  Following earlier study regarding Einstein-Gauss-Bonnet-massive black holes
in the presence of Born-Infeld nonlinear electromagnetic field [S. H. Hendi, B.
Eslam Panah and S. Panahiyan, arXiv:1510.00108], we study thermodynamical
structure and critical behavior of these black holes through various methods in
this paper. Geometrical thermodynamics is employed to give a picture regarding
phase transition of these black holes. Next, a new method is used to derive
critical pressure and horizon radius of these black holes. In addition, Maxwell
equal area law is employed to study the Van der Waals like behavior of these
black holes. Moreover, the critical exponents are calculated and by using
Ehrenfest equations, the type of the phase transitions are determined.
