1
Part 1
Soil Mechanics Review
620451
Foundations
2
Sieve Analysis
Particle size distribution
Coarse soils
Atterberg limits
Liquid limit & Plastic limit
Fine soils
Soil Classification
3The numerical values 1 to 9 are ratings, with 1 being the best
The chart only provides guidance and to make a preliminary assessment of the suitability of a soil for a particular use
(after Wagner, 1957)
Phase – Relationships
4
Field Density
5
max
max min
(%) 100
r
e e
D
e e
(field) (min) (max)
(max) (min) (field)
(%) 100
d d d
r
d d d
D
Relative Density, Dr
6
7
Flow of Water Through Soil
● Permeability or hydraulic conductivity, which is the ease with which water flows (seeps) through the soils
and represented by the coefficient of permeability of soils, k
● Hydraulic gradient (i) which is the total head difference between two points divided by the distance between
them
Governed by Darci’s law (discharge velocity = k i
Constant head Falling head
8
It is the stress transmitted through the soil
skeleton only (i.e. due to interparticle forces)
Effective Stress Principle
The stress that controls changes in the volume
and strength of a soil is known as the effective
stress.
Terzaghi first presented the concept of effective stress in
1925 and again, in 1936, at the First International
Conference on Soil Mechanics and Foundation
Engineering, at Harvard University
𝑓𝑜𝑟 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑 𝑠𝑜𝑖𝑙𝑠 𝜎′ = 𝜎 − 𝑢
9
js is called seepage force per unit volume = i w
In-situ Vertical Effective Stress
Hydrostatic (No flow)
𝑤ℎ𝑒𝑟𝑒 𝛾′ = 𝛾𝑠𝑎𝑡 − 𝛾𝑤
Downward flow
Upward flow
10
Shear Strength of Soils
• The shear strength of a soil is its resistance to shearing stresses
• When designing geotechnical systems, geotechnical engineers must consider both drained and undrained
conditions to determine which of these conditions is critical
• Drained condition occurs when the excess porewater pressure developed during loading of a soil dissipates, i.e.,
Du = 0.
• Undrained condition occurs when the excess porewater pressure cannot drain during loading of soil, at least
quickly, from the soil; that is, Du ≠ 0
• The existence of either condition—drained or undrained— depends on the soil type, the geological formation,
and the rate of loading.
• The permeability of coarse grained soils is sufficiently high that under static loading conditions the excess
porewater pressure dissipates quickly, and drained condition applies
• During construction and shortly after, called the short-term condition soils with low permeability (fine-grained
soils) do not have sufficient time for the excess porewater pressure to dissipate, and undrained condition applies
• During the life of a geotechnical structure, called the long-term condition, the excess porewater pressure
developed by a loading dissipates, and drained condition applies
• Dynamic loading, such as during an earthquake, is imposed so quickly that even coarse-grained soils do not have
sufficient time to dissipate the excess porewater pressure, and undrained condition applies.
H = m W
where m is called friction coefficient
Equation of a line with zero intercept and slope
of m
or m = tan f
where f is called the friction angle
In terms of stresses (dividing both sides by the cross
sectional area)
tan
n
f
H
W
f
Coulomb’s Failure Criterion
Initially – block will not fail until the bond is broken
tan
n
c f
H
W
f
c
Coulomb’s Failure Criterion
Natural soil deposits can be normally consolidated or overconsolidated
(or preconsolidated). If the present effective overburden pressure 𝜎𝑜
′ is
equal to the preconsolidation pressure (the maximum past pressure
applied on the soil) 𝜎𝑐
′ the soil is normally consolidated. However, if 𝜎𝑐
′
> 𝜎𝑜
′ , the soil is overconsolidated. The ratio 𝜎𝑐
′/𝜎𝑜
′ is called the
overconsolidation ratio (OCR) and it is greater than 1 if the soil is
overconsolidated.
Soils that shows cohesion are either overconsolidated or cemented soils
Mohr’s Circle for Stress States and Principal Stresses
Maximum Shear Stress
13
n
n
Stresses on inclined plane
• Normal stress (compression is positive)
• Shear stress (counter clockwise is
positive)
• The stresses on any plan are
represented by a point on the Mohr
circle
• If the angle between 2 plans is q, the
angle between the 2 points is 2q on the
Mohr circle
14
Failure plane angle,
45
2
f
q
2
1 3
tan 45 2 tan 45
2 2
c
f f
At failure, the relation between 𝜎1
′ , 𝜎3
′ , 𝜙′ and 𝑐′ can be found as follows:
Mohr–Coulomb Failure Criterion
By combining Mohr’s circle for finding stress states with Coulomb’s frictional law, we can develop a generalized failure
criterion
Note that the maximum shear stress is not the failure stress
Stresses on
failure plan
(𝜎𝑛,𝜏𝑓)
15
Tresca Failure Criterion
The shear strength of a fine-grained soil under undrained condition is called the undrained shear
strength, cu. We use the Tresca failure criterion—shear stress at failure is one-half the principal stress
difference—to interpret the undrained shear strength. The undrained shear strength, cu, is the radius
of the Mohr total stress circle; that is
𝑐𝑢 =
(𝜎1)𝑓 − (𝜎3)𝑓
2
Direct Shear Test
𝜏𝑓 = 𝜎
′𝑡𝑎𝑛𝜙′
Commonly used by geotechnical engineers to
obtain 𝜙′ an c’ for granular soils
17
The triaxial shear test is one of the most reliable methods
available for determining the shear strength parameters:
Typical diagram of a triaxial cell
1. Consolidated-drained test or drained test (CD test)
2. Consolidated-undrained test (CU test)
3. Unconsolidated-undrained test or undrained test (UU test)
Triaxial Test
18
The unconfined compression test is a special type of unconsolidated-undrained test that is commonly used for clay
specimens to find the undrained shear strength cu.
Unconfined Compression Test
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20
Short Term and Long Term Analysis
Short-term condition requires a total stress analysis
(TSA) applicable to fine-grained soils and the shear
strength parameter is the undrained shear strength of
the soil cu.
Long-term condition requires an effective stress
Analysis (ESA) applicable to all soils and the shear
strength parameters are c and f
Both analysis shall be checked for fine soils
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