Professor Alan Roberts from TUNRA Bulk Solids combines an analytical review of gate load determination with an experimental study employing a large, pilot scale mass-flow bin handling iron ore to examine the design of mass flow bins for train loading.
Storage bins for bulk solids handling operations rely on flow isolating gates to prevent outflow of bulk solids during initial bin filling from the empty condition, as well as during periods of stoppages in the plant operation. While in some cases slide gates may be employed in a flow ‘throttling’ mode to adjust the outflow, this action is not recommended in view of the negative influence this may have on the distribution of bin wall loads due to resulting eccentricities in the bulk solids discharge flow patterns. For efficient flow control, the gate must be fully opened during the plant operation and a flow rate controlling device, such as a belt or vibratory feeder, being employed to achieve the required discharge feed rate.
The motivation for the study presented in this paper concerns the design of isolating gates in load-out bins such as those employed in the iron ore and coal industries for the filling of bulk rail wagons while the train is in continual motion. The bins incorporate mass-flow hoppers which utilise slide- type flow isolating gates in conjunction with swing action, inclined chutes fitted with clam shell flow trimming gates to control the discharge of bulk solids into the moving train wagons. The discharge control chutes are fitted below the flow isolating slide gates. During the filling operation, the flow controlling clam shell chutes are held in the raised position to allow sufficient head room for the train locomotive to pass underneath. Once this happens, the chutes can then be lowered to a position just clear of the top of the rail wagons. The isolating gate is then opened, and the continuous wagon filling operation commences. The bins operate between ‘high’ and ‘low’ fill levels in conjunction with bin loading conveyors.
By way of background, the subject of gate loads is intrinsically linked to the study of feeder loads, a subject which has received significant research attention as indicated by the selected sample of references [1-3]. In essence, this research has emphasised the importance of treating the mass-flow hopper and feeder as an integral, interactive system in which the bulk solids stress fields in the hopper directly influence the feeder loads and the associated drive torques and powers. It has been well established that as a result of the change in stress states in the feed hopper, the vertical loads acting on a feeder during outflow are usually significantly lower than the loads acting during the initial filling of the hopper with the feeder not operating. The reduction in loads from filling to running in the order of 80 per cent have been recorded.
For bin flow isolating gates, the gate loads correspond to the initial filling case of feeders. The loads are influenced primarily by the degree of compressibility of the bulk solids and degree rigidity or stiffness of the gate. As discussed in Section 3 of this paper, the Australian Standard AS3774-1996 [4], provides some guidance for gate load determination by specifying appropriate so-called ‘j’ values based on notional bulk solid compressibility and gate stiffness levels. In view of the widely varying influence the values of ‘j’ has on the gate load determination, it is important that the subject of gate loads be investigated. This is the motivation for this paper, the aims of which are summarised as follows:
1. Examine the influence of surcharge loads and impact loads during the bin filling operations.
2. Outline experimental studies to measure gate loads on a pilot scale laboratory bin and corroborate the results with the theoretical results.
3. Examine the influence of bulk solids settlement following bin loading.
4. Establish gate load analysis procedures which incorporate improved methods for selection of the most appropriate value of ‘j’.
2. Review of mass-flow hopper and gate-load analysis
The gate loads of a mass-flow hopper are derived from wall load theory, the relevant aspects of which are now reviewed.
2.1 Mass-flow load model
Considering the equilibrium of the model presented in Figure 1, the following differential equation is derived:
m = hopper flow symmetry factor [-].
m = 0 for plane flow or wedge-shaped hopper [-]. m = 1 for axi-symmetric or conical hopper [-].
w = wall friction angle [degrees].
α = hopper half-angle [degrees].
ps = surcharge pressure [kPa].
γ = pg = bulk specific weight [N/m3].
p = bulk density [kg/m3].
kh = Pnh = pressure ratio [-]. pvh
pvh = average vertical pressure acting on slice at depth zh [kPa]. pnh = corresponding normal pressure acting on wall [kPa].
2.2 Stress fields
The two principal, fully-developed stress fields in a hopper are the ‘active’ stress state as shown in Figure 2(a) and the ‘passive’ stress state as shown in Figure 2(b). The ‘active’ state of stress normally accompanies the initial filling of a hopper from the empty condition and is characterised by the major consolidation stress, acting substantially in the vertical direction and curving away 1 slightly as the stress direction lines intersect the hopper walls as shown in Figure 2(a).
