Dilatancy is a common concept in the constitutive relationships in the study of rocks

soils

and concretes

etc. In its measurements

dilatancy angle is a primary parameter that

an objective quantity though

is closely related to constitutive models

particularly the Mohr-Coulomb model. This paper presents a comprehensive review for clarification of the origin and nature of dilatancy angle

discusses typical misconceptions about it

and demonstrates the internal connections and implicit assumptions between its different forms of expression under plane strain and triaxial testing conditions. To distinguish from the actual failure surface

we classify the theoretical failure surfaces into two categories－conventional strength-based failure surfaces defined by the Mohr-Coulomb strength criterion

and deformation-based failure surfaces defined by the zero extension line. The relationships of failure surfaces versus dilatancy angle

internal friction angle

and zero extension line are explored. We also discuss the reason that the angle between the displacement increment direction and the theoretical failure surface equals the internal friction angle

by using the Mohr-Coulomb associated flow model under plane strain conditions. And

the objectivity of the indexes in geomechanics is examined and classified. Further

combined with the definition of shear strength

we reveal that the measurement bases of shear strength indexes adopted by direct shear tests and triaxial tests are not exactly the same. For practical measurement of strength indexes

test methods should be selected according to different scenarios. The findings would deepen our understanding of fundamental concepts－such as dilatancy angle

zero extension line

failure surface

and shear strength－and their applicable conditions

thereby avoiding confusion and ambiguity.