Janssen Model Research Articles

Acoustics response of granular porous material: experiment and modeling

Granular porous materials such as activated carbon have drawn increasing attention due to their good sound absorption performance at low frequency. However, some unique acoustical behaviors have been observed during sound absorption measurements of granular porous materials in impedance tubes: e.g., circumferential edge-constraint effects, level-dependent absorption behavior, and time-dependent absorption behavior. In order to explain these observations, a 1-dimensional poro-elastic model was first applied to describe the sound propagation in granules stacked in a cylindrical sample holder, as in a standing wave tube. Then this model was extended to a 2-dimensional finite difference (2DFD) model with depth-dependent stiffness of the granule stack considered by combining Janssen's model and Hertzian contact theory. The 2DFD model was validated with the measurements of the granular porous materials, and it was found that the 2DFD model is a powerful tool to analyze the acoustic response of granular porous material, thus providing a means of characterizing the granular materials. In the present work, the above-mentioned experimental observations and the 2DFD model are introduced, and the experiment results are analyzed with the 2DFD model. Finally some future work on granular porous materials is introduced.

Methodological problems of friction force measurement of plant granular materials

The methodology for measuring the frictional force of granular materials of plant origin is complex, since it requires taking into account both variable material factors and the use of available measurement methods in an appropriate way. This article deals with one of the important aspects of the application of a measurement methodology using bottomless containers. The effect of grain pressure on the side walls of the measuring container on the value of grain pressure on the measuring surface was studied. Five different granular materials (wheat, oat, beans, maize, peas) were used as the research material. To analyse the problem, the Janssen model was used as a basis, which describes the normal pressure of the granular material at the bottom of the container depending on certain factors. The tests were carried out for different heights of the material layer and different load values. After analysing the measurement values with calculated values, modifications of the base model were proposed. This modification allowed a high (close to 1) model fit to the measured values. The proposed approach can be useful in carrying out measurements of the friction force of granular materials, since it allows one to estimate the value of the actual pressure of the material on the contact surface. This provides an opportunity to make better use of the horizontal tribometer with a measuring container with support.

Validating a predictive model for caesarean section in low-risk nulliparous pregnancies

ProblemCaesarean birth (CS) rates are steadily increasing. BackgroundIn 2017 Janssen et al. developed a model which could predict CB in nulliparous healthy woman with 71 % accuracy based on factors measurable on admission to the hospital. AimTo validate the predictive model for risk of caesarean birth among low-risk, nulliparous women in a new setting. MethodsA retrospective chart study in Abbotsford Regional Hospital (British Columbia, Canada) of healthy nulliparous women in spontaneous labour, at term, with a singleton fetus in cephalic position. Sociodemographic, pregnancy and labour-related characteristics were collected and independent predictors of CS were determined using multivariate logistic regression. The Janssen model was tested in the Abbotsford sample and additionally novel predictors were tested in an effort to improve the model. The area under the ROC curve (C-statistic) was computed and model calibration, sensitivity and specificity evaluated for the final model. Findings and discussionOf 348 women, 106 (30.5 %) had a CB. Applying the Janssen predictive model to the Abbotsford data resulted in a C-statistic of 0.77. No new predictors were added to the model. The mean predicted risk score for CS in the cohort was 0.30 ± 0.20. A risk score cut-off of 0.32 was determined resulting in a sensitivity and specificity of 69 %. The model had acceptable calibration. ConclusionA model with variables easily accessible at admission can predict caesarean birth in nulliparous women. The results from this study can guide provision of more intensive care during labour to women at higher risk, with the overall goal of reducing CB rates.

Experimental research and numerical simulation based on granary effect

Based on Janssen model and discrete element model, experiment and numerical simulation are used to verify the granary effect of coal storage silo in power plant. In the experiment, the bottom pressure of two different particles in a variable-diameter cylinder is measured. The type of particles and the diameter of the cylinder are used as the research objects to explore the function relationship between the bottom pressure of the cylinder and the particle filling quality. In the experiment with soybeans as filling particles, the granary effect is more obvious, and the smaller the cylinder diameter is, the more obvious the granary effect is. At the same time, establish a mathematical model of particles, simulation of particle accumulation process, solve the force information of particles. Through numerical simulation, it is found that the data is more in line with the Janssen model, and the granary effect is more obvious.

