Exponential Relationship Research Articles

A study on the evolution of microstructure of soil-rock mixtures based on the electrochemical conductive paths model under different rock and moisture content conditions

ABSTRACT To further improve the understanding of the evolution law of the microstructure of SRM in road engineering under moisture and rock content, the electrochemical impedance spectroscopy test under different moisture and rock conditions was carried out. This paper proposed an electrochemical model of different conductive paths based on different cementation states. The impact of rock and moisture content on the characteristic parameters of the conductive path model was analyzed. The results indicated the impedance spectrum curves became more pronounced with the continuous decrease in moisture content and increase in rock content. There was a well-defined exponential relationship between total impedance and both moisture and rock content. The total impedance decreased continuously with increasing moisture content and increased with increasing rock content. The characteristic parameters had practical significance in representing the microscopic structure. The moisture content primarily influenced the variation trends of the representation parameters by altering the channel width, length, and quantity of the continuous pore water solution pathways and the discontinuous rock-soil bonded bodies. The rock content affected the changes by compressing the external and internal pore water solution and soil particles, altering the compression and support between the continuous pore water solution pathways and the block rock framework.

DLC: Flexible bridge across heterogeneous interface between alumina filler and epoxy resin matrix

The heterogeneous interface between filler and matrix within composites often acts as a bottleneck for material performance. Carbon materials, particularly Diamond-Like Carbon (DLC), are representing a novel trend in interface design. This study investigates the nanoscale mechanical and electrical properties of the heterogeneous interface between DLC-coated alumina fillers and an epoxy resin matrix. The results demonstrate that the DLC layer is instrumental in creating a harmonious modulus transition between materials that exhibit significant variance in their elastic moduli, characterized by an exponential relationship, and approximately 50% enhancement in interfacial adhesion. Additionally, the DLC layer exhibits elevated sensitivity in dielectric response, attributed to a small RC time constant. This interface transition technology offers new tools for composite material design.

Relationship between Pelvic Dimensions and Maximum Traction Forces Required during Parturition in Holstein Cows Using a Biomechanical Obstetric Simulator.

The primary aim of this study was to investigate the effect of the pelvic dimensions of Holstein cows on the traction forces during parturition. Additionally, the relationship between calf measurements and traction forces was explored. For this purpose, a modified in vitro biomechanical model simulating obstetric tractions was used. For the requirements of the experiment, six bone pelvises of deceased Holstein cows were collected based on their estimated pelvic inlet area (EPA) and prepared. Additionally, six stillborn calves were collected based on their body weight (BW). The parameters of the pelvic inlet and cavity were measured using computed tomography (CT). Using the simulator, every calf was pulled in a random order through all pelvises, realizing a total of 36 obstetrical tractions, and the required forces were documented with appropriate software. In each extraction, three peaks of forces were recorded, with the first peak occurring at the entrance of the elbows into the maternal pelvic cavity, the second peak at the entrance of the thorax, and the third at the entrance of the calf's pelvis. Logistic regression revealed an exponential relationship between pelvic parameters and traction forces for the entrance of the elbows and the pelvis, with the recorded forces being higher in the two smallest pelvises and stabilizing at a lower level thereafter, while for the entrance of the thorax, the correlations were either exponential or linear. The adjusted coefficients of determination (r2) were generally above the threshold of 0.5 for the entrance of the elbows and pelvis and lower (0.3-0.4) regarding the thorax and were statistically significant (p < 0.05) in all cases. Regarding the relationships between the calf dimensions and the required traction forces, the types of correlations were primarily linear and of lower magnitude. The combination of pelvic and calf parameters in a multivariate model resulted in an r2 of 0.72 for the entrance of the elbows using the pelvic diagonal and calf's body weight, an r2 of 0.62 using the pelvic area and calf's thoracic circumference, and an r2 of 0.75 using the pelvic diagonal and calf's fetlock joint width. In conclusion, under the conditions of the present experimentation, the applied traction forces were mainly influenced by the pelvic dimensions in an exponential manner, whereas the calf body measurements showed a weaker effect. Based on these findings, critical cut-off points exist, different for every pelvic parameter, below which a significant increase in the required traction forces is expected.

