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Accurately measuring a crack length is a crucial aspect of experimental fracture tests. In this work, we present an innovative application of the A* (A-star) shortest path methodology to track different shapes of cracks from numerical simulations. This approach is highly efficient, significantly improving the speed and accuracy of crack length measurements. Furthermore, we introduce a modified weight cost function that follows the crack path in the damage field, enhancing the accuracy of our method. The effectiveness of the proposed procedure is shown by fabricating damage fields with different geometry and good agreement when compared to the exact values. In addition, we evaluate a time-dependent crack propagation case, achieving high accuracy. We present all features and steps of the procedure to showcase its efficacy in accurately measuring the length of a crack path. Finally, we validate our method using a phase-field fracture framework and compare it with the compliance technique. The results show that the proposed method is applicable in finite element analyses with recovering accurate results, The authors would like to acknowledge CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) for the scholarship under grant 88882.435204/2019-01. J.A. Avila is a Serra Hunter Fellow and a CNPq fellow., Postprint (published version)

Concrete under tension exhibits a great degree of post-peak non-linearity. Current design codes assume the tensile strength of concrete to be negligible, which is not only a gross oversimplification of the fracture process of concrete in tension, but is also overly conservative. However, research in the field of fracture mechanics has produced models that can accurately predict crack propagation in concrete using fracture parameters determined from testing. One of these models, which is both simple and reasonably accurate, estimates the post-peak tensile behavior of concrete as a bilinear approximation of the softening curve, known as the bilinear cohesive crack model. The American Concrete Institutes Committee 446 is developing a draft test method, ACI 446-5, which determines the key fracture parameters of the bilinear cohesive crack model using three-point bend notched beam tests. ACI 446-5 currently contains errors and some impractical methods, combined with complex and often obscure equations for the determination of the bilinear cohesive fracture parameters. To remedy this, the equations for the calculation of the fracture parameters of the bilinear cohesive crack model are derived, and the experimental methods examined and criticized. Experiments of normal strength concrete notched beams of three different sizes were also performed using the guidelines for Level II testing, provided in Chapters 2 and 4 of ACI 446-5, with modifications as needed in the case of ambiguity or impracticality. The results are analyzed and discussed, and potential size dependence of the fracture parameters is discussed. With the corrections provided in this thesis, ACI 446-5 is concluded to be adequate for the determination of the fracture parameters of the bilinear cohesive crack model, and modifications are suggested to improve the test method.'

Yucca Mountain, Nevada is the proposed site for the underground storage of high-level civilian nuclear waste in the United States. The repository must be isolated from the general environment for at least 10,000 years. Ground water and gases are potential carriers of radioactive materials. Fractures and connected pores in the host rock are the major pathways for ground water and gases. Therefore, the mechanical and flow properties of the host rock should be understood and utilized in the design of the underground repository. Samples of Topopah Spring tuff from Yucca Mountain were used in this study. Cylindrical specimens were prepared to perform uniaxial and triaxial "damage" tests where specimens are loaded to a particular stress level to induce damage and fracturing and then unloaded. Mechanisms of microcracking at different fracturing levels have been studied by using both an optical microscope and a Scanning Electron Microscope (SEM). The original rock sample without loading was also observed under the microscopes. Many kinds of defects including pores, preexisting fractures, and soft inclusions were found in the undamaged Apache Leap tuff samples. Pores were determined to be the main microstructures in Topopah Spring tuff that could influence the mechanical and hydrologic properties. Under compressive stresses, microcracking initiates from some of the pores. These microcracks will interact and coalescence to form large microcracks or macroscopic cracks as the load is increased. Crack propagation phenomena, such as pore cracking, pore linking, pore collapse and the formation of en echelon arrays were all found in specimens unloaded prior to complete failure. The failure of tuff specimens is often through a process of shear localization. In summary, the deformation and failure of both tuffs occurred by progressive fracturing, starting from microcracking on the small scale, and ending as fractures coalesced to form macroscopic fractures and shear localization. On

