Pore Structure of Grain-Size Fractal Granular Material

Towards replacing physical testing of granular materials with a Topology-based Model

In the study of packed granular materials, the performance of a sample (e.g., the detonation of a high-energy explosive) often correlates to measurements of a fluid flowing through it. The "effective surface area," the surface area accessible to the airflow, is typically measured using a permeametry apparatus that relates the flow conductance to the permeable surface area via the Carman-Kozeny equation. This equation allows calculating the flow rate of a fluid flowing through the granules packed in the sample for a given pressure drop. However, Carman-Kozeny makes inherent assumptions about tunnel shapes and flow paths that may not accurately hold in situations where the particles possess a wide distribution in shapes, sizes, and aspect ratios, as is true with many powdered systems of technological and commercial interest. To address this challenge, we replicate these measurements virtually on micro-CT images of the powdered material, introducing a new Pore Network Model based on the skeleton of the Morse-Smale complex. Pores are identified as basins of the complex, their incidence encodes adjacency, and the conductivity of the capillary between them is computed from the cross-section at their interface. We build and solve a resistive network to compute an approximate laminar fluid flow through the pore structure. We provide two means of estimating flow-permeable surface area: (i) by direct computation of conductivity, and (ii) by identifying dead-ends in the flow coupled with isosurface extraction and the application of the Carman-Kozeny equation, with the aim of establishing consistency over a range of particle shapes, sizes, porosity levels, and void distribution patterns.

Sound-Absorption Performance and Fractal Dimension Feature of Kapok Fibre/Polycaprolactone Composites

This article introduces a kind of composite material made of kapok fibre and polycaprolactone by the hot-pressing method. The effects of volume density, mass fraction of kapok fibre, and thickness on the sound-absorption performance of composites were researched using a single-factor experiment. The sound-absorption performance of the composites was investigated by the transfer function method. Under the optimal process parameters, when the density of the composite material was 0.172 g/cm3, the mass fraction of kapok was 40%, and the thickness was 2 cm, the composite material reached the maximum sound-absorption coefficient of 0.830, and when the sound-absorption frequency was 6300 Hz, the average sound-absorption coefficient was 0.520, and the sound-absorption band was wide. This research used the box dimension method to calculate composites’ fractal dimensions by using the Matlab program based on the fractal theory. It analysed the relationships between fractal dimension and volume density, fractal dimension and mass fraction of kapok fibre, and fractal dimension and thickness. The quantitative relations between fractal dimension and maximum sound-absorption coefficient, fractal dimension, and resonant sound-absorption frequency were derived, which provided a theoretical basis for studying sound-absorption performance. The results showed that kapok fibre/polycaprolactone composites had strong fractal characteristics, which had important guiding significance for the sound-absorption performance of kapok fibre composites.

Research on Strength Prediction Model of Sand-like Material Based on Nuclear Magnetic Resonance and Fractal Theory

Micro-pore structure has a decisive effect on the physical and mechanical properties of porous materials. To further improve the composition of rock-like materials, the internal relationship between microscopic characteristics (porosity, pore size distribution) and macroscopic mechanical properties of materials needs to be studied. This study selects portland cement, quartz sand, silica fume, and water-reducing agent as raw materials to simulate sandstone. Based on the Nuclear magnetic resonance (NMR) theory and fractal theory, the study explores the internal relationship between pore structure and mechanical properties of sandstone-like materials, building a compressive strength prediction model by adopting the proportion of macropores and the dimension of macropore pore size as dependent variables. Test results show that internal pores of the material are mainly macropores, and micropores account for the least. The aperture fractal dimension, the correlation coefficient of mesopores and macropores are quite different from those of micropores. Fractal characteristics of mesopores and macropores are obvious. The macropore pore volume ratio has a good linear correlation with fractal dimension and strength, and it has a higher correlation coefficient with pore volume ratio, pore fractal dimension and other variable factors. The compressive strength increases with the growth of pore size fractal dimension, but decreases with the growth of macropore pore volume ratio. The strength prediction model has a high correlation coefficient, credibility and prediction accuracy, and the predicted strength is basically close to the measured strength.

Resilient Properties of Soil-Rock Mixture Materials: Preliminary Investigation of the Effect of Composition and Structure

The physical composition and stress state of soil-rock mixture (SRM) materials have a crucial influence on their mechanical properties, and play a vital role in improving the performance of subgrade. To reveal the resilient behavior and mesostructure evolution of SRM materials, triaxial tests and discrete element method (DEM) numerical analysis have been carried out. In the triaxial test section, the mechanical response of SRM materials was investigated by preparing samples under different stress states and physical states and conducting triaxial tests on samples. Simultaneously, a new irregular particle modeling method was developed and applied to the discrete element modeling process to analyze the mesostructure evolution of SRM materials under cycling loading. First, a cyclic triaxial test of SRM material is performed on the SRM material, and the effects of bulk stress, octahedral shear stress and rock content on the resilient modulus of the SRM material are analyzed. It is revealed that the resilient modulus increases with increasing bulk stress and rock content, and decreases with increasing octahedral shear stress. Based on a new resilient modulus prediction model, the relationships among the rock content, stress state and resilient modulus are established. Then, based on an improved DEM modeling method, a discrete element model of the SRM is established, and the influence of rock content on coordination number and mesostructure evolution of the SRM is analyzed. The results show that in SRM materials, the increase of crushed rock changes the mesostructure of the SRM material. With the increase of rock content, the internal contact force changes from “between soil and rock” to “between rocks”, and the skeleton formed in the rocks gradually develops overall stiffness. Under the condition of low stress, the anisotropy of the SRM material is mainly caused by the shape and grade distribution of crushed rock. The induced anisotropy caused by the change of stress state has little effect on its mechanical behavior, which may lead to the greater dispersion of multiple SRM test results.

