Concrete Technology Workshop 2010 Lecture 2 - Strength of Concrete-Influencing Factors, Design Principles, Code Requirements - Dr. Hans Beushausen & Professor Mark Alexander

Strength of ConcreteInfluencing factors, design principles, code requirements

Dr. Hans Beushausen

Professor Mark Alexander

Concrete Technology for Structural EngineersMay 2010

Concrete Technology for Structural Engineers

Workshop, May 2010

Contents

� Definition of strength

� Factors affecting strength of concrete� Cement paste� Paste-aggregate bond

� Aggregates

� What does compressive strength in concrete mean?� Response of concrete to compressive stress

� Influence of Time & Temp. – the Maturity Concept

� Other types of concrete strength� Tensile and Flexural strength

� Practical and structural aspects: design and testing


Workshop, May 2010

Definition of Strength

� Depends on mode of stress

and definition of failure

� Different types of strength:

compressive, tensile, flexural,

shear, torsion

� In concrete design,

compressive strength is

usually of most concern.


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A concrete cylinder under a compression test


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Fundamental factors influencing compressive

strength

Strength = f [properties of various phases in concrete, interactions between them]

Thus, paste, aggregate, and interfaces (ITZ) are important

Also important are specimen type (cube, cyl.), size, and nature of loading

Chart on next slide shows the range of factors influencing strength of concrete


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Strength of cement paste

Primarily a function of paste porosity

Porosity:

Where

S = strength

S0 = intrinsic strength (i.e. at zero porosity)

p = fractional porosity

k depends on material

S

S0

= e-kp


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Porosity can be

expressed in

terms of:

(a) Gel/Space Ratio X

X = vol. of solid hydration products (incl. gel pores)

Space available for these hydration products


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Strength equation using X is:

σc = Axn (n = 2.6 – 3, depending on cement)

Powers and Brownyard:

σc = 235X3 (MPa) - implies cement paste has an intrinsic strength of

235 MPa

(This expression independent of w/c, age, etc.)


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(b) Water / cement ratio, i.e. essentially capillary porosity

Capillary porosity = f(w/c)proper compaction, any degree of hydration


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(b) Water / cement ratio (cont’d)

Abram’s w/c ratio law for σc:

A = empirical constant (14 000 p.s.i.)

B ≈ 4 (dep. on cement type)

Note: importance of full compaction – see next slide!

σc = A .

B1.5(w/c)


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Schematic of strength as a

function of compaction

Modern admixtures allow us to progress up this curve


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More correctly:

σc = f [w/c, A/c, aggregate characteristics (e.g. max.

size), etc.]

w/c: governs the pore system – size and distribution

Aggregates: influences paste-agg.

bond, heterogeneity of

microstructure, etc.

Concrete strength (cont’d)


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Concrete strength (cont’d)

Effect of pore size – e.g. pore refinement with CSF


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Effect of

cement fineness

(e.g. rapid

hardening type cements)

Concrete

strength (cont’d)


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Cement paste – aggregate bond

� Chemical bonding

It is probable that no aggregate is truly ‘inert’, i.e. all

aggregates interact chemically with cement paste to

some degree

� Physical bonding

This is mainly a function of micro and macro texture,

with micro-texture often being more important


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Cement paste – aggregate bond (cont’d)


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Cement paste – aggregate bond (cont’d)

E.g. well-known effect of andesite aggregates on concrete strength

Age

(d)

Percentage increase in strength

for w/c ratio

0.83 0.56 0.42

Cube Compressive

Strength

28 28% 23% 17%

Indirect Tensile

Strength

28 19% 24% 18%

Modulus of Rupture 35 16% 27% 9%

Strength premiums of andesite concrete over quartzite concrete (Alexander & Ballim, 1987)

Andesite surface

x2000

Quartzite surface

x2000


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Cement paste

– aggregate

bond

(Cont’d)

Effect of

ITZ - interfacial

transition zone


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Influence of aggregates

� Aggregate type


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Volume

fraction

of agg.


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Max.

Size of agg.


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What does compressive strength

in concrete mean?


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Nature of compressive testing

� Cube test

- Stresses in cubes

� Cube test

- Types of failures


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Nature of compressive testing (cont’d)

� Cube size


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Nature of compressive testing (cont’d)

� Cylinder

test


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Response of concrete to compressive stress

� Multi-phase

material –

implies strain

incompatibilities

and progressive micro-cracking


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Response of concrete to compressive stress (cont’d)

Progressive microstructural breakdown

Role of different types of cracking


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Deformations and matrix changes under short-term stress

application


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� Thus – concrete ‘fails’ under compressive

stress by a complex, system of internal

microcracking and microstructural breakdown

with extensive cracking:

� ‘bond’ cracking between aggregate and matrix

� ‘cleavage’ cracking in the matric itself.

� This cracking is largely tensile or shear/tensile in nature.

� As ultimate failure is approached, ‘cleavage’ cracking predominates leading to final rupture


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� Limits of response to stress: immediate vs. microstructural breakdown vs.

creep


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Influence of curing and temperature –

the Maturity Concept

(a) Effect of temperature


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Influence of curing and temperature – Maturity Concept (cont’d)

(b) Effect of moisture/relative humidity

(c) Period of curing


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Maturity = f [T x t] where T – curing temp.

t – curing time

Note inter-relationship between time and temperature!

Saul-Nurse Expression (datum = - 10oC)

Maturity = ∑t(T+10) t = time of curing (d)

T = temp. of curing (oC)

The Maturity Concept


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The Maturity Concept


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Other types of concrete strength

Tensile and flexural strength

Tensile/flexural strength are important in:

� Concrete pavements and slabs on grade

� Water retaining structures

� Crack-free concrete


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Tests for tensile strength

� Direct tensile strength – very difficult to do

successfully

Used for research mainly

� Indirect tensile

strength –

Split tensile test

(Brazilian test)

Good representation

of direct tensile

strength value.