In this dissertation, first, the theoretical and experimental viewpoints of instability and bifurcation in mechanics are reviewed and discussed. The onset of instability of bifurcation depends on the constitutive assumptions, and is marked by the loss of ellipticity, singularity of the stiffness matrix, and negative or complex eigenvalues. Non-traditional regularization is necessary to obtain useful post-instability solutions. Based on dissipated energy and elastic potential, energy based instability criterion is considered and developed. The global instability criterion is concerned with global non-uniform deformation while the surface degradation instability criterion deals with near surface non-uniformities. In addition, the connection between surface degradation and size, shape effects for brittle materials is examined. The energy based stability theory is applied for some typical problems through analytical and numerical implementations. It is shown that the onset of both surface instability and global degradation instability occurs in the strain hardening stage, that is, before and close to the peak strength. The theoretical results are compared with experimental observations. Both strain gage tests and ultrasonic scanning tests are processed to study the degradation mechanisms of a brittle material. The surface effects are highlighted by the experiments. Ultrasonically dissipated energy shows a random distribution and it follows, in general, the initial non-homogeneity pattern. The relationship between the ultrasonically dissipated energy and mechanically dissipated energy is dependent on deformation and can be approximated by a power function of the factor of load level. The theory for surface degradation consideration involves a few material constants, and these constants are identified against experimental observations. The degradation mechanism and damage growth patterning of simulated rock under uniaxial load are modeled numerically by implementing the t

A new approximate theory which links the inherent flaw concept and the theory of crack tip stress singularities at a bi-material interface has been developed. Three assumptions were made: (1) the existence of inherent flaw (i.e. , damage zone) at the tip of the crack was postulated, (2) a fracture of the filamentary composites initiates at a crack lying in the matrix material at the interface of the matrix/filament. (3) a laminate fails whenever the principal load-carrying laminae fails. This will imply that for a laminate consisting of 0 plies, cracks in the matrix perpendicular to the 0 filaments are the triggering mechanism for the final failure. Based on this theory, a parameter KQ which is similar to the stress intensity factor defined for isotropic materials but with a different dimension was defined. Utilizing existing test data, it was found that KQ can be treated as material constant. Based on this finding a fracture strength prediction methodology was developed. The analytical results are correlated well with the test results. This new approximate theory can apply to both brittle and metal matrix composite laminates with crack or hole.

Intact and fractured rock samples were studied in the laboratory in order to understand more fully the mechanism of closure of fractures subjected to high confining stresses and the resultant effect on specimen permeability. Confining stresses applied to the specimens ranged from 3.0 to 20.0 MPa, and the closure of fractures was observed by monitoring the change in the hydraulic conductivity of the specimens. Test results suggest that some resealing may occur due to crushing and realignment of mineral grains along a fracture surface. The closure of fractures is dependent upon the strength of the rock mass, the physical nature of the fracture, and the fluid pressure present in the fracture. Fracture closure is highly time dependent, and a number of nonlinear pressure flow relationships have been identified. These deviations are thought to represent two fundamentally different processes, the most important of which are turbulence in the flow and fracture expansion.

The computer model PT is used to analyze a three-corehole recirculation heat tracer test conducted in a fractured granitic rock mass near Oracle, Arizona. Results of hydraulic tests and geophysical logs are cross-correlated =o determine the location, orientation and thickness of a high permeability fault zone, in which flow between the potencies during the heat tracer test is believed to occur. A quasi-three-dimensional model of fluid flow and heat transport in the fault zone is used to qualitatively reproduce a steep rise in measured temperature within a monitoring borehole. Computed thermal breakthroughs are found to be sensitive to two numerical grid parameters-- Thickness and width. A grid thickness of 1.0 cm and a grid width of 0.7 m are sufficient to qualitatively reproduce the steep temperature increase. Further research into the importance of heat convection under static conditions during the test is recommended.

A method with which to estimate the equivalent saturated hydraulic conductivity and its associated spatial distribution in fractured rock situated in the vadose zone has been developed. Conductivity is estimated in part from outflow rates, induced by a constant hydraulic head, monitored over three meter intervals in boreholes which are oriented in a manner so as to intersect the major fracture sets of a field site. Outflow rates are monitored by means of a falling-head flowmeter while borehole intervals are isolated with a single inflatable packer. Upon collection of the field data, hydraulic conductivity values are estimated by means of two analytical solutions. The solutions are adapted to meet the special conditions posed by variable borehole orientations and multiple test intervals from existing solutions associated with borehole permeability tests. The developed methodology is subsequently utilized to determine the saturated hydraulic conductivity and the associated spatial variability of fractured tuff located near Superior, Arizona.