Effect of a heterogeneity on tensile failure: interaction between fractures in a limestone

Author(s):  
Anne Pluymakers ◽  
Richard Bakker ◽  
Auke Barnhoorn

<p>Not all rocks are perfect. Frequently heterogeneities will be present, either in the form of pre-existing fractures, or in the form of sealed fractures. Tensile strength and strength anisotropy of rocks has been investigated for strongly layered rocks, such as shales, sandstones and gneisses, but data is lacking on the effect of single planar heterogeneities, such as pre-existing fractures or stylolites. We have performed Brazilian Disc tests on limestone samples containing pre-existing fractures and stylolites, investigating Brazilian test Strength (BtS) and fracture orientation. We used Indiana limestone samples, pre-fractured with the Brazilian Disc method, and Treuchtlinger Marmor samples which contained central stylolites. All experiments were filmed. The planar discontinuity was set at different rotation angles of approximately 0–20–30–45–60–90⁰, where 90⁰ is parallel to the principal loading direction, and 0⁰ to the horizontal axis of the sample. Pre-fracturing Indiana limestone samples results in a cohesion-less planar discontinuity, whereas the stylolites in the Treuchtlinger Marmor samples are discontinuities which have some strength.</p><p>The results show that our imperfect samples with a planar discontinuity are always weaker than an intact sample. For the Indiana limestone, with a cohesion-less interface, there is 10 to 75% of weakening, which is angle-dependent. Once the angle is 30 or lower there is no influence from the initial fracture for the orientation of the new fracture. The stress-displacement pattern followed the expectation for Brazilian Disc testing. However, in the samples with a stylolite, strength is isotropic and between 25 and 65% of the strength of an intact sample. For all cases several new cracks appeared, of which the orientation is influenced by the orientation of the stylolite. The fracture pattern and associated stress drops are more complex for high angles. Interestingly, in the samples with stylolites, always more than one fracture was formed, whereas in the samples with a cohesionless interface usually only one new fracture formed, which for natural settings suggests a potential for higher fracture density when hydrofracturing a stylolite-rich interval.</p><p>A second difference between these datasets is the amplitude of the pre-existing interface. The effect of amplitude will be qualitatively investigated with a 2D Comsol model, to investigate the location of the first fracture occurring, which can then be compared to the camera data of the experiments.</p>

2021 ◽  
Author(s):  
Anne Pluymakers ◽  
Auke Barnhoorn ◽  
Richard Bakker

<p>Not all rocks are perfect. Frequently heterogeneities will be present, either in the form of pre-existing fractures, or in the form of sealed fractures. To date, investigation of sample heterogeneity, specifically tensile strength and strength anisotropy has focused on layered rocks, such as shales, sandstones and gneisses. Data is lacking on the effect of single planar heterogeneities, such as pre-existing fractures or stylolites, even though these frequently occur in geo-energy settings.</p><p>We have performed Brazilian Disc tests on limestone samples containing planar heterogeneities, investigating Brazilian test Strength (BtS) and the effects of orientation on strength. We used prefractured Indiana limestone to represent a planar heterogeneity without cohesion and Treuchtlinger Marmor samples with central stylolites to represent a planar heterogeneity of unknown strength (as an example of a sealed fracture). The planar discontinuity was set at different rotation angles of approximately 0–20–30–45–60–90⁰, where 90⁰ (steep angle) is parallel to the principal loading direction, and 0⁰ (low angle) to the horizontal axis of the sample. All experiments were filmed, and where possible Particle Image Velocimetry was used to determine internal particle motion. Moreover, we used a 2D Comsol model in which we simplified the stylolite surface as a sinusoid. The model was used to qualitatively determine how i) a different period of the sinusoid and ii) relative strength of sinusoid/matrix affect the results.</p><p>Our results show that all imperfect samples are weaker than intact samples. The 2D Comsol model indicates that the qualitative results remain unaffected by changing the period (assumed to be representative of roughness) of the cohesive heterogeneity, nor by the relative strength contrast: the location of the first fracture remains unaffected. For both heterogeneity types, the fracture patterns can be divided into four categories, with two clear endmembers, and a more diffusive subdivision in between.</p><p>For a cohesion-less heterogeneity:</p><ul><li>steep angles lead to frictional sliding along the interface, and only a small hypothesized permeability increase.</li> <li>Intermediate angles lead to a combination of tensile failure of the matrix and sliding along the interface, where for steeper angles more new fractures form which follow the path of the existing fracture.</li> <li>Low angles lead to closure of the old fracture and new tensile failure.</li> </ul><p>For a cohesive heterogeneity of unknown cohesion:</p><ul><li>Steep angles lead to intensive failure of the heterogeneous zone, attributed to the presence of a stress concentrator.</li> <li>Intermediate angles lead to partial failure along the heterogeneous zone, and the formation of new fractures in the matrix, potentially instigated by mode II failure to accommodate motion.</li> <li>Low angles lead to the formation of a new fracture plus opening within the heterogeneous zone.</li> </ul><p>These results imply that hydrofracture (i.e. creating tensile stresses) of a stylolite-rich zone will lead to more fractures than fractures in a homogeneous zone, where the orientation of the stylolites and bedding will control the orientation of the permeable pathways.</p>


