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.

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Research on Strength Prediction Model and Microscopic Analysis of Mechanical Characteristics of Cemented Tailings Backfill under Fractal Theory

Minerals ◽

10.3390/min11080886 ◽

2021 ◽

Vol 11 (8) ◽

pp. 886

Author(s):

Hongwei Deng ◽

Tao Duan ◽

Guanglin Tian ◽

Yao Liu ◽

Weiyou Zhang

Keyword(s):

Compressive Strength ◽

Fractal Dimension ◽

Prediction Model ◽

Pore Structure ◽

Uniaxial Compressive Strength ◽

Fractal Theory ◽

Correlation Coefficients ◽

Microscopic Analysis ◽

Strength Prediction ◽

Pore Characteristics

In order to further study the internal relationship between the microscopic pore characteristics and macroscopic mechanical properties of cemented tailings backfill (CTB), in this study, mine tailings and ordinary Portland cement (PC32.5) were selected as aggregate and cementing materials, respectively, and different additives (anionic polyacrylamide (APAM), lime and fly ash) were added to backfill samples with mass concentration of 74% and cement–sand ratios of 1:4, 1:6 and 1:8. After 28 days of curing, based on the uniaxial compressive strength test, nuclear magnetic resonance (NMR) porosity test and the fractal characteristics of pore structure, the relationships of the compressive strength with the proportion and fractal dimension of pores with different radii were analyzed. The uniaxial compressive strength prediction model of the CTB with the proportion of harmless pores and the fractal dimension of harmful pores as independent variables was established. The results show that the internal pores of the material are mainly the harmless and less harmful pores, and the sum of the average proportions of the two reaches 73.45%. Some characterization parameters of pore structure have a high correlation with the compressive strength. Among them, the correlation coefficients of compressive strength with the proportion of harmless pores and fractal dimension of harmful pores are 0.9219 and 0.9049, respectively. The regression results of the strength prediction model are significant, and the correlation coefficient is 0.9524. The predicted strength value is close to the actual strength value, and the predicted results are accurate and reliable.

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Effect of Grain Size on Microscopic Pore Structure and Fractal Characteristics of Carbonate-Based Sand and Silicate-Based Sand

Fractal and Fractional ◽

10.3390/fractalfract5040152 ◽

2021 ◽

Vol 5 (4) ◽

pp. 152

Author(s):

Shao-Heng He ◽

Zhi Ding ◽

Hai-Bo Hu ◽

Min Gao

Keyword(s):

Grain Size ◽

Fractal Dimension ◽

Pore Structure ◽

Pore Size ◽

Quartz Sand ◽

Glass Bead ◽

Fractal Theory ◽

Calcareous Sand ◽

Wide Range ◽

Fractal Characteristics

In this study, a series of nuclear magnetic resonance (NMR) tests was conducted on calcareous sand, quartz sand, and glass bead with a wide range of grain sizes, to understand the effect of grain size on the micro-pore structure and fractal characteristics of the carbonate-based sand and silicate-based sand. The pore size distribution (PSD) of the tested materials were obtained from the NMR T2 spectra, and fractal theory was introduced to describe the fractal properties of PSD. Results demonstrate that grain size has a significant effect on the PSD of carbonate-based sand and silicate-based sand. As grain size increases, the PSD of sands evolves from a binary structure with two peaks to a ternary structure with three peaks. The increase in the grain size can cause a remarkable increase in the maximum pore size. It is also found that the more irregular the particle shape, the better the continuity between the large and medium pores. In addition, grain size has a considerable effect on the fractal dimension of the micro-pore structure. The increase of grain size can lead to a significant increase in the heterogeneity and fractal dimension in PSD for calcareous sand, quartz sand and glass bead.

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PORE STRUCTURE CHARACTERIZATION FOR A CONTINENTAL LACUSTRINE SHALE PARASEQUENCE BASED ON FRACTAL THEORY

Fractals ◽

10.1142/s0218348x19400061 ◽

2019 ◽

Vol 27 (01) ◽

pp. 1940006 ◽

Cited By ~ 3

Author(s):

LEI ZHANG ◽

XUEJUAN ZHANG ◽

HAO CHAI ◽

YAOCAI LI ◽

YONGJIE ZHOU

Keyword(s):

