Kassem, Salaheldin, Imran, Chaudhry,

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TRB Annual Meeting Washington, D.C., January 12-16, 2003

Title: Numerical Modeling of Scour in Cohesive Soils around the Artificial Rock

Island of The Cooper River Bridge Submission Date: August 1, 2002 Word Count: 4177 (2677 text & 1500 figures-equivalent) Authors: Ahmed Kassem (Corresponding author) Research Assistant Professor, Dept. of Civil and Environmental Engineering, University of South Carolina, 300 S. Main St., Columbia, SC 29208 Tel: 803-576-5665, Fax: 803-777-0670, E-mail: Kassem@engr.sc.edu

Tarek M. Salaheldin Graduate Student, Dept. of Civil and Environmental Engineering, University of South Carolina, 300 S. Main St., Columbia, SC 29208 Tel: 803-777-7686, Fax: 803-777-0670, E-mail: tmsalahe@engr.sc.edu

Jasim Imran

Assistant Professor, Dept. of Civil and Environmental Engineering, University of South Carolina, 300 S. Main St., Columbia, SC 29208 Tel: 803-777-1210, Fax: 803-777-0670, E-mail: imran@engr.sc.edu

M. Hanif Chaudhry Mr and Mrs Irwin B. Kahn Professor and Chairman Dept. of Civil and Environmental Eng.,

University of South Carolina, 300 S. Main St., Columbia, SC 29208 Tel: 803-777-3614, Fax: 803-777-0670, E-mail: chaudhry@sc.edu

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Abstract A new laboratory-based methodology to predict the maximum scour depth in cohesive soil has been recently developed at the University of South Carolina. Due to the absence of field data, a numerical model, FLUENT CFD package, is used to test scale effects associated with such a methodology. In this paper, the numerical model is firstly verified against measurements obtained in the laboratory. The numerical results agree satisfactorily with the measurements. Then, the numerical model is applied to the rock island protecting the main piers of the Cooper River Bridge located in Charleston, South Carolina. The scour hole created around the island in the laboratory was scaled-up and used in the numerical model. The computed bed shear stresses compare satisfactorily with those scaled-up from the measurements and the shear stress at which the field sample begins to erode. It was found that the scour of 3.7 m represents the equilibrium state, which is similar to the results scaled-up from the laboratory experiments. The numerical results showed that the scour depth of 36 m calculated by the HEC-18 approach is highly overestimated. Introduction The old Cooper River Bridge in Charleston, South Carolina is being replaced by the longest cable-stay span in North America at 471 m. This project is the largest infrastructure project in the state of South Carolina with a total cost of $531 million. The bridge connects the historic Charleston peninsula to the growing town of Mount Pleasant with a 4.5 km of structures that include two interchanges, a pedestrian and bicycle, and the cable-stay span over the navigation channel. Artificial rock islands are provided to protect the piers of the main towers holding the cable-stay span as a first defense against ship impact, and offer extra stabilization in the event of hurricane force winds or seismic activity. The artificial islands are expected to obstruct the flow in the stream thereby changing the flow field significantly. The redistributed flow field may cause the bed shear stress to exceed the critical shear stress for soil erosion resulting in the development of scour hole. The scour depth around the artificial rock islands, if deep enough, could threaten the stability of the structure. It is necessary to predict the maximum possible scour around the island in order to develop appropriate countermeasure against scour. The foundations of the Cooper River Bridge and its rock islands are being constructed on the Cooper Marl, which is a strongly cohesive soil. A large number of investigations have been carried out to understand the flow field and the erosion mechanism around bridge piers in non-cohesive soils, e.g., Melville (1), Raudkivi and Ettema (2), Ahmed and Rajaratnam (3). However, only a few researchers have investigated the scour mechanism around piers in cohesive soils e.g. Hosny (4), Briaud et al. (5) and Ting et al. (6). The prediction of scour in clay beds is not as well-established as in sand beds. Moreover, reported methodologies provide contradictory results. For example, Hosny (4) found that the presence of clay with a percentage of 10% to 40% in sand soil decreases the scour depth, but Ting et al. (6) reported that the equilibrium scour in clay is about the same as in sand. Such a contradiction indicates that no general-purpose formula is available for the prediction of maximum scour depth in cohesive soil at a bridge pier.

