AHermitian C^(2) Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates

This work develops a Hermitian C^(2) differential reproducing kernel interpolation meshless(DRKIM)method within the consistent couple stress theory(CCST)framework to study the three-dimensional(3D)microstructuredependent static flexural behavior of a functionally graded(FG)microplate subjected to mechanical loads and placed under full simple supports.In the formulation,we select the transverse stress and displacement components and their first-and second-order derivatives as primary variables.Then,we set up the differential reproducing conditions(DRCs)to obtain the shape functions of the Hermitian C^(2) differential reproducing kernel(DRK)interpolant’s derivatives without using direct differentiation.The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs.As a result,the primary variables and their first-and second-order derivatives satisfy the nodal interpolation properties.Subsequently,incorporating ourHermitianC^(2)DRKinterpolant intothe strong formof the3DCCST,we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior.The Hermitian C^(2) DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature.Finally,the impact of essential factors on the transverse stresses,in-plane stresses,displacements,and couple stresses that are induced in the loaded microplate is examined.These factors include the length-to-thickness ratio,the material length-scale parameter,and the inhomogeneity index,which appear to be significant.

A numerical simulation study on mechanical behaviour of coal with bedding planes under coupled static and dynamic load

To investigate the bedding influence on coal mechanical behaviour in underground environments such as coal or rock burst, simulations of dynamic SHPB tests of pre-stressed coal specimens with different bedding angles were carried out using a particle flow code 2-dimensional(PFC2D). Three impact velocities of 4, 8 and 12 m/s were selected to study dynamic behaviours of coal containing bedding planes under different dynamic loads. The simulation results showed that the existence of bedding planes leads to the degradation of the mechanical properties and their weakening effect significantly depends on the angle h between the bedding planes and load direction. With h increaseing from 0° to 90°, the strength first decreased and subsequently increased and specimens became most vulnerable when h was 30° or 45°.Five failure modes were observed in the specimens in the context of macro-cracks. Furthermore, energy characteristics combined with ultimate failure patterns revealed that maximum accumulated energy and failure intensity have a positive relation with the strength of specimen. When bedding planes were parallel or perpendicular to loading direction, specimens absorbed more energy and experienced more violent failure with increased number of cracks. In contrast, bedding planes with h of 30° or 45° reduced the specimens' ability of storing strain energy to the lowest with fewer cracks observed after failure.

Mechanical properties and failure behavior of rock with different flaw inclinations under coupled static and dynamic loads

The deep fissured rock mass is affected by coupled effects of initial ground stress and external dynamic disturbance.In order to study the effect of internal flaw on pre-stressed rock mechanical responses and failure behavior under impact loading,intact granite specimens and specimens with different flaw inclinations are tested by a modified split Hopkinson pressure bar(SHPB)and digital image correlation(DIC)method.The results show that peak strain and dynamic strength of intact specimens and specimens with different flaw angles(α)decrease with the increase of axial static pressure.The 90°flaw has weak reduction effect on peak strain,dynamic strength and combined strength,while 45°and 0°flaws have remarkable reduction effect.Specimens with 90°flaw are suffered combined shear and tensile failure under middle and low axial static pre-stresses,and suffered shear failure under high axial static pre-stresses.Specimens with 45°and 0°flaws are suffered oblique shear failure caused by pre-existing flaw under different axial static pre-stresses.Besides,based on digital image correlation method,it is found that micro-cracks before formation of macro fractures(include shear and tensile fractures)belong to tensile cracks.Tensile and shear strain localizations at pre-existing flaw tip for specimen with 45°and 0°flaws are produced much earlier than that at other positions.

Failure mechanism and coupled static-dynamic loading theory in deep hard rock mining: A review

Rock failure phenomena,such as rockburst,slabbing(or spalling) and zonal disintegration,related to deep underground excavation of hard rocks are frequently reported and pose a great threat to deep mining.Currently,the explanation for these failure phenomena using existing dynamic or static rock mechanics theory is not straightforward.In this study,new theory and testing method for deep underground rock mass under coupled static-dynamic loading are introduced.Two types of coupled loading modes,i.e.'critical static stress + slight disturbance' and 'elastic static stress + impact disturbance',are proposed,and associated test devices are developed.Rockburst phenomena of hard rocks under coupled static-dynamic loading are successfully reproduced in the laboratory,and the rockburst mechanism and related criteria are demonstrated.The results of true triaxial unloading compression tests on granite and red sandstone indicate that the unloading can induce slabbing when the confining pressure exceeds a certain threshold,and the slabbing failure strength is lower than the shear failure strength according to the conventional Mohr-Column criterion.Numerical results indicate that the rock unloading failure response under different in situ stresses and unloading rates can be characterized by an equivalent strain energy density.In addition,we present a new microseismic source location method without premeasuring the sound wave velocity in rock mass,which can efficiently and accurately locate the rock failure in hard rock mines.Also,a new idea for deep hard rock mining using a non-explosive continuous mining method is briefly introduced.

