  We investigate the validity of the generalized second law (GSL) of
gravitational thermodynamics in the framework of f(T) modified teleparallel
gravity. We consider a spatially flat FRW universe containing only the
pressureless matter. The boundary of the universe is assumed to be enclosed by
the Hubble horizon. For two viable f(T) models containing
$f(T)=T+\mu_1{(-T)}^n$ and $f(T)=T-\mu_2 T(1-e^{\beta\frac{T_0}{T}})$, we first
calculate the effective equation of state and deceleration parameters. Then, we
investigate the null and strong energy conditions and conclude that a sudden
future singularity appears in both models. Furthermore, using a cosmographic
analysis we check the viability of two models. Finally, we examine the validity
of the GSL and find that for both models it is satisfied from the early times
to the present epoch. But in the future, the GSL is violated for the special
ranges of the torsion scalar T.
