V. Palchik

The influence of grain size and porosity on crack initiation stress and critical flaw length in dolomites

Abstract The influence of rock texture on crack initiation stress ( σ i ) and critical flaw length ( L i ) is studied by a series of triaxial tests performed on monomineralic dolomites. The critical flaw length, as predicted by analytical models, is shown to be larger than the measured mean grain size ( d m ) by two–three orders of magnitude. This discrepancy is explained by rock texture variations, which influence the fracture propagation mode and consequently fracture initiation stress. The quantification of rock texture is accomplished using porosity. Fracture initiation stress is shown to be inversely related to both porosity and mean grain size. When porosity is low, the sensitivity of σ i to mean grain size is high. This effect is reduced with higher porosity values. A model for initial flaw length is developed by a synthesis of Griffith initiation criteria with our empirical model for fracture initiation stress. Initial flaw length is found to be directly proportional to the elastic modulus, mean grain size and porosity of the rock. When porosity and mean grain size decrease simultaneously, the initial flaw length rapidly decreases and approaches the mean grain size value. Therefore, the classical assumption that grain size scales initial flaw size is shown to be valid only in the very restricted case of low porosity-low grain size rocks. In such textures, where void space is minimal, available crystal faces function as truly initial flaws, and variations in mean grain size influence crack initiation stress significantly. In more porous textures, however, the initial flaw length is shown to be up to two orders of magnitude higher than the mean grain size in the rock, depending upon the porosity and mean grain size values. In such textures crack initiation stress is much less sensitive to variations in mean grain size, indicating that the role of individual grains is less significant.

Crack damage stress as a composite function of porosity and elastic matrix stiffness in dolomites and limestones

Abstract Twenty-five uniaxial compression tests were performed to determine stress at onset of dilation, referred to herein as “the crack damage stress,” in heterogeneous dolomites and limestones. A simplified model for crack damage stress (σcd) is developed here using porosity, elastic modulus, Poissons ratio and three empirical coefficients. The model shows that when porosity decreases and elastic modulus increases, σcd rapidly increases and approaches its maximum value. On the other hand, when porosity increases and elastic modulus decreases, σcd rapidly decreases and approaches its minimum value. The proposed model is validated for six heterogeneous limestone and dolomite formations which are widely distributed in Israel.

Exploration via electromagnetic radiation and fractographic methods of fracture properties induced by compression in glass-ceramic

The fracture properties of glass ceramic induced by compression were investigated by combined electromagnetic radiation (EMR) and fractographic methods. The study of a transparent sample enabled us to elucidate the sequence of crack nucleation, growth and interaction, and the ultimate longitudinal splitting under incremental increase of uniaxial stress in five stages. The fracture process was accompanied by some 18 EMR pulses. The short EMR pulses (of a duration of 0. 8–1.5 μs) occur under low stresses (0.36–1.7 MPa) in association with microcracking at the sample outer surface. Medium pulses (durations of 15–25 μs) are associated with stresses of up to 65 MPa and are correlated with crack limited growth outside the specimen. A lengthy pulse (duration of more than 40 μs) occurs under greater stresses (112 MPa) and correlates with the longitudinal splitting at failure. A return to the 17–20 μs range occurs for the post-failure cracking during stress relaxation.

Use of Gaussian Distribution for Estimation of Gob Gas Drainage Well Productivity

This paper describes the development and application of new mathematical models for estimation of well productivity during drainage of methane gob gas associated with coal extraction. It is established that the relationship between methane emission from surface gob gas wells and the duration of well production can be described by Gaussian (normal) distribution. Mathematical models based on using the Gaussian error distribution function and the Gaussian density function were proposed to describe the correlation between parameters of methane emission from gob gas wells, duration of well production, and time coordinate of maximum gas emission. These models allow prediction of the total volume of gas which can be extracted for the entire period of well production, the maximum volumetric flow rate of gas emission and the time coordinate of maximum gas emission using at least three measurement of gas volumetric rate (or gas volume) from a gas well at any time during the well production period.

Prediction of hollows in abandoned underground workings at shallow depth

Composite statistical analysis of the lithological composition of the rock mass above underground workings in coal seams and experimental work (laboratory mechanical tests and boring for the determination of hollows) in Donetsk city (Ukraine) have been used to develop a method for predicting the presence of hollows. The empirical criteria K1−K2>0 and K3≤2.5 which relate to the physical characteristics of the overlying strata were found to predict the existence of such hollows in abandoned underground workings at shallow depth. The values of K1−K2 and K3 depend on the thicknesses of the different rock layers and the uniaxial compressive strength of the immediate roof over underground openings. The different layers e.g. sandstones, argillites, aleurolites and alluvium in the rock mass are shown to influence the existence of hollows in abandoned workings. Large thicknesses of sandstones in the rock mass or relatively high uniaxial compressive strength rock in the immediate roof contribute to the existence of hollows in abandoned workings. On the other hand, sandstones of small thickness, weak alluvium, argillites and aleurolites only give additional weight on immediate roof of the opening and allow collapse of the rock mass. The method of prediction for hollows was developed from the back-analysis of data from 41 boreholes which were drilled from the ground surface above underground openings.

Use of Descartes Folium Equation for Deriving a Relation between Total Aperture of Fractures after Uniaxial Compression and Strain Parameters of Different Rocks Exhibiting Negative Total Volumetric Strains

The axial, crack and total volumetric strains, porosity, elastic constants, crack damage stresses, uniaxial compressive strengths, as well as fracture apertures and number of fracture traces in rock samples surface after compression were defined for different chalk, basalt, dolomite, granite, limestone and sandstone samples exhibiting negative total volumetric strain at failure. It is established that the total (summed) aperture of vertical fractures obtained on the lateral surface of rock sample is related to three characteristic strain parameters: axial strain at the onset of negative total volumetric strain, axial failure strain and negative total volumetric strain at failure. The relation is based on Descartes folium equation, where the length of the loop of folium is equal to axial strain coordinate at the onset of negative total volumetric strain. This relation shows that the total aperture increases according to power law with increasing difference between axial failure strain and axial strain at the onset of negative total volumetric strain. Simultaneously, an increase in this difference leads to an increase in the value of negative total volumetric strain at failure. It is found that a direct correlation between total aperture of fractures and negative total volumetric strain at failure is relatively weak. Nevertheless, total aperture of fractures tends to increase with increasing absolute value of negative total volumetric strain at failure. It is revealed that there is no connection between the number of fracture traces and negative total volumetric strain at failure.

Grain Boundary Parameters in Sandstone and Limestone

In this paper, length of grain-to-grain contact, number of contacts per grain and ratios between the length of contacts and geometric characteristics of grains in heterogeneous Berea sandstone and Indiana limestone are studied. It is shown how hydrostatic pressure up to 40 MPa influences these grain boundary parameters. Observations show that there are different types of influence of hydrostatic pressure on grain boundary parameters in the studied sandstone and limestone.