Principle and application of pole point method of Mohr's circle

Mohr's circle is a geometric representation of the two-dimensional stress state and is very useful to perform quick and efficient estimations. It is also popularly used in geotechnical fields such as soil strength, stress path, earth pressure and bearing capacity. It is often used to interpret the test data, to analyze complex geotechnical problems, and to predict soil behaviors. The pole point on Mohr's circle is a point so special that it can help to readily find stresses on any specified plane by using diagram instead of complicated computation. However, the orientation of the pole point on Mohr's circle is closely related to the directions of stresses. In soil mechanics, conventionally, because the compressive normal stress is positive, the positive shear stress should be appropriately defined for using the pole point method correctly. Based on the equilibrium of the isolated element, the positive shear stress will cause a counterclockwise rotation of the infinitesimal element. In addition, the uniqueness of the pole point is verified by using the proof by the contradiction. The validity of the pole point method is testified by the corresponding theoretical method. It is concluded that the pole point method is used much more easily than the theoretical method. Finally, two relatively complex examples are given by using the pole point method to determine the stress state and the discontinuity in the undrained soils, respectively.