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CE-632
Foundation Analysis and
Design
Instructor:
Dr. Amit Prashant, FB 304, PH# 6054.
E-mail: aprashan@iitk.ac.in
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Foundation Analysis and Design by: Dr. Amit Prashant
Reference Books
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Foundation Analysis and Design by: Dr. Amit Prashant
Grading Policy
Two 60-min Mid Semester Exams ……. 30%
End Semester Exam ……………........... 40%
Assignment ……………………………… 10%
Projects/ Term Paper -…………………… 20%
TOTAL 100%
Course Website: http://home.iitk.ac.in/~aprashan/ce632/
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Foundation Analysis and Design by: Dr. Amit Prashant
Soil Mechanics Review
Soil behavour is complex:
Anisotropic
Non-homogeneous
Non-linear
Stress and stress history dependant
Complexity gives rise to importance of:
Theory
Lab tests
Field tests
Empirical relations
Computer applications
Experience, Judgement, FOS
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Foundation Analysis and Design by: Dr. Amit Prashant
Soil Texture
Particle size, shape and size distribution
Coarse-textured (Gravel, Sand)
Fine-textured (Silt, Clay)
Visibility by the naked eye (0.05mm is the approx
limit)
Particle size distribution
Sieve/Mechanical analysis or Gradation Test
Hydrometer analysis for smaller than .05 to .075 mm
(#200 US Standard sieve)
Particle size distribution curves
Well graded 2
D D30
Poorly graded Cu 60 Cc
D10 D60 D10
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Foundation Analysis and Design by: Dr. Amit Prashant
Effect of Particle size
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Foundation Analysis and Design by: Dr. Amit Prashant
Basic Volume/Mass Relationships
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Foundation Analysis and Design by: Dr. Amit Prashant
Additional Phase Relationships
Typical Values of Parameters:
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Foundation Analysis and Design by: Dr. Amit Prashant
Atterberg Limits
Liquid limit (LL):
the water
content, in
percent, at which
the soil changes
from a liquid to a
plastic state.
Plastic limit (PL): the water content, in percent, at which the soil
changes from a plastic to a semisolid state.
Shrinkage limit (SL): the water content, in percent, at which the
soil changes from a semisolid to a solid state.
Plasticity index (PI): the difference between the liquid limit and
plastic limit of a soil, PI = LL – PL.
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Foundation Analysis and Design by: Dr. Amit Prashant
Clay Mineralogy
Clay fraction, clay size particles
Particle size < 2 µm (.002 mm)
Clay minerals
Kaolinite, Illite, Montmorillonite (Smectite)
- negatively charged, large surface areas
Non-clay minerals
- e.g. finely ground quartz, feldspar or mica of "clay" size
Implication of the clay particle surface being
negatively charged double layer
Exchangeable ions
- Li+<Na+<H+<K+<NH4+<<Mg++<Ca++<<Al+++
- Valance, Size of Hydrated cation, Concentration
Thickness of double layer decreases when replaced by higher
valence cation - higher potential to have flocculated structure
When double layer is larger swelling and shrinking potential is larger
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Foundation Analysis and Design by: Dr. Amit Prashant
Clay Mineralogy
Soils containing clay minerals tend to be cohesive and plastic.
Given the existence of a double layer, clay minerals have an affinity
for water and hence has a potential for swelling (e.g. during wet
season) and shrinking (e.g. during dry season). Smectites such as
Montmorillonite have the highest potential, Kaolinite has the
lowest.
Generally, a flocculated soil has higher strength, lower
compressibility and higher permeability compared to a non-
flocculated soil.
Sands and gravels (cohesionless ) :
Relative density can be used to compare the same soil. However,
the fabric may be different for a given relative density and hence the
behaviour.
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Foundation Analysis and Design by: Dr. Amit Prashant
Soil Classification Systems
Classification may be based on – grain size, genesis, Atterberg
Limits, behaviour, etc. In Engineering, descriptive or behaviour
based classification is more useful than genetic classification.
