Showing papers on "Fracture (geology) published in 1997"

Fracture Processes of Concrete

Abstract: This book begins with a clear and thorough explanation of the mechanical properties and fracture processes of concrete, followed by an evaluation of test methods for assessing both experimental and numerical models. The book then presents different types of fracture models available to design experiments and analyze their accuracy. Numerous examples are included to support key concepts, and hundreds of photographs, diagrams, and tables further illuminate the text.

Rock Fractures and Fluid Flow: Contemporary Understanding and Applications

Abstract: How can fractures that are significant hydraulic conductors or barriers be located, identified, and characterized? How do flow and transport occur in fracture systems? How can changes in fracture systems be predicted and controlled? With a clear, well-stated focus, Rock Fractures and Fluid Flow seeks to address these questions by combining into one work the interdependencies of the disciplines needed to get at the answers.

Scaling properties of cracks

Abstract: Experiments concerning the morphology of fracture surfaces of various materials are reviewed. The observations are interpreted within the framework of models of lines moving in a random environment. This suggests that fracture of heterogeneous materials could be seen as a dynamic phase transition.

Water film flow along fracture surfaces of porous rock

Abstract: This study shows that hydraulic properties of individual fracture surfaces can be meaningfully defined and measured, and that water film flow is a mechanism contributing to fast, unsaturated flow in fractures. The hydraulic conductivity of an unconfined block of Bishop Tuff was measured over a range of near-zero matric potentials, where differences between hydraulic conductivities obtained without and with wax sealing of its lateral sides allowed isolation of film flow effects. Tensiometer and flux measurements showed that surface film flow in this system was significant for matric potentials greater (more positive) than about −250 Pa. In this range the average film thickness was shown to be potential dependent and proportional to the observed enhanced hydraulic conductivity. Measured average surface film thicknesses ranged from 2 to 70 μm, with average film velocities in the range of 2 to 40 m d−1 (about 103 times faster than that of the pore water under unit gradient saturated flow). Our experiments demonstrate that hydraulic properties of macroscopic surfaces of porous media are quantifiable, related to surface roughness, and potentially important in the flow of water in vadose environments. This study further shows that contrary to existing conceptual models, unsaturated flow in fractures cannot generally be predicted solely on the basis of aperture distribution information. The high velocities of these surface films suggest that film flow can be an important mechanism contributing to fast flow in unsaturated fractures and macropores, especially in media characterized by low-permeability matrix and along regions of convergent flow in partially saturated fractures.

Measurement of deformations on concrete subjected to compression using image correlation

Abstract: Because the nature of failure in concrete is complicated due to the material heterogeneity, a robust measuring method is essential to obtain reliable deformation data. A nondestructive displacement evaluation system using a digital image cross-correlation scheme, often called computer vision, is developed to make microscopic examinations of the fracture processes in concrete. This is a full-field measuring method that gives an accuracy within the micron range for a 100 mm × 75 mm viewing area. A feedback signal that combines the lateral and axial deformations provides a well-balanced imaging rate both before and after the peak load. Displacement vector diagrams or displacement contour maps of concrete reveal highly nonuniform deformations even in the elastic range. The processes of fracture in concrete are well defined at different deformation levels.

Mechanics of Hydraulic Fracturing

Abstract: Preface Fracturing of Wellbore and 2-D Fracture Models Three-Dimensional Fracture Modeling Proppant Transport in a 3-D Fracture Deviated Wellbores Link up of Mini-fractures From Perforated Holes Turning of Fracture From a Deviated Wellbore Experimental Studies Index

Preventing well fracture proppant flow-back

Abstract: Improved methods of propping a fracture in a subterranean zone whereby the subsequent flow-back of the proppant is prevented are provided. The methods basically include the steps of placing a mixture of fibrous bundles and the proppant in the fracture while maintaining the fracture open and then allowing the fracture to close on the mixture of fibrous bundles and proppant.

