Per-Arne Lindqvist

Effects of loading rate on rock fracture

Various types of rock fracture occur at different loading rates. For example, rock destruction by a boring machine, a jaw or cone crusher, and a grinding roll machine are within the extent of low loading rates, often called quasistatic loading condition. On the contrary, rock fracture in percussive drilling and blasting happens under high loading rates, usually named dynamic loading condition. This chapter presents loading rate effects on rock strengths, rock fracture toughness, rock fragmentation, energy partitioning, and energy efficiency. Finally, some of engineering applications of loading rate effects are discussed.

Numerical simulation of the rock fragmentation process induced by indenters

Rock fragmentation processes induced by single and double indenters were examined by a numerical method. The simulated results reproduce the progressive process of rock fragmentation in indentation. Rock deforms elastically at the initial loading stage. Then tensile cracks are initiated around the two corners of the truncated indenter and propagate in the well-known conical Hertzian manner. The rocks immediately under the indenter are in a highly tri-axial stress state, and some of them fail in the ductile cataclastic mode with the stress satisfying the ductile failure surface of the double elliptic strength criterion. With the tensile cone cracks and ductile cataclastic failure releasing the confining pressure, the rocks under the indenter are compressed into failure and the crushed zone gradually comes into being. With increasing loading displacement, the re-compaction behaviour of the crushed zone occurs. Side cracks initiated from the crushed zone or bifurcated from cone cracks are driven by tensile stress associated with the crushed zone to propagate in a curvilinear path and finally intersect with the free surface to form chips. It is pointed out that the curvilinear path is caused by heterogeneity. The simulated force-penetration curve is in fact the indication of the propagation of cracks, the crushing of microstructural grains and the formation of chips. It is found that the confining pressure has an important influence on the indentation results. With decreasing confining pressure, there is a decrease in the indentation strength and a change in the rock failure process from the formation of rock chips to a vertically axially splitting failure. The simulated fragmentation process in the double indenter test reproduces the side cracks, which are induced by two indenters, propagate, interact and finally coalesce, chipping the rock between the indenters. The line spacing is an important factor that affects the fragmentation efficiency in multiple indenter tests. It is pointed out that simultaneous loading with multiple indenters with an appropriate line spacing seems to provide a possibility of forming larger rock chips, controlling the direction of subsurface cracks and consuming a minimum total specific energy. According to the simulated results, it is believed that the numerical simulation method will contribute to an improved knowledge of rock fragmentation in indentation, which will in turn help to enhance mining and drilling efficiency through the improved design of mining tools and equipment.

The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results

Abstract The flattened Brazilian disc specimen is proposed for determination of the elastic modulus E , tensile strength σ t and opening mode fracture toughness K IC for brittle rocks in just one test. This paper is concerned with the theoretical analysis as well as analytical and numerical results for the formulas. According to the results of stress analysis and Griffiths strength criteria, in order to guarantee crack initiation at the centre of the specimen, which is considered to be crucial for the test validity, the loading angle corresponding to the flat end width must be greater than a critical value (2 α ⩾20°). The analysis shows that, based on the recorded complete load–displacement curve of the specimen (the curve should include the ‘fluctuation’ section after the maximum load), E can be determined by the slope of the section before the maximum load, σ t by the maximum load, and K IC by the local minimum load immediately subsequent to the maximum load. The relevant formulas for the calculation of E , σ t , K IC are obtained, and the key coefficients in these formulas are calibrated by finite-element analysis. In addition, some approximate closed-form formulas based on elasticity are provided, and their accuracy is shown to be adequate by comparison with the finite-element results.

Effects of loading rate on rock fracture : fracture characteristics and energy partitioning

By means of the Scanning Electron Microscope (SEM), an examination was performed of the fracture surfaces (including their vertical sections) of both Fangshan gabbro and Fangshan marble specimens fractured at the loading rates _ ka 10 ˇ2 010 6 MPa m 1/2 s ˇ1 . The results showed that one or more branching cracks near the fracture surfaces of dynamic rock specimens were clear and the cracks increased with increasing loading rates. However, such branching cracks were rarely seen near the static fracture surfaces. In addition, with the aid of the Split Hopkinson Pressure Bar (SHPB) testing system and a high-speed framing camera, the energy partitioning in the dynamic fracture process of a short rod (SR) rock specimen was analysed quantitatively. The total energy WL absorbed by an SR specimen in the dynamic fracture process mainly consisted of the fracture and damage energy WFD and the kinetic energy WK of flying fragments. The energies WL and WK could be quantitatively calculated through stress wave measurement and high-speed photography in the SHPB testing system. Thus, the fracture and damage energy WFD could be obtained. The results showed that: (1) the energy WK increased with an increase in the impact speed of the striker bar or the loading rate; (2) the energy WFD for dynamic rock fracture was markedly greater than that for static rock fracture, and the WFD increased with an increase in the impact speed of the striker bar or the loading rate; and (3) the value WL/WB (WB is the energy input into the loading system) in the case of dynamic fracture is much lower than that in the case of static fracture. In addition, the ratio decreases with an increase in the loading rate or the impact speed of the striker bar. This means that the energy utilisation decreases when the loading rate or the impact speed of the striker bar rises. Finally, some application problems are discussed in the paper. 7 2000 Elsevier Science Ltd. All rights reserved.

