Pier-loss Bridge
    • 22 Sep 2022
    • 9 Minutes to read
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    Pier-loss Bridge

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    Article summary

    The pier loss bridge computes the afflux at bridges where the dominant cause of losses is the friction from piers. It utilizes the empirical equation derived by Yarnell (1934)

    Data

    Pier-loss Bridge Data

    Parameter name

    Description

    Label name in data file

    Upstream label

    Upstream node name – immediately upstream node in network

    Label1

    Downstream label

    Downstream node name- immediately downstream node in network

    Label2

    Upstream river section

    Label of upstream RIVER section. Optional: This label is not required if the upstream RIVER section is Label1

    Label3

    Downstream river section

    Label of downstream RIVER section. Optional: This label is not required if the downstream RIVER section is Label2

    Label4

    Loss model method

    YARNELL. Keyword referring to the modelling method: currently only option is YARNELL, hence this is not included as a setting in the pier loss bridge interface. The software will set this value automatically in your network file.

    Keyword

    Calibration coefficient

    Global calibration coefficient: Can be any non-negative real number.

    Used to scale the calculated afflux if this is justified by observations. It should normally be set to 1. Setting cali to 0 removes the effect of the bridge (but not the effect of any flood culverts).

    cali

    alternative method

    Alternative method. Defines calculations to apply when bridge is surcharged. The default option is ORIFICE, set by the 'Model surcharged bridge as orifice flow' checkbox; if unchecked (not recommended, since the Yarnell equation is not validated for surcharged flow), this field is left blank and the Yarnell equation will apply for surcharged flow also.

    altmethod

    Orifice Discharge Coefficient

    orifice discharge/calibration coefficient – only used when calculations transition to ORIFICE alternative method (i.e. as bridge becomes surcharged). Must be real, non-negative number.

    cdorifice

    Lower Transition Distance

    Lower transition depth (distance below soffit in m or ft).

    When the upstream water level is below [max soffit level - rlower], the Yarnell bridge equations only are used. When this level is reached, it enters the transition phase between bridge and orifice flow where flow is calculated using both Yarnell and orifice equations and a weighted average is used.

    Constraint: rupper + rlower ≥ 0

    rlower

    Upper Transition Distance

    Upper transition elevation (distance above soffit in m or ft).

    When the upstream water level exceeds [max soffit level + rupper], the bridge to orifice transition ends and full orifice equations apply.

    Constraint: rupper + rlower ≥ 0

    rupper

    pier coefficient

    Pier (or Yarnell) coefficient, K: can be any real value in the range 0.7 to 2.5.

    This coefficient accounts for differences in friction caused by pier shape. Suggested values for different standard pier shapes are provided in Table 1 below (note this list may not be exhaustive):

    Table 1: Suggested values of pier coefficient

    Pier Shape

    Pier Coefficient (K)

    Semi-circular nose and tail

    0.9

    Twin-cylinder piers with connecting diaphragm

    0.95

    Twin-cylinder piers without diaphragm

    1.05

    90-degree triangular nose and tail

    1.05

    Square nose and tail

    1.25

    Pier consisting of multiple columns

    2.5

    Note: Adjustment of this coefficient can help with model calibration.

    K

    bridge width

    Width of bridge (in m or ft), i.e. distance between upstream and downstream faces of bridge. Not currently used by computation, entry is for reference only (in case you want to change to a different bridge type in future that requires this)

    Should be non-negative real number (can just be left as default = 0.0)

    rdlen

    Data for Channel Section at Upstream Face of Bridge

    Parameter name

    Description

    Label name in data file

    No. of data points

    Number of data entries describing the upstream face of the bridge cross-section.

    Not a data entry - solver sets this based on number of data rows defined in upstream section table. Minimum of 3 data points should be defined, i.e. a triangular section. OR can be set to zero, in which case the downstream section data will be adopted for both bridge faces (and so must be defined)

    The upstream bridge cross-section extends along the toe of any embankment on the left floodplain, across the channel, and along the toe of any embankment on the right flood plain. This can be thought of as the river and floodplain section prior to bridge construction

    npts_us

    Cross-chainage

    Cross-chainage (m or ft). Chainage is expected to be a real number and increasing

    usxpi

    Elevation

    Elevation of bed or flood plain (m or ft AD). Must be a real number

    usypi

    Mannings n

    Manning roughness coefficient. Must be a positive, real number

    usrni

    Embankment indicator

    Mandatory field of 1 character; only options are ‘L’ or ‘R’ to indicate left or right embankments of main channel

    Interface presents options “Left” and “Right” for you to select to set these indicators. The section can only have one left and one right marker.

    uschmaini

    Top level

    The top level represents the soffit elevation at your specified left and right embankment points (note that any top-level entries on rows that are not embankment indicators will be ignored by the solver). The top-level values should be measured using the same reference datum as the section elevation data.

    ustoplev

    Data for Channel Section at Downstream Face of Bridge

    Parameter name

    Description

    Label name in data file

    No. of data points

    Number of data entries describing the downstream face of the bridge cross-section.

