Closure to “Mean Velocity of Mudflows and Debris Flows” by Pierre Y. Julien and Anna Paris

The authors predicted mudflow and debris flow velocities with 350 field and laboratory measurements and obtained a slight trend for V=u to increase with h=d50, and the ratio of V=u is approximately 10 and rarely exceeds 30. The logarithmic relationship of turbulent resistance agrees reasonably well with the measurements. Good results also are obtained with the Manning-Strickler approach. The dispersive stress equation also compares well with the measurements, but only when h=d50 < 50. For individual series data such as Hashimoto and Puerco, there is a trend for V=u to increase with h=d50. But for other individual series data, such as Davies, Rickenmann, Paris, St. Helens, Nevado del Ruiz, Wanglin, Wang, and Wenhai, there is a trend for V=u to decrease with h=d50 (Fig. 1 of the original paper). The discussers have some field data that also show the same phenomena, which are presented in Fig. 1. The database includes a total of 119 flow velocity measurements, in which each point includes flow depth, density (volume concentration), median grain diameter d50, grain size of less than 10% d10, and slope. The data of Jiangjia were obtained from the field measurements in Jiangjia Ravine, Yunnan, China, in 1999; the data of Hunshui were obtained from the field measurements in Hunshui Ravine, Yunnan, China, in 1976–1978; and the data of Liuwan were obtained from the field measurements in Liuwan Ravine, Gansu, China, in 1963–1964. Debris flow is a gravity flow, and the gravity force plays an important role in the movement of debris flow. So debris flow moves on a large slope and deposits on a small slope. Fei and Su (2004) showed that the main driving force of debris flow is provided by particles, not by water. When the volume concentration C 1⁄4 0:27 (or density ρ 1⁄4 1:46 g=cm3), the particle driving force is equal to the water driving force in debris flow. They defined that the minimum density of debris flow is 1:46 g=cm3, and 1:46–1:80 g=cm3 is the range of less viscous debris flow. Therefore, the minimum density of viscous debris flow is 1:80 g=cm3 (C 1⁄4 0:47) (Fei and Su 2004; Yu 2008a). Two types of shear stresses describe these two kinds of debris flows: (1) the viscous stress for viscous debris flow, and (2) the turbulent stress for less viscous debris flow (Fei and Su 2004). As the driving force of debris flow is provided primarily by particles, the coarse particle plays an important role in the movement of debris flow, especially for viscous debris flow with a large volume concentration. So the larger particle diameter, the larger is the velocity. There is a trend for V to increase with d50, and there is a trend for V=u to increase with d50=h. Two empirical equations of mean velocity of viscous debris flow described this relationship (Wu et al. 1993; Yu 2001): V u 1⁄4 27:57 d50 h 0:245 ð1Þ