Damage response of conventionally reinforced two-way spanning concrete slab under eccentric impacting drop weight loading

Reinforced concrete(RC)structures are generally designed to carry quasi-static gravity loads through almost indispensable components namely slab,however,it may be subjected to high intense loads induced from the impact of projectiles generated by the tornado,falling construction equipment,and also from accidental explosions during their construction and service lifespan.Impacts due to rock/boulder falls do occur on the structures located especially in hilly areas.Such loadings are not predictable but may cause severe damage to the slab/structure.It stimulates structural engineers and researchers to investigate and understand the dynamic response of RC structures under such impulsive loading.This research work first investigates the performance of 1000×1000×75 mm^(3)conventionally reinforced two-way spanning normal strength concrete slab with only tension reinforcement(0.88%)under the concentric impact load(1035 N)using the finite element method based computer code,ABAQUS/Explicit-v.6.15.The impact load is delivered to the centroid of the slab using a solid-steel cylindroconical impactor(drop weight)with a flat nose of diameter 40 mm,having a total mass of 105 kg released from a fixed height of 2500 mm.Two popular concrete constitutive models in ABAQUS namely;Holmquist-Johnson-Cook(HJC)and Concrete Damage Plasticity(CDP),with strain rate effects as per fib MODEL CODE 2010,are used to model the concrete material behavior to impact loading and to simulate the damage to the slab.The slab response using these two models is analyzed and compared with the impact test results.The strain rate effect on the reinforcing steel bars has been incorporated in the analysis using the Malvar and Crawford(1998)approach.A classical elastoplastic kinematic idealization is considered to model the steel impactor and support system.Results reveal that the HJC model gives a little overestimation of peak displacement,maximum acceleration,and damage of the slab while the predictions given by the CDP model are in reasonable agreement with the experimental test results/observations available in the open literature.Following the validation of the numerical model,analyses have been extended to further investigate the damage response of the slab under eccentric impact loadings.In addition to the concentric location(P1)of the impacting device,five locations on a quarter of the slab i.e.,two along the diagonal(P2&P3),the other two along the mid-span(P4&P5),and the last one(P6)between P3 and P5,covering the entire slab,are considered.Computational results have been discussed and compared,and the evaluation of the most damaging location(s)of the impact is investigated.It has been found that the most critical location of the impact is not the centroid of the slab but the eccentric one with the eccentricity of 1/6th of the span from the centroid along the mid-span section.

Reinforcing effects of polypropylene on energy absorption and fracturing of cement-based tailings backfill under impact loading

Polypropylene(PP)fiber-reinforced cement-based tailings backfill(FRCTB)is a green compound material with superior crack resistance and has good prospects for application in underground mining.However,FRCTB exhibits susceptibility to dynamic events,such as impact ground pressure and blast vibrations.This paper investigates the energy and crack distribution behavior of FRCTB under dynamic impact,considering the height/diameter(H/D)effect.Split Hopkinson pressure bar,industrial computed tomography scan,and scanning electron microscopy(SEM)experiments were carried out on six types of FRCTB.Laboratory outcomes confirmed fiber aggregation at the bottom of specimens.When H/D was less than 0.8,the proportion of PP fibers distributed along theθangle direction of80°-90°increased.For the total energy,all samples presented similar energy absorption,reflectance,and transmittance.However,a rise in H/D may cause a rise in the energy absorption rate of FRCTB during the peak phase.A positive correlation existed between the average strain rate and absorbed energy per unit volume.The increase in H/D resulted in a decreased crack volume fraction of FRCTB.When the H/D was greater than or equal to 0.7,the maximum crack volume fraction of FRCTB was observed close to the incidence plane.Radial cracks were present only in the FRCTB with an H/D ratio of 0.5.Samples with H/D ratios of 0.5 and 0.6 showed similar distributions of weakly and heavily damaged areas.PP fibers can limit the emergence and expansion of cracks by influencing their path.SEM observations revealed considerable differences in the bonding strengths between fibers and the FRCTB.Fibers that adhered particularly well to the substrate were attracted together with the hydration products adhering to surfaces.These results show that FRCTB is promising as a sustainable and green backfill for determining the design properties of mining with backfill.

