Predictive competence of Existing Bridge Pier Scour Depth Predictors

Transcription

1 European International Journal of Science and Technology Vol. 2 No. 1 February 2013 Predictive competence of Existing Bridge Pier Scour Depth Predictors Mubeen Beg 1 1 Associate professor, Department of Civil Engineering, Z.H. College of Engineering & Technology, AMU, Aligarh , U.P., India, address: raisbeg@hotmail.com Abstract The accurate estimation of maximum local scour depth at the bridge piers is vital for safe and economical design of bridges. The available predictors produce wide range of scour estimates for the same set of data. In this paper fourteen commonly used and cited bridge pier scour predictors are testified against the published laboratory and field data obtained from various sources and author s experimental data in order to ascertain which of the predictors produce a reasonable estimate of the bridge pier local scour depth. The degree of performance of each predictor was accomplished by determining the percentage of data coverage between a band of discrepancy ratio of 0.5 to 2.0, by plotting scatter grams and by carrying out statistical tests. The study reveals that the predictors of Laursen and Toch and Jain & Fischer produce a reasonable estimate. The study is useful for the hydraulic engineers concerned with economical design and construction of bridges. KEY TERMS: bridge pier, local scour, bridge failure, economical design, accuracy, estimation. 1. Introduction Piers and abutments are integral part of a bridge structure that obstruct the natural river flow and result in local scouring around them. Local scour involves removal of material from around bridge piers and abutments. It is caused by an acceleration of flow around the bridge foundation. Local scour can be either clear-water or live-bed. Live-bed conditions occur when there is transport of bed material in approach reach. Clear-water conditions occur when there is no bed material transport. Live-bed local scour is cyclic in nature as it allows the scour hole that develops during the rising stage of the water flow to refill during the falling stage. Clear-water scour is permanent because it does not allow for a refill of the scour hole. Many bridges failed in many countries because of extreme scour around bridge piers and abutments during floods Shirole and Holt (1991). Foundation of a bridge pier in an erodible river-bed is quite expensive as it has to be taken deep enough to provide the minimum anchorage length for the safety of the foundation. Therefore, failure of bridges due to scour results in economical loss and may also result in losses of human life. An accurate estimation of scour depth at piers is essential for safe design of bridge foundation because under - estimation may lead to costly bridge failure and possibly the loss of lives, while over-estimation can result in huge money wasted on the construction of a bridge. As a result, local scour depth estimation around bridge piers has attracted considerable research interest and an extensive research has been conducted over the past several years (Chabert and Engeldinger (1991); Larsen and Toch (1956); Liu, Chang and Skinner (1961); Shen, Schneider, and Karaki (1969); Melville (1975); Hjorth (1975); Ettema (1980); Baker (1981); Jain (1981); Raudkivi and Ettema (1983); Melville and Sutherland (1988); Kothyari (1989); Yanmaz and Altinbilek (1991); Kothyari, Garde and Ranga Raju (1992 a,b); Garde and Kothyari (1995); Dey (1997); Dey, Bose and Sastry (1995); Sumer, Fredsoe and Christiansen (1992); Jones, Kilgore and Mistichelli (1992) and Sheppard et. 161

