Modelling blockages

How to model blockage scenarios in Flood Modeller

Many flooding incidents are caused or exacerbated by blockages in the watercourse, typically at the entrance to bridges or culverts. We may therefore wish to simulate design events with response to varying degrees of blockages at critical locations. Some questions a modeller might ask are - “how is it connected/what do all the five node labels mean?” and “what calculations does it actually use?”. In this article, all questions around the blockage unit are answered.

The blockage unit has been designed to be able to effectively model a single or a number of blockage scenarios for this purpose. The blockage proportion may also vary with time. The increase in upstream water level is calculated using the Bernoulli equation to derive the head loss … put simply,    .

The first thing to note is that the blockage is treated as a structure in its own right. Therefore, it has two connection node labels (label #1 and label #2, for the upstream and downstream nodes, respectively). As with any structure, the node label #1 of the blockage is connected to the channel section, junction or other structure immediately upstream of it. Conversely, node label #2 of the blockage (which must be different from label #1) is connected to the channel section, junction or other structure immediately downstream of it. General Flood Modeller 1D connectivity rule: each structure node label must appear exactly twice in a model network (excluding any reference/remote nodes).

So that’s the connectivity node labels sorted. Now for the remote or reference nodes (labels 3-5). Note that these do not affect connectivity in the model – they just tell the model where to obtain velocities from. Because the blockage unit needs a velocity for Bernoulli equation, it needs a wetted area    … and for that it needs a cross section – from a river, conduit or bridge unit. Put simply, label 3 needs to be the most appropriate (nearest) section upstream and label 4 the same downstream. Indeed, if label 1 is a river/conduit/bridge unit, then it makes sense for label 3 to be the same as label 1. I stress again that this does not mean the blockage unit is physically connected to labels 3 and 4. 

Similarly, node label 5 needs to be a river, conduit or bridge unit and represents the section to be constricted. Typically, this will be the bridge or conduit section immediately downstream of the blockage. 

In the schematisation below, the blockage is representing a blockage at a culvert, and is therefore placed between the open channel and the culvert (in this case upstream of the culvert inlet loss unit). Therefore, the upstream reference section is the river section upstream, i.e. same as the connectivity label, label #1 (EW01.023) in this case.

The downstream reference section is the upstream CONDUIT node (EW01.023c). Note this is different from the downstream connectivity node (label #2) since there is a CULVERT INLET loss immediately downstream of the blockage EW01.023in), and the reference section must contain cross-sectional information.

The constriction reference section in this case is also the upstream CONDUIT node (EW01.023c).

Usage

The head loss due to the blockage, Δh, is derived from the Bernoulli equation representing both a contraction and an expansion, as follows:

where

    inlet loss coefficient

    outlet loss coefficient

    blockage proportion

    velocity at label 3, the upstream section

    velocity at label 4, the downstream section

    velocity at label 5, the section to be obstructed

Note that:

•     is calculated using the area of section 3 at the upstream water level (WL at node 1);
•     is calculated using the area of section 4 at the downstream water level (WL at node 2); and
•     is calculated using the area of section 5 at the upstream water level (WL at node 1).
• The discharge – used to calculate velocity via v=Q/A – is the same at both node labels (mass is conserved and there is no storage in the unit).

Note that you can specify a time-varying blockage proportion, p, or keep it as a constant value. A value of p=0 indicates no blockage; a value approaching 1 would indicate a 100% blockage (p must be strictly less than 1).

If a Bridge unit is being used as a reference section, the area used to derive velocity is the wetted area of the bridge opening.

Note: If the upstream and constriction sections differ, there will be a contraction loss even for a zero blockage (with reference to the first term on the right-hand side of the equation, the areas, and hence velocities will be different). Thus, the blockage unit can model a pure contraction (or conversely expansion) loss. Alternatively, to prevent this, e.g. if the contraction loss is already accounted for elsewhere, one should set the upstream loss coefficient, K1, to zero.

For instance, in the example above, a blockage is placed in front of the culvert inlet. In this instance, one would be advised to set in the K1 coefficient to zero, i.e. to prevent double counting the head loss.

Note, when using a culvert inlet unit, one can also apply a blockage to a trash screen, which behaves in a similar manner. A significant difference is that the blockage proportion in the Culvert Inlet unit is fixed, and not time-varying.

Examples

Note that the following examples all relate to culverts; for the entry and exit blockage examples, the culvert unit could equivalently be replaced by a bridge, in which case the conduit reference section would be replaced by the appropriate bridge section.

Obstruction at the entrance to a culvert

The upstream and downstream sections are different. The user should set the constriction section to be the downstream section, and we have

Obstruction in a river section or culvert

Here, the upstream and downstream sections are the same. The constriction section should be the downstream section, K1 should be used to specify the inlet loss and K2 the outlet loss. The equations become

Obstruction at the exit from a culvert

The upstream and downstream sections are different. The user should set the constriction section to be the upstream section, and we have

Notes

If including both a contraction and expansion loss, a typical value for the upstream loss coefficient K1 would be 0.5, and the downstream loss coefficient K2 would be 1. The blockage is modelled as a vertical blockage, i.e. the blockage proportion does not vary with depth. In the unlikely scenario that one of the reference section labels is both a River and a Bridge section, there is no way of telling it which one to take. To avoid ambiguity, one is advised to separate the river and bridge by a junction unit. However, this is unlikely since if this scenario occurs, the blockage is likely to be between the River and Bridge anyway, hence they will already be separated. Blockage units can be used in event data files – this means one can model several different scenarios, e.g. different proportions or different time-profiles using the same network.