Recently, a new methodology has been developed at the University of South Carolina by Salaheldin et al. (7). The proposed approach includes the following steps: (1) Obtain undisturbed samples from the field; (2) Conduct surface erodibility test in the laboratory on the field samples to determine the incipient shear stress (τc) at which the soil sample starts to erode; (3) Select a model scale and scale down the incipient shear stress (τc) of the field soil according to scale of the physical model; (4) Develop a reduced-strength soil and use it in a physical model to predict the scour history and the maximum scour depth; (5) Scale-up the maximum scour depth obtained in

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the laboratory to estimate the corresponding depth in the field. They applied their methodology to predict the maximum scour depth around the artificial rock islands of the Cooper River Bridge. Different scale ratios were used in the experiments for the vertical and horizontal length scale. One of these experiments was RUN-2, which has 1/40 vertical scale, and 1/400 horizontal scale. However, scale effects may limit the use of laboratory data to accurately predict prototype scour depth (Ettema et al., 8), particularly if the model scale is distorted, i.e. the horizontal scale is different from the vertical scale. In order to test the scale effects of such a methodology, field data is needed for the verification. Since no field data is available, a numerical model is used instead in this study to calculate the equilibrium bed shear stress in the field and compare it to the predicted values from the experiments. In this paper, the numerical model is described, verified against laboratory data, and then applied to test the scale effect of the methodology developed by Salaheldin et al. (7). Site Description The existing Cooper River Bridge is located at the crossing of the I-17 over the Cooper River. Due to development and structural considerations, the old bridge is being replaced by a new bridge. The new bridge consists of a main cable-stay span with a length of 471 m, and east and west approaches with lengths 637 m and 1327 m, respectively. The navigation channel width is 305 m. There are two main towers in the main span, 11 piers in the east approach, and 20 piers in the west approach. The two main piers are protected by artificial rock islands. The islands are of prism shape with rounded edges. The dimension of the west island at the top is 50x65 m, and 118x134 m at the bottom. The east island has the same top dimension as the west island but has a wider bottom with the dimension of 124x140 m. Figure 1 shows the plan view and cross-sectional view of the west rock island. The artificial islands are being founded directly on the Cooper Marl and consist of a rock core with outer layers of heavy rock armor to provide protection against wave and current actions. Numerical Model Description The FLUENT computational fluid dynamics package is used here to predict the three-dimensional flow field around the rock island protecting the bridge pier. The model solves the Reynolds-averaged Navier-Stokes equations. Closure of the turbulence stress is obtained by the standard k-ε model. Ali and Karim (9) reported that the standard k-ε model performs satisfactorily for predicting the flow field around piers. The Reynolds-averaged equations of mass and momentum, the turbulent kinetic energy, k, and its dissipation rate, ε, are solved sequentially by the method of control-volume. The equations are integrated over each control volume, yielding discrete equations that conserve each quantity on a control-volume basis. An implicit scheme is used for converting the discretized equations into a system of linear equations for the dependent variables in every computational cell. Since the equations are nonlinear and physically coupled, several iterations of the solution loop are performed before a converged solution is obtained. More detail of the solution procedure is described in FLUENT 5 User’s Guide (10). Boundary Conditions At the inlet boundary, a uniform distribution of all the dependent variables is prescribed. At the downstream outlet, the normal gradients of all dependent variables are set to zero, i.e., variables at the downstream end are extrapolated from the interior domain. At the top surface, a symmetry boundary condition is used. Thus, there is neither convective flux nor diffusion flux across the top surface. This implies that the normal velocity component and the normal gradients of all flow variables are zero, and the water surface elevation in the channel is fixed. The water elevation at the outlet is specified. At the solid boundaries, the law-of-the-wall for mean velocity modified for roughness is used.