2 European International Journal of Science and Technology ISSN: al., (2004)). A number of formulae to estimate the maximum scour depth at bridge pier have been developed, however, as the physical processes involved are very complex and difficult to analyze, most design scour depth predictive models are based on laboratory scale experimental results. Most of the formulae are applicable to limited range of hydraulic and geometric conditions. Furthermore, variability of natural rivers often exceeds the limitations of these formulae and estimation of local scour depth becomes a big challenge to practicing engineers. In such situation, over-estimation is a usual practice in order to avoid uncertainties and possible failure. However, for a bridge, the designers should concern with both safety and economy. Due to economical reason, over design is undesirable. Therefore, it is important to estimate the local scour depth precisely around the piers. A literature survey of the various formulae for estimating the scour depth was published by Breusers, Nicollet and Shen (1977). Coleman and Melville (2001) presented evaluation on failure of three bridges in New Zeeland. Johnson (1995) made a comparison of pier scour formulae using field data. Koopaei and Valentine (2003) compared the difference between the local scour data collected from self formed laboratory channels with predicted local scour depth computed using some formulae for estimating local scour depth at pier site. They concluded that most of the formulae over-predicted the maximum local scour depth. Johnson (1992) developed safety factors that are direct reflection of the allowable level of risk using a probabilistic approach. Various formulae give widely differing estimates of local scour. These disparities have been discussed by Melville (1992), Kandasamy and Melville (1988) and Breusers and Raudkivi (1991). To ascertain which of the predictors produces a reasonable estimate of scour depth, fourteen of the commonly used and cited local scour formulae mentioned below are applied to author s laboratory data and published field and experimental data from New Zealand, Canada, India and Pakistan in this study. 2. Scour depth predictors considered in present study The formulae of Colorado State University (1993), Laursen and Toch (1956), Chitale (1962), Larras (1963), Shen I (1969), Shen II (1969), Breusers (1972), Breusers et. al., (1977), S.C. Jain (1981), Jain and Fischer (1980), Raudkivi I (1986), Raudkivi II (1986), Froehlich (1988), Melville and Sutherland (1988) and Sheppard et. al., (2004) were examined using new data from laboratory and published field and experimental data. The basis of selection of these formulae is due to their regional validity. 3. Data and Methodology The new experimental data collected by author from laboratory model study at Civil Engineering Department, Z.H. College of Engineering and Technology, Aligarh Muslim University, Aligarh, India given in Table 1, the data from published papers of Chiew and Melville (1987), S.C. Jain (1981), Jain and Fischer (1980), H.W. Shen (1969), E. M. Laursen 1960), Ferdous and Rajaratnam (1998) and field data collected by Inglis (1949),Arunachalam (1965), Published Canadian river data, field data for railway bridge over Tista river near Jalpaiguri (West Bengal), Shahdra railway bridge on Ravi river near Lahore, data for model studies at IRI Lahore (1981) and proto type data collected by RDSO (1972) were used in present study. The field data are given in Tables 3, 4 and Collection of new laboratory data The new experimental data given Table 1 were obtained from the laboratory model study done at Aligarh Muslim University, Aligarh, India. The experiments were performed in 1,100 cm long, 75.6 cm wide and 55 cm deep rectangular re-circulating tilting flume. Water was supplied to the flume from a constant head overhead tank which got its supply from the laboratory water supply system. Flow straightners were provided at the upstream end of the flume to ensure uniformly distributed flow with minimum turbulence across the width of the flume. Water supply into the flume was regulated by operating a valve provided in the pipe line supplying water to the 162

3 European International Journal of Science and Technology Vol. 2 No. 1 February 2013 flume. A calibrated bend meter was used for measuring discharge passing through the flume. Depth of flow and the level of the sediment bed in the flume were measured using a point gauge which could be moved over adjustable rails mounted on the walls of the flume. The uniform flow conditions were established with the help of inlet valve in the supply line and the tailgate provided at the downstream end of the flume. Graded layers of glass beads followed by a wooden transition were placed at the entrance of the flume to ensure smooth flow without disturbing the sediment bed in the flume. As such, water flowing out of the flume was clear and virtually sediment free. A sediment trap was provided at the downstream end to collect sediment coming from the upstream. Fig. 43 illustrates a schematic set up for the flume with a pier model. The sediment with d 50 of 0.95 mm and geometric standard deviation 1.2 was used to fill flume bed up-to a depth of 25 cm. Pier models of different diameters ranging between 33 mm to 72 mm were fixed at the center of the flume width. The objective of the laboratory experiments was to collect reliable data to validate the above mentioned fourteen local scour depth predictors. All the experiments were conducted at flow condition close to the incipient condition of sediment motion with constant flow depth of 14 cm, average flow velocity of 0.39 m/s and U * /U * c = Values of sediment coarseness ratio b/d 50 in present study were selected as suggested by Melville and Chiew (1999).The test section for all experiments was located at 4.5 m from the flume inlet. All the tests were carried out until the scour depth did not change by more than 5% of the pier diameter over a period of 24 hours, as suggested by Melville and Chiew (1999). At the end of the test, the scour features were photographed as shown in Fig. 44. The values of the various parameters of authors data used in the present study are shown in Table 1. The above mentioned data were processed, compiled and utilized, to estimate scour depth at piers using fourteen scour depth predictors. The predicted scour depths were then compared with the observed scour depth in terms of discrepancy ratio which is defined as the ratio of the scour depth calculated by using any of the selected formula to the measured scour depth. This ratio for each individual data using all the selected formulae was computed. The scour depths predicted by the predictors used in this study for author s new laboratory data and published experimental and field data are plotted against observed scour depths and shown in Figs. 1 to Analysis of Results and Discussion The plots of predicted versus measured scour depths for author s new laboratory data, published experimental and field data, are shown in figures 1 to 42. The closeness of data points to the line of perfect agreement indicates the accuracy of the predictor. Comparison of figures 1 to 42 reveals that in general the predictors (Jain and Fischer (1980), Shen, Schneider and Karaki (1969) and Colorado State University (1993) produce a more reasonable estimate as compared to other predictors. This observation is also supported by the three statistical tests conducted on the presently used predictors (Table 2) with minimum prediction errors. For author s new laboratory data, the comparison of Figs. 1 to 14, scatter plots reveal that the predictors of Colorado State University (1993) and Chitale (1962) give better results as compared to others. Scatter plots shown in Figs. 15 to 28 for published laboratoy data indicate that the predictors of Jain and Fischer (1980) and Shen, Schneider and Karaki (1969) yield better estimates of scour depth. The scatter grams for published field data shown in figures 29 to 42 reveal that the formulae of Jain and Fischer (1980), Shen-II (1969) and Laursen and Toch (1956) give better performance. 4.1 Statistical tests for assessment of productive ability of selected formulae The predictive ability of the selected formulae was tested by comparing the predicted scour depths with observed scour depths within a band of discrepancy ratio of 0.5 to 2.0. Three statistical tests were also carried out to determine the formulae with minimum prediction errors. These tests are Mean Absolute Error 163

