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Abstract:This paper presents a steady-state analytical hillslope stability model to study the role of topography on rain-induced shallow landslides. We combine a bivariate continuous function of the topographic surface, a steady-state hydrological model of hillslope saturated storage, and the infinite slope stability assumption to investigate the interplay between terrain characteristics, saturated storage within hillslopes and soil mechanics. We demonstrate the model by examining the stability of nine characteristic hillslope types (landform elements) with three different profile curvatures (concave, straight and convex) and three different plan shapes (convergent, parallel and divergent). For each hillslope type, the steady-state saturated storage corresponding to given recharge rates is computed for three different average bedrock slope angles. On the basis of the infinite slope stability method, the factor of safety (FS ) along the hillslopes is determined. Our results demonstrate that in the steep slopes, the least stable situation occurs in hillslopes with convergent plan shapes and concave length profiles, while the convex ones are more stable. In addition to testing our method for nine characteristic hillslope types, a general relationship between plan shape and profile curvature of landform elements and the factor of safety is derived for a pre-defined hillslope length scale. Our results show that slope stability increases when profile curvature changes from concave to convex. In terms of plan shapes, changing from convergent to divergent, slope stability increases for all length profiles. However, we find that the effect of plan shape is more pronounced for convex length profiles. Overall, we demonstrate that, in addition to bedrock slope, hillslope shape as represented by plan shape and profile curvature is an important control on hillslope stability.

The purpose was to determine the effects of the physical dimensions of the pen and group size and stocking density on cow activity. Cows (randomly assigned to 4 groups of 6 animals each) were tested in pens with 24 or 12 lying places and in groups with 12 or 6 cows. All groups were tested in each of the 4 treatments with treatment order allocated using a 4 × 4 Latin square. The distance moved and the number of movements were calculated using 5-min scan sampling of video recordings over a 48-h period. Time spent lying down, number of lying bouts, and the duration of each lying bout were recorded using activity sensors. Displacements at the feed bunk were assessed by continuous analysis of video for 3h after the delivery of the fresh feed in the afternoon. Cows moved greater distances when kept in a large versus small pens (330.2 vs. 270.1 ± 11.6 m/d; mean ± SE), irrespective of group size. Cows moved more often when kept in the larger pen (21.3 vs. 19.2 ± 0.63% of scans). The time spent lying down decreased when density increased (59.1 vs. 55.8 ± 2.3% of scans at 25% and 100% stocking, respectively). Treatment had no effect on the number of displacements at the feed bunk. Physical dimensions of the pen play an important role in how much cows move, and stocking density affects lying time.

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