2D depth averaged numeric model of a small creek elbow

FACULTÉ DE GÉNIE

DÉPARTEMENT DE GÉNIE CIVIL

GCI-724 – Hydraulique fluviale

Projet de session :

Modélisation numérique bidimensionnelle d’un coude dans un ruisseau aux cantons de l’Est, Québec

Présenté à :

Jay Lacey

Duguay, Jason

Walther Gravel, Christian

Le 2 décemebre 2011

i

Abstract

A 2D depth-average numeric model using a turbulence model was used to visualise the effects of boulder cluster configuration and placement on the flow parameters present on an elbow region of a small creek. The waterway is located close to the county of Lennoxville in the Eastern Townships of Québec, Canada. A total of 14 numerical simulations were performed by arranging combinations of two flow rates (Q=0.125 m3/s and Q=1 m3/s), three boulder placements along the creek bed and two different grouping numbers (3 boulders and six boulders). The results suggest that positioning boulder clusters downstream of a targeted erosion control section on a small waterway could prove to be an effective method of erosion control. The water depths of the reaches immediately upstream of the boulder cluster are elevated due to the damming action of the boulders. This damming effect reduces the velocity magnitudes upstream of the boulder grouping and consequently also diminishes the total shear stresses being applied to the bed and consequently the erosion of the bed sediments.

ii

Avant-propos

This study was performed during the fall of 2012 as a semester project for the graduate fluvial hydraulics course in civil engineering taught by Jay Lacey (Jr. Eng., Ph.D) at the University of Sherbrooke, Québec Canada.

iii

Table of Contents

Abstract .......................................................................................................................................................... i

Avant-propos ................................................................................................................................................ ii

Table of Contents ......................................................................................................................................... iii

Table of figures ............................................................................................................................................ iii

1 Introduction .......................................................................................................................................... 1

2 Methodology ......................................................................................................................................... 3

2.1 Bathymetry ................................................................................................................................... 4

2.2 2D Numerical Depth Averaged Model .......................................................................................... 4

2.3 Boulder simulation ........................................................................................................................ 6

2.4 Simulation flow parameters .......................................................................................................... 6

2.5 Data treatement ........................................................................................................................... 6

3 Results and discussion .......................................................................................................................... 8

3.1 Validation of the numerical model ............................................................................................... 8

3.2 Average depth values .................................................................................................................... 9

3.3 Velocity magnitude and specific discharge results ..................................................................... 10

3.4 Total bed shear stress ................................................................................................................. 11

3.5 Limitations of the model and proposed methods to improve the model .................................. 13

4 Conclusions ......................................................................................................................................... 14

5 References .......................................................................................................................................... 15

Annexe A ..................................................................................................................................................... 16

Annexe B ..................................................................................................................................................... 19

Table of figures

Figure 1 : Satellite view of the study region ................................................................................................. 3 Figure 2 : Organogram of the fourteen numerical simulations performed by CCHE GUI ............................ 5 Figure 3 : Positions of the eight monitor points on the numerical mesh ..................................................... 7 Figure 4 : Calculated depths for Q=0.125 m3/s in the absence of boulders ................................................. 8 Figure 5 : Average depth of the eight monitor points for all 14 simulations ............................................... 9 Figure 6 : Average velocity magnitude of the eight monitor points for all 14 simulations ........................ 10 Figure 7 : Average specific discharge of the eight monitor points for all 14 simulations ........................... 11 Figure 8 : Average total shear stress of the eight monitor points for all 14 simulations ........................... 13

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1 Introduction

Creek bank erosion can cause significant negative impacts on adjacent civil infrastructure. For example,

lost revenues incurred by a farmer due to the erosion of arable farmland neighbouring a nearby

waterway can have drastic effects on the farmer’s revenue over the course of few years. Another

possible scenario arises often in civil engineering projects, where, because of the topology of the land or

any another physical constraint, the natural course of a small waterway needs to be diverted in order to

improve some aspect of the construction. As a case in point, the green belt connecting the City of

Sherbrooke and the town of Lennoxiville Québec at one point passes over a small creek ( see figure 1).

The bicycle path is distanced by a maximum of four meters from the outer bank of one of the creek’s

elbows which over the past few years has received a considerable amount of attention from interest

groups directed towards reducing bank erosion to protect the bike path. Frequently, the mitigation

techniques adopted to address these types of erosion problems have limited longevity and need to be

maintained on an annual or semi-annual basis. It is for this reason that this study addresses the

potential in which strategically placing boulder clusters mid-flow in a small waterway could have as a

durable erosion control technique.

