On accumulation points of volumes of log surfaces

Let $mathcal Csubset(0,1]$ 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 $overline{mathcal C}subsetmathbb Q$ then all accumulation points of volumes are rational numbers, solving a conjecture of Blache. For the set of standard coefficients $mathcal C_2={1-frac{1}{n}mid ninmathbb N}cup{1}$ we prove that the minimal accumulation point is between $frac1{7^2cdot 42^2}$ and $frac1{42^2}$.