Y. Tsui

Numerical studies of the influence of microstructure on rock failure in uniaxial compression — Part I: effect of heterogeneity

Abstract A numerical parameter-sensitivity analysis has been conducted to evaluate the effect of heterogeneity on the fracture processes and strength characterization of brittle materials such as rock under uniaxial compression loadings. This was done using the Rock Failure Process Analysis code (RFPA 2D ). Studying the details of macrofracture formation from specimen to specimen due to local variation in a heterogeneous material, a number of features were consistently obtained in the numerical simulations. In relatively homogeneous specimens, the macrofracture nucleated abruptly at a point in the specimen soon after reaching the peak stress. Prior to macrofracture nucleation, a small number of acoustic emission (AE) events or microfractures were distributed randomly throughout the specimen. It is difficult to predict where the macrofracture will initiate for the homogeneous rock type since the failure of the specimen is completely brittle. On the other hand, relatively heterogeneous specimens show a somewhat different response. In this case, more diffused AE events or microfractures appear in the early stage of loading. As opposed to homogeneous specimens, macrofracture nucleation starts well before the peak stress is reached and the fracture propagation, as well as the coalescence, can be traced. These events are precursors for predicting unstable failure of the specimen. For specimens with the same property of heterogeneity, however, the numerical simulations show that the failure modes depend greatly on the fracture initiation location — which is found to be sensitive to local variations within the specimen. Peak strength is dependent on the heterogeneous nature of the specimens. Splitting and faulting failure modes often observed in experiments are also observed in the simulations under uniaxial compression. It is found that tension fractures are the dominant failure mechanism in both splitting and faulting processes. The numerical simulation shows that faulting is mainly a process of tensile fractures, often en echelon fractures, developed in a highly stressed shear band, just is as observed in actual uniaxial compression tests.

A modified Kachanov method for analysis of solids with multiple cracks

Abstract Kachanov proposed an approximate method for the analysis of multiple cracks by assuming that traction in each crack can be represented as a sum of a uniform component and a non-uniform component, and the interaction among the cracks are only due to the uniform components. These assumptions simplify considerably the mathematics and allow ‘closed-form’ solutions to be obtained for some cases. However, it is noted that the assumptions may not be valid when the cracks are very close. Therefore, an improved method of elastic solids with closely spaced multiple cracks is proposed. Unlike the Kachanov method, traction in a crack is decomposed into a linearly varying component and a non-uniform component so that the sum of the two components to be equal to the traction along the crack length. It is further assumed that the interaction effect due to the non-uniform component can be neglected, and therefore, only the effect of the linearly varying component has to be considered. The accuracy of the present method is validated by comparing the results of two and three collinear open cracks obtained by the present method with those of the exact solutions and the original Kachanov method. Applications of the approach in solving non-collinear parallel crack and friction crack problems are also presented to demonstrate the versatility and accuracy of the method.

Plate on layered foundation analyzed by a semi-analytical and semi-numerical method

Abstract A semi-analytical and semi-numerical method is developed for the analysis of plate-layered soil systems. Applying a Hankel transform, an expression relating the surface settlement and the reaction of the layered soil is derived. Such a reaction can be treated as a load acting on the plate in addition to the applied external load. Having the plate modeled by eight-noded isoparametric elements, the governing equations of the plate can be formed and solved. Numerical examples, including square, trapezoidal and circular plates resting on elastic layered soil, are given to demonstrate the advantages, accuracy and versatility of this method.

A boundary collocation method for cracked plates

A boundary collocation method is developed for analyzing cracked thin plates. Complex stress functions which satisfy the equilibrium equations of an infinite domain having a single crack are first derived. As the functions have also satisfied the stress singularity at the crack tips, it is only necessary to enforce the stress functions to satisfy the boundary conditions along the edges of the plates and the surfaces of the cracks, if there is more than one crack. This is achieved by the collocation least square approach. The unknown coefficients of the stress functions having been determined, the stress intensity factors can then be computed according to the related formulae. Examples of rectangular and circular plates with a different number of cracks and under different loadings are used to demonstrate the accuracy, versatility and advantages of the method.