Projectile impact on soft,porous rock

SummaryProjectile Impact on Soft, Porous Rock An experimental investigation was conducted to study the penetration phenomena associated with the normal impact of 60° conical and hemispherically-tipped cylindrical projectiles with a 6.35 mm diameter on green shale in the velocity range from 18 to 40 m/s. In addition to initial velocity, a special device measured the velocity history of the striker during penetration, and the deformation pattern of the target was obtained from grid lines inscribed on a vertical diametral section of the specimen which was reassembled by emplacement in a steel ring before testing. The results showed that the tip geometry controlled the penetration depth which was quadratically related to the initial kinetic energy. Comparison with other data using spherical strikers indicated that only the contact geometry, and not the configuration nor mass of the rest of the striker determined the indentation depth for the same initial bullet energy within the present range of impact parameters.The tests also indicated that target deformation was comprised of material compaction varying in degree from a maximum at the initial contact point towards the target interior and equivolumnial material distortion. A computational model was constructed incorporating both of these features based on an experimentalempirical relation between hydrostatic pressure and volumetric strain and two representations for the effective stress-strain relation of an elastic-perfectly plastic comportment of the material. It was found that good agreement was obtained between the observed deformation pattern and the predictions of this model when flow stress was considered to be independent of volumetric strain, but less so when this quantity was taken as a function of this strain. The model also adequately predicted the velocity history of the projectile both for the present tests and those involving spherical strikers conducted previously.With 15 Figures     

Effect of Specimen Geometry and Testing Method on Mixed Mode I–II Fracture Toughness of a Limestone Rock from Saudi Arabia

Summary The effect of testing method and specimen geometry such as diameter, thickness, and crack length and type on measured fracture toughness was investigated using specimens collected from a limestone rock formation outcropping in the Central Province of Saudi Arabia. Straight Edge Cracked Round Bar Bend (SECRBB), semicircular disk specimens under three point bending, and Brazilian disk specimens under diametrical compression were used in this investigation. SECRBB specimens were used for the Mode-I study, and notched Brazilian disk and semicircular specimens were used for the mixed Mode I–II study. The results show that specimen diameter and crack type have a substantial influence on the measured fracture toughness; however, loading rate, crack size, and specimen thickness seem to have a negligible effect on the fracture toughness. Mode-I fracture toughness is significantly influenced by specimen diameter and crack type, while their effects on Mode-II fracture toughness are generally negligible. The different specimens (SECRBB, Brazilian disk, and semicircular) can give comparable results only when the proper span to diameter ratio is used. The Brazilian disk with a straight notch was found to be the most convenient geometry to use for fracture toughness determination. A simple method of making a precise notch inside the disk is presented, using the combination of a drilling machine and a wire saw.     

The discovery and history of the Dalgaranga meteorite crater,Western Australia

The Dalgaranga meteorite crater, 100 km northeast of Yalgoo, Western Australia, was one of the first impact structures identified in Australia, the smallest isolated crater found in Australia, and the only confirmed crater in the world associated with a mesosiderite projectile. Seventeen years passed before the Dalgaranga meteorites were described in the scientific literature, and nearly 40 years passed before a survey of the structure was published. The reasons for the time gap were never explained and a number of factual errors about the discovery and early history remain uncorrected in the scientific literature. Using historical and archival documents, and discussions with people involved in Dalgaranga research, the reasons for this time gap are explained by a series of minor misidentifications and coincidences. The age of the crater has yet to be determined, but using published data, we estimate the projectile mass to be 500–1000 kg.     

花岗岩岩桥卸荷脆性破坏的能量特征

岩质边坡锁固段型岩桥的破坏和能量的累积与释放密切相关,利用MTS815伺服控制刚性力学试验机对花岗岩岩桥试样开展了常规三轴加荷试验和三轴加卸荷试验,采用基于轴向应力比的能量分析方法,可对不同工况下峰前加载各阶段能量变化趋势进行有效的对比分析。结果表明:应力峰值前能量特征变化主要分为压密阶段与弹性阶段,试样处于压密阶段,随着初始裂纹的闭合与摩擦,耗散能占比大幅增加;弹性阶段,荷载所做功大部分转化为弹性能储存在试样内部,弹性能占比大幅增加。由于预制裂隙存在,在临近破坏前没有出现明显的屈服阶段,岩桥试样表现为“突发式”的脆性破坏;初始围压的提升会使得应力峰值点的总能量、弹性能明显增大;花岗岩试样的岩桥越长,其吸收的总能量、弹性储能极限越大,应力峰值点的弹性能占总能量比值越高,岩桥长度变化则对耗散能没有明显影响。     

