Critical Contact Area Research Articles

Deformation Control Technology of Gob-Side Entry Retaining with Large Volume CFST Roadway Side Support in Top-Coal Caving Longwall and Stability Analysis: A Case Study

Considering the factors affecting the surrounding rock stability of gob-side entry retaining, the applicability of a large-diameter, concrete-filled steel tube roadside support body in a top-coal caving fully mechanized face is discussed, and a new approach to gob-side entry retaining is proposed in this study. The mechanical model of the surrounding rock structure of gob-side entry retaining in a top-coal caving fully mechanized face was established, the critical state of column–roof contact shear slip instability was clarified through Prandtl foundation failure theory, and the deformation mechanism of the surrounding rock of the retained roadway was analyzed through numerical simulation. The results indicated that the range of the tensile stress zone and extreme tensile stress of the roof between columns are closely related to the spacing of columns, which is the key factor influencing the deformation of the retained roadway. In addition, besides uncontrollable factors, the stability of the contact interface between the roof and columns is directly related to the area of the contact interface between the concrete-filled steel tubes and the roof, and the size of the critical contact area is directly related to the properties of top-coal mass. Finally, a field test was carried out in 91–101 working panels in the Wang-Zhuang Coal Mine; the maximum convergence of the roof and floor was 510 mm, and the area of the retained roadway section reached 12.9 m2, which is within a reasonable range.

Determining the patterns of extinguishing polar flammable liquids with a film-forming foaming agent

An issue related to the use of foaming agents to extinguish fires involving flammable liquids is to ensure the efficiency of vapor insulation of flammable liquid and the foam stability during operation. Therefore, the object of research was a change in the insulating properties of the foaming agent film when interacting with a polar combustible substance. It has been proven that the presence of foaming agent on a flammable liquid leads to the formation of an insulating film on the surface resistant to the combustion temperature of the liquid, due to which re-ignition shifts towards longer time. A film of foaming agent was formed on the surface of the flammable liquid by leaking from the screen, which led to the insulation of the surface. The measured contact area of the foaming film with the electrode was more than 6.2·10-3 m2, which indicates the formation of a barrier for temperature, which collapses over time. According to experimental data on changes in electrical resistance, the critical contact area of the foaming film with the electrode was calculated, at which the film is destroyed. Based on the derived dependences, the change in the process of mass transfer of the foaming film to a flammable liquid was calculated, equal to about 800 s. The maximum possible mass transfer of the foaming agent into the flammable liquid and the reduction of insulation capacity were evaluated. The peculiarities of foam supply to the surface of alcohol through the screen are that the quenching time was about 156 s while the critical intensity of the supply of the working solution of the foaming agent was 0.054 dm3/(m2·s). And the time interval before re-ignition was about 470 s, which is enough to cool the fire site. Thus, there is reason to assert the possibility of targeted control over the processes of extinguishing polar flammable liquids with a foaming agent

Investigation on the Behavior of Bridge Piers Considering Rocking Isolation Constructed on Non-plastic Silts and Sands Using 1g Shaking Table Tests

Occurred damages on the bridge piers during earthquakes lead to significant financial losses worldwide every year and can cause social problems by disrupting traffic flow and transportation services. Rocking isolation of foundations is one of the damage reduction approaches to avoid structural damage on piers by transferring plastic hinges from piers to underlying soil media. The behavior of rocking foundations on non-plastic silts has not been investigated well until now in the literature. In this research, the characteristic seismic behavior of a bridge pier considering rocking isolation is evaluated using small-scale physical modeling tests. To this aim, eight shaking table tests (with sinusoidal excitations) are conducted where both sandy and silty materials are employed as the soil media. In addition to the effects of the underlying soil, the effects of the critical contact area ratio of the foundation and frequency of input motions are evaluated. Achieved results indicate that the considered bridge pier shows the same behavior trend for underlying silty soil and sandy one. However, because of the frequency-dependent behavior of non-plastic silty soil, the pier attracts lower accelerations and higher moments. Therefore, the achieved results show that the proposed design approaches of rocking foundations that are mostly extracted based on experimental studies on sands (or rarely on clay) can lead to non-conservative designs in silty soils.

