Surface Fractal Dimension Research Articles

Effect of Coarse Aggregate Content on Bubble Formation Behavior in Corundum Permeable Brick for Tundish

Herein, corundum porous permeable bricks with different coarse aggregate contents are prepared using particle packing method. Based on the similarity principle, a local water model of a tundish is designed to investigate the bubbling behavior in porous permeable bricks at various argon flow rates. Through dimensionless analysis, empirical formulas of bubbling region diameter and initial bubble size in porous permeable bricks are proposed. The results show that an increasing aggregate content can increase the apparent porosity and the proportion of large pores, reduce the surface fractal dimension of the porous permeable bricks, and obtain a higher gas permeability. With the increase of argon flow rate and the decrease of gas permeability, the internal pressure gradient in porous permeable bricks increases. The larger the argon flow rate and the gas permeability value, the more beneficial it is to activate more pores and form a larger bubbling region on the upper surface of porous permeable bricks. The Sauter mean diameter of bubbles and the initial velocity of gas plumes are inversely correlated with the content of coarse aggregate; that is, the porous permeable brick with a higher content of coarse aggregate is beneficial to generating much more small bubbles.

Carbon nanotubes/polyaniline as hydrogen gas sensor: Optical bandgap, micro-morphology, and skin depth studies

In this study, multiwall carbon nanotubes (MWCNTs)/polyaniline nanocomposites deposited on ITO coated glass as substrate by the spin-coating technique were applied to the investigation of the effect of different contents of MWCNTs on the optical and electrical properties of polyaniline. Micrographs from an atomic force microscope were taken to analyze the 3-D microtexture parameters of surface texture factors and fractal dimension. By using optical spectroscopy of samples with different concentrations of MWNCTs in visible and ultraviolet regions, the transmission variations vs photon wavelength, optical bandgap, absorption coefficient, and skin depth were studied. The variation in the resistance of nanocomposite films exposed to 0.4 %vol of H2 gas at room temperature was monitored, and the results indicated that the sensitivity and responsibility of the composites increased with an increase in the MWCNT amount.

Fractal Dimension and Nuclear Magnetic Resonance Characteristics of Surfactants for Coal Gas Desorption

In this paper, the fractal dimension of coal surfaces was calculated using the fractal theory, and the influence of different surfactants on the fractal dimension of coal surface was studied. Six kinds of sustainable and traditional surfactants used in coal gas desorption processes were compared and analyzed. We used mineral gas fertilizer coal from Huainan Liuzhuang, China, as the research object and studied sodium dodecyl benzene sulfonate (SDBS), cohol diethanolamide (CDEA), nonylphenol polyoxyethylene ether (NP-10), tea saponin, sucrose ester and rhamnolipid surfactants used to modify coal. The methane adsorption capacity of coal before and after surfactant modification was measured by low field nuclear magnetic resonance methane adsorption, and Langmuir volume and Langmuir pressure were obtained according to the Langmuir fitting equation. The results showed that from the perspective of fractal dimensions, the best surfactant in the context of sustainability (in order) is rhamnolipid, CDEA, tea saponin, sucrose ester. According to the two important parameters VL and PL in the Langmuir equation, the coal sample modified by sucrose ester had the strongest gas adsorption capacity. According to the numerical analysis of the surface fractal dimension DS of the coal modified by surfactants, the soluble organic matter in the raw coal samples dissolved, and the micropore morphology evolved to become mesoporous or macroporous, which is more favorable for desorption. The coal samples modified by rhamnolipid and SDBS had the strongest gas desorption ability.