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Tests for tensile strength

� Flexural strength

Gives significantly higher strength values than indirect test.

Reason is assumed

shape of stress

distribution at failure.


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Factors affecting tensile strength

� Similar to factors influencing compressive strength

� Aggregate effect more important:

� aggregate bond

� max size

� Influence of strain and stress gradients e.g. due to drying


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Relationship between tensile and compr. strength

Age of concrete (d) 3 7 28 90 360

Compressive

strength

Rel.

Values

0.4 0.65 1.0 1.1 1.35

Tensile strength 0.4 0.7 1.0 1.05 1.1


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Typical ratios:

� ft/fc = 0.07 – 0.11 (direct tension)

� fct/fc = 0.08 – 0.14 (splitting tension)

� fr/fc = 0.11 – 0.23 (flexural tension)

Code suggestions:

� CEB, direct tension: ft = 0.3(fc)2/3 (MPa)

� ACI, flexural tension: fr = 0.62(fc)1/2 (MPa)


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Compressive strength

Structural designPractical aspects

Specification

Quality control


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Strength consideration in structural design


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Strength consideration in structural design

= 0.67 fcu

Actual behaviour!

In design: use safety factor

(commonly 1.5)

Note differences between cube, cylinder and bending strength:


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Deformations and matrix changes under short-term stress application

Strain at fracture (in compression): εcu = 2 – 2.5 mm/m

σ/fc [%]

ε

100

70-90

30-40

Major crack development, ongoing crack

development independent of increase in stress

Design stress (strains assumed linear)

Increased micro cracking (ITZ), stress increasingly results in long-term deformations


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Deformations and matrix changes under short-term stress

application


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Definition, specification and testing


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� Design strength� 28-day strength

� Concrete cured at 23oC in water

� Cubes, 150 mm3 or 100 m3

� Tested in saturated condition

� Average of 3 results (details given in SANS)

� Target strength� Consideration of statistical variability

� Commonly: Target strength + ~8 MPa (details in SANS)

� In-situ strength� Difference between cube strength (ideal curing) and structure

� SANS: “If the average core strength is at least 80% of the specified strength, and if no single core strength is less than 70% of thespecified strength, the concrete shall be accepted”


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� Specify: design strength = 30 MPa (= cube strength)

� Strength used in analysis = 0.67 x 30 MPa / 1.5 = 13.3 MPa

� Target strength = 38 MPa

� Acceptable in-situ (core) strength

= 0.8 x 30 MPa = 24 MPa


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� SANS 5860: 2006 (Dimensions, tolerances, uses of cast test specimens)

� SANS 5861-2: 2006 (Sampling of freshly mixed concrete)

� SANS 5861-3: 2006 (Making and curing of specimens)


Testing (cube)


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Stress path in a concrete cube under compression

ε

→ Tensile failure under compressive loading


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Stress path in a concrete column under high compressive loads


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In-situ testing of concrete strength


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In-situ testing (estimation) of concrete strength

Surface hardness testing – Rebound Hammer

� 1940 developed in Switzerland by Ernst Schmidt (“Schmidt Hammer”)

� Covered in BS 1881, ASTM standards, etc

� Empirical measure of surface hardness of a localized area


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Rebound Hammer

� Used to:

� Assess uniformity of concrete

� Determine areas of poor quality or deteriorated

concrete

� Estimate compressive strength

� Assess variation of strength within a structure


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Rebound Hammer

� Statistical reliability

� e.g.: ASTM: 12 readings per

area 300x300 mm, regular spaced grid

� Calibration against core

strength

� Influences:

� Carbonated surface area: region of greater hardness

� Moisture condition

� Formwork used

� Inclination of hammer during testing

� Properties of aggregates, etc


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Testing and conformity assessment of cores


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� SANS 5865: 2006 (Drilling, preparation and testing of

compr. strength of cores taken from hardened

concrete)

� Void ratio

� Reinforcement factor

� Equation for conversion

� Equivalent cube strength


Testing and conformity assessment of cores


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� Smooth and level

Compressive strength of concrete cores

End preparation


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� Strength decreases (significantly) with

increasing porosity


Void ratio


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� Account for voids

� → Who is to blame for low in-situ strength?


Void ratio


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Void ratio

?


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Void ratio


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� Steel reinforcement results in stress

concentrations, which lowers the

measured failure load


Steel reinforcement


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Account for steel reinforcement – SABS 865: 1994


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Convert core strength to equivalent cube strength

� The more slender the specimen, the lower the failure load

� → Aim at equal length-to-diameter ratio


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Convert core strength to equivalent cube strength


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Core strength summary: example

� Design strength = 30 MPa

� Measured failure stress = 21 MPa

� Correction factor for [length/diameter = 0.8]: 0.91

� Correction factor for rebar: 1.04

� Measured equivalent cube strength = 21 MPa x 0.91 x 1.04 = 19.9 MPa

� Who is to blame?

� Estimated voidage = 1.5%, void correction factor = 1.13

� Estimated ‘intrinsic potential strength’ = 19.9 x 1.13 = 22.5 MPa

� Acceptance criteria: 80% of design strength = 0.8 x 30 = 24 MPa

� What now?


Workshop, May 2010

Thank you

Documents

Concrete Technology Workshop 2010 Lecture 2 - Strength of Concrete-Influencing Factors, Design Principles, Code Requirements - Dr. Hans Beushausen & Professor Mark Alexander