See
http://www.math.uwaterloo.ca/~nwormald/papers/2connected.pdf
- Kemkes, Graeme; Sato, Cristiane M.; Wormald, Nicholas, Asymptotic enumeration of sparse $2$-connected graphs, Random Struct. Algorithms 43, No. 3, 354–376 (2013). Zbl 1273.05127. PDF
and references therein (in particular, to the Erdos/RenyiErdős–Rényi paper).
