A MODEL FOR THE EROSION RATE CURVE OF COHESIVE SOILS

Transcription

1 0 0 A MODEL FOR THE EROSION RATE CURVE OF COHESIVE SOILS Reza Rahimnejad and Phillip S.K. Ooi * Geotechnical Engineer, Ph.D. Geolabs, Inc. 00 Kalihi Street Honolulu, HI Professor, Department of Civil and Environmental Engineering University of Hawaii at Manoa Holmes Hall 0 Dole Street Honolulu, HI Tel: (0)00-00, Fax: (0)-0, rezarah@hawaii.edu Tel: (0)-, Fax: (0)-0, ooi@hawaii.edu * Corresponding author Submission date: October, 0 Word Count:

2 0 0 ABSTRACT The SRICOS EFA method provides more accurate and realistic scour predictions than the commonly-used Richardson and Davis equation in HEC-, which tends to over-predict scour especially in cohesive soils. Unlike scour of cohesionless soils, scour of cohesive soil occurs more slowly since they are more scour resistant due to inter-particle physico-chemical forces. The time-dependent nature of scour of cohesive soils can be accommodated by considering the variation of flood intensity with time through the use of a flood hydrograph, and the scour characteristics of the soil with an erosion rate curve obtained through the use of an erosion function apparatus (EFA). One drawback of the SRICOS-EFA method is that the EFA has a significant outlay. To make the method more affordable and ubiquitous, a model for the erosion rate curve is proposed based on EFA tests conducted on undisturbed fine-grained soils from water channels on the island of Oahu, Hawaii. A hyperbolic regression model was developed with four explanatory variables: water content, liquid limit, plasticity index and activity, all of which are easily measured in the laboratory. Parameter estimates for the model were then obtained using non-linear ordinary least squares. A key element of the model is that the parameter estimates logically affect the sign and magnitude of critical shear stress in accordance with observed soil behavior from experiments: i.e.; it was found that the model captures the effects of water content and plasticity index on the critical shear stress quite effectively. Also, the model provides reasonable estimates of the erosion rate curves. Use of this model in the SRICOS EFA method to estimate scour depth can result in less scour and can result in significant bridge cost savings.

3 0 0 0 INTRODUCTION The erosion function apparatus (EFA see Figure ) was developed by Briaud and his coresearchers (-) at Texas A&M University to provide an erosion rate curve used for predicting scour of cohesive soil beds with the Scour Rate In COhesive Soil Erosion Function Apparatus (or SRICOS EFA) method. This method has been shown to yield more accurate and realistic scour predictions (-) than the Richardson and Davis () equation in HEC-, which tends to over-predict scour especially in cohesive soils (Table corroborates this over-prediction by the Richardson and Davis equation as compared to the SRICOS EFA method). In an EFA test, water is run over a Shelby tube of soil placed at the bottom of a flume. The rate of scour (i.e., rate at which soil is pushed up as it is washed away) is measured under different flow velocities or shear stress to produce an erosion rate curve. The variation of scour depth with time is taken into account by considering the flood duration and intensity through the use of a flood hydrograph as well as the EFA erosion rate curve. Possible reasons why the Richardson and Davis equation over-predicts scour depths of cohesive riverbeds include:. The Richardson and Davis equation was derived based on experiments that measured scour of mostly cohesionless soils. Using this method for cohesive soils is known to lead to overestimated scour depths (Table ).. Steady flow is assumed in the Richardson and Davis equation and only the maximum flow rate is used to predict the scour depth. Unlike scour of cohesionless soils, scour of cohesive soils occurs more slowly since they are more scour resistant due to inter-particle physico-chemical forces. The time-dependent nature of scour of cohesive soils is accommodated in the SRICOS EFA method through the use of a flood hydrograph and an experimentally-derived erosion rate curve.. In the SRICOS EFA method, the erosion rate of the riverbed soil is directly measured. Richardson and Davis method does not require characterization of the erosion rate of the site-specific soil. One drawback of the SRICOS-EFA method is that the EFA apparatus requires a significant outlay. It is mostly owned by research institutions. Unquestionably, it is advantageous to make the method more affordable and ubiquitous. One way is to develop a model that can construct the erosion rate curve for any cohesive soil with a given set of soil parameters. Thus, the objectives are to () conduct numerous EFA tests on undisturbed samples of a number of cohesive soils in parallel with some common soil laboratory tests; and () develop a model to construct the EFA erosion rate curve based on these common soil parameters.