Constitutive model for concrete subjected to impact loading

To better design and analyze concrete structures, the mechanical properties of concrete subjected to impact loadings are investigated. Concrete is considered to be a two-phase composite made up of micro-cracks and solid parts which consist of coarse aggregate particles and a cement mortar matrix. The cement mortar matrix is assumed to be elastic, homogeneous and isotropic. Based on the Moil-Tanaka concept of average stress and the Eshelby equivalent inclusion theory, a dynamic constitutive model is developed to simulate the impact responses of concrete. The impact compression experiments of concrete and cement mortar are also carried out. Experimental results show that concrete and cement mortar are rate-dependent. Under the same impact velocity, the load-carrying capacity of concrete is higher than that of cement mortar. Whereas, the maximum strain of concrete is lower than that of cement mortar. Regardless of whether it is concrete or cement mortar, with the increase in the impact velocity, the fragment size of specimens after experiment decreases.

Calculating changes in fractal dimension of surface cracks to quantify how the dynamic loading rate affects rock failure in deep mining

The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitatively analyze the dynamic changes in the coal sample cracks under impact load conditions with different loading rates.The experimental results show that the fractal dimension can quantitatively describe the evolution process of coal fractures under dynamic load.During the dynamic compression process,the evolution of the coal sample cracks presents distinct stages.In the crack propagation stage,the fractal dimension increases rapidly with the progress of loading,and in the crack widening stage,the fractal dimension increases slowly with the progress of loading.The initiation of the crack propagation phase of the coal samples gradually occurs more quickly with increasing loading rate;the initial cracks appear earlier.At the same loading time point,when the loading rate is greater,the fractal dimension of the cracks observed in the coal sample is greater.

Long-term mechanical behavior and characteristics of cemented tailings backfill through impact loading

Cemented tailings backfill(CTB)structures are important components of underground mine stopes.It is important to investigate the characteristics and dynamic behavior of CTB materials because they are susceptible to disturbance by dynamic loading,such as excavation and blasting.In this study,the authors present the results of a series of Split-Hopkinson pressure bar(SHPB)single and cyclic impact loading tests on CTB specimens to investigate the long-term dynamic mechanical properties of CTB.The stress-strain relationship,dynamic strength,and dynamic failure characteristics of CTB specimens are analyzed and discussed to provide valuable conclusions that will improve our knowledge of CTB long-term mechanical behavior and characteristics.For instance,the dynamic peak stress under cyclic impact loading is approximately twice that under single impact loading,and the CTB specimens are less prone to fracture when cyclically loaded.These findings and conclusions can provide a new set of references for the stability analysis of CTB materials and help guide mine designers in reducing the amount of binding agents and the associated mining cost.

Responses of jointed rock masses subjected to impact loading

Impact-induced damage to jointed rock masses has important consequences in various mining and civil engineering applications. This paper reports a numerical investigation to address the responses of jointed rock masses subjected to impact loading. It also focuses on the static and dynamic properties of an intact rock derived from a series of laboratory tests on meta-sandstone samples from a quarry in Nova Scotia, Canada. A distinct element code(PFC2D) was used to generate a bonded particle model(BPM) to simulate both the static and dynamic properties of the intact rock. The calibrated BPM was then used to construct large-scale jointed rock mass samples by incorporating discrete joint networks of multiple joint intensities into the intact rock matrix represented by the BPM. Finally, the impact-induced damage inflicted by a rigid projectile particle on the jointed rock mass samples was determined through the use of the numerical model. The simulation results show that joints play an important role in the impactinduced rock mass damage where higher joint intensity results in more damage to the rock mass. This is mainly attributed to variations of stress wave propagation in jointed rock masses as compared to intact rock devoid of joints.

Crack dynamic propagation properties and arrest mechanism under impact loading

Crack dynamic propagation and arrest behaviors have received extensive attention over the years.However,there still remain many questions,e.g.under what conditions will a running crack come to arrest?In this paper,drop weight impact(DWI)tests were conducted to investigate crack arrest mechanism using single cleavage triangle(SCT)rock specimens.Green sandstone was selected to prepare the SCT specimens.Dynamic stress intensity factors(DSIFs)were calculated by ABAQUS code,and the critical DSIFs were determined by crack propagation speeds and fracture time measured by crack propagation gauges(CPGs).The test results show that the critical DSIF at propagation decreases with crack propagation speed.Numerical simulation for SCT specimens under different loading waves was performed using AUTODYN code.The reflected compressive wave from the incident and transmitted plates can induce crack arrests during propagation,and the number of arrest times increases with the wave length.In order to eliminate the effect of the incident and transmitted plates,models consisting of only one SCT specimen without incident and transmitted plates were established,and the same trapezoid-shaped loading wave was applied to the SCT specimen.The results show that for the SCT specimen with transmitted boundary(analogous to an infinite plate),the trapezoid-shaped loading wave cannot induce crack arrest anymore.The numerical results can well describe the occurrence of crack arrest in the experiments.

