Hardened Concrete

Strength

Water-to-Cement Ratio

According to Abrams (1918)

fc=k1/(k2w/c)

Where k1 and k2 are

empirically derived

constants

When w/c

Cement Type

Cement

Fineness

• Max size ~50µm diam.

• 10-15% particles

Air Entrainment

Rule of thumb:

Every 1% increase in air content, reduces fc by 5%

However, in very lean mixes, some air entrainment can

improve strength.

Strength, MPa

Air Entrainment

• Strength is

typically higher at

higher cement

content (richer

mixes)

• Effect of air

entrainment is

greater in richer

mixes

Strength, MPa

Aggregate

• Aggregate strength not commonly a factor

• Size

• Gradation

• Shape

• Surface texture

• Mineralogy

MSA

Moist curing period (days)

MSA

Two competing effects:

• Larger MSA, less water

for a given workability

• Larger ITZ with larger

MSA aggregate, with

more pronounced effect

at lower w/c

Gradation

• Relative amounts of

coarse and fine

aggregate influence

tendency toward

bleeding and

segregation.

• For a lower fine

aggregate content,

slump may decrease,

but so also might fc

Texture

• Rougher texture,

better physical

bond with paste

• Small advantage

may be lost by

increased water

necessary to

maintain

workability

Admixtures

• Accelerators and retarders affect the rate of strength

gain

• Ultimate strength is not really affected

• Some research has shown that retarders can

improve later strength

SCMs

• Effect on strength varies with type, dosage, and

characteristics of SCM and mix

• Generally, reduced rate of strength gain

• Generally, improved later strength

• Greater relative effect on tensile strength

Curing

Curing - procedures to promote the hydration of cement

over time (time, temperature, humidity)

• Concrete moist cured

is up to 3x stronger

than concrete air cured

• 7 day moist cure is

recommended

Curing

• Concrete placed and

cured at varying

temperatures

• The higher the

temperature, the

higher the initial

strength

• Effect diminished

over time

Curing

• Concrete cast

at varying

temperatures;

cured at 70F

• Concretes

cast at lower

temperatures

achieve higher

strength

Testing Conditions

• ASTM C39 for compression test

• Specimen size – U.S. standard is 6”x12” cylinder with h/d = 2

• the larger the diameter the lower the measured strength

Testing Conditions

• With a greater h/d, fc seems lower

• With lower h/d, fc seems higher

• for h/d =1, fc seems 10-15% higher than for the same

mixtures tested with 6x12 cylinders.

Testing Conditions

• Cylinders should be moist at time of testing

- air dry samples show 20-25% higher fc

• Loading rate should be 20-50psi/sec so that samples

fail within 2-3 minutes

- faster load rate yields higher fc

- load at 1000 psi/sec, fc seems 12% higher

- load at 1 psi/sec, fc seems 12% lower

Uniaxial Compression

• Linear elastic behavior in

concrete to ~ 0.30fc

• Gradual increase in curvature

up to 0.75 to 0.90 fc, then

flattens, and decreases

• At 0.30-0.50 fc some

extension or growth of pre-

existing cracks in TZ (stable

crack growth)

Uniaxial CompressionAt 0.50-0.75 fc,

further crack

growth in ITZ,

with some

instability

Splitting Tension

• Splitting tension test

introduces some

compressive stress

at top and bottom of

(6x12”) cylinder

• Measured strength

is 10-15% higher

than nominal

strength

ft = 2P/πLD

Third Point Bending

• 6x6x20” beam is loaded at a rate of 125-

175 psi/min.

• MOR = PL/bd2

L= span length

P= max load sustained

b = width

d=depth

• Tends to overestimate tensile capacity

by 50-100% because a linear

relationship between stress and strain is

assumed through the section

Schmitt Rebound Hardness

• ASTM C805

• Very simple

• Measures rebound of a hardened

steel hammer impacted on the

concrete surface by a spring

• Amount of rebound is related to

strength

• +/- 25% accuracy

• Very sensitive to smoothness,

moisture content, carbonation,

presence of agg at surface

• Good for comparison, not

absolute measurements

Penetration Resistance

• Windsor Probe ASTM C803

• A powder-actuated gun drives a hardened alloy probe (needle)

into the concrete.

• The exposed length of the probe is measured and related by a

calibration table to the compressive strength of the concrete

• Useful for measuring time to strip forms

Penetration Resistance

• Less affected by surface

texture and carbonation

• Affected by mix design and

aggregate hardness

• Must be calibrated

Pullout Test

• ASTM C900

• Steel insert with an enlarged

end is embedded

• Insert is either completely pulled

out or is pulled until a desired

resistance is measured

• Pullout strength (force) ~ 20% fc

• Approximates shear strength

• Can be installed during or after

casting

• Requires patching

Pullout Test

Maturity Method

• Not really at test, more of a concept

• Way to estimate the strength of a concrete, knowing

the curing time (t) and curing temperature (T)

• ASTM C1072 (calculating maturity) and C918

(estimating strength)

Maturity Method

M(t) = Σ(Ta-To)∆t Nurse-Saul equation

M(t) = maturity at some age, t

∆t = time interval, days or hours

Ta = average concrete temperature

during each time interval

To = datum temperature, below which

concrete will show no increase in

strength with time (32 and 14oF are

common)

• Correlate M(t) to fc

Maturity Method

• Effect of RH is neglected

• Large variations in temperature, which may greatly

affect fc and rate of hardening, are neglected

• Accelerated curing may affect accuracy

• Some uncertainty in knowing datum temperature;

testing often required