Prediction of foundation stiffness and damping ratio under horizontal translation and rocking motion

In this paper, the results of snapback, cyclic and forced-vibration tests performed by laboratory and full-scale facilities are collected and analysed to investigate the nonlinear response of shallow foundations. The outcomes of tests on a full-scale soil-foundation-structure prototype, performed during the EU-research project SISIFO, were exploited to fill the lack of data on foundation damping and stiffness associated with the translation motion and enrich the database relevant to low-amplitude rocking motion. Predictive equations are calibrated to estimate the nonlinear variation of the foundation stiffness and damping ratio with the increasing amplitude of the foundation translation and rocking motions. In the latter case, the availability of numerous experimental data allows differentiating the predictive damping equation according to the so-called ‘critical foundation-soil contact area’, which is the most influencing factor on the energy dissipation capacity of the foundation. To prove the reliability of the proposed approach, two different applications with an increasing level of complexity are discussed. First, simplified analytical formulas are employed to calculate the fundamental period and damping ratio of the prototype tested during the SISIFO project. Then, a flexible-base model of the same structure is calibrated to simulate the experimental forced-vibration tests. The outcomes of both applications successfully match the experimental measurements.

Research on pipeline connection structure of microwave load water-cooling system for spacecraft thermal test

The microwave load water-cooling system was operated in a vacuum cold black environment, and the pressure difference between the inside and outside of the water pipe could reach 0.3 to 0.4 MPa. To ensure the tightness of the water pipe, a conical seal structure was selected, the macro-static model and micro-boundary element contact model were established for the two forms with and without the Viton seal. The macro model simulation was performed by the finite element method to obtain the stress distribution inside the conical structure under different preload stress, the relationship between the contact pressure of the conical sealing interface and the contact area of the O-ring sealing interface as a function of preload stress; the method was used to calculate the micro-contact model, and the critical contact pressure and contact area to achieve the sealing requirements were obtained respectively without Viton seal and with Viton seal. As a result, a conical seal structure with a Viton seal was finally chosen for application. After verification, the structure meets the requirements for the use of microwave load water-cooling systems during the vacuum thermal test.

Data-Driven Modeling of Peak Rotation and Tipping-Over Stability of Rocking Shallow Foundations Using Machine Learning Algorithms

The objective of this study is to develop data-driven predictive models for peak rotation and factor of safety for tipping-over failure of rocking shallow foundations during earthquake loading using multiple nonlinear machine learning (ML) algorithms and a supervised learning technique. Centrifuge and shaking table experimental results on rocking foundations have been used for the development of k-nearest neighbors regression (KNN), support vector regression (SVR), and random forest regression (RFR) models. The input features to ML models include critical contact area ratio of foundation; slenderness ratio and rocking coefficient of rocking system; peak ground acceleration and Arias intensity of earthquake motion; and a categorical binary feature that separates sandy soil foundations from clayey soil foundations. Based on repeated k-fold cross validation tests of models, we found that the overall average mean absolute percentage errors (MAPE) in predictions of all three nonlinear ML models varied between 0.46 and 0.60, outperforming a baseline multivariate linear regression ML model with corresponding MAPE of 0.68 to 0.75. The input feature importance analysis reveals that the peak rotation and tipping-over stability of rocking foundations are more sensitive to ground motion demand parameters than to rocking foundation capacity parameters or type of soil.

Modeling of Seismic Energy Dissipation of Rocking Foundations Using Nonparametric Machine Learning Algorithms

The objective of this study is to develop data-driven predictive models for seismic energy dissipation of rocking shallow foundations during earthquake loading using multiple machine learning (ML) algorithms and experimental data from a rocking foundations database. Three nonlinear, nonparametric ML algorithms are considered: k-nearest neighbors regression (KNN), support vector regression (SVR) and decision tree regression (DTR). The input features to ML algorithms include critical contact area ratio, slenderness ratio and rocking coefficient of rocking system, and peak ground acceleration and Arias intensity of earthquake motion. A randomly split pair of training and testing datasets is used for initial evaluation of the models and hyperparameter tuning. Repeated k-fold cross validation technique is used to further evaluate the performance of ML models in terms of bias and variance using mean absolute percentage error. It is found that all three ML models perform better than multivariate linear regression model, and that both KNN and SVR models consistently outperform DTR model. On average, the accuracy of KNN model is about 16% higher than that of SVR model, while the variance of SVR model is about 27% smaller than that of KNN model, making them both excellent candidates for modeling the problem considered.

