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
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 QuĂŠbec, 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.
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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, QuĂŠbec Canada.
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Table of Contents Abstract .......................................................................................................................................................... i Avant-propos ................................................................................................................................................ ii Table of Contents ......................................................................................................................................... iii Table of figures ............................................................................................................................................ iii 1
Introduction .......................................................................................................................................... 1
2
Methodology......................................................................................................................................... 3
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
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. 3
Table 1 : Calculated on site flow rate (m /s)
Section number 1
2
3
4
0.1
0.2
0.26
0.03
0.08
0.19
0.25
0.1
0.06
0.11
0.14
0.01
0.080
0.167
0.217
0.047
Area of section (m )
0.075
0.230
0.330
0.175
Flow of the section 3 (m /s)
0.006
0.038
0.072
0.008
3
0.124
Velocity at depth 1 (m/s) Velocity at depth 2 (m/s) Velocity at depth 3 (m/s) Average (m/s) 2
Total flow (m /s):
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. 4
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.
Upstream Placement
Grouping of three boulders Grouping of six boulders Grouping of three boulders
At the elbow Entry flow rate Q= 0.125 m3/s
Grouping of six boulders
Downstream Placement
Absence of boulders 14 numerical simulations Upstream Placement
Grouping of three boulders Grouping of six boulders
Grouping of three boulders Grouping of six boulders Grouping of three boulders
At the elbow Grouping of six boulders
Entry flow rate Q= 1 m3/s
Dowstream placement
Absence of boulders
Grouping of three boulders Grouping of six boulders
Figure 2 : Organogram of the fourteen numerical simulations performed by CCHE GUI
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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 This choice of
of 1 s for a duration of 1000 s.
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.
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Figure 4 : Calculated depths for Q=0.125 m /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 m 3/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.
1.400
Depth (m)
1.000
0.91
0.800 0.600
1.21
1.20
1.200
0.71 0.55 0.50
0.55 0.50
0.50
0.56 0.50
Q=0.125 m^3/s 0.50
0.50
0.51
0.400 0.200 0.000
Figure 5 : Average depth of the eight monitor points for all 14 simulations
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Q=1 m^3/s
Velocity Magnitude (m/s)
0.300
0.28
0.26
Q=0.125 m^3/s
0.24
0.250
Q=1 m^3/s 0.20
0.200
0.14
0.150 0.100 0.06 0.050
0.07 0.05
0.05
0.03
0.04
0.07 0.04
0.03
0.000
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.
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0.180
0.16
0.160
0.15 0.15
Q=0.125 m^3/s
0.14
Q=1 m^3/s
0.140
0.12
m2/s
0.120 0.09
0.100
0.08
0.080 0.060 0.03
0.040
0.03
0.03
0.020
0.02
0.01
0.02
0.02
0.000
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
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Equation 2 : Lift force acting on a bed particle
Where:
CL Ax Zo ZT ZB
= = = = = =
boundry shear stress lift coefficient cross-sectional area depth of the water height above the bed of the top of the grain 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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1.200 1.04
Q=0.125 m^3/s
0.94
1.000
Q=1 m^3/s 0.800
kPa
0.62 0.600 0.39
0.400
0.17
0.200 0.04
0.03
0.04
0.01
0.01
0.000
0.02
0.04
0.040.03
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
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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
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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.
Annexe B
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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).