5:15 PM - 7:15 PM
[HCG21-P01] A New Statistical Model of the Water Infiltration of Pumiceous Materials with Bayesian Inference and Diffusion Equation
Keywords:Pumice, Diffusion Equation, Bayesian Inference, Bubble Network
Pumice is a type of pyroclastic material, with high porosity and low density (0.2-0.8g/cm3). The presence of pumice, dispersed by Plinian eruptions and phreatomagmatic explosions, can exacerbate the severity of mass movements including landslides. It is warned that earthquake-induced landslides are likely to occur in the areas with slopes composed of pyroclastic-fall deposits, containing the layers of halloysite due to the weathering. The earthquake centered in Eastern Iburi, Hokkaido caused approximately 6,000 slope failures in the Atsuma area. This region is covered with pyroclastic deposits, exemplifying the influence of pumice on disasters. Researchers investigated water infiltration of pumices based on experiments and models using Darcy’s and Fourier’s laws, demonstrating that the infiltration rate decreases over time, depending on pumice size and fluid temperature, and even the pore connectivity and shape. While these findings suggest the necessity of a statistical model accounting for the uncertainty of pumice’s internal structure, few studies have adopted statistical approaches for the infiltration.
The authors proposed a new model for pumice infiltration with the integration of diffusion equation and Bayesian inference.
The research methods are separated into two approaches: (1) water absorption experiments and density measurements, and resin-based internal structural investigations; (2) modeling of water absorption characteristics using Bayesian inference. (1) water absorption experiments and density measurements, and resin-based internal structural investigations: 122 pumice samples (En-a pumice derived from Mount Eniwa) collected from the landslide outcrops in Atsuma, Hokkaido were used. The samples were immersed in air-temperature water in a beaker using tweezers, and mass changes due to water absorption were recorded 2-300 seconds later. Similar tests were conducted on all samples, and the dimensionless mass (the ratio of mass after water absorption to dry mass) was used as the characteristic quantity. After all experiments, the mean bulk density σ0 and particle density σ0 of the pumice were measured using the Wax-Coating method and the particle density measurement method. Additionally, the internal structure of pumice was investigated with resin and subsequent cross-sectional examination to explore its relationship with water absorption properties. (2) Modeling Water Absorption Characteristics Using Bayesian Inference: A physical model employing the diffusion coefficient D, mean bulk density σ0, particle density σ0 as input data was used to construct the prior distribution. The diffusion coefficient was modelled using a uniform distribution within a range of 0.01-0.1, while the mean bulk density and particle density were modelled using normal distributions with means and variances derived from experimental data. The physical model substituted the input data into the 1D diffusion equation and averaged in the spatial direction to create a prior distribution related to mean bulk density. Multiplying the dimensionless mass obtained from experiments by the mean bulk density yielded density variation data, before forming a likelihood function modelled as a normal distribution with a mean of 0 and experimental error variance, considering the difference between the model and experiment values. Lastly, posterior distributions related to density variations were derived using the MCMC method (MH algorithm) from the obtained prior distribution and likelihood function. The density changes in pumice decreased over time, and the density differences in size diminished as time progressed. While the model relatively accurately reproduced the observed values, it showed overestimation or underestimation in certain cases. Internal structural investigations using resin suggested internal structural differences may be linked to the overestimation and underestimation by the model, indicating the necessity of determining diffusion coefficients for each structural variation to improve the model accuracy.
The authors proposed a new model for pumice infiltration with the integration of diffusion equation and Bayesian inference.
The research methods are separated into two approaches: (1) water absorption experiments and density measurements, and resin-based internal structural investigations; (2) modeling of water absorption characteristics using Bayesian inference. (1) water absorption experiments and density measurements, and resin-based internal structural investigations: 122 pumice samples (En-a pumice derived from Mount Eniwa) collected from the landslide outcrops in Atsuma, Hokkaido were used. The samples were immersed in air-temperature water in a beaker using tweezers, and mass changes due to water absorption were recorded 2-300 seconds later. Similar tests were conducted on all samples, and the dimensionless mass (the ratio of mass after water absorption to dry mass) was used as the characteristic quantity. After all experiments, the mean bulk density σ0 and particle density σ0 of the pumice were measured using the Wax-Coating method and the particle density measurement method. Additionally, the internal structure of pumice was investigated with resin and subsequent cross-sectional examination to explore its relationship with water absorption properties. (2) Modeling Water Absorption Characteristics Using Bayesian Inference: A physical model employing the diffusion coefficient D, mean bulk density σ0, particle density σ0 as input data was used to construct the prior distribution. The diffusion coefficient was modelled using a uniform distribution within a range of 0.01-0.1, while the mean bulk density and particle density were modelled using normal distributions with means and variances derived from experimental data. The physical model substituted the input data into the 1D diffusion equation and averaged in the spatial direction to create a prior distribution related to mean bulk density. Multiplying the dimensionless mass obtained from experiments by the mean bulk density yielded density variation data, before forming a likelihood function modelled as a normal distribution with a mean of 0 and experimental error variance, considering the difference between the model and experiment values. Lastly, posterior distributions related to density variations were derived using the MCMC method (MH algorithm) from the obtained prior distribution and likelihood function. The density changes in pumice decreased over time, and the density differences in size diminished as time progressed. While the model relatively accurately reproduced the observed values, it showed overestimation or underestimation in certain cases. Internal structural investigations using resin suggested internal structural differences may be linked to the overestimation and underestimation by the model, indicating the necessity of determining diffusion coefficients for each structural variation to improve the model accuracy.