Study On Dynamic Response Of Submerged Floating Tunnel Under The Explosion Effect

As a new type of traffic structure,the submerged floating tunnel(SFT)is very forward-looking.However,there are still many problems to be solved if the SFT is to be used in the actual construction.Among them,the SFT is affected by extreme load,which is the key problem in the construction and operation of the tunnel.In order to clarify the response of the SFT under underwater explosion,the main research contents and conclusions of this paper are as follows.The boundary of the submerged floating tunnel is set as a flexible dynamic boundary,and the influence of the support stiffness and damping is considered.The first mode of single span submerged floating tunnel is approximately the superposition of the first mode of simply supported beam and the horizontal motion of elastic supported rigid beam.At the same time,shock wave load and bubble fluctuating pressure are considered.The function of water is considered by using Morsion equation.According to D’Alembert principle,the dynamic balance equation is obtained.Based on Geers and hunter’s theory,the former loading stage provides the initial conditions for the latter.By using Galerkin method to solve the vibration differential equation,the analytical solutions of the displacement equation in five stages are obtained.The results show that the increase of the stiffness of anchor cable support,the increase of the vibration frequency of the structure and the increase of the sensitivity of the structure to the load are not conducive to the anti vibration of the structure.However,when the stiffness is small,the displacement at the end of the pipe section increases,which affects the structural safety and driving stability.The effect of damping on the maximum displacement in midspan is limited,but the increase of damping has a significant effect on the attenuation of amplitude,which is conducive to structural vibration reduction.If the stiffness of the brace increases,the damping effect will be weakened.The damping should be designed in combination with the stiffness.The vibration effect of the structure can be effectively reduced by increasing the distance between blasting centers in a certain range.The frequency of bubble oscillation may be close to that of tunnel vibration,which may lead to tunnel resonance.The analysis model of the submerged floating tunnel with cylindrical shell is established.According to the constitutive equation of love cylindrical shell,two kinds of vibration differential equations are established.The method of mode orthogonal and mode superposition is used to solve the equation in frequency and time domain.Finally,according to Duhamel integral,the displacement function of structure under generalized force is obtained.The distance difference between the explosion center and any point on the cylindrical shell surface and the time difference of shock wave propagation are considered for the explosion load.Based on the potential flow theory,the hydrodynamic pressure is calculated by velocity potential and the effect of hydrostatic pressure is considered.The results show that the vibration frequency and the maximum displacement of the cylindrical shell model are larger than that of the beam model under the same span.The response of the submerged floating tunnel of the cylindrical shell model to the load is more intense.The longer the pipe span is,the more difficult it is to stop the forced oscillation.Under different simplified structure models and load models,the conclusions of the two models are similar.That is to say,when the distance between blasting centers is in the range of 0-25 m,increasing the distance between blasting centers can effectively reduce the vibration effect of the structure;after 50 m,increasing the distance between blasting centers has no significant effect on the vibration reduction of the structure.In this paper,the concept of the limit distance between explosive centers is put forward,which is used to determine the minimum distance between explosive centers that will cause harm to human body when the explosive quantity is determined.The relationship between the explosive quantity and the limit distance between explosive centers can provide a reference for underwater blasting to prevent the human body in the tunnel from being damaged.The formula of damage area length can be used to estimate the range of human injury in tunnel after underwater explosion,so as to rescue in time.The stress and strain of tunnel structure are in direct proportion to the explosive quantity and in inverse proportion to the distance between blasting centers.After the explosion,the structure will have a large amplitude of repeated stretching and compression process in a short time.Energy absorption and vibration reduction protective layer shall be installed outside the tunnel to prevent possible damage.The damage scope and change of tunnel body are similar to human body,and the damage at the center point is the largest,and the center point is the origin of elliptical.