A novel approach to the dynamic response analysis of Euler-Bernoulli beams resting on a Winkler soil model and subjected to impact loads

This work presents a novel approach to the dynamic response analysis of a Euler-Bernoulli beam resting on a Winkler soil model and subjected to an impact loading.The approach considers that damping has much less importance in controlling the maximum response to impulsive loadings because the maximum response is reached in a very short time,before the damping forces can dissipate a significant portion of the energy input into the system.The development of two sine series solutions,relating to different types of impulsive loadings,one involving a single concentrated force and the other a distributed line load,are presented.This study revealed that when a simply supported Euler-Bernoulli beam,resting on a Winkler soil model,is subject to an impact load,the resulting vertical displacements,bending moments and shear forces produced along the span of the beam are considerably affected.In particular,the quantification of this effect is best observed,relative to the corresponding static solution,via an amplification factor.The computed impact amplification factors,for the sub-grade moduli used in this study,were in magnitude greater than 2,thus confirming the multiple-degree-of-freedom nature of the problem.

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.

Influence of railway wheel tread damage on wheel-rail impact loads and the durability of wheelsets

Dynamic wheel-rail contact forces induced by a severe form of wheel tread damage have been measured by a wheel impact load detector during full-scale field tests at different vehicle speeds.Based on laser scanning,the measured three-dimensional damage geometry is employed in simulations of dynamic vehicle-track interaction to calibrate and verify a simulation model.The relation between the magnitude of the impact load and various operational parameters,such as vehicle speed,lateral position of wheel-rail contact,track stiffness and position of impact within a sleeper bay,is investigated.The calibrated model is later employed in simulations featuring other forms of tread damage;their effects on impact load and subsequent fatigue impact on bearings,wheel webs and subsurface initiated rolling contact fatigue of the wheel tread are assessed.The results quantify the effects of wheel tread defects and are valuable in a shift towards condition-based maintenance of running gear,and for general assessment of the severity of different types of railway wheel tread damage.

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.

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.

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.

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.

Dynamic Failure Model of Thin Coal and Rock Mass under Uniform Impact Load

During the excavation of deep coal and rock mass, the radial stress of the free face changes from three-dimensional compression state to two-dimensional stress, bearing the combined action of dynamic disturbance and static load at the same time. With that, many mines suffer from dynamic disasters, such as coal and gas outburst, rock burst and rock caving during deep mining excavation, which is often accompanied by plate crack, spalling and other disasters, seriously affecting the stability of stope and roadway. Taking thin rectangular coal and rock mass as the research object, the dual equation of the free vibration was derived and the exact solution model of the free vibration was established with the use of Hamilton dual system. Based on the action characteristics of the uniform impact load, the effective mode of the forced vibration was obtained by using the Duhamel integral principle and the orthogonality of the mode function. Based on the third strength theory and the numerical simulation results, the dynamic damage process and development trend of coal and rock mass were analyzed under uniform impact load. It was concluded that the starting position of dynamic damage can be judged by the first order main mode, and the development direction and trend of the damage can be judged by the fifth and sixth order main modes. It was concluded that the vibration mode functions of coal and rock mass with four side fixed (C-C-C-C), the two sides fixed and simply supported on the other (S-C-S-C) are mainly composed of three modes that are the first order (dominant frequency), the fifth order and the sixth order, from which the dynamic damage mechanism is preliminarily studied.

Interval uncertain optimization for damping fluctuation of a segmented electromagnetic buffer under intensive impact load

Aiming at the problems of demagnetization effect of electromagnetic buffer(EMB)caused by high velocity under intensive impact load and the difficulty and error of machining composite thin-walled long tube,a segmented EMB is proposed.The inner tube and air-gap are divided into initial segments and the traversing segments.Through theoretical analysis,impact test and simulation,it can be found that the RRF curve has two peaks.Firstly,in order to reduce the resultant resistance force(RRF)peaks,the sensitivity analysis based on optimal Latin hypercube design(OLHD)and polynomial regression was performed.The results show that the smallest contribution ratio to the dynamic response is the seventh and ninth segments of the inner tube,which are less than 1%.Then,fully considering the uncertain factors,important parameters are selected for uncertain optimization after sensitivity analysis.The interval order and interval probability degree methods are used to establish interval uncertain optimization model of the RRF considering robustness.The model was solved using an interval nested optimization method based on radial basis function(RBF)neural network.Finally,the Pareto front is obtained and numerical simulation is performed to verify the optimal value.It indicates that the two kinds of RRF peak is obviously reduced,and the optimization object and strategy are effective.

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.

Dynamic response analysis of blocks-combined dam under impact load

In order to reduce the damage of ordinary gravity dam impacted by boulders in debris flow,a blocks-combined dam based practical project is proposed.The dynamic response of the proposed dam under impact load is investigated by using ABAQUS finite element software.Considering the impact velocity and impact height,the anti-impact performance of blocks-combined dam is discussed in terms of deformation,displacement,impact force,acceleration,and energy,and is compared with that of ordinary dam.Results show that the displacement,impact force and acceleration of dam increase with the increase of impact velocity and height.The impact energy of blocks-combined dam is mainly absorbed and consumed by the friction between the component interfaces,which is related to the location of impact point.Compared with the ordinary gravity dam,the blocks-combined dam has better impact resistance to boulders in debris flow.

Experimental Study of Flexural Behaviour of Reinforced Baked Clay Beams under Impact Loading

This paper presents behaviour of Reinforced Baked Clay (RBC) beams under drop weight impact loading. The beams were made of two different grades of baked clay with cube crushing strength of 20 MPa and 30 MPa, respectively. The RBC beams were subjected to repeated drop weight loading by a hammer of weight equal to that of the specimen being tested. The results showed that the impact resistance of the RBC beams was governed by the compressive strength of the baked clay. Failure of grade 20 beams occurred due to irregular cracks and the beams of grade 30 failed by opening of a single crack at mid span. It was observed that the beams of grade 30 had sustained about 1.5 times more number of impacts until steel in tension zone yielded and failed completely after necking.

