Ratholing in silos: rathole diameter and fill height
In funnel flow only a channel above the outlet flows, the bulk solid at the walls stays at rest. If this stationary bulk solid is strong enough, the channel empties and remains as a stable rathole – discharge stops although the silo is still full.
From the measured flow function we calculate the possible rathole diameter and the maximum fill height up to which no stable rathole forms.
How a stable rathole forms
The precondition is funnel flow: hopper inclination and wall friction lie outside the mass flow criterion. The stationary bulk solid is consolidated by the load above it – the greater the fill height, the higher the consolidation stress and the stronger the bulk solid. If it can carry the stresses at the edge of the flow channel, the channel stays open after emptying.
Contributing factors
- Funnel flow due to flat hoppers or high wall friction
- Cohesive bulk solid with high unconfined compressive strength, low flowability ffc
- Large fill height relative to the shaft diameter
- Small active discharge cross-section
- Time consolidation of the stationary bulk solid during long storage
Consequences in operation
- Discharge stops, a large part of the content remains in the silo
- Usable silo volume considerably smaller than planned
- Long residence times, ageing and caking in the stationary bulk solid
- When the rathole walls collapse, impact loads and uncontrolled flooding of aerated bulk solid
Calculating the rathole diameter and the maximum fill height
Possible rathole diameter
The possible rathole diameter bS,min is the width a channel in the stationary bulk solid can just have while remaining stable. It follows from the unconfined compressive strength σc at the consolidation stress in the stationary zone, the angle of internal friction φi and the bulk density ρb:
bS,min = G(φi) · σc(σ1) / (ρb · g)
If the shaft diameter dc is at least as large as bS,min, no stable rathole can hold.
Methods and fill height
The consolidation stress in the stationary bulk solid grows with the fill height and, like the silo pressure, tends towards a limit value. This gives the maximum fill height hmax up to which bS,min remains smaller than dc.
The calculation tool evaluates bS,min by several methods – via the vertical pressure calculation with the maximum consolidation stress, via anisotropy with the horizontal stress, and after Arnold, McLean, Roberts & Enstad. In addition, the minimum shaft diameter Dmin against a plug of bulk solid caused by local wall imperfections is calculated.
Measurements for assessing ratholing
The flow function is measured up to the consolidation stresses that occur in the stationary bulk solid of your silo.
| Measurement | Parameters | Use |
|---|---|---|
| Yield locus | flow function σc(σ1), angle of internal friction φi, effective angle of internal friction φe, lateral pressure ratio K | possible rathole diameter bS,min, stresses in the vertical section |
| Compression density | density function ρb(σ) | bulk density in the stationary zone |
| Wall friction | wall friction coefficient μ, wall friction angle φw | mass or funnel flow, stresses in the vertical section |
| Time consolidation | time flow function σc,t(σ1) (optional) | ratholing after storage at rest |
Measures against ratholing
The most effective measure is mass flow – without a stationary zone there is no rathole. Where a conversion is not possible, fill height, discharge and operation help.
- Mass flowSteeper hopper or a wall material with lower wall friction, so that the entire bulk solid flows.
- Fill heightLimit the fill height to hmax or choose the shaft diameter so that dc ≥ bS,min.
- DischargeA feeder that activates a large part of the cross-section instead of drawing off only a central channel.
- Bulk solidAdjusting moisture, particle size or flow aids – the effect can be proven by comparative measurements.
- OperationLimit the storage time at rest if the bulk solid tends to time consolidation.
Frequently asked questions about ratholing
- When does ratholing occur?
- Only in funnel flow. There the bulk solid at the walls remains at rest and is consolidated by the load above it. In mass flow the entire bulk solid is in motion, so a stationary zone and therefore a stable rathole cannot form.
- What is the difference between ratholing and arching?
- An arch is a vault above the hopper outlet, a rathole a vertical, emptied channel in the stationary bulk solid of the vertical section. Both are calculated from the flow function but are separate criteria: an outlet large enough to prevent arching does not prevent a rathole.
- What does the maximum fill height mean?
- With increasing fill height the consolidation stress in the stationary bulk solid rises, and with it its unconfined compressive strength. Up to the maximum fill height the possible rathole diameter remains smaller than the shaft diameter dc, so no stable rathole can hold.
- Which measurements are needed?
- Yield loci at a minimum of three consolidation stresses for the flow function, the angle of internal friction φi and the effective angle of internal friction φe, compression density, the lateral pressure ratio K for the stresses in the vertical section, and wall friction for the mass or funnel flow criterion. For longer storage times, time consolidation is added.
Rule out ratholing before construction
Describe your bulk solid and your silo – we put together the right measurements and prepare a non-binding quote for you.
- Flow function up to the stresses in your silo
- Possible rathole diameter by several methods and maximum fill height
- Mass or funnel flow for your hopper geometry