Strain Rate Dependency of Coarse Crystal Marble Under Uniaxial Compression: Strength,Deformation and Strain Energy

Strain rate during testing, uniaxial or triaxial, has important influence on the measured mechanical properties of rocks. Uniaxial compression tests were performed at nine pre-specified static-to-quasistatic strain rates (ranging from 1 × 10^?5 to 1 × 10^?1 s^?1) on coarse crystal marble. The aim is to gain deep insight into the influence of strain rate on characteristic stresses, deformation properties and conversion of strain energy of such rock. It is found that the strain rate of 5 × 10^?3 s^?1 is the threshold to delineate the failure modes the tested coarse marble behaves in. At a strain rate less than this threshold, single-plane shear and conjugate X-shaped shear are the main failure modes, while beyond this threshold, extensile and splitting failures are dominant. The stress for crack initiation, the critical stress for dilation, the peak stress, and Young’s modulus are all found to increase with strain rate, with an exception that the above stresses and modulus appear relatively low compared to the strain rate in the range of between 1 × 10^?4 and 5 × 10^?3 s^?1. The pre-peak absorbed strain energy, damage strain energy and elastic strain energy are found to increase with strain rate. In addition, the elastic strain energy stored before peak point favors brittle failure of the specimen, as the more stored elastic energy in the specimen, the stronger the fragmenting.     

An analytical and experimental investigation of the effect of impact on coarse granular rocks

SummaryAn Analytical and Experimental Investigation of the Effect of Impact on Coarse Granular Rocks The interaction between metallic strikers and coarse, granular rock, associated with many mechanical rock breaking methods was investigated by theoretical and experimental methods. Cylindrical steel strikers of 12.7 mm diameter with flat, conical and hemispherical tips and masses of about 18.5 g were fired by means of a gas gun at blocks of diorite and spessartite with initial energies ranging from 4 to 34 J, generating substantial fracturing. The damage pattern in the rocks was ascertained, partly with the aid of a scanning electron microscope. A synthetic model consisting of long square bars of cement paste bonded with an adhesive was constructed as a simulator of diorite and tested to further delineate the failure mechanisms in this material.As previously, it was also found here that the geometry of the striker tip significantly affects the damage pattern and extent in diorite. A crucial difference in this pattern was observed between that found in diorite, a coarsegrained rock, and in spessartite, a more finely-grained substance. The crack network in diorite consisted of numerous kinked fractures extending a distance not in excess of 20 grain lengths, whereas only 5 to 7 nearly straight cracks with a length in excess of 20 times the grain size were found in spessartite that appeared to have propagated without regard to the grain packing structure or material defects. The synthetic rock model successfully reproduced the crack pattern found in diorite under impact.An analytical model to predict the region of grain and grain boundary failure incorporating one failure criterion for grains and another for grain boundaries was constructed. The first involved the development of failure surfaces based on an empirical limiting strength analogous to the modified Griffith criterion. Grain boundary failure was stipulated upon attainment of a combination of critical tensile and Coulomb type of shear stress. The model successfully delineated the major features of damage in the synthetic rock and in diorite and established upper bound predictions for the extent of damage.With 19 Figures     

Reconstructing the Wolfe Creek meteorite impact: deep structure of the crater and effects on target rock

The Wolfe Creek Meteorite Crater is an impact structure 880 m in diameter, located in the Tanami Desert near Halls Creek, Western Australia. The crater formed?<?300 000 years ago, and is the second largest crater from which fragments of the impacting meteorite (a medium octahedrite) have been recovered. We present the results of new ground-based geophysical (magnetics and gravity) surveys conducted over the structure in July?–?August 2003. The results highlight the simple structure of the crater under the infilling sediments, and forward modelling is consistent with the true crater floor being 120 m beneath the present surface. The variations in the dip of the foliations around the crater rim confirm that the meteorite approached from the east-northeast, as is also deduced from the ejecta distribution. Crater scaling arguments suggest a projectile diameter of?>?12.0 m, a crater formation time of 3.34 s, and an energy of impact of ～0.235 Mt of TNT. We also use the distribution of shocked quartz in the target rock (Devonian sandstones) to reconstruct the shock loading conditions of the impact. The estimated maximum pressures at the crater rim were between 5.59 and 5.81 GPa. We also use a Simplified Arbitrary Langrangian–Eulerian hydrocode (SALE 2) to simulate the propagation of shock waves through a material described by a Tillotson equation of state. Using the deformational and PT constraints of the Wolfe Creek crater, we estimate the maximum pressures, and the shock-wave attenuation, of this medium-sized impact.     