Effect of Pore‐Wall Roughness and Péclet Number on Conservative Solute Transport in Saturated Porous Media

AbstractWhile modeling solute transport has been an active subject of research in the past few decades, the influence of pore‐wall roughness on contaminant migration has not yet been addressed. We therefore conduct particle tracking simulations in three porous domains that have different pore‐wall roughness characteristics. Specifically, we consider five surface fractal dimensions ds = 1.0, 1.1, 1.2, 1.4, and 1.6, and four different Péclet numbers Pe = 10, 102, 103, and 105. Overall, arrival time distributions are simulated for 60 scenarios (3 domains 5 surface fractal dimensions 4 Péclet numbers) some of which show heavy‐tailed patterns indicating non‐Fickian transport. To interpret the simulations and quantify the transport behavior, we analyze the resulting arrival time distributions by the continuous time random walk (CTRW) approach. Results show that, on average, as the surface fractal dimension increases from 1.0 to 1.6, the CTRW model parameters , an exponent showing the degree of anomalous transport, v, the average solute velocity, and t2, the cut‐off time to Fickian transport, remain nearly constant. However, the dispersion coefficient, D, increases and the characteristic transition time, t1, decreases. We found t1 and D are more sensitive to pore‐wall roughness compared to the other CTRW parameters. We also found that as the Péclet number increases from 10 to 105, on average, v and D increase, t1 and decrease, and t2 remains nearly constant. The simulations demonstrate that the exponent and the dispersion coefficient are correlated to the average solute velocity.

Correlations between unconfined compressive strength, sorptivity and pore structures for geopolymer based on SEM and MIP measurements

The objective for this research was to investigated the unconfined compressive strength, sorptivity, pore structures and their correlations of recycled concrete fine powder (RCFP) based geopolymers mixed with different granulated blast furnace slag (GBFS). The unconfined compressive strength and sorptivity tests were utilized to measure the unconfined compressive strength and sorptivity coefficient. The pore structures were analyzed using optical method (SEM) and mercury intrusion method (MIP). The particles (pores) and cracks analysis system (PCAS) and image-pro plus (IPP) software were employed to quantitatively characterize the multi-scale micropores in the SEM images. Furthermore, based on MIP measurement and two fractal theories, the variations in pore structural characteristics were evaluated. The findings demonstrate the incorporation of GBFS effectively reduced the sorptivity coefficient and enhanced the unconfined compressive strength, and this effect grew stronger with increasing content of GBFS. The sorptivity coefficient and 28-day unconfined compressive strength had a strong linear negative connection. According to SEM analysis, increasing GBFS facilitated the generation of that greater number of gelling products by improving the degree of reaction, which led to a refinement of internal pore structure and an increase in structural complexity. Meanwhile, the addition of GBFS and increasing its content could effectively facilitate the conversion of macropores into micropores by filling with gel products, and significantly reduce the porosity, threshold pore size and most probable pore size. The unconfined compressive strength and sorptivity coefficient had good linear relationships with its internal porosity. The pore structures of geopolymers had clear fractal features as a whole. Among the two models, the thermodynamic model was more suitable to evaluate the fractal characteristic of the pores for geopolymer. The unconfined compressive strength rose with increasing surface fractal dimension, while the sorptivity coefficent exhibited an opposite trend.

Experimental investigations of CO2 adsorption behavior in shales: Implication for CO2 geological storage

Injecting CO2 into shale reservoirs has dual benefits for enhancing gas recovery and CO2 geological sequestration, which is of great significance to ensuring energy security and achieving the “Carbon Neutrality” for China. The CO2 adsorption behavior in shales largely determined the geological sequestration potential but remained uncharted. In this study, the combination of isothermal adsorption measurement and basic petro-physical characterization methods were performed to investigate CO2 adsorption mechanism in shales. Results show that the CO2 sorption capacity increase gradually with injection pressure before reaching an asymptotic maximum magnitude, which can be described equally well by the Langmuir model. TOC content is the most significant control factor on CO2 sorption capacity, and the other secondary factors include vitrinite reflectance, clay content, and brittle mineral content. The pore structure parameter of BET-specific surface area is a more direct factor affecting CO2 adsorption of shale than BJH pore volume. Langmuir CO2 adsorption capacity positive correlated with the surface fractal dimension (D1), but a significant correlation is not found with pore structure fractal dimension (D2). By introducing the Carbon Sequestration Leaders Forum and Department of Energy methods, the research results presented in this study can be extended to the future application for CO2 geological storage potential evaluation in shales.

