Motivations for Improved Methods to Predict Bulk Material Loads

Abstract

The accurate prediction of loads exerted by bulk materials is central to the design of safe and effective storage and handling equipment. Despite this, many engineering applications involve complex load cases that are not fully addressed by current design standards. This paper illustrates engineering applications encountered by Agilitus in which the limitations of existing methodology must be considered during the design process. Key examples are presented in which DEM modelling is applied alongside existing standards and materials handling theory to inform load prediction, with a focus on the sensitivity of results to key modelling simplifications and inputs. The results demonstrate that suitable agreement between numerical and analytical methods can be achieved, but requires more than just calibration of DEM parameters to laboratory or field results. Rather the validity of wider modelling simplifications must also be considered. Once validated, the DEM approach provides a flexible analysis tool for complex load cases.

1. Introduction

The prediction of bulk material induced loads is increasingly being informed by the application of Discrete Element Method (DEM) modelling, as continued advances in software and computing power enables DEM to be scaled to storage applications that were previously impractical for simulation. This sees modern design practice at an intersection of fundamental techniques and numerical methods, where both of which involve unique advantages and drawbacks. In many ways this supports a design approach where continuum based calculations (such as those described by AS 3774 [1] and EN 1991-4 [2]) are complemented by DEM, however the limitations of both approaches mean that practitioner experience continues to be required to produce sound design outcomes. This is particularly true of applications that involve complex geometry or dynamics such as those described by Donohue et al [3] and Chen et al [4].

This paper has been motivated by practical design examples undertaken by Agilitus, where the prediction of bulk material loads has a significant impact on equipment and plant design. Two case studies are presented, each involving the determination of wall and gate loads using both fundamental methods and DEM analysis. The two industrial applications are introduced in this section, with results presented in Section 2.

The first case study involves a batching style train load out (TLO). Key system components are shown in Figure 1, whereby the main bin discharges via batching hoppers into a smaller weigh bin. The weigh bin is charged to a target mass before discharging into the train wagons. Both the batch hopper and weigh bin discharge processes are controlled via ‘clamshell’ style gates.

When sizing the hydraulic clamshell actuators the designer must understand the force required to open and close the gates under surcharge, which is governed by both bulk material and hopper characteristics. Taking the most simplistic view, the load acting on the weigh bin gates is developed according to an active stress state within the hopper during each batching cycle. This state is usually assumed for initial fill conditions (before flow is commenced) and represents a stress field that acts primarily vertically, producing an approximately hydrostatic load on the gates [5].

In the experience of the author a more realistic representation of the load acting on similar gates under a steep walled hopper is presented by EN 1991-4, whereby a partial transition to a passive stress regime (arched stress field) is predicted to occur due to compression of the bulk solid as the vessel is filled. This results in a stress distribution where the majority of the bulk material load is imparted in the normal direction against the hopper walls and the load is reduced commensurately at the base or gates. The degree to which this effect occurs is influenced by the hopper, bulk material and filling characteristics. The reader is directed to Roberts et al [7] for further reading on passive settling within a stored bulk solid.

The analysis presented in Section 2.1 includes the prediction of loads on the weigh bin gates using EN 1991-4 methodology and via DEM analysis of the filling process. Being a relatively standard hopper geometry, this instance provides for a validation of load prediction and enables a sensitivity study with respect to the influence of wall friction on gate loads.

Case Study 2 exhibits the reject bin geometry shown in Figure 2. This bin integrates with a reclaim tunnel and involves eccentric discharge via a bypass arrangement. Such a geometry creates stress concentrations that require structural consideration, but is not readily represented by wall load standards such as EN 1991-4 or AS3774. After demonstrating that a properly implemented DEM model is capable of load prediction with sufficient agreement to analytical models via Case Study 1, the analysis for Case Study 2 relies more heavily upon DEM to predict the load distribution. The resulting analysis is presented in Section 2.2 and demonstrates the versatility of DEM as a wall loads analysis tool, but also demonstrates the impact of certain modelling simplifications on results.

2. Wall and Gate Load Analysis

2.1 TLO Weigh Bin (Case Study 1)

This section presents the results of analysis for the TLO weigh bin geometry introduced in Section 1. The non-hydrostatic stress distribution at the focus of this study is evident in comparison of the DEM predicted loading profiles for the weigh bin and the gates, as shown in Figure 3. The total mass increases over ~6 seconds of batching time, however the load recorded on the gates plateaus after only ~2 seconds, demonstrating the transfer of surcharge predominantly to the hopper (as would be expected for a passive stress state and in contrast to a hydrostatic state).