Unveiling the mechanical response and accommodation mechanism of pre-rolled AZ31 magnesium alloy under high-speed impact loading

Split Hopkinson pressure bar(SHPB)tests were conducted on pre-rolled AZ31 magnesium alloy at 150–350℃ with strain rates of 2150s-1,3430s^(-1) and 4160s-1.The mechanical response,microstructural evolution and accommodation mechanism of the pre-rolled AZ31 magnesium alloy under high-speed impact loading were investigated.The twin and shear band are prevailing at low temperature,and the coexistence of twins and recrystallized grains is the dominant microstructure at medium temperature,while at high temperature,dynamic recrystallization(DRX)is almost complete.The increment of temperature reduces the critical condition difference between twinning and DRX,and the recrystallized temperature decreases with increasing strain rate.The mechanical response is related to the competition among the shear band strengthen,the twin strengthen and the fine grain strengthen and determined by the prevailing grain structure.The fine grain strengthen could compensate soften caused by the temperature increase and the reduction of twin and shear band.During high-speed deformation,different twin variants,introduced by pre-rolling,induce different deformation mechanism to accommodate plastic deformation and are in favor for non-basal slip.At low temperature,the high-speed deformation is achieved by twinning,dislocation slip and the following deformation shear band at different deformation stages.At high temperature,the high-speed deformation is realized by twinning and dislocation slip of early deformation stage,transition shear band of medium deformation stage and DRX of final deformation stage.

Effect of roughness on the shear behavior of rock joints subjected to impact loading

The shear behavior is regarded as the dominant property of rock joints and is dramatically affected by the joint surface roughness.To date,the effect of surface roughness on the shear behavior of rock joints under static or cyclic loading conditions has been extensively studied,but such effect under impact loading conditions keeps unclear.To address this issue,a series of impact shear tests was performed using a novel-designed dynamic experimental system combined with the digital image correlation(DIC)technique.The dynamic shear strength,deformability and failure mode of the jointed specimens with various joint roughness coefficients(JRC)are comprehensively analyzed.Results show that the shear strength and shear displacement characteristics of the rock joint under the impact loading keep consistent with those under static loading conditions.However,the temporal variations of shear stress,slip displacement and normal displacement under the impact loading conditions show obviously different behaviors.An elastic rebound of the slip displacement occurs during the impact shearing and its value increases with increasing joint roughness.Two identifiable stages(i.e.compression and dilation)are observed in the normal displacement curves for the rougher rock joints,whereas the joints with small roughness only manifest normal compression displacement.Besides,as the roughness increases,the maximum compression tends to decrease,while the maximum dilation gradually increases.More-over,the microstructural analysis based on scanning electron microscope(SEM)suggests that the roughness significantly affects the characteristics of the shear fractured zone enclosing the joint surface.

Influence of confi ning pressure and impact loading on mechanical properties of amphibolite and sericite-quartz schist

In order to investigate the dynamic mechanical properties of amphibolite and sericite-quartz schist under confi ning pressure, two rocks are subjected to impact loadings with different strain rates and confi ning pressures by using split Hopkinson pressure bar equipment with a confi ning pressure device. Based on the experimental results, the stress-strain curves are analyzed and the effects of confi ning pressure and strain rates on the dynamic compressive strength, peak strain and failure mode are summarized. The results show that:(1) The characteristics of two rocks in the ascent stage of the stressstrain curve are basically the same, but in the descent stage, the rocks gradually show plastic deformation characteristics as the confi ning pressure increases.(2) The dynamic compressive strength and peak strain of two rocks increase as the strain rate increases and the confi ning pressure effects are obvious.(3) Due to the effect of confi ning pressure, the normal stress on the damage surface of the rock increases correspondingly, the bearing capacity of the crack friction exceeds the material cohesion and the slippage of the fractured rock is controlled, which all lead to the compression and shear failure mode of rock. The theoretical analysis and experimental methods to study the dynamic failure mode and other related characteristics of rock are useful in developing standards for engineering practice.