The ‘passive’ state of stress occurs when there is any downward movement of the bulk solid such as during discharge. It can even occur due to load settlement as discussed in Section 6 of this paper. In this case the convergence of the downward movement of the bulk solids in the hopper causes an increase in the normal wall loads as the stress field switches from the ‘peaked’ or ‘active’ stress state to the ‘arched’ ‘passive’ state depicted in Figure 2(b). For the ‘passive’ stress state, the major consolidation stress, for each arch stress line is constant in magnitude around the arch but varies 1 in direction. Once the ‘passive’ stress state is established, it remains in a stable condition even if the discharge is stopped before the hopper is emptied. The only way that the ‘active’ stress state can be re-established is for the hopper to be fully emptied and then refilled from the empty condition. The ‘passive’ or ‘arch’ stress field is an important property that is employed in feeder load determination and load control, as outlined in the work of Roberts [3].
The ‘active/passive’ stress field occurs when the ‘passive’ state is partly developed as shown in Figure 2(c). An example of this is ‘load cushioning’ where the hopper is never emptied completely, so retaining the arched, ‘passive’ stress state when being refilled. Another case of the ‘active/passive’ stress state occurs when filling from the empty condition. The associated downward settlement of the bulk solid as it approaches its critical consolidation condition results in load transfer to the hopper walls and hence, a zone of ‘passive’ state of stress as illustrated in Figure 2(c).
3. Hopper gate loads
For bin and gate load design, the initial bin filling and subsequent refilling conditions are of primary concern. Since the active stress state depicted in Figure 2(a) is perceived to dominate in this case, the selection of the parameter ‘j’ has a significant influence on the magnitude of the calculated gate loads. The Australian Standard AS3774-1996 [4] ‘Loads on Bulk Solids Containers’ combines gate loads with feeder loads and specifies that the value of ‘j’ be selected as follows:
(a) j = 0.1 for very incompressible materials stored above stiffly supported feeders.
(b) j = 0.45 for moderately compressible materials stored above flexibly supported feeders.
(c) j = 0.9 for very compressible materials stored above softly supported feeders.
It is noted that for a completely incompressible bulk solid and rigid gate, the value of j =0 in Equation (3) reduces to the ‘hydrostatic’ load given by:
With the corresponding pressure ratio given as:
While a gate will generally be quite ‘stiff’, there is considerable uncertainty as to the degree of compressibility of the bulk solid during the bin filling operation. While the ‘safe’, conservative approach is to select a low value of ‘j’, such as j = 0.1, the design will almost be far too conservative due to the high, unrealistic values of the computed loads. This provided the motivation for the test program that is now described.
4. Pilot scale test bin and test procedure
The test bin used for this research is shown in Figure 3. Figure 3(a) shows the bin geometrical details while Figure 3(b) shows the test set up with the bin being filled with iron ore. The bin is of ‘Perspex’ construction comprising a five section, variable geometry mass-flow with hopper half-angles α1 = 5.88o, α2 = 8.03o and α3 = α4 = α5 = 9.84o. The bin is mounted on three support columns, each of which is mounted on load cells to enable the bin load to be measured. For the measurement of the gate load, a special load cell was developed comprising a flat plate mounted on three load transducers that, in turn, were attached to a base plate. Adjusting screws were incorporated to enable the clearance between the hopper outlet and gate surface to be set. The gate load cell unit is completely independent of the bin structure. For the loading and load settlement stages of the tests, the bin and gate load cell clearance was set at a minimum clearance of approximately 0.5 mm, while making sure that the gate did not make contact with the bin. It was important that there was the independence of the bin and gate load measurements, while, at the same time, simulating a ‘stiffly‘ supporting gate.
The test bulk solid was dry iron ore. The quantity of ore used for the experiments was 767 kg, the average bulk density following the filling of the bin being 2.03 t/m3. As shown in Figure 3(b), the bin is filled using a rectangular skip containing the iron ore, the skip being hoisted and tipped to the bin loading position using an overhead crane. While some minor variations in the loading cycle occurred from one test run to the next, the average bin loading rate was approximately 30 to 35 t/h. This information is required for the determination of the impact loads during the bin-filling operation.
During each test run, the net bin loads and gate loads were recorded using a data logger in conjunction with a laptop computer. The loads were recorded from the commencement of bin loading to the completion of the bin-filling operation. The load recording continued on for a period of approximately two hours in order to measure the changes in the bin and gate loads due to the settlement of the iron ore in the bin.