4 European International Journal of Science and Technology ISSN: (MAE), Root Mean Square Error (RMSE) and Theil s Cofficient (U).Theil s coefficient U and Mean Absolute Error (MAE) and Root Mean square Error (RMSE). U = [1/n 164 n i= 1 n MAE = i= 1 n RMSE = i= 1 (d s ) c - (d s ) o ] 1/2 / [1/n e i / n e i 2 / n n i= 1 (d s ) c 2 ] 1/2 + [1/n n i= 1 (d s ) o 2 ] Where U = 0 for perfect prediction; U = 1 for unsuccessful model. e i = Abs (observed predicted) ; (d s ) c = computed scour depth (d s ) 0 = observed scour depth The values of Theil s coefficient U and Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) yielded by all fourteen scour depth predictors for authors data and published flume and field data are presented in Table 2. The lower values of statistical test parameters U, MAE and RMSE mentioned against different predictors in bold in Table 2, indicate the more comparable scour depth predictors. Taking into consideration the over all accuracy of all the predictors given in Table 2, the predictors of Laursen and Toch and Jain and Fischer seem to give better estimates than others. Taking into account the flume and field data, the large scattering of data around the line of perfect agreement shown in some of Figs. 1 to 42 indicates the large discrepancy between predicted and observed scour depths. This discrepancy may be attributed to various factors which are different than which are used in the development of these predictors, for example, the conditions in the laboratory are different from prototype. Sometimes, scour of the river bank leads to the stream changing its course altogether and outflanking the bridge. Major scour occurs during floods, that is, when the flow is unsteady. At low flow, scour may take place due to obliquity. Sometimes problems may be caused by floating debris and ice packs also. The formulae are derived on the basis that upstream velocity profile is uniform, the bed around the cylinder is nearly horizontal and that the sediment grain size distribution is relatively homogenous. Also, some times, the pier is shaped differently what has been investigated in the previous studies. Therefore, estimation by these formulae can be uncertain for some situations and thus as the laboratory conditions are different from that existed in prototype, validation of the various formulae using both the laboratory as well as the field data assumes significance in order to improve the prediction of maximum local scour depth at bridge piers. An accurate prediction of scour depth will decrease the unnecessary expenses on scour counter measures and will increase the confidence in bridge designers and safety of the users. 5. Conclusions Following conclusions are drawn from present study (1) In general the predictors of Larsen and Toch. (1956), Jain and Fischer (1980), Shen (1969), Schneider and Karaki (1969) and Colorado State University (1993) produce a more reasonable estimate as compared to other predictors. (2) For author s new laboratory data, the predictors of Larsen and Toch (1956), Colorado State University (1993) and Chitale (1962), give better results as compared to others. (3) For published field data the predictors of Jain and Fischer (1980) and Shen, Schneider and Karaki (1969), yield better estimates of scour depth. (4) For published experimental data the formulae of Jain and Fischer (1980) and Shen-II (1969) give better performance.