Experimental and numerical study on dynamic mechanical behaviors of shale under true triaxial compression at high strain rate

High-energy gas fracturing of shale is a novel,high efficacy and eco-friendly mining technique,which is a typical dynamic perturbing behavior.To effectively extract shale gas,it is important to understand the dynamic mechanical properties of shale.Dynamic experiments on shale subjected to true triaxial compression at different strain rates are first conducted in this research.The dynamic stress-strain curves,peak strain,peak stress and failure modes of shale are investigated.The results of the study indicate that the intermediate principal stress and the minor principal stress have the significant influence on the dynamic mechanical behaviors,although this effect decreases as the strain rate increases.The characteristics of compression-shear failure primarily occur in shale subjected to triaxial compression at high strain rates,which distinguishes it from the fragmentation characteristics observed in shale under dynamic uniaxial compression.Additionally,a numerical three-dimensional Split Hopkinson Pressure Bar(3D-SHPB),which is established by coupling PFC3D and FLAC3D methods,is validated to replicate the laboratory characteristics of shale.The dynamic mechanical characteristics of shale subjected to different confining stresses are systematically investigated by the coupling PFC3D and FLAC3D method.The numerical results are in good agreement with the experimental data.

Mechanical properties of rock under coupled static-dynamic loads

Rock drilling machine,INSTRON testing system,and SHPB device are updated to investigate the characteristics of rocks at great depth,with high loads from overburden,tectonic stresses and dynamic impacts due to blasting and boring.It is verified that these testing systems can be used to study the mechanical properties of rock material under coupled static and dynamic loading condition and give useful guidance for the deep mining and underground cavern excavation.Various tests to determine the rock strength,fragmentation behavior,and energy absorption were conducted using the updated testing systems.It is shown that under coupled static-dynamic loads,if the axial prestress is lower than its elastic limit,the rock strength is higher than the individual static or dynamic strength.At the same axial prestress,rock strength under coupled loads rises with the increasing strain rates.Under coupled static and dynamic loads,rock is observed to fail with tensile mode.While shear failure may exist if axial prestress is high enough.In addition,it is shown that the percentage of small particles increases with the increasing axial prestress and impact load based on the analysis of the particle-size distribution of fragments.It is also suggested that the energy absorption ratio of a specimen varies with coupled loads,and the maximum energy absorption ratio for a rock can be obtained with an appropriate combination of static and dynamic loads.

Numerical experiment rock fragmentation by combined dynamic and static loads under dual-cutter head

This paper puts forward a new rock fragmentation loading method of dual-cutter head combined dynamic and static loads. By applying the numerical simulation software - RFPA2D, we have done numerical experiment about the sihstone＇ s crushing effect by dynamic load on single cutter head without confining pressure, dynamic load on single cut- ter head with confining pressure 10 MPa and different dual-cutter heads spacing by combined dynamic and static loads with confining pressure 10 MPa. Experimental results show that the confining pressure can obviously affect the rock frag- mentation effect. Combined dynamic and static loads can greatly improve the rock fragmentation effect. There exists an optimal spacing of dual-cutter head that can make the rock fragmentation achieve the desired effect. Through analyzing the acoustic emission accumulative energy and quantity, the authors make a conclusion that the optimum spacing is 30 mm.

Constitutive model of rock under static-dynamic coupling loading and experimental investigation

The importance of study on constitutive model of statically loaded rock experiencing dynamic load is set forth, and the studying methods on dynamic constitutive model are classified according to the current studying status. By way of combining statistic damage model and viscoelastic model, uni-axial and multi-axial constitutive models of statically loaded rock experiencing dynamic load (static-dynamic coupling constitutive model) under intermediate strain rate are established. The verification experiment on 2D constitutive model under different static stress and dynamic stress with different frequencies is designed and performed. It is found that there is a good agreement between the experimental stress-strain curves and the theoretical stress-strain curves.

