In this talk, I will show that the positive Lyapunov exponents imply non-uniformly expanding for partially hyperbolic systems under a certain assumption. As a result, I will show that there exists a physical SRB measure for a $C^{1+\alpha}$ diffeomorphism map $f$ that admits a dominated splitting under assumptions that $f$ has non-zero Lyapunov exponents for Lebesgue at almost every point.