Transcript Introduction to Soils - College of Engineering Home Page

Flow through Soils II
(ch8)
2D flow
Vel. vectors are confined to a single plane
1D flow
vel vectors parallel
2D flow
vel vectors not necessarily parallel
wall
soil
Laplace’s Equation
- Darcy’s law
1D flow
2D flow
- Laplace’s equation
x
vz
z
dx
L
vx
dz
vz 
vz
dz
z
vx
vx 
dx
x
Rate of D in vel in z-dir
Laplace’s Equation
Laplace’s equation
“represents energy loss through any resistive medium”
Assumptions
Darcy is valid
S = 100%
is of constant volume
Isotropic
kx = kz
Homogeneous
k = same throughout
Remember main point = get Q
Examples
Q beneath a dam
 h  h
 2 0
2
x
z
2
Solving
Mathematics
Q in excavations
2
Graphical
Flownets
Flownets
wall
Flowline
Equipotential
line
impervious
Flowpath – “channel” between two flowlines
Equipotential line – along any eqpl, the total head is the same
Flownets
1st eqpl: starts in inlet
Of soil
last eqpl: ends at outlet
1st eqpl
last eqpl
impervious
Flownets
vel
node
eqpl
Requirements:
Perpendicular crossings at nodes
Maintain “squareosity”
Flownets
X
Mistake – redraw!
Flownets - Example
L = 100 m
14m
2m
2m
10m
B
A
k = .1 cm/s
Flownets - Example
Dh = 14 – 2 = 12 m
h at first eq = 24 m
h at last eq = 12 m
NFP = 3
NED = 12
Q = Dh L k (NFP/NED)
Q = 0.3 m3/sec
Flownets - Example
h at first eq = 24 m
Head loss per drop = Dh/NED = 12 / 12 = 1 m
he at A = 8 m
h at A = 24 – 8 = 16 m
hp at A = h – he = 16 – 8 = 8 m
uA = (hp)(gw)
= 78.5 kPa
Flownets - Example
h at first eq = 24 m
Head loss per drop = Dh/NED = 12 / 12 = 1 m
he at B = 10 m
h at B = 24 – 9 = 15 m
hp at B = h – he = 15 – 10 = 5 m
uB = (hp)(gw)
= 49 kPa
Uplift pressures
Concrete dam
Concrete dam
s = W/A
uuplift
If uuplift ~ s, structure can float away!
Uplift Pressures
Case 1 (no flow)
u = (hp)(gw) = uhydrostatic
Case 2 (with flow)
Draw flownet
Compute h at several points along the structure’s base
Determine hp at these points
Find u at these points by u = (hp)(gw)
Filters
Problem
- water pressure
Sol.
- drains
Problem
- Soil particles migrate out
Sol.
- soil filter
Filters
2 filter purposes
Allow adequate drainage
Disallow particle migration
Soil retained is called base soil
Filter soil
Filters
2 filter failure types
Clogging: base clogs filter pores – (k decreases)
Piping: base migrates through filter
Filters - principles
Interstice Sizes
D
Simple Cubic Packing
dmax
D/dmax = 2.4
D
Tetrahedral Packing
dmax
D/dmax = 6.5
Filters - principles
Arching
Bridging
Terzaghi’s Filter criteria
To disallow
particle
migration
D15
 4to5
d85
To allow adequate
drainage (maintain
proper k)
D15
 4to5
d15
Sherard’s Filter criteria
See table 8.2 in book…
Example:
Example: Filter selection
Example (see notes (pad (lined sheet))…