1 ce-632 foundation analysis and design instructor: dr. amit prashant, fb 304, ph# 6054. e-mail:...

1

CE-632Foundation Analysis and Design

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

Foundation Analysis and Design by: Dr. Amit Prashant

2

Reference Books


3

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/


4

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


5

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

DC

D

230

60 10c

DC

D D


6

Effect of Particle size


7

Basic Volume/Mass Relationships


8

Additional Phase Relationships

Typical Values of Parameters:


9

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.


10

Clay Mineralogy

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

Clay mineralsKaolinite, 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+<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


11

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.


12

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


13

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


14

Grain Size Distribution Curve

Gravel: Sand:


15

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

Developed in 1856

Unit flow,

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

hq k

L

Definition of Darcy’s Law

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


16


17

Permeability of Stratified Soil


18

Seepage

1-D Seepage: Q = k i A

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

Downward seepage increases effective stressUpward seepage decreases effective stress

2-D Seepage (flow nets)


19

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


20

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


21

Effective Stress Profile in Soil Deposit


22

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 γw) from total stress

Steps in solving seepage and effective stress problems:


23

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:


24

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-


25

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:


26

Stress due to a Circular Load


27

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.


28

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=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:


29

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:


30

Consolidation Settlement – total amount of settlement Consolidation – time dependent settlement Consolidation occurs during the drainage of pore water

caused by excess pore water pressure


31

Settlement Calculations Settlement is calculated using the change in void ratio


32

Settlement Calculations


33

Example


34

Consolidation Calculations

Consolidation is calculated using Terzaghi’s one dimensional consolidation theory

Need to determine the rate of dissipation of excess pore water pressures


35

Consolidation Calculations


36

Example


37

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


38

Direct shear test

Simple, inexpensive, limited configurations


39

Triaxial Testmay be complex, expensive, several configurations

Consolidated Drained Test


40

Triaxial Test

Undrained 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


41

Stress-Strain Relationships


42

Failure Envelope for Clays


43

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,


44

Stress Path


45

Elastic Properties of Soil


46

Elastic Properties of Soil


47

Hyperbolic Model

Empirical Correlations for cohesive soils


48

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

Five elastic parameters

1 ce-632 foundation analysis and design instructor: dr. amit prashant, fb 304, ph# 6054. e-mail:...

Documents

foundation analysis

amit prashant

effect of particle size

graded slide

soil texture particle

design instructor

fos slide

aprashanc slide