Strength of Concrete Influencing factors, design principles, code requirements Dr. Hans Beushausen Professor Mark Alexander Concrete Technology for Structural Engineers May 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 Concrete Technology for Structural Engineers 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. Concrete Technology for Structural Engineers Workshop, May 2010 A concrete cylinder under a compression test Concrete Technology for Structural Engineers Workshop, May 2010 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 Concrete Technology for Structural Engineers Workshop, May 2010 Concrete Technology for Structural Engineers Workshop, May 2010 Strength of cement paste Primarily a function of paste porosity Porosity: Where S = strength S 0 = intrinsic strength (i.e. at zero porosity) p = fractional porosity k depends on material S S 0 = e -kp Concrete Technology for Structural Engineers Workshop, May 2010 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 Concrete Technology for Structural Engineers Workshop, May 2010 Strength equation using X is: σc = Ax n (n = 2.6 – 3, depending on cement) Powers and Brownyard: σc = 235X 3 (MPa) - implies cement paste has an intrinsic strength of 235 MPa (This expression independent of w/c, age, etc.)
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
Concrete Technology for Structural Engineers
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.
Concrete Technology for Structural Engineers
Workshop, May 2010
A concrete cylinder under a compression test
Concrete Technology for Structural Engineers
Workshop, May 2010
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
Concrete Technology for Structural Engineers
Workshop, May 2010
Concrete Technology for Structural Engineers
Workshop, May 2010
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
Concrete Technology for Structural Engineers
Workshop, May 2010
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
Concrete Technology for Structural Engineers
Workshop, May 2010
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.)
Concrete Technology for Structural Engineers
Workshop, May 2010
(b) Water / cement ratio, i.e. essentially capillary porosity
Capillary porosity = f(w/c)proper compaction, any degree of hydration
Concrete Technology for Structural Engineers
Workshop, May 2010
(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)
Concrete Technology for Structural Engineers
Workshop, May 2010
Schematic of strength as a
function of compaction
Modern admixtures allow us to progress up this curve
Concrete Technology for Structural Engineers
Workshop, May 2010
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)
Concrete Technology for Structural Engineers
Workshop, May 2010
Concrete strength (cont’d)
Effect of pore size – e.g. pore refinement with CSF
Concrete Technology for Structural Engineers
Workshop, May 2010
Effect of
cement fineness
(e.g. rapid
hardening type cements)
Concrete
strength (cont’d)
Concrete Technology for Structural Engineers
Workshop, May 2010
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
Concrete Technology for Structural Engineers
Workshop, May 2010
Cement paste – aggregate bond (cont’d)
Concrete Technology for Structural Engineers
Workshop, May 2010
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
Concrete Technology for Structural Engineers
Workshop, May 2010
Cement paste
– aggregate
bond
(Cont’d)
Effect of
ITZ - interfacial
transition zone
Concrete Technology for Structural Engineers
Workshop, May 2010
Influence of aggregates
� Aggregate type
Concrete Technology for Structural Engineers
Workshop, May 2010IAggregates (cont’d)
Volume
fraction
of agg.
Concrete Technology for Structural Engineers
Workshop, May 2010IAggregates (cont’d)
Max.
Size of agg.
Concrete Technology for Structural Engineers
Workshop, May 2010
What does compressive strength
in concrete mean?
Concrete Technology for Structural Engineers
Workshop, May 2010
Nature of compressive testing
� Cube test
- Stresses in cubes
� Cube test
- Types of failures
Concrete Technology for Structural Engineers
Workshop, May 2010
Nature of compressive testing (cont’d)
� Cube size
Concrete Technology for Structural Engineers
Workshop, May 2010
Nature of compressive testing (cont’d)
� Cylinder
test
Concrete Technology for Structural Engineers
Workshop, May 2010
Response of concrete to compressive stress
� Multi-phase
material –
implies strain
incompatibilities
and progressive micro-cracking
Concrete Technology for Structural Engineers
Workshop, May 2010
Response of concrete to compressive stress (cont’d)
Progressive microstructural breakdown
Role of different types of cracking
Concrete Technology for Structural Engineers
Workshop, May 2010
Response of concrete to compressive stress (cont’d)
Deformations and matrix changes under short-term stress
application
Concrete Technology for Structural Engineers
Workshop, May 2010
Response of concrete to compressive stress (cont’d)
� 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
Concrete Technology for Structural Engineers
Workshop, May 2010
Response of concrete to compressive stress (cont’d)
� Limits of response to stress: immediate vs. microstructural breakdown vs.
creep
Concrete Technology for Structural Engineers
Workshop, May 2010
Influence of curing and temperature –
the Maturity Concept
(a) Effect of temperature
Concrete Technology for Structural Engineers
Workshop, May 2010
Influence of curing and temperature – Maturity Concept (cont’d)
(b) Effect of moisture/relative humidity
(c) Period of curing
Concrete Technology for Structural Engineers
Workshop, May 2010
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
Concrete Technology for Structural Engineers
Workshop, May 2010
The Maturity Concept
Concrete Technology for Structural Engineers
Workshop, May 2010
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
Concrete Technology for Structural Engineers
Workshop, May 2010
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.
Concrete Technology for Structural Engineers
Workshop, May 2010
Tests for tensile strength
� Flexural strength
Gives significantly higher strength values than indirect test.
Reason is assumed
shape of stress
distribution at failure.
Concrete Technology for Structural Engineers
Workshop, May 2010
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
Concrete Technology for Structural Engineers
Workshop, May 2010
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
Concrete Technology for Structural Engineers
Workshop, May 2010
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)
Concrete Technology for Structural Engineers
Workshop, May 2010
Compressive strength
Structural designPractical aspects
Specification
Quality control
Concrete Technology for Structural Engineers
Workshop, May 2010
Strength consideration in structural design
Concrete Technology for Structural Engineers
Workshop, May 2010
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:
Concrete Technology for Structural Engineers
Workshop, May 2010
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
Concrete Technology for Structural Engineers
Workshop, May 2010
Deformations and matrix changes under short-term stress
application
Concrete Technology for Structural Engineers
Workshop, May 2010
Compressive strength
Definition, specification and testing
Concrete Technology for Structural Engineers
Workshop, May 2010
Compressive strength
Definition, specification and testing
� 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”