Key influence factors in magneto-controlled motion of micro-nano graphite flakes

Magneto-controlling micro-nano materials’ motion is a promising way that enable the noncontact, remote, and nondestructive controlling of their macrostructure as well as functionalities. Here, an optical microscope with an electromagnet was constructed to in-situ monitor the magneto-controlled motion process microscopically. Taking micro-nano graphite flake (MGF) as a model system, we experimentally demonstrate the key factors that influence the magneto-controlling of materials’ motion. First, the product of intensity and gradient of the magnetic field (B∇B) has been confirmed as the dominant driving force and the flipping direction of the MGFs is accordingly determined by the vector direction of B×∇B. Second, quantitatively comparative experiments further revealed that the threshold driving force has an exponential relationship with the structural aspect ratio (b/a) of MGFs. Third, the critical magneto-driving force is found as proportional to the viscosity of the solvent. Accordingly, a dynamic model is developed that describes the flip of the diamagnetic flake under external magnetic field excitation considering the shape factor. It is shown experimentally that the model accurately predicts the flip dynamics of the flake under different magnetic field conditions. In addition, we also discovered the delay effect, multiple cycle acceleration effect, and the fatigue effects due to gas adsorption in magneto-controlled MGFs flipping. These findings can be used to achieve magneto-controlling materials’ macrostructure as well as their functionalities.

Simulating flows in backward-facing step for various expansion ratios by finite element-lattice Boltzmann

The development of fluid flow in a channel with constant width and a backward-facing step was investigated through numerical simulation. For the first time, by employing the finite element lattice Boltzmann method, a series of numerical calculations were performed to explore the flow behavior across various Reynolds numbers and expansion ratios (the ratio of the outlet section width to the inlet section width). Analysis was conducted on the macroscopic flow parameters, including velocity fields, streamlines, and reattachment points, for different Reynolds numbers and expansion ratios. It was found that the reattachment length in flows over a backward-facing step is dependent on both the Reynolds number and the expansion ratio, rather than being a function of a singular variable. It was concluded, as the Reynolds number increases, the reattachment length also increases. For a Reynolds number range of 10≤ReD≤100, this increase can be described by an exponential relationship, with an expansion ratio of 1.94. The impact of the expansion ratio is less pronounced at lower Reynolds numbers when compared to that at higher ones. The minimum skin friction factor within the return zone is significantly influenced by the Reynolds number, emphasizing the dominant effects of viscosity in near-wall flows. The lattice Boltzmann method is a computationally efficient algorithm for simulating fluid flows through complex geometries, potentially offering significant processing time savings.

BSE risk posed by ruminant collagen and gelatine derived from bones.

The European Commission requested an estimation of the BSE risk (C-, L- and H-BSE) from gelatine and collagen derived from ovine, caprine or bovine bones, and produced in accordance with Regulation (EC) No 853/2004, or Regulation (EC) No 1069/2009 and its implementing Regulation (EU) No 142/2011. A quantitative risk assessment was developed to estimate the BSE infectivity, measured in cattle oral infectious dose 50 (CoID50), in a small size batch of gelatine including one BSE-infected bovine or ovine animal at the clinical stage. The model was built on a scenario where all ruminant bones could be used for the production of gelatine and high-infectivity tissues remained attached to the skull (brain) and vertebral column (spinal cord). The risk and exposure pathways defined for humans and animals, respectively, were identified. Exposure routes other than oral via food and feed were considered and discussed but not assessed quantitatively. Other aspects were also considered as integrating evidence, like the epidemiological situation of the disease, the species barrier, the susceptibility of species to BSE and the assumption of an exponential dose-response relationship to determine the probability of BSE infection in ruminants. Exposure to infectivity in humans cannot be directly translated to risk of disease because the transmission barrier has not yet been quantified, although it is considered to be substantial, i.e. much greater amounts of infectivity would be needed to successfully infect a human and greater in the oral than in the parenteral route of exposure. The probability that no new case of BSE in the cattle or small ruminant population would be generated through oral exposure to gelatine made of ruminant bones is 99%-100% (almost certain) This conclusion is based on the current state of knowledge, the epidemiological situation of the disease and the current practices, and is also valid for collagen.

Humidity sensing by tailoring light absorption of SiO2/bromophenol blue (BPB) thin film on optical fiber

The fabrication of an evanescent wave fiber optic humidity sensor based on bromophenol blue (BPB) doped SiO2 thin film was demonstrated, modulating in light intensity. The sensing film was coated on a fiber core via a single-step dip coating method, followed by sol-gel processing of the precursor. A good exponential relationship was established between output light intensity and relative humidity. The sensor exhibited a high sensitivity and fast response and recovery, as well as low hysteresis, good stability and repeatability. Adsorption of ambient water triggered a ring-opening reaction of BPB, which enhanced light absorption of the sensing film significantly and affected the transmission of the evanescent wave.

