Pier and Contraction Scour in Cohesive Soils (2004)

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NOMENCLATURE α Pier attack angle θ Transition angle for bridge contraction ρ Mass density of water γ Unit weight of water ε Roughness coefficient µQ Mean value of daily stream-flow σQ Standard deviation of daily stream-flow #200 Percentage of soil passing No.200 sieve a Width of the cross section of the rectangular pipe in EFA b Length of the cross section of the rectangular pipe in EFA B Pier width B′ Pier projection width B1 Channel upstream width B2 Contracted channel width C Pier center-center spacing CEC Cation exchange capacity CSS Critical shear stress of soil d Scour depth, a random variable and its statistics can be studied in detail to determine the risk of failure asso- ciated with difference choices of the design value of the scour depth D50 Particle size f Friction factor obtained from Moody Chart Fr Froude number g Acceleration due to gravity h Length of soil sample eroded in EFA test H Average water depth upstream bridge piers H1 Average water depth in approaching flow upstream contraction H2 Average water depth in contracted channel HHec Initial average water depth in contracted channel calculated by HEC-RAS L Length of contraction channel Lpier Length of rectangular pier kw Correction factor of water depth for the initial shear stress of pier scour ksh Correction factor of pier shape effect for the initial shear stress of pier scour ksp Correction factor of pier spacing effect for the initial shear stress of pier scour kα Correction factor of pier attack angle effect for the initial shear stress of pier scour kc-R Correction factor of contraction ratio effect for the initial shear stress of contraction scour kc-L Correction factor of contraction length effect for the initial shear stress of contraction scour kc-H Correction factor of flow water depth effect for the initial shear stress of contraction scour kc-θ Correction factor of transition angle effect for the initial shear stress of contraction scour Kw Correction factor of water depth for pier scour depth Ksh Correction factor of pier shape effect for pier scour depth Ksp Correction factor of pier spacing effect for pier scour Kα Correction factor of pier attack angle effect for pier scour depth KL Correction factor of contraction length effect for contraction scour depth Kθ Correction factor of transition angle effect for contraction scour depth KL/Zmax Correction factor of contraction length effect for maximum contraction scour depth KL/unif Correction factor of contraction length effect for uniform contraction scour depth KL/Xmax Correction factor of contraction length effect for location of maximum contraction scour depth Kθ/Zmax Correction factor of transition angle effect for maximum contraction scour depth Kθ/unif Correction factor of transition angle effect for uniform contraction scour depth Kθ/Xmax Correction factor of transition angle effect for location of maximum contraction scour Lt Life of structure n Manning’s coefficient pH Log Scale Unit of Measure, and is used to express the degree of acidity of a substance. PI Plasticity index Q Daily stream-flow discharge 116

117 R Level of risk associated with the choice of different design values of scour depth and project lives Re Reynolds number = VB/v Rh Hydraulic radius S Piers center-center spacing SAR Sodium adsorption ratio Si Initial erodibility SU Undrained shear strength of soil t Time required for soil sample to be eroded in EFA test te Equilibrium time for multi-flood scour depth calculation Tr Return period in risk analysis τ Shear stress on the surface of soil sample τc Critical shear stress of soil τmax Initial shear stress which also is the maximum value during shear stress history τmax(Deep) Initial shear stress which also is the maximum value during shear stress history for pier sour or contraction scour in deep water case τmax(Circle) Initial shear stress which also is the maximum value during shear stress history for pier sour or contraction scour in circular pier case τmax(0 degree) Initial shear stress which also is the maximum value during shear stress history for pier sour or contraction scour in no attack angle case τmax(Cont) Initial shear stress which also is the maximum value during shear stress history for contraction scour τmax(Single) Initial shear stress which also is the maximum value during shear stress history for pier sour or contraction scour in single pier case τ(z) Shear stress on the bottom of scour hole at depth z ν Kinematics viscosity of water V Approaching average velocity for pier scour V1 Approaching average velocity for contraction scour V2 Average velocity in the contracted channel VHEC Calculated velocity in the contracted channel by HEC-RAS Xa Location of maximum bed shear stress due to abutment Xc Location of maximum bed shear stress around pier or the abutment (most interested) Xmax Location of the maximum contraction scour Z˙ Erosion rate Z˙ i Initial erosion rate Zmax (Cont) Equilibrium maximum contraction scour depth Zmax (Deep) Equilibrium pier scour depth or equilibrium maximum contraction scour depth in deep water case Zunif(Cont) Equilibrium uniform contraction scour