Using Eurocode in replacement of Australian Standards for silo design

Hatch regional lead engineer Luke Stone and mechanical engineer Samuel Lord investigate some of the key differences between EN1991-4:2006 and AS3774:1996 and provide recommendations to be implemented with respect to updates and endorsement of AS3774.

Australian Standard AS3774-1996 “Loads on bulk solids containers” has been withdrawn by Standards Australia due to its age and, because the committee BD/65 is no longer active, it was not reviewed or endorsed. As such, guidance is being sought by companies in the mining and metals sector, and other industries, regarding which design standard should be used for bins and silos.

The comparison of these two standards is based on a presentation titled “Advancements in Bulk Storage Vessel Design Utilising Finite Element Analysis and Discrete Element Method Modelling” given by Luke Stone at the International Conference for Bulk Solids Handling 2023.

This white paper utilises a typical silo type found in industry, namely a simple medium/intermediate sized cylindrical silo with a steep conical hopper, refer Figure 1. The material property data contained in Table 1 has been used as the basis for generating pressures profiles in accordance with each standard.

Figure 1: Steep bin dimensions a) AS3774 nomenclature; b) EN1991-4 nomenclature

Before delving into the details and equations of each standard the following are highlighted as key shortcomings of EN1991-4 in comparison to AS3774:

No guidance for impact loads either from material rolling down a repose pile or material being dumped into the container
No guidance for pressure applied to gates and feeders with the consideration of stiffness
No guidance for end wall effects for slot hoppers
No guidance for loads on internal structures

The following are highlighted as key shortcomings of AS3774 in comparison to EN1991-4:

No guidance on how the vessel should be analysed and verified (Eurocode 1 part 4 forms a part of a larger collection that covers assessment, including fatigue analysis)

AS3774 has reduced resolution of silo load case assessment compared to EN1991-4, which defines:

Action Assessment Classes 1, 2 and 3; allowing different levels of analysis complexity based on silo size
Differentiation between slender, intermediate, and squat formulas and assumptions
Differentiation between steep and shallow hopper formulas and assumptions

Generally, each standard follows a similar method for generating the material loads with similar nomenclature and equations.

There are subtle differences with respect to classifications, assumptions, multipliers/factors, and reference locations. For example, in AS3774 a medium tall silo is classified by 1 ≤ hb/dc ≤ 3.0 compared to EN1991-4, which uses 1 < hc/dc < 2 for the basis; the key difference being the reference heights of hb and hc where one includes the hopper and the other does not.

When comparing the standards the following aspects are noteworthy:

Normal pressures on vertical walls during initial filling:

These are calculated using the Janssen depth function, unit weight, lateral pressure ratio, and characteristic dimension of the silo are used
AS3774 provides an equation for the lateral pressure ratio whereas EN1991-4 provides a testing procedure or, in lieu of this, an approximation based on internal friction
For the example data and silos, a value for KAS3774 = 0.35 (for lower, upper, and mean values) and KEN1991-4 = 0.17, 0.23 and 0.2 (for lower, upper, and mean values)
The difference in K calculation results in different normal pressures being calculated

Shear tractions on vertical walls during initial filling:

This is simply the normal pressure multiplied by the wall friction, which is common to both standards

Normal pressures on hoppers walls during initial filling:

Both standards derive the hopper pressure based on vertical pressure using the same equation; however, there is a difference in factors used to scale this value
AS3774 calculates the hopper pressure on the basis of vertical pressure with the addition of a hydrostatic component and normal pressure multiplier
Using this approach results in a linearly increasing profile
EN1991-4 takes a different approach, first applying a constant bottom load magnifier to capture unforeseen load transfer to the hopper from the silo before adding a power-based load factor using hopper shape characteristics and weight of material
Using this approach results in an initial peak load at the transition / upper portion of the hopper before decreasing at the outlet (for steep hoppers) and a similar profile to AS3774 for shallow hoppers (however still decreases to the outlet), refer Figure 2

Figure 2 Figure 2: AS3774 normal pressure initial fill profile (extracted from [1])

Figure 3: EN1991-4 normal pressure initial fill profile (extracted from [2])