Suevite of the ries crater,Germany: Source rocks and implications for cratering mechanics

Suevites are impact breccias with a montmorillonitic matrix that contains shocked and unshocked mineral and rock fragments from the crystalline basement, glass inclusions and a small amount of sedimentary clasts. Data are given of the modal composition of fall-out suevites (deposited at isolated points around the crater) and crater suevite (forming a layer below post-impact lake sediments in the crater cavity). Fall-out suevites contain aerodynamically shaped bombs which are absent in crater suevite. Taking into account not only large glass fragments and bombs, but also the finer fractions, the glass content of fall-out and crater suevites amounts to 47 and 29 vol%, respectively. Crystalline clasts in suevites consist of all igneous and metamorphic rock types that constitute the local basement which consists of an upper layer of igneous rocks (mainly granites) and a lower series of gneisses and amphibolite. Based on a collection of 1 200 clasts from 13 suevite occurrences the average crystalline clast population of suevites was determined. Suevites contain on the average 46 % igneous and 54 % metamorphic clasts. In constrast, weakly shocked and unshocked crystalline ejecta of the Ries structure consist of 82 % igneous and 18 % metamorphic rocks. From 138 analyses of crystalline rock samples average compositions of the major rock types were calculated. Comparison of these averages with the average glass composition leads to the conclusion that suevite glasses were formed by shock melting of gneisses in deeper levels of the basement. Suevite matrices consist in most cases of 80 to 90 % montmorillonite, in special cases of celadonite. Chemical analyses are given of some matrices and montmorillonite formulas calculated. It is supposed that montmorillonite was formed by early hydrothermal alteration of rock flour or fine glass particles. In the latter case the original glass content of suevites was higher than at present. Of all ejecta from the Ries crater only crystalline rocks contained in suevites occur in all stages of shock metamorphism up to complete fusion. The overwhelming majority of the ejecta from the sedimentary sequence (about 580 m) show no indications of shock pressures above 10 GPa. The same holds true for crystalline megablocks and breccias around the crater which consist mainly of granites from upper levels of the basement. We assume that the Ries impact can be approximated by a deep-burst model: The projectile penetrated through the sedimentary cover into the basement in such a way that the highest pressures and temperatures developed within the gneiss complex below the upper, predominately granitic layer and that rocks of the sedimentary sequence experienced weak shock compression. Numerical data are given for such a model of the Ries impact on transient crater geometry and volumes of vaporized, melted, shocked and excavated rocks. Fall-out suevites are supposed to have been lifted from the central zone by an expanding plume of vaporized rocks and deposited as fluidized turbulent masses outside the crater whereas the main mass of crater suevite was not removed from the crater cavity.     

Modeling the 3D crack network and anisotropic permeability of saturated cracked soil

Cracks on a natural soil surface provide preferential pathways for water infiltration and contaminant solute transport. Before the mechanical property and permeability of cracked soil can be studied, a crack network model must first be established. Based on statistical analysis of crack geometry from field observations, a new method of representing a 3D crack network was developed. A horizontal plane of a crack network was derived using the Voronoi diagram. Each vertical crack was idealized as an inverted triangular prism. The 3D permeability tensor was determined by modeling the water flow through the crack network. A computer program was developed to generate a 3D crack network automatically and compute the permeability tensor of cracked soil at different depths. The model was verified by comparing the measured permeability and computed permeability of cracked soil. The results showed that the computed permeability was consistent with the measured permeability.     