Application of machine learning algorithms to performance prediction of rocking shallow foundations during earthquake loading

The objective of this research is to develop preliminary predictive models for the performance of rocking shallow foundations using machine learning algorithms and supervised learning technique. Data from a rocking foundation database, consisting of dynamic base shaking experiments conducted on centrifuges and shaking tables, have been used for the development of multivariate linear regression (MLR) model using stochastic gradient descent optimization and distance-weighted k-nearest neighbors (k-NN) regression model. Seismic energy dissipation in soil, permanent settlement of foundation, and the maximum acceleration transmitted to the structure are considered as the performance parameters of rocking foundations, while the input features to machine learning algorithms include critical contact area ratio and rocking coefficient of soil-foundation system, and peak ground acceleration and Arias intensity of earthquake ground motion. It is found that both MLR and weighted k-NN models perform satisfactorily in capturing the complex relationships between the performance parameters and input features of rocking foundations, and that both models perform better than simple statistical models. Based on multiple k-fold cross validation tests across all performance parameters and the mean absolute percentage errors, it is found that the weighted k-NN model consistently outperforms the MLR model in terms of accuracy for the problem considered.

A revised contact stiffness model of rough curved surfaces based on the length scale

Based on the continuity of length scale for asperities, a complete model of normal stiffness between curved fractal surfaces considering friction factor is proposed. Through the coupling of critical base diameter and contact area, deformation modes of all asperities are determined, and contact stiffness of the whole rough surface is derived by double integral. Accordingly, effects of contact load, surface topography, friction factor, size parameters and material properties on the contact stiffness are investigated. Results show that contact stiffness depends sensitively on the fractal dimension, and exhibits nonmonotonic characteristics as fractal roughness varies across scales. Finally, predicted values of normal stiffness are compared with existing contact models as well as experimental data.

A Stiffness Model for Bolted Joints Considering Asperity Interactions of Rough Surface Contact

Abstract A revised fractal contact model considering asperity interactions is proposed. The displacement of the mean of asperity heights is used to represent the effects of the asperity interactions. Then, the critical contact area will be dependent on the contact load, and the contact stiffness will be an integral whose integrand is an implicit expression. The fractal dimension and the fractal roughness are obtained by the measurement of the surface profile to calculate the theoretical contact stiffness. The measurement of deformation is conducted to obtain the actual contact stiffness for verification, and the results show that the proposed model is closer to the experimental results than other models without considering asperity interactions. Once the contact stiffness is determined, a new equivalent normal stiffness model for bolted joints considering the contact of two rough surfaces is also proposed. Since the contact stiffness is dependent on the clamped force, the equivalent normal stiffness for bolted joints is calculated iteratively at given initial preload and external separating force. Different from the classical model, the equivalent normal stiffness for bolted joint decreases with the external separating force increases, and this stiffness loss will become larger with initial preload decreases. In this sense, the proposed equivalent normal stiffness model is a way to determine the suitable initial preload for different sizes of bolts when the stiffness loss is restricted to a certain range.

Percolation and Reynolds Flow in Elastic Contacts of Isotropic and Anisotropic, Randomly Rough Surfaces

In this work, we numerically study the elastic contact between isotropic and anisotropic, rigid, randomly rough surfaces and linearly elastic counterfaces as well as the subsequent Reynolds flow through the gap between the two contacting solids. We find the percolation threshold to depend on the fluid flow direction when the Peklenik number indicates anisotropy unless the system size clearly exceeds the roll-off wave length parallel to the easy flow direction. A critical contact area near 0.415 is confirmed. Heuristically corrected effective-medium treatments satisfactorily provide Reynolds fluid flow conductances, e.g., for isotropic roughness, we identify accurate closed-form expressions, which only depend on the mean gap and the relative contact area.Graphic

