In the rockfall prevention and control project, the reinforced concrete (RC) slab and sand (gravel soil) soil cushion layer are commonly used to form the protection structure, thereby resisting the rockfall impact. Considering that the oversized deformation of the cushion layer under impact load using the finite element simulation cannot converge, this article establishes a numerical calculation model using smoothed particle hydrodynamics–finite-element method coupling (SPH–FEM). First, the standard Lagrange finite-element mesh is established for the whole model using ABAQUS, and then the finite-element mesh of the soil cushion layer is converted to SPH particle at the initial moment of the calculation, and finally the calculation results are solved and outputted. The results indicate that, compared with the results of the outdoor rockfall impact test, the relative errors of the rockfall impact force and the displacement of the RC slab are within 10%, which proves the rationality of the coupling algorithm; moreover, in terms of the numerical simulation, the SPH–FEM coupling algorithm is more practical than the finite element for reproducing the mobility of the rockfall impacting the sand and soil particles. In addition, at an impact speed of less than 12 m·s−1, the cushion layer is able to absorb more than 85% of the impact energy, which effectively ensures that the RC slab is in an elastic working state under small impact energy and does not undergo destructive damage under large impact energy; the peak impact force of the rockfall is approximately linear with the velocity, and the simulated value of the peak impact force is basically the same as that of the theoretical value of Hertz theory; the numerical simulation is good for reproducing the damage process of the RC slab in accordance with the actual situation. The SPH–FEM coupling algorithm is more justified than the FEM in simulating the large deformation problem, and it can provide a new calculation method for the design and calculation of the rockfall protection structure.

中文翻译：

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基于光滑粒子流体力学与有限元耦合的垫层-钢筋混凝土板落石冲击动力响应研究

在落石防治工程中，常用钢筋混凝土（RC）板和砂（砾石土）土垫层层形成防护结构，从而抵抗落石冲击。针对有限元模拟中缓冲层在冲击载荷作用下变形过大无法收敛的问题，采用平滑粒子流体力学-有限元法耦合（SPH-FEM）建立了数值计算模型。首先利用ABAQUS对整个模型建立标准的拉格朗日有限元网格，然后在计算初始时刻将土垫层有限元网格转换为SPH粒子，最后求解计算结果并输出。结果表明，与室外落石冲击试验结果相比，落石冲击力与RC板位移的相对误差均在10%以内，证明了耦合算法的合理性；此外，在数值模拟方面，SPH-FEM耦合算法比有限元更实用，可以再现落石冲击沙土颗粒的活动性。此外，冲击速度小于12 m·s−1缓冲层能够吸收85%以上的冲击能量，有效保证RC板在小冲击能量下处于弹性工作状态，在大冲击能量下不发生破坏性损坏；落石峰值冲击力与速度近似呈线性关系，峰值冲击力模拟值与赫兹理论理论值基本一致；数值模拟有利于根据实际情况再现RC板的损伤过程。SPH-FEM耦合算法在模拟大变形问题时比FEM更合理，可为落石防护结构的设计计算提供新的计算方法。