Exact solutions for Janssen effect of lattice disk packings

The rhombic lattice packing model proposed here clearly shows the micro causes of the Janssen effect and is solved analytically. Based on the analysis of force equilibrium equations with an exterior product method, a recurrence relation with a force transmission matrix Q is obtained which shows that a contact force will be transmitted and accumulated along the lattice vector direction and then be reflected by lateral walls, and eventually, reach a saturation value if the packing is frictional. A method based on tensor algebra and difference equation is proposed for the diagonalization of Q. Using roundup and remainder functions, we give the exact and approximate expressions which can describe the piecewise smoothness of the pressure function data given by numerical calculations. Numerical results also show the non-uniformity of pressure distribution. These quantitative results have certain deviations with Janssen model except for very small top load or large force reflectivity.

Study of Clogging Phenomenon for a Conical Hopper: The Influence of Particle Bed Height and Hopper Angle

The granular flow is one of the principal issues for the design of pebble bed reactors. Particularly, the clogging phenomenon raises an important issue for pebble bed reactors. In this paper, we conduct experiments and discrete particle simulation of two-dimensional discharge granular flow from a conical hopper, to study the effect of the particle bed height h and hopper angle α on the clogging phenomenon. In general, the clogging probability J increases with height h and starts to saturate when h is larger than a critical value. The experimental result trends are supported by discrete simulations. To understand the underlying physical mechanism, we conduct discrete particle simulations for various h values, focusing on the following parameters: the statistical averaging of the volume fraction, velocity, and contact pressure of particles near the aperture during the discharge. We found that, among all relevant variables, the contact pressure of particles is the main cause of the increasement of J when h increases. An exponential law between the pebble bed h and clogging probability J has been established based on these observations and Janssen model. As for hopper angle α , J shows an almost constant behavior for any rise in α followed by a sudden regression at α = 75 ° . Surprisingly, the effect of α is most obvious for intermediate values of h , where we observe a sharp increasement of clogging probability. The same trend is observed in the two-dimensional discrete simulation results.

Force change of the gravel side support during gangue heaping under a new non-pillar-mining approach

The force change characteristics of gravel side support structures during gangue heaping can provide useful information about roadway stability in a new non-pillar-mining approach—noncoal pillar mining with automatically formed gob-side entry (NMAFG). Considering the dynamic shock and static stacking phenomena during gangue heaping, the coefficient of restitution and Janssen model are introduced into the theoretical analysis. Analytical results show that the impact force decreased with increasing gangue heaping height under dynamic shock, while under static stacking, the gangue extrusion force first increased sharply, then increased slowly and stabilized, and the final force was unrelated to the gangue heaping height. Field monitoring was conducted to verify the rationality of the pattern obtained from theoretical analysis. The gangue support structure lateral stress from field monitoring can be divided into two periods. In Period I, the peak value at the lower monitoring point was greater than that at any other point. The lowest sensor was subjected to the greatest impact, at 59.09 kN. In Period II, the stress value first rapidly increased, then slowly increased and stabilized. The final force was unrelated to the gangue height. The sensors at #2 (highest position), #4 (middle position), and #6 (lowest position) measured 31.91 kN, 44.82 kN and 38.19 kN, respectively. The analysis confirmed the variation characteristics of the impact force and extrusion force.

Digital Image Correlation Based Internal Friction Characterization in Granular Materials

Based on the realization that Newtonian fluids have the unique property to redirect the forces applied to them in a perpendicular direction, a new apparatus, called the Granular Friction Analyzer (GFA), and the related GFA index, were proposed for characterizing the internal friction and related flow behavior of granular materials under uniaxial compression loading. The calculation of the GFA index is based on the integration of the internal pressure distribution along the cylinder wall, within which the granular material is being uniaxially compressed by a piston. In this paper an optical granular friction analyzer (O-GFA) is presented, where a digital image correlation (DIC) method is utilized to assess the cylinder strains used to calculate the internal pressure distribution. The main advantage of using the DIC method is that the starting point (piston–powder contact point) and the length of the integration considering the edge effects can be defined. By using the DIC full-field, instead of a few points strain measurements, a 2% improvement of the GFA index’s accuracy has been achieved and its robustness with respect to the number of points has been demonstrated. Using the parametric error analysis it has been shown that most of the observed total error (7.5%) arises from the DIC-method-based measurements of the strains, which can be improved by higher-resolution cameras and DIC algorithms for the strain evaluation. Additionally, it was shown that the GFA index can be used for determining the well-known Janssen model parameters. The latter was demonstrated experimentally, by testing three SS 316 L granular material samples with different mean particle sizes. The results confirm that the mean particle size regulates the internal friction of granular materials.