Effects of rocking coefficient and critical contact area ratio on the performance of rocking foundations from centrifuge and shake table experimental results

The major objective of this study is to correlate rocking foundation performance parameters with their capacity parameters and earthquake demand parameters using results obtained from 142 centrifuge and shaking table experiments, which include a variety of soil conditions, foundation geometries, structural models, and types of ground motions. The analysis presented in this paper considers all experimental results together, collectively as big data, through nondimensional parameters to identify hidden relationships among different parameters in a capacity-demand-performance framework. Rocking system performance parameters such as seismic energy dissipation in soil, permanent settlement, peak and permanent rotation, tipping-over stability ratio, self-centering ratio, rocking moment capacity, and acceleration amplification ratio are correlated with rocking system capacity parameters such as critical contact area ratio, rocking coefficient, and slenderness ratio of rocking systems and the earthquake demand parameters such as Arias intensity and peak ground acceleration of earthquake. It is found that energy dissipation and settlement correlate reasonably well with rocking coefficient and Arias intensity of earthquake, while peak rotation and acceleration amplification ratio correlate reasonably well with slenderness ratio, rocking coefficient, and peak ground acceleration of earthquake. Rocking foundations in clayey soils show superior performance in terms of seismic energy dissipation and permanent settlement compared to those in sandy soils, especially for relatively small to medium intensity shakings, and the ability of rocking foundations to de-amplify the earthquake motion increases as the magnitude of shaking increases.

Research on the loading–unloading fractal contact model between two three-dimensional spherical rough surfaces with regard to friction

A loading–unloading fractal contact model between two three-dimensional spherical rough surfaces with regard to friction is developed. The contact model of single asperity for the load–unload cycle with regard to friction is obtained. The expressions between contact load and real contact area in the loading and unloading processes in different deformation stages of three-dimensional spherical contact surfaces are deduced. The impacts of some parameters in the model are discussed by numerical analysis. The numerical results show that the critical contact load and the critical real contact area in different deformation stages of spherical contact surfaces with friction are positively related to the fractal dimension and the curvature radius, negatively correlated with the fractal roughness, influenced by the contact type. In the elastoplastic stage of spherical contact surfaces with friction, the real contact area in the unloading process is larger than that in the loading process with the same contact load; for a given contact load, the real contact area of the loading–unloading process, as well as the differences of the real contact area in the loading–unloading processes, increases with the increase in the fractal dimension and the curvature radius, decrease in the fractal roughness, or the substitution of internal contact for external contact.

Effects of loading obliquity on field performance of rocking shallow foundations in cohesive soil

This paper presents a field study of obliquely loaded rocking shallow foundations resting on cohesive soil. Lateral snap-back and cyclic loading tests at an oblique angle of 45° with respect to the footing axes were carried out. During the snap-back tests, an initial drift ratio was applied to the deck and then the system was released to enable the free vibration. The cyclic loading consisted of five packets containing three to four cycles of similar displacement amplitude. The rocking system consisted of a 1·5 m by 1·0 m concrete footing, steel column and deck. The factors of safety against bearing failure were varied from 4 to 20. It was observed that the system primarily rocked in plane. The moment capacities about footing axes deviated from the calculated values at the orthogonal loading conditions. A method of estimating the rocking moment capacity of a footing subjected to oblique loading was developed and validated by the tests. Natural periods, damping ratio, re-centring ratio, settlement and stiffness degradation during the tests are discussed and compared with the results from previous studies with orthogonal loading. The soil–footing contact area was approximately triangular. A method of calculating the critical contact area was developed based on the bearing capacity theory with two-way eccentricity and then confirmed by observation.

