Continuous rigid frame bridges across valleys are often at the risk of rockfalls caused by heavy rainfalls, earthquakes and debris flows in a mountainous country. Hollow thin-walled bridge piers (HTWBP) in valleys are exposed to the threat of the impact of accidental rockfalls. In the current research, ANSYS/LS-DYNA is used to establish a high-precision rockfall-HTWBP model. The rockfall-HTWBP model is verified against a scaled impact test of a previous research. A mesh independence test is also performed to obtained an appropriate mesh size. Based on the rockfall-HTWBP model, the impact force, damage and dynamic response characteristics of HTWBP under the rockfall impact are studied. In addition, a damage assessment criteria is proposed based on the response surface model combined with Central Composite Design method and Box-Behnken Design method. The main conclusions are as follows: 1）The impact force of rockfall has a substantial impulse characteristic, and the duration of the impulse load is approximately 0.01s. 2）The impacted surface of the pier is dominated by the final elliptic damage with the conical and strip damage areas as the symmetry axis. The cross-sectional damage mode is compression failure in the impact area and shear failure at the corner. 3）The maximum displacement occurs in the middle height of the pier. The maximum displacement increases with impact height, impact velocity and rockfall diameter and decreases with the uniaxial compressive strength of the concrete. 4) The initial impact velocity and diameter of the rockfall are the most significant parameters affecting the damage indices. In addition, a damage assessment method with a damage zoning diagram based on the response surface method is established for the fast assessment of the damage level of impacted HTWBP.