  The notion of broken $k$-diamond partitions was introduced by Andrews and
Paule. Let $\Delta_k(n)$ denote the number of broken k-diamond partitions of
$n$. They also posed three conjectures on the congruences of $\Delta_2(n)$
modulo 2, 5 and 25. Hirschhorn and sellers proved the conjectures for modulo 2,
and Chan proved cases of modulo 5. For the case of modulo 3, Radu and Sellers
obtained an infinite family of congruences for $\Delta_2(n)$. In this paper, we
obtain two infinite families of congruences for $\Delta_2(n)$ modulo 3 based on
a formula of Radu and Sellers, the 3-dissection formula of the generating
function of triangular number due to Berndt, and the properties of the
$U$-operator, the $V$-operator, the Hecke operator and the Hecke eigenform. For
example, we find that $\Delta_2(243n+142)\equiv
\Delta_2(243n+223)\equiv0\pmod{3}$. The infinite family of Radu and Sellers and
the two infinite families derived in this paper have two congruences in common,
namely, $\Delta_2(27n+16)\equiv\Delta_2(27n+25)\equiv0 \pmod{3}$.