Effect of Reinforcement on Deflection and Cracks in Baked Clay Beams Subjected to Impact Loading

Attempts are being made to utilize Reinforced Baked Clay (RBC) as a substitute of Reinforced Cement Concrete (RCC) for construction of low cost houses in plains of Pakistan. Since baked clay is considered to be more brittle as compared to concrete. Therefore, it is necessary to investigate how deflection and crack width of RBC beams subjected to impact loading are governed by amount of reinforcement. This paper presents the behaviour of RBC beams under drop weight impact loading. The beams were reinforced with two steel bars, one in compression zone and the other in tension zone. In group A beams, the diameter of steel bars was 12.7 mm, while the beams of group B were reinforced with steel bars of 15.8 mm diameter. The RBC beams were subjected to repeated impacts of a hammer of mass 21 kg falling from a height of 1000 mm. The results show that 1) three times reduction in deflection, and 2) 2.5 times decrease in crack width, were achieved in RBC beams by increasing the area of steel to 50%. In addition to this, all the RBC beams failed within nine blows of the hammer, irrespective of area of reinforcement.

Experimental study on dynamic mechanical property of cemented tailings backfill under SHPB impact loading

Cemented tailings backfill(CTB) have increasingly been used in recent years to improve the stability of mining stopes in deep underground mines. Deep mining processes are often associated with rock bursting and high-speed dynamic loading conditions. Therefore, it is important to investigate the characteristics and dynamic mechanical behavior of CTB. This paper presents the results of dynamic tests on CTB specimens with different cement and solid contents using a split Hopkinson pressure bar(SHPB). The results showed that some CTB specimens exhibited one to two lower stress peaks after reaching dynamic peak stress before they completely failed. The greater the cement-to-tailings ratio is, the more obvious the strain reaction. This property mainly manifested as follows. First,the dynamic peak stress increased with the increase of the cement-to-tailings ratio when the impact velocity was fixed. Second, the dynamic peak stress had a quadratic relationship with the average stress rate. Third, the cement-to-tailings ratio could enhance the increase rate of dynamic peak stress with strain rate. In addition, the dynamic strength enhancement factor K increased with the increase of strain rate, and its value was larger than that of the rock samples. The failure modes of CTB specimens under low-speed impact were tensile failure and X conjugate shear failure, where were nearly the same as those under static uniaxial and triaxial compression. The CTB specimens were crushed and broken under critical strain, a failure mode similar to that of low-strength concrete. The results of the experimental research can improve the understanding of the dynamic mechanical properties of CTB and guide the strength design of deep mining backfills.

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.

Analytical and numerical studies on the nonlinear dynamic response of orthotropic membranes under impact load

Orthotropic membrane components and structures are widely used in building structures, instruments and meters, electronic engineering, space and aeronautics, etc., because of their light weights. However, the same lightweight combined with low stiffness make membranes prone to vibration under dynamic loads, and in some cases the vibration may lead to structural failure. Herein, the undamped nonlinear vibration response of pretension rectangular orthotropic membrane structures subjected to impact loading is studied by analytical and numerical methods. The analytical solution is obtained by solving the governing equations by the Bubnov-Galerkin method and the Lindstedt-Poincaré perturbation method. Numerical analysis has also been carried out based on the same theoretical model. The analytical and numerical results have been compared and analyzed, and the infl uence of various model parameters on membrane vibration discussed. The results obtained herein provide some theoretical basis for the vibration control and dynamic design of orthotropic membrane components and structures.

Dynamic response of cylindrical cavity to anti-plane impact load by using analytical approach

The transient response of an unlimited cylindrical cavity buried in the infinite elastic soil subjected to an anti-plane impact load along the cavern axis direction was studied.Using Laplace transform combining with contour integral of the Laplace inverse transform specifically,the general analytical expressions of the soil displacement and stress are obtained in the time domain,respectively.And the numerical solutions of the problem computed by analytical expressions are presented.In the time domain,the dynamic responses of the infinite elastic soil are analyzed,and the calculation results are compared with those from numerical inversion proposed by Durbin and the static results.One observes good agreement between analytical and numerical inversion results,lending the further support to the method presented.Finally,some valuable shear wave propagation laws are gained: the displacement of the soil remains zero before the wave arrival,and after the shear wave arrival,the stress and the displacement at this point increase abruptly,then reduce and tend to the static value gradually at last.The wave attenuates along the radial,therefore the farther the wave is from the source,the smaller the stress and the displacement are,and the stress and the displacement are just functions of the radial distance from the axis.

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.

Methods for Progressive Collapse Analysis of Building Structures Under Blast and Impact Loads

Progressive collapse of building structures under blast and impact loads has attracted great attention all over the world. Progressive collapse analysis is essential for an economic and safe design of building structures against progressive collapse to blast and impact loads. Because of the catastrophic nature of progressive collapse and the potentially high cost of constructing or retrofitting buildings to resist it, it is imperative that the progressive collapse analysis methods be reliable. For engineers, their methodology to carry out progressive collapse evaluation need not only be accurate and concise, but also be easily used and works fast. Thus, many researchers have been spending lots of effort in developing reliable, efficient and straightforward progressive collapse analysis methods recently. In the present paper, current progressive collapse analysis methods available in the literature are reviewed. Their suitability, applicability and reliability are discussed. Our recent proposed new method for progressive collapse analysis of reinforced concrete frames under blast loads is also introduced.