4 TABLE Comparison of scour depths from the Richardson and Davis equation versus the SRICOS EFA method Scour (ft) Water Crossing Location Richardson SRICOS Field Soil Type Reference & Davis -EFA Measured Waiahole Stream - Kamehameha Hwy. Oahu, HI..0 - Elastic Silt () Honouliuli Stream - Ft. Weaver Road Oahu, HI.0. - Elastic Silt () Moanalua Stream - H Freeway Oahu, HI Elastic Silt () Kaloi Drainage Channel - Pier Honolulu High Capacity Transit Oahu, HI Sandy Silt () Corridor Project Halawa Stream - Kamehameha Hwy. Oahu, HI.. - Elastic Silt () Coarse Sand with Kaelepulu Stream Oahu, HI.0..0 () Gravel Des Plaines River - Cermak Road Cook, IL. 0 - Silty Clay () Des Plaines River - Touhy Avenue Cook, IL. 0 - Sand Loam () Des Plaines River - Palatine Road Cook, IL Clay () Salt Creek - IL DU Page, IL. 0 - Sand Loam () Indian Creek - IL La Salle, IL Loam () La Moine River - CR 0N McDonough, IL.. - Silty-Clay Loam () Kaskaskia River - CR 0N Douglas, IL. 0 - Clay-Loam () Lake Fork - CR 00N Piatt, IL. 0 - Clay-Loam () Spring Creek - IL Sangamon, IL. 0 - Silty-Clay Loam () Little Wabash River - US Clay, IL. - Loam () Kaskaskia River - US Fayette, IL. 0 - Loam (Till) () Macoupin Creek - US Greene, IL.. - Silty-Clay Loam () Little Crooked Creek - IL Washington, IL Silty-Clay Loam () Big Muddy River - IL Franklin, IL.. - Clay Loam () Big Muddy River - IL Jackson, IL.. - Silty-Clay Loam () MD over Seneca Creek Montgomery, MD Silt (0) Lean Clay with MD over Great Seneca Creek Montgomery, MD. - Sand (0) Lean Clay with MD over Monocacy River Frederick, MD.. - (0) Sand MD over Whitemarsh Run Baltimore, MD.. - Sandy Lean Clay (0) I-/ over Woodrow Wilson Border of George Silty Clay (0) Bridge County, MD and VA Woodrow Wilson Bridge - Pier W George County, MD...0 Clay () Woodrow Wilson Bridge - Pier E George County, MD..0. Sandy Clay () Woodrow Wilson Bridge - Pier E George County, MD...0 Silt () Clayey Silt with Sloop Channel Bridge - Pier Nassau County, NY organics () Clayey Silt with Sloop Channel Bridge - Pier Nassau County, NY Organics () Sandy Silt with Goose Creek Bridge - Pier N Long Island, NY Organics () Sandy Silt with Goose Creek Bridge - Pier N Long Island, NY Organics () Navasota River Bridge at SH Grimes County, TX..0. Silty and Sandy Clay () Brazos River Bridge at US 0A Austin, TX Sandy Clay and Sand () Trinity River Bridge at FM Wise County, TX... Sandy Clay and Clayey Sand () San Marcos River Bridge at SH0 San Marcos, TX... Low Plasticity Clay () Sims Bayou Bridge at SH Harris County, TX.. 0. Clay () Bedias Creek Bridge at US McCulloch County, TX... Low Plasticity Clay ()