    Not a data entry – solver sets this based on number of data rows defined in downstream section table. Minimum of 3 data points should be defined, i.e. a triangular section. OR can be set to zero, in which case the upstream section data will be adopted for both bridge faces (and so must be defined)

    The downstream bridge cross-section extends along the toe of any embankment on the left floodplain, across the channel, and along the toe of any embankment on the right flood plain. This can be thought of as the river and floodplain section prior to bridge construction

    npts_ds

    Cross-chainage

    Cross-chainage (m or ft). Chainage is expected to be a real number and increasing

    dsxpi

    Elevation

    Elevation of bed or flood plain (m or ft AD). Must be a real number

    dsypi

    Mannings n

    Manning roughness coefficient. Must be a positive, real number

    dsrni

    Embankment indicator

    Mandatory field of 1 character; only options are ‘L’ or ‘R’ to indicate left or right embankments of main channel

    Interface presents options “Left” and “Right” for you to select to set these indicators. The section can only have one left and one right marker.

    dschmaini

    Top level

    The top level represents the soffit elevation at your specified left and right embankment points (note that any top-level entries on rows that are not embankment indicators will be ignored by the solver). The top-level values should be measured using the same reference datum as the section elevation data.

    dstoplev

    Bridge Pier Data

    Parameter name


    Description

    Label name in data file

    No. of piers

    Number of piers in bridge: must be integer value >0

    Not a data entry – solver sets this based on number of data rows defined in pier data table. Minimum of 1 pier must be defined.

    Pier data used to define blockage ratio (α).

    npiers

    Left x

    left x-location of pier - must be a positive real number

    Coordinates of pier edges assumed to use the same reference datum as cross-section chainage. Values should be defined left and right embankment indicators

    xleft

    Right x

    right x-location of pier - must be a positive real number

    Coordinates of pier edges assumed to use the same reference datum as cross-section chainage. Values should be defined left and right embankment indicators

    xright

    Left height

    height of pier at left x-location. Must be positive real number

    htleft

    Right height

    height of pier at right x-location. Must be positive real number

    htright

    Check

    (Optional) check for duplicate/overlapping entries

     


    RiverNodesimagesPLdata.pngRiverNodesimagesPLdata.png
    Visual Representation of Parameters for Pier Loss Bridge Unit

     Theory and Guidance

    Aim

    The pier loss bridge unit provides an improved calculation of flows through bridges where the dominant cause of energy loss is the friction from bridge piers. This is particularly useful when low flows are more frequent. The method utilizes the empirical equation derived by Yarnell (1934).

    This option can be considered for any bridge that incorporates one or more piers.

    Theory

    The formula utilized was derived by analyzing results from a large number of experiments and on-site measurements. It is known as the Yarnell equation (1) and relates the water stage (H) at the upstream and downstream areas of the bridge.

    RiverNodesimagesyarnell.png

    The subscripts US and DS denote the upstream and downstream sections respectively. The formula shows that the afflux is dependent on the shape of the piers (coefficient K), the ratio (α) of the area blocked by the structure to the total effective area upstream of the bridge, and the flow characteristics (velocity and depth) at the downstream end of the structure. In particular, VDS the velocity downstream and ω is the ratio of the velocity head (V2DS/2g) to the downstream water depth.

    RiverNodesimagesPL2.png

    Plan view of a bridge showing the relative position of cross sections (numbered) needed to apply Yarnell equation. The embankments are also shown.

    Based on the plan view of a bridge shown in the above figure, without the actual piers, the river cross sections (2) and (3) are located at the very end of bridge embankments at the upstream and downstream faces of the structure. Sections (1) and (4) are further up or down of the bridge, i.e. the adjacent river cross sections in your network. Note that if your structure is not attached directly to river sections, e.g. attached to a junction to enable incorporation of spill units with bridge, then sections (1) and (4) in the above diagram will be the closest “remote” sections to your bridge.

    Limitations

    This method has been validated through multiple experiments and on-site measurements and only applies to bridges where losses are dominated by the friction on the piers. Furthermore, there are some additional limitations to consider when applying this unit. The most important condition that needs to be satisfied is that the flow through the opening has the following criteria:

    There are some limitations when it comes to applying this modelling technique. The most important condition that needs to be satisfied is that the flow through the opening is a class A, low flow. Specifically, the flow should be:

    1. Not surcharged: the water stage should be below the soffit of the bridge opening
    2. Subcritical: the Froude number should be below 1 (0.9 for tolerance)
    3. Not choked: i.e. specific energy is above the critical value in the constriction

    The unit can still accommodate surcharging, but in this case the calculated hydraulics will assume an orifice type flow through the defined bridge openings (see below).

    The other limitation is your bridge must include one or more piers, since a fundamental part of this unit is to calculate the blockage caused by them. Thus, this method will not be suitable for all bridges.

    Orifice Flow

    The pier loss bridge unit will switch to orifice flow at a given depth, which is defined in the unit form. This has the benefits of representing surcharged flow as an orifice, which may be more representative, whilst retaining the bridge afflux calculations when not surcharged.

    You need to specify a lower level (specified as distance below highest arch soffit) at which the transition from bridge flow to orifice flow commences, and an upper level (specified as distance above highest arch soffit) at which the transition to orifice flow is complete. This allows a smooth transition from bridge to orifice flow to occur.

    The orifice equation used is the standard orifice equation in Flood Modeller, although you can adjust the coefficient by changing the orifice discharge coefficient within the bridge unit.

    Datafile Format

    Line 1: BRIDGE (keyword)

    Line 2: PIERLOSS (keyword to distinguish from other types)

    Line 3: Label1, Label2, Label3, Label4 (first two: directly connected, second two: remote units)

    Line 4: YARNELL (keyword referring to the modelling method)

    Line 5: cali, altmethod, cdorifice, rlower, rupper

    Line 6: K, rdlen

    Line 7: npts_us

    Line 8 to line 8+npts_us: usxpi, usypi, usrni, uschmaini, ustoplev

    Line 8+npts_us+1: npts_ds

    Line 8+npts_us+2 to Line 8+npts_us+2+npts_ds: dsxpi, dsypi, dsrni, dschmaini, dstoplev

    Line 8+npts_us+2+npts_ds+1: npiers

    Line 8+npts_us+2+npts_ds+2 to line 8+npts_us+2+npts_ds+2+npiers: xleft, xright, htleft, htright.


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