Statistical Properties of Fracture Precursors

Abstract: We present the data of a mode-I fracture experiment. The samples are broken under imposed pressure. The acoustic emission of microfractures before the breakup of the sample is registered. From the acoustic signals, the position of microfractures and the energy released are calculated. A measure of the clustering of microfractures yields information about the critical load. The statistics from energy measurements strongly suggest that the fracture can be viewed as a critical phenomenon; energy events are distributed in magnitude as a power law, and a critical exponent is found for the energy near fracture. [S0031-9007(97)04346-9] PACS numbers: 62.20.Mk, 46.30.Nz Fracture is a problem which has recently received a lot of attention in the physics community [1–3]. It is troublesome to calculate the force needed to break a heterogeneous material. Instead, it is customary to resort to tests involving the destruction of the sample. Therefore it is interesting to provide additional knowledge about cracks by studying the events that occur prior to the fracture. Besides , despite great experimental and numerical efforts [1– 6], many aspects still remain unclear about the fracture process itself. Conceptually simple models, such as per-colation [6] and self-organized criticality [7], are attractive but often fail to convey the complex phenomenology observed. The main motivation of this work is to understand if these models can reproduce the main features of crack formation. We report here some experimental results that may help to gain valuable information in that direction. Our main tool is the monitoring of the microfractures, which occur before the final breakup, by recording their acoustic emissions (AE). Because of its ability to pinpoint the emission source, this technique has been widely used in seismography and to map the nucleation of fractures [8]. From these signals, we have also obtained the acoustic energy of each microfracture, which is a fraction of the total energy released. The behavior of the energy just before fracture is a good parameter to compare with the above mentioned models. In order to avoid noise, we have designed a setup in which there are no moving parts, the force being exerted by pressurized air (see Fig. 1). A circular sample having a diameter of 22 cm and a thickness of 5 mm is placed between two chambers between which a pressure difference P ෇ P 2 2 P 1 is imposed. The deformation of the plate at the center is bigger than its thickness, then the load is mainly radial [9,10]. Therefore, the experience can be thought of as a mode-I test with circular symmetry. The pressure difference P supported by the sample is slowly increased and it is monitored by a differential transducer. This measure has a stability of 0.002 atm. The fracture pressure for the different tested materials ranges from 0.7 to 2 atm. We regulate P by means of a feedback loop and an electronically controlled valve which connects one of the two chambers to a pressurized air reservoir. The time taken to correct pressure variations (about 0.1 s) is smaller than the characteristic time of the strain rate. An inductive displacement sensor gives the deformation at the center of the plate with a precision of about 10 mm (the deformation just before fracture is of the order of 1 cm). The apparatus is placed inside a copper box covered with a thick foam layer to avoid both electrical and acoustical noise. Four wide-band piezoelectric microphones are placed on the side of the sample (see Fig. 1). The signal is amplified, low-pass filtered at 70 kHz, and sent to a digitizing oscilloscope and to an electronic device which measures the acoustic energy detected by the microphones. The signal captured by the oscilloscope is sent to a computer where a program automatically detects the arrival time of the AE at each microphone. Afterwards, a calculation yields the position of the source inside the sample. A fraction of the detected events is rejected, either as a result of a large uncertainty of the location, or because they are regarded as noise. The mean standard error for the calculated positions is about 6 mm, which results mainly from the uncertainty of the arrival time. The electronic device that measures the energy performs the square of the AE amplitude and then integrates it over a time window of 30 ms, which is the maximum duration of one acoustic event. The output signal is proportional to the energy of the events [11], and

Scaling of quasibrittle fracture: asymptotic analysis

Abstract: Fracture of quasibrittle materials such as concrete, rock, ice, tough ceramics and various fibrous or particulate composites, exhibits complex size effects. An asymptotic theory of scaling governing these size effects is presented, while its extension to fractal cracks is left to a companion paper (1) which follows. The energy release from the structure is assumed to depend on its size , on the crack length, and on the material length governing the fracture process zone size. Based on the condition of energy balance during fracture propagation and the condition of stability limit under load control, the large-size and small-size asymptotic expansions of the size effect on the nominal strength of structure containing large cracks or notches are derived. It is shown that the form of the approximate size effect law previously deduced (2) by other arguments can be obtained from these expansions by asymptotic matching. This law represents a smooth transition from the case of no size effect, corresponding to plasticity, to the power law size effect of linear elastic fracture mechanics. The analysis is further extended to deduce the asymptotic expansion of the size effect for crack initiation in the boundary layer from a smooth surface of structure. Finally, a universal size effect law which approximately describes both failures at large cracks (or notches) and failures at crack initiation from a smooth surface is derived by matching the aforementioned three asymptotic expansions.