Dynamic response characteristics of dry and watersaturated schist under impact loading

Many geological engineering hazards are closely related to the dynamic mechanical properties of rock materials.However,most existing studies on the dynamic mechanical properties of rock materials were conducted on the hard rocks such as sandstone,granite,limestone,and marble,whereas soft rocks,such as schist,are less studied.Therefore,in this study,a series of triaxial impact tests were conducted on dry and saturated schist by employing a modified triaxial split Hopkinson pressure bar system to reveal the coupling effects of water,strain rate,and triaxial confining pressure on the mechanical properties of schist.The results show that schist is a type of watersensitive rock and the stress-strain curve of saturated schist has apparent ductility.The effects of strain rate on dynamic strain,deformation modulus and peak stress were analyzed.The results also show that the dynamic peak stress is affected by the combined softening effect and viscous effect of water under impact loading.Finally,it was found that the failure mode of schist belongs to typical axial tensile failure under uniaxial impact tests,and shear failure is the main failure mode under triaxial impact tests.With the increase in confining pressure,the failure modes of schist change from tensile failure to shear failure.This research can provide useful parameters for geological engineering hazard prevention in mountain areas.

Multi-objectives nonlinear structure optimization for actuator in trajectory correction fuze subject to high impact loadings

This paper presents an actuator used for the trajectory correction fuze,which is subject to high impact loadings during launch.A simulation method is carried out to obtain the peak-peak stress value of each component,from which the ball bearings are possible failures according to the results.Subsequently,three schemes against impact loadings,full-element deep groove ball bearing and integrated raceway,needle roller thrust bearing assembly,and gaskets are utilized for redesigning the actuator to effectively reduce the bearings’stress.However,multi-objectives optimization still needs to be conducted for the gaskets to decrease the stress value further to the yield stress.Four gasket’s structure parameters and three bearings’peak-peak stress are served as the four optimization variables and three objectives,respectively.Optimized Latin hypercube design is used for generating sample points,and Kriging model selected according to estimation result can establish the relationship between the variables and objectives,representing the simulation which is time-consuming.Accordingly,two optimization algorithms work out the Pareto solutions,from which the best solutions are selected,and verified by the simulation to determine the gaskets optimized structure parameters.It can be concluded that the simulation and optimization method based on these components is effective and efficient.

Design of Bridge Expansion Joints with Perforated Dowels Under Impact Loading

The expansion joints are expected to have movement capacity, bearing capacity for static and dynamic loading, water-tightness, low noise emission and traffic safety. In particular, the failure due to impact loading is the main reason for the observed damages. The problem of dynamic behavior of the expansion joints is so complex that we shall focus our attention on the impact factor for vehicle load that is governed by traffic impact. In order to overcome this difficulty, the cantilever-toothed aluminum joint (finger joint) is one of the promising joints under impact loading. In this study, from the viewpoint of design methodology, numerical studies for impact behavior were conducted for aluminum alloy expansion joints with perforated dowels. The design impact factor for the expansion joints with the perforated dowels against traffic impact loading was examined by using numerical simulations.

Catastrophe model and its experimental verification ofstatic loading rock system under impact load

According to the catastrophe model for impact buckling of static loading structures, a new catastrophe model for impact loading failure of a static loading rock system was established, and one dimension (1D) catastrophe model was analyzed. The analysis results indicate that the furcation collection where catastrophe may take place is not only decided by mechanical system itself but also relates to exterior loading, which is different from the results obtained under mono-static loading where the bifurcation collection is only determined by mechanics of the system itself and has nothing to do with exterior loading. In addition, the corresponding 1D coupled static-dynamic loading experiment is designed to verify the analysis results of catastrophe model. The test is done with Instron 1342 electro-servo controlled testing system, in which medium strain rate is caused by monotony rising dynamic load. The parameters are obtained combining theoretical model with experiment. The experimental and theoretical curves of critical dynamic load vs static load are rather coincided, thus the new model is proved to be correct.

Numerical study of RC beams under various loading rates with LS-DYNA

Having an accurate understanding of concrete behavior under effects of high strain rate loading with the aim of reducing incurred damages is of great importance. Due to complexities and high costs of experimental research, numerical studies can be an appropriate alternative for experimental methods. Therefore, in this research capability of the finite element method for predicting concrete behavior at various loading conditions is evaluated by LS-DYNA software. First, the proposed method is presented and then is validated in three stages under different conditions. Results of load-lnidspan displacement showed good agreement between experimental and finite element results. Capability of finite element method in analyses of beams under various rates of loading was also validated by low error of the results. In addition, the proposed method has reasonable ability to evaluate reinforced concrete beams under various loading rates and different conditions.