Janssen effect in dynamic particulate systems.

The Janssen model of stress redistribution within laterally bounded particulate assemblies is a longstanding and valuable theoretical framework, widely used in the design of industrial systems. However, the model relies on the assumption of a static packing of particles and has never been tested in a truly dynamic regime nor for a constraining system whose geometry is dynamically altered. In this paper, we explore the pressure distributions of granular beds housed within a container possessing a laterally mobile sidewall, allowing the depth, height, and cross-sectional areas of the systems studied to be dynamically altered, thus, inducing particle rearrangements and flow in the particulate system constrained thereby. We demonstrate that the systems studied can be successfully described by the Janssen model across a wide range of system expansion rates, including those for which liquidlike flow is clearly observed and propose an extension to the model allowing for an improved characterization of constrained dynamic systems.

Development and applications of a material library for pharmaceutical continuous manufacturing of solid dosage forms.

The purpose of this study is to establish a material library and discuss its potential application to the development and lifecycle management of a continuous manufacturing process for solid dosage forms. Particularly, this study addresses the importance of selecting process-relevant testing conditions for material characterization, proposes a methodology to capture relevant information with a reduced set of measurements, and correlates material properties with process performance. This study included 20 pharmaceutical materials, and each material was characterized by 44 properties, capturing 880 data points. The stress conditions of a commonly used feeder hopper were calculated using the Janssen model for six selected materials. Multivariate analysis, such as principal component analysis and clustering analysis, was used to explore the knowledge space of the material library. Statistically similar and dissimilar material properties were evaluated for material feeding performance from a loss-in-weight feeder to test utility of the material library. 20 materials included in this study show a wide range of material properties. Consolidation stress during testing significantly impacts obtained material properties. Based on a material similarity metric, a reduced set of characterization tests that captures >95% of the relevant information was identified. Materials were then grouped into six clusters. The material loss-in-weight feeding results show that the materials within the same cluster show similar feeding performance, while selected materials from different cluster have different feeding performance. Additional material understanding regarding flow properties may be needed to implement a continuous manufacturing process. Characterization using multiple tests under process-relevant conditions can be helpful to establish the correlation between material properties and process and product performance using multivariate analysis tools.

Stress distribution along sidewall of a granular column: Local fluctuation and global determination

Apparent mass on bottom and stress distributions along sidewall are studied experimentally for a silo prepared by pouring grains from a fixed height. Measurements of the apparent mass, a macroscopic property, are found to be deterministic and stable, reproducible for many experimental runs. The mesoscopic stress distribution, both normal and tangential to the wall, are measured with force detectors of several grain diameters. It fluctuates strongly from one experiment to another, and may also drift with time. The results show that the local fluctuations do not destroy the deterministic nature of a macroscopic property, and therefore supports a continuum mechanical description for the latter. The measured macro-scaled stresses on the silo wall do vary with preparations, indicating history effects that may be accounted for by applying the appropriate boundary conditions of the continuum mechanical theory. Statistical means of local stresses are also discussed in connection with the Janssen model.

Modeling and experimental investigation of drilling into lunar soils

Dry drilling only with the assistance of an auger is a reliable and realistic approach to remove abundant soils from the side of a bit in the harsh, dry conditions on the Moon. Based on an elementary analysis, using Janssen's model to reflect the coupling effect among the different components of the stress, the present paper models the conveying dynamics along the helical groove and the sampling mechanism in the centering hole of the stem for an auger drilling into lunar soil simulant. Combining the two parts as well as a simple cutting model for the bit, a whole drilling model is established to investigate the complicated relation among the conveying ability of the auger, the coring rate, and drilling parameters such as the penetration and rotation speeds. The relation is revealed by the complicated transition between different sub-models with the help of the physical transition conditions. A series of experiments with constant penetration and rotation speeds are conducted to verify the model. Three aspects of characteristics of the drilling dynamics are manifested, (ⅰ) the loads on the bit are almost independent of penetration; (ⅱ) three obvious drilling stages with respect to cut per revolution are grouped; (ⅲ) a linear relationship is found between the coring rate and the revolution per penetration.

