Experimental investigation on dynamic response and damage models of circular RC columns subjected to underwater explosions

Reinforced concrete(RC) columns are widely used as supporting structures for high-piled wharfs.The study of damage model of a RC column due to underwater explosion is a critical issue to assess the wharfs antiknock security.In this study,the dynamic response and damage model of circular RC columns subjected to underwater explosions were investigated by means of scaled-down experiment models.Experiments were carried out in a 10.0 m diameter tank with the water depth of 2.25 m,under different explosive quantities(0.025 kg-1.6 kg),stand-off distances(0.0 m-7.0 m),and detonation depths(0.25 m-2.0 m).The shock wave load and dynamic response of experiment models were measured by configuring sensors of pressure,acceleration,strain,and displacement.Then,the load distribution characteristics,time history of test data,and damage models related to present conditions were obtained and discussed.Three damage models,including bending failure,bending-shear failure and punching failure,were identified.In addition,the experie nce model of shock wave loads on the surface of a RC column was proposed for engineering application.

The damage to model concrete gravity dams subjected to water explosions

Over the past century,the safety of dams has gradually attracted attention from all parties.Research on the dynamic response and damage evolution of dams under extreme loads is the basis of dam safety issues.In recent decades,scholars have studied the responses of dams under earthquake loads,but there is still much room for improvement in experimental and theoretical research on small probability loads such as explosions.In this paper,a 50-m-high concrete gravity dam is used as a prototype dam,and a water explosion model test of a 2.5-m-high concrete gravity dam is designed.The water pressure and the acceleration response of the dam body in the test are analysed.The pressure characteristics and dynamic response of the dam body are assessed.Taking the dam damage test as an example,a numerical model of concrete gravity dam damage is established,and the damage evolution of the dam body is analysed.By combining experiments and numerical simulations,the damage characteristics of the dam body under the action of different charge water explosions are clarified.The integrity of the dam body is well maintained under the action of a small-quantity water explosion,and the dynamic response of the dam body is mainly caused by the shock wave.Both the shock wave and the bubble pulsation cause the dam body to accelerate,and the peak acceleration of the dam body under the action of the bubble pulsation is only one percent of the peak acceleration of the dam body under the action of the shock wave.When subjected to explosions in large quantities of water,the dam body is seriously damaged.Under the action of a shock wave,the dam body produces a secondary acceleration response,which is generated by an internal interaction after the dam body is damaged.The damage evolution process of the dam body under the action of a large-scale water explosion is analysed,and it is found that the shock wave pressure of the water explosion causes local damage to the dam body facing the explosion.After the peak value of the shock wave,the impulse continues to act on the dam body,causing cumulative damage and damage inside the dam body.

Blast resistance of air-backed RC slab against underwater contact explosion

Reinforced concrete(RC)structures are common in engineering,and usually exposed to air or water,may be subjected to various blast scenarios.This paper aims to investigate the blast resistance of an airbacked RC slab against underwater contact explosions(UWCEs).A detailed numerical model based on CLE method considering explosive,water,air,and RC slab is developed to examine the structural behavior of the air-backed RC slab due to UWCEs.At first,the reliability of the numerical method is validated by comparing the numerical results of an UWCE test with experimental data.Then,the difference in dynamic behavior of air-backed and water-backed RC slabs due to UWCEs is explored with the calibrated model.The results indicate that the blast response of the air-backed slab induced by UWCE is fiercer than that of water-backed slab with equal charge mass.In addition,parametric studies are also conducted to explore the effects of the charge mass,standoff distance,reinforcement spacing,concrete compression strength,and boundary condition on the blast performance of the air-backed RC slab.