Dynamic response of fixed-roof oil-storage tank structure under blast loading

In order to investigate the damage and deformation mechanism of large scale steel fixed-roof oil-storage tanks under the combustible gas explosion, a series of explosion experiments of scaled models are conducted. The l： 25 scaled numerical models of oil-storage tanks with a capacity of 5 000 m3 are also set up by ANSYS/LS-DYNA software, and their damage processes under the blast impact are numerically simulated. Both the experimental results and the numerical simulations show that the blast loading curve displays a pressure jump instantaneously at the moment of contact with the experimental models, and the overpressure peaks at the stagnation area of the outer surface on the blast side. The yield range first appears at the stagnation area and then propagates to the neighboring parts, and the irregular plastic hinge circle obviously appears around the deformation area, which results in the concaved buckling of the tank inner surface. During the whole process, the inner liquid not only impacts on the structures, but also absorbs and consumes part of the blast energy.

A HALF PLANE CRACK UNDER THREE-DIMENSIONAL COMBINED MODE IMPACT LOADING

The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear line loads is consid- ered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented.

SEMI-ELLIPTIC SURFACE CRACK IN AN ELASTIC SOLID WITH FINITE SIZE UNDER IMPACT LOADING

In this paper a semi-elliptic surface crack problem in an elastic solid of finite size under impact loading is investigated. An analysis is performed by means of fracture dynamics and the finite element method, and a three-dimensional finite element program is developed to compute the dynamic stress intensity factor. The results reveal that the effects of the solid＇s boundary surface, crack surface, material inertia and stress wave interactions play significant roles in dynamic fracture.

Degradation mechanism of rock under impact loadings by integrated investigation on crack and damage development

Failure of rock under impact loadings involves complex micro-fracturing and progressive damage. Strength increase and splitting failure have been observed during dynamic tests of rock materials. However, the failure mechanism still remains unclear. In this work, based on laboratory tests, numerical simulations with the particle flow code(PFC) were carried out to reproduce the micro-fracturing process of granite specimens. Shear and tensile cracks were both recorded to investigate the failure mode of rocks under different loading conditions. At the same time, a dynamic damage model based on the Weibull distribution was established to predict the deformation and degradation behavior of specimens. It is found that micro-cracks play important roles in controlling the dynamic deformation and failure process of rock under impact loadings. The sharp increase in the number of cracks may be the reason for the strength increase of rock under high strain rates. Tensile cracks tend to be the key reason for splitting failure of specimens. Numerical simulation of crack propagation by PFC can give vivid description of the failure process. However, it is not enough for evaluation of material degradation. The dynamic damage model is able to predict the stress-strain relationship of specimens reasonably well, and can be used to explain the degradation of specimens under impact loadings at macro-scale. Crack and damage can describe material degradation at different scales and can be used together to reveal the failure mechanism of rocks.

Dynamic response of UHMWPE plates under combined shock and fragment loading

Ultra-high molecular weight polyethylene(UHMWPE)fiber composite has been extensively used to construct lightweight protective structures against ballistic impacts,yet little is known about its performance when subjected to combined blast and fragment impacts.Built upon a recently developed laboratory-scale experimental technique to generate simulated combined loading through the impact of a fragment-foam composite projectile launched from a light gas gun,the dynamic responses of fullyclamped UHMWPE plates subjected to combined loading were characterized experimentally,with corresponding deformation and failure modes compared with those measured with simulated blast loading alone.Subsequently,to explore the underlying physical mechanisms,three-dimensional(3D)numerical simulations with the method of finite elements(FE)were systematically carried out.Numerical predictions compared favorably well with experimental measurements,thus validating the feasibility of the established FE model.Relative to the case of blast loading alone,combined blast and fragment loading led to larger maximum deflections of clamped UHMWPE plates.The position of the FSP in the foam sabot affected significantly the performance of a UHMWPE target,either enhancing or decreasing its ballistic resistance.When the blast loading and fragment impact arrived simultaneously at the target,its ballistic resistance was superior to that achieved when subjected to fragment impact alone,and benefited from the accelerated movement of the target due to simultaneous blast loading.