Supporting characteristics analysis of constant resistance bolts under coupled static-dynamic loading

To study the tensile mechanical properties of constant resistance bolts, the RFPA(Rock Failure Process Analysis) statics software is used to perform a uniaxial tensile test on a constant resistance bolt. The numerical test results show that the plastic strain value is 12 times the magnitude of the elastic strain. During plastic deformation, the fluctuation in the stress magnitude is relatively stable, indicating that the bolt has good constant resistance characteristics. The numerical test results are in good agreement with the laboratory test results of M.C. He, and the accuracy and reliability of the numerical test method are verified. Therefore, the RFPA software with coupled static-dynamic loading is further adopted to study the supporting effects of traditional bolts and constant resistance bolts under coupled staticdynamic loading. The numerical comparison of the test results show that the constant resistance bolts can effectively control the deformation amount and rate of the laneway surrounding rock, reduce the total and rate of increase in the accumulated acoustic emissions,decrease the stress on the units in the model and protect the stability of the laneway. This paper verifies that a constant resistance bolt has better impact resistance mechanical properties than those of a traditional bolt and provides an effective way to control rock burst and soft rock that is prone to large deformation damage.

Investigation on automated loading of dynamic 3D heat source model for welding simulation

Since programing complex and dynamic heat source model for welding simulation is a complex job,the parametric methods are studied in this paper.Firstly,an overall flow to achieve automatically modeling welding was introduced.Secondly,an expert module rule for selecting welding heat source model was founded,which is based on simulation knowledge and experiences.Thirdly,a modularity routine method was investigated using writing with C++programing,which automatically creates subroutines of 3D dynamic heat source model for user.To realize the dynamic weld path,the local weld path coordinate system was moved in the global coordinate system and it is used to model the direction of weld gun,welding path and welding pose.The weld path data file was prepared by the automatic tool for the welding heat source subroutines.All above functions were integrated in the user interface and the connection with architecture was introduced.At last,a laser beam welding heat source modeling was automatically modeled and the weld pool geometry was compared with the reported literature.It demonstrated that the automated tool is valid for welding simulation.Since modeling became convenient for welding simulation using the tool proposed,it could be easy and useful for welding engineers to acquire the needed information.

Dynamic mechanical characteristics of deep Jinping marble in complex stress environments

To reveal the dynamic mechanical characteristics of deep rocks,a series of impact tests under triaxial static stress states corresponding to depths of 300-2400 m were conducted.The results showed that both the strain rates and the stress environments in depth significantly affect the mechanical characteristics of rocks.The sensitivity of strain rate to the dynamic strength and deformation modulus shows a negative correlation with depth,indicating that producing penetrative cracks in deep environments is more difficult when damage occurs.The dynamic strength shows a tendency to decrease and then increase slightly,but decreases sharply finally.Transmissivity demonstrates a similar trend as that of strength,whereas reflectivity indicates the opposite trend.Furthermore,two critical depths with high dynamically induced hazard possibilities based on the China Jinping Underground Laboratory(CJPL)were proposed for deep engineering.The first critical depth is 600-900 m,beyond which the sensitivity of rock dynamic characteristics to the strain rate and restraint of circumferential stress decrease,causing instability of surrounding rocks under axial stress condition.The second one lies at 1500-1800 m,where the wave impedance and dynamic strength of deep surrounding rocks drop sharply,and the dissipation energy presents a negative value.It suggests that the dynamic instability of deep surrounding rocks can be divided into dynamic load dominant and dynamic load induced types,depending on the second critical depth.

Static Analysis of Doubly-Curved Shell Structures of Smart Materials and Arbitrary Shape Subjected to General Loads Employing Higher Order Theories and Generalized Differential Quadrature Method

The article proposes an Equivalent Single Layer(ESL)formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions.A parametrization of the physical domain is provided by employing a set of curvilinear principal coordinates.The generalized blendingmethodology accounts for a distortion of the structure so that disparate geometries can be considered.Each layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum.In addition,re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model.The unknown variables are described employing a generalized displacement field and pre-determined through-the-thickness functions assessed in a unified formulation.Then,a weak assessment of the structural problem accounts for shape functions defined with an isogeometric approach starting fromthe computational grid.Ageneralizedmethodology has been proposed to define two-dimensional distributions of static surface loads.In the same way,boundary conditions with three-dimensional features are implemented along the shell edges employing linear springs.The fundamental relations are obtained from the stationary configuration of the total potential energy,and they are numerically tackled by employing the Generalized Differential Quadrature(GDQ)method,accounting for nonuniform computational grids.In the post-processing stage,an equilibrium-based recovery procedure allows the determination of the three-dimensional dispersion of the kinematic and static quantities.Some case studies have been presented,and a successful benchmark of different structural responses has been performed with respect to various refined theories.