CO2 emissions of tropical peat soils under controlled groundwater table depths: A laboratory-based experiment

The groundwater table (GWT) is widely recognized as a key factor influencing CO2 emissions in tropical peatlands. However, previous studies investigating this relationship have reported diverse results. This variability likely stems from the dynamic nature of field-based groundwater conditions. To address this, our study investigated the relationship between controlled GWT and CO2 emissions in a laboratory experiment using PVC columns filled with peat soil. GWT depths were adjusted to 20 cm, 30 cm, 40 cm, 50 cm, and 60 cm within a large container filled with peat pore water. CO2 emissions were measured using an Infra Red Gas Analyzer - Environmental Gas Monitoring-4 instrument, with a closed-chamber system. Our findings revealed significant differences in CO2 emissions between treatments, except for the transition from 20 cm to 30 cm GWT. Correlation analysis showed a positive correlation (R² = 0.25). Notably, CO2 emission factor values based on average yearly emission rates displayed a substantial increase with decreasing GWT, exhibiting a strong exponential relationship (R² = 0.99).

A Theoretical and Practical Approach to Exponential Relation between Innovation and Sustainable Development

A Aside from the political, geographic, economic, legal, social, and cultural problems that every nation, state, and government faces, it is evident that sustainable development is the key to sustainability, progress, and improving the quality of life. Achieving SDG targets has been seen as the primary trend for the past 15 years and the foreseeable future. In this direction, with an eye towards the fifth industrial revolution, innovation has been viewed as one of the primary production variables, along with land, labor, capital, and entrepreneurship, to help address current and future difficulties facing humanity. This study aimed to shed light on the connections between innovation and sustainable development. To test Hypothesis H1, which states a positive solid relationship between the SDG Index and ISO 9001 Index, we conducted a statistical analysis using regressive analysis between the Sustainable Development Goals Index and Innovation Index. This was done to compare the results to Hypothesis H0, which suggests no such relationship exists. The research's findings indicate that scientific management of the factors of production opens up possibilities for long-term sustainable development, ensuring the prosperity of society and everyday life for future generations, encouraging economic growth, and improving the quality of life without endangering the environment. Innovation, embodied in the ISO 56000 family of standards, is applied as an efficient and effective tool, which is urgently needed. The overall conclusion of the study – which also serves as a practical and social contribution to the field – is that, to achieve and sustain sustainable development scenarios, all interested parties – individuals, public and private institutions, decision-makers, and civil society – should look forward to ensuring that the SDG and innovation are built and maintained. Innovation principles can be applied as effective and efficient tools.

High Output Power Holmium-Doped Fiber Laser at 2100 nm

A theoretical model of three levels describing Holmium-doped fiber lasers pumped by Laser-diodes 1150nm is present. Based on the model, efficiency as well as output power depend on the length of active media, are investigate, using the MATLAB program (R 2019 a). The results shows that output power and efficiency of optical fibers are exponential inverse relationship with increment fiber length, for 1m output power have highest value 100.4W, while efficiency have 44.6% at 0.05m.

Experimental study on the mechanical characteristics of a novel high-strength-and-high-toughness steel

To effectively control large deformation disasters, our team has developed a novel high-strength and high-toughness (HSHT) steel. This study aims to conduct a comparative analysis of the mechanical properties of HSHT steel and typical commercial steel under tension and impact. Testing was carried out using a universal testing machine and a self-developed drop-hammer-type longitudinal impact dynamic mechanical tester, with dynamic axial force sensors and infrared equipment utilized for monitoring. The results of the experiments are as follows: In the tensile test, HSHT steel exhibited superior performance in terms of tensile strength, elongation, and uniform deformation, particularly in radial deformation. The strength-ductility product of HSHT steel was more than two times that of typical commercial steel, indicating better energy-absorbing properties. Infrared data analysis showed that HSHT steel bars displayed uniform warming throughout their entire length. In the impact test, HSHT steel reinforcement demonstrated higher mechanical properties compared to commercial steel. Following failure, HSHT steel bars did not exhibit significant necking at the fracture site and showed a larger area of impact deformation. The axial forces experienced by the different steel bars were similar under various conditions. Data fitting analysis revealed an exponential relationship between the static tensile maximum strains of all bar types and the number of cyclic impacts. For HSHT steel bars, the number of impacts was also exponentially related to displacement, cyclic height, and energy absorbed prior to failure. Additionally, HSHT bars exhibited better uniform heating characteristics during cyclic impacts, with higher heating temperatures compared to typical commercial steels.