一种评估非接触水下爆炸对海军复合船体影响的设计方法

Despite the non-contact underwater explosion phenomena(UNDEX)have been studied for decades and several numerical methods have been proposed in literature,its effects on military structures,especially composite ones,are even nowadays matter of research.In early design phases,it is not always possible to verify the shock resistance of hull structures modelling the whole phenomenon,in which fluid,gas and solid properties must be properly set in a fully coupled fluid-structure interaction(FSI)numerical model.These ones are extremely complex to set,computationally demanding and certainly not suitable for everyday design practice.In this paper,a simplified finite element(FE)model,easy to use in an early design phase,is proposed.Both,the structure and the fluid are simulated.In this approximation,the fluid behaviour is simplified,using special finite elements,available in a commercial software environment.This choice reduces the computational time and numerical efforts avoiding the problem of combining computational fluid dynamics(CFD)and FE domains and equations in a fully coupled fluid-structure interaction model.A typical parallel body block of a minesweeper is modelled,using two-dimensional multi-layered shell elements to properly account for the composite materials behaviour.For the fluid instead,three dimensional volumetric elements,directly coupled to the structural elements,are placed.In addition,the same calculation is performed,modelling separately fluid in the CFD environment and structures in the finite element one.Thus,realizing a fully coupled fluid-structure interaction model.The results obtained by applying both numerical models are compared with the structural response measured on board of a composite ship during a full-scale shock test.The simplified proposed procedure provides results in satisfactory agreement with experiments,allowing the validation of the model.Approximations are discussed and differences with the real phenomenon and fully coupled CFD+FE method are shown,providing a better understanding of the phenomena.Eventually,the modelling strategy has been considered a valuable and cost-effective tool for the concept and preliminary design of composite structures subject to underwater explosions.

3-D NUMERICAL SIMULATION OF UNDERWATER EXPLOSION BUBBLE

The problem is solved by use of the boundary integral equation method and the high order finite element discretization on the assumption that the flow of water is inviscid, incompressible and irrotational, and the bubble gas obeys the isoentropic rule. The evolution of bubble is simulated by means of mixed Euler-Lagrangian method. The comparison of the numerical results with the 'exact solution' of a spheric bub ble and experimental data shows that the mathematical model is reasonable and the 3-D numerical method has high accuracy. Important behaviour of bubble, such as immigration and jetting, and dynamic load on an ellipsoid near explosion are derived.

Blast Pressure Measurements of an Underwater Detonation in the Sea

Blast pressure measurements of a controlled underwater explosion in the sea were carried out.An explosive of 25-kg trinitro-toluene(TNT)equivalent was detonated,and the blast pressures were recorded by eight diferent high-performance pressure sensors that work at the nonresonant high-voltage output in adverse underwater conditions.Recorded peak pressure values are used to establish a relationship in the well-known form of empirical underwater explosion(UNDEX)loading formula.Constants of the formula are redetermined by employing the least-squares method in two diferent forms for best ftting to the measured data.The newly determined constants are found to be only slightly diferent from the generally accepted ones.

Numerical study on local failures of reinforced concrete slabs against underwater close-in explosions

Reinforced concrete(RC)slabs are the primary load-carrying member of underwater facilities.They can suffer severe local failures such as cratering,spalling,or breaching as a result of underwater close-in(UWCI)explosions.In this study,we established a fully validated high-fidelity finite element analysis approach to precisely reproduce the local failures of RC slabs after a UWCI explosion.A recently proposed dynamic constitutive model is used to describe wet concrete.The effects of free water content on the material properties,including the tensile/compressive strength,elastic modulus,strain rate effect,failure strength surface,and equation of state,are comprehensively calibrated based on existing test data.The calibrated material parameters are then verified by a single-element test.A high-fidelity finite element analysis(FEA)approach of an RC slab subjected to a UWCI explosion is established using an arbitrary Lagrangian-Eulerian(ALE)algorithm.Simulating previous UWCI explosion tests on RC orifice targets and underwater contact explosion tests on saturated concrete slabs showed that the established FEA approach could accurately reproduce the pressure-time history in water and damage patterns,including the cracking,cratering,and spalling,of the RC orifice target and saturated concrete slab.Furthermore,parametric studies conducted by simulating an RC slab subjected to a UWCI explosion showed that:(i)the local failure of an RC slab enlarges with increased charge weight,reduced standoff distance,and reduced structural thickness;(ii)compared to a water-backed RC slab,an air-backed RC slab exhibits much more obvious local and structural failure.Lastly,to aid the anti-explosion design of relevant underwater facilities,based on over 90 simulation cases empirical formulae are summarized to predict local failure modes,i.e.,no spall,spall,and breach,of water-and air-backed RC slabs subjected to a UWCI explosion.