The load determined to act on a single gate via both DEM and EN 1991-4 analysis is compared in Figure 4. The hydrostatic prediction is also included for comparison. The nature of the transition to a partially passive stress field (and resulting relief on the gates) is primarily a function of the wall friction acting between the bulk material and the fixed angle hopper. In Figure 4 the wall friction coefficient () is presented as a wall friction angle (φ), calculated according to Equation 1. To facilitate comparison, an effective wall friction angle representing the DEM particle–wall interaction was obtained via simulated calibration experiments for all four parameter sets.

φ=tan-1(µ)⁡(1)

The results predicted by the analytical and DEM models compare relatively well, with both showing significantly less load acting on the gates than the hydrostatic value. By comparison, the gate load calculation method provided by Section 6 of AS 3774 would require a j-factor of >1.5 to align with the results determined via EN 1991-4 and DEM. It is noted that the curve presented for the DEM results reflects the specific particle calibration that was converged upon for this project. More comprehensive analysis would result in a series of DEM derived curves representing an envelope of load outcomes that demonstrate sensitivity to secondary parameters in addition to the primary influence that is wall friction.

By demonstrating reasonable agreeability between DEM and fundamental analysis for this standard bin geometry, some confidence can be developed regarding the utility of the DEM approach to load prediction in non-standard bin geometry.

2.2 Reject Bin (Case Study 2)

This section presents the results of analysis for the reject bin introduced in Section 1, with a focus on the more complex loads associated with the irregular geometry and bypass arrangement. The scale of the reject bin requires significant model simplifications to permit feasible analysis and these simplifications are first explored by examining their influence on predicted stress distribution.

An immediate opportunity for simplification that was identified for this application was making use of the symmetry that occurs along the tunnel centreline and simulating only one half of the bin. The bypass door could then either be included or excluded as required.

Another common simplification in DEM modelling is the reduction of particle stiffness, which allows the use of a larger simulation timestep to improve computational efficiency [8]. While many fast flow applications permit a significant reduction in stiffness without adversely influencing outcomes, this is less often suitable when high consolidation applications such as the reject bin are considered. Figure 5 shows the variation in predicted normal stresses on the non-bypass wall for three particle stiffness values of 1e7, 1e8 (default value in the simulation package) and 1e9. It is evident that the particle stiffness selection contributes significantly to the model’s ability to develop an accurate lateral pressure ratio. Approaching this selection via sensitivity analysis enables an optimal particle stiffness to be selected that balances simulation efficiency with robust model behaviour. In this case a particle stiffness of 1e9 was elected for further study.

A further opportunity for simplification involves simulated bin filling method, since filling at the actual design rate over a period of hours is not compatible with a DEM study. Common approaches that overcome this limitation include filling the bin at an artificially high rate (over a fill time of 1-2 minutes instead of hours), installing particles instantaneously in a predetermined packing arrangement (volume fill), or some combination thereof. The chosen approach must be applied carefully to avoid creating stress distributions or packing arrangements that distort the simulation results, particularly when cohesive models are used. The influence of filling method on the predicted stress distribution in the reject bin is shown in Figure 6, using an identical colour scale as presented in Figure 5. The influence of the filling method is evident in the more uniform distribution of normal stress when a volume-fill approach was employed. The accelerated fill rate method was utilised across all other simulations presented, with care being taken to minimise excessive impact load in critical regions.

With suitable simplifications for particle stiffness and fill methodology established the practitioner must next determine appropriate particle characteristics to balance efficient computation with adequate resolution. Figure 7 presents a comparison of the stress distributions predicted by two different spherical particle representations, using the same colour scale as Figure 5. The mono-sized particle outcome is shown on the left and required ~1M particles, whereas the distributed particle size model shown on the right required ~2M particles. The particle model is expected to influence the resulting lateral pressure ratio and ability to capture settling effects. While some sensitivity is observed in the resulting stress distribution it is not as significant as was observed for the particle stiffness and fill method investigations.

Once appropriate scaling and domain simplifications have been determined the DEM model can then be calibrated to provide for suitable mechanical behaviour within the simulation. The topic and current state-of-the-art in DEM calibration is well documented by others including Coetzee [8] and Roessler et al [9] and is not addressed explicitly here. A basic calibration was undertaken for the waste material model based on available laboratory data, with key parameters assessed via sensitivity studies to develop an envelope of load predictions.