The results and conclusions of this study are intended only to shed light on the potential of installing

boulder clusters as an erosion control method. This study is in no way considered an exhaustive

treatment of the subject and further research is needed in order to establish a better understanding of

how introduced boulder clusters can inadvertently generate undesirable effects on the waterway. A few

examples include increased sedimentation in the newly created slower regions, scouring around the

boulders, increased bank overflow frequency caused by the damming effects of a downstream boulder

cluster and environmental considerations such as fish habit destruction.

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2 Methodology

The topological data of the elbow region of the creek studied in this article were taken using a total

station (Leica TPS-300) in early October 2011. The length of the reach is approximately equal to 50 m

along its centerline. The width of the bed used in the model varies between 9.5 m and 7.3 m. An

arbitrary elevation of 1000 m (the elevation of the optical measuring device on the total station) was

fixed as the point of reference for the elevations of all the data points taken. Reference points of 1000

m in the x and 1000 m in the y were equally used as reference points for the lateral and longitudinal

coordinates of the data points. In all 186 topological points were measured from one installation point

located on the outer region of the elbow as depicted by the black dot in figure 1. This number of

topological points was sufficient to thoroughly cover the study region and produce a high quality mesh

for the 2D depth averaged model used to perform the simulations.

Figure 1 : Satellite view of the study region (www.google.com)

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2.1 Bathymetry

The water velocity was taken at three different heights along the water column for a cross-section

located in the elbow region of the creek. This cross section was chosen because of its narrowness and

the fact that it facilitated the flow measurements. It is important to note that the obtained flow rate

was used primarily to give only a quantitative idea of a realistic flow rate to apply in the numerical

model and secondarily to verify the depth results produced from the numerical model. The data used to

calculate the total flow rate are presented in table 1.

Table 1 : Calculated on site flow rate (m3/s)

Section number

1 2 3 4

Velocity at depth 1 (m/s)

0.1 0.2 0.26 0.03


0.08 0.19 0.25 0.1


0.06 0.11 0.14 0.01

Average (m/s) 0.080 0.167 0.217 0.047

Area of section (m2) 0.075 0.230 0.330 0.175

Flow of the section (m

3/s)

0.006 0.038 0.072 0.008

Total flow (m3/s): 0.124

2.2 2D Numerical Depth Averaged Model

The program CCHE GUI (beta release 3.28.6) along with the Mesh Generator (beta release 3.22.6),

developed by the National Center for Computational Hydroscience and Engineering, were chosen to

perform the 2D depth averaged simulations of the elbow section of the creek. The topological data

obtained in the field were first converted into an acceptable format to be used in the Mesh Generator.

A mesh with 100 divisions in the i and 100 divisions in the j was produced overtop the data points and

the bed elevations were interpolated using the random interpolation feature of the Mesh Generator.

An x-y plane image of the produced mesh along with the initial bed elevations for the unaltered creek

bed is presented in the Annexe A.

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A total of 14 simulations were run in the numerical modeller CCHE GUI. Three different boulder cluster

placements were examined; (1) upstream of the elbow, (2) at the elbow and (3) downstream of the

elbow. A fourth simulation was also performed in the absence of boulders clusters. For each of these

four scenarios two flow rates were studied Q = 0.125 m3/s and Q = 1 m3/s. Furthermore, for the three

boulder simulations two boulder groupings were examined; a grouping of three boulders and a grouping

of six boulders. The figure 2 presents how the fourteen simulation runs were organised.

Figure 2 : Organogram of the fourteen numerical simulations performed by CCHE GUI

14 numerical simulations

Entry flow rate Q= 0.125 m3/s

Upstream Placement

Grouping of three boulders

Grouping of six boulders

At the elbow



Downstream Placement



Absence of boulders

Entry flow rate Q= 1 m3/s

Upstream Placement



At the elbow



Dowstream placement



Absence of boulders

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2.3 Boulder simulation

The boulders were simulating in CCHE GUI by raising the initial bed elevations to 1000.5 m. Please refer

to the annexe B to see the placement configurations for each of the three different boulder placements.

This elevation was chosen in order to insure that the boulders protruded from the water surface for

each of the boulder placement simulations. Each boulder within a given grouping has an approximate

length of 1 m parallel to the flow and a width of 0.7 m perpendicular to the flow. The boulders are

spaced from each other by approximately 0.35 m in all directions. The same boulder configurations

were used for all the Q=0.125 m3/s and Q=1 m3/s simulations for the placements (upstream, elbow and

downstream).

2.4 Simulation flow parameters

A bed roughness value of 0.025 (Manning’s n) was applied everywhere to the mesh environment to

simulate a cobbled river bed (White 2008). Furthermore, the - turbulence model was applied to all of

the simulations. Each numerical simulation was performed using a of 1 s for a duration of 1000 s.

This choice of as well as the duration of the simulation were sufficient to achieve a steady state flow

in all of the simulations.

