We generalize Nakamaye’s description, via intersection theory, of the augmented base locus of a big and nef divisor on a normal pair with log-canonical singularities or, more generally, on a normal variety with non-lc locus of dimension $\le 1$. We also generalize Ein-Lazarsfeld-Mustaţă-Nakamaye-Popa’s description, in terms of valuations, of the subvarieties of the restricted base locus of a big divisor on a normal pair with klt singularities.