Stereological Estimation of Fractal Number of Fracture Planes in Concrete

1995 ◽  
Vol 407 ◽  
Author(s):  
P. Stroeven

ABSTRACTConcrete is a man-made material containing a particulate filler designed on the basis of a sieve curve. In case of river aggregate, the particles are approximately spherical and smoothtextured. The particle-matrix interface is mostly the weakest chain link in the mechanical system. This implies damage evolution to start at particle-matrix interfaces. In case of direct tension, these interface cracks will be on average perpendicular to the loading direction. In case of direct compression, they will be parallel to the loading direction. A single fracture surface is formed in tension and a series of fracture surfaces in compression. They are the result of crack concentration within a process zone, in which the engineering crack closely meanders around a dividing plane. This allows to model these fracture surfaces on different resolution levels. It is shown, using stereological notions, that the very phenomenon is of a non-ideal fractal nature. Estimates for fractal dimension of fracture surfaces in concretes based on sieve curves at the border of the practical range are found to closely match experimental data reported in the literature.

1995 ◽  
Vol 117 (4) ◽  
pp. 361-367 ◽  
Author(s):  
Zdeneˇk P. Bazˇant

The paper represents an extended text of a lecture presenting a review of recent results on scaling of failure in structures made of quasibrittle materials, characterized by a large fracture process zone, and examining the question of possible role of the fractal nature of crack surfaces in the scaling. The problem of scaling is approached through dimensional analysis, the laws of thermodynamics and asymptotic matching. Large-size and small-size asymptotic expansions of the size effect on the nominal strength of structures are given, for specimens with large notches (or traction-free cracks) as well as zero notches, and simple size effect formulas matching the required asymptotic properties are reported. The asymptotic analysis is carried out, in general, for fractal cracks, and the practically important case ofnonfractal crack propagation is acquired as a special case. Regarding the fractal nature of crack surfaces in quasibrittle materials, the conclusion is that it cannot play a signification role in fracture propagation and the observed size effect. The reason why Weibull statistical theory of random material strength does not explain the size effect in quasibrittle failures is explained. Finally, some recent applications to fracture simulation by particle models (discrete element method) and to the determination of size effect and fracture characteristics of carbon-epoxy composite laminates are briefly reviewed.


2018 ◽  
Author(s):  
Mirko Carlini ◽  
Giulio Viola ◽  
Jussi Mattila ◽  
Luca Castellucci

Abstract. Fault and fracture planes (FFP) that cut through multilayer sequences can be significantly refracted at layer-layer interfaces due to the different mechanical properties of the contiguous layers, such as shear strength, friction coefficient and grain size. Detailed studies of different but coexisting and broadly coeval failure modes (tensile, hybrid and shear) within multilayers deformed in extensional settings have led to infer relatively low confinement and differential stress as the boundary stress conditions at which FFP refraction occurs. Although indeed widely recognized and studied in extensional settings, the details of FFP nucleation, propagation and refraction through multilayers remain not completely understood, partly because of the common lack of geological structures documenting the incipient and intermediate stages of deformation. Here we present the results of a study on strongly refracted strike-slip FFP within the mechanically layered turbidites of the Marnoso Arenacea Formation (MAF) of the Italian Northern Apennines. The MAF is characterized by the alternation of sandstone (strong) and carbonate mudstone (weak) layers. The studied refracted FFP formed at the front of the regional-scale NE-verging Palazzuolo anticline and post-date almost any other observed structure except for a set of late extensional faults. The studied faults display coexistence of shear and hybrid (tensile-shear) failure modes and we suggest that they initially nucleated as shear fractures (mode III) within the weak layers and, only at a later stage, propagated as dilatant fractures (mode I-II) within the strong layers. The tensile fractures within the strong layers invariably contain blocky calcite infills, which are, on the other hand, almost completely absent along the shear fracture planes deforming the weak layers. Paleostress analysis was performed to constrain the NNE-SSW compressional stress field that produced the refracted FFP and to exclude the possibility that the present attitude of these structures may result from the rotation through time of faults with an initial orientation. Slip tendency analysis was also performed to infer the relative slip and dilation potentials of the observed structures. Mesoscopic analysis of preserved structures from the incipient and intermediate stages of development and evolution of the refracted FFP allowed us to build an evolutionary scheme wherein: a) Nucleation of refracted FFP occurs within weak layers; b) Refraction is primarily controlled by grain size and clay mineral content and variations thereof at layer-layer interfaces but also within individual layers; c) Propagation within strong layers occurs primarily by fluid-assisted development ahead of the FFP tip of a “process zone” defined by a network of hybrid and tensile fractures; d) The process zone causes the progressive weakening and fragmentation of the affected rock volume to eventually allow the FFP to propagate through the strong layers; e) Enhanced suitable conditions for the development of tensile and hybrid fractures can be also achieved thanks to the important role played by pressured fluids.