To interrogate the DEM results, a novel application of the Janssen model [10] was considered. The lower bin was rationalised into 4 cylindrical sections as shown in Figure 8, with diameters drawn perpendicular to the reclaim tunnel and passing through nominated points on the circumference of the bin. The resulting calculations are compared to the DEM prediction for normal stress versus height below the reclaim tunnel roof at the nominated positions in Figure 9 and Figure 10. Above the reclaim tunnel a hydrostatic load represents the surcharge, as would be expected for the relatively squat bin geometry above this point. It is seen that towards the narrow extremity of the segment the DEM and analytical models compare well for a lateral pressure ratio K=0.35 (Figure 9), while as the section widens the two results converge reasonably when K=0.4 (Figure 10). The most significant deviation between the two methods occurs at the centreline (0° reference point) where the DEM results demonstrate ‘under-pressures’ in the lower bin region (>4 m below the tunnel roof).

A more complex load case occurs on the bypass side of the bin, involving a more dynamic and less uniform pressure distribution. Figure 11 shows the DEM prediction of steady state stress acting on the inside of the bin for two sets of material properties, using the same contour scale as presented in Figure 5. The utility of the DEM method for examining complex cases such as this is evidenced in the pressure irregularities observed above the bypass door and the sensitivity of this effect to cohesion in the model, where such behaviour would not be predicted via standard fundamental models.

3. Summary

The accurate prediction of loads within bulk material storage equipment requires a strong appreciation of the factors that influence them. These factors include inherent material properties and external characteristics such as loading methods and vessel geometry. For many typical cases modern wall loads standards can be relied upon for design, however additional complexity in the form of asymmetry and dynamic loads commonly exhausts the limits of standardised methods. In these cases DEM modelling provides the design engineer a tool with sufficient resolution to examine complex behaviour, but it also demands critical thought as to the influence of key modelling simplifications on the outcome.

The two case studies presented in this paper demonstrate that with appropriate understanding of DEM model sensitivity and characteristics, numerical models can be established with comparable results to fundamental analysis. The importance of this benchmarking against standardised methods for a given application is emphasised, such that confidence is developed in the DEM model before more complex behaviour is examined. Furthermore, the prediction of loads with sufficient accuracy requires more than just the calibration of ‘flow parameters’ to replicate laboratory or field results, rather the wider system simplifications must be validated methodically to ensure appropriate representation of loads.

In the continued development and refreshment of modern wall loads codes it is important to consider the necessity for design engineers to analyse complex load cases, including those developed by atypical geometry and load cases involving dynamics (quaking). While such cases may not be possible to parcel within a standard methodology, it is important that the base methodology is accessible enough and not overly empiricised, such that it can be applied flexibly to approximate more complex instances. In this way fundamental materials handling practises can be applied to complement DEM and other numerical methods and yield robust design outcomes.

References

1. Standards Australia, AS 3774—1996: Loads on Bulk Solids Containers, Standards Australia, Sydney, 1996.
2. European Committee for Standardization (CEN), EN 1991-4-4:2006 Eurocode 1 – Actions on Structures – Part 4: Silos and Tanks, CEN, Brussels, 2006.
3. Donohue, T.J., Wensrich, C.M., Roberts, A.W., Ilic, D., Katterfeld, A., “Analysis of a Train Load-Out Bin using combined continuum methods and Discrete Element Modelling”, 7th International Conference for Conveying and Handling of Particulate Solids, Friedrichshafen, Germany, 10th–13th September 2012
4. Chen, B., Roberts, A.W., Donohue, T.J., Reid, S., “Predicting gate loads from hopper with insert(s) using discrete element method (DEM) modelling”, 14th International Conference on Bulk Materials Storage, Handling and Transportation (ICBMH 2023), Wollongong, Australia, pp. 333–340
5. Roberts A., Basic Principles of Bulk Solids, Storage, Flow and Handling, The University of Newcastle Research Associates (TUNRA), 1998.
6. Shen J., Roberts A., Wheeler C., DEM Simulations on Gate Loads and Bin Storage Characteristics Before Discharge, Powder Technology, 383, 2021, pp. 280–291.
7. Roberts A., Shen J., Beh B., Chen B., Donohue T., Study of Gate Loads Related to Stress States in Mass-Flow Bins During Bulk Solids Filling and Settlement, Advanced Powder Technology, 32(3), 2021, pp. 683–692.
8. Coetzee C.J., Review: Calibration of the Discrete Element Method, Powder Technology, 310, 2017, pp. 104–142.
9. Roessler T., Richter C., Kunze G., Katterfeld A., Will F., Development of a Standard Calibration Procedure for the DEM Parameters of Cohesionless Bulk Materials – Part I: Solving the Problem of Ambiguous Parameter Combinations, Powder Technology, 343, 2019.
10. Janssen H.A., ‘Experiments on Grain Pressure in Silo Cells’, Zeitschrift des Vereines
11. Deutscher Ingenieure, vol. 39, 1895, pp. 1045–1049 (English translation).