• Title/Summary/Keyword: weighting functions

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Quantitative assessment of spalling depth and width using statistical inference theory in underground openings (통계추론을 이용한 지하암반공동에서의 스폴링 깊이와 폭에 대한 정량적 평가)

  • Bang, Joon-Ho;Lee, In-Mo
    • Journal of Korean Tunnelling and Underground Space Association
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    • v.12 no.1
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    • pp.1-14
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    • 2010
  • Until now, the evaluation method of spalling depth using Martin et al. (1999)'s linear regression relations has long been known applicable. However, it is not likely that the proposed equation is applicable to the openings other than circular type and mostly overpredict the spalling depth in comparison with actual spalling cases. Moreover, the evaluation method to estimate the spalling width has not been presented yet; it is essential to evaluate the spalling width in addition to the spalling depth, because the shape of the spalled region influences the choice of suitable rock reinforcement. In this study, linear regression equations, in which normalized spalling depth ($d_f/W_D$) and normalized spalling width ($w_f/W_D$) are functions of three spalling evaluation indices, ${\sigma}_1/{\sigma}_c,\;D_{is}(={\sigma}_{max}/{\sigma}_c)$ and ${\sigma}_{dev}/{\sigma}_{cm}$, are established based on in-situ spalling observations and CWFS simulation results. Confidence intervals of 95% using the statistical inference theory are used in verifying the reliability of linear regression equations. Spalling depth ($d_f$) and spalling width ($w_f$) predicted from the proposed linear regression relations, which take three spalling evaluation indices into account, showed reasonable match with in-situ observations by adopting weighting factors considering the degree of variance of linear regression relations.