Theoretical study on mechanical properties of rockfall impact concrete shed slabs based on viscoelastic contact
CHEN Taijiang1，ZHANG Guangcheng1，XIANG Xin2
(1. Faculty of Engineering，China University of Geosciences(Wuhan)，Wuhan，Hubei 430074，China；
2. China Three Gorges Corporation，Wuhan，Hubei 430010，China)
Abstract：Concrete shed slab is the main disaster-bearing project for rockfall prevention. In the existing theoreties，the contact model is elastic or elastic-plastic contact，and the shed slab is simplified as a beam or a thin plate element，which leads to underevaluate the impact resistance of shed slabs. Considering the damping characteristics in the contact process between the rockfall and the shed and combining viscoelastic contact theory and orthotropic plates，a mechanical model of rockfall impact shed slab is built up，and then the dynamic control equation of rockfall impacting on shed slab is obtained. According to the different initial conditions，such as the displacement，velocity and acceleration of rockfall，the corresponding theoretical solutions of the characteristic parameters about the impact process are obtained with the differential equation algorithm. In order to verify the correctness of the theoretical solutions，the impact processes of rockfall and shed slabs are simulated by the numerical method. It is shown that the linear elastic model can only approximately describe the rockfall impact process，while the theoretical solution based on the viscoelastic contact model with the initial condition combinations of velocity and acceleration is more similar with the numerical solution. The viscoelastic contact model can consider comprehensively the deformation of the shed slab and the energy loss of rockfall during the impact，which is closer to the actual. The sensitivity of rockfall parameters is analyzed，and the maximum impact force，the time of the maximum impact force and the impact duration of the rockfall are proportional to the rockfall mass. With increasing the rockfall mass，the rockfall impact parameters increase significantly，and the damage to the shed slab would be greater. The proposed theoretical solution in this paper is in good agreement with the experimental results，it provides the guidance for the actual shed protection design.
[1] ASTERIOU P，SAROGLOU H，TSIAMBAOS G. Geotechnical and kinematic parameters affecting the coefficients of restitution for rock fall analysis[J]. International Journal of Rock Mechanics and Mining Sciences，2012，54(9)：103–113.
[2] ARYAEI A，HASHEMNIA K，JAFARPUR K. Experimental and numerical study of ball size effect on restitution coefficient in low velocity impacts[J]. International Journal of Impact Engineering，2010，37(10)：1 037–1 044.
[3] LI Z H，HUANG H W，XUE Y D，et al. Risk assessment of rockfall hazards on highways[J]. Georisk，2009，3(2)：147–152.
[4] BAILLIFARD F，JABOYEDOFF M，SATORI M. Rockfall hazard mapping along a mountainous Road in Switzerland using a GIS-based Parameter rating approach[J]. Natural Hazards and Earth System Science，2003，3(5)：435–442.
[5] 章广成，向 欣，唐辉明. 落石碰撞恢复系数的现场试验与数值计算[J]. 岩石力学与工程学报，2011，30(6)：1 266–1 273.(ZHANG Guangcheng，XIANG Xin，TANG Huiming. Field test and numerical calculation of recovery coefficient of rockfall impact[J]. Chinese Journal of Rock Mechanics and Engineering，2011，30(6)：1 266–1 273. (in Chinese))
[6] 黄润秋，刘卫华，周江平，等. 滚石运动特征试验研究[J]. 岩土工程学报，2007，29(9)：1 296–1 302.(HUANG Ruiqiu，LIU Weihua，ZHOU Jiangping，et al. Experimental study on the motion characteristics of rolling stones[J]. Chinese Journal of Geotechnical Engineering，2007，29(9)：1 296–1 302.(in Chinese))
[7] GIANI G，GIACOMINI A，MIGLIAZZ A，et al. Experimental and theoretical studies to improve rock fall analysis and protection work design[J]. Rock Mechanics and Rock Engineering，2004，37(5)：369–389.
[8] VOLKWEIN A，SCHELLENBERG K，LABIOUSE V，et al. Rockfall characterisation and structural protection-a review[J]. Natural Hazards and Earth System Science，2011，11：2 617–2 651.
[9] DELHOMME F，MOMMESSIN M，MOUGIN J P，et al. Damage mechanisms of a reinforced concrete rock-shed slab impacted by blocks[J]. Journal of Structural Engineering-ASCE，2007，133(10)：1 426–1 433.
