  In a Bruhat-Tits building of split classical type (that is, of type $A_n$,
$B_n$, $C_n$, $D_n$, and any combination of them) over a local field, the
simplicial volume counts the vertices within the given simplicial distance from
a special vertex. This paper aims to study the asymptotic growth of the
simplicial volume. A formula of the simplicial volume is deduced from the
theory of concave functions. Then the dominant term in its asymptotic growth is
found using the theory of $q$-exponential polynomials developed in this paper.
