Modelling a Breach
- 21 Sep 2022
- 13 Minutes to read
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Modelling a Breach
- Updated on 21 Sep 2022
- 13 Minutes to read
- Print
- DarkLight
Article Summary
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Flood Modeller has the option to overlay a breach on top of an existing Spill unit in order to model a breach in an embankment, bank or dam. The breach formation is modelled as a time series of deformation dimensions, with time specified as an offset either from the model start time or from when a trigger level at the spill/breach unit is exceeded. This can therefore be used to represent the overtopping or piping failure of an existing dam or embankment, the outflow from which can then be propagated through a 2D or 1D model.
The Breach unit provides functionality to model two different types of breach:
- An open breach models an overtopping failure of the structure, with the breach emanating from the crest of the spill.
- A piping breach starts as a small [enclosed] hole in a structure, enlarges over time, and may ultimately collapse into an open breach.
The Breach unit operates in conjunction with a single Spill unit. The Breach must have the same node labels as the corresponding Spill. If there is no Spill with the same labels, then the Breach will be ignored. The rules for positioning the Breach unit in the data file are the same as for any structure; it does not have to appear adjacent to its corresponding Spill, although it is recommended for clarity they are located together. The Breach may also be specified separately in an event data (*.ied) file.
The user specifies a time series of breach dimensions; the first time value specified in the breach unit is the time at which the breach forms. If a trigger level is being used, this time is relative to the first time the water level exceeds the trigger; otherwise this is the simulation time. No breach will be modelled before then, i.e. the corresponding Spill unit will act as being intact until the Breach is activated. Click the links below to navigate the various sections of this help:
Data
Field in Data Entry Form | Description | Name in Datafile |
|---|---|---|
Node Labels – Upstream | Label upstream of spill unit | Label 1 |
Node labels – Downstream | Label downstream of spill unit | Label 2 |
Breach method | Keyword: Must be ‘USER’ (reserved for future use). | method |
Weir coefficient | Weir coefficient for weir flow through open/piping breach. Default value = 1.7 [metric]; 3.08 [US]). Must be > 0. | Cdweir |
Orifice coefficient | Orifice discharge coefficient factor for orifice flow through piping breach. Default value = 1. Must be > 0. | Cdorifice |
Piping modular limit | Modular limit for piping breach weir flow. Default value = 0.9. Must be > 0. | modlimit |
Interpolation method | Method of interpolation for piping breach formation [keyword]: ‘SINE’ (default) – use a sine curve to interpolate between two successive values; ‘LINEAR’ – linearly interpolate between two successive values | interp |
Piping breach collapse factor | Piping breach collapse factor. Height of piping hole as a proportion of dam/embankment height (Hb) at which piping breach will deform into an open breach. Default value = 0.6; range: 0 < fcollapse ≤ 1 | fcollapse |
Hb | Height of dam/embankment (m or ft [US]). If zero, obtained from dimensions of spill unit and upstream unit. Default value = 0. | Hb |
Minimum elevation | Minimum elevation of breach. If set to null (-9999.99), calculated from spill crest and Hb. Default value = null. | elvmin |
n/a | Number of lines in table to follow | n1 |
Time-Datum adjustment | Optional time datum adjustment – tlag will be subtracted from each ti in the table below | tlag |
Units of Time | Optional keyword or value for units of time in the following data set. Can be any numerical multiplier or one of the following: seconds (the default), minutes, hours, days, weeks, fortnight, lunar (month), months (of 30 days), quarter, years or decades | tm |
Data Extending Method | Policy for extending data if the run finishes after the end of the time series data. Options are: REPEAT – if the data are to be repeated from the beginning. EXTEND – if the flow is to be fixed at the last given value. NOEXTEND – no extension. If NOEXTEND is used or the field is left blank, then the program will stop with an error message if there are insufficient time series data | repeat |
Use trigger level | If checked (Trigger flag = ‘TRIGGER’) the time of breach formation (ti) will be relative to the first time the specified trigger level is exceeded | Trigger_flag |
Trigger Level | The trigger level. Breach timings will be relative to the time at which this is first exceeded (m [ft, US] AD) | Trigger_level |
Time | Time (in units of tm). This will be the model time, unless a trigger level is set, in which case it will be relative to the time at which this is first exceeded. | Ti |
Centre Offset | Horizontal offset of centre of breach at time ti (m [ft, US]) | xi |
Bottom Width | Breach bottom width or piping width/diameter at time ti (m [ft, US]) (must be at least zero) | bi |
Breach Elevation | Elevation of lowest point (open) or centre (piping) of breach at time ti, assumed to be at the centre of the breach (m [ft, US] AD) | hi |
Base Depth | Depth of base of breach, i.e. the crest height relative to hi at a distance bi/2 from offset xi (m [ft, US]) (not used for piping breach) | di |
Side Slope | Breach side slope at time ti. Si = 0.0 indicates vertical walls (must be at least zero) (not used for piping breach) | 1/si |
Breach type | [Keyword] Type of breach (‘OPEN’ [default] or ‘PIPING’) | type |
Piping hole shape | Shape of piping hole (‘RECTANGLE’ [default] or ‘CIRCULAR’). Only applicable to type = ‘PIPING’ | shape |
Theory and Guidance
Open Breach
The open breach can be rectangular, trapezoidal or vee-shaped (or a combination of these), and its shape, size and location within a single Spill can vary in time.
