• Title/Summary/Keyword: Mode expansion method

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Numerical study on mechanical and failure properties of sandstone based on the power-law distribution of pre-crack length

  • Shi, Hao;Song, Lei;Zhang, Houquan;Xue, Keke;Yuan, Guotao;Wang, Zhenshuo;Wang, Guozhu
    • Geomechanics and Engineering
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    • v.19 no.5
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    • pp.421-434
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    • 2019
  • It is of great significance to study the mechanical properties and failure mechanism of the defected rock for geological engineering. The defected sandstone modeling with power-law distribution of pre-cracks was built in this paper by Particle Flow Code software. Then the mechanical properties of sandstone and the corresponding failure process were meticulously analyzed by changing the power-law index (PLI) and the number of pre-cracks (NPC). The results show that (1) With the increase of the PLI, the proportion of prefabricated long cracks gradually decreases. (2) When the NPC is the same, the uniaxial compressive strength (UCS) of sandstone increases with the PLI; while when the PLI is the same, the UCS decreases with the NPC. (3) The damage model of rock strength is established based on the Mori-Tanaka method, which can be used to better describe the strength evolution of damaged rock. (4) The failure mode of the specimen is closely related to the total length of the pre-crack. As the total length of the pre-crack increases, the failure intensity of the specimen gradually becomes weaker. In addition, for the specimens with the total pre-crack length between 0.2-0.55 m, significant lateral expansion occurred during their failure process. (5) For the specimens with smaller PLI in the pre-peak loading process, the concentration of the force field inside is more serious than that of the specimens with larger PLI.

Experimental Study for Confirmation of Relaxation Zone in the Underground Cavity Expansion (지중 내 공동 확장에 따른 이완영역 확인을 위한 실험적 연구)

  • Kim, Youngho;Kim, Hoyeon;Kim, Yeonsam;You, Seung-Kyong;Han, Jung-Geun
    • Journal of the Korean Geosynthetics Society
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    • v.16 no.4
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    • pp.231-240
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    • 2017
  • Recently, there have been frequent occurrences of ground sink in the urban area, which have resulted in human and material damage and are accompanied by economic losses. This is caused by artificial factors such as soil loss, poor compaction, horizontal excavation due to the breakage of the aged sewage pipe, and lack of water proof at vertical excavation. The ground sink can be prevented by preliminary restoration and reinforcement through exploration, but it can be considered that it is not suitable for urgent restoration by the existing method. In this study, a model experiment was carried out to simulate the in-ground cavities caused by groundwater flow for developing non-excavation urgent restoration in underground cavity and the range of the relaxation zone was estimated by detecting the around the cavity using a relaxation zone detector. In addition, disturbance region and relaxation region were separated by injecting gypsum into cavity formed in simulated ground. The shape of the underground cavity due to the groundwater flow was similar to that of the failure mode III formed in the dense relative density ground due to water pipe breakage in the previous study. It was confirmed that the relaxed region detected using the relaxation zone detector is formed in an arch shape in the cavity top. The length ratio of the relaxation region to the disturbance region in the upper part of the cavity center is 2: 1, and it can be distinguished by the difference in the decrease of the shear resistance against the external force. In other words, it was confirmed that the secondary damage should not occur in consideration of the expandability of the material used as the injecting material in the pre-repair and reinforcement, and various ground deformation states will be additionally performed through additional experiments.

Effect of Ta/Cu Film Stack Structures on the Interfacial Adhesion Energy for Advanced Interconnects (미세 배선 적용을 위한 Ta/Cu 적층 구조에 따른 계면접착에너지 평가 및 분석)

  • Son, Kirak;Kim, Sungtae;Kim, Cheol;Kim, Gahui;Joo, Young-Chang;Park, Young-Bae
    • 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.