Sand cushions for passive protection structures could reduce the damage that is induced by rockfall impact. Therefore, evaluation of the peak impact force generated by rockfall on the sand cushion is significant to the design of passive protection structures. This study aims to estimate the peak impact force using the elastoplastic linear strengthening model when a rockfall hits the sand cushion. Impact tests were conducted to study the effect of rockfall mass, impact velocity, and cushion thickness on the rockfall impact force. The experimental results indicate that the decreasing rockfall mass, impact velocity, and increasing cushion thickness could decrease the impact force of rockfalls. The sensitivity analysis results show that the main factor that influences the peak impact force is impact velocity, followed by rockfall mass and cushion thickness. In addition, the calculation method for the peak impact force and penetration depth of rockfall was proposed by the elastoplastic linear strengthening model. The impact force-deformation curves of this model were provided and discussed. The relationship between the strengthening coefficient and influencing factors was established. In addition, the simulation results indicate that the elastoplastic linear strengthening model showed good reliability when estimating the impact force compared with the five classical models. The strengthening coefficient of other cushion materials needs to be calibrated.

Reinforced concrete (RC) sheds with sand cushions laying on the top are commonly adopted to resist rockfall impacts. To improve the rockfall-impact resistance of RC shed with sand cushion, this study investigated the buffering performance of sand cushion and examined the effect of sand cushion on the dynamic behaviors of RC shed. Firstly, a series of impact tests on sand cushion were conducted to analyze the influence of cushion thickness and falling height of rockfall on the penetration depth into the cushion, impact force and impact duration, as well as the development of vertical and horizontal stresses inside the cushion. Then, a finite elementdiscrete element coupling model was established to consider the particle interaction of sand cushion under rockfall impacts and impact behaviors of RC shed. Finally, based on the validated numerical analysis method, the effect of sand cushion on the dynamic responses and damage of prototype RC shed subjected to the impact of rockfall was simulated and evaluated. The results showed that: (i) with the increase of cushion thickness, the peak impact force was reduced, but the penetration depth and duration increased; as the falling height elevated, the impact force and penetration depth increased while the duration was shortened; (ii) sand cushion had excellent buffering performance to attenuate vertical and horizontal stresses inside the cushion; (iii) stress diffusion angle formed in the sand cushion can enlarge the load-bearing area at the bottom of the cushion, and the buffering performance of sand cushion can be improved through increasing the stress diffusion angle; (iv) compared with the non-cushion one, the rockfall-impact resistance of RC shed was effectively improved by the sand cushion through reducing impact force, penetration depth, dynamic bending moment and shear force of the shed roof, as well as transforming brittle punching-shear failure of the shed roof into flexural failure.