The repose angle and characteristics of the vertical stress distribution beneath the sandpile can help to understand the physical and mechanical properties of the granular matter and guide the foundation design of the rock-soil deposits such as the rockfill dam and the storage structures of granular materials. Researches previously found that the stress dip phenomenon exists in piles constructed by the localized-source procedure, where the maximum vertical stress underneath the pile deviates from the center. The repose angle and the stress dip are affected by many internal and external factors and exhibit highly nonlinear and sensitive characteristics. However, the variation of the repose angle and the stress dip with influencing factors and the cause of the stress dip have not yet been fully explored. Based on the localized-source conical sandpile experiments and the discrete element method (DEM) simulation analysis, this paper studied the influences of the internal friction angle of granular matter and the construction history (the slowly raising funnel method SRFM and the fixed funnel method FFM) on the repose angle and the vertical stress dip beneath the pile; while the formation mechanism of the stress dip phenomenon was analyzed. The experimental results showed that the repose angle, physically different from the internal friction angle, has a relatively larger value and is positively related to the internal friction angle in the sandpile constructed by the FFM; the localized-source procedure and the internal friction angle are conducive to the formation of the macroscopic force chain arch structure in granular matter, which produces the arching effect and the stress shielding effect and leads to the stress dip beneath the pile; and the ratio of the stress dip RSD decreases with the increase of the local impact effect and the internal friction angle.