andrew simon usda-ars national sedimentation laboratory, oxford, ms andrew.simon@arsda
DESCRIPTION
Equilibrium, Shear Stress, Stream Power and Trends of Vertical Adjustment. Andrew Simon USDA-ARS National Sedimentation Laboratory, Oxford, MS [email protected]. Non-Cohesive versus Cohesive Materials. Non-cohesive: sands and gravels etc. - PowerPoint PPT PresentationTRANSCRIPT
Andrew Simon USDA-ARS National Sedimentation Laboratory, Oxford, MS
Equilibrium, Shear Stress, Stream Power and Trends of Vertical
Adjustment
Non-Cohesive versus Cohesive Materials
• Non-cohesive: sands and gravels etc.
Resistance is due solely to particle size, weight, shape and “hiding”.
• Cohesive: silts and clays
Resistance is derived from electro-chemical inter-particle forces under zero normal stress
Shields Diagram
Denotes uncertainty
Cohesive
Materials
Shields Diagram by Particle Diameter
Excludes cohesives
Heterogeneous Beds
ks = 3* D84
Need for a means to determine critical shear stress (c) and the erodibility coefficient (k) in-situ for soils and sediments.
National Sedimentation Laboratory
Erosion of Cohesives by Hydraulic Shear
Erosion Rate is a Function of Erodibility and Excess Shear Stress
= k (o- c)
= erosion rate (m/s)
k = erodibility coefficient (m3/N-s)
o = boundary shear stress (Pa)
c = critical shear stress (Pa)
(o-c) = excess shear stress
Critical shear stress is the stress required to initiate erosion.
Obtained from jet-test device
Impinging Jet Applies Shear Stress to Bed
Jet Nozzle
National Sedimentation Laboratory
Impinging Jet Applies Shear Stress to Bed
As scour hole depth increases, shear stress decreases.
Jet Nozzle
National Sedimentation Laboratory
From Relation between Shear Stress and Erosion We Calculate c and
Time
Ero
sion
Dep
th,
cm
c
National Sedimentation Laboratory
(cm3/Pa/sec)k
General Relation for Erodibility and Critical
Shear StressErodibility, m3/N-s
k = 0.1 c -0.5
Where; c = critical shear stress (Pa), x, y = empirical constants
CRITICAL SHEAR STRESS, IN Pa
0.01 0.1 1 10 100 1000
ERODIB
ILIT
Y C
OEFF
ICIE
NT (k), I
N cm
3 /N-s
0.0001
0.001
0.01
0.1
1
10
k = 0.09 c -0.48
44
Revised Erodibility Relation
y = 1.3594x-0.8345
R2 = 0.5253
0.0001
0.0010
0.0100
0.1000
1.0000
10.0000
100.0000
1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03
CRITICAL SHEAR STRESS (Pa)
ER
OD
IBIL
ITY
CO
EF
FIC
IEN
T (
k)
Distributions: Critical Shear Stress
0
10
20
30
40
50
60
70
80
90
100
0.1 1.0 10.0 100.0 1000.0
CRITICAL SHEAR STRESS (Pa)
PE
RC
EN
TIL
E
Yalobusha River System
Kalamazoo River
James Creek
Shades Creek
Missouri River
Upper Truckee River
W. Iowa, E. Nebraska
N Fork Broad River
Tualatin River System
Tombigbee River
S Branch Buffalo River
All Data
Distributions: Erodibility Coefficient
0
10
20
30
40
50
60
70
80
90
100
0.001 0.010 0.100 1.000 10.000 100.000
ERODIBILITY COEFFICIENT (k)
PE
RC
EN
TIL
E
Yalobusha River System
Kalamazoo River
James Creek
Shades Creek
Missouri River
Upper Truckee River
W. Iowa, E. Nebraska
N Fork Broad River
Tualatin River System
Tombigbee River
S Branch Buffalo River
All Data
Mapping Critical Shear Stress: Yalobusha River Basin, Mississippi
National Sedimentation Laboratory
Idealized Adjustment TrendsIdealized Adjustment Trends
For a given discharge (Q)
VS
Se
n
c
d
National Sedimentation Laboratory
Adjustment: Boundary Shear Stress
Adjustment: Increasing Resistance
Adjustment: Increasing Resistance
Adjustment: (Excess Shear Stress)Degrading Reach
Boundary Shear Stress: Range of FlowsSh
ear
stre
ss, i
n N
/m2
Adjustment: Excess Shear StressDegrading Reach
Exce
ss s
hear
