Hardened concrete

1. Unit no.3
Hardened Concrete
Mr. Kiran R. Patil
Assistant Professor,
Department of Civil Engineering,
D. Y. Patil College of Engineering & Technology, Kolhapur

2.  Strength of concrete:
• The compressive strength of concrete is one of the most important and useful properties of
concrete. In most structural applications concrete is employed primarily to resist
compressive stresses.
• In those cases where strength in tension or in shear is of primary importance, the
compressive strength is frequently used as a measure of these properties. Therefore, the
concrete making properties of various ingredients of mix are usually measured in terms of
the compressive strength.
• Compressive strength is also used as a qualitative measure for other properties of hardened
concrete. No exact quantitative relationship between compressive strength and flexural
strength, tensile strength, modulus of elasticity, wear resistance, fire resistance, or
permeability have been established nor are they likely to be.
• The compressive strength of concrete is generally determined by testing cubes or cylinders
made in laboratory or field or cores drilled from hardened concrete at site or from the non-
destructive testing of the specimen or actual structures.
• Strength of concrete is its resistance to rupture. It may be measured in a number of ways,
such as, strength in compression, in tension, in shear or in flexure. When concrete fails
under a compressive load the failure is essentially a mixture of crushing and shear failure.
• It can be assumed that the concrete in resisting failure, generates both cohesion and
internal friction. The cohesion and internal friction developed by concrete in resisting
failure is related to more or less a single parameter i.e., w/c ratio.

3. • Factors affecting the compressive strength of concrete are,
1. Water-cement ratio
2. Gel/ space ratio
3. Age of concrete
4. Aggregate-cement ratio
5. Maximum size of aggregate
• In the above it can be further inferred that water/cement ratio primarily affects the strength,
whereas other factors indirectly affect the strength of concrete by affecting the water/
cement ratio.
 Water Cement ratio:
• Strength of concrete primarily depends upon the strength of cement paste. It has been
shown that the strength of cement paste depends upon the reduction of paste or in other
words, the strength of paste increases with cement content and decreases with air and water
content.
• In 1918 Abrams presented his classic law in the form
𝑆 =
𝐴
𝐵𝑥
Where, x = water/cement ratio by volume and for 28 days results the constants A and B are
14,000 psi and 7 respectively.
• Abrams water/cement ratio law states that the strength of concrete is only dependent upon
water/cement ratio provided the mix is workable.

4. • In 1897, Feret formulated a general rule defining the strength of the concrete paste and
concrete in terms of volume fractions of the constituents by the equation,
𝑆 = 𝐾
𝑐
𝑐 + 𝑒 + 𝑎
2
Where, S = strength of concrete
c, e and a = volume of cement, water and air respectively
K = a constant

5. • In this expression the volume of air is also included because it is not only the water/
cement ratio but also the degree of compaction, which indirectly means the volume of air
filled voids in the concrete is taken into account in estimating the strength of concrete.
• The relation between the water/cement ratio and strength of concrete is shown in above
Fig. It can be seen that lower water/cement ratio could be used when the concrete is
vibrated to achieve higher strength, whereas comparatively higher water/cement ratio is
required when concrete is hand compacted.
• In both cases when the water/cement ratio is below the practical limit the strength of the
concrete falls rapidly due to introduction of air voids.
• The graph showing the relationship between the strength and water/cement ratio is
approximately hyperbolic in shape.
 Gel space ratio:
• The strength of concrete not only depends on water cement ratio. The strength at any
water/cement ratio depends on the degree of hydration of cement and its chemical and
physical properties, the temperature at which the hydration takes place, the air content in
case of air entrained concrete, the change in the effective water/cement ratio and the
formation of fissures and cracks due to bleeding or shrinkage.
• Instead of relating the strength to water/cement ratio, the strength can be more correctly
related to the solid products of hydration of cement to the space available for formation of
this product.
• It is the ratio of the volume of the hydrated cement paste to the sum of volumes of the
hydrated cement and the capillary pores.

