2010-02-09 Soil Mechanics Intro

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COURSE TITLE: Geotechnics 2

COURSE CODE: GEOT221B

ELEMENT NAME: Soil Mechanics 2


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Course Author: The Centre for Project Managementand Civil Infrastructure Systems

Date : December 2008 Course Instructor: Russell Ramrattan

Contact Information:

Mobile : 740 9495

Email :[email protected]

Availability times in office: To be determined


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Darcys Law


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Darcys Law


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Permeability is a measure of the ease of which water flows

through rocks and soil.

It is of importance to the civil engineer when dealing with

seepage under dams, land drainage or groundwater lowering.

Darcys Law is the mathematical relationship discovered

(1856) by the French engineer Henri Darcy that governs the

flow of groundwater through granular media or the flow of

other fluids through permeable material, such as petroleumthrough sandstone or limestone.

Permeability


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The flow of water through soils is assumed to follow Darcys

law: Q = k A H

t l

where: Q = quantity of water flowing;

t = time for quantity Q to flow;

k = coefficient of permeability for the soil

A = area of x-section through which water flows;H = hydraulic head across soil;

l = length of flow path through soil.

Permeability


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The ratio H/l is known as the hydraulic gradient and is

denoted as i.

The coefficient of permeability k therefore equals;

Q/t

Ai

and may be defined as the rate of flow per unit area of soil,

under unit hydraulic gradient. This coefficient is expressed in mm/s

Permeability


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Typical values of permeability:

Soil type Values of Drainage

permeability, k properties

(mm/s)

Gravels 100010 Good

Sands 1010-2 Good

Silts 10-2 - 10-5 PoorClays >10-5 Impervious

Permeability


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This apparatus is known as a constant head permeameter and

is shown next. The water may be arranged to flow either up

the sample or down. A sand filter is incorporated above and

below the sample to help prevent it washing away.

Permeability


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The constant-head permeameter

Permeability


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Water under a constant head is allowed to percolate through a

sample contained in a cylinder of cross-sectional area A. The

quantity of water Q, passing the sample in time t, is collected

in a measuring cylinder. Manometers tapped on the side ofthe sample cylinder give the loss of head H, over a length of

sample l, and hence the hydraulic gradient i.

From Darcys law: coefficient of permeability

k = Q/t

Ai

The constant-head permeameter.


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Example

A constant-head permeameter test has been run on a sand

sample 250mm in length and 2000 mm2 in area. With a head

loss of 500mm the discharge was found to be 260 ml in 130

seconds. Determine the coefficient of permeability of the soil.

If the specific gravity of the grains was 2.62 and the dry

weight of the sand 916g, find the void ratio of the sample.

and is shown above.

Permeability


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In natural conditions soil is rarely homogeneous.

Stratification will occur giving thin layers of varying

permeability. On the larger geological scale, the strata may

vary widely from a relatively impervious clay to permeablesand within a small depth.

These variations will have a marked effect on the overall

permeability with the average value in the direction ofstratification being quite different from the value at right

angles to it.

Multi-layer permeability


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In a series of strata, thickness H1, H2, H3 etc. with

permeability k1, k2, k3etc. The rate of flow per unit area along

each stratum will vary but the hydraulic gradient will be

constant. The average permeability in this direction can beshown to be equal to kH where

kH = k1H1 + k2H2 + k3H3+ . knHn

H1 + H2 + H3+.Hn



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With flow at right angles to the strata, the hydraulic gradient

will vary in each stratum, but the rate of flow per unit area

must be constant. The average permeability at right angles to

the strata can be shown to be equal to kv where:

kH = ___H1 + H2 + H3+ . Hn____

H1/k1 + H2/k2 + H3/k3+.Hn/kn



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From these two equations it can be proved that kH/kV > 1 i.e.

the permeability in the direction of the strata is always greater

than the permeability at right angles to the strata.

As soil samples for laboratory testing are frequently taken at

right angles to the strata, it can be seen that laboratory tests

can give a low value of the actual permeability on the site.



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AREA OF STUDY 1. PERMEABILITY Revision of Total Head, Piezometric / Pressure Head and Piezometric level, etc. Permeabilit. of soils. One-dimensional seepage. Darcys Law. Measurement of Permeabilit in Field and Laboratory. Seepage through layers of soil of different permeability. 2. EFFECTIVE STRESS Revision of effective stress, total stress. Effective stress profiles when there is

seepage. Coefficient of earth pressure at rest K0. Calculation of horizontaleffective stress profiles.

Geotechnics 2 (Soil Mechanics) September 2008

3. STRESS and STRAIN Definitions of stresses and strains. Sign conventions. Principal stresses in axi-svmmetric and plane strain problems. 4. MOHRS CIRCLES of STRESS and STRESS PATHS Mohrs circle of stress (total and effective). Pole of Mohrs circle. Stress paths t-s. q-p. u1-u3 (total and effective).


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5. LABORATORY TESTING OF SOILS Introduction to laborator testing (triaxial. shear box, one-

dimensional compression). Conditions of drainage in laborator tests.

Failure conditions on Mohr diagram. Stress-paths in tests.Application to practical problems. 6. ONE-DIMENSIONAL COMPRESSION Normal consolidation line (and illustration on stress-void ratio

plots). Stress history, normal, over-consolidation. Concept of yield stress. Analysis of Consolidation test - determination of yield stress, OCR,

m. C, c. Prediction of settlement under one-dimensional loading in simple

cases. Spring-piston analogue. Role of pore-water in controlling rate of

consolidation.


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7. SHEAR STRENGTH OF SATURATED SOILS Failure criteria. Terzaghi/Coulomb effective stress equation for strength. Geometry of Mohrs circle at failure. Failure envelope. Mohr-Coulomb failure criterion.

Shear strength parameters. Determination of shear strength parameters from drained andundrained triaxial test data. Prediction of strength under drained conditions. Dilation andcontraction on shear.

Peak strength and its relation to dilatancy. Parallels in behaviour between sands and clays. Residual strength of clays. Measurement in ring-shear apparatus. Pore pressure generation during undrained loading/unloading. Pore pressure parameters. Prediction of pore pressure changes under changes of total stress. Undrained shear strength. = 0. Prediction of strength under undrained conditions. Inferred changes of stress during sampling of clay soils. Use of laboratory tests for measurement of shear strength parameters and application to

practical problems. Concept of Critical State. Critical state line and its relation to normal consolidation line. Implied behaviour of loose and dense sands and normally and over-consolidated clays in

drained and undrained shear.


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8. SUCTION and CAPILLARITY

Suction and capillarit. Effective stress above the water table.

Prediction of strength in unconfined compression.

9. COMPACTION Introduction to earthworks and compaction. Effect of moisture

on compaction. Optimum moisture content. BS Standard andHeavy compaction. In-situ density determination.

LABORATORY CLASSES

1. Proctor compaction 2. Permeametry and seepage tank

3. Shear box test on sand

4. Unconsolidated undrained triaxial test on clay


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ASSESSMENT

DELIVERY

INDICATIVE READING 1. Craig RF. Soil Mechanics. 6th Ed. E & FN Spon,

1997.

2. Lambe 1W & Whitman RV. Soil Mechanics. Wiley.

3. Scott CR. Introduction to Soil Mechanics andFoundations. Applied Science.

Geotechnics 2 (Soil Mechanics) September 2008

2010-02-09 Soil Mechanics Intro

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