Shape factors for concrete shrinkage and drying creep in model B4 refined by nonlinear diffusion analysis

The source of shrinkage and drying creep is the drying process. From the diffusion analysis of drying one can estimate the shrinkage strain. Same as drying, the shrinkage times scale as the square of the effective specimen thickness (or size), D, commonly characterized by the volume-surface ratio. But there is also an additional effect of cross section shape. In the creep and shrinkage prediction model B4 (a new Draft RILEM Recommendation, Mater Struct 48:753–750, 2015), the shape effect is taken into account by shape factor ks\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{\rm{s}}$$\end{document} multiplying D. However, because of the strong nonlinearity of the diffusion equation for drying, the optimal ks\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{\rm{s}}$$\end{document} values depend also on the environmental humidity. In model B4, as well as its predecessors since 1975, the ks\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{\rm{s}}$$\end{document} values have been specified for typical shapes, i.e. the slab, cylinder, prism, sphere and cube, with values calculated approximately for only one relative humidity—65 %. Here the ks\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{\rm{s}}$$\end{document} values for the same typical shapes are calculated with greater accuracy and for different environmental humidities—30, 40, 50, 60, 70 and 80 %, which allows interpolation in between. The ks\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{\rm{s}}$$\end{document} values for the typical shapes range from 1.00 to 1.41.