Post on 28-Aug-2018
Rich Lamb
651‐366‐5595
rich.lamb@state.mn.us
Blake Nelson
651‐366‐5599
blake.nelson@state.mn.us
Stress/Strain in Soils
Subsurface Investigations
Soil Classification
Lab Testing
Vertical Soil Pressures
Load Distribution
Settlement
Bearing Capacity
Shallow Foundations
Deep Foundations
Lateral Earth Pressure
Slope Stability
Our Handouts
Geotechnical Engineering Handbook
Civil Engineering Reference Manual
Stress/strain of soils/rock is
highly non linear but is
approximated with linear
relationship
3 phases
Gas, water, solids
Relative proportion of each
determines properties
V=Volume, W=Weight, v=voids,
s=solids, a=air, w=water
Moisture Content = 100s
w
W
W
Pg 41
Lab Sample
Wet weight = 1100 grams
Dry weight = 900 grams
Specific Gravity = 2.7
Degree of Saturation =1.0
Compute void ratio (e)
What can you compute from
knowing wet and dry weights?
Find equation to use from chart above
w=Se/G
where w=moisture content
S =degree of saturation
G=specific gravity
e = void ratio
e = wG/S
Moisture content (w) = Ww
/Ws
Ww
= wet weight – dry weight
Ws
= dry weight
w=1100‐900/900 = 0.22
e = wG/S
e=0.22 (2.7)/1.0 = 0.594
Purpose of subsurface investigations is
to determine the following for design of
structures foundations:
Soil classification
Soil strength parameters
Soil stiffness parameters
Ground water levels
Bedrock depths, parameters
Extract sample or test in‐place
Split spoon samples, Standard
Penetration Test (SPT)
Split spoon sampler is driven in three
equal six inch increments
Blows are recorded for each six inch
increment
N value is total of 2nd
and 3rd
six inch
increment
Blow counts from first six inch
increment are discounted because of
possible disturbance by drilling
activities
N0-6
N6-12
N12-18
SPT N = N6-12
+ N12-18
Thinwall
Sampler (Shelby Tube)
3 inch diameter, 30 inches long
Used to get “undisturbed”
samples for
laboratory testing
Standard Penetration Tests (SPT)
Cone Penetration Test (CPT)
Pressuremeter
(PMT)
Vane Shear Test (VST)
Flat Plate Dilatometer Test (DMT)
Piezometers
Inclinometers
Gradation Tests
Soil Classification
Unconfined Compression Test
One dimensional consolidation test
Moisture test
Organic content test
Permeability test
Direct shear test
Triaxial
Test
Index tests
Atterberg
limits (LL, PL)
Textural Triangular
Unified Soil Classification System
(USCS)
AASHTO
All three based on soil grain sizes
USCS and AASHTO also based on soil
plasticity and gradation
Solid, semi‐solid, plastic and viscous liquid
In order of increasing water content
Plasticity Index PI = LL=PL, denotes the
range in water content the soils acts as a
plastic material
Fine grained soils (silts, clays) pass
through no. 200 sieve
Coarse grained soils (Sands, gravels) are
retained on no. 200 sieve
Used to determine relative quality of
soils for highway applications
(embankments, subgrades, subbasess,
bases)
Granular soils: more than 50% by
weight retained on No. 200 sieve
Group classification A‐#‐sub#
Fine grained soils
Plasticity Index (PI) = Liquid Limit (LL)-Plastic Limit (PL)
Similar to AASHTO, relies on grain
size, gradation and plasticity
Two letter classification
S=sands
G=gravel
W=well graded
P=poorly graded
C=clay
M=silt
L=low plasticity
H=high plasticity
O=organic
Pt=Peat
Plastic or fine grained soils
A sieve analysis and gradation was performed
on a soil sample and the results are
summarized below.
According to the USCS, the classification of the
sample is most nearly:
A) SC
B) CH
C) CL
D) ML
Sieve #
%Passing#4
100#10
95#20
88#40
60#100
40#200
75Liquid Limit 30Plastic Limit 10
First step: Determine if soil is coarse or
fine grained.
% passing no. 200 sieve is 75%, so
sample is fine grained (use bottom half
of chart)
Step 2: Narrow down classification by
using Liquid Limit
Liquid limit is 30 which is less than 60
so classification low plasticity and will
be either ML, CL or OL
Step 3: Use plasticity chart to select
classification
LL=30, PL=10
Plasticity Index (PI) = LL‐PL
PI=30‐10=20
Answer is C (CL, low plasticity Clay)
Stress in saturated soil mass is initially
taken up by soil grains and water, this
stress it called the “total stress”
As water drains, more stress is taken by
soil grains
Effective stress refers to the inter‐
granular contact stress between soil
grains
σtotal
=σeffective
+ u
Where u = pore pressure and σ
= soil
pressure
Pressure on soil particle in ground
Existing overburden pressure
Effective vertical stress
In‐situ stress
σ
σ’
p
p0
σ‘= γ
* z
σ=120 pcf
* 20 ft = 2400 psf
Sand with γ
= 120 pcf
20 ft.
