• Tunnel and Underground Space
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• v.13 no.1
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• pp.52-63
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• 2003

Discontinuities such as faults, fractures and joints in rock mass play the dominant role in the mechanical and hydraulic properties of the rock mass. The key factors that influence on the flow of groundwater are hydraulic and geometric characteristics of discontinuities and their connectivity. In this study, a program that analyzes groundwater flow in the 3D discontinuity network was developed on the assumption that the discontinuity characteristics such as density, trace length, orientation and aperture have particular distribution functions. This program generates discontinuities in a three-dimensional space and analyzes their connectivity and groundwater flow. Due to the limited computing capacity In this study, REV was not exactly determined, but it was inferred to be greater than 25$\times$25$\times$25 ㎥. By calculating the extent of aperture that influences on the groundwater flow, it was found that the discontinuities with the aperture smaller than 30% of the mean aperture had little influence on the groundwater flow. In addition, there was little difference in the equivalent hydraulic conductivity for the the two cases when considering and not considering the boundary effect. It was because the groundwater flow was mostly influenced by the discontinuities with large aperture. Among the parameters considered in this study, the length, aperture, and orientation of discontinuities had the greatest influence on the equivalent hydraulic conductivity of rock mass in their order. In case of existence of a fault in rock mass, elements of the equivalent hydraulic conductivity tensor parallel to the fault fairly increased in their magnitude but those perpendicular to the fault were increased in a very small amount at the first stage and then converged.

• Journal of the Microelectronics and Packaging Society
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• v.28 no.1
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• pp.39-46
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• 2021

The quantitative measurement of interfacial adhesion energy (Gc) of multilayer thin films for Cu interconnects was investigated using a double cantilever beam (DCB) and 4-point bending (4-PB) test. In the case of a sample with Ta diffusion barrier applied, all Gc values measured by the DCB and 4-PB tests were higher than 5 J/㎡, which is the minimum criterion for Cu/low-k integration without delamination. However, in the case of the Ta/Cu sample, measured Gc value of the DCB test was lower than 5 J/㎡. All Gc values measured by the 4-PB test were higher than those of the DCB test. Measured Gc values increase with increasing phase angle, that is, 4-PB test higher than DCB test due to increasing plastic energy dissipation and roughness-related shielding effects, which matches well interfacial fracture mechanics theory. As a result of the 4-PB test, Ta/Cu and Cu/Ta interfaces measured Gc values were higher than 5 J/㎡, suggesting that Ta is considered to be applicable as a diffusion barrier and a capping layer for Cu interconnects. The 4-PB test method is recommended for quantitative adhesion energy measurement of the Cu interconnect interface because the thermal stress due to the difference in coefficient of thermal expansion and the delamination due to chemical mechanical polishing have a large effect of the mixing mode including shear stress.