Fractal Parameters Research Articles

New insights into pore fractal dimension from mercury injection capillary pressure in tight sandstone

Mercury injection capillary pressure (MICP) has been widely used for pore fractal dimension determination and thus leads to a variety of calculation models with different results. Here, taking the tight sandstone gas reservoir of Shaximiao Formation in Jinhua-Zhongtaishan area, central Sichuan Basin as the object, the theory, method and application of pore fractal dimension determination from MICP are explored. Based on Yu-Xia model and Washburn equation, rigorous analytical expressions on fractal dimension, capillary pressure and mercury saturation are deduced. After pre-processing including validation, consistency correction and shape-preserving interpolation, the fractal turning point is located with the local maximum of the front-back moving variance ratio of mercury saturation, and then the global, macropore and micropore fractal dimensions are determined respectively by nonlinear fitting. As suggested by the data processing results of the 39 MICP samples, there is no significant direct correlation between pore fractal dimensions and petrophysical properties represented by permeability. However, the combination of fractal model related parameters, especially global fractal dimension and entry pressure, can identify effectively reservoir quality ranks. Meanwhile, for gas layers with relatively high permeability, larger global fractal dimensions may imply roughly more favorable pore structure and better reservoir quality, while the total quality of the relatively low-permeability gas layers is poor and nearly independent of the fractal dimensions. The representative MICP-based pore fractal models, He-Hua and Shen-Li, are critically reviewed. The theoretical simplification and calculative approximate of these two models lead to some degree of error in pore fractal dimension determination, despite their slight correlation in the fitting results with those of the present model. This study may improve the understanding of the pore fractal dimension determined from MICP and provide reference for pore structure evaluation, reservoir quality classification and capillary pressure modeling.

Learning Fractals by Gradient Descent

Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model pre-training. In this paper, we study the inverse problem --- given a target image (not necessarily a fractal), we aim to generate a fractal image that looks like it. We propose a novel approach that learns the parameters underlying a fractal image via gradient descent. We show that our approach can find fractal parameters of high visual quality and be compatible with different loss functions, opening up several potentials, e.g., learning fractals for downstream tasks, scientific understanding, etc.

Analysis of the Total Leakage Characteristics of Finger Seal Considering Fractal Wear and Fractal Porous Media Seepage Effects

As an advanced flexible dynamic sealing technology, the leakage characteristics of a finger seal (FS) is one of the key research areas in this technology field. Based on the fractal theory, this paper establishes a mathematical model of the FS main leakage rate considering the fractal wear effect by taking into account the influence of the wear height on the basis of the eccentric annular gap flow equation. Based on the Hagen-Poiseuille law and the fractal geometry theory of porous media, a mathematical model of the FS side leakage rate considering the fractal porous media seepage effect is developed. Then, a mathematical model of the FS total leakage rate is established. The results show that the mathematical model of the FS total leakage rate is verified with the test results, the maximum error rate is less than 5%, and the mathematical model of the FS total leakage rate is feasible. With the gradual increase in working conditions and eccentricity, the FS main leakage rate gradually increases. In addition, the effects of the fractal dimension, fractal roughness parameters and porosity after loading on the FS main leakage rate are negligible. As the fractal dimension of tortuosity after loading gradually decreases, the fractal dimension of porosity after loading gradually increases, and the FS side leakage rate gradually increases. As the porosity after loading gradually increases, the FS side leakage rate gradually increases. Under different working conditions, different fractal characteristic parameters and different porosities after loading, the weight of the FS main leakage rate is much greater than that of the FS side leakage rate by more than 95%.

Complex roughening dynamics and wettability mechanism in MoS2 thin films — A system theoretic approach

We utilized fractal geometry to advance insights into the complex roughening and its facilitated wettability mechanism of sputtered MoS2 film surfaces with varying thickness are studied. Fractal parameters indicate the dominance of shadowing at lower thickness while enhancement in vertical growth rate and variation in local irregularities are observed at higher thicknesses along with anomalous roughening up to thickness of 200 nm. In addition, anti-persistent trend of surface heights was observed to be independent of thickness. Multifractal analysis exposed the non-linear variation in multifractality strength and vertical complexities of surface heights. The results corroborates the stereometric analysis revealing the 3D surface topography of analyzed films. The wettability was observed to increase with thickness. In consideration, the roughening expedited wetting trend is defined in light of stereometric parameters and multifractility strength suggesting increases the penetration of water droplets into the surface voids with decline in the surface complexities. The mechanism for increase in contact angle is realized from the augmentation in curvature pressure indicating the existence of large air pressure within the void lying lower than the water droplets as compared to the pressure from the meniscus sides of the droplets. In addition, principal component analysis is utilized to reveal the significance of fractal parameters in probing the surface roughening. The results hold prospects in surface engineering of MoS2 thin films as a function of thickness for enhanced catalytic activity in electrochemical splitting of water for hydrogen evolution reactions.