6. • It is pointed out that the relationship between the strength and water/cement ratio will hold
good primarily for 28 days strength for fully compacted concrete, whereas, the
relationship between the strength and gel/space ratio is independent of age.
• Gel/space ratio is a better approach than Abram’s law. As it considers following factors
which are also responsible for strength of concrete,
1. Degree of hydration of cement
2. Volume of hydrated cement gel
3. Volume of capillary pores
Gel/ space ratio = 𝑥 =
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑔𝑒𝑙
𝑠𝑝𝑎𝑐𝑒 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒

7.  Gain of Strength with Age:
• The concrete develops strength with continued hydration. The rate of gain of strength is
faster to start with and the rate gets reduced with age. It is normal to assume the 28 days
strength as the full strength of concrete. Actually concrete develops strength beyond 28
days also.
• Earlier codes have not been permitting to consider this increase of strength beyond 28
days for design purposes. The increase in strength beyond 28 days used to get apply with
the factor of safety.
• With better understanding of the material, advanced designers have been trying to reduce
the factor of safety and make the structure more economical. In this direction, the increase
in strength beyond 28 days is taken into consideration in design of structures.
• The quantum of increase in strength depends upon the grade and type of cement, curing
and environmental conditions etc.
• The strength of concrete is generally estimated at 28 days by crushing field test cubes or
cylinders made from the representative concrete used for the structure.
• It is then rather too late for remedial measures, if the result of the test cube at 28 days is
too low. On the other hand, the structure will be uneconomical if the result of the test cube
is too high. It is, therefore, of tremendous advantage to be able to predict 28 days strength
within a few hours of casting the concrete so that we have a good idea about the strength
of concrete, so that satisfactory remedial measures could be taken immediately before it is
too late.

8. Age Strength
1 day 16 %
3 days 40 %
7 days 67 %
28 days 100 %
3 months 115 %
6 months 120 %
1 year 125 %

9.  Maturity Concept of Concrete
• Increase in the strength of concrete does not depend only on curing period. It also depends on the
temperature at which curing is done.
• Maturity of concrete is expressed as a summation of the product of temperature and time of curing.
Maturity is measured in ºC days or ºC hours.
• Maturity = 𝑡𝑖𝑚𝑒 𝑥 𝑐𝑢𝑟𝑖𝑛𝑔
• M = 𝑇. ∆𝑡
• Where, ∆𝑡 is the time interval (in hours or days) during which the temperature is 𝑇.
• T is the temperature measured from a datum of -11ºC which is the temperature below which strength
development stops.
• In standard calculations the maturity of fully cured concrete is taken as 19800 ºC hours. By knowing
this value, we can calculate the percentage strength of identical concrete at any other maturity by
using the following equation given by Plowman,
• Strength at any maturity as a percentage of strength at maturity of 19800 ºCh
= 𝐴 + 𝐵 log10
𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦
103
• The values coefficients A and B depends on the strength level of concrete.
Strength after 28 days at 18ºC
( Maturity of 19800 ºCh) MPa
Coefficient
A B
Less than 17.5 10 68
17.5 – 35 21 61
35 – 52.5 32 54
52.5 – 70 42 46.5

10.  Effect of Maximum size of Aggregate on Strength
• At one time it was thought that the use of larger size aggregate leads to higher strength.
This was due to the fact that the larger the aggregate the lower is the total surface area and,
therefore, the lower is the requirement of water for the given workability. For this reason,
a lower water/cement ratio can be used which will result in higher strength.
• However, later it was found that the use of larger size aggregate did not contribute to
higher strength as expected from the theoretical considerations due to the following
reasons.
1. The larger maximum size aggregate gives lower surface area for developments of gel
bonds which is responsible for the lower strength of the concrete.
2. Bigger aggregate size causes a more heterogeneity in the concrete which will prevent the
uniform distribution of load when stressed.
3. When large size aggregate is used, due to internal bleeding, the transition zone will
become much weaker due to the development of micro cracks which result in lower
compressive strength.
• Generally, high strength concrete or rich concrete is adversely affected by the use of large
size aggregate. But in lean mixes or weaker concrete the influence of size of the aggregate
gets reduced.
• In lean mixes larger aggregate gives highest strength while in rich mixes it is the smaller
aggregate which yields higher strength.

11.  Effect of storage of cement
• Cement bags stored in godowns gradually deteriorates due to hydration. The loss in
strength for different periods of storage is,
At 3 months – 20 %
At 6 months – 30 %
At 1 year – 40 %
 Effect of aggregate/ cement ratio
• Compressive strength goes on decreasing as the aggregate / cement ratio increases.
 Effect of slump variation
• A variation in slump by 25 mm will be caused by a 3 % change in water content and this
would affect the concrete strength by 2 N/mm².
 Effect of compaction
• 1 % voids in concrete would reduce the strength of concrete by 5 %.
• 5 % voids in concrete would reduce the strength of concrete by 30 %.
• 10 % voids in concrete would reduce the strength of concrete by 50 %.

