ce 632 soil mechanics review.pps

1CE-632Foundation Analysis and Design

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

Foundation Analysis and Design by: Dr. Amit Prashant

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Reference Books


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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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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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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 Poorly graded

60

10u

DCD

230

60 10c

DCD D


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Effect of Particle size


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Basic Volume/Mass Relationships


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Additional Phase Relationships

Typical Values of Parameters:


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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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Clay Mineralogy Clay fraction, clay size particles

Particle size < 2 m (.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 layerExchangeable ions

- Li+


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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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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 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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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

Group names: several descriptions

Plasticity Chart


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Grain Size Distribution Curve

Gravel: Sand:


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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

Darcys Law

Developed in 1856

Unit flow,

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

hq kL

Definition of Darcys Law

Darcys 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 /Lh = change in TOTAL head

Downward seepage increases effective stressUpward seepage decreases effective stress

2-D Seepage (flow nets)


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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, , is defined as the total stress, t, minus the pore water pressure, u, ' = u


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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: c = preconsolidation pressure Critical hydraulic gradient = 0 when i = (b-w) /w = 0


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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 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 w) from total stress

Steps in solving seepage and effective stress problems:


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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 undergoStress 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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Vertical Stress Increase with Depth For the previous solution, material properties such as Poissons

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.

Boussinesqs 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:

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


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Newmarks Influence Chart The Newmarks 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=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:


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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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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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Settlement Calculations Settlement is calculated using the change in void ratio


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Settlement Calculations


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Example


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Consolidation Calculations Consolidation is calculated using Terzaghis one dimensional

consolidation theory Need 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 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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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 ( = 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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Stress-Strain Relationships


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Failure Envelope for Clays


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Unconfined Compression Test A special type of unconsolidated-undrained triaxial test in

which the confining pressure, 3, 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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Stress Path


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Elastic Properties of Soil


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Elastic Properties of Soil


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Hyperbolic Model

Empirical Correlations for cohesive soils


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Anisotropic Soil MassesGeneralized Hooks Law for cross-anisotropic material

Five elastic parameters

CE-632 Foundation Analysis and DesignReference BooksGrading PolicySoil Mechanics ReviewSoil TextureEffect of Particle sizeBasic Volume/Mass RelationshipsAdditional Phase RelationshipsAtterberg LimitsClay MineralogySlide 11Soil Classification SystemsSlide 13Grain Size Distribution CurvePermeabilitySlide 16Permeability of Stratified SoilSeepageEffective StressSlide 20Effective Stress Profile in Soil DepositExampleVertical Stress Increase with DepthSlide 24Stress due to a Circular LoadSlide 26Stress due to Rectangular LoadNewmarks Influence ChartSimplified MethodsConsolidationSettlement CalculationsSlide 32Slide 33Consolidation CalculationsSlide 35Slide 36Shear StrengthDirect shear testTriaxial TestSlide 40Stress-Strain RelationshipsFailure Envelope for ClaysUnconfined Compression TestStress PathElastic Properties of SoilSlide 46Hyperbolic ModelAnisotropic Soil Masses

ce 632 soil mechanics review.pps

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