To define the shape of the open breach, the user specifies a time series of offset x (m), crest width b (m), crest elevation h (mAD), crest depth d (m) and side wall slope s (m horizontal/m vertical) as shown on the diagram below. The thick line shows the breach.
Open Breach definition data:
Item | Legal Range | Default |
|---|---|---|
x = offset of centre of breach as a function of time t. The offset is measured relative to the zero offset of the spill. | Any | Arithmetic average of first and last spill point chainages |
b = breach invert width as a function of time t | 0.0 ≤ b(t) for all t | 0.0 |
h = breach invert elevation as a function of time t (above datum) | Any | 0.0 |
d = breach invert depth as a function of time t | Any | 0.0 |
1/s = breach side slope as a function of time t | 0.0 ≤ s(t) for all t | 0.0 |
The offset is measured relative to the zero offset of the Spill unit. The crest elevation is relative to datum.
The coefficient of discharge and modular limit for the Breach are the same as for the Spill.
Using these parameters, breaches of different shapes can be specified. For example, a rectangular breach would have a zero side slope and zero invert depth. A Vee-shaped breach would have zero width and invert depth, but a positive slope.
After the first breach time, the breach dimensions and position will be obtained by linear interpolation between the values given in the table.
The unit state for the breach is the width of the base of the breach after truncating it to the width of the spill.
Inserting the breach in the spill
An open type breach is inserted in the spill section as follows:
- Start with unmodified spill section
- Extend horizontally to infinity in both directions
- Calculate breach section without sidewalls
- Extend sidewalls upwards at specified slope until they first intersect the spill section
- If a sidewall fails to intersect the spill section, then extend it downwards instead
- Delete the portion of the original spill between the ends of the breach and merge the breach into the section
- Trim the section back to its original extents, removing part or all of the breach if necessary
Piping Breach
A piping breach starts as a small [enclosed] hole in a structure, enlarges over time, and may ultimately collapse into an open breach. The flow hydraulics through a piping breach are therefore represented by orifice-type flow (which could also act as a weir when not submerged), whereas that through an open breach is represented entirely by weir-type flow. The piping hole may be defined as circular or square, and is assumed that the centre remains in the same location, i.e. the evolution of the hole radiates from the centre.
Hydraulics
The orifice equation allows for weir flow based on a flat or circular weir crest (i.e. at water levels low enough such that orifice flow does not develop). The following modes of flow are possible:
- Weir [overtopping] only flow – piping hole has not yet developed OR piping hole has collapsed into a fully open breach.
- Orifice-only flow (including orifice acting as a weir) – piping hole has developed; WL below spill (dam) crest
- Orifice and weir overtopping flow – piping hole has developed, and WL is above dam crest
Thus the above modes will be determined primarily by the spill geometry (noting that overtopping will depend additionally on water level).
Coefficients
Discharge coefficients will be specified for both orifice and weir flow in the breach unit. Note that the weir coefficient within the breach will supersede that specified in the associated spill unit.
Note:
the weir coefficient should be specified differently in metric and US units (i.e. the coefficient is not dimensionless, due to the √g term implicit in the formulation).
Equations
Note that the unit modes for flow through a piping breach mirror those for the orifice unit, with ten added, i.e. Mode 12 for a piping breach is equivalent to Orifice flow Mode 2 (Free Weir Flow).