5 Flume Velocity Sensor Thermometer Shelby Tube Velocity Control Valve 0 0 FIGURE Erosion function apparatus LITERATURE REVIEW EFA Erosion Rate Curve A typical EFA test yields a plot of measured scour rate, Z, versus known values of velocity or shear stress,, an example of which is shown in Figure a. From the flow velocity, the shear stress, can be derived as follows: V f where = mass density of water, f = friction factor obtained from the Moody chart () = f(r e, relative roughness), V = flow velocity, R e = Reynold s number = VD/v, D = hydraulic diameter = A/P, v = kinematic viscosity of water (= 0 - m /s at 0 C), A = area of flume, P = wetted perimeter of flume, relative roughness = D, = 0.D 0 and D 0 = median soil grain size. To interpret the critical shear stress, cr, which is defined as the value of shear stress upon the onslaught of scour, Rahimnejad and Ooi () proposed swapping the axes and graphing the shear stress on a log scale to magnify the plot in the area of interest (Figure b). Another advantage of plotting the shear stress on a log scale is that the curve now approximates a hyperbola which can be mathematically represented using Equation. ()

6 Z log Z () where and are model parameters. represents the intercept of the hyperbola on the vertical axis: i.e.; = cr = critical shear stress. and can be estimated by linearly regressing all points with non-zero Z (points B through F in Figure b) with the following constraint: lower limit ( A - last point with Z = 0) cr < upper limit ( B - first point with Z > 0). Physically, is related to the initial slope (S i ) of the hyperbola. Therefore by differentiating d/dz in Equation and calculating d/dz when Z = 0, it can be shown that ln0 ln0 S i S cr () i 0 Also, is related to the asymptotic value of the hyperbola ( max ). As Z in Equation, it can be shown that log max cr () 0 From equations, and, all three parameters of the hyperbolic model are functions of cr. Thus, it is important to understand the soil properties that influence cr. Factors Affecting Critical Shear Stress Careful control of the soil properties can be attained by reconstituting cohesive soils in Shelby tubes for EFA testing. Using this idea, Rahimnejad and Ooi () consolidated four samples of the same soil to different consolidation stresses and subjected them to EFA testing. These samples have different water contents, void ratios, unit weights and consolidation stresses. For each sample, these parameters were all inter-related, measured and known. Using the hyperbolic model (Equation ) to determine the critical shear stresses, Rahimnejad and Ooi () showed that the critical shear stress increased with decreasing water content, decreasing void ratio, increasing unit weight and increasing consolidation stress. That the soils can be considered normally consolidated also suggests that the critical shear stress increased with undrained shear strength although the undrained shear strengths were not directly measured.

7 Shear Stress (Pa) Scour Rate (mm/hr) Rahimnejad and Ooi Shear Stress (Pa) (a) F.00 E D 0.0 C B A Scour Rate (mm/hr) (b) FIGURE (a) Typical EFA erosion rate curve (b) Semi-log plot of same EFA curve with hyperbolic regression line.

8 0 0 Another significant factor that influences cr is plasticity index. Dunn (), Mobley and Parker (), and Smerdon and Beasley () showed that as a soil s plasticity index increases, the critical shear stress increases. In a recent FHWA report, Shan et al. () developed a model to predict the critical shear stress of compacted cohesive soils measured using a new apparatus called the ex situ erosion testing device. They related cr to the water content (w in %), percent fines (% Fines), plasticity index (PI in dimensionless form; i.e.; not in percent) and unconfined compression strength (q u in Pa) as follows: w. 0. cr ( Pa) 0. PI qu % Fines () These trends relating cr and other soil parameters were not observed in NCHRP Report () on bridge scour. The report indicated that there was a lack of a relationship between critical shear stress and common soil parameters based on observations from a large EFA test database. This is because when soils from multiple sources are used to derive such relationships, there may be observed heterogeneity among the data sets whereby the different soils may exhibit the same trends, but the trends may be offset or may have a different rate of variation. Also, there are multiple influencing factors as discussed above that can cloud visualization of the effects of a single factor. TEST PROGRAM EFA tests were conducted on different undisturbed cohesive soil samples from the vicinity of different water channels on the island of Oahu, Hawaii (Figure ). Laboratory tests were also conducted on the undisturbed samples to measure the natural water content, Atterberg limits, grain size distribution, undrained shear strength from unconsolidated undrained triaxial tests and consolidation test parameters. Of the tests, two were discarded because of erroneous test results. Soil parameters for the remaining cohesive soils are summarized in Table. It should be noted that the database consists of high plasticity silts, low plasticity silts, high plasticity clays and low plasticity clay.

9 WAIAHOLE KALOI DRAINAGE CHANNEL HONOULIULI HALAWA KEEHI INT. FIGURE Soil sampling locations at the five water channels.