Tree Species Classification Using Optimized Features Derived from Light Detection and Ranging Point Clouds Based on Fractal Geometry and Quantitative Structure Model

Tree species classification is a ubiquitous task in the forest inventory field. Only directly measured feature vectors have been applied to most existing methods that use LiDAR technology for tree species classification. As a result, it is difficult to obtain a satisfactory tree species classification performance. To solve this challenge, the authors of this paper developed two new kinds of feature vectors, including fractal geometry-based feature vectors and quantitative structural model (QSM)-based feature vectors. In terms of fractal geometry, both two fractal parameters were extracted as feature vectors for reflecting how tree architecture is distributed in three-dimensional space. In terms of QSM, the ratio of length change and the ratio of radius change of different branches were extracted as feature vectors. To reduce the feature vector dimensionality and explore valuable feature vectors, feature vector dimension reduction was conducted using the classification and regression tree (CART). Five hundred and sixty-eight individual trees with five tree species were selected for evaluating the performance of the developed feature vectors. The experimental results indicate that the tree species of Fagus sylvatica achieved the highest overall accuracy, which is 98.06%, while Quercus petraea obtained the lowest overall accuracy, which is 96.65%. Four other classical supervised learning methods were adopted for comparison. The comparison result indicates that the proposed method outperformed the other four supervised learning methods no matter which accuracy indicator was adopted. In comparison with the relevant method, the eight feature vectors developed in this paper also performed much better. This indicates that the fractal geometry-based feature vectors and QSM-based feature vectors developed in this paper can effectively improve the performance of tree species classification.

Impact of storage at different thermal conditions on surface characteristics of 3D printed polycaprolactone and poly(ε-caprolactone-co-p-dioxanone) scaffolds

Fused filament fabrication (FFF) is a commonly used method for producing three-dimensional scaffolds using synthetic, degradable polymers. However, there are several variables that must be considered when fabricating devices for clinical use, one of which is storage conditions after printing. While the academic community has examined the impact of FFF on mechanical and thermal properties, there has been less focus on how storage conditions would affect the surface texture of scaffolds. Our hypothesis was that the surface, thermal and physical properties of FFF scaffolds are significantly influenced by the storage conditions. We evaluated the surfaces of FFF poly (ε-caprolactone) (PCL) and poly (ε-caprolactone-co-p-dioxanone) (PCLDX) strands that were stored at 4 °C, 20 °C, and 37 °C for 28 days. We monitored surface texture, physical and thermal changes to understand the effect of storage on the strands. The implementation of scale-sensitive fractal analysis and feature parameters revealed that storage conditions at 37 °C increased the number of hills and dales, as well as the density of peaks and pits compared to 20 °C and 4 °C, for both materials. The feature roughness parameters for PCL had up to 90% higher values than those of PCLDX, which correlated with the physical and thermal properties of the materials. These differences may impact further surface-cell interaction, highlighting the need for further evaluation for faster clinical translation. Our findings emphasize the importance of considering storage conditions in the design and manufacture of FFF scaffolds and suggest that the use of feature roughness parameters could facilitate the optimization and tailoring the surface properties for specific applications.

Fractal analysis of anisotropic shear-fracture roughness from rocks and analogue laboratory models: A new approach for heterogeneous-slip characterization

Shear fracture surfaces are commonly rough on varied scales, and understanding the roughness properties is crucial to predict their slip behaviour. Using natural rock samples from the Singhbhum Shear Zone, eastern India, this study develops an approach to heterogeneous surface roughness analysis of shear fractures, forming two distinct domains: striated, anisotropic zone and non-striated, isotropic zone. Analogue experiments run on brittle-ductile models under a pure shear condition produce similar heterogeneous roughness characteristics of shear fractures. Using a laser profilometer, we constructed 3D topologies of both natural and experimental shear surfaces, which are presented to show the distinctive roughness characteristics of the striated and non-striated zones in terms of their fractal properties. ΔD, which stands for the difference between across- (D⊥) and along- (D∥) the slip direction, is calculated to evaluate the degree of their roughness anisotropy. This fractal parameter indicates strong anisotropy with ΔD = 0.0787–0.2118 in striated zones, which is significantly weak, where ΔD = 0.0024–0.0603 in non-striated zones. Finally, the article presents an in-depth discussion of this roughness study from the perspective of slip-stuck kinematics on shear surfaces from laboratory experiments and their geophysical implications, e.g., interpretation of earthquake event patterns on seismic faults and permeability of fractured rocks.