Statistical Physics of Fracture and Breakdown in Disordered Systems

Abstract: 1. Introduction 2. Electrical breakdown in disordered solids 3. Fracture strength of disordered solids 4. Earthquakes in model systems References Index

A governing equation for fluid flow in rough fractures

Abstract: Fluid flow in a rock fracture bounded by two irregular surfaces is complex even under a laminar flow regime. The major factor causing deviation of predicted fracture flow behavior from the ideal parallel plate theory is the nature of nonparallel and nonsmooth geometry of fracture surfaces. Important questions on the validity of the cubic law and the Reynolds equation for complicated fracture geometries have been studied by many researchers. The general conclusion from these efforts is that the cubic law is valid provided that an appropriate average aperture can be defined. Many average apertures have been proposed, and for some cases, some work better than others. Nonetheless, to date, these efforts have not converged to form a unified definition on the fracture aperture needed in the cubic law, which stimulates the current effort to develop a general governing equation for fracture flow from a fundamental consideration. In this study, a governing equation stemming from the principle of mass conservation and the assumption that the cubic law holds locally is derived for incompressible laminar fluid flow in irregular fractures under steady state conditions. The equation is formulated in both local and global coordinates and explicitly incorporates two vectorial variables of fracture geometry: true aperture and tortuosity. Under the assumption of small variations in both tortuosity and aperture, the governing equation can be reduced to the Reynolds equation. Two examples are provided to show the importance and generality of the new governing equation in both local and global coordinate systems. In a simple fracture with two nonsmooth and nonparallel surfaces, the error in permeability estimation can be induced using the Reynolds equation with the apparent aperture and can reach 10% for a 25° inclination between the fracture surfaces. In a fracture with sinusoidal surfaces, the traditional method can cause significant errors in both permeability and pressure calculation.

Comparison of the fracture and failure behavior of injection‐molded α‐ and β‐polypropylene in high‐speed three‐point bending tests

Abstract: The fracture and failure mode of α- and β-isotactic polypropylene (α-iPP and β-iPP, respectively) were studied in high speed (1 m/s) three-point bending tests on notched bars cut from injection-molded dumbbell specimens and compared. The fracture response of the notched Charpy-type specimens at room temperature (RT) and −40°C, respectively, was described by terms of the linear elastic fracture mechanics (LEFM), namely fracture toughness (Kc) and fracture energy (Gc). Kc values of both iPP modifications were similar, while Gc values of the β-iPP were approximately twofold of the reference α-iPP irrespective of the test temperature. It was demonstrated that β-iPP failed in a ductile and brittle-microductile manner at RT and −40°C, respectively. By contrast, brittle fracture dominated in α-iPP at both testing temperatures. Based on the fracture surface appearance, it was supposed that β-to-α (βα) transformation occurred in β-iPP. The superior fracture energy of β-iPP to α-iPP was attributed to a combined effect of the following terms: morphology, mechanical damping, and phase transformation. Results indicate that their relative contribution is a function of the test temperature. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 2057–2066, 1997

Some fractal models of fracture

Abstract: The paper deals with applications of fractal geometry methods to problems of fracture in brittle and quasibrittle materials. Possible ways to construct models, taking into account the fractal properties of the phenomenon, are discussed. It is shown that classical approaches do not work in fractal fracture and lead to the paradoxical conclusion that fractal cracking is impossible. Some new concepts appropriate for fractal fracture are introduced. In particular, the concept of specific energy-absorbing capacity for a unit of a fractal measure of a fractal set is considered. It is shown that fractal properties of a fractal pattern of microcracks can characterize the fracture energy of polyphase materials such as rock, concrete, ceramics, etc., and that fractal properties of the main crack surface can be inessential.

