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As if it has become a consensus that the slope of the granular heap isstraight, and from that, an angle of repose is defined. However, closerinspection shows that the slopes are not truly straight, instead, more oftenthey have convex shapes, although with small convexity. Similar curvature isobserved on the sand dunes' surfaces. We derive equations together withexperiments on 10 types of granular materials to show that, in general, theslope of the granular heap is convex while the straight slope is a criticalstate that rarely occurs. The angle of repose is allowed to vary within anarrow range around a critical value. If the angle of repose is slightlygreater (smaller) than the critical value, the slope is convex (concave). Themodel also answers why the surfaces of granular heaps, including sand dunes,are more often convex rather than concave or straight, and advocate thesimultaneous estimation of the coefficient of friction on the grain and thetype of packing in the heap. The results might open new understandings relatedto granular material properties as well as sand transport and geologicalrecords in several deserts.

Slope of Dry Granular Materials Surface is Generally Curved