Experimental‐based study of gear vibration characteristics incorporating the fractal topography of tooth surface

AbstractMicroscopic roughness is inevitable on the gear meshing surface, which is also a key parameter affecting the dynamic response. The surface roughness exhibits self‐affine characteristics across multiscales. To explore the influence of surface fractal topography on the vibration amplitude of the gear system under different rotational speeds and loads, an experimental setup of spur gear transmission is devised. The fractal dimension and fractal roughness of the meshing surface are calculated by the power spectral density method. The relationships between gear response and fractal parameters are revealed experimentally. Results indicate that a rougher tooth surface, that is, a smaller fractal dimension or larger fractal roughness, corresponds to an intense vibration amplitude. The sensitivity of dynamic response to the tooth surface topography varies at different rotational speeds and loads. Under low speed and light load conditions, the fractal dimension and fractal roughness have a more obvious influence on the dynamic response of the gear transmission system. With the increase of speed and load, the macroworking conditions gradually become the main factor attributed to vibration amplitude.

Fractal Analysis of Four Xerogels Based on TEGylated Phenothiazine and Chitosan

The present article describes novel massive materials (in the solid phase) based on TEGylated phenothiazine and chitosan that possess great capability to recover mercury ions from constituent aqueous solutions. These were produced by chitosan hydrogelation accompanied by formyl subsidiary item of TEGylated phenothiazine, attended by lyophilization. The delineation and structure description of the obtained material or supramolecular assembly were realized by FTIR (Fourier transform infrared) spectroscopy, X-ray diffraction, and POM (Polarized Light Optical Microscopy). The morphology of their texture was kept under observation by SEM (Scanning Electron Microscopy). The obtained SEM images were evaluated by fractal analysis. The fractal parameters of interest were calculated, including the fractal dimension and lacunarity.

Sealability Analyses of Premium Connections Characterized by a Surface Fractal Function

With the development of high-pressure, high-temperature wells, the sealability of premium connections is being threatened by heavy loads. For the sake of researching the sealability of premium connections at the microlevel on the sealing surface, a rough profile was characterized according to a fractal function, and the influence of the fractal parameters of contact behavior on the rough surface was analyzed. A full-size premium connection model with a fractal surface FEM was established using ABAQUS software to analyze the Von Mises stress and contact pressure, and the sealability was then analyzed using contact strength theory. It was found that utilizing fractal functions to describe the rough morphology on the sealing surface of premium connections could reveal the contact behavior of the sealing surface more realistically. The premium connection’s fractal FEM was closer to the actual situation, considering the effect of the asperities’ elastic–plastic deformation on the sealability. The fractal dimension D had a greater influence on the contact area and contact pressure than the scale coefficient G. When the fractal dimension D was less than 2.5, the maximum Von Mises stress and maximum contact pressure on the sealing surface were 8.81 × 108 Pa and 1.20 × 109 Pa, respectively, making the surface prone to gluing. The sealability of the premium connection was primarily affected by the axial tension. When the axial tension was 1.2 × 106 N, the sealing surface experienced significant displacement along the axial direction, the effective contact length reduced from 2.72 × 10−3 m to 2.24 × 10−3 m, and the maximum contact pressure reduced from 8.10 × 108 Pa to 6.39 × 108 Pa, which led to a 30% decrease in sealing strength, which may pose a high risk of sealing failure. When the internal pressure reached 1 × 108 Pa, the effective contact length increased from 9.08 × 10−3 m to 1.06 × 10−2 m, the maximum contact pressure increased from 8.67 × 108 Pa to 1.37 × 109 Pa, and the sealing strength increased by 23%.

