Approximate model for blunt objects indenting cohesive‐frictional materials

An approximate two‐dimensional model for indentation of blunt objects into various types of rigid‐perfectly plastic cohesive‐frictional material is derived. Particular emphasis is placed on considering indentation as a process involving evolution of the boundary of material displaced by the indenter. Force–penetration relationships are obtained by an incremental approach utilizing key kinematic and static information from indentation of a flat punch. Albeit approximate, the proposed model applies to arbitrary indenter geometry and weightless or ponderable cohesive‐frictional materials exhibiting associated or non‐associated plastic flow. Two specific indenter geometries, the cylinder and blunt wedge, are explored in detail. Favorable agreement is found between the analytic results and those obtained using the finite element method (FEM). For both the wedge and cylinder, it is further shown that accurate analytic expressions relating indentation force explicitly to penetration can be derived. In the case of the wedge and weightless material, predictions of indentation force obtained from the derived expressions are very close to those computed from implicit equations available in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

Identification of the governing parameters related to rock indentation depth by using similarity analysis

This paper focuses on the indentation depth in rocks caused by a hemispherical indenter. The problem is approached by a combination of similarity methods with an artificial neural network. The similarity methods offer a profound understanding of the physical problem and help to identify the most important governing parameters or factors that reflect the essence of the rock indentation events, thus simplifying the target problem. The artificial neural network provides an advanced computing model, which allows more factors to be involved. The predictions obtained using this combined approach are in better agreement with the experimental results than predictions using other methods.     

一个新的岩石力学特性测定方法

当前,压痕试验是测定金属、高聚物和陶瓷等材料力学特性的一种十分有效且简便的方法。本文旨在探讨如何应用该方法测定岩石材料的力学特性。介绍了一种新的用于岩石材料测试的微痕试验（微米级压痕试验）系统和它的校准方法,具体阐述了该方法在岩石上的应用。通过和常规单压试验结果的比较,讨论了岩石杨氏弹性模量和抗压强度指标的测量结果。介绍了该设备在进行有压微痕试验的改进,并通过对砂岩的有压微痕试验反映出砂岩力学性能对于围压的依赖性。     

Determination of unconfined compressive strength and Young's modulus of porous materials by indentation tests

The formation of a compacted zone under the indenter seems to be the major factor controlling the indentation process in porous rocks. In the case of very porous materials, where the pore structure fails and deformation (by structural collapse) proceeds with almost no increase in the applied load and with very limited damage to the surrounding material, no chipping is observed. The extent of the compacted zone is controlled by the porosity of the material and by the strength of its porous structure. This paper presents an interpretation model developed by the authors to obtain the uniaxial compressive strength of porous materials from the results of indentation tests. It is based on the model proposed by Wilson et al. (Int. J. Mech. Sci., 17, 1975, 457) for the interpretation of indentation tests on compressible foams and on an estimation by the authors of the extent of the compacted zone under the indenter. The results of indentation tests can also be used to obtain the Young's modulus of the material with a model proposed by Gill et al. (Proceedings of the 13th Canadian Symposium on Rock Mechanics, 1980, 1103). Uniaxial compression and indentation tests have been performed on artificial porous materials showing porosities varying between 44 and 68%. The uniaxial compressive strength values obtained from both types of test show a very good agreement. For the Young's modulus, the values obtained from the two types of test are different but the variation of the moduli with porosity is the same. Finally, a parameter called permanent penetration modulus is proposed as a means of characterizing the uniaxial compressive strength of porous materials.     

APPLICATION OF A SPLITTING FRACTURE MODEL TO THE SIMULATION OF ROCK INDENTATION SUBSURFACE FRACTURES

A two-dimensional fracture model based on micro-fracture mechanics is applied to the Hertzian indentation stress field to simulate subsurface fractures in an axi-symmetrical plane. The simulation of fracture development reveals quantitatively the effects of loading force, mechanical properties of the rocks, and original micro cracks on the formation of subsurface fractures. The distribution patterns of the subsurface fractures are determined by the magnitudes and trajectories of the indentation stresses. Lateral confinement prohibits the fracture development. Simulations of the subsurface fractures in granite and marble are in good agreement with the indentation experiments. © 1997 by John Wiley & Sons, Ltd.     

