Joseph F. Labuz

Strain-softening of concrete in uniaxial compression

0025-5432/97

Reducing frictional constraint in compression testing through lubrication

J. F. LABUZ~ J. M. BRIDELL~ INTRODUCTION A basic assumption in material testing is the existence of a uniform stress state, where the loading surfaces are usually the principal planes. During compressive load- ing, however, this condition becomes untenable because a frictional constraint develops at the interface between the material and loading system [1-4]. A cylindrical geometry, for example, takes on a barrel shape and a nonuniform stress state develops throughout the cylin- der. This is especially important in studying failure of rock-like materials, as the observed response may be due to the unknown boundary conditions [5, 6]. Homogeneous deformation can be achieved by finding an appropriate friction reducer [7]. In compression test- ing of high-strength materials such as hard rock, this means using a lubricant that performs well at normal stresses up to several hundred MPa, at displacements on the order of hundreds of microns, and at displacement rates of a few microns per second. The objective of this research was to find such a lubricant. LUBRICANTS Boyd and Robertson [8] used a torsional shear appar- atus to measure the coefficient of friction (COF) of various substances subjected to large (up to 1.4GPa) normal stresses. They evaluated solid lubricants, greases, mineral oils, animal and vegetable oils and fatty acids. The COF for graphite measured 0.036, while the COF for both tungsten disulfide and molybdenum disulfide was 0.032. Stearic acid, a fatty acid, showed remarkable friction behavior, with the lowest COF (0.022) of all substances tested. Tarrant [9] measured a low COF, 0.040, for grease containing a slight excess of highly polar fatty acid molecules. For some polar hydrocarbons, friction seems to decrease with increasing chain length [10]. Stearic acid, a polar hydrocarbon with a chain length of 16 [stearic acid

EXPERIMENTAL ANALYSIS OF CRACK PROPAGATION IN GRANITE

An experimental approach is used to demonstrate the concept of an effective crack length with double-edge-notched specimens of charcoal and rockville granite. Crack propagation in rock is characterized by microcracking around the crack tip and interlocking along a portion of the crack; this region is called the fracture process zone, and together with the traction free length defines the effective crack length. Twenty closed-loop, strain-controlled fracture tests were conducted on charcoal and rockville granite. Crack growth was monitored with a travelling optical microscope (100 x magnification). By comparing the post-peak behaviour of both granites, it is suggested that the process zone is larger for the larger grain-sized rock (rockville). Conventional linear elastic fracture mechanics techniques are used to calculate the apparent fracture toughness of charcoal granite at various crack lengths. In addition, a j-integral expression is derived for the double-edged-notched geometry in terms of the area under the load-displacement record. The shortcomings of both analyses are discussed. An attempt is made to explain the inadequacies by including the process zone in the calculations of the fracture toughness. (Author/TRRL)

Simulation of failure around a circular opening in rock

Abstract A biaxial compression test was performed on a sandstone specimen with a circular opening to simulate a loading-type failure around an underground excavation in brittle rock. The axial force and displacements were monitored throughout the failure process, and microcracking was detected by the acoustic emission technique. To model the observed damage zone around the opening, the distinct element computer program, particle flow code (PFC2D), was used. The numerical model consisted of several circular elements that can interact through contact stiffness, exhibit strength through contact bonds and particle friction, and develop damage through fracture of bonds. For the determination of micro-mechanical parameters needed in the calibration process of the computer program, only the macroscopic parameters of Youngs modulus, Poissons ratio and uniaxial compressive strength were used. It is shown that PFC2D was capable of simulating the localization behavior of the rock and the numerical model was able to reproduce the damage zone observed in the laboratory test.

Mohr–Coulomb Failure Criterion

List of Symbols a (m 1)/(m ? 1) b 1/(m ? 1) c Cohesion C0 Uniaxial compressive strength m (1 ? sin /)/(1 sin /) S0 Inherent shear strength (cohesion) T Uniaxial tensile strength T0 Theoretical MC uniaxial tensile strength / Angle of internal friction l = tan / Coefficient of internal friction r Normal stress on plane s Shear stress on plane r1, r2, r3 Principal stresses, with no regard to order rI, rII, rIII Major, intermediate, minor principal stresses rm (rI ? rIII)/2 sm (rI rIII)/2 rI * C0 mT rIII * -T 1 Description

Damage mechanisms in stressed rock from acoustic emission

To better understand the phenomena leading to the failure of rock, unconfined compression experiments on Charcoal granite specimens were performed with the monitoring of acoustic emission (AE). Localization in the form of spalling near the free surface was detected by the concentration of hypocenters. The AE locations, which look random in space and time before localization, actually were clustered and have fractal structure in either space or time. After localization, the fractal dimensions reduced significantly in a certain range of distance and time. The analysis of interaction between spatial and temporal clustering revealed the size of clusters in both space and time. The cluster sizes may be related to the intrinsic properties of the rock. The seismic moment tensor was evaluated through a deconvolution technique to obtain the source mechanism and orientation of each AE event. The dominant mode of failure from AE was sliding on inclined planes, although a significant number of source planes were parallel to the loading axis, while the growth of cracks perpendicular to the loading axis was inhibited. This preferential growth of microcracks is related to a tensorial measure of damage and is used to study stress-induced anisotropy.