Robust superhydrophobic magnetic melamine sponge inspired by lotus leaf surface for efficient continuous oil–water separation

Inspired by the oily surface layer and hierarchical structure on the lotus leaf surface, a magnetic sponge with robust superhydrophobicity (water contact angle up to 155°) and surface protection was synthesized by one-pot solvothermal method by introducing (3-Mercaptopropyl)trimethoxysilane into the melamine sponge. After hydrolysis and self-polymerization, (3-Mercaptopropyl)trimethoxysilane can grow as a low surface energy polysiloxane coating on the surface of sponges and magnetic particles. It not only provides a hydrophobic surface layer for sponges, but also this cooperation of micro-submicron-nanostructure from micron sponge skeleton, submicron Fe3O4 particles and nanoscale polysiloxane builds rough surfaces at multiple scales. Based on the triadic Koch curve model, the theory of superhydrophobic surface is elucidated in detail from the surface fractal behavior, fractal dimension, and surface composition. The sponge can be integrated into a negative pressure system as a filter element for continuous and efficient oil–water separation. The formed polysiloxane can not only provide protection for the sponge skeleton and magnetic particles, but also provide strong cross-linking between the two materials, which can effectively resist the damage to the functional structure caused by oil erosion. In addition, a conceptual diagram of a portable oil suction device similar to a vacuum cleaner was proposed. Combining the basic theory of robust superhydrophobic surface and innovatively clarifying the influence of filter element structure on oil–water separation efficiency from the perspective of interface force, it is expected to bring more practical and potential ideas for the design of a portable vacuum cleaner-like oil–water separation device.

Micro-structure and morphology of tailings sand under different oxidation and acidification degree

The tailings pond is a dangerous source of man-made debris flow with high potential energy. The oxidative acidification of tailings may cause the instability of the pond and induce serious safety accidents. The influence of oxidation and acidification degree on macro mechanical properties of tailings is discussed from the aspects of mineral composition and microstructure. The results show that as the degree of oxidation and acidification of tailings sand increases, the overall structural performance and load-bearing capacity decrease, and its cohesion (c) and internal friction angle (φ) show a decreasing trend. In fact, the engineering properties of tailings with different oxidation and acidification degrees are dominated by the physicochemical composition and structural characteristics. On the one hand, as the degree of oxidation increases, acidic substance will neutralize with CaCO3 and CaMg(CO3)2, resulting in the loss of cemented substance and the decrease of cementation force between tailing sand particles as well as the gradual destruction of the integrity of tailing sand. On the other hand, the increase of oxidation and acidification degree of tailing sand leads to a gradual reduction of outline (2D) fractal dimension and gray surface (3D) fractal dimension of surface laminated structure as well as the obvious reduction of laminated structure and its roughness of tailings sand.

Multiple-experimental investigation on the physicochemical structures alternation during coal biogasification

The aim of microbially-enhanced coalbed methane (MECBM) generation is to replicate the natural process of microbial methane production in coal seams and to increase coalbed methane production. However, a systematic evaluation of the response of coal structure during biogasification is still lacking. Here, alternations of the pore and molecular structures were investigated during the bioconversion of coal to methane using proximate/ultimate analysis, scanning electron microscope, low-field nuclear magnetic resonance (LNMR), low-pressure nitrogen adsorption (LPNA), micro-Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction (XRD) techniques. The results showed that MECBM is a process of carbon enrichment, nitrogen/sulfur fixation and dehydrogenation/deoxygenation. Moreover, microbial modify coal pore structure by destroying aliphatic side chains, dissociating small molecular clusters and reducing the degree of aromaticity. These changes in the coal pore structure result in the “loose” of the coal reservoir spatial structure. We found that micropores (<10 nm) became transition pores (10–100 nm) and mesopores (100–1000 nm) after microbial degradation, which then led to the increase of the average pore width and the reduction of the specific surface area. This process benefits the desorption and transportation of coalbed methane. In addition, the surface fractal dimension decreased, and the volume fractal dimension increased according to the fitting date of LPNA. The fractal dimension of transition pores and mesopores increased of most coal after biotreatment based on NMR. These results led us to draw the hypothesis that the organic compounds formed by biodegradation may adhere to the pores, thus blocking the pores, making the structure of transition pores and mesopores complex, as demonstrated by the SEM images. This phenomenon is thought to be improved by continuous degradation or water movement.