煤系钻探岩石可钻性分级方法的研究

研究了煤系中采用硬质合金钻进工艺时岩石可钻性分级的指标体系及测试方法;研制了一套能在野外流动条件下进行岩石可钻性分级测试的轻便仪器及工具。在7项分级指标体系中,压入强度、研磨性、塑性系数和用微型针状硬质合金钻头测试“微钻钻速”是首次应用,尤以用小试样测试“压入强度”及用微型针状硬质合金钻头测试“微钻钻进速度”两项指标能有效地反映煤系软岩石分级档次,可以弥补用微型孕镶金刚石钻头在6级以下较软岩石中无法钻进或达不到钻进指标的不足。     

Estimating the Peak Indentation Force of the Edge Chipping of Rocks Using Single Point-Attack Pick

This article establishes a new model for estimating the peak indentation force of the edge chipping of rocks when using a conical or a pyramidal point-attack pick. The investigation points out that the existing formulation in the literature is based on an inappropriate stress assumption and equilibrium, and hence leads to incorrect cutting force estimations. The new model developed in this study is based on an analysis of the penetration force and energy dissipation using fracture mechanics, similarity of chip geometry, and edge chipping tests on four different rock materials. It is found that the peak indentation force and the depth of cut follow a power law, that the new model can reasonably estimate the experimental measurements, and that it provides useful information for the shape optimization of point-attack picks in mechanical excavation.     

Syn-convergence exhumation of the Central Alps

Abstract

The exhumation of rocks in a plate convergence setting is commonly related to erosion and/or tectonic denudation accompanied by isostatic adjustment. Isostatic compensation is the physical response to denudation. It leads to unroofing of deep levels of the crust. A new model for producing topographic relief is proposed which explains well the rapid exhumation of high-temperature rocks in the Central Alps via erosion and tectonic denudation (i.e. gravitational collapse and normal faulting). It is shown that the forward motion of the cold and rigid Adriatic indenter into the European crust is twofold. Firstly, horizontal compression led to the vertical extrusion of the deepest ductile European basement into shallower levels. This tectonic process induced heat transfer through the southern steep belt as well as heat advection together with the extruded material, resulting in the metamorphic aureole observed in the Central Alps. Secondly, the lower part of the Adriatic crust protruded into the warm European crust as a result of continuous forward motion. Geophysical data suggest that the isostatic response to indentation (i.e. deepening of the alpine root) has been inhibited by the mechanical strength of the cold and rigid Adriatic crust. Then, the indentation process induced a deviation from isostatic equilibrium by creating a tremendous topographic relief. This relief disappeared rapidly, possibly as fast as it forms, by enhanced erosion and tectonic denudation leading to rapid exhumation of the metamorphic dome.     

楔形刀具侵入岩石损伤破坏影响因素的理论分析及数值模拟

通过空腔膨胀理论研究楔形刀具几何参数（刃角）、岩石力学参数（抗压强度、泊松比）对刀具与岩石接触面下岩石弹-塑性交界面半径的影响。结果表明：刀具与岩石接触宽度一定时,刃角越小,岩体的损伤区域越大,从而导致弹-塑性交界面半径增大。在其他因素不变的前提下,岩石泊松比增大或者抗压强度增加都导致弹-塑性交界面半径减小。采用参数敏感性分析方法对3种影响因素的敏感性进行了分析,在接触宽度一定的条件下,刃角的大小对弹-塑性交界半径的影响最大。采用ABAQUS软件建立刀具侵入岩石的数值模型,研究表明,刃角的变化对文中定义的岩体内最大拉应力点空间位置以及最小梯度方向有着显著影响。     

How hydrofractures become arrested

Fluids in the earth's crust are commonly transported by hydrofractures, such as dykes and mineral veins, many of which become arrested at various crustal depths. Hydrofractures are commonly arrested – some showing blunt tips – at contacts between soft (low Young's modulus) and stiff (high Young's modulus) layers. For example, many dyke tips are arrested at contacts between soft pyroclastic rocks and stiff basaltic lava flows, and vein tips at contacts between soft marl and stiff limestone. Theoretical models indicate that overpressured, buoyant hydrofractures in homogeneous, isotropic host rocks should normally reach the surface. In layered host rocks, however, abrupt changes in Young's moduli, horizontal discontinuities, and layers with unusually high fracture-perpendicular stresses encourage hydrofracture arrest. It is proposed that for layer-parallel loading, stiff layers favour hydrofracture arrest during active compression but soft layers during extension. It is concluded that for hydrofracture propagation to occur, the stress field along its potential pathway must be essentially homogenous.     