5 European International Journal of Science and Technology Vol. 2 No. 1 February 2013 (5) Based on statistical test parameters U, MAE and RMSE, over all accuracy of Laursen and Toch and Jain & Fischer, give better estimates than others. (6) The percentiles in bold mentioned against different predictors signify degree of predictive ability of the corresponding predictors. (7) The large scattering of data around the line of perfect agreement shown in some of figures indicates the large discrepancy between predicted and observed scour depths. (8) The scattering of data around the line of perfect agreement may be attributed to various factors which are different than which are used in the development of these predictors. The formulae are derived on the basis that upstream velocity profile is uniform, the bed around the cylinder is nearly horizontal and that the sediment grain size distribution is relatively homogenous. Also, some times, the pier is shaped differently what has been investigated in the previous studies. Therefore, estimation by these formulae can be uncertain for some situations and thus as the laboratory conditions are different from that existed in prototype, validation of the various formulae using both the laboratory as well as the field data assumes significance in order to improve the prediction of maximum local scour depth at bridge piers. An accurate prediction of scour depth will decrease the unnecessary expenses on scour counter measures and will increase the confidence in bridge designers and safety of the users. 6. References Ahmed, F. & Rajaratnam, N. (1998). Flow around bridge piers, Journal of Hyd. Engrg. ASCE, Vol. 124 No. 3, Arunachalam, K. (1965). Scour around bridge piers, Journal of Indian Roads Congr. 29 No.2, Sumer, B. M. Fredsoe, J.& Christiansen, N. (1992). Time scale of scour around a vertical pile, in Proc. 2nd Int. Offshore and Polar Engineering Conference., Vol. 3, San Francisco, C. A., Baker, C.J. (1981). New design equation for scour around bridge piers, Journal of Hydraulic Division, A.S.C.E., Vol. 107 HY-4. Breusers, H.N.C. (1972). Local scour near offshore structures, Delft Hydraulics Laboratory, Publication No Breusers, H.N.C. & Raudkivi, A.J. (1991). Scouring, Hydraulic Structure, Manual, I.A.H.R., Balkema, Rotterdam, Netherlands. Breusers, H.N.C., Nicollet, G., & Shen, H.W. (1977). Local scour around cylindrical piers, Journal of Hydraulic Research, Vol. 15 No, Chabert, J. & Engeldinger, P. (1956). Etude des Affouillement autour des Piles des ponts (Study on scour around bridge Piers), Laboratoire National d Hydraulique, Chatou, France. Chiew, Y.M. & Melville, B.M. (1987). Local scour around piers, Journal of Hydraulic Research, Vol. 25 No. 1, Chitale, S.V. (1962). Discussion of scour at bridge crossings, by E.M. Laursen, Transactions, ASCE, Vol Part 1, Coleman, S.E. & Melville, B.W. (2001). Case study: New Zeeland Bridge scour experiences, Journal of Hydraulic Eng., ASCE, 127, Coleman, S.E. & Melville, B.W. (2001). Case study: New Zealand bridge scour experiences, J. of Hydraulic Engrg., ASCE, 127, pp Richardson, E.V., Harrison, L.J., Richardson, J.R., and Davis, S.R. (1993). Evaluating scour at bridges Colorado state university 1993, (2nd ed.). Washington, DC, Federal Highway Administration Hydraulic Engineering Circular, April 1993 revision, FHWA-IP , 237 p. Dey, S. (1997). Local scour at cylindrical piers, part I, a review of developments of research and part II: bibliography, International Journal of Sediment Research, WASER, China, Vol. 12 No. 3,