Dynamic Brazilian Tests of Granite Under Coupled Static and Dynamic Loads

Rocks in underground projects at great depth, which are under high static stresses, may be subjected to dynamic disturbance at the same time. In our previous work (Li et al. Int J Rock Mech Min Sci 45(5):739–748, 2008), the dynamic compressive behaviour of pre-stressed rocks was investigated using coupled-load equipment. The current work is devoted to the investigation of the dynamic tensile behaviour of granite rocks under coupled loads using the Brazilian disc (BD) method with the aid of a high-speed camera. Through wave analyses, stress measurements and crack photography, the fundamental problems of BD tests, such as stress equilibrium and crack initiation, were investigated by the consideration of different loading stresses with abruptly or slowly rising stress waves. The specially shaped striker method was used for the coupled-load test; this generates a slowly rising stress wave, which allows gradual stress accumulation in the specimen, whilst maintaining the load at both ends of the specimen in an equilibrium state. The test results showed that the tensile strength of the granite under coupled loads decreases with increases in the static pre-stresses, which might lead to modifications of the blasting design or support design in deep underground projects. Furthermore, the failure patterns of specimens under coupled loads have been investigated.     

Modeling soil desiccation cracking by analytical and numerical approaches

An energy approach is proposed as a complement to the stress approach commonly considered for investigating soil desiccation cracking. The elastic strain energies before and after crack initiation are estimated by both numerical and analytical solutions. The energy released by cracking is then compared with the fracture energy to discuss crack initiation conditions. This leads to combined energy and stress conditions for crack initiation following Leguillon's theory. An approximate analytical solution is derived from a variational formulation of the porous elastic body equations. A cohesive zone model and finite element code are used to simulate crack propagation in an unsaturated porous body. This analysis shows that the energy criterion is reached before the stress criterion, and this can explain unstable crack propagation at the beginning. The approximate analytical solution allows predicting correctly the crack depth and opening in its initiation stage.     

Testing the resolution of a 3D velocity tomogram across the Chicxulub crater

An integrated offshore/onshore reflection and refraction experiment was shot across the Chicxulub impact crater in 1996. The refraction data were previously inverted in 3D using first-arrival travel-time tomography. A regularized inversion, in which both data misfit and model roughness are minimized simultaneously, was used to determine a smooth velocity tomogram across the inner crater region. However, the experimental geometry for the refraction data was irregular, causing concern that this velocity model might not be well resolved. In this paper, we present a suite of checkerboard tests to investigate the lateral resolution of our velocity model. The Chicxulub crater is located partly onshore and partly offshore, with its centre close to the Yucatan coastline in Mexico. The shallow water limited acquisition of marine reflection data to distances of not closer than 25 km from the crater centre, and the centre of the structure is imaged with refraction data only. Intriguing velocity anomalies were observed across the central crater region, providing constraints on the lithological and structural form of Chicxulub. A high-velocity body within the central crater is most likely to represent lower-crustal rocks that were stratigraphically uplifted during the formation of this complex crater. The concave shape of this stratigraphic uplift suggests clues to the mechanics of large-crater collapse—the rocks appear to have moved upward and outward. An inward-dipping zone of lowered velocity has been interpreted as delimiting the outer edge of a central zone of melt-rich rocks. The resolution tests presented here indicate that these observed velocity anomalies are likely to be real.     

Fracture mechanics analysis of multiple cracks in anisotropic media

This paper presents a single‐domain boundary element method (BEM) for linear elastic fracture mechanics analysis in the two‐dimensional anisotropic material. In this formulation, the displacement integral equation is collocated on the un‐cracked boundary only, and the traction integral equation is collocated on one side of the crack surface only. A special crack‐tip element was introduced to capture exactly the crack‐tip behavior. A computer program with the FORTRAN language has been developed to effectively calculate the stress intensity factors of an anisotropic material. This BEM program has been verified having a good accuracy with the previous researches. Furthermore, by analyzing the different anisotropic degree cracks in a finite plate, we found that the stress intensity factors of crack tips had apparent influence by the geometry forms of cracks and media with different anisotropic degrees. Copyright © 2010 John Wiley & Sons, Ltd.     