Nanochemo-mechanical signature of organic-rich shales: a coupled indentation–EDX analysis

The organic–inorganic nature of organic-rich source rocks poses several challenges for the development of functional relations that link mechanical properties with geochemical composition. With this focus in mind, we herein propose a method that enables chemo-mechanical characterization of this highly heterogeneous source rock at the micron and submicron length scale through a statistical analysis of a large array of energy-dispersive X-ray spectroscopy (EDX) data coupled with nanoindentation data. The ability to include elemental composition to the indentation probe via EDX is shown to provide a means to identify pure material phases, mixture phases, and interfaces between different phases. Employed over a large array, the statistical clustering of this set of chemo-mechanical data provides access to the properties of the fundamental building blocks of clay-dominated organic-rich source rocks. The versatility of the approach is illustrated through the application to a large number of source rocks of different origin, chemical composition, and organic content. We find that the identified properties exhibit a unique scaling relation between stiffness and hardness. This suggests that organic-rich shale properties can be reduced to their elementary constituents, with several implications for the development of predictive functional relations between chemical composition and mechanical properties of organic-rich source rocks such as the intimate interplay between clay-packing, organic maturity, and mechanical properties of porous clay/organic phase.     

Normal Wedge Indentation in Rocks with Lateral Confinement

Summary The paper reports results of a numerical analysis of the wedge indentation problem. The main objective of this research is to investigate the influence of the lateral confining stress on the development of the plastic zone under the indenter and on the initiation of tensile fractures. Numerical analysis indicates that the location of maximum tensile stress (interpreted as the point of crack initiation) moves away from the indentation axis as the lateral confinement increases. It is found that a small increase in the confining stress from zero induces a large increase in the inclination of this point on the indentation axis. However, the confinement does not reduce significantly the maximum tensile stress and it hardly influences the indentation pressure. These numerical results shed some light on the mechanism of formation of lateral or sub-horizontal tensile cracks observed in the indentation experiments.     

Brittle deformation events at the western border of the Bohemian Massif (Germany)

Investigations of brittle deformation structures, present within the crystalline rocks of the Bavarian Oberpfalz, reveal a complex late to post-Variscan crustal evolution. Upper Carboniferous (mainly Westphalian) granites were emplaced into semibrittle to brittle rocks of the ZEV (zone of Erbendorf-Vohenstrauß) and the EGZ (Erbendorf greenschist unit), respectively. From both the alignment of the granites and the direction of granite-related tension gashes a north-east-south-west extension must be assumed for the period of magmatic activities. Apart from the granite intrusions, rapid crustal uplift (about 1.5 km/my) led to an increase in the geothermal gradient from < 30 °C/km (late Variscan pre-granitic) to > 40 °C/km (late Variscan post-granitic). The increased geothermal gradient persisted during the succeeding reverse faulting which results from late Carboniferous (probably Stephanian) east-west and northeast-south-west compression. Although not evidenced directly in the area considered, strike-slip faults seem to have played an important part during the late Variscan crustal evolution, particularly in the Early Permian. The strike-slip events indicate further crustal shortening and indentation under north-south compression.A similar indentation was present in Cretaceous time. After a weak phase of Early Cretaceous reverse faulting, which results from north-south compression, strike-slip faults formed under north-west-south-east and north-south compression. All these faults, in particular the strike-slip faults, seem to be related to the Cretaceous and lowermost Tertiary convergence of the Alpine/Carpathian orogeny.A late stage of crustal extension, characterized by a radial stress tensor (₂ = ₃), is indicated through high angle normal faults which probably formed during the subsidence of the adjacent Neogene Eger Graben.     