A Generalization of Poiseuille’s Law for the Flow of a Self-Similar (Fractal) Fluid through a Tube Having a Fractal Rough Surface

In this paper, a generalization of Poiseuille’s law for a self-similar fluid flow through a tube having a rough surface is proposed. The originality of this work is to consider, simultaneously, the self-similarity structure of the fluid and the roughness of the tube surface. This study can have a wide range of applications, for example, for fractal fluid dynamics in hydrology. The roughness of the tube surface presents a fractal structure that can be described by the surface fractal noninteger dimensions. Complex fluids that are invariant to changes in scale (self-similar) are modeled as a continuous medium in noninteger dimensional spaces. In this work, the analytical solution of the Navier–Stokes equations for the case of a self-similar fluid flow through a rough “fractal” tube is presented. New expressions of the velocity profiles, the fluid discharge, and the friction factor are determined analytically and plotted numerically. These expressions contain fractal dimensions describing the effects of the fractal aspect of the fluid and of that of the tube surface. This approach reveals some very important results. For the velocity profile to represent a physical solution, the fractal dimension of the fluid ranges between 0.5 and 1. This study also qualitatively demonstrates that self-similar fluids have shear thickening-like behavior. The fractal (self-similarity) nature of the fluid and the roughness of the surface both have a huge impact on the dynamics of the flow. The fractal dimension of the fluid affects the amplitude and the shape of the velocity profile, which loses its parabolic shape for some values of the fluid fractal dimension. By contrast, the roughness of the surface affects only the amplitude of the velocity profile. Nevertheless, both the fluid’s fractal dimension and the surface roughness have a major influence on the behavior of the fluid, and should not be neglected.

Fractal Research on Surface Topography of Profile Milling CFRT

Carbon Fiber Reinforced Thermoplastic Composites (CFRT) are recognized as a new generation of advanced strategic materials due to their excellent mechanical properties and high recycling rate. However, in the milling process, affected by the coupling of force and thermal, the heat-sensitive resin in CFRP is easily softened and deformed, leading to difficulties in achieving high-quality material removal. Especially in the complex and long-period surface milling process, the processed surface has a complex and irregular microscopic topography, hard to be accurately characterized by traditional roughness measurement methods. To evaluate the surface quality of CFRT profile after milling more precisely, in this paper, the influence of cutting parameters on fractal dimension is systematically analyzed by solving the image gray surface based on the fractal dimension algorithm and calculating the fractal dimension of the surface after milling via the variational method. The experimental results show that the surface fractal dimension of thermoplastic composites processed by PCD milling cutter is between 2.46 and 2.52, and the sensitivity ranking of fractal dimension to cutting parameters is: v f<A e<A p.

Preliminary Study on the Phenomenon and Mechanism of Granite Core Discing in Laboratory Drilling Test

It is generally believed that core discing is a rock failure phenomenon under high in-situ stress, and high stress is closely related to the characteristics of core discing. The core drilling tests of intact granite were conducted on the laboratory servo-controlled drilling test platform. It was observed that the granite core showed discing phenomenon at a high drilling rate (&gt; 15 mm/min) under no confining pressure (0 MPA). The fluctuation of the drilling parameter was consistent with the core discing section along the core. The failure mode of the core discs was determined by morphology and surface fractal dimension characteristics. Numerical simulation models considering the interaction between the drill bit and the rock were established using ANSYS software. Based on core drilling tests, failure morphology analysis of the core discs, and numerical simulation, the mechanism of granite core discing under low confining pressure is as follows: Tensile failure is caused by the stress concentration of the bit at the core root. The drilling rate is the critical factor affecting core discing.