The final stage of the tests involved progressively lowering the gate load cell in order to record the decrease in gate load as the clearance between the bin outlet and the gate surface increased. The purpose of this final stage of the test was to observe the potential decrease in gate cell load due to the stress field change from active to passive states as a result of the downward movement, albeit very small, of the iron ore in the bin. This particular information is of relevance to feeder design in view of the importance of a passive stress state in controlling feeder loads and drive powers.
5. Predicted performance
As an aid to the review of the measured test results, a selection of relevant predicted performance characteristics of the test bin of Figure 3 are presented. The predicted performance is based on established bin and feeder load theories with a specific focus on gate and feeder loads as presented in AS3774-1996 [4]. The following flow properties of the iron ore and relevant operating parameters of the pilot scale test bin are assumed.
Average bulk density p = 2.03 t/m3
Wall friction angle = 25o
Bin fill rate Qm = 35 t/h
Effective angle of internal friction = 50o
Drop height, load-out skip to filling surface hd = 1.0 m
Parameter ‘j’ for ‘active‘ stress field j = 0.45
Based on the average fill rate of 35 t/h, relevant performance data has been determined as functions of bin fill height during the filling operation as illustrated in Figure 4. Figure 4(a) shows the increase in storage capacity while Figure 4(b) shows the increase in time and the corresponding decrease in impact pressure.
The following load cases based on the load prediction theory presented in Section 2 are reviewed:
(i) Gate loads during bin filling – active stress state, assumed value of j = 0.45
The computed results are plotted in Figure 5 which shows the vertical pressure on the gate and corresponding loads for increasing fill heights up to the top level of 1.866 m. The loads increase from 20.23 kg at the HT = 0.272 m level to 85.26 kg at the top level HT = 1.866 m.
(ii) Gate loads, at maximum fill level HT = 1.866m for a range of j values – active case
It is clear that the value of the load parameter ‘j’ has a significant influence on the gate load determination. This is illustrated in Figure 6 which shows the decrease in gate loads as the value of j increases. For reference purposes, the values of j = 0.1, 0.45 and 0.9 based on AS3774-1996 [4] are also shown.
(iii) Active/passive stress states (Figure 2(c))
The case when the stress state switches from ‘active’ to fully developed ‘passive’ state due to converging flow in the lower part of the hopper is now considered. As an example of this, the case of load cushioning was cited in Section 2. For the bin of Figure 3(a), the vertical stress distributions have been determined for the four switch heights ysw =0.272 m, 0.605 m, 1.111 m and 1.615 m. For the ‘active’ case j = 0.45 for which the corresponding calculated values of the pressure ratio for the four switch stress levels are 0.222, 0.285, 0.335 and 0.335. For the ‘passive’ case the values of jf for each switch level as determined in accordance with the procedures described in Section 2 are, respectively, jf = 17.123, 13.145, 10.13 and 10.13. The corresponding values for the corresponding ‘passive’ pressure ratios are khf =1.89,1.76,1.656and1.656.
The computed vertical pressure distributions are shown in Figure 7(a). As the graphs indicate, the vertical pressure on the hopper outlet decreases rapidly since the ‘arched’ or ‘passive’ stress field transfers the substantial part of the bin load to the hopper walls. The vertical pressure and potential gate load reduction due to switching from ‘active’ to ‘passive’ is further illustrated in Figure 7(b) which shows the load under the fully ‘active’ state is 85 kg decreasing as switching from ‘active’ to ‘passive’ to 5 kg at the switch level ysw = 0.22 m then approaching, asymptotically, 4 kg as ysw further increases.
6. Test results
(i) Initial filling
Several test runs involving the filling of the bin from the empty condition with iron ore were conducted, a typical set of recorded bin and gate load results being presented in Figures 8 and 9. Figure 8 illustrates the initial filling of the bin from the empty condition, the filling time being approximately 90 secs. Figure 8(a) shows that the load on the gate increases very quickly to around 20 kg and then gradually increases to FG = 38 kg as the bin fill level of 1.88 m is reached. On the other hand, the bin load, shown in Figure 8(b) increases gradually at first then, as the fill height increases along with the bin volume capacity, the load increases at a faster rate reaching the full bin load of FB = 730 kg. The total filled load supported by the bin and gate is equal to FT = FG + FB = 768 kg. Since the bin load component is primarily due to the contact of the bulk solids with the bin or hopper walls, the gate initially carries the major proportion of the load, albeit small, before the wall support can begin to take effect. With the bin loaded to the maximum fill height of 1.88m, the gate load represented as little as 5 per cent of the total load, 95 per cent being carried by the bin or hopper walls.