6 European International Journal of Science and Technology ISSN: Dey, S., Bose, S.K. & Sastry, G. L.N. (1995). Clear-water scour at circular piers: a model, Am. Soc. Civ. Eng., J. of Hydr. Engrg., 121(12), Ettema, R. (1980). Scour at bridge piers, Report No. 216, School of Engrg., University of Auckland, Auckland, New Zealand. Froehlich, D.C. (1988). Analysis of onsite measurements of scour at piers, American Society of Civil Engineers National Conference on Hydraulic Engineering: Colorado Springs, CO, American Society of Civil Engineers, Garde, R.J. & Kothyari, U.C. (1995). State of art report on scour around bridge piers, UNEP, India HEC-18. (1991). Evaluating scour at bridges, Hydraulic Engineering Circular No. 18, Federal Highway Administration (FHWA), USDOT, Washington, D.C. Hjorth, P. (1975). Studies on the nature of local scour, Bulletin Series A, No. 46, Department of Water Resources Engrg. Lund Institute of Technology, Lund, Sweden. Inglis, C.C. (1949). The behaviour and control of rivers and canals, Central Water Power Irrigation and Navigation Report, Poona Research Station, Research Publication 13, Part I and II. Jain S.C.& Fischer. (1980). Scour around bridge piers at high flow velocities, journal of Hyd. Div., ASCE, Vol. 95, No HY11. Jain, S.C. (1981). Maximum clear-water scour around piers, Journal of Hydraulic Division, ASCE, 107, Johnson, P.A. (1992). Reliability-based pier scour engineering, Journal of Hydraulic Engrg., ASCE, 118, Johnson, P.A. (1995). Comparison of pier scours equations using field data, Journal of Hydraulic Engrg., ASCE, 121, Jones, S.T., Kilgore, R.T., & Mistichelli, M.P. (1992). Effects of footing location on bridge pier scour, J. of Hydr. Engrg., ASCE, 118(2), Kandasamy, J.K. & Melville, B.W. (1988). Maximum local scour depth at bridge piers and abutments, Journal. of Hydraulic Research, IAHR, Vol. 36 No.2, Koopaei, K.B. & Valentine, E.M. (2003). Bridge pier scour in self formed laboratory channels, Technical Report, University of Glasgow, Glasgow, U.K. Kothyari, U.C. (1989). Scour around bridge piers, Ph.D. Thesis, Univ. of Roorkee, Roorkee, India. Kothyari, U.C., Garde, R.J. & Ranga Raju, K.G. (1992 a). Temporal variation of scour around circular bridge piers, Journal of Hydraulic Engrg. ASCE. Vol. 118 No. 8, Kothyari, U.C., Garde, R.J. & Ranga Raju, K.G. (1992 b). Live-bed scour around cylindrical bridge piers, J. of Hydraulic Research, I.A.H.R., Vol. 30, No. 5, pp Larras, J. (1963). Profondeurs Maximales d Erosion des Fonds Mobiles autour des Piles en Riviero, Annales des Ponts et Chausses, Vol. 133 No. 4, Larsen, E.M.& Toch, A. (1956). Scour around bridge piers and abutments, Iowa Highway Research Board, Bulletin No. 4, Ames, Iowa, USA. Laursen E. M. (1960). Scour at bridge crossings, Journal of Hyd. Div., ASCE, Discussion by Chitale, S.V., Liu, H.K., Chang, F.M. & Skinner, M.M.. (1961). Effect of bridge construction on scour and backwater, Res. No. CER-60-HKL-22, Dept. of Civil Engrg. Colorado State University, U.S.A. Melville, B.W. (1975). Local scour at bridge sites, Report No. 117, Univ. of Auckland, School of Engrg., Auckland, New Zealand. Melville, B.W. (1992). Local scour at bridge abutment, journal of Hydraulic Engrg., ASCE, 18,

7 European International Journal of Science and Technology Vol. 2 No. 1 February 2013 Melville, B.W. & Sutherland, A.J. (1988). Design method for local scour at bridge piers, Journal of Hydraulic Engrg., ASCE, 114, Melville, B.W. & Chiew, Y.M. (1999). Time scale for local scour at bridge piers, Journal of Hydr. Engrg., ASCE, 125(1), Qadar, A. (1981). The vortex scour mechanism at bridge piers, Proceedings of Institution of Civil Engineers, Vol. 71, Pt. 2, pp Raudkivi, A.J. (1986). Functional trends of scour at bridge piers, Journal of Hydr. Engrg. ASCE, 112(1), Raudkivi, A.J. & Ettema, R. (1983). Clear-water scour at cylindrical piers, Journal of Hydraulic Engrg., ASCE, 109, Research Design Standards Organization Lucknow, (1972). Scour around piers, Bridges and Floods Report No. RBF-10. Richardson, E.V. & Abed, L. (1993). Top width of pier scour holes in free and pressure flow. Proc., Nat. Conf. Hydraulic Engrg. Part 1 (of 2) Jul 25-30, pt ASCE p 911. Shen, H.W., Schneider, V.R. & Karaki, S. (1969). Local scour around bridge piers, J. of Hydraulic Div., A.S.C.E., Vol. 95 No. 6, Sheppard et. al., (2004). Large scale clear-water local pier scour experiments, J. of Hydr. Engrg., Volume 130, Issue 10, Shirole, A.M., & Holt, R.C. (1991). Planning for a comprehensive bridge safety assurance program, transportation research record Transportation Research Board of the National Academies, Washington, DC; Yanmaz, M.A. & Altinbilek, H.D. (1991). Study of Time Dependent Local Scour around Bridge Piers, J. of Hydraulic Engrg. A.S.C.E., Vol. 117 No. 10, TABLE 1: Author s New Laboratory Data S.No. Average Average depth Mean sediment velocity of flow V (m/s) of Flow D (cm) size d (mm) Pier size b (cm) Observed. scour depth (ds 0 ) (cm)