Normal contact stiffness of rough surfaces considering oblique asperity contact

The contact stiffness of the machined surface has an important effect on the performance of the complex mechanical product. A modified fractal model based on oblique asperity contact is proposed in this research. First, the contact radius and the critical contact area are analyzed based on oblique contact condition. The normal contact stiffness and elastic–plastic force are calculated. The ratio of the actual contact area and a new parameter related to the current contact angle are introduced. Second, numerical simulations indicate the difference. The results show that the stiffness of the oblique contact is smaller, and with the increment of the fractal dimension, the extent of the stiffness reduction is larger. In contrast, the uniform distribution has the lower proportion of the elastic force in the total normal contact force. Finally, experiments including specimen surface observation and load-deformation measurement are utilized to obtain contact stiffness of the machined surface. To some extent, the modified fractal stiffness model is more reasonable and accurate from the result.

Critical shoe contact area ratio for sliding on a tennis hard court

Dimples have been used in the design of some modern tennis shoe outsoles to enhance sliding ability on hard courts. Experiments were performed with bespoke rubber samples possessing various numbers of holes, which served to simulate dimples in tennis shoe treads. The aim of the research was to assess the effect of contact area on sliding friction. As the ratio of holes to solid rubber increased, a critical ratio was reached whereby the static friction coefficient decreased by more than 11% for tread-to-court pressures comparable to real tennis play. Although this study analyzed bespoke rubber samples and not actual tennis shoe treads, shoe manufacturers should be interested in the existence of a critical dimple ratio that could aid them in the creation of tennis shoes suited for sliding on hard courts.

Macroparticle generation in DC arc discharge from a WC cathode

We have studied macroparticle generation from a tungsten carbide cathode used in a dc vacuum arc discharge. Despite a relatively high decomposition/melting point (∼3100 K), there is an intensive generation of visible particles with sizes in the range 20–35 μm. Visual observations during the discharge and scanning electron microscopy of the cathode surface and of collected macroparticles indicate a new mechanism for particle formation and acceleration. Based on the W-C phase diagram, there is an intensive sublimation of carbon from the melt resulting from the cathode spot. The sublimation supports the formation of a sphere, which is accelerated upon an explosion initiated by Joule heating at the critical contact area between the sphere and the cathode body. The explosive nature of the particle acceleration is confirmed by surface features resembling the remains of a splash on the droplet surface.

Elastoplastic contact mechanics model of rough surface based on fractal theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ϕ, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.

Rolling–sliding contact fatigue of surfaces with sinusoidal roughness

Surfaces of mechanical components under combined rolling and sliding motions may be subjected to accelerated contact fatigue failure due to increased number of microscopic stress cycles and pressure peak heights caused by rough-surface asperity contacts. Available rolling contact fatigue (RCF) theories were developed mainly for rolling element bearings, for which the effect of sliding is usually insignificant. In various types of gears, however, considerable sliding exist in the critical tooth contact area below the pitch line, where excessive wear and severe pitting failures originate. Ignorance of sliding is most likely the reason why the conventional RCF models often overestimate gear fatigue life. This paper studies the effect of sliding motion on the contact fatigue life of surfaces with sinusoidal roughness that mimicks the topography from certain manufacturing processes. A set of simple equations for stress cycle counting is derived. Mixed elastohydrodynamic lubrication simulations are executed with the considerations of normal loading and frictional shear. Relative fatigue life evaluations based on a subsurface stress analysis is conducted, taking into account the two sliding-induced mechanisms, which are the greatly increased number of stress cycles and the pressure peak heights due to surface interactions. Obtained results indicate that sliding leads to a significant reduction of contact fatigue life, and rough surface asperity contacts result in accelerated pitting failure that needs to be considered in life predictions for various mechanical components.

Yield inception of a soft coating on a flat substrate indented by a rigid sphere

The yield inception of a deformable half space covered by a soft coating and indented by a rigid sphere is studied using the finite element method. A soft coating parameter, which controls the yield behavior of this problem, is defined. Dimensionless empirical expressions for the critical load, critical contact area and critical interference at yield inception are derived as functions of the dimensionless soft coating parameter. Three different locations of the yield inception of the coated system are observed. A comparison of yield inception behavior for an uncoated substrate and substrates with soft and hard coatings is made. A minimum value of dimensionless coating thickness, which is required to protect the substrate from yielding, is proposed. It is shown that a coating with low Young's modulus and high yield strength is most desirable for protecting the substrate against yielding.