P.K.K. Lee

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 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.

A study on socketed steel H-piles under vertical load

Socketed steel H-piles are one of the popular foundation systems in Hong Kong. Such piles are normally designed to a carry vertical load by assuming the load will be transferred to the rock socket section and carried by the shaft resistance developed along the socket surface. Irrespective of its popularity, its load transfer mechanism is not yet fully understood and it is the practice to design such piles by ignoring the contribution of the shaft resistance along the shaft section embedded in the soil layer. To address this issue, a comprehensive study was carried out. The study includes (1) determination of the load along the pile by carrying out the pile load test on instrumented piles and (2) numerical modelling of the piles by the finite element method. In this paper, the factual data are shared and the findings of the study are reported.