8 European International Journal of Science and Technology ISSN: TABLE 2: Summary of the Statistical Tests on the Selected Formulae Scour depth Predictors Theil s coefficient, U Mean absolute error MAE Field author Flum Field author Flum data s data e data data s data e data Laursen & Toch(1956) Larras(1963) Chitale(1962) Shen I(1969) Shen II(1969) Breusers et. al., (1977) S.C. Jain(1981) Jain & Fischer(1981) Raudkivi I(1986) Raudkivi II(1986) Melville & Sutherland (1988) Frohelich(1988) C.S.U (1993) Sheppard(2004) *The figure in bold indicates the smallest value (best prediction) Fiel d data Root mean square error RMSE author s data Flume data

9 European International Journal of Science and Technology Vol. 2 No. 1 February 2013 TABLE 3 Indian River data collected by Inglis Bridge site/river Discharge Intensityq (m2/s) Pier Dia. b (mm) Sed.Size d (mm) D=1.34(q2/f )1/3 Observ Scour depth ds Hardinge Bridge over Ganga Brahmaputra Bridge at Amingaon Par Railway Bridge Jhelam Bridge at Shahpur Alexandra Bridge near Wazirabad on Chenab Chenab Bridge at Shershah Chenab Bridge at Chiniot Ravi Bridge at Dear Baba Nanak Sutlej Bridge near Phillaur Sutlej Bridge near Adamwahan Chenab Bridge at Chund TABLE 4 Indian River Data (Broad gauge Railway Bridge over Tista River near Jalpaiguri, West Bengal, Bridge site/river Broad gauge Railway Bridge over Tista River, West Bengal Broad gauge Railway Bridge over Tista River, West Bengal Indian Data (RDSO, Lucknow, India) Bridge No. 1225/1, Jhansi, Manikpur Section CR, India Bridge No. 505, Itarsi, Jabalpur Section CR, India Bridge No. 155, Secundrabad Deoranchallum Section CR, India Bridge No. 661, Manmad, Secundrabad Section SCR, India Discharge intensity q (m 2 /s) Pier Dia. b (mm) Sed.size d (mm) D=1.34 Obs.sco (q 2 /f) 1/3 ur depth ds (cm)

10 European International Journal of Science and Technology ISSN: TABLE 5 Pakistan Data (Irrigation Research institute, Lahore, 1965) Bridge site/river Discharge Intensityq (m2/s) Pier Dia. (b) (m) Sed.Size d (mm) Obs. scour depth ds (m) Shahdra Bridge over Ravi River Fine sand Jhelam Bridge over Jhelam River Fine sand Shakarpur over Deg River Fine sand Kasur over Rohi River Fine sand Dhok Patahn over Sohan River Fine sand Thatha Sujjawal over Indus River Fine sand Pakistan River Data (Shahdra Railway Bridge on Ravi River near Lahore) Shahdra Railway Bridge over Rivi River -do do do do do do do do do do New Zealand Data (Raudkivi 1976) Tuakau Bridge Waitangi Bridge Wanganui River Bridge Matawhero Railway Bridge Canadian River Data Beaver Crossing LaCorey Crossing

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18 178 FLOW FLOW Fig (43) Schematic Diagram of Flume with Pier Pier Mound FLOW Scour hole Fig (44) Photograph Showing Scour Features Developed around a Pier 178