American Assoc of State Highway & Transportation Officials
(AASHTO)
Originally proposed in 1945
Classification system based on eight major groups (A-1 to A-8)
and a group index
Based on grain size distribution, liquid limit and plasticity indices
Mainly used for highway subgrades in USA
Unified Soil Classification System (UCS)
Originally proposed in 1942 by A. Casagrande
Classification system pursuant to ASTM Designation D-2487
Classification system based on group symbols and group names
The USCS is used in most geotechnical work in Canada
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Foundation Analysis and Design by: Dr. Amit Prashant
Soil Classification Systems
Group symbols:
G - gravel
S - sand
M - silt
C - clay
O - organic silts and clay
Pt - peat and highly
organic soils
H - high plasticity
L - low plasticity
W - well graded
P - poorly graded Plasticity Chart
Group names:
several descriptions
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Foundation Analysis and Design by: Dr. Amit Prashant
Grain Size Distribution Curve
Gravel: Sand:
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Foundation Analysis and Design by: Dr. Amit Prashant
Permeability
Flow through soils affect several material properties such as shear strength
and compressibility
If there were no water in soil, there would be no geotechnical engineering
Darcy’s Law Definition of
Darcy’s Law
Developed in 1856
h
Unit flow, qk
L
Where: K = hydraulic conductivity
∆h =difference in piezometric or “total” head
∆L = length along the drainage path
Darcy’s law is valid for laminar flow
Reynolds Number: Re < 1 for ground water flow
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Foundation Analysis and Design by: Dr. Amit Prashant
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Foundation Analysis and Design by: Dr. Amit Prashant
Permeability of Stratified Soil
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Foundation Analysis and Design by: Dr. Amit Prashant
Seepage
1-D Seepage:
Q=kiA
where, i = hydraulic gradient =∆h /∆L
∆h = change in TOTAL head
Downward seepage increases effective stress
Upward seepage decreases effective stress
2-D Seepage (flow nets)
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Foundation Analysis and Design by: Dr. Amit Prashant
Effective Stress
Effective stress is defined as the effective pressure that occurs at a
specific point within a soil profile
The total stress is carried partially by the pore water and partially by
the soil solids, the effective stress, σ’, is defined as the total stress,
σt, minus the pore water pressure, u, σ' = σ − u
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Foundation Analysis and Design by: Dr. Amit Prashant
Effective Stress
Changes in effective stress is responsible for volume change
The effective stress is responsible for producing frictional resistance
between the soil solids
Therefore, effective stress is an important concept in geotechnical
engineering
Overconsolidation ratio,
Where: σ´c = preconsolidation pressure
Critical hydraulic gradient σ′ = 0 when i = (γb-γw) /γw → σ′ = 0
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Foundation Analysis and Design by: Dr. Amit Prashant
Effective Stress Profile in Soil Deposit
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Foundation Analysis and Design by: Dr. Amit Prashant
Example
Determine the effective stress distribution with depth if the head in the
gravel layer is a) 2 m below ground surface b) 4 m below ground
surface; and c) at the ground surface.
Steps in solving seepage and
effective stress problems:
set a datum
evaluate distribution of
total head with depth
subtract elevation head
from total head to yield
pressure head
calculate distribution
with depth of vertical
“total stress”
subtract pore pressure
(=pressure head x γw)
from total stress
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Foundation Analysis and Design by: Dr. Amit Prashant
Vertical Stress Increase with Depth
Allowable settlement, usually set by building codes, may control the
allowable bearing capacity
The vertical stress increase with depth must be determined to
calculate the amount of settlement that a foundation may undergo
Stress due to a Point Load
In 1885, Boussinesq developed a mathematical relationship for
vertical stress increase with depth inside a homogenous, elastic and
isotropic material from point loads as follows:
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Foundation Analysis and Design by: Dr. Amit Prashant
Vertical Stress Increase with Depth
For the previous solution, material properties such as Poisson’s ratio
and modulus of elasticity do not influence the stress increase with
depth, i.e. stress increase with depth is a function of geometry only.
Boussinesq’s Solution for point load-
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Foundation Analysis and Design by: Dr. Amit Prashant
Stress due to a Circular Load
The Boussinesq Equation as stated above may be used to derive a
relationship for stress increase below the center of the footing from a
flexible circular loaded area:
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Foundation Analysis and Design by: Dr. Amit Prashant
Stress due to a
Circular Load
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Foundation Analysis and Design by: Dr. Amit Prashant
Stress due to
Rectangular Load
The Boussinesq Equation may also
be used to derive a relationship for
stress increase below the corner of
the footing from a flexible
rectangular loaded area:
Concept of superposition may also be employed
to find the stresses at various locations.
