Discussion of “Circular and Logarithmic Spiral Slip Surface”

Mr. Chen Does Not Agree With the Author in the Conclusion That There Is No Justification for Assuming That the Shape of the Spiral Is Determined by the Value of the Angle of Shearing Resistance. The Results Reported Emphasize the Point That the Particular Choice of the Angle of the Spiral Curve Being Equal to the Angle of Shearing Resistance of the Soil Is a Very Proper One. The Various Normal Stress Assumptions for the Circular Arc Slip Surface Lead Only to Minor Differences in the Stability Conditions, as Pointed Out by Taylor. The Results Reported by the Author Further Demonstrate That the Stability Conditions Are Not Sensitive to the Various Shapes of the Spiral Surface for Which the Circular Arc Is a Special Case. The Problem of Finding the Distribution Function Is Stated. The Use of Spiral Surface of the Angle Does Not Require the Assumption of Normal Stress Distribution Along the Surface And, in Addition, Permits the Stability Problem to Be Solved in a Relatively Simple Mathematical Form. Mr. Da Silveira Presents the Results of Study on the Question of Shearing Forces on Vertical Planes, Which Are Connected to the Validity of the Hypothesis of Slip Surfaces for the Investigation of the Limit Equilibrium of Soils. The Method of Virtual Work Gives the Safety Factor as the Ratio Between the Resisting Work Forces to the Work Realized by Disturbing Forces, if Only Tangential Forces, Applied Along the Sliding Surfaces, Are Considered. Results Presented in a Table Express Conclusively That the Cylinder of Revolution Must Be the Sliding Surface Corresponding to the Limit Equilibrium for This Loading Case. A Digital Computing Program Can Be Easily Modified to Be Used for Checking Different Sliding Surfaces and the Effect of Any Load Groups. References: Circular and Logarithmic Spiral Slip Surfaces, Eric Spencer, Asce Proc. Paper 6361, January 1969.