Review of Soil Mechanics II

1
Review of Soil Mechanics II

• Prof. Jie Han, Ph.D., PE
• The University of Kansas

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Outline of Presentation

• Introduction
• Water flow in Soil
• Soil Compaction
• Stresses in Soil

3
Water Flow in Soil
4
Darcys Experimental Study
h
A
Flow
Sand Filter
1
2
L
5
Definition of Permeability (Hydraulic
Conductivity)
Velocity
Turbulent flow zone
Transition zone
Laminar flow zone
k
1
Hydraulic Gradient, i h/L
6

Darcys Law
Average velocity of flow
Actual velocity of flow
Rate (quantity) of flow
7
Constant Head Test
h
L
Soil
Q
A
8
Falling Head Test
a
At tt1
dh
At tt2
h1
h2
Soil
L
Valve
A
9
Typical Permeability of Soils
Soil or rock formation
Range of k (cm/s)
Gravel
1 - 5
Clean sand
10-3 - 10-2
10-3 - 10-1
Clean sand and gravel mixtures
10-2 - 10-1
Medium to coarse sand
Very fine to fine sand
10-4 - 10-3
10-5 - 10-2
Silty sand
10-9 - 10-7
Homogeneous clays
10-11 - 10-7
Shale
10-8 - 10-4
Sandstone
Limestone
10-7 - 10-4
Fractured rocks
10-6 - 10-2
10
Flow Net
h
Li
Nd
Bi
Bi Li
Nf
11
Example of Flow Net
4 m
1m
Permeable stratum
10 m
k3x10-5m/s
Impervious Stratum
Rate of flow
q k?hNf/Nd 3x10-5x3x5/95x10-5m3/s/m
12
Soil Compaction
13

Laboratory Compaction Tests
Type of test
Weight of Hammer (lb)
Drop distance (in)
Blows Per layer
Layers
Standard Proctor
5.5
12
3
25
Modified Proctor
10
18
5
25
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Dry Unit Weight as Compacted
Moist unit weight
Dry unit weight
Zero air voids
15
Compaction Curve
Zero air voids (S100)
Maximum unit weight
Dry Unit Weight
Wet of optimum
Dry of optimum
Optimum moisture content, wopt
Moisture Content ()
16
Effect of Compaction Energy
High energy
Zero air voids (S100)
Dry Unit Weight
Low energy
Line of optimum
Moisture Content ()
17
Permeability of Compacted Soil
Permeability
Moisture Content
Dry Unit Weight
Moisture Content ()
18
Strength of Compacted Soil
As compacted
Strength
After soaking
Moisture Content
Dry Unit Weight
Moisture Content
19
Shrinkage and Swell of Compacted Soil
Shrinkage
Kneading
Swell
Axial Shrinkage or Swell ()
Vibratory
Static
Moisture Content
Dry Unit Weight
Moisture Content
20

Quality Control of Soil Compaction
Field determination of soil unit weight
Jar
- Sand cone method
Valve
Steel plate
- Rubber balloon method
Sand
Compacted soil
- Nuclear gauge method
- Dynamic cone penetrometer (DCP)
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Stresses in Soil
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Vertical Stress at A Point in Soil
p
?z Vertical overburden stress or insitu stress
induced by weight of soil ??z
Additional stress induced by external loads
23
Vertical Overburden Stress
P
Soil layer, ?
z
A
24
Vertical Stress Profile
?z
z
Soil layer, ?
szgz
z
25
Vertical Stress Profile in Multi-Layer System
sz
Soil layer 1, ?1
z1
A
g1z1
z2
Soil layer 2, ?2
B
g1z1 g2z2
z3
Soil layer 3, ?3
C
g1z1 g2z2 g3z3
z
26
Effective Stress and Pore Water Pressure
Soil layer, ?sat
z
Water, ?w
P
Pui
Pi
? total stress ? effective stress u pore
water pressure
A
27
Vertical Stress Profile with A Ground Water Table
sz
zw
Soil, ?
szgzw
sz gzw gsat(z-zw)
Soil, ?sat
z
Water, ?w
A
ugw(z-zw)
sz?zw(gsat- gw)(z-zw)
z
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Boussinesq Solution - A Point Load
P
x
r
y
x
??z
z
L
y
??x
??y
z
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Vertical Stress Induced by A Rectangularly Loaded
Area
p
x
dx
dy
B
L
y
??z
z
30
Example 1
1
2
A
3
4
31
Example 2
A

-
1
2
3
4
A
A
32
Stress Distribution Method
p
L
?
B
z
??z
L
B
If tan? 1/2