Limiting stress states and CS

The treatment of the vector components of stress on slip planes up to here in this book would have been familiar to eighteenth-century engineers such as Coulomb. All changed after Cauchy (1789–1857). Late nineteenth- and twentieth-century engineers learned about the stress and strain circles that will be developed in this section. For a student who needs to familiarise themselves with the mathematical concepts of stress and strain, a starting point is that properties do not change when samples are moved from place to place or are trimmed. This is the principle behind soil sampling and laboratory testing, and it is also behind the concept of strain. Triaxial and simple shear test specimens look different, but the two tests can be shown to be fully equivalent by this principle. The shape changes in Figure 4.1 are linked with strain increments in the triaxial and the simple shear tests. In Figure 4.1 a square element of a plane body is moved and trimmed in five steps that restore it to the original shape. Step a** is simple shear distortion. Step b* is rotation. Step c* trims corners of the specimen, to leave a rectangular shape without displacement or distortion. Step d** distorts the rectangle back to the original square. Step e* rotates it back to the original position. The deformation geometry of the specimen in steps a** and d** resembles the simple shear apparatus (SSA) and the triaxial test. These deformations do not involve slip on any plane.