Fractal Dimension ◽

Pore Structure ◽

Pore Size ◽

Clay Mineral ◽

Mineral Content ◽

Fractal Theory ◽

Average Pore Size ◽

Structure Characterization ◽

Imaging Method ◽

Average Pore

Fractal dimension is an important parameter in the evaluation of tight reservoirs. For an outcrop section of the Nenjiang formation in the Songliao Basin, China, the pore structure and pore fractal characteristics of shale parasequences were investigated using fractal theory. In addition, factors causing pore structure changes were analyzed using the results of low-temperature nitrogen adsorption and scanning electron microscope (SEM) experiments. Conducive to gas migration and secondary pores development such as dissolution, results showed that nanoscale pores dominated by fracture-like morphology and consequent good internal connectivity were observed in each pore size section within the target layer. Each parasequence is characterized by a sequential upward decrease of average pore size and an upward increase of total pore volume, with an increasing number of pores from 2[Formula: see text]nm to 50[Formula: see text]nm. Pores are isolated from each other, with poor connectivity and relatively complex composition of brittle minerals and clay minerals. Main components of the brittle minerals, quartz and feldspar, occur in 20–50% and higher clay mineral content ranging from 50% to 70%. In the parasequence cycle, clay mineral gradually decreases while the brittle mineral content increases. Fractal dimension is negatively correlated with clay mineral content and positively correlated with brittle mineral (quartz and feldspar) content. The fractal dimension calculated by the imaging method and the FHH method shows an upward increasing tendency in each of the parasequence cycles. This is as a result of different phenomena, varied sediment hydrodynamic forces leading to particle size differences and increased brittle minerals resulting in microcracks, therefore, the fractal dimension of the large pores (imaging method) increases upward in the parasequence. Simultaneously, with increased content and accompanied dissolution of brittle minerals causing an increase of small pores from base to top of the parasequence, the fractal dimension of the small pores (FHH method) grows.

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Determining Soil-Water Characteristic Curves from Mercury Intrusion Porosimeter Test Data Using Fractal Theory

Energies ◽

10.3390/en12040752 ◽

2019 ◽

Vol 12 (4) ◽

pp. 752 ◽

Cited By ~ 3

Author(s):

Gaoliang Tao ◽

Yin Chen ◽

Henglin Xiao ◽

Qingsheng Chen ◽

Juan Wan

Keyword(s):

Fractal Dimension ◽

Pore Size ◽

Soil Water ◽

Unsaturated Soils ◽

Fractal Theory ◽

Characteristic Curve ◽

Accurate Determination ◽

Size Difference ◽

Mercury Intrusion ◽

Long Duration

Accurate determination of soil-water characteristic curve (SWCC) is of immense importance for understanding the mechanical behavior of unsaturated soils. Due to the difficulty and long duration of experimental procedures, it is of great significance to estimate the SWCC by indirect methods. To address this issue, in this article an effective fractal method is proposed for predicting the SWCC based on mercury intrusion porosimeter (MIP) data. Only two characteristic parameters, namely the fractal dimension and air-entry value, are needed in the presented approach. Detailed procedures for determining the parameters are clearly elaborated. Due to the influence of sample size difference on the equivalent connected pore size, a sample scale effect coefficient is proposed to predict air-entry values. The concept of “critical pore size” is introduced to obtain the optimal fractal dimension, which can accurately reflect the fractal behaviour of SWCC samples. By comparisons between predicted and experimental SWCCs, the validation of the proposed method is verified. The comparisons reveal the good agreement between the proposed approach and laboratory experiments.

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Applications of Fractal Theory in Selecting Bridging Materials in Jilin Oilfield

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.327.161 ◽

2013 ◽

Vol 327 ◽

pp. 161-165

Author(s):

Hui Hong Luo ◽

Ze Hua Wang ◽

Yu Xue Sun ◽

Jiu Zhou Sun

Keyword(s):

Fractal Dimension ◽

Pore Size Distribution ◽

Pore Size ◽

Geometric Distribution ◽

Fractal Theory ◽

Successful Implementation ◽

Distribution Characteristics ◽

The Core ◽

Liquid Phases ◽

Temporary Blocking

Bridging technology is one of the most effective methods to prevent the solid and liquid phases into the well fluid from invading the reservoir. And selecting the bridging agent which best matches with the reservoir pore size is the key of the successful implementation of bridging technology. Because of the lack of precise and quantitative degree of the preferred theory of bridging agent in field applications, temporary blocking fractal theory has been introduced. The reservoir pore size distribution and the fractal geometric distribution characteristics of bridging agent have been described. At the same time, the temporary blocking fractal theory and the fractal dimension calculation have been introduced. Conduct temporary blocking experiments on the core of Jilin Oilfield by this theory and the results proved to be perfect. As a result, the correctness of temporary blocking fractal theory has been verified.