2.5 Data treatement

An array of eight nodal monitor points was established in the elbow section of the numerical mesh used

for the simulations. The locations of the points were determined in such a way as to not receive any

interference from the presence of the boulders in the elbow boulder placement groupings. For each of

the fourteen simulations, the flow data (water depth, velocity magnitude, total specific discharge and

total shear stress) for each of these eight points were obtained from the simulation’s history output file

and then treated to find the averages. The locations of the eight monitor points in the mesh

environment are depicted in the figure 3.

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Figure 3 : Positions of the eight monitor points on the numerical mesh (black dots)

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3 Results and discussion

3.1 Validation of the numerical model

The depths obtained from the numerical simulation for the measured flow rate of Q = 0.125 m3/s

recreate fairly accurately the actual depths measured in the creek. The water depths in the elbow

region of the simulations correspond with the measured depth values used to calculate the flow rate of

the creek. The calculated depths produced by the numerical model for the simulation where Q=0.125

m3/s in the absence of boulder clusters are shown by the coloured contours in the figure 4. The black

diagonal line represents the approximate location were the bathymetry measurements were taken. The

deepest measured depth along the creek cross section was 0.35 m. The contour values observed in the

figure 4 fall within the measured depth range of 0.1 to 0.3 m. There are, however, some regions in the

modeled flow with values in the 0.5 m to 0.7 m. Although these values were not observed along the

measured cross section, they are probably due to bed elevation interpolation imprecision in the Mesh

Generator. However, in general, the 2D numerical model seems to have realistically represented the

water depth distribution of the creek witnessed during the field day.

Figure 4 : Calculated depths for Q=0.125 m3/s in the absence of boulders

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3.2 Average depth values

The average depth values of the eight monitor points for all of the 14 different simulations are

presented in figure 5. For the simulations run with a steady state entry flow rate of 1 m3/s, the water

depth in the elbow region reaches its highest value in the simulation with a configuration of 6 boulders

placed in the middle of the downstream section of creek. Whereas, for the steady state entry flow rate

of 0.125 m3/s little depth change is observed among all of the 14 simulations. This lack of variation in

the water depth is most likely attributable to the fact that the creek bed can easily accommodate the

Q=0.125 m3/s in its width with little increase in depth. On the contrary, for Q=1 m3/s the creek bed

becomes restrictive in its width and the surplus in flow needs to be accommodated for by increasing the

depth. The dramatic increases in the average water depths in the elbow region for the simulations

performed with downstream boulder placements are most likely caused by a damming effect created by

the presence of the boulders.

Figure 5 : Average depth of the eight monitor points for all 14 simulations

0.50 0.50 0.50 0.50 0.50 0.50 0.51 0.55 0.55

0.71

0.56

0.91

1.20 1.21

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

Dep

th (

m)

Q=0.125 m^3/s

Q=1 m^3/s

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Figure 6 : Average velocity magnitude of the eight monitor points for all 14 simulations

3.3 Velocity magnitude and specific discharge results

The average velocity magnitudes for the eight monitor points for all of the fourteen different

simulations are presented in the figure 6. For the entry flow rate of 1 m3/s, a pronounced decrease in

the velocity magnitude is observed for the simulations with downstream boulders placements in

comparison to the simulations run with upstream and elbow section boulder placements. Moreover,

the average velocity magnitudes for the seven simulations with an entry flow rate of 0.125 m3/s share

the same descending trend as the 1 m3/s entry flow rate, however they are significantly less

pronounced. These observed decreases in the average velocity magnitude with respect to downstream

boulder cluster groupings are most likely explained by the increased energy dissipation of the flow as

the arriving upstream waters mix with the higher water depths produced in the elbow region by the

restrictive presence of the downstream boulders. A similar argument can be made to explain the

decreases in the specific discharges for the two flow rates observed in figure 7.

0.06 0.05 0.05 0.03

0.03

0.04 0.04

0.28 0.26

0.20

0.24

0.14

0.07 0.07

0.000

0.050

0.100

0.150

0.200

0.250

0.300

Vel

oci

ty M

agn

itu

de

(m/s

) Q=0.125 m^3/s

Q=1 m^3/s

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Figure 7 : Average specific discharge of the eight monitor points for all 14 simulations

3.4 Total bed shear stress

The average total bed shear stresses (boundry shear stress) for the eight monitor points for all fourteen

simulations are presented in the figure 8. Not surprisingly, another descending trend for the average

total bed shear stresses is once again reproduced as the boulder cluster locations are moved from

upstream to downstream of the elbow region of the creek. Since both the drag and lifting forces acting

on a sediment particle are linearly proportional to the boundary shear stress( ) as seen in the

equations 1 and 2, the boundry shear stress produced by the creek’s flow has an important influence on

the size of the sediments which can carried downstream.

