Published Resources Details
Journal Article
- Title
- Critical planes and curves of rupture in cohesive material
- In
- Transactions of the Institution of Engineers Australia
- Imprint
- vol. 9, 1928, pp. 147-212
- Url
- https://search.informit.org/doi/10.3316/informit.265030678600523
- Abstract
Cohesive Material is what has resistance to shear apart from that due to friction ; such resistance is called the Cohesion, and is concomitant with Tensile Strength. The author considers cohesion as an external stress introduced on a plane in frictional non-cohesive material, and shows that in cohesive material, principal planes exist differing in direction and amount from those for no-cohesion. The equations for obtaining the principal stresses are developed and solved. When cohesion is present, the Plane of Rupture or 'Critical Plane of Equilibrium' as the author prefers to call it, is infinitesimal, and changes in direction with the ratio of cohesion to the load ; consequently a Curve of Rupture or Critical Curve of Equilibrium exists; the equation of the curve is given. The author shows the existence of 'Twin Critical Curves,' and of 'Twin Reciprocal Critical Curves,' and how and when they function. By simple constructions the precise Critical Curves are represented diagrammatically, and traced from any point to the surface. The results allow of analysis for any variation in friction angle or cohesion. To assume in frictional cohesive earth a plane of rupture of any definite length is wrong, except as an approximation for small or varying cohesions. This is the primary assumption of the Coulomb theory and that of A. L. Bell which are, in this sense, the same. Near the surface, the effect of cohesion predominates : so much so that the Critical Curve there is vertical. The curve only begins to approximate to the Rankine Line at such a depth that the effect of cohesion is very small. The existence of a 'Virtual Angle of Friction' which was assumed in the author's 'Stress in Cohesive Material' is proved. The Ellipse is 'virtual,' not actual. That is to say, it gives the true plane of rupture and stresses thereon, but the true ellipse must be used to obtain the stress on any other plane. However, the Virtual Ellipse gives directly the inclination of the Critical Plane with reference to the vertical; furthermore, it allows the problem to be readily visualised. Under 'Special Cases' an outline is given of the application of the author's method to important practical examples, more especially when amendments to accepted results are involved.