Microscopic analyses of stress profile within confined granular assemblies

Bottom pressure of confined granular assemblies saturates at a certain value even this packing bed is being continuously charged. Corresponding formulation has been established to describe this interesting phenomenon. In this work, the influences of particle size and friction on the bottom stresses of granular matter were numerically investigated by discrete element method (DEM). It is found that the Janssen model can well predict the stress profile only when the size ratio of the container versus the particle is larger than 16. Moreover, a hydrostatic linear relation between apparent mass and filling mass can be obtained when the friction coefficient becomes insignificant (μ ≤ 0.01). To further interpret the Janssen effects, the granular assemblies are characterized and evaluated from the overall interactions with sidewalls, angular distribution function, void size distribution, coordination number, contact networks, contact orientation and distributions of contact forces within the packing structure. It is believed that these results will be helpful to comprehend the granular behaviors and may offer instructive reference to industrial processes in related fields.

Progressive friction mobilization and enhanced Janssen's screening in confined granular rafts

Confined two-dimensional assemblies of floating particles, known as granular rafts, are prone to develop a highly nonlinear response under compression. Here we investigate the transition to the friction-dominated jammed state and map the gradual development of the internal stress profile with flexible pressure sensors distributed along the raft surface. Surprisingly, we observe that the surface stress screening builds up much more slowly than previously thought and that the typical screening distance later dramatically decreases. We explain this behavior in terms of progressive friction mobilization, where the full amplitude of the frictional forces is only reached after a macroscopic local displacement. At further stages of compression, rafts of large length-to-width aspect ratio experience much stronger screenings than the full mobilization limit described by the Janssen's model. We solve this paradox using a simple mathematical analysis and show that such enhanced screening can be attributed to a localized compaction front, essentially shielding the far field from compressive stresses.

Stress distribution in two-dimensional silos.

Simulations of a polydispersed two-dimensional silo were performed using molecular dynamics, with different numbers of grains reaching up to 64 000, verifying numerically the model derived by Janssen and also the main assumption that the walls carry part of the weight due to the static friction between grains with themselves and those with the silo's walls. We vary the friction coefficient, the radii dispersity, the silo width, and the size of grains. We find that the Janssen's model becomes less relevant as the the silo width increases since the behavior of the stresses becomes more hydrostatic. Likewise, we get the normal and tangential stress distribution on the walls evidencing the existence of points of maximum stress. We also obtained the stress matrix with which we observe zones of concentration of load, located always at a height around two thirds of the granular columns. Finally, we observe that the size of the grains affects the distribution of stresses, increasing the weight on the bottom and reducing the normal stress on the walls, as the grains are made smaller (for the same total mass of the granulate), giving again a more hydrostatic and therefore less Janssen-type behavior for the weight of the column.

Method to Detect Granary Storage Weight Based on the Janssen Model

Abstract: This study proposes a new model of granary storage weight detection based on the Janssen model to satisfy the strategic requirements of granary storage quantity detection in China. The model theoretically elucidates the relationship between granary storage weight and bottom/side pressure. A new layout of pressure sensors along the inner and outer rings is also proposed to obtain the pressure value. The experimental results indicate that the detection error of the proposed model is significantly lower than 1% with respect to the low-cost detection system, and this effectively satisfies the actual requirement for real-time monitoring of granary storage quantity. Supported by Natural Science Project of Henan Provincial Science and Technology Department (172106000013); State Key Laboratory of Grain Information Processing and Control, Ministry of Education (KFJJ-2016-102); Grain Information Processing Technology of University Science and Technology Innovation Team in Henan Province (16IRTSTHN026)

DEM simulation on the vibrated packing densification of mono-sized equilateral cylindrical particles