Effect of mechanical interactions on the scaling of fracture length and aperture

Abstract: The aperture (or opening) of a fracture indicates the energy available for fracture growth and controls fracture permeability. The relationship between aperture and fracture length can therefore be used to infer the factors affecting fracture formation at different length scales and is of practical importance to hydrogeologists and petroleum engineers. A recent study1 of the scaling properties of tensile fractures in the Krafla fissure swarm, Iceland, revealed a distinct break in slope in the aperture–length scaling relationship, corresponding to fractures a few metres in length: this break in slope was interpreted qualitatively as indicative of non-universal, scale-dependent growth mechanisms1. Here we show, using quantitative fracture simulations, that the observed non-universal scaling of fracture apertures can be reproduced without recourse to multiple growth mechanisms. We argue that the break in slope is instead intrinsic to the fracturing process and represents the maximum length scale at which the apertures of smaller fractures are affected by stress perturbations induced by larger fractures.

Dynamic rock mechanics testing for optimized fracture designs

Abstract: To optimize fracture designs, rock mechanics data are needed at multiple locations in the formation and adjacent zones. This paper will review a laboratory technique that reduces testing time and cost by 60 to 80%. The technique has been successfully used on a wide variety of core and also reduces core-size requirements. Ultrasonic (dynamic) test equipment and procedures are discussed to standardize the method for petroleum industry applications and provide reliable data for fracture designs. The primary data provided are Young's modulus and Poisson's ratio. Dynamic testing has been performed on 600 cores from about 60 formations. The data are also compared to static uniaxial and triaxial data on the same cores to determine correlation coefficients between the static and dynamic data. Procedures and apparatus for performing ultrasonic testing have been successfully developed that determine the dynamic Young's moduli for weakly consolidated cores, with Young's moduli of 60 thousand psi, to hard limestone with Young's moduli of 14 million psi. Several equations are also provided that have applications to sonic logging for mechanical property evaluation of formations. The same equipment has been used to determine fracture azimuth from oriented core at significant cost savings over other techniques. The paper will also review the relative importance of rock mechanics data on optimized fracture designs.

A molecular dynamics investigation of rapid fracture mechanics

Abstract: Dynamic fracture is investigated for two-dimensional notched solids under tension using million atom systems. Brittle material and ductile material are modeled through the choice of interatomic potential functions which are Lennard-Jones and embedded-atom potentials, respectively. Numerical calculations are carried out on the IBN SP parallel computer and molecular dynamics is implemented using a spatial-decomposition algorithm. Many recent laboratory findings occur in our simulation experiments. A detailed comparison between laboratory and computer experiments is presented, and microscopic processes are identified. For rapid brittle fracture, the dynamic instability of the crack growth is observed as the crack velocity approaches one-third of the Rayleigh wave speed. At higher crack velocity, the crack either follows a wavy path or branches and the anisotropy due to the large deformation at the crack tip plays the governing role in determining the crack path. Limited comparison of rapid brittle fracture process with the rapid ductile fracture process is made.

Correcting for Diffusion in Carbon‐14 Dating of Ground Water

Abstract: It has generally been recognized that molecular diffusion can be a significant process affecting the transport of carbon-14 in the subsurface when occurring either from a permeable aquifer into a confining layer or from a fracture into a rock matrix. An analytical solution that is valid for steady-state radionuclide transport through fractured rock is shown to be applicable to many multilayered aquifer systems. By plotting the ratio of the rate of diffusion to the rate of decay of carbon-14 over the length scales representative of several common hydrogeologic settings, it is demonstrated that diffusion of carbon-14 should often be not only a significant process, but a dominant one relative to decay. An age-correction formula is developed and applied to the Bangkok Basin of Thailand, where a mean carbon-14-based age of 21,000 years was adjusted to 11,000 years to account for diffusion. This formula and its graphical representation should prove useful for many studies, for they can be used first to estimate the potential role of diffusion and then to make a simple first-order age correction if necessary.