stre
ss
Adjustment: (Excess Shear Stress)Aggrading Reach
Adjustment of Force and Resistance
Results of AdjustmentDecreasing Sediment Loads with Time
Toutle River System
Experimental Results
Total and Unit Stream Power = w y V S = Q S = total stream power per unit length of channel = specific weight of water w = water-surface width y = hydraulic depth v = mean flow velocity Q = water discharge S = energy slope
w = / ( w y) = V S where w = stream power per unit weight of water
Adjustment: Unit Stream Power
Flow Energy• Total Mechanical EnergyTotal Mechanical Energy
H = z + y + (H = z + y + ( v v22 / 2 g)/ 2 g)where H = total mechanical energy (head)where H = total mechanical energy (head)
z = mean channel-bed elevation (datum head)z = mean channel-bed elevation (datum head)
= coefficient for non-uniform distribution velocity= coefficient for non-uniform distribution velocity
y = hydraulic depth (pressure head)y = hydraulic depth (pressure head)
g = acceleration of gravityg = acceleration of gravity
• Head Loss over a reach due to FrictionHead Loss over a reach due to Friction
hhff = [z = [z11 + y + y11 + ( + (11 v v1122 / 2g)]- [z/ 2g)]- [z22 + y + y22 + ( + (22 v v2222 / / 2g)]2g)]
• Head, Relative to channel bedHead, Relative to channel bed
EEss = y + ( = y + ( vv22 / 2g) =/ 2g) = y + [y + [ Q Q22 / (2 g w / (2 g w22 y y22)])]
As a working hypothesis we assume that a fluvial system has been disturbed in a manner such that the energy available to the system (potential and kinetic) has been increased. We further assume that with time, the system will adjust such that the energy at a point (head) and the energy dissipated over a reach (head loss), is decreased.
Now, for a given discharge, consider how different fluvial processes will change (increase or decrease) the different variables in the energy equations.
Adjustment: Total Mechanical Energy
Adjustment: Energy Dissipation
Minimization of energy dissipation
Trends of Vertical Adjustment and Determining Equilibrium
Determining Equilibrium
Recall definitionA stream in equilibrium is one in which over a
period of years, slope is adjusted such that there is no net aggradation or degradation on the channel bed (or widening or narrowing)
ORThere is a balance between energy conditions at
the reach in question with energy and materials being delivered from upstream
Causes of Channel Incision
Trends of Incision: Channelization
Trends of Incision: Below Dams
Bed-level Trends Along a Reach
Bed-level Trends Along a Reach
Empirical Functions to Describe Incision E = a t b
E = elevation of the channel bed
a = coefficient; approximately, the pre-disturbance elevation
t = time (years), since year before start of adjustment
b = dimensionless exponent indicating rate of change on the bed
(+) for aggradation, (-) for degradation
E/ Eo = a + b e-kt
E = elevation of the channel bed
Eo = initial elevation of the channel bed
a = dimensionless coefficient, = the dimensionless elevation
a > 1 = aggradation, a < 1 = degradation
b = dimensionless coefficient, = total change of elevation
b > 0 = degradation, b < 0 = aggradation
k = coefficient indicating decreasing rate of change on the bed
Empirical Model of Bed-level Response
Comparison of the Two Bed-level Functions
A Natural Disturbance (Toutle River System)
Bed-Level Response
Bed Response: Toutle River System
Upstream disturbance, addition of potential energy, sub-alpine environment
Comparison with Coastal Plain Adjustment
Downstream disturbance, increase in gradient, coastal plain environment
Model of Long-Term Bed Adjustment