Shape Effect of Rockfall Impacting Sandy Soil Cushion Layer–Reinforced Concrete Slab Composite Structure


  • Xuefeng MEI Weifang University of Science and Technology
  • Teng WANG Weifang University of Science and Technology
  • Tian SU Shandong University of Technology / Krirk University
  • Jianli WU Zhejiang University of Water Resources and Electric Power
  • Dong ZHU The 3rd Geological Brigade of Zhejiang Province
  • Bangxiang LI Shandong University of Technology



rockfall, shape factor, impact response, SPH-FEM coupling method


The impact effects of falling rocks on sand–reinforced concrete slab composite protective structures involve several factors. Among them, the existing codes are unable to consider the effect of rockfall shape and the angle of contact between the rockfall and the object on the impact force as well as the depth of penetration. Based on extensive field investigation, this paper proposes a shape factor to simplify the rockfall into an ellipsoid and determines the shape and dimensions of the rockfall by three-dimensional axis length. Besides, a coupled SPH-FEM numerical calculation model is established and validated through comparison with a large-scale outdoor test of a rockfall impact protection structure. Finally, the effects of rockfall shape and impact angle on the symbolic parameters including impact force, impulse and energy in the impact process are revealed. The findings indicate that the maximum force and displacement of the midpoint of the bottom of the reinforced concrete slab have relative errors within 5.0 % when compared to the model test, confirming the precision of the models discussed in this paper. For the same rockfall, the peak force decreases with the impact angle increasing; taking the same volume of spherical rockfall as the reference, under the same rockfall pattern, the peak impact force and impulse amplification factor decreases with the increase in contact attitude angle. Additionally, the scaling effect becomes more pronounced when the shape factor of the rockfall is smaller; under the same shape factor, the impact depth of the cushion layer is the smallest when the attitude angle is 45°, and the maximum when the impact angle is 90°; the SPH-FEM coupling algorithm could reasonably reproduce the pit-forming process of sand and soil, and it is very effective in simulating the flow effect of soil particles under impact.