10 TABLE Soil samples and parameters Sample No. USCS Symbol w (%) PL (%) LL (%) LI S u (kpa) % < A D 0 (mm) % Fines RR CR e vm ' (kpa) OCR B/SH MH µm B/SH MH B/SH MH BA/SH MH BB/SH MH BB/SH ML BB/SH MH BA/SH MH BA/SH MH BB/SH CH BB/SH MH BB/SH MH BB/SH MH BB/SH MH BB/SH MH BB/SH MH B/SH CH B/SH ML B/SH CL B/SH ML B/SH ML B/SH ML B/SH ML B/SH MH B/SH MH B/SH MH B/SH MH B/SH MH B/SH MH B/SH MH B/SH MH Notes: () USCS = Unified Soil Classification System. () w = water content. () PL = plastic limit. () LL = liquid limit. () LI = liquidity index. () S u = undrained shear strength. () % < = percent soil mass finer than microns. () A = activity. () D 0 = medium grain size. (0) % Fines = percent fines. () RR = recompression ratio. () CR = compression ratio. () e = void ratio. () vm ' = preconsolidation pressure. () OCR = overconolidation ratio. 0

11 0 0 0 CRITICAL SHEAR STRESS MODEL From equations through, all hyperbolic parameters are functions of cr. Therefore, it is important to have a model for cr that will embody how the soil properties influence cr : i.e.; cr must decrease with increasing water content [and increasing void ratio, decreasing unit weight, decreasing consolidation stress and decreasing undrained shear strength ()] and with decreasing plasticity index (). In addition, these model parameters should be selected based on whether they:. Are easily attainable in practice; and. Statistically correlate to cr. This was examined with the aid of a bivariate correlation matrix (Table ) involving some common soil parameters and cr. From Item and Table, the following parameters are most correlated with cr : activity (0.), plasticity index (0.), liquid limit (0.), compression ratio (0.), water content/liquid limit (-0.) and liquidity index (-0.). It was decided not to use compression ratio (and for that matter all the consolidation and strength parameters) in the model because sample disturbance can affect its value significantly. Sample disturbance is less of a concern with carefully pushed and sampled thin walled Shelby tubes or Pitcher samplers. However, samples extracted using the Dames and Moore, modified California and Denison samplers can be highly disturbed. Using consolidation and strength parameters from soil obtained from these latter group of samplers or from highly disturbed Shelby tube and Pitcher samples can compromise the accuracy of the model and hence, the scour predictions. It should be noted that all samples tested were obtained from Shelby tubes with the exception of the Kaloi Drainage Channel, which were all extracted using the Pitcher sampler. Based on the above discussion and by trial and error, the following soil parameters were selected for correlation with cr : activity, plasticity index and water content/liquid limit. The following model for cr was developed: PI () cr A w LL PI where through are model parameters, PI = plasticity index, w = water content, LL = liquid limit and A = activity. At this stage, the magnitude of the model parameters are not important as they will be re-estimated using all the EFA test data set of shear stress versus scour rate rather than just the critical shear stress alone. OVERALL MODEL SPECIFICATION Each of the EFA tests contains between and data points with non-zero erosion rates giving a total of data points. These data points form the basis of a model that was developed to predict an EFA erosion rate curve for a given cohesive soil. The resulting model was developed using equations through as a basic premise, engineering judgment and a statistical software named R (). Equations,, and represent the final model.

12 TABLE Bivariate correlation matrix involving some common soil and EFA erosion rate curve parameters cr S i w PL LL PI w/ll LI S u % < µ A % Fines RR CR e vm OCR cr (kpa) S i w PL LL PI w/ll LI S u % < µ A % Fines RR CR e vm 0. (kpa) OCR S Y M M E T R I C Notes: () = cr = critical shear stress. () = hyperbolic parameter related to the initial slope (S i ) of the hyperbola. () = hyperbolic parameter related to the asymptote of the hyperbola. () S i = initial slope of the hyperbola. () w = water content. () PL = plastic limit. () LL = liquid limit. () PI = plasticity index. () LI = liquidity index. (0) S u = undrained shear strength. () % < = percent soil mass finer than microns. () A = activity. () % Fines = percent fines. () RR = recompression ratio. () CR = compression ratio. () e = void ratio. () vm ' = preconsolidation pressure. () OCR = overconolidation ratio.

