Theoretical Analysis And Numerical Simulation Of Low-speed Impact Of Half Steel Ball On San

Rockfall is one of the common natural disasters in mountainous areas,posing a great safety threat to local people’s lives,infrastructure and structures.Mountain shed holes play an important role in reducing the impact of falling rocks on roads.A shed hole generally consists of a reinforced concrete load-bearing structure with a sandy soil bedding layer covering the top of the structure.As an easily accessible and good energy dissipator,the sandy soil effectively absorbs the rockfall impact energy and plays the role of protecting the reinforced concrete loadbearing structure.Rockfall impact load is an important factor affecting the design of shed cave structure.At present,there is no unified calculation method for rockfall impact load,and there is a certain blindness in the design of shed cavern structure.Therefore,it is of theoretical and application value to carry out the study of falling stone impact load to guide the design and engineering application of shed cavern structure.Based on the test of low velocity impact of steel hemisphere on sandy soil,the paper combines theoretical analysis and numerical simulation to investigate the influencing factors of falling stone impact load and its change law,and conducts research on the analytical method of distributed stress at the bottom of sandy soil under falling stone impact.The study contents and results are as follows:(1)A reinforced concrete reaction force test base was designed and fabricated independently,and 16 sets of tests were conducted for low-speed impact drying of sand with a245 mm diameter steel hemisphere.The key parameters of the tests were sand soil thickness(0.2 m～0.5 m)and falling stone impact height(0.5 m～2.0 m).The changes of the sand soil thickness and impact height on the impact force of falling stones and the reaction force distributed at the bottom of the sand soil were analyzed and studied.The test results showed that the time course curves of the impact force of falling stones and the time course curves of the distributed reaction force at the bottom of the sand soil were similar,and both showed fluctuation decay.The time course curve of the bottom center reaction force of the sand soil lagged behind the time course curve of the falling stone impact force by about 1 ms～3 ms.The maximum impact force of the falling stone and the peak reaction force of the bottom center of the sand soil were linearly increasing with the impact height.(2)Numerical simulations of falling rocks impacting sandy soils were carried out using smooth particle hydrodynamics(SPH)coupled with finite element method(FEM).Numerical simulations were performed by varying the impact height and the thickness of the sandy soil for the case of falling rocks impacting the sandy soil.The results show that the coupled SPHFEM method reproduces the whole process of falling stone impacting sandy soil well.The variation law of the falling stone impact force and the distributed reaction force at the bottom of the sandy soil obtained from the numerical simulation is basically consistent with the test.Compared with the experimental results,the errors of the maximum impact force of the falling stone and the peak of the distributed reaction force at the bottom of the sand soil given by the numerical model are less than 10%.The peak stresses at the bottom of the sand soil are approximately distributed as a Gaussian function.There is a linear ratio between the maximum impact force of falling stones and the peak stress at the center point of the sand bottom.(3)A theoretical analysis of the stress law at the bottom of the sandy soil under rockfall impact was carried out.By analyzing the calculation results of the numerical model,it is found that the stress distribution at the bottom of the sandy soil is similar to the structure of the Boussinesq solution.A point force model was introduced on the basis of the Boussinesq solution,and a general calculation formula for the stress distribution at the bottom of the sandy soil under rockfall impact was proposed by combining the calculation results of the numerical model.The calculation results using this formula are compared and analyzed with the experimental results,and it is shown that the Boussinesq solution based on the static conditions can reasonably predict the dynamics of the sandy soil under the impact of falling rocks within the parameters of this test.The results of the study are useful for determining the quantitative calculation of the distributed reaction forces at the bottom of the sandy soil under the impact of falling rocks.