12.  Relation between Compressive Strength and Tensile Strength
• Usually, the compressive strength of concrete is considered in reinforced concrete works.
Tensile strength is not given much importance. However, the design of concrete pavement
slabs is based on the flexural strength of concrete.
• It has been found the type of coarse aggregate influences this relationship. Crushed
aggregate gives higher flexural strength than compressive strength.
• The Central Road Research Institute (CRRI) has established the following statistical
relationships between compressive strength and tensile strength of concrete,
(i) 𝑦 = 15.3 𝑥 − 9 for 20 mm maximum size aggregate.
(ii) 𝑦 = 14.1 𝑥 − 10.4 for 20 mm maximum size natural gravel.
(iii) 𝑦 = 9.9 𝑥 − 0.55 for 40 mm maximum size crushed aggregate.
(iv) 𝑦 = 9.8 𝑥 − 2.52 for 40 mm maximum size natural gravel
Where,
• y is the compressive strength of concrete in N/mm2 and
• x is the flexural strength of concrete in N/mm2
• The general relationship established by the CRRI is,
• 𝑦 = 11 𝑥 − 3.4
• IS: 456 – 2000 gives the following relationship between compressive strength and flexural
strength of concrete,
• 𝐹𝑙𝑒𝑥𝑢𝑟𝑎𝑙 𝑠𝑡𝑟𝑒𝑛𝑔𝑡𝑕 = 0.7 𝑓𝑐𝑘
• Where, fck is the characteristic compressive strength of concrete in N/mm2.

13. • Elastic Properties of Concrete
1. Stress and strain characteristics of concrete
• A typical stress and strain curve of concrete is shown above. The relation is linear in the
initial stages but becomes nonlinear reaching a maximum value and then a descending
portion is obtained before concrete finally fails.
2 Deformation of hardened concrete under load
• In the R.C.C. theory, it is assumed that concrete is elastic and conforms to Hook’s law.
Actually this is not exactly true and concrete is not a perfectly elastic material. Concrete
deforms when load is applied but this deformation does not follow any simple rule. The
response of concrete to applied load is quite complex.

15.  Modulus of Elasticity
• The modulus of elasticity is determined by subjecting a cube or cylinder specimen to
uniaxial compression and measuring the deformation by means of dial gauges fixed
between certain gauge lengths. Dial gauge reading divided by cross-sectional area will
give stress. A series of readings are taken and the stress-strain relationship is established.
• By considering the complex behaviour of stress-strain relationship, the modulus of
elasticity of concrete is defined in some different manner.
• The Young’s modulus of elasticity can strictly be applied only to the straight part of the
curve. In the case of concrete, since no part of the graph is straight, the modulus of
elasticity is found out with reference to the tangent drawn to the curve at the origin. The
modulus found from this tangent is called initial tangent modulus.
• The tangent can also be drawn at any other point on the stress-strain curve. The modulus
of elasticity calculated with reference to this tangent is called tangent modulus.
• A line can also be drawn connecting a specified point on the stress-strain curve to the
origin of the curve. If the modulus of elasticity is calculated with reference to the slope of
this line, the modulus of elasticity is called secant modulus.

16.  Relation between modulus of elasticity and compressive strength
• Stronger the concrete, higher is the modulus of elasticity. For stronger concrete, strain will
be less for given load. Due to this lower strain, the modulus of elasticity will be higher.
Modulus of elasticity of concrete increases approximately with the square root of the
compressive strength.
Ec ∝ 𝑓𝑐𝑘
 Shrinkage
• Shrinkage is a volumetric reduction of concrete even in the absence of load. This
volumetric contraction may be due to temperature variations, moisture content variations,
alkali-aggregate reaction and due to applied loads.
1. Plastic shrinkage
• When the cement paste is plastic, it undergoes a volumetric contraction whose magnitude
is about 1 % of the volume of dry cement. This shrinkage is called plastic shrinkage
because it takes place while the concrete is still in the plastic state. Plastic shrinkage is
caused by the loss of water by evaporation from the surface of the concrete or by suction
by dry concrete below. The contraction induces tensile stress in the surface layers and
since the concrete is very weak in its plastic state, plastic cracking at the surface can
occur.
• Plastic shrinkage can be prevented by avoiding the rapid loss of water from surface. This
can be done by covering the surface with polyethylene sheets immediately on finishing
operation or by working at night.
• Plastic shrinkage cracks can be removed by revibrating the concrete in a controlled
manner.