1994 ◽  
Vol 364 ◽  
Author(s):  
Petra Specht ◽  
Markus Brede ◽  
Peter Neumann

AbstractFracture toughness data of stoichiometric FeAl and NiAl single crystals were measured in four-point-bending tests and the crystallographic orientations of the resultant fracture surfaces were determined.For FeAl single crystals unexpectedly high fracture toughness values were measured even at low temperatures (17 MPa [001] at 77K). However, these crystals failed in a brittle manner for temperatures up to 300K. The crystallographic orientation of the fracture surfaces were strongly dependent on the environment due to hydrogen embrittlement.The NiAl specimens were precracked and the fracture toughness was measured in the weakest crystal orientation. The fracture surfaces were similar to those obtained in previous investigations. Although the room temperature (RT) KIC-value was the highest for pure weak-oriented NiAl (7.5 MPa [001]) the BDT temperature was found in the same region where it occurs for the hard orientation (673K to 693K). The onset of the BDT will be discussed.


2005 ◽  
Vol 41 (1) ◽  
pp. 62-66 ◽  
Author(s):  
V. V. Usov ◽  
N. M. Shkatulyak

2021 ◽  
Author(s):  
Jin Lai ◽  
Dong Li ◽  
Yong Ai ◽  
Hongkun Liu ◽  
Deyang Cai ◽  
...  

Abstract. The Lower Cretaceous Bashijiqike Formation of Kuqa depression is ultra-deeply buried sandstone in fold-and-thrust belts. Few researches link diagenetic processes with structure. To fill this gap, a comprehensive analysis integrating diagenesis with structure pattern, fracture and in situ stress is performed following a structural diagenetic approach. The results show that the pore spaces include residual intergranular pores, intergranular and intragranular dissolution pores, and micro-fractures. The sandstones experienced a high degree of mechanical compaction, and compaction is limited in well-sorted rocks or abundant in rigid quartz grains. The most volumetrically important diagenetic minerals are calcites. The framework grains experienced a varied degree of dissolution, and intergranular and intragranular dissolution pores are formed. Special aims are paid on the dissolution associated with the fracture planes. Most natural fractures are cemented by carbonate cements, which limit fluid flow. In addition, presences of fracture enhance dissolution, and the fracture planes are enlarged by dissolution. Cementation and dissolution can occur simultaneously in fracture surfaces, and the enlarged fracture surfaces can be cemented by late-stage cements. The in situ stress magnitudes are calculated using well logs. The horizontal stress difference (Δσ) determines the degree of mechanical compaction, and rocks associated with low Δσ experienced a low degree of compaction, and there contain preserved intergranular pores. Natural fractures are mainly related to the low Δσ layers. The presences of intergranular and intragranular dissolution pores are mainly associated with the fractured zones. The high quality reservoirs with intergranular pores or fractures are related to low Δσ layers. The structural diagenesis researches above help the prediction of reservoir quality in ultra-deep sandstones, and reduce the uncertainty in deep natural gas exploration in Kuqa depression.