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Numerical Simulation and Microscopic Stress Mechanism for the Microscopic Pore Deformation during Soil Compression

Advances in Civil Engineering ◽

10.1155/2019/1542797 ◽

2019 ◽

Vol 2019 ◽

pp. 1-14

Author(s):

Gaoliang Tao ◽

Wan Peng ◽

Henglin Xiao ◽

Xiaokang Wu ◽

Yin Chen

Keyword(s):

Mechanical Properties ◽

Numerical Simulation ◽

Pore Size ◽

Fractal Theory ◽

Physical And Mechanical Properties ◽

Microscopic Mechanism ◽

The Difference ◽

Microscopic Deformation ◽

Soil Compression ◽

The Relationship

Pore structure is closely related with strength, constitutive relation, consolidation characteristics, and permeability properties of soil. Consequently, improving the understanding of the relationship between microscopic structure and macroscopic physical and mechanical properties has extremely important scientific significance. A large number of studies have shown that pores of soil have fractal features, and hence, the carpet model can be used to approximately simulate the fractal structure of clay. In the present study, ANSYS software was selected to establish a microscopic model of clay to study the distribution of microscopic stress and microscopic deformation characteristics of pores under different consolidation pressures. Besides, the variation law of microscopic pore size was quantitatively determined by using IPP (Image-Pro Plus) software. Combined with the fractal theory, the changes of microscopic pore of numerical simulation and that of physical experiment during compression of clay are studied. All the results indicated that the microscopic stress distribution of clay is not uniform on the compaction process. The larger the pore size is, the bigger the compression stress on both sides and the greater the bending deformation of upper part of the pore is, which leads to the deformation of larger pores which is bigger than that of smaller pores. Based on the results, issues about the microscopic mechanism of the difference in vertical and horizontal permeability under compression of clay, the relationship between the changes of pore shape and microscopic stress, the preliminary principle of “preferential crush of larger particles” for granular soil, skeleton stress across the region where stiffness is relative larger, and the self-protection of particles and pores are also discussed. The results of this study are of great importance in understanding of soil compression and related physical and mechanical properties from the microscopic view.

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Fractal characteristics of reservoir structural fracture: a case study of Xujiahe Formation in central Yuanba area, Sichuan Basin

Earth Sciences Research Journal ◽

10.15446/esrj.v22n2.72250 ◽

2018 ◽

Vol 22 (2) ◽

pp. 113-118 ◽

Cited By ~ 2

Author(s):

Cunhui Fan ◽

Qirong Qin ◽

Dongfeng Hu ◽

Xiaolei Wang ◽

MengYue Zhu ◽

...

Keyword(s):

Fractal Dimension ◽

Correlation Coefficient ◽

Oil And Gas ◽

Fractal Theory ◽

Quantitative Relationship ◽

Fold Belt ◽

Xujiahe Formation ◽

Capacity Dimension ◽

Fracture Development ◽

Fractal Characteristics

The reservoir structural fractures have excellent fractal characteristics, as well as self-similarities. Based on the fractal theory, the surface fractal characteristics of faults and the fractal characteristic of fractures in the core of the Xujiahe Formation in the Fault-Fold Belt of the central Yuanba area were studied, and a quantitative relationship was set up between them. Based on the fractal characteristics of faults, predictions were made of the favorable fracture zone, which provides a new idea for the research of fracture, as well as offers theoretical references for exploring the fracture development zone during oil-gas exploration. The results show the following: the seismic value of reflection fault fractal dimension of the Xujiahe Formation is 1.5284; the correlation coefficient R2 is bigger than 0.9901; the capacity dimension linear regression correlation coefficient of the fracture in core of the Xujiahe Formation is bigger than 0.98; the fractal dimension D can well reflect the fault and fracture development degree, as well as the complexity of the fracture system; it can quantitatively calculate the density of the fracture of the reservoir in the area; the areas of capacity dimension bigger than 1.45 are the fracture development zones in the Fault-Fold Belt of the central Yuanba area; the oil and gas enrichment degree is high; the areas with the fractal dimension value between 0.95 and 1.45 are the fracture relatively-developed zones; the fractal dimension with values smaller than 0.95 are the lack of fracture areas.