Experimental investigations on small-and full-scale ship models with polyurea coatings subjected to underwater explosion

Nowadays, the mitigation of damage to a ship caused by the underwater explosion attracts more and more attention from the modern ship designers. In this study, two kinds of scale tests were conducted to investigate the effects of polyurea coatings on the blast resistance of hulls subjected to underwater explosion. Firstly, small-scale model tests with different polyurea coatings were carried out. Results indicate that polyurea has a better blast resistance performance when coated on the front face, which can effectively reduce the maximum deflection of the steel plate by more than 20% and reduce the deformation energy by 35.7%-45.4%. Next, a full-scale ship(approximately 50 m × 9 m) under loadings produced by the detonation of 33 kg of spherical TNT charges was tested, where a part of the ship was coated with polyurea on the front face(8 mm + 24 mm) and not on the contrast area. Damage characteristics on the bottom were statistically analyzed based on a 3D scanning technology, indicating that polyurea contributes to enhancing the blast protection of the ship. However, damage results of this test were different from those of the small-scale tests. Moreover, the deformation area of the bottom with polyurea was greatly increased by 40.1% to disperse explosion energy, a conclusion that cannot be drown from the small-scale tests.

Parallel Computing of the Underwater Explosion Cavitation Effects on Full-scale Ship Structures

As well as shock wave and bubble pulse loading, cavitation also has very significant influences on the dynamic response of surface ships and other near-surface marine structures to underwater explosive loadings. In this paper, the acoustic-structure coupling method embedded in ABAQUS is adopted to do numerical analysis of underwater explosion considering cavitation. Both the shape of bulk cavitation region and local cavitation region are obtained, and they are in good agreement with analytical results. The duration of reloading is several times longer than that of a shock wave. In the end, both the single computation and parallel computation of the cavitation effect on the dynamic responses of a full-scale ship are presented, which proved that reloading caused by cavitation is non-ignorable. All these results are helpful in understanding underwater explosion cavitation effects.

Prolonged simulation of near-free surface underwater explosion based on Eulerian finite element method

n the area of naval architecture and ocean engineering,the research about the underwater xplosion problem is of great significance.To achieve prolonged simulation of near-free surface underwater explosion,the underwater explosion transient numerical model is established in this paper based on compressible Eulerian finite element method(EFEM).Compared with Geers Hunter formula,EFEM is availably validated by simulating the free-field underwater xplosion case.Then,the bubble pulsation and flow field dynamic characteristics of the cases with different underwater explosive depth are compared in this work.Lastly,the height of the water hump and the pressure of flow flied are analyzed quantitatively through the simulation results.

Shock wave and bubble characteristics of underwater array explosion of charges

In this study, we focused on the effect of the underwater explosion parameters of multi-point array explosion. The shock wave and bubble parameters of aggregate charge, two charges, and four charges were measured through an underwater explosion test, and their influence on the explosion power field of charge quantity and array distance was analyzed. Results show that the multi-shock wave collision of array explosion can be approximated to a linear superposition, and the interaction of delayed shock wave can be deemed as the increase of the shock wave baseline. Shock wave focusing and delayed superposition increase the shock wave peak pressure. Compared with the aggregate charge, the greater the number of array explosion points is, the higher the impulse and the gain of the bubble peak pressure are. At the same array distance, the smaller the charge quantity is, the higher the bubble impulse will be. At the same charge quantity, the smaller the array distance is, the higher the bubble impulse will be. The bubble period decreases gradually with the increase of the charge quantity, but the test orientation has little effect on the bubble period.

Dynamic Adaptive Finite Element Analysis of Acoustic Wave Propagation Due to Underwater Explosion for Fluid-structure Interaction Problems

In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes：a） calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b） fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c） adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.