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Inflow Conditions The inflow conditions, i.e.water surface elevations and flow velocity, are specified based on the study carried out by Ayres Associates (11). As part of their hydraulic study of the Charleston harbor, they used the RMA-2 two-dimensional model to study the Cooper-Wando River Basin where the Cooper River Bridge is located. They investigated the 100-year event of both riverine floods and hurricane storm surges and found that the flow at the upstream boundaries, even during major storm events, is dominated by tidal action rather than riverine flow. The velocity profile in the lateral direction at the bridge site is extracted from their model. The results of the model showed that the maximum velocity associated with the peak flow is 1.83 m/s, and the velocity at the end of storm surge is 1.22 m/s. The peak flow with high velocity at the site occurs for approximately two hours and then the normal conditions prevail. Since the erosion of clay is a long-term process, the flow velocity associated with the peak flow is not considered. The average value of 1.22 m/s is used for the flow velocity at the upstream end of the rock island. The associated depth with the average velocity at the upstream end is 15.2 m. Model calibration and verification FLUENT is widely used for industrial flow application with complex three-dimensional geometry. Ali and Karim (9) used FLUENT to predict the three-dimensional flow field around a circular cylinder for rigid and erodible beds. There was satisfactory agreement between the bed shear stresses predicted by FLUENT and those calculated from the experimental velocities near the bed. However, they indicated a need for more refined measurements for proper verification. For more verification and calibration of FLUENT, experiments were carried out on a rock island with a flat bed, i.e. no scour hole. The experimental data of the RUN-2 with a flat bed is used herein for such verification. In the computational domain, the rock island is placed in the middle with the upstream and downstream reaches of approximately 10 times the length of the rock island at the bottom. A non-uniform grid with total elements of 107,000 is used with clustering around the island in the horizontal plane and near the bottom in the vertical direction. The water depth and the inflow velocity are 0.375 m and 0.193 m/s, respectively. The model was run until steady state flow conditions were established. Figure 2 shows the comparison of the measured and calculated velocity profile at a point located near the right side of the island. The difference near the top is due to the effect of the rigid-lid boundary condition assumed at the top surface, but the computed profile matches the measured data very well near the bottom. Accuracy of the near- bed velocity is crucial to predicting the bed shear stress correctly. The bed shear stress distribution calculated from the measurements and predicted by numerical model are shown in Figure 3 a, and b, respectively. The results are qualitatively similar since the zones of maximum shear stresses are located at the front edges of the rock island. The magnitude of the shear stress around the model is not symmetrical because of the unsymmetric shape of rounding of the island edges. The shear stress computed by the numerical model shows a fair agreement with those measured in the laboratory. Model Application The maximum equilibrium scour of the experiment RUN-2 was 9.2 cm, which is equivalent to 3.7 m in the field. The scour-hole depths are scaled-up to the field scale and then used in the numerical model. An inflow velocity of 1.22 m/s and a water-depth of 15.2 m are used in the numerical model. Figure 4 (a) and (b) show the bed shear stress distribution predicted from the experimental and numerical models, respectively. The distribution of bed shear stress differs but the magnitude and the location of the maximum shear stress are similar. Figure 4 shows that the maximum shear stress predicted by both the experiment and the computations is 2.6 Pa, which is just below the incipient shear stress required for soil erosion. This represents the maximum scour and the equilibrium condition. The prediction of the bed shear stress and its comparison to the