Mode 10 – zero flow
Condition | y1 – zc < 0 |
Equation | Q = 0 |
Mode 12 – Free Weir flow through piping hole
Condition | y1 - zc ≤ 1.5h (rectangular) y1 - zc ≤ 1.25d (circular) (y2 - zc) ≤ h (y2 - zc) / (y1 -zc)) < m |
Equation | Q =Cweir b (y1 - zc)1.5 (rectangular) Q =Crweir ceφi d2.5 (circular) |
Mode 13 – Drowned Weir flow through piping hole
Condition | y1 - zc ≤ 1.5h (rectangular) y1 - zc ≤ 1.25d (circular) y2 - zc ≤ h (y2 - zc) / (y1 -zc)) ≥ m |
Equation | Q = fd Qfree Where Qfree is the free discharge weir flow, as defined above, and the drowning factor fd is given by: fd = √ [(1 - (y2 - zc)/(y1 - zc)) / (1 - m)] or fd = (1 - (y2 - zc)/(y1 - zc))/ (0.3* (1 - m)), if the first formula for the drowning factor gives fd < 0.3 |
Mode 14 – Orifice flow through piping hole
Condition | y1 - zc < 1.5h (rectangular) y1 - zc < 1.25d (circular) Or y2 - zc > h |
Equation | Q = cori cd A √ (2gΔh) Where the orifice discharge coefficient, cd is given by: cd = 0.799 (rectangular hole) cd = 0.6 (circular hole) and Δh = min(y1-y2, y1-0.8h) (rectangular hole) Δh = min(y1-y2, y1-0.5d) (circular hole) |
Definition of terms used in equations:
Term | Definition |
|---|---|
Q | Discharge |
y1 | Upstream water elevation above piping hole base |
y2 | Downstream water elevation above piping hole base |
zc | Piping hole base elevation |
A | Full bore area of piping hole |
h | Total depth of piping hole (diameter if circular) |
b | Breadth of rectangular piping hole (=A/h) |
d | Diameter of circular piping hole |
m | Modular limit |
cweir | Weir discharge coefficient (default = 1.7 m½s-1 or 3.08 ft½s-1) |
crweir | Circular weir relative discharge coefficient (=cweir/1.7 [metric] or cweir/ 3.08 [US]). Thus the same magnitude weir coefficient should be entered whether the hole shape is rectangular or circular (for consistency with the spill unit) |
cori | Orifice coefficient (default = 1) |
ceφ1 | Product of discharge coefficient and φ factor for circular weirs (see below – NB the dimensions in the table shown have units of m½s-1) |
y1/d | 0.000 | 0.067 | 0.134 | 0.202 | 0.270 | 0.339 | 0.408 | 0.478 | 0.550 | 0.622 | 0.696 | 0.772 | 0.851 | 0.933 | 1.020 | 1.115 | 1.221 | 1.348 | 1.520 | 1.834 |
ceφ1 | 0.000 | 0.008 | 0.033 | 0.074 | 0.131 | 0.203 | 0.289 | 0.389 | 0.503 | 0.630 | 0.771 | 0.925 | 1.092 | 1.274 | 1.472 | 1.690 | 1.936 | 2.224 | 2.598 | 3.210 |
The onset of piping hole will be user defined. A time offset must be specified from either the model start time or from when a critical water level is reached at the location upstream of the spill/breach (e.g. adjoining reservoir or channel section).
Where overtopping occurs in addition to flow through the hole, the unit mode is further increased by ten, e.g. mode 24 indicates orifice flow combined with overtopping flow. The resultant discharge is the sum of orifice flow and overtopping weir flow.
Triggers
Onset of full collapse – this may be specified explicitly by selecting an “OPEN” breach at the time of collapse, which will be explicit within a time-series specified evolution. Alternatively, an automatic collapse may be triggered by the piping hole depth reaching a specified proportion, defaulting to 0.6, of the spill (e.g. dam or embankment) height. The open hole then immediately assumes vertical sides above the initial hole, and the top continues to propagate laterally at the specified rate (i.e. becomes approximately trapezoidal).
The spill (dam/embankment) height may be specified explicitly in the breach unit, as may the minimum elevation; if not specified, the minimum elevation is deemed as being the minimum ground elevation of the unit upstream (e.g. reservoir or channel). The dam/embankment height is then the difference between the maximum elevation of the associated spill unit and the specified/calculated minimum elevation.