Quantitative response of the spatial distribution of diesel oil to freezing and thawing temperatures in groundwater

The mobilization and redistribution of organic contaminants in groundwater is the basis and key to explore its dynamic evolution and appropriate remediation. The naturally occurring diametrical temperature gradient during freezing and thawing cycle leads to distinct behaviors of organic contaminants in groundwater. In this study, the pore-scale distribution of diesel oil in the porous media was quantitatively divided into capillary fluid state (CFS) and free fluid state (FFS) based on multiphase flow dynamics, employing low-field nuclear magnetic resonance (LF-NMR) technology. The pore-scale distribution of diesel oil depends not only on the freezing and thawing cycle but also on the temperature gradient according to LF-NMR results. The content of diesel oil in the CFS generally increases with a positive temperature gradient (e.g. freezing) compared to a negative temperature gradient (e.g. thawing), while the content of diesel oil in the FFS generally decreases. This dependence of the temperature gradient on pore-scale distribution of the diesel oil is positively correlated with the particle size of the porous medium. Furthermore, the pore-scale distribution of the diesel oil during the freezing and thawing cycle is influenced by the kinematic viscosity of the diesel oil. There is an exponential relationship between the diesel oil content and the kinematic viscosity, independent of the freezing or thawing process. During the freezing process, the diesel oil migrates from FFS to CFS, while this migration is reversed during the thawing process. The reverse migration of the diesel oil between the freezing and thawing processes leads to a spatial redistribution of the diesel oil, which is controlled by both the fluid energy and the capillary force. The present work provide meaningful guidance for the remediation of groundwater contamination in cold regions.

Lymphocyte radiosensitivity: An extension to the linear-quadratic model?

Background and purposeThe linear-quadratic (LQ) model has been pivotal for evaluating the effects of radiation on cells, but it is primarily characterized by linear responses, which has exhibited limitations when applied to lymphocyte data. The present research aims to address these limitations and to explore an alternative model extended from the conventional LQ model. Materials and methodsLiterature providing lymphocyte counts from assays investigating apoptosis and survival after in vitro irradiation was selected. To address the nonlinearity in lymphocyte responses to radiation, we developed a saturation model characterized by a negative exponential relationship between radiation dose and cellular response. We compared the performance of this saturation model against that of conventional models, including the LQ model and its variants (linear model LM and linear-quadratic-cubic model LQC), as well as the repair-misrepair (RMR) model. The models were evaluated based on prediction-residual plots, residual standard errors, and the Akaike information criterion (AIC). We applied the saturation model to two additional datasets: (1) a dataset from the existing literature that assessed stimulated and unstimulated human lymphocytes exposed to gamma irradiation in vitro and (2) a novel dataset involving T lymphocytes from rodent spleens after exposure to various radiation types (X-rays and protons). ResultsThe literature (n = 15 out of 2342) showed that lymphocyte apoptosis varies with dose, time and experimental conditions. The saturation model had a lower AIC of 718 compared to the LM, LQ, LQC and RMR models (AIC of 728, 720, 720 and 734, respectively). The saturation model had a lower residual error and more consistent error distribution. Integrating time as a covariate, the saturation model also had a better AIC for demonstrating time-dependent variations in lymphocyte responses after irradiation. For datasets involving unstimulated lymphocytes before irradiation, the saturation model provided a more accurate fit than did the LM, LQ, and RMR models. In these cases, the fit of the saturation model was comparable to that of the LQC model but offered an advantage when extrapolating to higher doses, where the LQC model might underestimate survival. For stimulated lymphocytes, which are radioresistant, all the models approximated the LM. Both the LQ and saturation models indicated greater radiosensitivity to protons in vitro. ConclusionThe new “saturation model” performed better than the LQ model in quantifying lymphocyte apoptosis and survival, estimating time dependency and assessing the role of radiation modalities or lymphocyte stimulation. Further experiments are warranted to experimentally explore the validity of the saturation model as a promising alternative in the clinical setting.