What are the effects of
groundwater?
Soil particles are subject to
buoyancy forces which reduces the
unit weight to an effect unit weight
γ’=γ
–
γwater
Effective stress σ‘=γ’ * z
Find the effective stress at pt. A.
γ’ = 120‐62.4=57.6 pcf
σ’ = (120*10) + (57.6 * 10) = 1776 psf
10 ft.
10 ft.
Sand with γ
= 120 pcf
Required for foundation design
calculations
Function of Loading condition
(magnitude and geometry)
Load distributes with depth in soil, i.e.
load at surface is more than load at
some depth z
See handouts for different loading
conditions
Δp
Δσ
Immediate Compression
Elastic compression of material
Reduction in pore space (non saturated
materials) due to expulsion of air
Mainly in granular soils
Primary Consolidation
Consolidation Settlement
Fine Grained Soils under stress
Water is squeezed out, pore space
decreases and soil volume decreases
Secondary Compression
Continued strain after primary
consolidation
creep
Hough Method, for Granular Soils only
Where C’
= Bearing Capacity Index
H = layer thickness
P0 = existing effective vertical stress at
center of layer
ΔP = distributed pressure from load at
center of layer
0
010log
'
1
p
pp
CHH
z
Perform Analyses at Mid Points
Layer 1
Layer
2
Layer
3
Pg 56
Clay soils
Pre‐Consolidated Clays
Loaded to a higher stress
in past than currently
exists
Glaciers, fill
Normally Consolidated
Clays
Have not been previously
loaded
One Dimensional Consolidation
Test
Stress, σ
Str
ain,
є
n
i v
vvcc H
e
CS
0
0100
0 '
'log
1
Cc = compression index from
consolidation lab test
e0
= initial void ratio (lab test)
H0
= thickness of layer n
σ’v0
= initial effective stress at the
center of layer n
Δσv
= increase in vertical stress at
the center of layer n
Pg 58
n
i v
vvRc H
e
CS
0
0100
0 '
'log
1
CR
= compression index from
consolidation lab test
0
0100
00100
0 '
'log
1'log
1 v
vvcn
i v
cRc H
e
CPH
e
CS
What is settlement?
Expelling of water molecules
What controls how fast water is
expelled from soil?
Drainage path distance
Permeability of soil mass
t= time in days
Hd
=maximum length of drainage path
in feet
Cv
=coefficient of consolidation in ft2
per day
T=time factor
v
d
c
Ht
2
U% T
0 0
10 0.008
20 0.031
30 0.071
40 0.126
50 0.197
60 0.287
70 0.403
80 0.567
90 0.848
100 ∞
clay
sand
sand
clay
sand
impermeable
Single drainage
Hd
= layer thickness
Double drainage
Hd
=1/2 layer thickness
Shale bedrock (incompressible)
Well graded fine to medium silty
sandγ=120 pcfN1 60
=10Water table at 10 ft.
Square tankP=1,00,000 lbs.L=B=15
30 ft.
How much will tank settle?
Hough Method, for Granular Soils only
Where C’
= Bearing Capacity Index
H = layer thickness
P0 = existing effective vertical stress at
center of layer
ΔP = distributed pressure from load at
center of layer
0
010log
'
1
p
pp
CHH
Freebee, H=30 ft.
C’= 42
Next find p0
Do calculation at center of layer
z=15 ft.
Or, in a more simple form
psfpso
psfpcfu
watersubtractmust
psfftpcfp
14883121800
3124.62*1015
180015*120
0
0
psf
ftpcfpcfftpcfp
1488
5*4.6212010*1200
Next, find ΔP
Where P=1,000,000 lbs.
z=15 ft.
B=L=15 ft.
zLzB
PP
*
psfP 111,11515*1515
000,000,1
0.173 ft. x 12 =2.1 in.
.173.01488
111,11488log
42
130 10 ftH
Strength of soil is generally discussed in
terms of shear strength, τ
Shearing resistance = Pn
* tan θ
If Block B and plane x y are same
material, then θ=φ
τ=c + σn*tan φ
Where c =cohesion value
θ
Pn
Fa
Frx y
Unconfined Compression
Compressive strength, qu
is peak
strength from test
Un‐drained shear strength, su
is ½ qu
Su=qu/2
qu
Triaxial
Test
Simulates soil sample in ground with
vertical and lateral confining pressure
UU – Unconsolidated Un‐drained
CD – Consolidated Drained
CU – Consolidated Un‐drained
ShearStress, τ
Effective normalStress, σn
’
c
One Dimensional Consolidation
Test
sample
Vert. displacement
Load