Pore structure characterization based on NMR experiment: A case from the Shanxi Formation tight sandstones in the Daning-Jixian area, eastern Ordos Basin

The study of pore structure requires consideration of important factors including pore throat size, pore radius composition, and pore-throat configuration. As the nuclear magnetic resonance (NMR) experimental results contain rich information about pore structures and fluid occurrence states, this study investigated the pore structures of the tight sandstone reservoirs of the Shanxi Formation in the Daning-Jixian area, eastern Ordos Basin. Firstly, by making the inverse cumulative curve of the NMR T2 spectrum coincide with the capillary pressure curves which were obtained by the mercury injection capillary pressure (MICP) technique, this study derived a conversion coefficient that can be used to convert the NMR T2 spectrum into the pore throat radius distribution curves based on the NMR experimental results. Subsequently, we determined the pore radius intervals corresponding to irreducible water distribution using the NMR-derived pore radius distribution curves. Finally, the NMR T2 distribution curves based on the fractal theory were analyzed and the relationships between fractal dimensions and parameters, including permeability, porosity, reservoir quality index (RQI), flow zone indicator (FZI), irreducible water saturation, RT35, and RT50, were also discussed. The NMR-derived pore throat radius distribution curves of the study area are mainly unimodal, with some curves showing slightly bimodal distributions. The irreducible water mainly occurs in small pores with a pore radius less than 100 nm. As the permeability decreases, the contribution rate of small pores to the irreducible water gradually increases. The NMR-based fractal dimensions of pores show a two-segment distribution. Small pores have small fractal dimensions and are evenly distributed, while large pores have large fractal dimensions and complex pore structures. The fractal dimension of large pores (Dmax) is poorly correlated with porosity but strongly correlated with FZI, RQI, RT35, and RT50. These results indicate that large pores are the main pore zones that determine the seepage capacity of the reservoirs. Additionally, there is a certain correlation between Dmax and the irreducible water saturation.

Analytically decoupling of friction coefficient between mixed lubricated fractal surfaces

Herein, we present a generalized close-formed model of the friction coefficient between fractal surfaces in mixed lubrication. A mathematical transformation from asperity area to oil film thickness is conducted, which changes the fractal method’s traditional basis of the area distribution to establish an analytical fractal model of oil film thickness. A dynamic film thickness model with external load under the determination of the surface roughness is further proposed. Based on the fractal-based oil film thickness, the contact force for each part is solved under the external normal force, and decoupling is achieved presented by contact ratio. Through the contact ratio, the constitutive model of friction coefficient is elucidated. The effects of fractal parameters and important working parameters on friction coefficient are then analyzed, and comparison with experimental data is conducted. This work provides a general analytical expression for friction coefficient in mixed lubrication with explicit form and wide applications.

Analysis and Experimental Verification of the Sealing Performance of PEM Fuel Cell Based on Fractal Theory

Aiming to accurately predict the leakage rate of the sealing interface, this work proposes a two-dimensional finite element model of a proton exchange membrane fuel cell, which includes the microscopic surface morphology and the asperity contact process of the components. First of all, we constructed the surface morphology of the seal by the two-dimensional W-M (Weierstrass–Mandelbrot) fractal function and explored the influence of fractal dimension (D) and scale parameter (G) on the surface profile. Furthermore, the finite element method and Poiseuille fluid theory were adopted to obtain the deformation variables of the asperity under different clamping pressures and leakage rates. Moreover, we quantitatively analyzed the impact of surface roughness on the clamping pressure and leakage rate. It was found that both the surface amplitude and surface roughness are positively correlated with G and negatively correlated with D. Surface morphology is proportional to D but has no relationship with G. Additionally, the deformation asperity decreases exponentially with growing clamping pressure, and the leakage rate is consistent with the experimental values at a clamping pressure of 0.54 MPa. With the same leakage rate, when the seal surface roughness value is less than 1 μm, a doubled roughness value leads to an increase of 31% in the clamping pressure. In contrast, when the surface roughness of the seal is greater than 1 μm, a doubled roughness value induces an increase of 50% in the corresponding clamping pressure.

