shear strength in soils

7/29/2019 shear strength in soils

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CE 240

Soil Mechanics & FoundationsLecture 11.1

Shear Strength of Soil I

(Das, Ch. 11)


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Shear strength in soils Introduction

Definitions

Mohr-Coulomb criterion

Introduction

Lab tests for getting the shear strength

Direct shear test

Introduction Procedure & calculation

Critical void ratio

Class Outlines


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Shear Strength The strength of a material is the

greatest stress it can sustain;

So that the unit of strength is the same

as stress (Pa in SI unit system);


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Significance of Shear Strength

The safety of any geotechnical structureis dependent on the strength of the soil;

If the soil fails, the structure founded onit can collapse.

Understanding shear strength is thebasis to analyze soil stability problemslike:

lateral pressure on earth retainingstructures (Chs. 12, 13),

slope stability (Ch. 14), and

bearing capacity (Ch. 15).


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Shear Failure in Soils


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Slope Failure in Soils

Failure due to inadequatestrength at shear interface


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Static: Transcosna Grain Elevator

Canada (Oct. 18, 1913)

West side of foundation sank 24-ft


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Bearing Capacity Failure

D i F d ti f il b li f ti


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Dynamic: Foundation failure by liquefaction

after the 1964 Niigata Earthquake. (USGS)


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Dynamic: Lateral Spreading caused by the 1906 San

Francisco Earthquake at Moss Landing, CA

(USGS Professional Paper 993)


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Shear Strength in Soils

The shear strength of a soil is its resistance toshearing stresses.

It is a measure of the soil resistance to

deformation by continuous displacement of itsindividual soil particles

Shear strength in soils depends primarily on

interactions between particles Shear failure occurs when the stresses between

the particles are such that they slide or roll past

each other


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Shear Strength in Soils

(cont.) Soil derives its shear strength from two

sources: Cohesion between particles (stress

independent component)

Cementation between sand grains

Electrostatic attraction between clay particles

Frictional resistance between particles (stressdependent component)


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Shear Strength of Soils: Cohesion

Cohesion (C), is a measure of the forces thatcement particles of soils

Dry sand with no cementation

Dry sand with some cementation Soft clay

Stiff clay


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Shear Strength of Soils; Internal

Friction Internal Friction angle (), is the measure of the

shear strength of soils due to friction


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Mohr-Coulomb Failure Criteria

This theory states that a material fails

because of a critical combination ofnormal stress and shear stress, and not

from their either maximum normal orshear stress alone.


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Mohr-Coulomb Failure

Criterion

ShearStrength,S

=

C

Normal Stress, n = = h


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' '

tan (11.2)

tan ' (11.3)

f n n

f n n

c c

c c

= + = +

= + = +

f

whereshear strength

c = cohesion; c =effective cohesion

= angle of internal friction; = effective angle of internal friction

= coefficient of friction; ' = effective coefficient of frictio

=

n.


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=tan

0.51-0.58

0.58-0.70

0.70-0.78

0.58-0.700.70-0.84

0.84-1.00

0.67-1.110.49-0.70


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Mohr-Coulomb shear failure criterion

1

1

33n

f

1

3

2

f=c+

n

c

Failed Zone

(, )

ff


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From trigonometric equalities we have


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Way 1: Increase the normal

stress in one direction

1

1 major principle stress

n

f3 3

Minor principle stress

Confining stress


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Way 2: directly apply the shear stress

Consider the following situation:

- A normal stress is appliedvertically and held constant- A shear stress is then applied

until failureShear

stress

Normal stress n

Normal stress n

D t i ti f Sh St th P t


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Determination of Shear Strength Parameters

The shear strength parameters of a soil aredetermined in the lab primarily with two types

of tests: 1) Direct Shear Test; and 2) Triaxial

Shear Test.(1) (2)

Soil

Normal stress n

Shear stress 3

3

1


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Direct Shear Test

Direct shear test is Quick and Inexpensive

Shortcoming is that it fails the soil on adesignated plane which may not be theweakest one

Used to determine the shear strength ofboth cohesive as well as non-cohesive

soils

ASTM D 3080


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Direct Shear Test (cont.)

The test equipment consistsof a metal box in which thesoil specimen is placed

The box is split horizontallyinto two halves

Vertical force (normalstress) is applied through ametal platen

Shear force is applied bymoving one half of the boxrelative to the other tocause failure in the soilspecimen

Soil

Normal stress n

Shear stress 3


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Direct Shear Test


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Direct Shear Test


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Direct Shear Test


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Direct Shear Test Data

Shearstress

Residual Strength

Peak Strength

Direct Shear Test Data:


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Direct Shear Test Data:

Volume change

H


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Direct Shear Test: Procedure

1.Measure inner side or diameter of shear box and find thearea

2.Make sure top and bottom halves of shear box are in

contact and fixed together.3.Weigh out 150 g of sand.

4.Place the soil in three layers in the mold using the funnel.

Compact the soil with 20 blows per layer.5.Place cover on top of sand

6.Place shear box in machine.

7.Apply normal force. The weights to use for the three runsare2 kg, 4 kg, and 6 kg if the load is applied through a lever arm,or 10 kg, 20 kg, and 30 kg, if the load is applied directly.

Note: Lever arm loading ratio 1:10 (2kg weight = 20 kg)



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8. Start the motor with selected speed (0.1 in/min) so thatthe rate of shearing is at a selected constant rate

9. Take the horizontal displacement gauge, verticaldisplacement gage and shear load gage readings.

Record the readings on the data sheet.

10. Continue taking readings until the horizontal shear loadpeaks and then falls, or the horizontal displacement

reaches 15% of the diameter.


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Calculations

1. Determine the dry

unit weight, d

2. Calculate the void

ratio, e

3. Calculate the normal

stress & shearstress

1=d

wGse

A

V

A

N== ;


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Figures

Peak Stress

s3

s2

s1

Shear

stress,s

N3 = 30 kg

N2 = 20 kg

N1 = 10 kg

Horizontal displacement, H


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Figures (cont)

S

hear

Stres

s,s

(psf)

C

(1,s1)

(3,s3)(2,s2)

Normal Stress , psf


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Figures (cont)

Verticaldisplacemen

t

Horizontal displacement


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Reading Assignment:

Das, Ch. 11

HW: Problem 11.1

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shear strength in soils