Novel Geometric Construction Methods and Application for Embankment Surface

Embankments are extensively applied in civil engineering and exist naturally, characterized by a constant slope ensuring stable material stacking. Despite their ubiquity, research on embankment surface geometric modeling remains limited. Three novel construction methods for embankment surfaces are proposed: the envelope of a one-parameter family of cones, the envelope of constant-slope tangent planes, and the geometric limit. Subsequently, the properties of embankment surfaces and their geometric interpretation are elaborated. Specific examples are provided to illustrate that these methods offer convenient and feasible alternatives for engineering geometric design related to these surfaces.