13 ln0 w cr w 0PI cr cr As with Equation, through are model parameters. The rationale for having cr in both Equations and is that and are both related to cr as seen in Equations and. By using ordinary least squares regression to minimize the following objective function defined as the sum of the squares of the difference between the measured and predicted shear stress as follows: () () min OF( ) N calculated ( ) measured i () 0 where OF = objective function, calculated and measured are calculated and measured values of shear stress, respectively, is the vector of regression parameters to be estimated and N = number of data points, the model parameters were derived as shown in Table. In this model, only common and easily measured soil parameters (water content, plasticity index, liquid limit and activity) and model parameters are needed to define an erosion rate curve. Absolute values of the t-statistics for the model parameters are mostly or more, indicating they are significant at a % confidence level (Table ). Two parameters have absolute t-statistics that are approximately., suggesting that they are significant at a slightly lower but yet satisfactory confidence level (~ 0%). A comparison of predicted versus measured shear stress values for this model is presented in Figure. It can be seen that the fit is reasonably good with a coefficient of determination of 0.. TABLE Final regression parameters and t-statistics for the overall model Parameter Parameter Estimate t-statistic

14 Calculated Shear Stress (Pa) Rahimnejad and Ooi y =.0x R² = Measured Shear Stress (Pa) FIGURE Calculated versus measured shear stress from EFA tests (Total number of data points = ) PROCEDURE SUMMARY Steps of the method are as follows:. Perform water content determination, Atterberg limit testing and grain size analysis (including hydrometer testing) to estimate the water content, liquid limit, plasticity index and activity of the cohesive soil.. Estimate the critical shear stress, cr =, using Equation, constants through from Table, and the soil water content, liquid limit, plasticity index and activity from Step.. Estimate using Equation, constants and from Table, the soil water content from Step, and cr from Step.. Estimate using Equation, constants through from Table, the soil plasticity index from Step, and cr from Step.. Calculate the shear stress for different values of scour rate using Equation, cr = from Step, from Step and from Step. Alternatively, by rearranging Equation, one can calculate the scour rate for different values of shear stress as follows: Z (0) log

15 Critical Shear Stress (Pa) Rahimnejad and Ooi REASONABLENESS OF MODEL An important consideration is whether the parameter estimates all have logically correct signs: i.e.; as water content increases and PI decreases, cr should decrease. Figures and show a plot of cr versus water content and cr versus plasticity index, respectively. To generate Figure, the following parameters were used:. Liquid limit = %. Plasticity index = 0%. Activity =.0 (% finer than = %). Water content varying from 0% to 0% % 0% 0% 00% Water Content (%) FIGURE Influence of water content on the critical shear stress calculated using the model To investigate the effects of varying plasticity index on the critical shear stress as shown in Figure, the following parameters were used:. Water content = 0%. Plastic limit = %. % finer than = %. Liquid limit varying from % to % implying plasticity index varying from % to 0% and activity varying from 0. to.0. As seen in figures and, the model is well behaved since cr decreases with increasing water content and decreasing plasticity index.

16 Critical Shear Stress (Pa) Rahimnejad and Ooi 0 0% % 0% % 0% % Plasticity Index (%) FIGURE Influence of varying plasticity index on the critical shear stress calculated using the model From a statistical viewpoint, a somewhat surprising result is that the following combinations of parameters are in the expression for cr (Equation ):. Plasticity index (PI) and activity (A) and. Plasticity index (PI) and liquid limit (LL) since each of the above parameter pairs are highly correlated. Specifically, PI A () % PI LL PL () 0 0 where % < = percent of soil particles finer than microns by mass and PL = plastic limit. However, since the t-statistics of all model parameters indicate high significance plus the signs of the model parameters lead to intuitively correct trends, use of these highly correlated variables is admissible. This result stresses the importance of complementing statistical analysis with sound engineering judgment. Another important consideration is that the predicted versus measured shear stress-erosion rate curves match reasonably well. Summarized in Figure but individual plots of the erosion rate curves are omitted for the sake of brevity, it was observed that the model provides reasonable estimates of the erosion rate curves. Lastly, Figure presents calculated values of critical shear stress from the model versus experimentally derived values. It can be seen that overall, the model under-predicts the critical shear stress by only % on average and the fit is reasonably good.