[10] DELHOMME F，MOMMESSIN M，MOUGIN J P，et al. Behavior of a structurally dissipating rock-shed：experimental analysis and study of punching effects[J]. International Journal of Solids and Structures，2005，42：4 204–4 219.
[11] HAZARIKA H. Stress-strain modeling of EPS geofoam for large-strain applications[J]. Geotextiles and Geomembranes，2006，24(2)：79–90.
[12] WANG D P，HE S M，WU Y，et al. Cushioning effect of rock sheds with EPS cushion on rock-falls action[J]. Journal of Vibration and Shock，2014，33(4)：199–214.
[13] KAWAHARA S，MURO T. Effects of dry density and thickness of sandy soil on impact response due to rockfall[J]. Journal of Terramechanics，2006，43(3)：329–340.
[14] 何思明，吴 永. 新型耗能减震滚石棚洞作用机制研究[J]. 岩石力学与工程学报，2010，29(5)：926–932.(HE Siming，WU Yong. Research on cushioning mechanism of new-typed energy dissipative rock shed[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(5)：926–932.(in Chinese))
[15] 闫帅星，何思明，李新坡. 滚石冲击作用下钢筋混凝土棚洞板动力学响应及冲切损伤评估研究[J]. 兰州大学学报：自然科学版，2019，55(1)：64–72.(YAN Shuaixing，HE Siming，LI Xinpo. Dynamic responses and punching damage assessment of a reinforced concrete slab impacted by rock-falls[J]. Journal of Lanzhou University：Natural Sciences，2019，55(1)：64–72.(in Chinese))
[16] OLSSEN R. Analytical model for delamination growth during small mass impact on plates[J]. International Journal of Solids and Structures，2010，47(21)：2 884–2 892.
[17] 王东坡，何思明，欧阳朝军，等. 滚石冲击荷载下棚洞钢筋混凝土板动力响应研究[J]. 岩土力学，2013，34(3)：881–886.(WANG Dongpo，HE Siming，OUYANG Chaojun，et al. Study on dynamic response of reinforced concrete slab under rock impact load[J]. Rock and Soil Mechanics，2013，34(3)：881–886.(in Chinese))
[18] 李忠献，岳福青，周 莉. 地震时桥梁碰撞分析的等效Kelvin撞击模型[J]. 工程力学，2008，(4)：128–133.(LI Zhongxian，YUE Fuqing，ZHOU Li. Equivalent Kelvin impact model for bridge impact analysis during earthquake[J]. Engineering Mechanics，2008，(4)：128–133.(in Chinese))
[19] 宋男男. 落石冲击作用下消能棚洞的结构动力破坏机制[硕士学位论文][D]. 重庆：重庆交通大学，2018.(SONG Nannan. Structural dynamic failure mechanism of energy-dissipating shed tunnels under the impact of rockfall[M. S. Thesis][D]. Chongqing：Chongqing Jiaotong University，2018.(in Chinese))
[20] 王 星，周天跃，师江涛，等. 基于自由落体的落石冲击土层的理论及LS-DYNA模拟研究[J]. 北京交通大学学报，2019，43(4)：9–17.(WANG Xing，ZHOU Tianyue，SHI Jiangtao，et al. Theoretical and LS-DYNA Simulation based on the theory of free-fall rockfall impacting on soil layer[J]. Journal of Beijing Jiaotong University，2019，43(4)：9–17.(in Chinese))
[21] 张 伟. 落石冲击下钢筋混凝土板破坏机制的试验研究[硕士学位论文][D]. 西安：西安理工大学，2016.(ZHANG Wei. Experimental study on failure mechanism of reinforced concrete slab under rockfall impact[M. S. Thesis][D]. Xi?an：Xi?an University of Technology，2016.(in Chinese))
[22] 陈泰江，章广成，向 欣. 落石冲击混凝土棚洞力学特性研究[J]. 岩土力学，2022，43(1)：277–285.(CHEN Taijiang，ZHANG Guangcheng，XIANG Xin. Research on the mechanical characteristics of concrete sheds impacted by rockfall[J]. Rock and Soil Mechanics，2022，43(1)：277–285.(in Chinese))
2023, Vol. 42 