The Fractal Approach in the Biomimetic Urban Design: Le Corbusier and Patrick Schumacher

Biomimetic design process approaches have been emphasized systematically as a result of works among disciplines of current technology and biological science. In order to find solutions for a decrease in biodiversity, pollution, and issues of the ecosystem, the nature experience shows itself in areas of biomimetic products, architecture, and urban designs in which nature-focused invasions are basically being imitated. Nature-focused designs have set their own framework by examining forms of different nature dynamics (scale, function, formation process) by presenting a sustainable environment. It can be seen that designs are made real by adhering to the resolution of forms, understanding, and interpretation of nature and by embracing fractal designs with the effort of creating a sustainable environment. In this study, emphasis was placed on revealed nature-based design approaches. The article addresses biomimetic design processes, reveals the role of fractal parameters in the design process, and examines the use of biomimetic approaches. By drawing attention to the importance of studying and understanding these internal dynamics, the contribution of natural inspiration and fractal concepts to the design process is examined. We examine research related to the concept of biomimetics, creation/development of conceptual proposals, and analysis of the established theoretical proposal through selected urban design examples in order to determine the respective overlaps between these areas. Our study takes the form of an analysis of the formal organization of living things together with a formal analysis focusing on the design principles. We try to analyze the design principles and the changes in the principles, and discuss the resulting data within the framework of these concepts. The urban designs of Le Corbusier and Patrick Schumacher, who are important names of the 20th century, were examined in line with the findings obtained in terms of biomimesis levels, namely, the organism level, behavior level, ecosystem level, and functional level. Comparisons of urban design approaches are made using the meta-analysis method with respect to findings obtained as a result of an examination of the golden ratio, modular system, fractal, and parameter concepts of urban design. For this reason, when the fractal concept, which is one of the dynamics of biomimetic-oriented nature, is handled with biomimetic levels and its contribution to the design processes is investigated, we are able to determine that it has important parameters in terms of sustainability. This study aims to contribute to the field of industrial products and urban design disciplines in architectural design.

Digital Characteristics of Microstructure of Diamond—Silicon Carbide Composites

As an example of the implementation of digital materials science approaches based on statistical processing of electron micrographs with the analysis of fractal parameters, the digital characteristics of microstructure of diamond–silicon carbide ceramic composite material are calculated. The lacunarity parameter characterizing the non-uniform distribution of filler particles in the matrix is found. Based on lacunarity values calculated at different scales, scale invariance parameter characterizing the dependence of lacunarity on the scale is evaluated. Voronoi entropy characterizing the structure based on the quantity of information is also calculated and used to determine the average number of neighboring particles and average distance between them. For the composites with high mechanical properties, the number of nearest neighbors approaches six, indicating an almost closest packing.

Human osteosarcoma cells in response to ELF-MF: Morphological remodeling compared to cell proliferation.

The present study aimed to assess the effects of extremely low-frequency electromagnetic fields (ELF-MF) on structural changes of human osteosarcoma cells by analyzing the stained cytoskeleton for assessing the relationship between the fractal dimension parameter and proliferation rate of radiation-induced cells. In this study, 2-mT magnetic fields with various waveforms, including sinusoidal, triangular, and pulsed shapes, were employed to determine the biological effects of ELF-EMF on the human osteosarcoma MG-63 cell line. All experiments were performed in two modes: continuous exposure at 3 h and fractionated irradiations at 3 consecutive days. Afterward, the proliferation assay was implemented for assessing the cell proliferation in each group. Moreover, immunofluorescence staining and confocal imaging were performed to determine the cell shape index. Furthermore, fractal dimension analysis was carried out by processing morphological images. The proliferation and shape index parameters of radiation-induced osteosarcomas significantly decreased compared with non-irradiated cells. In addition, fractal dimensions significantly increased following fractionated exposure at 3 consecutive days. Assessing the fractal dimensions can be considered as a new morphological index for the prognosis of the structural remodeling of human osteosarcoma cells in response to fractionated irradiation of ELF-MF. In addition, various waveforms induce a similar effect on morphological remodeling and cell proliferation.

Retinal vessel architecture and geometry are not impaired in normal-tension glaucoma