Morphometric Analysis toward Mapping Relative Tectonic Activity of Lebanon

The analysis of geomorphic indices, computed using a digital elevation model and a geographical information system, was carried out to look for signs of tectonic activity in the river basins of Lebanon. The tectonic activity analysis was conducted on the thirty-eight basins through two methods: (1) shape-based, which estimates topography (stream gradient, hypsometry integral, and valley floor), form (asymmetry factor and basin shape), and sinuosity indices (fractal dimension of drainage patterns and mountain front), and (2) terrain-based, which extracts terrain (stream power index, valley depth, flow width, and relief ratio), and surface fractal dimension complexity indices. The results obtained were combined to produce two Relative Active Tectonic Maps (RATMshape and RATMterrain). This study demonstrated that active tectonics matched well with the extracted geomorphic indices and allowed to define the relative tectonic activity in Lebanon: about 65% of the basins correspond to class 1 low; 28% to class 2 moderate; 5% to class 3 high; and 2% to class 4 very high. The east part of the Yammouneh fault and the entire Serghaya fault are moderate to highly active based on the relative tectonic activity analysis. The more active tectonic areas are concentrated in the north ends of Lebanon, while moderate tectonics are focused on the south ends. The entire Rachaya and Roum faults are low to moderately active. The northern part of the Lebanon mountain range, which sits west of the Yammouneh fault, has exceptionally high relative tectonic activity.

Mixed mode fracture parameters and fracture characteristics of diorite using cracked straight through Brazilian disc specimen

In this study, the cracked straight through Brazilian disc (CSTBD) specimen was applied to study the I/II mixed mode static fracture of diorite. The fracture load and fracture toughness for different prefabricated crack angles β were determined. The fracture and morphological characteristics were analyzed using digital image correlation (DIC), scanning electron microscope (SEM) and 3D topography scanning techniques. In addition, the key fracture parameters such as fracture energy, crack mouth opening displacement (CMOD) and fracture process zone (FPZ) were characterized, and a fracture energy calculation method considering the primary crack growth was proposed. The results show that the fracture mechanical behavior and fracture trajectories are controlled by the crack angle. At the millimeter measurement scale, the fractal dimensions of fracture surfaces do not vary with crack angle. Further SEM observation shows that intergranular fracture and transgranular fracture are the dominate micro fracture modes of fracture surfaces under mode I and mode II loading, respectively. With the increase of crack angle, the fracture energy first increases and then decreases, while the allowable CMOD decreases monotonically and even appears negative when β ≥ 45°. Based on the displacement gradient method, the calculated width of FPZ for the mode I fracture specimen at peak load is 0.5–1.4 mm and the length is 2.66 mm. Finally, the stress-based and strain-based fracture criteria were modified. It is found that the proposed EEMTSN criterion has the best prediction effect on the mixed mode fracture toughness of diorite.

Fractal Characteristics of Geopolymer Mortar Containing Municipal Solid Waste Incineration Fly Ash and Its Correlations to Pore Structure and Strength

Compression and mercury intrusion porosimetry (MIP) tests were conducted to analyze the effect of municipal solid waste incineration fly ash (MSWIFA) content on the mechanical performance and pore structure of geopolymer mortar. The MSWIFA weight contents were 0%, 5%, 15%, 25%, and 35% and the pore diameter distribution, specific surface area, and pore volume were considered to assess the pore structure of the geopolymer mortars. The popular fractal model was used to investigate the fractal features of the geopolymer mortars. Additionally, mathematical models of fractal dimension with pore structural parameters and compressive strength were established. The results showed that the compressive strength of geopolymer mortars decreased while the total pore volume and total specific surface area of mortars increased with the increase in MSWIFA content. As the MSWIFA content increased, the harmless pores (pore diameter &lt; 20 nm) were refined. Specifically, the pores with a diameter of 5–10 nm increased in number but the pores with a diameter of 10–20 nm decreased in number with the increase in MSWIFA content. The pore structure in the mortars showed scale-dependent fractal characteristics. All fractal curves were divided into four segments according to the pore diameter, namely, Region I (&lt;20 nm), Region II (20–50 nm), Region III (50–200 nm), and Region IV (&gt;200 nm). The surface fractal dimension (DS) in Region I and Region IV was between 2 and 3. However, the DS in Region II and Region III was greater than 3, indicating the pores in Region II and Region III were non-physical according to the surface geometry because of the presence of ink bottle pores which distorted the result of the MIP. The complexity of pores in Region I and Region IV was reduced by the addition of MSWIFA. The DS is a comprehensive parameter that well describes the spatial and morphological distribution of pores in geopolymer mortars and exhibited a good correlation with the specific surface area, pore volume, and compressive strength. A mathematical model based on the DS was established to predict the compressive strength of the geopolymer mortar containing MSWIFA.