17 Calculated Critical Shear Stress from Model (Pa) Calculated Critical Shear Stress from Model (Pa) Rahimnejad and Ooi 0 y = 0.x Measured Critical Shear Stress (Pa) FIGURE Measured versus calculated critical shear stress using Equation In contrast, the predicted versus measured critical shear stress using the model proposed by Shan et al. () for compacted cohesive soils in FHWA-HRT--0 is shown in Figure. 0 0 y = 0.x Measured Critical Shear Stress (Pa) FIGURE Measured versus calculated critical shear stress using Shan et al. s () model On average, Shan et al. s () model tends to under-predict the critical shear stress of soils tested in this study probably due to one or more of the following:

18 Their model is based on tests conducted on compacted cohesive soils, which do not have an intact soil structure or soil fabric;. Their critical shear stress was measured using an ex situ erosion testing device rather than the EFA; and. Their model is based on the unconfined compression strength, which can decrease due to sample disturbance. Shan et al. () related critical shear stress to soil plasticity, water content, fines content and the unconfined compression strength as shown in Equation. For the most part, the critical shear stress model developed by the authors (Equation ) contains a similar choice of parameters in that it includes soil plasticity and water content but not soil shear strength from quick tests. This is because it is well known that the unconfined compressive strength can be greatly affected by sample disturbance and it is not uncommon to have large scatter in the results. LIMITATIONS OF MODEL A limitation of the model is that it is applicable for the range of soil parameters tested in this study. The database contains mostly silts simply because that is the nature of the five cohesive riverbeds on Oahu. Therefore, this model is most appropriate for use with Hawaiian silty riverbeds. While the correlation has been shown to be causal for our dataset studied, it will be helpful if more of such tests are performed on a wider range of soil types and geographic coverage to verify this correlation further. Only potable water was used in all EFA tests conducted although it is recognized that the characteristics of the flowing water (e.g.; salinity and ph) may have an influence on soil erodibility. SUMMARY AND CONCLUSIONS The EFA provides an erosion rate curve that can be used to provide more realistic scour estimates of cohesive soil beds using the SRICOS EFA method (-) than the Richardson and Davis equation (). However, the EFA has a significant outlay. To make the SRICOS EFA method more affordable and ubiquitous, EFA and some common soil tests were performed on undisturbed fine-grained soils from water channels on the island of Oahu, Hawaii. A methodology based on practicality (all soil parameters must be easily measured in the laboratory), experimental evidence of influencing parameters and existence of statistical correlation with critical shear stress was then used to identify explanatory variables to incorporate into a hyperbolic model for the EFA erosion rate curve. The hyperbolic model is expressed in terms of four explanatory variables, which are merely common soil parameters. They include water content, liquid limit, plasticity index and activity. Parameter estimates for the model were obtained using non-linear ordinary least squares. Twelve model parameters were derived to fully define an erosion rate curve. A key element of the model is that the parameter estimates logically affect the sign and magnitude of critical shear stress in accordance with observed soil behavior from experiments: i.e.; it was found that the model captures the effects of water content and plasticity index on the critical shear stress quite effectively. Also, the model provides reasonable estimates of the erosion rate curves. Use of this model in the SRICOS EFA method to estimate scour depth can

