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NCHRP Report 516: Pier and Contraction Scour in Cohesive Soils (2004)
National Cooperative Highway Research Program (NCHRP)

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Wang, J, Briaud, J-L, Li, Y, Chen, H-C, Nurtjahyo, P, Transportation Research Board. "4.6 Equivalent Time." NCHRP Report 516: Pier and Contraction Scour in Cohesive Soils. Washington, DC: The National Academies Press, 2004.

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21
Front Matter (R1-R10)
Summary (1-7)
1.4 Why Was This Problem Addressed? (8-8)
1.5 Approach Selected to Solve the Problem (9-9)
2.4 Erodibility and Correlation to Soil and Rock Properties (10-13)
3.3 EFA Test Data Reduction (14-14)
3.4 EFA Precision and Typical Results (15-16)
4.2 Small Flood Followed by Big Flood (17-17)
4.3 Big Flood Followed by Small Flood and General Case (18-18)
4.4 Hard Soil Layer Over Soft Soil Layer (19-20)
4.6 Equivalent Time (21-21)
4.7 Extended and Simple SRICOS-EFA Method (22-23)
4.8 Case Histories (24-25)
4.9 Predicted and Measured Local Scour for the Eight Bridges (26-28)
4.10 Conclusions (29-29)
5.4 Measuring Equipment (30-31)
5.5 Soils and Soil Bed Preparation (32-32)
5.6 Flume Tests: Procedure and Measurement (33-33)
5.8 Shallow Water Effect on Maximum Pier Scour Depth (34-35)
5.9 Shallow Water Effect on Initial Shear Stress (36-36)
5.11 Pier Spacing Effect on Maximum Scour Depth (37-37)
5.12 Pier Spacing Effect on Initial Scour Rate (38-38)
5.15 Pier Shape Effect on Initial Scour Rate (39-39)
5.18 Attack Angle Effect on Maximum Scour Depth (40-41)
5.20 Attack Angle Effect on Scour Hole Shape (42-42)
5.21 Maximum Scour Depth Equation for Complex Pier Scour (43-44)
6.2 Existing Knowledge on Numerical Simulations for Scour (45-45)
6.5 Shallow Water Effect: Numerical Simulation Results (46-46)
6.6 Shallow Water Effect on Maximum Shear Stress (47-47)
6.7 Pier Spacing Effect: Numerical Simulation Results (48-48)
6.9 Pier Shape Effect: Numerical Simulation Results (49-50)
6.10 Pier Shape Effect on Maximum Shear Stress (51-51)
6.11 Attack Angle Effect: Numerical Simulation Results (52-52)
6.12 Attack Angle Effect on Maximum Shear Stress (53-53)
6.13 Maximum Shear Stress Equation for Complex Pier Scour (54-55)
7.3 Flume Tests and Measurements (56-56)
7.4 Flume Tests: Flow Observations and Results (57-58)
7.5 Flume Tests: Scour Observations and Results (59-59)
7.6 Maximum and Uniform Contraction Depths for the Reference Cases (60-62)
7.7 Location of Maximum Contraction Depth for the Reference Cases (63-63)
7.8 Correction Factors for Transition Angle and Contraction Length (64-64)
7.9 SRICOS-EFA Method Using HEC-RAS Generated Velocity (65-65)
7.11 Scour Depth Equations for Contraction Scour (66-67)
8.3 Transition Angle Effect: Numerical Simulation Results (68-68)
8.4 Contracted Length Effect: Numerical Simulation Results (69-71)
8.6 Maximum Shear Stress Equation for Contraction Scour (72-75)
9.3 The Integrated SRICOS-EFA Method: Step-by-Step Procedure (76-80)
9.5 The SRICOS-EFA Program (81-83)
9.6 Output of the SRICOS-EFA Program (84-84)
10.4 Gill (1981) Database: Contraction Scour (85-87)
10.5 Remarks (88-88)
11.2 Preparation of the Future Hydrographs (89-89)
11.3 Risk Approach to Scour Predictions (90-90)
11.4 Observations on Current Risk Levels (91-92)
12.2 Example 2: Single Rectangular Pier with Attack Angle and Approaching Hydrograph (93-94)
12.3 Example 3: Group Rectangular Piers with Attack Angle and Approaching Constant Velocity (95-98)
12.4 Example 4: Contracted Channel with 90-Degree Transition Angle and Approaching Constant Velocity (99-102)
12.5 Example 5: Contracted Channel with 60-Degree Transition Angle and Approaching Hydrograph (103-104)
12.6 Example 6: Bridge with Group Piers and Contracted Channel with Hydrograph in Contracted Section (105-110)
13.1 Conclusions (111-112)
13.2 Recommendations, (113-113)
References (114-115)
Nomenclature (116-117)
Unit Conversions (118-118)
Appendix A - Photographs from the Flume Tests (119-125)
Abbreviations used without definitions in TRB publications (126-126)

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21 Figure 4.5. Scour of a two-layer soil (hard layer over soft layer). is contained in Layer 1 and does not reach Layer 2. If, how- identical to having had Layer 2 scoured over an equivalent ever, the scour depth reaches z ­1 (Point A on Figure 4.5a), time t* (Point B on Figure 4.6b). Therefore, when Layer 2 Layer 2 starts to be eroded. In this case, even though the scour starts being eroded, the scour depth versus time curve pro- depth z ­1 was due to the scour of Layer 1 over a time t1, at that ceeds from Point B to Point C on Figure 4.6b. The combined time the situation is identical to having had Layer 2 scoured curve for the two-layer system is OAC on Figure 4.6c. over a time t* (Point B on Figure 4.5b). Therefore, when Layer In the general case, there may be a series of soil layers with 2 starts being eroded, the scour depth versus time curve pro- different erosion functions. The computations proceed by ceeds from Point B to Point C on Figure 4.5b. The combined stepping forward in time. The time steps are t long, the curve for the two-layer system is OAC on Figure 4.5c. velocity is the one for the corresponding flood event, and the erosion function (z versus t) is the one for the soil layer cor- ­ responding to the current scour depth (bottom of the scour 4.5 SOFT SOIL LAYER OVER HARD SOIL hole). When t is such that the scour depth proceeds to a new LAYER AND GENERAL CASE soil layer, the computations follow the process described in Layer 1 is soft and z ­1 thick. Layer 2 underlies Layer 1 and Figures 4.5 or 4.6 depending on the case. The same SRICOS is harder than Layer 1. The scour depth z ­ versus time t curve program mentioned for the velocity hydrograph also handles for Layer 1 is given by Equation 4.4 (Figure 4.6a), and the z ­ these calculations. The output of the program is the scour versus t curve for Layer 2 is given by Equation 4.5 (Figure depth versus time curve for the multilayered soil system and 4.6b). If z ­1 is larger than the maximum depth of scour in for the complete velocity hydrograph. Layer 1, z­ max 1, then the scour process is contained in Layer 1 and does not reach Layer 2. If, however, the scour depth 4.6 EQUIVALENT TIME reaches z ­1 (Point A on Figure 4.6a), Layer 2 starts to erode. In this case, even though the scour depth z ­1 was due to the The computer program SRICOS is required to predict the scour of Layer 1 over a time t1, at that time the situation is scour depth versus time curve as explained in the preceding