Note:
It is not currently possible to trigger a full collapse by hydraulic conditions, i.e. upstream water level.
Breach evolution
The evolution of the breach is specified by supplying the following information:
- time vs dimensions
- trigger water elevation level (optional) at which the breach commences (if omitted, the time is relative to the model start time)
- type, i.e. piping or open
- shape of breach (square or circular), if type = piping
- linear or sine interpolation. For a sine interpolation, the maximum rate of evolution is at the central time point; the minimum rate is at the beginning and end.
The evolution of a piping breach is represented diagrammatically by the following four stages:
- Onset of small hole (orifice):
- Growth to a large hole:
- Full collapse of hole:
- Transformation into open breach:
The following shows the above interpolation graphically. The resulting plot demonstrates how the sinusoidal interpolation of breach evolution produces a slower progression at the beginning and end, with a more rapid transition in the middle. This is commonly accepted as being more representative of reality:
The user is required to specify time offset and dimensions for a number of times as the breach progresses. For the piping hole, three values (elevation, width/diameter and lateral offset) are required to define the breach; if an open breach is subsequently specified, the five values defined above for the Open breach are required.
A piping breach may develop into an open breach, but the converse is not true, i.e. a piping breach may not be preceded by an open breach.
If a breach is specified manually as a piping breach deforming into an open breach (i.e. not automatically deforming), an open breach will occur instantaneously at the time of the first open breach value; prior to this, the final piping breach values will persist.
Outputs
If “Output breach profiles” is selected in the 1D run options, coordinates of the breach (for a circular hole, 12 coordinates are given) are output to the diagnostics (*.zzd) file.
Note:
Discontinuities between orifice and weir flow (piping to open breach) are acknowledged as being likely, particularly when the piping hole deforms into an open breach. It is therefore recommended in such cases that the schematization each side of the breach is chosen to be able to handle the discontinuity, e.g. a reservoirs, which use volume balance are appropriate, or the 2D TVD method receiving the output, are designed to cope with a discontinuity/rapid change.
Datafile Format
The format of the datafile is as follows.
Line 1 - keyword "BREACH #revision#2" [comment]
Line 2 - Label1, Label2
Line 3 – method, cdweir, cdorifice, modlimit, interp, fcollapse, H, elvmin, shape
Line 4 – n1 , [tlag], [tm], [repeat], trigger_flag, trigger_level
Line 5 to 4+n1 – ti, xi, bi, hi, di, si, type
An example of the datafile format is given below.
Breach Errors
The following errors/warnings may be generated.
Code | Message | Comments |
|---|---|---|
E1605 | Version number is not supported in this version of Flood Modeller | The breach was generated using a more recent version of Flood Modeller. Contact your supplier for an upgrade |
E1606 | Negative breach width is invalid |
|
E1607 | Negative breach side slope is invalid. | The breach side slope is the slope of the right-hand wall of the breach, specified as (horizontal change / vertical change). The walls are not allowed to project over the breach. |
E1580 | Unrecognised time factor keyword | Same error as occurs in Flow Time Boundaries |
E1106 | No data after time t | Same error as occurs in Flow Time Boundaries and other units |
E1175 | Number of spill segments has exceeded 30 | >Same error as occurs in spills anyway, but caused directly by the incorporation of the breach. The breach itself requires up to 5 of the 30 allowed points in the spill section |
E1608 | Unable to fit breach section into spill profile | Check the data for the breach and the spill. If they look OK, then contact support. (Internal engine error) |
E1786 | A PIPING breach cannot occur after an OPEN breach | One cannot specify an OPEN breach followed by a PIPING breach in the same time series |
E1787 | Cannot interpolate from a PIPING to an OPEN breach | A PIPING breach time series must contain at least two rows of PIPING breach data, i.e. a first row of PIPING breach data may not be followed by a second row of OPEN breach data |
E1788 | You need at least two rows of data for a piping breach to evolve | A PIPING breach time series must contain at least two rows of data |
W2328 | Sine interpolation between three+ points may produce strange results | Sine interpolation is intended for interpolation between two values. It will still interpolate piecewise sinusoidally between each pair, although will produce an extra point of inflexion. |
W2329 | Weir discharge coefficient for open breach not set | Discharge coefficient of associated spill unit will be used for weir flow in the breach |
W2330 | Spill/dam height not set | Height will be calculated from spill crest & connected bed levels |
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