Shear tractions on hopper walls during initial filling:

This is simply the normal pressure multiplied by the wall friction, which is common to both standards

Normal pressure on vertical walls during flow:

AS3774 and EN1991-4 follow a similar method albeit using different factors for flow loads; both standards take the calculated normal pressures for initial filling and multiply them by a pressure multiplier
AS3774 uses the wall pressure multiplier, which is a function of geometry and a constant exponent or a constant factor of 1.2 (whichever is larger) and a constant factor of either 1 or 1.2 for axisymmetric or planar flow to further factor the pressures
AS3774 also offers guidance on reduced pressure due to funnel flow behaviour
EN1991-4 uses the discharge factor for horizontal pressure which, depending on action class, varies from 1.0 to 1.15 or a calculated value based on eccentricity, diameter, and a patch load factor

Shear tractions on vertical walls during flow:

AS3774 uses a constant friction traction multiplier of 1.2 or 1.4 depending on axisymmetric of plane flow container geometry to factor the initial fill tractions
EN1991-4 uses the discharge factor for wall friction traction which, depending on the action class, varies from 1.0 to 1.1 or a calculated value based on eccentricity, diameter, and a patch load factor

Normal pressure on hopper walls during flow:

AS3774 takes the calculated vertical pressure and factors it using a similar power based factor function to EN1991-4 and then applies an additional normal pressure ratio for flow conditions.

Figure 4: Vertical pressure factored equation (extract from [1])

Figure 5: Vertical pressure factored equation (extract from [2])

EN1991-4 utilises the same method as the initial filling but with a modified hopper characteristic value for the discharge flow loads
The two methods result in a similar pressure profile plot.

Figure 6: AS3774 normal pressure flow profile (extracted from [1])

Figure 7: EN1991-4 normal pressure flow profile (extracted from [2])

Shear tractions on hopper walls during flow:

This is simply the normal pressure multiplied by the wall friction which is common to both standards

The preceding section has presented insights into some of the key differences between the standards, but it is not until comparing the results directly that it becomes clear what influence these differences have. Refer Figure 3 and Figure 4 for the silo load pressures calculated, and Table 2, which outlines the definition of each load case used for the load profiles and is adapted from Table 6.1 [1] and Table 3.1 [2].

AS3774 and EN1991-4 initial loads appear similar for the silo section while the hopper loads are approximately 30 per cent larger for EN1991-4 and with a different profile. Overall, the EN1991-4 initial filling loads are approximately 15 per cent larger than those derived to AS3774.

Figure 8: Comparison of AS3774 to EN1991-4 Initial Filling and Flow Loads: Load Case 1

Figure 9: Comparison of AS3774 to EN1991-4 Initial Filling and Flow Loads: Load Case 2

Figure 10: Comparison of AS3774 to EN1991-4 Initial Filling and Flow Loads: Load Case 3

A key trend for the flow loads is also observed with AS3774 tending to result in much larger silo wall pressures (approximately 26 per cent) while EN1991-4 results in significantly larger hopper loads (approximately 67 per cent). Overall, the EN1991-4 discharge loads are approximately 28 per cent larger than those derived to AS3774.

These differences in pressure profile, shape, and magnitude, will impact on the hopper design with respect to sizing of stiffeners and strength assessment; particularly where flat surfaces are present on slot hoppers and at transition details. It would appear from this review that EN1991-4 results in a more conservative load being applied to the bin.

Table 3: Load case 1 normalised in terms of Kilonewtons

Following this assessment, it is recommended that:

Eurocode is adopted as an interim method as an endorsed standard for bin and silo design; while AS3774 is updated and goes through the endorsement process.
AS3774 should be adapted and updated to include information from EN1991-4, namely inclusion of:
patch loads
class definitions
increased resolution on assessment methodology (influence of the silo size and hopper shape)
Eurocode standards for engineering and strength assessment (level of analysis required)
AS3774 should also be updated to include guidance:
on the use of Finite Element Analysis techniques (in particular non-linear analysis)
on the inclusion of multiple hopper segments
on silo quaking and effect of cycles on fatigue life.