“…The resistance force acting on intruders during penetration into granular materials is of interest not only in granular physics [1][2][3][4][5][6][7][8][9][10][11][12], but also in engineering applications, such as cone penetration tests [13][14][15][16][17][18][19][20][21], pile installations [22][23][24][25][26][27][28], the digging of mining machineries [29], and the locomotion of legged robots over rough terrain [30]. Previous studies have demonstrated that the penetration resistance is affected by the particle size [12,14,16,17,20,21,31], bulk packing fraction [2,9,12,17,19,21,25], penetration depth [3,4,7,…”