Influences of MgO and PVA Fiber on the Abrasion and Cracking Resistance, Pore Structure and Fractal Features of Hydraulic Concrete

Abrasion resistance and cracking resistance are two important properties determining the normal operation and reliability of hydropower projects that are subjected to erosion and abrasive action. In this study, polyvinyl alcohol (abbreviated as PVA) fiber and magnesium oxide expansive agents (abbreviated as MgO) were used together to solve the problems of cracking and abrasive damage. The effects of PVA fiber and MgO on the mechanical property, abrasion and cracking resistance, pore structures and fractal features of high-strength hydraulic concrete were investigated. The main results are: (1) The incorporation of 4–8% Type I MgO reduced the compressive strength, splitting tensile strength and the abrasion resistance by about 5–12% at 3, 28 and 180 days. Adding 1.2–2.4 kg/m3 PVA fibers raised the splitting tensile strength of concrete by about 8.5–15.7% and slightly enhanced the compressive strength and abrasion resistance of concrete. (2) The incorporation of 4–8% Type I MgO prolongs the initial cracking time of concrete rings under drying by about 6.5–11.4 h, increased the cracking tensile stress by about 6–11% and lowered the cracking temperature by 2.3–4.5 °C during the cooling down stage. Adding 1.2–2.4 kg/m3 PVA fibers was more efficient than adding 4–8% MgO in enhancing the cracking resistance to drying and temperature decline. (3) Although adding 4% MgO and 1.2–2.4 kg/m3 PVA fibers together could not enhance the compressive strength and abrasion resistance, it could clearly prolong the cracking time, noticeably increase the tensile stress and greatly lower the racking temperature; that is, it efficiently improved the cracking resistance to drying and thermal shrinkage compared with the addition of MgO or PVA fiber alone. The utilization of a high dosage of Type I MgO of less than 8% and PVA fiber of no more than 2.4 kg/m3 together is a practical technique to enhance the cracking resistance of hydraulic mass concretes, which are easy to crack. (4) The inclusion of MgO refined the pores, whereas the PVA fiber incorporation marginally coarsened the pores. The compressive strength and the abrasion resistance of hydraulic concretes incorporated with MgO and/or PVA fiber are not correlated with the pore structure parameters and the pore surface fractal dimensions.

Chaos Analysis of Single-Stage Spur Gear System Considering Backlash Fractal

PurposeConsidering the time-varying pressure angle and dynamic clearance, the effects of rotational speed, tooth surface friction, and tooth surface morphology on the system’s dynamic response are studied.MethodAn improved gear nonlinear model is proposed, which considered nonlinear factors such as time-varying pressure angle, position angle, tooth surface morphology, and tooth surface friction. The time-varying dynamic backlash is deduced, and the nonlinear dynamic equation of the gear is established. The nonlinear dynamic response of the gear system is obtained based on Runge–Kutta method.ResultsThe influence of the rotational speed and tooth surface friction on single-stage spur gear system response is analyzed through the analysis of the bifurcation diagram, the three-dimensional spectrum diagram, the proportion of the meshing state, and the largest dynamic meshing force (LDMF). Dynamic response differences between the three different model are compared. In addition, by changing the tooth surface roughness and fractal dimension, the influence of tooth surface morphology on the dynamic response of the system is studied.ConclusionCompared with the traditional model, when the dynamic center distance and dynamic pressure angle are considered, the system response may enter a chaotic state earlier. When the tooth surface friction is further considered, the chaotic state of the system response is suppressed. At the same time, the velocity of the dynamic transmission error is significantly reduced, and the fluctuation amplitude of the dynamic pressure angle is increased. The value of LDMF rose overall. The stability of the system response decreases with the increase of tooth surface roughness and fractal dimension. Compared with the fractal dimension, the tooth surface roughness has a more obvious effect on the dynamic response of the system.

