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Rich Lamb 6513665595 [email protected] Blake Nelson 6513665599 [email protected]

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Page 1: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Rich Lamb

651‐366‐5595

[email protected]

Blake Nelson

651‐366‐5599

[email protected]

Page 2: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · 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

Page 3: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Our Handouts

Geotechnical Engineering Handbook

Civil Engineering Reference Manual

Page 4: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Stress/strain  of soils/rock is 

highly non linear but is 

approximated with linear 

relationship

Page 5: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

3 phases

Gas, water, solids

Relative proportion of each 

determines properties

Page 6: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

V=Volume, W=Weight, v=voids, 

s=solids, a=air, w=water

Moisture Content =  100s

w

W

W

Page 7: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Pg 41

Page 8: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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?

Page 9: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 10: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 11: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 12: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Extract sample or test in‐place

Page 13: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Split spoon samples, Standard 

Penetration Test (SPT)

Page 14: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 15: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us
Page 16: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Thinwall

Sampler (Shelby Tube)

3 inch diameter, 30 inches long

Used to get “undisturbed”

samples for 

laboratory testing

Page 17: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Standard Penetration Tests (SPT)

Cone Penetration Test (CPT)

Pressuremeter

(PMT)

Vane Shear Test (VST)

Flat Plate Dilatometer Test (DMT)

Piezometers

Inclinometers

Page 18: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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)

Page 19: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 20: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 21: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Fine grained soils (silts, clays) pass 

through no. 200 sieve

Coarse grained soils (Sands, gravels) are 

retained on no. 200 sieve

Page 22: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us
Page 23: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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#

Page 24: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Fine grained soils

Plasticity Index (PI) = Liquid Limit (LL)-Plastic Limit (PL)

Page 25: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 26: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us
Page 27: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Plastic or fine grained soils

Page 28: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 29: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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)

Page 30: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 31: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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)

Page 32: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 33: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Pressure on soil particle in ground

Existing overburden pressure

Effective vertical stress

In‐situ stress

σ

σ’

p

p0

Page 34: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

σ‘= γ

* z

Page 35: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

σ=120 pcf

* 20 ft = 2400 psf

Sand with γ

= 120 pcf

20 ft.

Page 36: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 37: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 38: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 39: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us
Page 40: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us
Page 41: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us
Page 42: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 43: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 44: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

z

Perform Analyses at Mid Points

Layer 1

Layer

2

Layer

3

Page 45: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Pg 56

Page 46: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 47: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

One Dimensional Consolidation 

Test

Stress, σ

Str

ain,

є

Page 48: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 49: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 50: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

Page 51: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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 ∞

Page 52: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us
Page 53: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

clay

sand

sand

clay

sand

impermeable

Page 54: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

Single drainage

Hd

= layer thickness

Double drainage

Hd

=1/2 layer thickness

Page 55: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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?

Page 56: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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.

Page 57: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us
Page 58: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

C’= 42

Page 59: Rich Lamb 651 366 5595 rich.lamb@state.mn.us 651 … Notes/pe review soils and foundations.pdf · Rich Lamb 651‐366‐5595 rich.lamb@state.mn.us Blake Nelson 651‐366‐5599 blake.nelson@state.mn.us

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

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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

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0.173 ft. x 12 =2.1 in.

.173.01488

111,11488log

42

130 10 ftH

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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

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Unconfined Compression

Compressive strength, qu

is peak 

strength from test

Un‐drained shear strength, su

is ½ qu

Su=qu/2

qu

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Triaxial

Test

Simulates soil sample in ground with 

vertical and lateral confining pressure

UU – Unconsolidated Un‐drained

CD – Consolidated Drained

CU – Consolidated Un‐drained

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ShearStress, τ

Effective normalStress, σn

c

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One Dimensional Consolidation 

Test

sample

Vert. displacement

Load