Ce 632 soil mechanics review

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CE-632Foundation Analysis and D i

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Design

Instructor:Dr. Amit Prashant, FB 304, PH# 6054. E-mail: [email protected]

Foundation Analysis and Design by: Dr. Amit Prashant

Reference Books

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Grading Policy

Two 60-min Mid Semester Exams ……. 30%End Semester Exam ……………........... 40%Assignment ……………………………… 10%

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gProjects/ Term Paper -…………………… 20%

TOTAL 100%

Course Website: http://home.iitk.ac.in/~aprashan/ce632/

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Soil Mechanics Review

Soil behavour is complex:AnisotropicNon-homogeneousNon-linearStress and stress history dependant

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Stress and stress history dependantComplexity gives rise to importance of:

TheoryLab testsField testsEmpirical relationsComputer applicationsExperience, Judgement, FOS


Soil Texture

Particle size, shape and size distributionCoarse-textured (Gravel, Sand)Fine-textured (Silt, Clay)Visibility by the naked eye (0.05mm is the approx limit)

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)Particle size distribution

Sieve/Mechanical analysis or Gradation TestHydrometer analysis for smaller than .05 to .075 mm (#200 US Standard sieve)

Particle size distribution curvesWell gradedPoorly graded 60

10u

DCD

=230

60 10c

DCD D

=


Effect of Particle size

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Basic Volume/Mass Relationships

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Additional Phase Relationships

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Typical Values of Parameters:


Atterberg Limits

Liquid limit (LL):the water content, in percent, at which the soil changes

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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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Clay MineralogyClay fraction, clay size particlesParticle size < 2 µm (.002 mm)

Clay mineralsKaolinite, Illite, Montmorillonite (Smectite)- negatively charged, large surface areas

Non-clay minerals

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Non clay minerals- e.g. finely ground quartz, feldspar or mica of "clay" size

Implication of the clay particle surface being negatively charged double layerExchangeable ions

- Li+<Na+<H+<K+<NH4+<<Mg++<Ca++<<Al+++

- Valance, Size of Hydrated cation, ConcentrationThickness of double layer decreases when replaced by higher

valence cation - higher potential to have flocculated structureWhen double layer is larger swelling and shrinking potential is larger


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

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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.


Soil Classification SystemsClassification 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

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g y p pClassification system based on eight major groups (A-1 to A-8) and a group indexBased on grain size distribution, liquid limit and plasticity indicesMainly used for highway subgrades in USA

Unified Soil Classification System (UCS)Originally proposed in 1942 by A. CasagrandeClassification system pursuant to ASTM Designation D-2487Classification system based on group symbols and group namesThe USCS is used in most geotechnical work in Canada

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Soil Classification SystemsGroup symbols: G - gravel S - sand M - silt C - clay O - organic silts and clay

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g yPt - peat and highly

organic soils H - high plasticity L - low plasticity W - well graded P - poorly graded

Group names: several descriptions

Plasticity Chart


Grain Size Distribution Curve

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Gravel: Sand:


PermeabilityFlow through soils affect several material properties such as shear strength and compressibilityIf there were no water in soil, there would be no geotechnical engineering

Darcy’s Law

Developed in 1856

hΔ

Definition of Darcy’s Law

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Unit flow,

Where: K = hydraulic conductivity∆h =difference in piezometric or “total” head∆L = length along the drainage path

hq kL

Δ=

Δ

Darcy’s law is valid for laminar flowReynolds Number: Re < 1 for ground water flow

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Permeability of Stratified Soil

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Seepage

1-D Seepage: Q = k i A

where, i = hydraulic gradient =∆h /∆L∆h = change in TOTAL head

Downward seepage increases effective stressU d d ff ti t

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Upward seepage decreases effective stress

2-D Seepage (flow nets)

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Effective StressEffective stress is defined as the effective pressure that occurs at a specific point within a soil profileThe 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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Effective Stress

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Changes in effective stress is responsible for volume changeThe effective stress is responsible for producing frictional resistance between the soil solids

Therefore, effective stress is an important concept in geotechnical engineeringOverconsolidation ratio,

Where: σ´c = preconsolidation pressureCritical hydraulic gradient σ′ = 0 when i = (γb-γw) /γw → σ′ = 0


Effective Stress Profile in Soil Deposit

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ExampleDetermine 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.

set a datum

Steps in solving seepage and effective stress problems:

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set a datumevaluate distribution of total head with depthsubtract elevation head from total head to yield pressure headcalculate distribution with depth of vertical “total stress”subtract pore pressure (=pressure head x γw) from total stress


Vertical Stress Increase with DepthAllowable settlement, usually set by building codes, may control the allowable bearing capacityThe vertical stress increase with depth must be determined to calculate the amount of settlement that a foundation may undergo

Stress due to a Point LoadIn 1885, Boussinesq developed a mathematical relationship for vertical stress increase with depth inside a homogenous, elastic and

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isotropic material from point loads as follows:


Vertical Stress Increase with DepthFor 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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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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Stress due to a Circular Load

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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:

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Concept of superposition may also be employed to find the stresses at various locations.

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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

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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=AB3. 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:


Simplified MethodsThe 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

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increase in stress proportional to a slope of 2 vertical to 1 horizontalAccording to the method, the increase in stress is calculated as follows:


ConsolidationSettlement – total amount of settlementConsolidation – time dependent settlementConsolidation occurs during the drainage of pore water caused by excess pore water pressure

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Settlement CalculationsSettlement is calculated using the change in void ratio

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Settlement Calculations

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Example

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Consolidation CalculationsConsolidation is calculated using Terzaghi’s one dimensional consolidation theoryNeed to determine the rate of dissipation of excess pore water pressures

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Consolidation Calculations

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Example

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Shear StrengthSoil strength is measured in terms of shear resistanceShear resistance is developed on the soil particle contactsFailure occurs in a material when the normal stress and the shear stress reach some limiting combination

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Direct shear test

Simple, inexpensive, limited configurations

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Triaxial Testmay be complex, expensive, several configurations

Consolidated Drained Test

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Triaxial TestUndrained Loading (φ = 0 Concept)

Total stress change is the same as the pore water pressure increase in undrained loading, i.e. no change in effective stressChanges in total stress do not change the shear strength in undrained loading

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Stress-Strain Relationships

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Failure Envelope for Clays

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Unconfined Compression TestA special type of unconsolidated-undrained triaxial test in which the confining pressure, σ3, is set to zeroThe 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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g y


Stress Path

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Elastic Properties of Soil

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Elastic Properties of Soil

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Hyperbolic Model

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Empirical Correlations for cohesive soils


Anisotropic Soil MassesGeneralized Hook’s Law for cross-anisotropic material

Five elastic parameters

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