The fracture process zone in granite: evidence and effect

Abstract Evidence of the fracture process zone and its effect on fracture toughness were examined for Charcoal and Rockville granite, average grain sizes of 1 and 10mm. Fracture tests were conducted on wedge-loaded, double cantilever beam specimens, 500 mm long × 200 mm wide × 40 mm thick . The seismic techniques of ultrasonic probing and acoustic emission were utilized to measure the inelastic region. The beginning of the process zone was interpreted by a three-fold increase in transmission of ultrasound from an open crack to a partially closed crack; the end of the damage zone was found by comparing surface wave amplitudes before and after fracture. Following these procedures, the inelastic region in Charcoal granite was about 40 mm; whereas in Rockville granite, a region over 90 mm long was estimated. The major acoustic activity was located within the macrocrack, being released from unbroken or interlocked crystals. The experimental evidence indicated an effective crack to be composed of a traction free length and a ligament process zone, which was observed to form a single, multiconnected region within the macrocrack. The effective crack was used for an R-curve calculation, so that the energy consumed in the process zone was included in an approximate manner by elongating the crack length. A model of crack propagation in rock, consistent with measurements of the inelastic region, describes the effect of a process zone on fracture toughness testing.

Plane-strain compression of rock-like materials

Abstract A new apparatus for determining the constitutive response of rock and concrete, named the University of Minnesota Plane-Strain Apparatus, was designed and built on a passive stiff-frame concept. The biaxial device, with U.S. Patent number 5,063,785, is unique, because it allows the failure plane to develop and propagate in an unrestricted manner, as opposed to conventional systems where the material is constrained by the testing apparatus. By placing the upper platen on a low friction linear bearing, the prismatic specimen, subjected to confining pressure and compressed axially, has the freedom to translate in the lateral direction once the deformation has localized across the entire specimen. In addition, homogeneous deformation is prompted by the use of a stearic-acid based lubricant, which is placed on the four surfaces of the specimen contacting hardened-steel platens. Thus, the apparatus combines the positive features of a conventional triaxial compression test and a direct shear test. Some 30 experiments on sandstone and mortar indicated that even though localization of deformation was detected by locations of acoustic emission prior to peak load, the failure plane was not fully formed at the peak. For the mortar, one more or less planar shear band, the orientation of which is well predicted by plasticity theories, was observed. A kinked rupture zone with two main portions, one steep and one less inclined, appeared in the sandstone; the steep portion may be a result of fracture phenomena. The dilatancy characteristics of rock-like materials may dictate the type of failure mode, either shear banding for ductile behavior or crack propagation for brittle behavior.

DETERMINING THE LOW-TEMPERATURE FRACTURE TOUGHNESS OF ASPHALT MIXTURES

There has been a sustained effort in applying fracture mechanics concepts to crack formation and propagation in bituminous pavement materials. Adequate fracture resistance is an essential requirement for asphalt pavements built in the northern part of the United States and Canada, for which the prevailing failure mode is cracking due to low-temperature shrinkage stresses. The current Superpave® specifications address this issue mainly through the use of strength tests on unnotched (smooth boundary) specimens. However, recent studies have shown the limitations of this approach and have suggested that fracture mechanics concepts, based on tests performed on notched samples, should be used instead. Research in progress at the University of Minnesota investigates the use of fracture mechanics principles to determine the low-temperature fracture properties of asphalt mixtures. A testing protocol is presented that makes it possible to obtain multiple measurements of fracture toughness as a function of crack propagation based on the compliance method to measure crack length. An increase in fracture toughness with crack length is observed, which is consistent with the behavior displayed by other brittle materials. The plateau of the curves may be representative of the asphalt concrete resistance to fracture, because the initial values can be significantly influenced by the presence of the inelastic zone at the crack tip.

Characteristic strength of quasi-brittle materials

Abstract The failure of rock-like, quasi-brittle materials is influenced by the development of an intrinsic process zone in the form of a localized region of microcracking. In particular, the process zone has a fundamental importance for defining the structural or system behavior in terms of the post-peak instability, a qualitative size effect, and the maximum stress or material strength, a quantitative size effect. For geometrically similar beams of different sizes, this paper presents experimental evidence from locations of acoustic emissions of the process-zone development, at maximum stress, in terms of shape and size. The experiments suggest that a notch effect developed in the specimens, with assumed uniform tractions being transmitted between the two boundaries of the notch; the radius of curvature of the notch was taken to be one-half the width of the intrinsic process zone. The failure criterion was that at peak load the stress at the notch tip reached the theoretical tensile strength, the so-called characteristic strength of the material. It is shown that the quantitative size effect can be explained by extending the classical Neuber results on stress concentrations around notches through an account of the intrinsic process zone and its cohesive interaction. A notable outcome of the analysis is that two competing factors define the nominal strength of a quasi-brittle material: the positive contribution of the process zone and the competing aspects of the undamaged volume, that is, the size.