Equation 1 : Drag force acting on a bed particle

Where: = boundry shear stress

CD = drag coefficient Ax = cross-sectional area f(z/zo) = velocity profile of the

0.03 0.03 0.03

0.02 0.01 0.02 0.02

0.16 0.15

0.15 0.14

0.12

0.09

0.08

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

0.180

m2 /

s

Q=0.125 m^3/s

Q=1 m^3/s

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Equation 2 : Lift force acting on a bed particle

Where: = boundry shear stress

CL = lift coefficient Ax = cross-sectional area Zo = depth of the water ZT = height above the bed of the top of the grain ZB = height above the bed of the bottom of the grain

From the equations 1 and 2 we see that an increase in the boundary shear stress will proportionally

increase the drag and lift forces acting on the bed particle. Consequently, elevated drag and lift forces

enable the flow to erode and carry away bed particles having a wider range of diameters. This in turn

increases the erosion rate of the bank’s substrate. From an erosion standpoint, the bed shear stresses

are singularly the most important flow parameter affecting the erosion rate of the outer curve’s bank

material. Accordingly, erosion control techniques aimed at decreasing total shear stresses acting on the

affected region can prove beneficial. The marked decrease in the average total shear stress observed in

the data calculated for the simulations involving downstream boulder cluster configurations suggests

that this practice could potentially be implemented to reduce the erosion rate of a creek elbow heavily

affected by bank erosion due to excessive total shear stresses.

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Figure 8 : Average total shear stress of the eight monitor points for all 14 simulations

3.5 Limitations of the model and proposed methods to improve the model

Although this study has proven effective in briefly identifying the impacts which a few boulder cluster

configurations may have on limiting bed sediment erosion, there are a number of refinements and

additions which could be introduced to the study. These modifications would help improve the

numerical model’s accuracy and fashion a more comprehensive understanding of the use of boulder

clusters as an erosion mitigation method.

The accuracy of the results produced by the numerical modeller CCHE GUI is founded on the precision in

which the measured field data represents the actual terrain after having been processed by the bed

elevation interpolator in the Mesh Generator. Consequently, a more comprehensive field data

collection effort with attention on reproducing a realistic representation of the creek bed would

generate a more faithful simulation of the creek’s actual hydraulic conditions.

In addition, further mesh refinement coupled with a smaller and a longer simulation duration would

most likely increase the accuracy of the outputs. Moreover, increasing the number of monitor points

0.04 0.03 0.04 0.01 0.01 0.02 0.04

1.04

0.94

0.39

0.62

0.17

0.04 0.03

0.000

0.200

0.400

0.600

0.800

1.000

1.200 k

Pa

Q=0.125 m^3/s

Q=1 m^3/s

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and furthering their extent along the outer elbow region would improve the accuracy of the flow

parameter averages.

Further understanding could be gained by performing additional simulations with an assortment of

entrance flow rates found within the range of the creek’s annual high and low flows. Enlarging the study

area of the creek channel to accommodate a bank overflow analysis for elevated entrance flow rates

would provide a realistic depiction of the total shear stress distribution along the creek bed during

elevated flows, which from observed on site evidence, frequently occur on the creek. Furthermore, a

larger assortment of boulder cluster configurations and placements would also be instructive to identify

the most economical configurations.

The addition of a long-term sedimentation/deposition analysis into the study model would provide a

more quantitative understanding the boulder clusters contribution to lowering the erosion rate of the

bank over the span of a few years.

4 Conclusions

The results obtained from this study suggest that the placement of large boulder groupings at strategic

locations within small waterways could prove to be an effective bank erosion control method. The

counter intuitive method of installing a boulder cluster downstream of a targeted erosion control

section stands out as the best option for erosion control. This erosion mitigation method, however, will

most likely be favourable only for applications involving where the form of the creek bed in and around

the targeted erosion protection region is deep enough and of the correct profile to form a small pool

upstream of the boulder clusters. The form of the creek bed at the area where the boulder clusters are

to be place needs to be able to constrict the flow without giving away to excessive bed erosion itself.

Considerations must also be given to the possibility of increasing the frequency of overbanking events in

the elbow region and to the detrimental effects that they engender on the surroundings.

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5 References

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Annexe A

The image above is an XY plane view of the mesh environment produced by the Mesh generator. This mesh was used as the basic form of the creek bed for the fourteen simulations. The coloured contours in the image indicate the initial bed elevations.

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Annexe B

Upstream boulder cluster placement (top two figures) and elbow region boulder cluster groupings (two lower figures).

Downstream boulder grouping placements three boulders and the six boulders (orange groupings).

2D depth averaged numeric model of a small creek elbow

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