(ii) Load settlement
In order to investigate the influence of load settlement with undisturbed storage time, the recording of the bin and gate loads continued for a period of, nominally, two hours following the completion of the filling operation. As shown in Figure 9, this resulted in a decrease of 8 kg in the gate load and a corresponding increase of 8 kg in the hopper wall support load as indicated in Figure 9. This indicates the effect of load transfer to the hopper walls due to the downward converging creep as the iron ore approaches its critical consolidation condition. It also highlights the transitional phase of the changes in the stress fields from ‘active’ to ‘passive’. The results of this phase of the gate load measurement indicate the influence of the degree of compressibility of the iron ore.
(iii) The ‘j’ parameter
For the measured value of FG = 38 kg, reference to Figure 6 shows that the corresponding value of ‘j’ = 1.8 which is significantly higher than the values of ‘j’ recommended in AS3774-1996 [4] as indicated in Table 1 below.
In the case of the test bin, the value j = 1.8 may be regarded as, a ‘global’ value based on the ‘active’ stress state theory. More than likely, the stress field is a combination of ‘active’ and ‘passive’ as described in Section 5 (iii).
(iv) Transition considerations
The important influence of the ‘active’ to ‘passive’ change in the stress field in the hopper in controlling the gate load is demonstrated in Figure 10. The graph shows the variation of the gate load as a ratio of the total bin load from the commencement of the filling operation. For the first 8 seconds the gate carries 100 per cent of the loaded iron ore without bin or hopper wall support. The stress field is deemed to be ‘active’. During the next four seconds, as the load transfer to the bin walls commences, the gate load decreases rapidly to 30 per cent as shown. This is due to the transition to the ‘passive’ stress state. Then for the remainder of the filling operation, as the transition to the fully developed ‘passive’ stress state continues, the gate load further decreases approaching, asymptotically, the value of 5 per cent of the total bin load.
For the pilot scale bin of Figure 3, the stress switch commences after approximately 12 seconds from the commencement of filling. This corresponds to the fill level of 0.7 m which is approximately 0.1 m above the bottom level of the hopper of Section S3 of Figure 3. This clearly demonstrates the importance of the ‘passive’ stress field in controlling the gate load as discussed in Sections 2 and 5(iii). In effect, the natural consolidation due to load settlement of the iron ore in the lower hopper sections of the bin and the associated ‘passive’ or ‘arched’ stress field state is sufficient to support the major proportion of the total stored load in the bin without any further increase in the gate load.
(v) Influence of gate clearance
In the test program, following the nominal two-hour load settlement period, the gate was progressively lowered to increase the clearance between the bottom of the hopper outlet and the gate. The measured gate loads for three separate tests are plotted in Figure 11. As shown, the gate loads decrease quickly as the clearance increases over the range 0 to 4 mm, after that load approaches asymptotically the value 5 kg as the clearance further increases. It is interesting to compare the results plotted with the predictions presented in Figure 7(b) where the ‘active’ and ‘passive’ stress state combination is considered. That is, when the switch level ysw is such that the ‘passive’ stress state is fully developed in the hopper. It is noted that the measured value of the gate load FG = 5 kg is very close to the predicted value of FG = 4 kg.
These test results are an indication of the inferred significant influence of decreasing gate stiffness on the reduction in gate loads. In this case a clearance of 5 mm or 2.5 per cent of the hopper opening dimension of 200 mm corresponds to a gate load of 5 kg or 13.2 per cent of measured initial gate load of 38 kg.
(vi) Cohesive strength considerations
An aspect of mass-flow bin design concerns the possible impact on the gate load determination of the cohesive strength of the bulk solid which is the basis of determining the critical hopper outlet dimension, BCR. When the actual opening dimension B > BCR, discharge flow can occur. Also, loads can be transferred to the gate. But when B ≤ BCR, a stable arch will form over the outlet without load transfer to the gate and without the possibility for discharge flow. This is a plausible explanation as to why the measured gate loads in the pilot scale tests are lower than those that were predicted. However, it is an aspect of gate load determination that warrants further investigation. By way of background, the study of stable arch formation in wedge-shaped, plane-flow hoppers handling iron ore was performed by Guo [5]. Also, the work of Roberts [6] is of relevance.
Conclusions
This paper has raised a number of important aspects of gate load determination as well as, in the wider sense, the fundamental properties of bulk solids relating the consolidation behaviour to the stress fields under storage and flow. These matters are the subject of ongoing research.
This article was originally published in the 13th International Conference on Bulk Materials Storage, Handling and Transportation ICBMH 2019 Proceedings. Permission has been given to ABHR to republish