Shear fracture (Mode II) of brittle rock
ABSTRACT Mode II fracture initiation and propagation plays an important role under certain loading conditions in rock fracture mechanics. Under pure tensile, pure shear, tension- and compression-shear loading, the maximum Mode I stress intensity factor, , is always larger than the maximum Mode II stress intensity factor, . For brittle materials, Mode I fracture toughness, KIC, is usually smaller than Mode II fracture toughness, KIIC. Therefore, reaches KIC before reaches KIIC, which inevitably leads to Mode I fracture. Due to inexistence of Mode II fracture under pure shear, tension- and compression-shear loading, classical mixed mode fracture criteria can only predict Mode I fracture but not Mode II fracture. A new mixed mode fracture criterion has been established for predicting Mode I or Mode II fracture of brittle materials. It is based on the examination of Mode I and Mode II stress intensity factors on the arbitrary plane θ,KI(θ) and KII(θ), varying with θ(−180°⩽θ⩽+180°), no matter what kind of loading condition is applied. Mode I fracture occurs when or and at θIC. Mode II fracture occurs when and at θIIC. The validity of the new criterion is demonstrated by experimental results of shear-box testing.Shear-box test of cubic specimen is a potential method for determining Mode II fracture toughness KIIC of rock since it can create a favorable condition for Mode II fracture, i.e. is always 2–3 times larger than and reaches KIIC before reaches KIC. The size effect on KIIC for single- and double-notched specimens has been studied for different specimen thickness B, dimensionless notch length a/W (or 2a/W) and notch inclination angle α. The test results show that KIIC decreases as B increases and becomes a constant when B is equal to or larger than W for both the single- and double-notched specimens. When a/W (or 2a/W) increases, KIIC decreases and approaches a limit. The α has a minor effect on KIIC when α is within 65–75°. Specimen dimensions for obtaining a reliable and reproducible value of KIIC under shear-box testing are presented. Numerical results demonstrate that under the shear-box loading condition, tensile stress around the notch tip can be effectively restrained by the compressive loading. At peak load, the maximum normal stress is smaller than the tensile strength of rock, while the maximum shear stress is larger than the shear strength in the presence of compressive stress, which results in shear failure.
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ABSTRACT: A new approach has been devised for calibrating contact-bonded particle models using ‘experimental design’ and ‘optimization’ in uniaxial compression simulation. These are applied to calculate an optimum set of microparameters used in generation of models to be tested in uniaxial compression simulations. Sensitivities of microparameters with respect to uniaxial compressive strength (UCS), Young's modulus, and Poisson's ratio (i.e. macroscopic responses of model) were tested by the Plackett–Burman (PB) design method. Then, for each macroscopic response, two microparameters having the largest impacts were singled out and their non-linear relations to macroscopic responses were estimated by statistical Central Composite Design (CCD) method. Using the results from PB design and CCD method, the problem of finding a set of microparameters was solved. Using an optimization method, the optimum set is obtained that gives the best agreement either in quantitative or in qualitative ways between the results both from the bonded particle model simulations and laboratory. The overall procedure was applied to calculate optimum sets of microparameters for generation of bonded particle models for uniaxial compression simulations on different rock types. Results from both simulations and laboratory tests gave fair agreements. The method currently provides adequate solutions and shows relatively fair applicability to simulation of rock materials with their physical properties falling within the following ranges: UCS (40–170 MPa), Young's modulus (20–50 GPa), and Poisson's ratio (0.19–0.25).International Journal of Rock Mechanics and Mining Sciences 04/2013; · 1.20 Impact Factor
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ABSTRACT: In order to obtain shear-mode fracture toughness of the original(nondistributed) frozen soil which constitutive relation, water contained and temperature distribution are not distributed, a four-point banding experimental model to measure the nonlinearity fracture toughness under shear-mode loading in frozen soil was presented. The certain experimental methodology including specimen's preparation of the original state frozen soil, the precrack of frozen soil specimen, the measurement of critical crack length using dye penetrant technique, non-linearity correction factor determination and relationships between non disturbed frozen soil and disturbed frozen soil, etc. has been studied in the paper. There exist obvious differences of fracture toughness between undisturbed and disturbed soils although the samples are tested under the same conditions of initial water content, dry density and temperature. Both the experiment method of testing the nonlinear fracture toughness of the shear mode(type II) and the experimental data of the nonlinear fracture toughness for the original state frozen soil in this paper can offer the basis for the frozen soil nonlinear fracture theory research and engineering application.Computational Sciences and Optimization (CSO), 2011 Fourth International Joint Conference on; 05/2011
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ABSTRACT: The failure of cracked rock masses is mainly due to the influence of both opening (mode I) and sliding (mode II) of deformation. In this paper, mixed mode I/II fracture toughness of an Iranian white marble (Harsin marble) was investigated both experimentally and theoretically. Several mixed mode fracture tests were conducted on Harsin marble using cracked semi circular bend (SCB) specimens to obtain the mixed mode fracture resistance envelope in the complete range from pure mode I to pure mode II. However, the experimental results were not consistent with the classical mixed mode brittle fracture criteria. It was demonstrated that the low fracture resistance of the tested rock was mainly due to the influence of large positive T-stresses that exist in the SCB specimen when the specimen is subjected to mixed mode loading. It was also shown that the GMTS criterion which uses three fracture parameters i.e. KI, KII and T can provide significantly better estimates for mixed mode fracture in the Harsin marble when tested by the SCB specimens.Procedia Engineering. 01/2011; 10:311–318.