A parametric optimization framework for fin-and-tube heat exchangers based on response surface methodology and artificial intelligence

This study presents a numerical investigation and provides a novel framework for the rapid parametric optimization of attack angles (α) and aspect ratios (e) in plate fin-and-tube heat exchangers (PFTHEs) featuring elliptical tubes. The methodology incorporates three-dimensional numerical simulations, response surface methodology (RSM), backpropagation neural network (BPNN), and Entropy-VIKOR. The study focuses on a PFTHE with a single elliptical tube, varying the attack angles (α) from −30° to 0° in 5° increments and the aspect ratios (e) from 0.4 to 1.0 in a step of 0.1. Air velocities (u) range from 0.4 to 3.2 m/s with an interval of 0.2 m/s, corresponding Reynolds number from 200 to 2200. The results indicate that using elliptical tubes reduces Δp and enhances heat transfer capacity, with the most significant improvements at an e of 0.4. Exponential relationships between dimensionless parameters Nu or f and Re are established for different range of α at specific e values. The synergistic effect of e, α, and Re or u on PFTHE performance is confirmed through RSM and BPNN analysis. Their R2 values are no less than 0.896 and reach a maximum of 0.998, indicating excellent predictive accuracy. Utilizing Entropy-VIKOR method, the framework identifies a suitable design solution with e = 0.6, α = -20°, and u = 3.2 m/s. This solution exhibits a 5 % increase in h and a 58 % reduction in Δp relative to the corresponding circular tube. The study provides specific expressions relating design variables to thermal–hydraulic behavior and indicates carefully selecting the α and e can improve the overall performance. In summary, these findings have significant implications for reducing optimization design period for PFTHEs with small tube diameters.

Normal spectral emissivity measurement study of high-temperature alloy (316L) at 673–1273 K with a thermal oxidation surface

One effective approach to better understanding the performance characteristics of high-temperature alloys is to study their thermal oxidation behavior, and to accurately determine their spectral emissivity is helpful for increasing the accuracy of temperature measurements. Using a self-developed high-temperature emissivity testing system, the normal spectral emissivity across the range 673–1273 K and a spectral band of 1–14 μm was measured relative to this background radiation. The normal spectral emissivity of 316L high-temperature alloy was investigated during the thermal oxidation process. The change in emissivity of 316L high-temperature alloy during thermal oxidation was observed. The emissivity of the 316L high-temperature alloy undergoes great changes during thermal oxidation; for example, at 1273 K it was 0.055 in its un-oxidized state but after 50 h’ thermal oxidation went up to 0.829. Below 1073 K the emissivity of 316L high-temperature alloy in 8–14 μm range showed little change, making it ideal for radiation thermometry. By fitting the measurement data, we derived that the emissivity of 316L high-temperature alloy has an exponential relationship with thermal oxidation temperature, and is a power function relationship with thermal oxidation time.

Aridity regulates the impacts of multiple dimensional plant diversity on soil properties in the drylands of northern China

Relationships between plant diversity and soil properties are important for restoring ecosystem function to adapt climate change in drylands. Taxonomic, functional and phylogenetic diversity are widely used for understanding community assembly and the responses of plant communities to environmental change. However, one dimension of diversity index is difficult to reflect the multiple dimensional plant diversity, and their effects on soil properties (i.e., moisture, nutrients, and texture characteristics) along aridity gradient in drylands are limitedly understood. In this study, we proposed a holistic biodiversity (HB) index to integrate all the characteristics of plant diversity, and investigated the relationships between plant diversity and soil properties across 41 sites along aridity gradient (from hyperarid to arid and semiarid levels) in drylands of northern China. The results showed that the taxonomic diversity and phylogenetic diversity increased significantly while most of functional diversity indices did not differ significantly along the aridity gradient. The functional diversity was more important than taxonomic and phylogenetic diversity to plant communities, and the importance of taxonomic and phylogenetic diversity varied greatly and inversely along the aridity gradient. The HB index could much better reflect the positive or negative exponential relationships with soil properties compared to the single diversity index. Further, the aridity weakened the positive effects of plant diversity on several soil properties (including soil water content, soil organic carbon and soil total nitrogen), and indirectly strengthened the accumulation of soil total phosphorus, as well as intensified the soil coarsening by limiting the negative effects of plant diversity on soil sand content. Our findings suggest that the holistic biodiversity index can represent the overall traits of plant diversity in drylands, and guide a further step to understand the role of plant diversity in plant-soil relationships of dryland ecosystems.