The packing densification of mono-sized equilateral cylindrical particles under mechanical vibration is numerically reproduced using discrete element method (DEM). The influences of vibration frequency, amplitude and container size on the macro property (e.g. packing density) of each packing are studied. Meanwhile, various micro-properties including coordination number (CN), radial distribution function (RDF), local structures, contact types, particle position/orientation distributions, forces/stresses of the vibrated dense packing are characterized and compared with those of the loose initial poured packing. The results show that properly controlling vibration conditions can realize the transition of equilateral cylindrical particles from random loose packing (RLP) to random close packing (RCP). The maximum packing density without wall effects can reach about 0.7166, which agrees with experimental and numerical results in literature. Micro property analyses demonstrate that the average CN increases slightly after vibration. The RDF curves indicate three obvious peaks for both poured and vibrated packings. The distributions of intersection angles imply that the perpendicular arrangements of the cylindrical particles are common in both packing structures. From RLP to RCP, the probability of side-edge, bottom-edge and edge-edge contacts between two particles decreases, while that of side-side, side-bottom and bottom-bottom contacts increases. Both particle position and orientation distributions illustrate that the structure in the center of the vibrated packing is disordered. The distribution of strong forces follows the exponential law, while that of weak forces follows the power law. The static vertical stresses in both packings can be predicted by Janssen model. After vibration, a much denser and more stable structure with a larger saturation stress is obtained due to the reducing inter-particle friction effects.

Lattice model for pressure problems in two-dimensional granular columns

In order to make it easier to investigate some problems such as the mechanism of Janssen effect and the stress distribution in granular medium, we simplify a granular column into a lattice system, in which a lattice point represents a small lump of granular medium and only neighbor interactions are considered. To study the disordered granular columns, a force propagation lattice model determined by the absorption coefficient p and the lateral transfer coefficient q is proposed, and this model is analyzed from the theoretical view. Firstly, the equation of force propagation in the matrix form is given, and this equation is determined by a tridiagonal matrix A(p,q) that is called transfer coefficient matrix. Based on the force transfer equation, the bottom force distribution varying with the top force distribution and the layer of lattice system is deduced, and its analytical solution refers to the similarity diagonalization of matrix A(p, q). Then, a method based on the second order difference equations is proposed to obtain the eigenvalues and eigenvectors of the transfer coefficient matrix. The eigenvalues and eigenvectors of A(p, q) can be rigorously deduced for a typical case, and with these results the pressure distribution relationship between the top and the bottom of the container is given. Based on these theoretical expressions, the relationship between the effective mass and the total mass of granular medium is deduced, and it means that the force propagation model and the Janssen model can lead to similar results. Moreover, the bottom stress distribution is calculated without the top load. Calculations show that the stress distribution reaches a maximum at the center bottom and drops down to either side. Finally, numerical calculations are performed to investigate the effects of parameters p and q on the relation between bottom pressure and packing height. Numerical results show that the saturated value of pressure decreases while parameter p or q increases.

Deformation profiles of elastic cylindrical tubes filled with granular media under an overload

The deformation of a thin-walled vertical tube, filled with a liquid or a cohesionless granular material is investigated theoretically and experimentally. Experiments with an overload and without it were made with latex tubes filled with water or spherical glass beads and the results were compared with the theoretical profile derived from the Janssen model. The results suggest that the soft elastic tubes could provide a simple and convenient means to investigate the forces that arise in different materials.

Bottom stresses of static packing of granular chains

We experimentally measure the static stress at the bottom of a granular chains column with a precise and reproducible method. The relation, between the filling mass and the apparent mass converted from the bottom stress, is investigated on various chain lengths. Our measurements reconfirm that the scaling behavior of the stress saturation curves is in accord with the theoretical expectation of the Janssen model. Additionally, the saturation mass is displayed as a nonmonotonic function of the chain length, where a distinguishing transition of the saturation mass is found at the persistence length of the granular chain. We repeat the measurement with another measuring methodology and a silo with different size, respectively, the position of the peak maintains robust. In order to understand the transition of the saturation mass, the friction coefficient and the volume fraction of granular chains are also measured, from which Janssen parameter can be calculated. Finally, we preliminarily measure the bottom stress for two distinct packing structures of long chains, find the effect of the entanglements on the bottom stress, and argue that the entanglements might be responsible for the transition of the saturation mass.