水力切缝上方TBM滚刀贯入破坏机制模拟研究

为了提高坚硬岩层隧道掘进机（tunnel boring machine, TBM）贯入度和降低滚刀受力,高压水射流辅助TBM滚刀破岩已在工业界初步应用。为了揭示水力切缝滚刀破岩机制,基于水力切缝岩石滚刀贯入试验进行了三维颗粒流模拟,研究了滚刀贯入力和贯入刚度随切缝深度的变化规律,揭示了不同切缝深度滚刀纵横剖面内的裂纹扩展和力链演化过程,分析了拉裂纹和剪裂纹随切缝深度的变化规律,明确了不同切缝岩石滚刀贯入的破坏模式和破坏机制。结果表明,第1次贯入的贯入刚度和贯入力随切缝深度的增加大致呈线性降低,第2次贯入的峰值力和贯入刚度小于第1次。而且,50～80 mm刀间距的变化对峰值贯入力的影响并不显著。随着切缝深度的增加,滚刀下方力链集中区边缘的倾角变大。由此导致破坏倾向于倾斜向下发展,当刀间距增加时,破坏由切缝一侧倾斜破坏向两切缝中间岩脊倾斜破坏转变,研究结果可为TBM滚刀与水射流布置和切缝深度的选取提供一定参考。     

Improved discrete element modeling for proppant embedment into rock surfaces

Brinell indentation tests were performed on Montney siltstone, and the results were compared with discrete element indentation simulations that use the micro-parameters calibrated using compression test data from the same siltstone samples. The simulated proppant indentation into the rock surface can be 15% less than the laboratory measurements. A lower effective particle–particle modulus and thus a lower Young’s modulus are needed in discrete element models for proper simulation of indentation. An equation to find the appropriate value of Young’s modulus for indentation simulation is proposed using Brinell indentation tests including 198 laboratory tests and 32 discrete element simulations. This equation can improve the prediction of Young’s modulus and thus the particle–particle effective modulus for indentation simulations to match the measured force–indentation depth curve in the laboratory. Using the improved micro-parameters, a parametric analysis of the influence of rock Young’s modulus and proppant particle size on proppant embedment was performed. An equation to estimate Brinell hardness as a function of Young’s modulus and closure stress was derived. A practical procedure was developed to predict proppant embedment from the estimated hardness. The predictions agree with the laboratory measurements in a case study on the Montney Formation.

     

Response of dry- and liquid-filled porous rocks to static and dynamic loading by variously-shaped projectiles

Summary The present investigation was undertaken to study the response of both dry and liquid-filled porous rocks to static and dynamic loading of penetrators with various tip shapes. Eighteen static and forty-eight dynamic tests were conducted involving 6.35 mm diameter indenters featuring flat, hemispherical and 60° conical tip shapes on three different rocks in the energy range from 1.57 to 5.63 J. Force-penetration data were collected by means of strain gages attached to the penetrators. For all three materials, the magnitude of the resistive forces for a given input energy decreased in the following order: (i) dynamic penetration into a dry sample, (ii) dynamic penetration into a fluid-filled specimen, (iii) static loading of the fluid-filled rock, and (iv) static, loading of the dry rock.An unusual observation for the dynamic force-penetration curves was the temporal disparity between the peak force and maximum deformation, which must be attributed to inertial factors. Based on the experimental data, an analytical rigid-body model was constructed that contained both a static and a dynamic component of the resistive force with the objective of quantifying the effect of dynamic loading and the presence of fluid on the response of the rocks. The dynamic component was portrayed as a viscous resistance proportional to the velocity of the penetrator and the contact surface area which is a function of the indentation. It was found that the model provides a good predictive capability for the dynamic force-indentation relations for prescribed materials and tip geometries upon use of but a single constant for the viscosity.This paper is dedicated to the memory of Corwin O. Rogers.     

