  Let $\mathcal C\subset(0,1]$ be a set satisfying the descending chain
condition. We show that any accumulation point of volumes of log canonical
surfaces $(X, B)$ with coefficients in $\mathcal C$ can be realized as the
volume of a log canonical surface with big and nef $K_X+B$ and coefficients in
$\overline{\mathcal C}\cup\{1\}$, with at least one coefficient in
$Acc(\mathcal C)\cup\{1\}$.
  As a corollary, if $\overline{\mathcal C}\subset\mathbb Q$ then all
accumulation points of volumes are rational numbers, solving a conjecture of
Blache.
  For the set of standard coefficients $\mathcal C_2=\{1-\frac{1}{n}\mid
n\in\mathbb N\}\cup\{1\}$ we prove that the minimal accumulation point is
between $\frac1{7^2\cdot 42^2}$ and $\frac1{42^2}$.
