Foundation Design based on soil test reports and column loads

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Part 1

Soil Mechanics Review

620451

Foundations

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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

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Field Density

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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

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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

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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

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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

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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

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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

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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)

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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

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Direct Shear Test

𝜏𝑓 = 𝜎 ′𝑡𝑎𝑛𝜙′

Commonly used by geotechnical engineers to obtain 𝜙′ an c’ for granular soils

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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

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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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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