2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xin Kang ◽  
Sheng-li Yang ◽  
Ping Zhan ◽  
Liang-hui Li

Application of a horizontal section top-coal caving in a steeply inclined thick coal seam not only effectively resolves the problem of the large dip angle of the coal seam and slipping and dumping of mining equipment but also significantly reduces the tunnel drivage ratio and improves the extraction yield. In addition, it allows for a safe and efficient mining from a steeply inclined thick coal seam. In this paper, the roof fracture pattern of a steeply inclined thick coal seam has been studied by a similar simulation experiment. The results of the simulation are consistent with those of the numerical calculations, thus verifying the accuracy of the simulation. The experimental simulation results show that the roof can form a step-like toppling failure pattern after drawing the coal, and it is difficult to release a triangular coal mass near the floor, which is the main concentration area of coal loss. The numerical simulation results show that, with the excavation of the coal seam, the rock mass around the goaf produces plastic failure, and the damage is mainly concentrated in the roof area. The upper part of the goaf mainly shows a tensile failure, while the other areas mainly show yield failure.


2020 ◽  
Author(s):  
Naveed Ahsan ◽  
Muhammad Armaghan Faisal Miraj ◽  
Hamza Tariq ◽  
Abdul Qayyum

<p> Hazara Basin is a NE-SW trending fold and thrust belt, emerged as a consequence of ongoing collision between the Indian and Eurasian plates. Hazara Basin is bounded by Panjal Thrust (PT) in the North and Main Boundary Thrust (MBT) is located in the South. The present work deals with the paleostresses and outcrop fracture pattern (orientations, opening, fracture density) in different rock units exposed in Ghumanwan area located in the vicinity of Abbottabad, in Hazara Basin. PT and MBT juxtapose various lithological units along the Hazara Kashmir Syntaxes (HKS). The imbricate fault system between these two faults indicates a sinistral relative movement. We adopted circle inventory method in the field and collected data (fracture length, width, orientations and dip azimuth) from diverse rock units at 11 visited outcrop stations of the Ghumanwan Dome. These rock units include Upper Cretaceous (Kawagarh Formation) and Paleogene carbonates (Lockhart Formation and Margalla Hill Limestone). We observed highly dense, non-systematic fracture pattern in which mostly fractures are oriented in N-W direction normal to the bedding. Moreover, MOVE<sup>TM</sup> 2018 (Midland Valley) Stress Analysis module (Stereonet Plot) was used for paleostresses analysis. The results show that the Slip Tendency (ratio of shear stress to normal stress) magnitude of σ2 lies closer to the σ3 (on Stereonet) and suggests compressional stresses in which NW-SE oriented fractures developed. The N-S compressive stresses which have mainly affected the concerned area are presumably linked to be late Eocene-Oligocene tectonic event.</p>