A Novel Method for Estimating the Undrained Shear Strength of Marine Soil Based on CPTU Tests

The undrained shear strength is an essential parameter in the foundation design of marine structures. Due to the complex marine environment and technical limitations, it is difficult and costly to obtain offshore samples. Piezocone penetration tests (CPTU) are relatively low-cost compared to drilling and sampling methods. Therefore, based on the soil behavior type index (Ic) derived from CPTU results, a model for estimating cone factors (Nkt, Nke) is proposed to improve the accuracy of estimation of undrained shear strength. The result shows that the soil behavior type index (Ic) and cone factors take on a negatively correlated exponential relation. Incorporating a cone factor that varies with the soil behavior type index (Ic) significantly enhances the accuracy of undrained shear strength predictions compared to the conventional method of using a constant cone factor. This approach reduces the root mean square error (RMSE) for Nkt (Nke) from 0.124 (0.126) MPa to 0.056 (0.06) MPa, and the mean absolute error (MAE) from 0.0154 (0.016) MPa to 0.0032 (0.0036) MPa. The method was validated at an additional location and the predictions were in high agreement with the results of the consolidated quick direct shear test. The developed method can serve as an effective tool used in the design of foundations of marine structures.

Enhanced humidity sensing performance of a triple-electrode ionization sensor utilizing carbon nanotubes

This paper introduces a novel ionization humidity sensor featuring a carbon nanotube triple-electrode design, aimed at achieving sensitivities of 381.67 %RH−1 in nitrogen and 11.83 %RH−1 in air, a detection ranges from 25.8 % RH to 100 % RH in nitrogen and 30 % RH to 100 % RH in air, and response times of 11 s and recovery times of 5 s. The sensor leverages the exponential relationship between collecting current and relative humidity, enhanced by the exceptional adsorption properties of CNTs, particularly their large surface area which allows for efficient water molecule attraction, to offer superior performance across diverse detection environments. Two structural configurations are proposed to optimize the sensor’s efficiency: one integrating carbon nanotubes directly onto the cathode and another utilizing a silicon strip as a substrate for CNT growth. The design’s effectiveness is further validated through simulations that calculate electron distribution, positive ion concentration, and collected current, highlighting the sensor’s potential for high-precision humidity detection in real-world applications.

Echo characteristics of pulsed lasers in non-uniform smoke environments

This work establishes a pulsed laser backscattering echo signal model based on an improved semi-analytical Monte Carlo method. The developed model is applied in non-uniform smoke environments to mitigate the smoke interference of laser fuzes for ground proximity detection. The model considers variations of the photon step size according to the concentration of the smoke environment, and the computational speed is accelerated by implementing an improved semi-analytical reception method. The proposed echo signal model is employed to investigate the effects of smoke-related parameters and laser detection system parameters on the backscattering echo waveform of smoke. Finally, the model is validated based on experiments. The results show that the intensity of the smoke backscattering echo and the emission pulse width approximately conform to a logarithmic relationship. Specifically, the echo intensity is positively correlated with the emission pulse width, and the ratio of the time between the rising edge and the falling edge of the echo signal is positively correlated with the pulse width. Meanwhile, the intensity of the smoke backscattering echo and the distance between the transmitter and receiver approximately adopt an exponential relationship. Herein, we describe the characteristics of a laser backscattering echo in a non-uniform smoke environment. The results can guide future research regarding laser fuze detection methods and strategies relevant for ground targets in smoke environments.

INVESTIGATION OF THE EFFECT OF GEOMETRIC IRREGULARITIES ON CAPACITY OF TRAFFIC CIRCLES BY USING PARTIAL LEAST SQUARE REGRESSION METHOD

This paper examined the impact of geometric irregularities on the intersection capacity at traffic circles. A new empirical capacity relation was proposed to predict the capacity of the traffic circle as a function of geometric elements, exit and circulating flows. Within this scope, firstly, the relationship between the vehicles entering from the minor approach and the circulating flow from the turning movement in the traffic circle was examined based on the K-Means cluster analysis method. The analysis was created in accordance with an exponential relationship between entry and circulating flow. Secondly, two clusters were selected by the partial least squares regression method to improve the model's effectiveness. Lastly, to validate the model, "leave-one-out" cross validation was used to select the components that maximize the model's predictive ability. The results show that geometric parameters of a traffic circle create different effects on capacity, especially in different circulating flow conditions.