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incipient shear stress are important in order to check whether the corresponding scour hole represents the equilibrium state or not. The distribution of the shear stress is not as important as the magnitude and location of the maximum shear stress is. Since the scaling-up procedure is capable of predicting a satisfactory estimate of the magnitude and location of the maximum shear stress as shown in Figure 4, the proposed approach (7) for scour prediction could be used for other applications with confidence. Most of the currents practices use HEC-18 to calculate the maximum scour depth around bridge piers. When applied to our case, it gives approximately 36 m of scour around the rock island. Since the HEC-18 was developed for a non-cohesive soil environment, it overestimates the scour in a case with cohesive bed material. At the maximum equilibrium scour depth of 3.7 m, the bottom shear stress was found to be 2.6 Pa, which is slightly less than the critical shear stress of the soil. Additional numerical experiments were performed with maximum scour depth of 7.4 m and 11.1 m, which are larger then the equilibrium scour depth. The numerical results showed that the bed shear stress reduces substantially with the increase of the scour depth. With increasing the maximum scour depth to 7.4 m, and 11.1 m, the corresponding shear stress decreases respectively to 2.0 Pa, and 1.75 Pa; values significantly lower than the critical shear stress. This vindicates the validity of the new scour prediction methodology. Summary and Conclusion A numerical model, FLUENT CFD package, was utilized to test the scale effects of the laboratory-based methodology developed at the University of South Carolina for scour prediction in cohesive soil. The numerical model was applied for scour prediction around rock islands being constructed for the protection of the main piers of the new Cooper River Bridge located in Charleston, South Carolina. The scour depths and shapes measured in the laboratory were scaled-up and incorporated in the numerical model to predict the corresponding scour in the field. It was found that the scaling-up procedures adopted in the methodology are accurate enough to be used for general applications. Also, the study showed that the scour depth predicted by HEC-18 is overestimated in cohesive soil. Acknowledgement This research was supported by the South Carolina Department of Transportation (SCDOT) and the Federal Highway Administration (FHWA).

References (1) Melville, B.W. Local Scour of Bridge Sites. University of Auckland, School of Engineering,

Auckland, New Zealand, Report No. 117, 1975. (2) Raudkivi, A.J., and Ettema, R. Clear Water Scour at Cylindrical Piers. J. Hydr. Engrg., ASCE,

109(3), 1983, 338-350. (3) Ahmed, F., and Rajaratnam, N. Flow around Bridge Piers. J. Hydr. Engrg., ASCE, 124(3),

1998, 288-300. (4) Hosny M. M. Experimental Study of Local Scour Around Circular Bridge Piers in Cohesive

Soils. Ph.D. Dissertation, Civil Engineering Department, Colorado State University, Fort Collins, Colorado, USA, 1995.

(5) Briaud, J. L., F. C. K. Ting, H. C. Chen, R. Gudavalli, S. Perugu, and G. Wei. SRICOS: Prediction of Scour Rate in Cohesive Soils at Bridge Piers. J. of Geotechnical Engineering, ASCE, Vol. 125, No.4, 1999, pp. 237-246.

(6) Ting, F. C. K., J. L. Briaud, H. C. Chen, R. Gudavalli, S. Perugu, and G. Wei. Flume Tests for Scour in Clay at Circular Piers. J. of Hydraulic Engineering, ASCE, Vol. 127, No. 11, 2001, pp. 969-978.

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(7) Salaheldin, T.M., Imran, J., Kassem, A., and Chaudhry, M.H. Scale Physical Modeling of Local Scour in Cohesive Soil. Submitted to the TRB Annual Meeting, Washington, D.C., January 12-16, 2003.

(8) Ettema, R., Melville, B.W., and Barkdoll, B. Scale Effect in Pier-Scour Experiments. J. Hydr. Engrg., ASCE, 124(6), 1998, 639-642.

(9) Ali, K.H.M, and Karim, O. Simulation of Flow around Piers. J. Hydr. Research, IAHR, 40(2), 2002, 161-174.

(10) Fluent Incorporated. FLUENT 5 User’s Guide. Lebanon, New Hampshire, 2000. (11) Ayres Associates. Scour Evaluation Study: Cooper, Ashley, and Wando Rivers. Report

SCDOT Contract 2201-99, Colmbia, South Carolina.

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Figures:

Figure 1. Plan and cross-sectional views of the rock island protecting the main piers of the new

Cooper River bridge.

Figure 2. Velocity profile at the right side of the island at laboratory scale of RUN-2 with fixed

bed

(a) measured (b) computed

Figure 3. Bed shear stress at laboratory scale of RUN-2 with fixed bed

(a) experimental model (b) numerical model

Figure 4. Bed shear stress at field scale of RUN-2 with scour hole

(a) experimental model (b) numerical model

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Figure 1

15 m

Cooper Marl

Graded Stones

6 37 m 50 m 37 m 6

3.6 m

2:1

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2:12:1

50 m 37 m37 m

37 m

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Velocity, m/s

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Figure 2

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0.0350.035

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0.35

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0.5

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1.00

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