19 result in less scour than the conventionally used Richardson and Davis equation, and can result in significant bridge cost savings. ACKNOWLEDGEMENT The financial support of the State of Hawaii Department of Transportation (HDOT) in cooperation with the Federal Highway Administration (FHWA) is greatly appreciated and acknowledged. The contents of this paper reflect the view of the authors, who are responsible for the facts and accuracy of the data presented. The contents do not necessarily reflect the official views or policies of HDOT or FHWA. The contents contained herein do not constitute a standard, specification or regulation. REFERENCES. Briaud, J.-L., Ting, F.C.K., Chen, H.C., Gudavalli, R., Perugu, S. and Wei, G. SRICOS: Prediction of scour rate in cohesive soils at bridge piers. Journal of Geotechnical and Geoenvironmental Engineering, Vol., No.,, pp. -.. Briaud, J.-L., Chen, H.C., Kwak, K.W., Han, S.W., Ting, F.C.K. Multiflood and Multilayer Method for Scour Rate Prediction at Bridge Piers. Journal of Geotechnical and Geoenvironmental Engineering, Vol., No., 00, pp. -.. Briaud, J.-L., Chen, H.-C., Li, Y, Nurtjahyo, P. and Wang, J. Pier and contraction scour in cohesive soils. NCHRP Report. Transportation Research Board, Washington D.C Tecca, N. (0). Hydrological analysis and Improved Bridge Scour Prediction for Selected Steams in Hawai i. MS Thesis. University of Hawai i at Manoa, Honolulu, HI.. Wang, Jun. (0). The SRICOS-EFA Method for Complex Pier and Cintraction Scour. Ph.D Dissertation. Texas A&M University, College Station, TX.. Kwak, K. (000). Prediction of Scour depth Versus Time for Bridge Piers in Cohesive Soils in the CAse of Multi-Flood and Multi-Layer Soil Systems. College Station, TX: Dissertation: Texas A&M University.. Richardson, E. V., and Davis, S. R. Evaluating scour at bridges. Hydraulic Engineering Circular No. (HEC-). Rep. No. FHWA-NHI 0-00, Federal Highway Administration, Washington, D.C Rahimnejad, Reza. (0). Evaluation of the SRICOS-EFA Method for Predicting Scour in Hawai ian Rivers. Ph.D. Dissertation, University of Hawaii at Manoa, Honolulu, HI.. Straub, T.D. and Over, T.M. (00). A Pier and contraction scour prediction in cohesive soils at selected bridges in Illinois. ICT-0-0. Illinois Department of Transportation. Springfield, IL. 0. Brubaker, K.L., Ghelardi, V., Goodings, D., Guy, L., and Pathak, P: Estimation of Long- Term Scour at Maryland Bridges Using EFA/SRICOS. Report No. SP0BE. Maryland State Highway Administration, University of Maryland, Maryland, 00.. Moody, L.F. (). "Friction Factors for Pipe Flow." Transaction of the American Society of Civil Engineers, Vol., Reston, Virginia, USA.. Rahimnejad, R. and Ooi, P.S.K. Factors affecting the critical shear stress of scour of cohesive soil beds. Transportation Research Record, Journal of the Transportation Research Board. 0.

20 0. Dunn, I. S. Tractive resistance of cohesive channels. Journal of Soil Mechanics and Foundation Division, Vol., No.,, pp. -.. Mobley, J. M. and Parker, F. Evaluation of Scour Potential of Cohesive Soils. Report No. 0-. Highway Research Center, Auburn University, Alabama Smerdon, E. T., and Beasley, R. T. The tractive force theory applied to stability of open channels in cohesive soils. Research Bulletin No.. Agriculture Experiment Station, University of Missouri, Columbia, MO... Shan, Y., Shen, J., Kilgore, R. and Kerenyi, K. Scour in Cohesive Soils. Rep. No. FHWA-HRT--0, Federal Highway Administration, Washington, D.C. 0.. R-project. (0). Accessed 0. 0

21 0 LIST OF TABLES TABLE Comparison of scour depths from the Richardson and Davis equation versus the SRICOS EFA method TABLE Soil samples and parameters TABLE Bivariate correlation matrix involving some common soil and EFA erosion rate curve parameters TABLE Final regression parameters and t-statistics for the overall model LIST OF FIGURES FIGURE Erosion function apparatus (EFA) FIGURE (a) Typical EFA erosion rate curve (b) Semi-log plot of same EFA curve with hyperbolic regression line. FIGURE Soil sampling locations at the five water channels. FIGURE Calculated versus measured shear stress from EFA tests (Total number of data points = ) FIGURE Influence of water content on the critical shear stress calculated using the model FIGURE Influence of varying plasticity index on the critical shear stress calculated using the model FIGURE Measured versus calculated critical shear stress using Equation FIGURE Measured versus calculated critical shear stress using Shan et al. s () model