Report Topic:Estimation of characteristic value using the weakest-path model
Reporter: Prof. KK Phoon, National University of Singapore
Time: 10:30, Jun. 27, 2017
Location: Academic Hall of State Key Laboratory
Eurocode 7 (EN 1997−1:2004), 126.96.36.199(2) recommends that the “characteristic value of a geotechnical parameter shall be selected as a cautious estimate of the value affecting the occurrence of the limit state.” Much attention has been focused on how to obtain a “cautious estimate”. For example, EN 1997−1:2004, 188.8.131.52(11) notes that “If statistical methods are used, the characteristic value should be derived such that the calculated probability of a worse value governing the occurrence of the limit state under consideration is not greater than 5%.” There is less discussion on the “value affecting the occurrence of the limit state”. One notes that the occurrence of a limit state in terms of its physical manifestation as a critical slip surface is dependent on spatial variability. The value affecting this occurrence, called the mobilized shear strength, is thus dependent on spatial variability. It is the 5% quantile of this mobilized shear strength, rather than the 5% quantile of borehole data (unrelated to any critical slip surface), that is relevant for design.
It is tempting to think that the mobilized shear strength is the same as the conventional spatial average defined over a prescribed path (also called the Vanmarcke-type spatial average). However, this is not true, because the mobilized shear strength is related to the spatial average along the critical slip curve. This critical slip curve is NOT a prescribed curve – it changes from one realization to another. Hence, the spatial average of interest is very special and its probabilistic model is difficult to derive in closed form. It is certainly qualitatively different from the conventional prescribed path spatial average, which has an elegant closed form probabilistic solution (the variance reduction function). One key take away from this lecture is an effective yet practical weakest-path model that can produce the statistics of this special spatial average approximately without invoking very costly random finite element analyses. The 5% quantile of this special spatial average can be adopted as the characteristic value for design.