Coupled flow network and discrete element modeling of injection-induced crack propagation and coalescence in brittle rock

We present a numerical analysis on injection-induced crack propagation and coalescence in brittle rock. The DEM network coupling model in PFC is modified to capture the evolution of fracture geometry. An improved fluid flow model for fractured porous media is proposed and coupled with a bond-based DEM model to simulate the interactions among cracks induced by injecting fluid in two nearby flaws at identical injection rates. The material parameters are calibrated based on the macro-properties of Lac du Bonnet granite and KGD solution. A grain-based model, which generates larger grains from assembles of particles bonded together, is calibrated to identify the microscopic mechanical and hydraulic parameters of Lac du Bonnet granite such that the DEM model yields a ratio between the compressive and tensile strength consistent with experiments. The simulations of fluid injection reveal that the initial flaw direction plays a crucial role in crack interaction and coalescence pattern. When two initial flaws are aligned, cracks generally propagate faster. Some geometrical measures from graph theory are used to analyze the geometry and connectivity of the crack network. The results reveal that initial flaws in the same direction may lead to a well-connected crack network with higher global efficiency.

     

Fracture energy release and size effect in borehole breakout

The paper presents a simple approximate analytical solution of the remote stresses that cause the collapse of a borehole or other circular cylindrical cavity in an infinite elastic space. Regions of parallel equidistant splitting cracks are assumed to form on the sides of the cavity. Their boundary is assumed to be an ellipse of a growing horizontal axis, the other axis remaining equal to the borehole diameter. The slabs of rock between the splitting cracks are assumed to buckle as slender columns, and their post-critical stress is considered as the residual stress in the cracked rock. The buckling of these slab columns is assumed to be resisted not only by their elastic bending stiffness but also shear stresses produced on rough crack faces by relative shear displacements. The energy release from the infinite medium caused by the growth of the elliptical cracking region is evaluated according to Eschelby's theorem. This release is set equal to the energy dissipated by the formation of all the splitting cracks, which is calculated under the assumption of constant fracture energy. This yields the collapse stress as a function of the elastic moduli, fracture energy, ratio of the remote principal stresses, crack shear resistance characteristic and borehole diameter. The collapse stress as a function of crack spacing is found to have a minimum, and the correct crack spacing is determined from this minimum. For small enough diameters, the crack spacing increases as the (4/5)-power of the borehole diameter, while for large enough diameters a constant spacing is approached. In contrast to plastic solutions, the breakout stress exhibits a size effect, such that for small enough diameters the breakout stress decreases as the (? 2/5)-power of the borehole diameter, while for large enough diameters a constant limiting value is approached. Finally, some numerical estimates are given and the validity of various simplifying assumptions made is discussed.     

一种基于弹性应变能的裂隙岩体等效弹性模量评价方法

基于线弹性断裂力学裂隙面张开位移及剪切位移理论公式,考虑裂隙存在常法向和常切向刚度情况,研究了含单个裂隙岩体加载过程中由于裂隙存在而附加的弹性应变能。基于应变能等效方法并假设两种裂隙变形模型--非均匀变形模型和均匀变形模型,研究了二维非贯通裂隙岩体的等效杨氏模量和等效剪切模量解析表达式。研究结果表明,对于贯通裂隙规则分布情况,均匀变形模型得到的解析解与Amadei等的结果一致;对于非贯通裂隙正态分布情况,考虑裂隙相互作用的非均匀变形模型解明显低估裂隙岩体的等效杨氏模量和等效剪切模量,而考虑裂隙相互作用的均匀变形模型解与有限元数值解的偏差在10%以内。得到的解析表达式在一定条件下可以作为裂隙岩体等效弹性模量评价方法之一。     

Investigation of crack formation during loading of brittle rock

Conclusions The response of elastic/brittle targets to loading by conical-, wedge-and hemispherical-indenter shapes representing jackhammer bit tips was analyzed. Theoretical predictions of crack extent and direction are based on values of the maximum principal strains and the associated extension strain criterion in the target assuming a semi-infinite, homogeneous and isotropic solid.Corresponding static experiments using an MTS machine and dynamic percussive tests involving an encased circular target disk of Sierra granite have been conducted. The damage pattern consisting of a crater, a crushed zone, a region of multiple minor cracks as well a some longer fissures has been delineated. Comparison with theoretical predictions indicate that cracks are produced by maximum tensile strain, with their directions predicted well by the present theory. The upper bound predictions of the crack extent are also in reasonable accord. Deviations are due to the presence of inhomogeneities and anisotropies in the tests specimens.     