Comparison between the Influence of Finely Ground Phosphorous Slag and Fly Ash on Frost Resistance, Pore Structures and Fractal Features of Hydraulic Concrete

Hydraulic concrete in cold regions is necessary for good frost resistance. The utilization of finely ground PS (FGPS) in the construction of hydropower projects could solve the pollution issue and the fly ash shortage problem. In this work, the influence of FGPS and fly ash on frost resistance, pore structure and fractal features of hydraulic concretes was investigated and compared. The main results are: (1) The inclusion of 15–45% FGPS reduced the compressive strength of plain cement concretes by about 21–52%, 7–23% and 0.4–8.2% at 3, 28 and 180 days, respectively. (2) The inclusion of FGPS less than 30% contributed to the enhancement of 180-day frost resistance. At the same dosage level, the FGPS concrete presented larger compressive strengths and better frost resistance than fly ash concrete at 28 and 180 days. (3) At 3 days, both the addition of FGPS and fly ash coarsened the pore structures. FGPS has a much stronger pore refinement effect than fly ash at 28 and 180 days. The correlation between frost resistance of hydraulic concrete and pore structure is weak. (4) At 28 days, the incorporation of FGPS and fly ash weakened the air void structure of hydraulic concrete. At 180 days, the presence of FGPS and fly ash was beneficial for refining the air void structure. The optimal dosage for FGPS and fly ash in terms of 180-day air void refinement was 30% and 15%, respectively. The frost resistance of hydraulic concretes is closely correlated with the air void structure. (5) The pore surface fractal dimension (Ds) could characterize and evaluate the pore structure of hydraulic concretes, but it was poorly correlated with the frost resistance.

A Revised Continuous Observation Length Model of Rough Contact without Adhesion

The real contact area of rough surfaces has significant importance in many engineering applications, such as tribology, wear, lubrication and seals. A continuous observation length-dependent mechanic model of rough contact without adhesion is proposed, which assumes that the rough surface is divided into ideal subplanes. However, the model ignores the elastoplastic deformation of asperities, and the standard deviation of ideal subplanes’ heights is assumed to vary linearly with continuous observation length, which is not precise for all the surface fractal dimensions. In this work, a revised continuous observation length model is proposed with elastic, elastoplastic and fully plastic stages. The expressions of force and real contact areas are derived. For surfaces with different fractal dimensions, the quadratic polynomial, cubic polynomial and power relationships between standard deviation and observation length are proposed, respectively. In addition, the influences of the dimensionless observation length, fractal dimension and equivalent elastic modulus on the real contact areas in different contact stages are also analyzed. It can be concluded that the quadrate real contact area decreases as the dimensionless observation length decreases, which can be applied to the percolation theory for leak seal problems.

Fractal Dimension of Digital 3D Rock Models with Different Pore Structures

The macroscopic physical properties of rocks are profoundly determined by their microstructure, and the research of accurately characterizing rock pore structure has been extensively carried out in the fields of petroleum engineering and geoscience. Fractal geometry is an effective means of quantitatively estimating the pore structure properties of porous media. In this study, the evolution law of the fractal dimension and the quantitative relationship between the fractal dimension and porosity were investigated based on the digital 3D rock models. First, three kinds of models with gradually changing pore structures, namely sedimentation, compaction, and cementation, were systematically reconstructed by the process-based approach. Then, the fractal dimensions of the skeleton, pore, and surface of the models were computed and analyzed. Finally, the relationships among the fractal dimension, porosity, and complexity were explored qualitatively. These works reveal the changing laws of three types of fractal dimensions for different pore structure models. The pore structure differences in sedimentation model can only be distinguished by the surface fractal dimension, while both pore and surface fractal dimensions are available parameters for characterizing different pore structures in compaction and cementation models. The quantitative relations between box-counting fractal dimension and porosity were established, which can be expressed by combining linear and logarithmic formulas. The comparison of fractal dimensions of compaction and cementation models proves that fractal dimensions can distinguish the subtle pore structure differences in digital 3D rock models. Understanding the evolution law between the fractal dimension and pore structure parameters provides more references for classifying and evaluating rock pore structure features using fractal dimensions.