A mechanical model for Merapi-type pyroclastic flow

A numerical simulation model of Merapi-type pyroclastic flow for predicting a potential hazardous area is given, and its applicability is examined by numerically reproducing actual phenomena that occurred in 1991 at Unzen Volcano, Kyushu Japan. Merapi-type pyroclastic flow arises from collapse of the lava dome whereby large lava blocks are crushed into smaller particles during movement down the steep slope. The early stage of flow (it may be called the debris avalanche stage), in which the dominant particles are coarser than about 1 mm in diameter, is considered as a grain (granular) flow. In an inertial grain flow particle collision stress plays an important role in the mechanism of flow, and the effect of gas emitted from the lava blocks is minimal. Most of the particles composing the inertial grain flow deposit over a comparatively short range on steep slope due to marked resistance within the flow. The remainder which is composed of mainly fine particles smaller than 1 mm continues to run down by a support of the upward flow of gas ejected from the material itself, thereby the resistance to flow becomes small. Thus, the pyroclastic flow stage in a narrow sense appears. The main body of the pyroclastic flow is composed of lower insufficiently fluidized layer (bottom layer) and upper fluidized layer in which the entire weight of the particles is supported by the upward gas flow. Sometimes, the fluidized layer cannot exist if gas emission is insufficient. As the slope down which the pyroclastic flow moves becomes milder downstream, the bottom layer deposits some solids because the driving force due to gravity within this layer becomes smaller than the resistance due to inter-particle contact. Then, a part of the fluidized layer, if exists, changes to a part of the bottom layer because of the shortage of the upward gas flow that is caused by deposition of the gas-emitting particles upstream. Thus, the entire main body stops when it arrives at a gently sloping area. Smaller particles and gas escape from the main body, generating a hot ash cloud layer above the main body. The hot ash cloud layer can travel independent of the main body, but its development or attenuation depend on the conditions of the supply of particles and gas from the main body. When the hot ash cloud lacks the supply of particles and gas due to the stopping of the main body upstream, or by its swerving from the course of the main body, it becomes soon weakened and stops. The entrainment of ambient air, the escape of air and ash from the upper boundary as a buoyant plume, and the particle settling also affect the behaviors of the hot ash cloud. Fundamental mechanics of the grain (granular) flow stage, the pyroclastic flow stage and the transition from the former to the latter stages are discussed theoretically and experimentally, and mathematical formulae describing the phenomena are obtained. These one-dimensional equations are extended to fit the planar two-dimensional system. Behaviors of the main body as well as the hot ash cloud are simulated using the obtained system of equations. The results of simulation are very satisfactory in comparison to the actual phenomena.