17. Plastic Shrinkage Cracks
2 Drying Shrinkage
The shrinkage that takes place after the concrete has set and hardened is called drying
shrinkage. Withdrawal of water from concrete stored in dry air causes drying shrinkage.
Drying shrinkage is an everlasting process, when concrete is subjected to drying conditions.

18. 3 Carbonation Shrinkage
 The carbon dioxide present in atmosphere reacts in presence of moisture with hydrated
cement minerals. This reaction is called carbonation. This reaction forms carbonic acid
which reacts with Ca(OH)2 to give CaCO3. As a result of carbonation process, the
concrete gets contracted and this contraction is called carbonation shrinkage. The
carbonation shrinkage occurs mainly in intermediate humidity. Carbonation also results in
increased strength and reduced permeability.
 Factors affecting shrinkage:
1. W/C ratio: Shrinkage goes on increasing as the W/C ratio increases.
2. Cement content: The shrinkage increases with the cement content.
3. Humidity: The shrinkage increases with the decrease in humidity.
4. Type of aggregate: The aggregate having low modulus of elasticity cause large
shrinkage.
5. Type of cement: More fine cements (e.g. 53 Grade O.P.C.) shrink more.

19.  Creep of concrete:
• Creep is defined as the increase in strain under continuous load. When a concrete member
is loaded, the member deforms to a certain amount as soon as the load is applied. The
deformation of the member increases with time, even when the load is kept constant. This
phenomenon of increase in the deformation of concrete under a constant load is called
creep of concrete.
• Creep is also called plastic flow or plastic deformation. The deformation which occurs
immediately after the application of load is called instantaneous deformation. The
deformation beyond instantaneous strain is creep. Creep is function of time. The rate of
creep decreases with time and the creep attained at a period of 5 years is taken as terminal
value. About 75 % creep occur in twelve months.
• When the load on the specimen is removed, the instantaneous strain decreases
immediately. This instantaneous recovery is followed by a gradual decrease in the strength
called creep recovery.

20. • The creep may be due to viscous flow of cement paste and closure of internal voids but the
major portion is caused by seepage of colloidal water from the gel that is formed by
hydration of cement.
• Creep occurs both in compressive and tensile loading and it is assumed that the magnitude
of the creep is same in both the cases.
• Effect of creep:
1. Creep of concrete increases the deflection of R.C.C. beams.
2. In eccentrically loaded and slender columns creep increases the deflection and can cause
buckling.
3. In tall buildings differential creep between inner and outer columns may cause movement
and cracking of partitions.
• Factors affecting creep:
1. Aggregate: uniformly graded aggregate reduces creep.
2. W/C ratio: lean mixes show more creep than rich mixes.
3. Type of cement: blast furnace slag cement causes higher creep than O.P.C.
4. Humidity: lower the humidity higher will be the creep.
5. Size of member: the magnitude of creep decreases with increase in size of the member.

21.  Tests on Hardened Concrete
1 Compressive strength
• The compressive strength of concrete is most important property. The compressive
strength is generally determined by,
• Testing cubes (150 X 150 X 150mm) made in laboratory or field
• Testing cylinders (150mm dia. And 300mm long) made in laboratory or field
• Core drilled from hardened concrete at site
• Non-destructive testing (N.D.T.) on in-situ concrete.
• Generally, cubes of size 150 X 150 X 150mm are filled with the prepared concrete in the
lab or at site are used to determine compressive strength of the concrete. The cubes are
tested in a compression testing machine at 7 days and 28 days.
Compressive strength of concrete =
𝐋𝐨𝐚𝐝 𝐚𝐭 𝐟𝐚𝐢𝐥𝐮𝐫𝐞 (𝐍)
𝑪𝒓𝒐𝒔𝒔−𝐬𝐞𝐜𝐭𝐢𝐨𝐧𝐚𝐥 𝐚𝐫𝐞𝐚 𝐨𝐟 𝐜𝐮𝐛𝐞 (𝒎𝒎𝟐)

22. Grade of
concrete
Minimum
Compressive
strength @ 7 days
( N/mm2 )
Minimum
Compressive strength
@ 28 days
( N/mm2 )
M10 7.0 10
M15 10.0 15
M20 13.5 20
M25 17.0 25
M30 20.0 30
M35 23.5 35
M40 27.0 40
• Comparison between Cube and Cylinder strength
The strength of the cylinder is taken as 0.8 times the strength of the cube.
• https://youtu.be/QZSYS932_Lo