To investigate the associations between retinal vessel parameters and normal-tension glaucoma (NTG). We conducted a case–control study with a prospective cohort, allowing to record 23 cases of NTG. We matched NTG patient with one primary open-angle glaucoma (POAG) and one control per case by age, systemic hypertension, diabetes, and refraction. Central retinal artery equivalent (CRAE), central retinal venule equivalent (CRVE), Arteriole-To-Venule ratio (AVR), Fractal Dimension and tortuosity of the vascular network were measured using VAMPIRE software. Our sample consisted of 23 NTG, 23 POAG, and 23 control individuals, with a median age of 65 years (25–75th percentile, 56–74). No significant differences were observed in median values for CRAE (130.6 µm (25–75th percentile, 122.8; 137.0) for NTG, 128.4 µm (124.0; 132.9) for POAG, and 135.3 µm (123.3; 144.8) for controls, P = .23), CRVE (172.1 µm (160.0; 188.3), 172.8 µm (163.3; 181.6), and 175.9 µm (167.6; 188.4), P = .43), AVR (0.76, 0.75, 0.74, P = .71), tortuosity and fractal parameters across study groups. Vascular morphological parameters were not significantly associated with retinal nerve fiber layer thickness or mean deviation for the NTG and POAG groups. Our results suggest that vascular dysregulation in NTG does not modify the architecture and geometry of the retinal vessel network.

An innovative technique to solve a fractal damping Duffing-jerk oscillator

The idea of the present article is to look into the nonlinear dynamics and vibration of a damping Duffing-jerk oscillator in fractal space exhibiting the non-perturbative approach. Using a new analytical technique, namely, the modification of a He’s fractal derivative that converts the fractal derivative to the traditional derivative in continuous space, this study provides an effective and easy-to-apply procedure that is dependent on the He’s fractal derivative approach. The analytic approximate solution has a significant match with the results of the numerical simulation as the fractal parameter is very closer to unity, which proves the reliability of the method. Stability behavior is discussed and illustrated graphically. These new powerful analytical tools are developed in an attempt to obtain effective analytical tools, valid for any fractal nonlinear problems.

Methodological features of the analysis of the fractal dimension of the heart rate

Objectives. The aim of the present work is to determine the fractal dimension parameter calculated for a sequence of R–R intervals in order to identify the boundaries of its change for healthy and sick patients, as well as the possibility of its use as an additional factor in the detection of cardiac pathology.Methods. In order to determine the fractal dimension parameter, the Hurst-, Barrow-, minimum coverage area-, and Higuchi methods are used. For assessing the stationarity of a number of electrocardiography (ECG) intervals, a standard method is used to compare arithmetic averages and variances from samples of the total data array of ECG intervals. To identify differences in fractal dimensions of healthy and sick patients, this parameter was ranked. Using the Kolmogorov–Smirnov two-sample criterion, the difference between the distribution laws in the samples for healthy and sick patients is shown.Results. Among the considered methods for calculating the fractal dimension, the Higuchi method demonstrates the smallest data spread between healthy patients. By ranking the calculated fractional dimension values, it was possible to identify the difference between this parameter for healthy and sick patients. The difference in the distribution of fractal dimension of healthy and sick patients is shown to be statistically significant for the coverage and Higuchi methods. At the same time, when using the traditional Hurst method, there is no reason to reject the null hypothesis that two groups of patients belong to the same general population.Conclusions. Based on the obtained data, the difference between the fractal dimension indicators of the duration of R–R intervals of healthy and sick patients is shown to be statistically significant when using the Higuchi method. The fractal dimensions of healthy and sick patients can be effectively distinguished by ranking samples. The results of the research substantiate prospects for further studies aimed at using fractal characteristics of the heart rhythm to identify abnormalities of the latter, which can serve as an additional factor in determining heart pathologies.

The mechanics of frost heave with stratigraphic microstructure evolution

Frost heave is a major cause of engineering geology hazards in cold regions, which is mainly the result of frost-heaving pressure due to the non-linear transport-freezing of water in the pore network. However, few studies have fully quantified the contribution of the strata pore-network structure to that pressure and the hazard to cold-region projects under multifactorial effects. Therefore, to address this long-term challenge in cold regions, we pioneered a generic, interdisciplinary, thermal-hydrological-mechanical fractal model for the quantitative study of the effect of strata microstructure on frost heave and hence the assessment of construction risk for engineering geology projects. First, a strata frost heave model based on fractal theory is proposed, with pore fractal dimension, maximum pore diameter, and pore tortuosity fractal dimension used to characterize strata pore density, pore size, and throat complexity, respectively. Secondly, the numerical model is compared with field observations in cold-region projects, and reasonable agreements can be obtained. The results indicate that various fractal parameters have different effects on engineering geology projects in cold regions. The strata displacement changes by 9.7–20.3% as microscopic parameters change. This study contributes to a better understanding of the micro- and macro-interactions of soil in cold regions, as well as a reference for geoengineering stability in cold regions under frost heave conditions.