Effects of high temperatures on dynamic rock fracture

Abstract The dynamic fracture toughness of Fangshan gabbro and Fangshan marble subjected to high temperature was measured by means of the split Hopkinson pressure bar (SHPB) system. The specimens for measuring the fracture toughness were manufactured according to the requirements for the Short Rod (SR) specimen suggested by ISRM. Two cases were investigated: (1) the SR specimens of the gabbro and marble were fractured at high temperature (100–330°C), and (2) the specimens of the rocks were first pre-heat-treated at 200°C for the marble and 600°C for the gabbro, and then fractured at room temperature. The experimental results showed that under dynamic loading the fracture toughness of both the gabbro and the marble tested in the above-mentioned cases increased with increasing loading rates. The relationship between the fracture toughness and the loading rates in the two cases is similar to that obtained in the room temperature environment, i.e., without high temperature. (This is defined as the third case.) It can be concluded that temperature variation affects the dynamic fracture toughness of the two rocks to a limited extent within the temperature ranges tested. This is different from the results obtained under the static loading condition. Furthermore, by means of the scanning electronic microscope (SEM), the vertical sections of the fracture surfaces for some gabbro specimens were examined. In addition, the fractal dimensions of the fracture surfaces of some specimens were measured by means of fractal geometry. The results showed that under dynamic loading: (1) macro-crack branching near the fracture surfaces was universal; (2) the fractal dimensions increased with increasing loading rates; (3) in the sections of the specimens tested at high temperature there were many micro-cracks that were probably induced by thermal cracking. On the basis of the above macro- and micro-experimental investigation, an energy analysis of the process of dynamic rock fracture was performed. The results showed that the energy utilisation in dynamic fracture was much lower than that in static fracture.

Numerical investigation of particle breakage as applied to mechanical crushing : Part I, Single-particle breakage

Abstract A numerical approach to particle breakage is applied using the Rock Failure Process Analysis code, RFPA 2D . The numerical tool is validated by simulating the Brazilian test with a two-dimensional disk sample. Then two irregularly shaped particles with an exact geometry and exact mechanical properties are numerically modelled to investigate their breakage behaviour under unconfined and confined loading conditions. The numerical results indicate that the dominant mode of failure is catastrophic splitting and progressive crushing, which mainly depends on the loading conditions with respect to confinement. The analysis of the load–displacement curves obtained from the simulations suggests a brittle-ductile transition between the two cases. The lateral constraint increases the initial stiffness and the maximum breakage strength of the particle. Most of the energy released during the failure process comes from the crushing of highly stressed areas, particularly, in the vicinity of the contact points where a crushed zone forms. It is also found that the particle shape governs the breakage strength in addition to the material properties themselves, and that the heterogeneity of the particles governs the fracture propagation paths.

Application of the DDM and fracture mechanics model on the simulation of rock breakage by mechanical tools

Abstract A DDM (displacement discontinuity method) program coupled with a modified energy criterion is used to simulate the development of cracks and chips by indentation tools. In our analysis a cavity model is applied to represent the expansion of crushed rock to the surrounding rock and the cracks are formedin two-dimensional and quasi-static conditions. The model parameters, rock properties and load magnitudes are varied in the numerical calculations. The results show that chips are formed by multiple mechanisms of either tension or shear, or their combinations. The cracks may either propagate to the free surface to form chips or rest in the rock subsurface. The crack development is dependent upon rock and fracture properties, loading force and tool characteristics. The DDM is a convenient tool in the study of rock fragmentation and cracks.

Numerical simulation of the cutting of inhomogeneous rocks

In this study, the possible modes of crack initiation and propagation leading to chip formation in rock cutting are studied numerically by using a rock failure process analysis code referred to as ...

More accurate stress intensity factor derived by finite element analysis for the ISRM suggested rock fracture toughness specimen—CCNBD

More accurate stress intensity factor derived by finite element analysis for the ISRM suggested rock fracture toughness specimen-CCNBD

Influence of the mineralogical composition and textural properties on the quality of coarse aggregates

To evaluate the influence of the petrographic variables on the quality of coarse aggregates consisting of granitoid (granite to tonalite) rocks, 17 samples selected from the Swedish part of the Baltic shield have been studied concerning their petrographic properties, for example, mineral composition, grain size, grain boundaries, and the frequency of micro-cracks. All of the samples selected also have been studied in mechanical tests used to evaluate the quality of aggregates in Sweden. The quality has been determined by means of flakiness, impact value, abrasion value I, and abrasion value II. An analysis of the influence of the mineral composition and textural properties on the aggregate quality has been performed using statistical correlation and linear models. The results indicate that an increasing content of feldspar negatively influences the strength against impact, while an increasing content of mica (tested to 35 vol.%) combined with a diminishing grain size and more irregular grain boundries has a positive influence on the resistance of granitoids to mechanical impact. Abrasion value II seems to be mainly influenced negatively by an increasing frequency of micro-cracks. The practical implementation of the results is suggested.