3D numerical simulation on fluid-structure interaction of structure subjected to underwater explosion with cavitation

In the underwater-shock environment, cavitation occurs near the structural surface. The dynamic response of fluid-structure interactions is influenced seriously by the cavitation effects. It is also the difficulty in the field of underwater explosion. With the traditional boundary element method and the finite element method （FEM）, it is difficult to solve the nonlinear problem with cavitation effects subjected to the underwater explosion. To solve this problem, under the consideration of the cavitation effects and fluid compressibility, with fluid viscidity being neglected, a 3D numerical model of transient nonlinear fluid-structure interaction subjected to the underwater explosion is built. The fluid spectral element method （SEM） and the FEM are adopted to solve this model. After comparison with the FEM, it is shown that the SEM is more precise than the FEM, and the SEM results are in good coincidence with benchmark results and experiment results. Based on this, combined with ABAQUS, the transient fluid-structure interaction mechanism of the 3D submerged spherical shell and ship stiffened plates subjected to the underwater explosion is discussed, and the cavitation region and its influence on the structural dynamic responses are presented. The paper aims at providing references for relevant research on transient fluid-structure interaction of ship structures subjected to the underwater explosion.

Investigation on charge parameters of underwater contact explosion based on axisymmetric SPH method

This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics （SPH） method. The dynamic boundary particle is proposed to improve the pressure fluctuation and numerical accuracy near the symmetric axis. An in-depth study is carried out over the influence of charge shapes and detonation modes on the near-field loads in terms of the peak pressure and impulse of shock waves. For different charge shapes, the cylindrical charge with different length-diameter ratios may cause strong directivity of peak pressure and impulse in the near field. Compared with spherical charge, the peak pressure of cylindrical charge may be either weakened or enhanced in different directions. Within a certain range, the greater the length-diameter ratio is, the more obvious the effect will be. The weakened ratio near the detonation end may reach 25% approximately, while the enhanced ratio may reach around 20% in the opposite direction. However, the impulse in different directions seems to be uniform. For different detonation modes, compared with point-source explosion, the peak pressure of plane-source explosion is enhanced by about 5%. Besides, the impulse of plane-source explosion is enhanced by around 5% near the detonation end, but close to those of the point-source explosion in other directions. Based on the material constitutive relation in the axisymmetric coordinates, a simple case of underwater contact explosion is simulated to verify the above conclusions, showing that the charge parameters of underwater contact explosion should not be ignored.

Wall Effect of Underwater Explosion Load Based on Wave Motion Theories

Owing to the existence of the flow field boundary, the shock wave load near the boundary is different from the freefield shock wave load. In the present paper, the hull plate load subjected to underwater shock wave is investigated based onwave motion theories; in addition, the experimental study of the hull plate load is carried out. According to the theoreticalanalysis of the hull plate pressure, we find that the hull plate pressure oscillates repeatedly and decays rapidly with timepassing, the maximum hull plate pressure is 2/（1＋n） times the maximum free field pressure, where n is the ratio ofimpedance, and the impulse is much smaller than the free field impulse. Compared with the experimental study, thetheoretical results agree well with the experimental data.

Investigation on the Determination of Initial Shock Pressure at Near Interface Field of TNT Charge and Water for Underwater Explosion

There are few report on the directly measurement of the initial shock pressure of explosive charge at its interface of water for underwater explosion. The special technologies have been taken to the measurement system with manganin piezoresistive gauge （PRG） in order to measure the initial shock pressure at the interface and its near field of TNT chare and water. The free-holding PRG film gauge can directly determine the shock peak pressure at the interface and near field of TNT charge up to 12.85 GPa, which is satisfying for the good agreement to the 12.97 GPa with one dimensional theoretical analysis and 12.86 GPa with numerical simulation. The maximum discrepancy is 0.93 %. The results show that it is precise and reliable to determine the initial shock pressure of underwater explosion charge with the PRG technology.