岩石非理想裂纹圆盘试件动态断裂韧性测试的有限元分析及试验研究

采用中心裂纹圆盘-霍普金森压杆(CCCD-SHPB)试验系统对大理岩中心裂纹圆盘试件进行不同加载速率下的纯Ⅰ型加载试验,研究岩石材料动态断裂韧性的加载速率相关性。考虑到试验中所使用的圆盘试件是带有中心切口的非理想裂纹,结合试件的实际加工情况,提出采用切口尖端形状为小圆弧形的预制裂纹,介绍了试件的制作方法,并利用有限元计算论证了采用这种形状非理想裂纹试件的试验可行性。结果表明,采用圆弧形裂尖、裂纹宽度为1 mm的中心切口非理想裂纹圆盘试件来代替理想裂纹圆盘试件是可行的,误差不超过2.13%。分析试验数据得出：非理想裂纹圆盘试件在纯Ⅰ型加载条件下,其断裂韧度表现出明显的速率相关性,且随着加载速率的增大而增大。     

Identification of the projectile at the Brent crater,and further considerations of projectile types at terrestrial craters

Impact melt samples from drill hole B1-59 at the 3.8 km diameter Brent crater (Ontario) have been analysed for siderophile trace elements indicative of meteoritic contamination. Samples from the basal melt zone at 823–857 m depth are enriched in Ir, Os, Pd, Ni, Co, Cr and Se over basement, with the abundance pattern suggesting a chondritic projectile for Brent. From a Ni-Cr correlation of 10 melt samples an L or LL chondrite is inferred. The contribution of an ultramafic country rock (alnoite) in the melt is too small to significantly influence its $\text{Ni}\text{Cr}$ ratio. Glass-rich breccias from the allochthonous breccias filling the crater also contain a meteoritic component. Interelement ratios (e.g. $\text{Ni}\text{Cr}$) are, however, fractionated relative to the melt zone samples. This, as well as the low Au content of all Brent samples, is probably a product of alteration.Additional data on impact melts from the 65 km diameter crater Manicouagan still did not reveal a meteoritic component, as also for the Mistastin crater (28 km diameter) where Cr analyses set an upper limit of 1% of an achondritic projectile component in the melt. Irghizites (tektite like glasses) from the Zhamanshin impact structure have been found to contain high Ni and Co concentrations, and our data show that Ir is also enriched. It is however not possible to define the projectile-type. Enrichment of an Ivory Coast tektite in Ir is confirmed. There are large differences in siderophile element concentrations among tektites, with otherwise similar chemical composition.There are now four known craters formed by chondrites (Clearwater East, Lapparjärvi, Wanapitei, and Brent), with Brent being the smallest of these. For smaller craters the projectiles appear to be limited to iron or stony-iron meteorites, because of atmospheric destruction of relatively small stony meteorites. It appears, however, that all major classes of meteorites are represented among the projectiles at terrestrial impact craters.     

Influence of boundary conditions,specimen geometry and material heterogeneity on model calibration from triaxial tests

The recent capability of measuring full‐field deformations using advanced imaging techniques provides the opportunity to improve the predictive ability of computational soil mechanics. This paper investigates the effects of imperfect initial specimen geometry, platen‐soil and apparatus compliance, and material heterogeneity on the constitutive model calibration process from triaxial tests with nonlubricated platens. The technique of 3D‐Digital Image Correlation (3D‐DIC) was used to measure, from digital images, full‐field displacements over sand specimen surfaces throughout triaxial compression tests, as well as actual specimen initial shape, and deformations associated with platen and apparatus compliance and bedding settlement. The difference between predicted and observed 3D specimen surface deformations served to quantify an objective function in the optimization algorithm. Four different three‐dimensional finite element models (FEMs), each allowing varying degrees of material variability in the solution of the inverse problem, were used to study the effect of material heterogeneity. Results of the parametric study revealed that properly representing the actual initial specimen geometry significantly improves the optimization efficiency, and that accounting for boundary compliance can be critical for the accurate recovery of the full‐field experimental displacements. Allowing for nonsymmetric material variability had the most significant impact on predicted behavior. A relatively high coefficient of variation in model parameters was found among a statistical ensemble of tests, underscoring the importance of conducting multiple tests for proper material characterization. Copyright © 2009 John Wiley & Sons, Ltd.