Solid Earth ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 343-356 ◽  
Author(s):  
Mirko Carlini ◽  
Giulio Viola ◽  
Jussi Mattila ◽  
Luca Castellucci

Abstract. Fault and fracture planes (FFPs) affecting multilayer sequences can be significantly refracted at layer–layer interfaces due to the different mechanical properties of the contiguous layers, such as shear strength, friction coefficient and grain size. Detailed studies of different but coexisting and broadly coeval failure modes (tensile, hybrid and shear) within multilayers deformed in extensional settings have led to infer relatively low confinement and differential stress as the boundary stress conditions at which FFP refraction occurs. Although indeed widely recognized and studied in extensional settings, the details of FFP nucleation, propagation and refraction through multilayers remain not completely understood, partly because of the common lack of geological structures documenting the incipient and intermediate stages of deformation. Here, we present a study on strongly refracted strike-slip FFPs within the mechanically layered turbidites of the Marnoso Arenacea Formation (MAF) of the Italian northern Apennines. The MAF is characterized by the alternation of sandstone (strong) and carbonate mudstone (weak) layers. The studied refracted FFPs formed at the front of the regional-scale NE-verging Palazzuolo anticline and post-date almost any other observed structure except for a set of late extensional faults. The studied faults document coexisting shear and hybrid (tensile–shear) failure modes and, at odds with existing models, we suggest that they initially nucleated as shear fractures (mode III) within the weak layers and, only at a later stage, propagated as dilatant fractures (modes I–II) within the strong layers. The tensile fractures within the strong layers invariably contain blocky calcite infills, which are, on the other hand, almost completely absent along the shear fracture planes deforming the weak layers. Paleostress analysis suggests that the refracted FFPs formed in a NNE–SSW compressional stress field and excludes the possibility that their present geometric attitude results from the rotation through time of faults with an initial different orientation. The relative slip and dilation potential of the observed structures was derived by slip and dilation tendency analysis. Mesoscopic analysis of preserved structures from the incipient and intermediate stages of development and evolution of the refracted FFPs allowed us to propose an evolutionary scheme wherein (a) nucleation of refracted FFPs occurs within weak layers; (b) refraction is primarily controlled by grain size and clay mineral content and variations thereof at layer–layer interfaces but also within individual layers; (c) propagation within strong layers occurs primarily by fluid-assisted development ahead of the FFP tip of a “process zone” defined by a network of hybrid and tensile fractures; (d) the process zone causes the progressive weakening and fragmentation of the affected rock volume to eventually allow the FFPs to propagate through the strong layers; (e) enhanced suitable conditions for the development of tensile and hybrid fractures can be also achieved thanks to the important role played by pressured fluids.


2007 ◽  
Vol 80 (5) ◽  
pp. 820-825 ◽  
Author(s):  
B. Adamu ◽  
G. R. Hamed

Abstract T-peel tearing of a model black-filled natural rubber tread ply vulcanizate has been carried out. Tearing alternates between slow (“stick”) and fast growth stages (“slip”). “Stick” fracture involves sideways cracking into the loading direction. This blunts the peel front, slows forward tearing, and results in rough fracture surfaces. “Slip” fracture is the sudden forward growth of a crack, leaving relatively smooth fracture surfaces. “Stick-slip” fracture is characteristic of highly reinforced rubbers; it is also seen in edge-cut tensile specimens and trouser tear specimens of black-filled NR.


Author(s):  
Russell L. Steere ◽  
Michael Moseley

A redesigned specimen holder and cap have made possible the freeze-etching of both fracture surfaces of a frozen fractured specimen. In principal, the procedure involves freezing a specimen between two specimen holders (as shown in A, Fig. 1, and the left side of Fig. 2). The aluminum specimen holders and brass cap are constructed so that the upper specimen holder can be forced loose, turned over, and pressed down firmly against the specimen stage to a position represented by B, Fig. 1, and the right side of Fig. 2.


Author(s):  
Kathleen B. Reuter

The reaction rate and efficiency of piperazine to 1,4-diazabicyclo-octane (DABCO) depends on the Si/Al ratio of the MFI topology catalysts. The Al was shown to be the active site, however, in the Si/Al range of 30-200 the reaction rate increases as the Si/Al ratio increases. The objective of this work was to determine the location and concentration of Al to explain this inverse relationship of Al content with reaction rate.Two silicalite catalysts in the form of 1/16 inch SiO2/Al2O3 bonded extrudates were examined: catalyst A with a Si/Al of 83; and catalyst B, the acid/phosphate Al extracted form of catalyst A, with a Si/Al of 175. Five extrudates from each catalyst were fractured in the transverse direction and particles were obtained from the fracture surfaces near the center of the extrudate diameter. Particles were also obtained from the outside surfaces of five extrudates.


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