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Pore size fractal dimension for characterizing Au/TiO2 catalyst

Modern Physics Letters B ◽

10.1142/s0217984918504158 ◽

2018 ◽

Vol 32 (33) ◽

pp. 1850415

Author(s):

Asif Mahmood

Keyword(s):

Fractal Dimension ◽

Pore Size ◽

Surface Area ◽

Pore Volume ◽

Bet Surface Area ◽

Negative Slope ◽

Phase Saturation ◽

Maximum Pore Size ◽

Second Procedure ◽

The Relationship

The quality and assessment of a catalyst can be documented in detail by the application of pore size. This research aims to calculate fractal dimension from the relationship among pore size, maximum pore size and wetting phase saturation and to confirm it by the fractal dimension derived from the relationship among the ratio between surface area per unit pore volume, entry surface area per unit pore volume and wetting phase saturation. In this research, pore size was measured on Au/TiO2 using Brunauer–Emmett–Teller (BET) surface area. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, pore size, maximum pore size and fractal dimension. The second equation implies to the wetting phase saturation as a function of surface area per unit pore volume, entry surface area per unit pore volume and the fractal dimension. Two procedures for obtaining the fractal dimension have been utilized. The first procedure was done by plotting the logarithm of the ratio between pore size and maximum pore size versus logarithm wetting phase saturation. The positive slope of the first procedure = 3 − Df (fractal dimension). The second procedure for obtaining the fractal dimension was determined by plotting the logarithm of the ratio between surface area per unit pore volume, entry surface area per unit pore volume versus the logarithm of wetting phase saturation. The negative slope of the second procedure = Df − 3. It was found that the plasma + thermally treated Au/TiO2 has the highest fractal dimension value owing to possibility of having holes and channels. The results also show similarity between pore size fractal dimension and surface area per unit pore volume fractal dimension. In our case, as conclusions, the higher the fractal dimension, the better the catalytic activity.

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Pore structure and strength of waste fiber recycled concrete

Journal of Engineered Fibers and Fabrics ◽

10.1177/1558925019874701 ◽

2019 ◽

Vol 14 ◽

pp. 155892501987470 ◽

Cited By ~ 1

Author(s):

Jinghai Zhou ◽

Tianbei Kang ◽

Fengchi Wang

Keyword(s):

Mechanical Properties ◽

Fractal Dimension ◽

Pore Structure ◽

Fiber Length ◽

Volume Fraction ◽

Fractal Theory ◽

Recycled Concrete ◽

Recycled Aggregate ◽

Cement Ratio ◽

Water Cement Ratio

The pore structure is one of the major factors affecting the mechanical properties of waste fiber recycled concrete. In this article, the pore structure and strength performance of waste fiber recycled concrete are experimentally studied. The design variables are water–cement ratio, recycled aggregate replacement rate, waste fiber length, and volume fraction of waste fibers. The pore structure characteristic parameters of waste fiber recycled concrete are investigated using mercury intrusion porosimetry test and fractal theory. The complex distribution of pore structure in space is quantitatively described by fractal dimension, and the pore structure is comprehensively evaluated. The results show that the water–cement ratio has the largest influence on the pore structure, and the fiber length has the least influence. The optimum volume fraction of waste fibers is 0.12%. There is an obvious linear relationship between the pore volume fractal dimension and strength. With the increase in the fractal dimensions, the compressive and splitting tensile strengths increase. Macroscopic mechanical properties of waste fiber recycled concrete can be predicted by the pore structure.

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A NEW METHOD FOR CALCULATING FRACTAL DIMENSIONS OF POROUS MEDIA BASED ON PORE SIZE DISTRIBUTION

Fractals ◽

10.1142/s0218348x18500068 ◽

2018 ◽

Vol 26 (01) ◽

pp. 1850006 ◽

Cited By ~ 45

Author(s):

YUXUAN XIA ◽

JIANCHAO CAI ◽

WEI WEI ◽

XIANGYUN HU ◽

XIN WANG ◽

...

Keyword(s):

Porous Media ◽

Fractal Dimension ◽

Pore Size Distribution ◽

Pore Size ◽

Size Distribution ◽

Pore Space ◽

Fractal Theory ◽

Fractal Dimensions ◽

New Method ◽

Distribution Data

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

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