Effects of Microstructure on Quasi⁃Static Transverse Loading Behavior of 3D Circular Braided Composite Tubes

The effects of microstructure on quasi-static transverse loading behavior of 3D circular braided composite tubes were studied. Transverse loading tests were conducted. Transverse load-deflection curves were obtained to analyze the effects of braiding parameters including the braiding angle, the wall thickness, and the diameter on the transverse loading of 3D circular braided composite tubes. Breaking loads, moduli and strengths had also been used to describe the transverse loading behaviors. The failure morphologies were shown to reveal damage mechanisms. From the results, the increase in braiding angle, wall thickness and diameter increases the ability of anti-deformation and breaking load of braided tubes. The breaking load of specimen with a braiding angle of 45° is about 1.68 times that of specimen with a braiding angle of 15°. The breaking load of specimen with 4 layers of yarns is about 2.15 times that of specimen with 2 layers of yarns. The breaking load of the tube with a diameter of 25.5 mm is about 2.39 times that of the tube with a diameter of 20.5 mm.

NMR-based damage characterisation of backfill material in host rock under dynamic loading

It is not uncommon that backfill material used in underground mining being exposed to repetitive dynamic stresses induced by blasting operations or rockburst events. Understanding the strength and fracture evolution of backfilled stopes is critical to maintain the long-term stope stability and ensure safe mining activities. This paper aims to study the damage evolution of the backfill material and its host rock behaviour under three-dimensional(3D) dynamic loading. Using a true-triaxial testing machine, multiple samples of backfill material enclosed by country rock were fabricated and tested under various dynamic loadings with different true-triaxial confining stress conditions. In addition, the nuclear magnetic resonance(NMR) measurement was conducted on the samples before and after exerting static and dynamic loading to obtain their porosity distribution changes. The experiment results suggested that with the increase of the dynamic loading, the porosity of the backfill sample goes through a two-stage process,which shows a slightly linear decrease and then followed by an exponential increase. The research findings can help understand the damage mechanism and fracture development of backfilled stopes and its host rock in deep underground mines, which are constantly subject to the combination of 3D static confining stress and dynamic loading.

Numerical simulation of dynamic fracture properties of rocks under different static stress conditions

When underground cavities are subjected to explosive stress waves,a uniquely damaged zone may appear due to the combined effect of dynamic loading and static pre-load stress.In this study,a rate-dependent two-dimensional rock dynamic constitutive model was established to investigate the dynamic fractures of rocks under different static stress conditions.The effects of the loading rate and peak amplitude of the blasting wave under different confining pressures and the vertical compressive coefficient(K_(0))were considered.The numerical simulated results reproduced the initiation and further propagation of primary radial crack fractures,which were in agreement with the experimental results.The dynamic loading rate,peak amplitude,static vertical compressive coefficient(K_(0))and confining pressure affected the evolution of fractures around the borehole.The heterogeneity parameter(m)plays an important role in the evolution of fractures around the borehole.The crack propagation path became more discontinuous and rougher in a smallerheterogeneity parameter case.

A Strategy for Loading Oblique Photogrammetry Models and Multilayer Basemap Data

With the development of drone technology and oblique photogrammetry technology, the acquisition of oblique photogrammetry models and basemap becomes more and more convenient and quickly. The increase in the number of basemap leads to excessively redundant basemap tiles requests in 3D GIS when loading oblique photogrammetry models, which slows down the system. Aiming at improving the speed of running system, this paper proposes a dynamic strategy for loading basemap tiles. Different from existing 3D GIS which loading oblique photogrammetry models and basemap tiles inde-pendently, this strategy dynamically loads basemap tiles depending on different height of view and the range of loaded oblique photogrammetry models. We achieve dynamic loading of basemap tiles by predetermining whether the basemap tiles will be covered by the oblique photogrammetry models. The experimental results show that this strategy can greatly reduce the num-ber of redundant requests from the client to the server while ensuring the user’s visual requirements for the oblique photogrammetric model.