Experimental analysis and computational modelling of damage and fracture

Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

Crack Front Propagation and Fracture in a Graphite Sheet: A Molecular-Dynamics Study on Parallel Computers

Abstract: Crack propagation in a graphite sheet is investigated with million atom molecular-dynamics simulations based on Brenner{close_quote}s reactive empirical bond-order potential. For certain crystalline orientations, multiple crack branches with nearly equal spacing sprout as the crack tip reaches a critical speed of 0.6V{sub R}, where V{sub R} is the Rayleigh wave speed. This results in a fracture surface with secondary branches and overhangs. Within the same branch the crack-front profile is characterized by a roughness exponent, {alpha}=0.41{plus_minus}0.05. However, for interbranch fracture surface profiles the return probability yields {alpha}=0.71{plus_minus}0.10. Fracture toughness is estimated from Griffith analysis and local-stress distributions. {copyright} {ital 1997} {ital The American Physical Society}

Fractal effects of surface roughness on the mechanical behavior of rock joints

Abstract: Extensive studies show that the naturally developed rock joint surfaces have the properties of fractals. The surface roughness of rock joints can be well described within the framework of fractal geometry. To give a better understanding of the roughness of rock fracture surfaces in relation to the mechanical properties and behavior of rock joints in loading, a systematic investigation has been carried out. By means of a laser scanning instrument, the fracture surfaces induced in rocks are measured. The fractal characters of rough fracture surfaces of rocks are analysed according to the variogram method, which elaborates explicitly the importance of the geometric parameters — fractal dimension D and the intercept A . Investigation extends to the anisotropy and heterogeneity of rock fracture surfaces, and the scale effect on the fractal estimation. The shear tests on rock joints show a combined effect of the fractal parameters on the mechanical properties and behavior of rock joints. To control the roughness and show the effects in a direct manner, a series of fractal joints with different fractal dimensions are generated on the basis of the Weierstrass-Mandelbrot function and then manufactured in the polycarbonate plates. By using the photoelastic method, the manners of normal and shear deformation, the stress field in the vicinity of the joint surface and the contact behaviour of the fractal joints have been studied in detail under uniaxial compression and direct shear. Based on the experimental results, the dependence of deformation stiffness on the fractal dimensions of rock joints has been recognized. The empirical criteria of shear strength and the evolution law of surface damage during the shear process are developed.

Evaluation of crack propagation properties of asphalt mixtures

Abstract: Current failure criteria of asphalt pavements are either empirical or assume linear elastic material response and use a single load level to relate the number of load repetitions to fatigue failure. To better understand the crack propagation properties of asphalt pavements, laboratory tests and nonlinear analysis were performed to evaluate the low-temperature fracture parameters of conventional asphalt concrete and asphalt-rubber mixture. Two approaches based on nonlinear fracture mechanics, the compliance approach and the R-Curve approach, were used. Beam specimens were prepared with different binder contents and tested under three-point bending flexural conditions at two test temperatures. A closed-loop servohydraulic test system was used with the crack mouth opening as the control parameter. Nonlinear fracture parameters were obtained at different stages of crack propagation. Results show that the asphalt-rubber mixture has higher fracture toughness and consequently larger resistance to cracking than asphalt concrete. Also, the asphalt-rubber mixture is less sensitive to temperature than asphalt concrete. Increasing the binder content increased the toughness values for both asphalt concrete and asphalt-rubber mixture in most cases. The R-Curve approach provides a good measure of characterizing the fracture behavior of asphalt mixtures.

Comparative analysis of direct (core) and indirect (borehole imaging tools) collection of fracture data in the Hot Dry Rock Soultz reservoir (France)

Abstract: Attributes of several thousand fractures were collected in three boreholes of 2.2, 3.6, and 3.8 km depth, penetrating the Soultz Hot Dry Rock reservoir (France). The fractures were sampled from cores and from several high-resolution imaging techniques such as borehole televiewer (BHTV), ultrasonic borehole imager (UBI), formation microscanner (FMS), formation microimager (FMI), and azimuthal resistivity imaging (ARI). A comparison was made between the data collected on cores and those provided by different imaging techniques. The comparison clearly establishes that the different wall-images are not as exhaustive as the core data and cannot provide a complete characterization of the fracture network. Discrete fractures thinner than 1 mm are not properly detected. This is also the case for discrete fractures closer than 5 mm, which appear only as single traces. The imaging techniques are, nevertheless, very powerful for characterizing altered fracture clusters. Whatever the technique used, the fracture strikes were correctly sampled with the different systems. This comparison allowed us to calibrate the fracture population data obtained from the imaging system in order to correct for the filtering effect introduced by the technique itself and by the alteration of the rock mass.