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OCR for page 116

116
NOMENCLATURE
Pier attack angle
Transition angle for bridge contraction
Mass density of water
Unit weight of water
Roughness coefficient
µQ Mean value of daily stream-flow
Q 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
k 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- 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
K Correction factor of pier attack angle effect for pier scour depth
KL Correction factor of contraction length effect for contraction scour depth
K 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
K/Zmax Correction factor of transition angle effect for maximum contraction scour depth
K/unif Correction factor of transition angle effect for uniform contraction scour depth
K/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

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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
Shear stress on the surface of soil sample
c Critical shear stress of soil
max Initial shear stress which also is the maximum value during shear stress history
max(Deep) Initial shear stress which also is the maximum value during shear stress history for pier sour or contraction
scour in deep water case
max(Circle) Initial shear stress which also is the maximum value during shear stress history for pier sour or contraction
scour in circular pier case
max(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
max(Cont) Initial shear stress which also is the maximum value during shear stress history for contraction scour
max(Single) Initial shear stress which also is the maximum value during shear stress history for pier sour or contraction
scour in single pier case
(z) Shear stress on the bottom of scour hole at depth z
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
i
Z 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