23. 2 Flexural Strength/ Modulus of Rupture
• It is difficult to find the tensile strength of concrete by conducting a direct tension test.
Therefore, it is computed by flexure testing. The flexural tensile strength at failure or the
modulus of rupture is thus determined and used when necessary. Its knowledge is useful in
the design of pavement slabs and airfield runways as flexural tension is critical in these
cases.
• The modulus of rupture is determined by testing standard test specimens of 150 X 150 X
700 over a span of 600 mm or 100 X 100 X 500 over a span of 400 mm, under
symmetrical loading.
• https://youtu.be/wI5hFajlrrM
Modulus of rupture, fb =
PL
bd2 N/mm²
Where,
b = width of specimen in mm
d = depth of specimen in mm
P = load at failure in N
L = length of specimen in mm
3. Relation between Compressive and Tensile strength of concrete
According to the IS 456:2000, Flexural strength = 0.7 𝑓𝑐𝑘
Where 𝑓𝑐𝑘 is the characteristic compressive strength of concrete in N/mm²

24. 4 Tensile Strength
• Tensile strength of concrete can also be determined by conducting splitting tensile strength
test (split cylinder test).
• The test consists of applying compressive load on the concrete cylinder placed
horizontally between the platens as shown in the figure. The magnitude of the tensile
stress is given by
2𝑃
𝜋𝐷𝐿
.
https://youtu.be/C5h9nfufG9Y

25.  Non Destructive Testing (N.D.T.) of Concrete
• The tests conducted on cube, cylinder or beam specimens to determine compressive
strength are classified as destructive tests because the specimens are destroyed during
testing.
• In non-destructive testing, the tests are performed directly on the in-situ concrete without
the removal of sample. These tests do not affect the proposed performance of the member
being tested.
• Various N.D.T.s are,
1. Rebound hammer test
2. Ultrasonic pulse velocity (U.P.V.) test
1. Rebound Hammer Test/ Schmidt Hammer Test
• This is the most common method adopted for checking strength of in-situ concrete. This
test is based on the principle that the rebound of an elastic mass depends on the hardness
of the surface against which the mass strikes.

26. 5Relationship between Rebound Number and
Compressive Strength
Relationship between Rebound Number and Compressive Strength

27. • In rebound hammer, a spring loaded mass has a fixed amount of energy imparted to it by
pressing the hammer on the surface. On release, the mass rebounds back from the plunger
and the distance travelled by the mass as a percentage is defined as Rebound Number or
Rebound Value. The graph provided with the hammer gives the compressive strength
corresponding to the Rebound Value.
• Limitations:
• The test is sensitive to local variations in concrete e.g. if the plunger strikes the aggregate
underneath, then it would indicate very high rebound value. If it strikes a void, it would
indicate very low rebound value. Thus, it is desirable to take at least 12 readings at each
test location and to determine their average.
• https://youtu.be/83AcFYK-Eno
• https://youtu.be/-MbVlyyRl0Y

28. 2. Ultrasonic Pulse Velocity (U.P.V.) Test
• In this test, ultrasonic pulses are transmitted through the concrete. The pulses are generated
by electronic transducers. The time of travel between initial onset and the reception of the
pulse is measured electronically. The path length between the transducers divided by the
time of travel gives the average velocity of wave propagation.
• Under certain specified conditions the velocity and strength of concrete are directly related.
The common factor is the density of concrete. A change in the density results in a change in
the pulse velocity. Higher the density of concrete, higher will be the pulse velocity.

29. • The quality of concrete can be easily be graded as defined in IS: 13311 (Part-I) – 1992
Different UPV Test Methods
Pulse Velocity km/sec Concrete Quality
Above 4.5 Excellent
3.5 to 4.5 Good
3.0 to 3.5 Medium
Below 3.0 Doubtful

30. • The U.P.V. method is used to find,
1. The homogeneity of the concrete.
2. The presence of cracks and voids.
3. Quality/ strength of the concrete.
4. Assessment of concrete damage due to fire, mechanical or chemical actions.
5. Measurement of layer thickness.
• On the display of the machine, the compressive strength will be displayed only when the
velocity is in between 3900 m/s and 4450 m/s at R = 30.
• https://youtu.be/M9hkvS_OLmk
• https://youtu.be/sTkZBc9mYzo