Nonlinear Dynamic Response of a Fixed Offshore Platform Subjected to Underwater Explosion at Different Distances

In this paper,the dynamic response of a fixed offshore platform subjected to the underwater explosion(UNDEX)and probable events following it have been investigated.The pressure load due to UNDEX in a specified depth has been applied with a model that considers the effect of blast bubble fluctuations into account.The effect of water on the natural frequency and Fluid-Structure interaction has been modeled as equivalent added mass formulation.The effect of explosion distance on platform response is studied.In this regard,three cases of near,medium,and far-distance explosions are considered.For a case study,a real fixed offshore jacket platform,installed in the Persian Gulf,has been examined.Only the UNDEX pressure load is considered and other dynamic loads such as surface water waves and winds have been neglected.Dead loads,live loads and hydrostatic pressure has been considered in the static case based on the design codes.The results indicated that in near-distance explosions,the UNDEX pressure load can locally damage parts of the platform that are located at the same level as that of explosive material and it can destabilize the platform.In the medium to far distance explosion,a very large base shear was applied to the platform because more elements were exposed to the UNDEX load compared to the near-distance explosion.Therefore,precautionary measures against UNDEX such as risk assessment according to design codes are necessary.As a result of this,member strengthening against explosion may be required.

Similarity research of anomalous dynamic response of ship girder subjected to near field underwater explosion

The final anomalous sag distortion of the ship girder subjected to the near field underwater explosion （undex） below the middle ship is studied. The sinking exercise of Spruance class destroyer DD973 sunk by one MK48 torpedo is first presented, and a simulation model is established. The exponential attenuation phase, the reciprocal attenuation phase, the post reciprocal attenuation phase, and the negative pressure phase of the undex load are precisely applied in this model. The fluid-solid interaction, the added water mass, the gravity, and the change of buoyancy are also taken into account. The similarity theory is then used to analyze the dynamic response of the ship girder. Similarity parameters and theory prediction formulae of the dynamic response of the ship girder are presented, The physical meaning and influences of these similarity parameters are analyzed.

Interaction of underwater explosion bubble with complex elastic-plastic structure

Considering the elastic-plasticity of the structure, the combination of boundary element method and finite element method （FEM） is employed to present the calculation method for solving the complex coupled dynamic problem of bubble, elastic-plastic structure and the free surface, and the complete three-dimensional calculation program is developed as well. The error between the calculated result and the experimental result is within 10%. Taking a surface ship for example, the three-dimensional calculation program is extended to engineering filed. By employing the program, the response of the ship under the bubble loading is analyzed. From the stress-time history curves of typical elements of the structure, it can be seen that the pressure reaches its maximum when the bubble collapses and this validates that the pressure generated by the bubble collapse and the jet can cause serious damage on the ship structure. From the dynamic process of the interaction between the three-dimensional bubble and the ship, the low order vertical mode of the ship is provoked and the ship presents whip-shaped motion. And the ship does elevation and subsidence movement with the expansion and shrinkage of the bubble. Some rules and conclusions which can be applied to the engineering problems are obtained from the analysis in this paper.

Investigation on the Cavitation Effect of Underwater Shock near Different Boundaries

When the shock wave of underwater explosion propagates to the surfaces of different boundaries, it gets reflected. Then, a negative pressure area is formed by the superposition of the incident wave and reflected wave. Cavitation occurs when the value of the negative pressure falls below the vapor pressure of water. An improved numerical model based on the spectral element method is applied to investigate the cavitation effect of underwater shock near different boundaries, mainly including the feature of cavitation effect near different boundaries and the influence of different parameters on cavitation effect. In the implementation of the improved numerical model, the bilinear equation of state is used to deal with the fluid field subjected to cavitation, and the field separation technique is employed to avoid the distortion of incident wave propagating through the mesh and the second-order doubly asymptotic approximation is applied to simulate the non-reflecting boundary. The main results are as follows. As the peak pressure and decay constant of shock wave increases, the range of cavitation domain increases, and the duration of cavitation increases. As the depth of water increases, the influence of cavitation on the dynamic response of spherical shell decreases.