*2.5. Growing Mechanism of Burden Surface*

The characterization of the growing of burden surface mainly requires the determination of the radius locations of the left and right edges of the pile according to the width of burden flow measured from previous physical experiments [12] under various angles of coal-gimbal chute and DRI-flap. Since the stable initial burden profile is composed of three segments, the growing mechanisms at different locations are more complicated than that on a horizontal flat profile. In this model, there are mainly five pile patterns as shown in Figure 6. In the figure, L and R represent the left and right ends of the burden pile, respectively, on a horizontal plane. OM represents the radius of the pile ring which is determined by the angles of coal-gimbal chute and DRI-flap. Point O is the intersection point between the old burden surface and the vertical line at pile ring radius, and point M can be obtained according the dump volume. The critical width of burden pile (*W*critical) is the width when the pile attains stable

repose angles, and is determined by the height of stock line, the angle of chute or flap, and the physical property parameters including size distribution and rolling friction coefficient. L, R, O and *W*critical are measured on a horizontal flat burden surface by previous physical experiment under various angles of the coal-gimbal chute and DRI-flap, and these data has just been listed in the above Section 2.3.

To characterize the formation of such complicated piles, the growing of a pile is calculated by iteration with a small volume step till the dump volume. In this way, the growth mechanism of burden pile on the horizontal section is shown in Figure 6a, including an early developing phase and a later developed phase. In the developing phase, both the inner and outer angles of the pile increase before the pile reaches the developed phase, where the pile undergoes a parallel growing mechanism similar to that in a BF. The horizontal distance LR is the width of burden flow arriving at the original burden surface, while OM represents the radial location of the burden ring.

The growing mechanism of a burden pile sitting on the turning point from a horizontal segment to a declining one is shown in from Figure 6b, where both points L and M are on the horizontal segment and point R is on the declining segment. In such cases, the point L is set as the left end of the burden flow. The right end of the first-step burden pile is the first intersection R0, between the old burden surface and the line segment of MR. When the right point R0 reaches R, the outer angle starts increasing until it reaches the developed phase, and then the growing mechanism becomes parallel in growth with the outer angle, similar to that in a BF. The evolution of the inner angle follows a similar procedure as the outer angle.

**Figure 6.** *Cont*.

**Figure 6.** Growing mechanism of burden surface. (**a**) on the horizontal section; (**b**) from a horizontal segment to a declining one; (**c**) on the horizontal section; (**d**) near the furnace center section; and (**e**) near the furnace wall section.

When a pile is developed on the declining segment, its growing mechanism is shown in Figure 6c, where all the three points L, R, and M are on the declining segment. In this case, point R is set as the right end of the burden flow. The left point of first-step burden pile is the first intersection L0 between the old burden profile and the horizon line. The inner angle increases until it reaches the developed phase and then turns to parallel growth with inner angle similar to that in the BF.

The special cases where one side of the pile reaches the furnace center and the furnace wall are considered as shown in Figure 6d,e. Regardless of whether the inner angle or the outer angle is in the developed or developing phases, as long as one side of the pile encounters an obstacle (furnace center or furnace wall), the inner or outer angle will decrease until it reaches the horizontal level, that is, a flat platform is formed by the center or wall.
