通过极点，可以求得任意分析平面的应力状态。特别是对于求解复杂状态下的应力问题，莫尔圆极点法具有简便、快捷的优点。提出了定义极点的新方法--射线法，利用应力隔离体力的平衡法则证明了该方法定义极点的正确性及惟一性，并且发现定义极点的平行线法和法线法是射线法的两种特殊情况。通过比较，发现不同方法所得到的极点位置并不相同，但求得的任意面上的应力状态是相同的，而且平行线法更便于使用。然而，所提出的射线法能加深对莫尔圆极点的理解，从而进一步推动其广泛应用。

A new method for determining pole point of Mohr circle

Mohr circle is extensively used in strength theory of geotechnical materials, stress path and bearing capacity of foundations. The pole point is a special point on the Mohr circle. It is unique and can help to determine stresses acting on any plane. In particular, the pole point method is capable of solving complex stress problems. Based on the parallel line and normal line methods stated in textbooks of soil mechanics and material mechanics, a new method to find the pole point, i.e. the ray method, is put forward. The validity and the uniqueness of the ray method are proved by using the stress equilibrium method of the isolated element. It is concluded that the parallel line method and the normal line method are special cases of the ray method. The pole points obtained by using the parallel line method and the normal line method separately are not in the same position. But the desired stress state for any plane by using the two methods are the same. However, the parallel line method is relatively easy to use. Although the ray method is relatively complex to use, it can help to understand the concept of the pole point thoroughly.