Sound Absorption Performance of the Poplar Seed Fiber/PCL Composite Materials

Composite materials were prepared by the hot pressing method using poplar seed fibers and polycaprolactone (PCL) as the raw materials to solve the problems related to the recycling of waste fibers. The effects of mass fraction of poplar seed fibers, the volume density, and thickness on the sound absorption performance of the resulting composite materials were studied. The sound absorption coefficient curves of the composite material were obtained by the acoustic impedance transfer function method. The sound absorption coefficient of the composite material that was prepared under the optimal process conditions was higher than 0.7, and the effective sound absorption frequency band was wide. According to the box counting dimension method, which is based on the fractal theory, the fractal dimensions of the composite materials were calculated while using the Matlab program. The relationships between the fractal dimensions and the volume densities, mass fractions of poplar seed fibers, and thicknesses of the composite materials were also analyzed. Subsequently, the quantitative relationship between the fractal dimension and the sound absorption property parameters of the composite material was established in order to provide a theoretical basis for the design of the sound absorption composite material.

Improved Packing Model for Functionally Graded Sand-Fines Mixtures—Incorporation of Fines Cohesive Packing Behavior

Binary soil mixture, containing large silica particles (sand) mixed with variable content of very fine silt or clay, is an example of a functionally graded material that is important for several science and engineering applications. Predicting the porosity (or void ratio), which is a fundamental quantity that affects other physical properties, of such material as function of fines (clay or silt) fraction can be significant for sediment research and material design optimization. Existing analytical models for porosity prediction work well for binary mixed soils containing multi-sized non-cohesive particles with no clay, while such models frequently underestimate the porosity of sand-clay mixtures. This study aims to present an analytical model that accurately predicts the porosity of mixed granular materials or soils containing sand and very fine silt or clay (cohesive particles). It is demonstrated that accounting for the cohesive nature of very fine particles, which exists due to the effect of inter-particle forces, is a major missing aspect in existing packing models for mixed soils. Consequently, a previously developed linear packing model is modified so that it accounts for fines cohesive packing in sand-fines mixtures. The model prediction is validated using various experimental published data sets for the porosity of sand-fines mixtures. Improvement in the prediction of permeability and maximum packing dry density when incorporating cohesive packing behavior is discussed. The current model also provides important insights on the conditions under which, the lowest permeability and maximum packing state are expected.

Reversible and Irreversible Processes in Drying and Wetting of Soil

In this article, we provide a detailed description of a modeling technique for the capillary hysteresis in a soil-like porous material based on a Generalized Preisach Model. The identification of the reversible and irreversible Preisach distributions was performed with the first-order reversal curve (FORC) diagram technique, which is very popular now in magnetism and in other areas of science to give a fingerprint of the studied system. A special attention was given to the evaluation of the reversible component. In this case, we used a set of data published in 1965 by Morrow and Harris which has been used as a reference by many other researchers since. The advantage of this approach is that the experimental FORC distributions can be described with analytical functions and easily implemented in the mentioned Preisach-type model. Our research is also focused on the development of a characterization tool for the soil using the soil-moisture hysteresis. The systematic use of scanning curves provides a (FORC) diagram linked to the physical properties of the studied soil. The agreement between the experimental data and the Preisach model using the set of parameters found through the FORC technique is really noticeable and gives a good practical option to the researchers to use a method with a strong predictive capability.

Fractal Analysis of the Fracture Evolution of Freeze-Thaw Damage to Asphalt Concrete

AC (asphalt concrete)-13, as the main material used in pavement construction, has been applied widely in seasonal frozen areas. In order to understand the fracture mechanism in the freeze-thaw (F-T) damage process, the mesoscale structure of AC-13 is obtained by computed tomography (CT). The fractal dimension of cracks is used as a damage evaluation index. Most previous studies have only focused on the fractal dimensions of whole cracks, while ignoring the fractal tectonic process and the self-similarity degree of a single fracture. Therefore, in this study, the intrinsic mechanism of fractures and damage were investigated. In addition, the critical crack stress and fracture toughness models of a single fracture in a freeze-thaw damage process are established for AC-13. The results indicate that in terms of the critical crack stress and fracture toughness, with the increase of F-T times, there is an obvious decreasing trend. The fracture model can effectively describe the fracture toughness calculated by ABAQUS in the process of freeze-thaw cycles.