扰动诱发高应力岩石动力响应及岩爆灾变机制

为揭示深部矿山岩爆发生机制,以硬质红砂岩为研究对象,利用岩石动静组合加载试验系统开展了无轴向静压及4个轴压条件下的不同入射能冲击试验,获得了纯动载及动静组合加载下岩样的力学行为与破坏特征。结果表明:试样最终形态分为完整、轴向劈裂、表面剥离、即时型粉碎和滞后型粉碎五类,其中,表面剥离和滞后型粉碎两类破坏模式表现出“岩爆”特征,即Ⅰ型应力−应变曲线、峰后释放能量、岩石自身静应变储能驱动碎片弹射、明显压剪破坏面;根据碎片弹射与动力加载的相对时间,进一步将表面剥离与滞后型粉碎破坏分别对应深地工程中的“即时型”和“滞后型”岩爆;动力扰动是岩爆的关键诱发因素,触发岩爆的临界扰动能随轴压比升高而逐渐降低。

岩体弱化方法及其在深部高应力硬岩机械化开采中的应用

战略性矿产资源的安全保供是国家重大战略需求,向地球深部要矿产资源在未来相当长一段时间内具有不可替代的战略性。为了保障矿产资源需求,深部高应力硬岩的安全高效开采是深部采矿必须解决的重大问题。首先,本文阐述了深部高应力硬岩采矿的技术挑战及“变害为利”的采矿变革思路,提出了高应力硬岩弱化后再开展机械破岩以实现商业化开采的关键技术对策。然后,总结了“接触式”和“非接触式”岩体弱化方法的机理、具体特点与发展现状,并对比分析了两类岩体弱化方法在辅助高应力硬岩机械破岩领域的发展潜力。最后,展望了以深部高应力硬岩热剥落损伤弱化辅助机械破岩为代表的安全高效连续采矿技术,为深部战略性矿产资源安全保供与深地工程发展提供了有益指导。

动静组合加载下砂岩剪切力学特性试验研究

动载扰动作用是影响遗煤复采过程中围岩稳定性的重要因素,为研究不同预静载水平下动载扰动对砂岩抗剪强度、黏聚力、内摩擦角、应变场及声发射等参数的影响,采用动静载多场耦合试验系统、声发射监测系统和DIC应变监测系统对砂岩进行了动静组合加载变角剪切试验。研究结果表明:在组合加载下,随着预静载水平的增大,砂岩抗剪强度和黏聚力呈先增大后减小的趋势,内摩擦角和扰动前后最大主应变差值呈先减小后增大的趋势,均在75%τ预静载水平处达到极值;在组合加载下,声发射累计能量和累计振铃计数整体上可划分为第一稳定增长期、第一突增期、平静期、第二突增期、第二稳定增长期和第三突增期6个阶段,在扰动阶段声发射信号活跃程度随着预静载水平的增大呈先减小后增大的趋势,极值出现在60%τ预静载水平处。研究成果可为动静组合加载下围岩稳定性控制提供理论参考。

砂型3D打印类煤试样动静组合加载力学特性

深部煤矿巷道围岩软弱、裂隙发育,动载影响下易引发动力灾害,其中软岩及节理岩体动力学试验研究是解决上述问题的关键。3D打印技术因其能突破浇筑法在制作复杂节理试样上的局限,被广泛应用于岩石力学试验研究,而应用该技术的关键是所制类煤试样的静态和动态力学特性与天然岩石相似。基于砂型3D打印试样,通过开展单轴压缩、巴西劈裂等力学试验,揭示了砂型3D打印试样与煤样弹塑性力学特性的相似性,利用分离式霍普金森压杆(SHPB)装置开展不同动静组合加载试验,采用宏观破碎块度和细观电镜扫描综合分析等手段,对不同动静组合荷载下砂型3D打印试样的动力响应与破坏特征进行研究。结果表明:砂型3D打印试样的动态强度和组合强度与冲击气压的增大呈正相关关系,动态强度与轴压的增大呈负相关关系,组合强度随轴压的增大呈先增大后减小的变化,这说明岩石抵抗动载的能力随轴压的增大呈先增强后减弱的变化;随着静、动荷载水平的提高,试样的破碎块度逐渐细粒化,其中动载对试样破碎程度的影响最显著。揭示了砂型3D打印试样的动力学特性并验证了其应用于煤岩动力学试验的可行性,为采用砂型3D打印技术开展岩石动力学试验提供了重要基础,研究结果有助于进一步揭示不同地应力与动载条件下围岩动力破坏规律。