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Foundation Analysis and Design by: Dr. Amit Prashant
Newmark’s
Influence Chart
The Newmark’s Influence Chart
method consists of concentric circles
drawn to scale, each square
contributes a fraction of the stress
In most charts each square contributes
1/200 (or 0.005) units of stress
(influence value, IV)
Follow the 5 steps to determine the
stress increase:
1. Determine the depth, z, where you
wish to calculate the stress
increase
2. Adopt a scale of z=AB
3. Draw the footing to scale and place
the point of interest over the center
of the chart
4. Count the number of elements that
fall inside the footing, N
5. Calculate the stress increase as:
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Foundation Analysis and Design by: Dr. Amit Prashant
Simplified Methods
The 2:1 method is an approximate method of calculating the
apparent “dissipation” of stress with depth by averaging the stress
increment onto an increasingly bigger loaded area based on 2V:1H.
This method assumes that the stress increment is constant across
the area (B+z)·(L+z) and equals zero outside this area.
The method employs
simple geometry of an
increase in stress
proportional to a slope
of 2 vertical to 1
horizontal
According to the
method, the increase
in stress is calculated
as follows:
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Foundation Analysis and Design by: Dr. Amit Prashant
Consolidation
Settlement – total amount of settlement
Consolidation – time dependent settlement
Consolidation occurs during the drainage of pore water
caused by excess pore water pressure
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Foundation Analysis and Design by: Dr. Amit Prashant
Settlement Calculations
Settlement is calculated using the change in void ratio
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Foundation Analysis and Design by: Dr. Amit Prashant
Settlement
Calculations
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Foundation Analysis and Design by: Dr. Amit Prashant
Example
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Foundation Analysis and Design by: Dr. Amit Prashant
Consolidation Calculations
Consolidation is calculated using Terzaghi’s one dimensional
consolidation theory
Need to determine the rate of dissipation of excess pore water
pressures
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Foundation Analysis and Design by: Dr. Amit Prashant
Consolidation Calculations
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Foundation Analysis and Design by: Dr. Amit Prashant
Example
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Foundation Analysis and Design by: Dr. Amit Prashant
Shear Strength
Soil strength is measured in terms of shear resistance
Shear resistance is developed on the soil particle
contacts
Failure occurs in a material when the normal stress and
the shear stress reach some limiting combination
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Foundation Analysis and Design by: Dr. Amit Prashant
Direct shear test
Simple, inexpensive, limited configurations
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Foundation Analysis and Design by: Dr. Amit Prashant
Triaxial Test
may be complex, expensive, several
configurations
Consolidated Drained Test
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Foundation Analysis and Design by: Dr. Amit Prashant
Triaxial Test
Undrained Loading (f = 0 Concept)
Total stress change is the same as the pore water pressure increase
in undrained loading, i.e. no change in effective stress
Changes in total stress do not change the shear strength in
undrained loading
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Foundation Analysis and Design by: Dr. Amit Prashant
Stress-Strain Relationships
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Foundation Analysis and Design by: Dr. Amit Prashant
Failure Envelope for Clays
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Foundation Analysis and Design by: Dr. Amit Prashant
Unconfined Compression Test
A special type of unconsolidated-undrained triaxial test in
which the confining pressure, σ3, is set to zero
The axial stress at failure is referred to the unconfined
compressive strength, qu (not to be confused with qu)
The unconfined shear strength, cu, may be defined as,
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Foundation Analysis and Design by: Dr. Amit Prashant
Stress
Path
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Foundation Analysis and Design by: Dr. Amit Prashant
Elastic Properties of Soil
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Foundation Analysis and Design by: Dr. Amit Prashant
Elastic Properties of Soil
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Foundation Analysis and Design by: Dr. Amit Prashant
Hyperbolic Model
Empirical Correlations for cohesive soils
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Foundation Analysis and Design by: Dr. Amit Prashant
Anisotropic Soil Masses
Generalized Hook’s Law for cross-
anisotropic material
Five elastic parameters
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