Abstract
The Mohr-Coulomb theory of strength identifies cohesion and internal friction as the two principal contributions to the shear strength of a granular material. The contribution of cohesion in over-compacted granular materials has been challenged and replacing cohesion with interlocking has been proposed. A theory of rupture strength that includes interlocking is derived herein. The physics-chemistry concept of critical state is elaborated to accommodate granular materials, based on empirical definitions established in the fields of soil mechanics and bulk solids’ flow. A surface in state space, called the critical compaction surface, separates over-compacted states from lightly compacted states. The intersection of this surface with the Mohr-Coulomb envelope forms the critical state surface for a granular material. The rupture strength of an over-compacted granular material is expressed as the sum of cohesion, internal friction and interlocking strength. Interlocking strength is the shear strength contribution due to over-compaction and vanishes at critical state. The theory allows migrations from one critical state to another. Changes in specific volume during such migrations are related to changes in mean-normal effective stress and uncoupled from changes in shearing strain. The theory is reviewed with respect to two established research programs and underlying assumptions are identified.
Highlights
The particulate nature of granular materials distinguishes them from ideal solids and fluids and introduces an order of complexity to mechanical descriptions that is absent in the descriptions for solids and fluids
The rupture strength of an over-compacted granular material is expressed as the sum of cohesion, internal friction and interlocking strength
This paper develops a theory of the rupture strength of an over-compacted granular material and addresses several issues related to the Mohr-Coulomb theory of strength that researchers have raised over the last three decades
Summary
The particulate nature of granular materials distinguishes them from ideal solids and fluids and introduces an order of complexity to mechanical descriptions that is absent in the descriptions for solids and fluids. Finite element software incorporates the mechanical properties of material bodies through so-called constitutive relations. This paper develops a theory of the rupture strength of an over-compacted granular material and addresses several issues related to the Mohr-Coulomb theory of strength that researchers have raised over the last three decades. In 1773, Charles Augustin de Coulomb defined the shear strength of a material as the sum of cohesion and internal friction on a slip plane [2]. Cohesion is the contribution to shear strength related to the area of the plane, and is independent of the normal force on it. Internal friction is the contribution related to the normal force on the plane, and is independent of its area. Jacques Heyman has noted that it was precisely the introduction of two parameters describing the soil properties that is of the utmost importance in Coulomb’s analysis and that no writer before
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