2010 ◽  
Vol 97-101 ◽  
pp. 1569-1572
Author(s):  
Cheng Fan ◽  
Li Chi Han

Fracture of dental all-ceramic restoration is often observed in clinic. And the fracture mechanisms and processes of three-unit all-ceramic fixed partial dentures (FPDs) are still not clear. In this paper, the fracture mechanism and process of a three unit zirconia ceramic FPDs framework under simulated mechanical loading are calculated by using a self-developed numerical modeling code, the RFPA2D code. Acoustic emission showed that the fracture mechanism was tensile failure and the crack started at the lower boundary of the framework. The result revealed that the framework fracture pattern obtained by using the numerical simulation agreed with that observed in a previous laboratory test. The fracture process could be followed both in step-by-step and step-in-step. The RFPA2D code is suitable for the use as a complement to other tests and clinical observations in studying stress distribution, fracture mechanism and fracture process in ceramic FPDs framework.


2020 ◽  
Author(s):  
Zenghui Zhao ◽  
Peng Yang ◽  
Shaojie Chen ◽  
Dawei Yin ◽  
Hao Liu ◽  
...  

Abstract To define the critical criterion between tensile failure and shear failure of Brazilian disc is crucial for determination of tensile strength under combination of tensile and compressive stresses. Although Griffith's tensile failure criterion is consistent with theoretical solution of radial splitting disc, there are still some shortcomings in which the compression-tension ratio is regarded as a constant and the critical criterion only depend on single parameter of tensile strength. Therefore a critical criterion for tensile-shear failure including tensile truncation was proposed firstly based on Mohr-Coulomb criterion. Then, a new calculation method of shear strength parameters was deduced based on the critical state stress circle. Finally, effective diameter and range of compression-tension ratio of Brazilian disc under tensile failure are proposed, and failure process of Brazilian disc from meso to macro is carried out based on numerical simulation. The results show that the modified Mohr-Coulomb criterion can be determined by two indexes of compressive strength and tensile strength. The deduced compression-tension ratio is in good agreement with experiment results. The accuracy of tensile strength test results is closely related to this ratio. When the ratio is greater than 6, failure of rock can be regarded as ideal tensile failure. If the ratio is less than 6, wedge-shape failure in loading area is the main failure type. On this condition, even if radial crack occurs, it is still not considered to be caused by pure tension.


Author(s):  
F. I. Grace

An interest in NiTi alloys with near stoichiometric composition (55 NiTi) has intensified since they were found to exhibit a unique mechanical shape memory effect at the Naval Ordnance Laboratory some twelve years ago (thus refered to as NITINOL alloys). Since then, the microstructural mechanisms associated with the shape memory effect have been investigated and several interesting engineering applications have appeared.The shape memory effect implies that the alloy deformed from an initial shape will spontaneously return to that initial state upon heating. This behavior is reported to be related to a diffusionless shear transformation which takes place between similar but slightly different CsCl type structures.


1996 ◽  
Vol 12 (2) ◽  
pp. 124-131 ◽  
Author(s):  
Carlos Santoyo

The present paper deals with behavioral assessment of social interaction in natural settings. The design of observational systems that allow the identification of the direction, contents, quality and social agents involved in a social interchange is an aim of social interaction assessment and research. In the first part a description of a system of behavioral observation of social interaction is presented. This system permits the identification of the above mentioned aspects. Secondly a strategy for the behavioral assessment of social skills is described. This strategy is based on the consequences and effects of social interaction, and it is supported by three basic processes: social effectiveness, social responsiveness and reciprocity.


Author(s):  
Laurent Grégoire ◽  
Pierre Perruchet ◽  
Bénédicte Poulin-Charronnat

Grégoire, Perruchet, and Poulin-Charronnat (2013) claimed that the Musical Stroop task, which reveals the automaticity of note naming in musician experts, provides a new tool for studying the development of automatisms through extensive training in natural settings. Many of the criticisms presented in the four commentaries published in this issue appear to be based on a misunderstanding of our procedure, or questionable postulates. We maintain that the Musical Stroop Effect offers promising possibilities for further research on automaticity, with the main proviso that the current procedure makes it difficult to tease apart facilitation and interference.


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