The Central Granites-Gneiss-Migmatite Belt (CGGMB) of Madagascar: the Eastern Neoproterozoic Suture of the East African Orogen

The northeastern part of Madagascar is characterized by Archaean to early Proterozoic rocks composed principally of Archaean granite and greenstone/amphibolite as well as reworked migmatite with subordinate Proterozoic paragneisses. The southern part is mostly occupied by Proterozoic rocks, composed mostly of Meso to Neo-Proterozoic and less metamorphic metasediments (Itremo Group) in the northwest, para- and ortho-gneisses in most other areas, with minor granitic gneisses with some Archaean components in the southeast. The north-northwest trending Central Granite-Gneiss-Migmatite Belt (CGGMB) is situated at the western margin of the Archaean-early Proterozoic terrain. The CGGMB is composed of granite, gneiss and migmatite with distinct lithologies and structures. They are: i) many types of granites including alkaline to mildly alkaline granites, and calc-alkaline granites; ii) batholitic granites, migmatitic granites and granite dyke swarm, iii) eclogite, and iv) the Ankazobe-Antananarivo-Fianarantsoa Virgation.

The CGGMB was formed by the collision of the palaeo-Dharwar Craton to the east and the East African Orogen to the west at ca. 820-720 Ma and suffered indentation by a part of the western part of the East African Orogen at ca. 530 Ma that produced the Ankazobe-Antananarivo-Fianarantsoa Virgation at the centre of the CGGMB. Thus, the CGGMB is proposed to be the continuation of the eastern suture between the palaeo Dharwar Craton and the East African Orogen, and carries the main feature of the Pan-African collisional event in Madagascar.     

Arcuate accretionary wedge formation at convex plate margin corners: results of sandbox analogue experiments

Indentation of a rigid box into a sand layer leads to accretion of sand into a wedge which has an arcuate shape in map-view. Curvature of the wedge is most pronounced at the corners of the indentor, where deformation has been investigated in detail in this study. Several features of the arcuate wedge in the corner region depend on the indentation angle, i.e. the angle between the indentation direction and the normal to the frontal face of the indentor: (a) The ratio between the widths of the lateral and frontal parts of the wedge increases linearly with increasing indentation angle. (b) Orogen-parallel extension (OPE) in the corner area is initially high and leads thus to large finite OPE in the firstly formed nappes, but decreases and attains a stable level during progressive convergence. Finite OPE in the corner region is smaller at larger indentation angles. (c) Displacement vectors of accreted material exhibit fanning around the arc, but in oblique indentation the spread of their orientation is smaller than the change of structural strike (nappe traces and fold axes). Displacement vectors trend mainly in such positions normal to structural strike where displacement is parallel to the indentation direction. The results from these experiments can be applied to natural arcuate fold–thrust belts if natural conditions do not differ much from experimental boundary conditions. Such an application may give information about the former plate movement direction across an arcuate plate margin. In the example of the Eastern Carpathian arc, a Tertiary plate-movement direction of approx. 125–130° was determined. This direction is in accordance with current models of large-scale tectonics of the Carpathian region, which indicates the applicability of the experimental results to natural examples.     

Nanoindentation approach characterizing strain rate sensitivity of compressive response of asphalt concrete

This paper presents the results of a study on the use of nanoindentation test to characterize the strain rate-dependent compressive response of asphalt concrete. Nanoindentation is now widely used for characterization and testing of composite as well as single-phase materials. Using a small piece of sample, nanoindentation tests can evaluate material behavior and structure in terms of the elasticity, time-dependent response, yield strength, damage, crack advance, debonding, and fatigues. In this study, a mixture of asphalt and calcium carbonate filler powder filling the intergranular void space of the asphalt concrete was characterized in terms of strain rate sensitivity at room temperature. The indentation hardness is observed to continuously decrease during constant indentation strain rates, but the hardness response clearly indicates positive strain rate dependency when compared at the same indentation depths. Following the constant strain rate tests, indentation creep response of the asphalt–filler mixture was tested at constant load conditions. The strain rate sensitivity values characterized from double logarithmic relationships between indentation hardness and strain rate during constant strain rate and constant load tests are comparable with that determined from uniaxial compression test of cylindrical asphalt concrete samples. The observed indentation size effect on hardness value was analyzed based on an existing size effect model. The size effect in the asphalt–filler mixture, which is stronger than that defined by the model, could be attributed to a plastically graded surface of asphalt–filler sample.