1. Strength of Concrete

2. DEFINITION
The strength of a material is defined as the ability to resist stress without failure. Failure is sometimes identified with the appearance of cracks. However, it should be noted that unlike most structural materials, concrete contains fine cracks even before it is subjected to external stresses.
In concrete, therefore, strength is related to the stress required to cause fracture and is synonymous with the degree of failure at which the applied stress reaches its maximum value.
In tension tests fracture of the test piece usually signifies failure; in compression the test piece is considered to have failed when no sign of external fracture is visible, yet internal cracking is so advanced that the specimen is unable to carry a higher load without fracture.

3. SIGNIFICANCE
In concrete design and quality control, strength is the property generally specified. This is because, compared to most other properties, testing of strength is relatively easy.
Furthermore, many properties of concrete, such as elastic modulus, watertightness or impermeability, and resistance to weathering agents including aggressive waters, are directly related to strength and can therefore be deduced from the strength data.

4. Strength Classification of Concrete
Low-strength concrete
<20 MPa compressive strength
Moderate-strength concrete
20~40 MPa compressive strength
High-strength concrete
40~200 MPa compressive strength
Ultra high-strength concrete
>200 MPa compressive strength

5. STRENGTH-POROSITY RELATIONSHIP
In general, there exists a fundamental inverse relationship between porosity and strength of solids which, for simple homogeneous materials, can be described by the expression
S = So exp (-kp)
Where So is the strength at zero porosity, p is the porosity and k is a constant.
For many materials the ration S/S0 plotted against porosity follows the same curve.
S = strength of the material which has a given porosity

6. Effect of Porosity Normally cured cements, autoclaved
cements and aggregates
Iron, plaster of paris, sintered alumina,
zirconia

7. Power’s model
Powers found that the 28-day compressive strength fc of three different mortar mixtures was related to the gel/space ratio, or the ratio between the solid hydration products in the system and the total space:
fc=ax3
where (a) is the intrinsic strength of the material at zero porosity (p) and (x) the solid/space ratio or the amount of solid fraction in the system, which is therefore equal to (1 − p).
S = So(1- p)3
Experimentally Power’s found the value of a to be 234 MPa

8. Portland cement mortars with different mix proportions
Power’s model
Portland cement mortars with different mix proportions

10. Interfacial Transition Zone
The similarity of the three curves in the above figure confirms the general validity of the strength-porosity relationship in solids.
Whereas in hardened cement paste or mortar the porosity can be related to strength, with concrete the situation is not simple.
The presence of microcracks in the transition zone between the coarse aggregate and the matrix makes concrete too complex a material for prediction of strength by precise strength-porosity relations.

11. Three-phase theory in concrete
Three phases:
aggregate
hardened cement paste (hcp)
transition (interface) zone.

12. Concrete is brittle in tension but relatively tough in compression?
The component of concrete when tested separately under uniaxial remain elastic until fracture, whereas concrete itself shows inelastic behavior?
The compressive strength of a concrete is higher than its tensile strength by an order of magnitude?
At a given cement content, water-cement ratio, and age of hydration, cement mortar will always be stronger than the corresponding concrete? Also, the strength of concrete goes down as the coarse aggregate size increased.
The permeability of a concrete containing even a very dense aggregate will be higher by an order of magnitude than the permeability of the corresponding cement paste?
On exposure to fire, the elastic modulus of a concrete drops more rapidly than its compressive strength?
The answers to the above and many other enigmatic questions on concrete behavior lie in the interfacial zone that exists b/w large particles of aggregate and the hydrated cement paste!!!

13. Interfacial Transition Zone (ITZ)
Stress-strain behavior for both the aggregate and cement paste alone are nearly linear elastic.
Unlike the aggregate and the cement paste, concrete is not an elastic material. Neither is the strain on instantaneous loading of a concrete specimen found to be directly proportional to the applied stress, nor is it fully recovered upon unloading.
Because of the ITZ, concrete displays some nonlinear and inelastic behavior in compression.

14. Interfacial Transition Zone
A thin shell layer (10-50 μm thick) around large aggregate.
Formation: Water films form around large aggregate particles during mixing. This would account for a higher water-cement ratio closer to the larger aggregate than away from it.
Characteristic: Owing to the high w/c ratio, these crystalline products in the vicinity of the coarse aggregate consist of relatively larger CH and ettringite crystals; therefore form more porous framework; relatively weak zone.
Fraction of transition zone in size is much smaller than other two phases, its influence on concrete properties is far greater.
It lower the strength
It increase the permeability
It prompt non-linear behavior
It favorites crack formation

15. Interfacial Transition Zone
Because of the increased volume available for crystal growth, calcium hydroxide (CH) and ettringite crystals formed in this region tend to be larger and form oriented layers, serving as preferred sites for cleavage. In addition, microcracks tend to form in the transition zone, even before the concrete is loaded, due to differential shrinkage and drying. Amount of microcracking related to:
aggregate size, gradation
cement content
w/c ratio
degree of consolidation (fresh concrete)
curing conditions
RH (relative humidity)
thermal history

16. Interfacial Transition Zone
By tailoring the concrete mixture to reduce the influence of the ITZ, strength, modulus of elasticity (E), and impermeability are increased.
Lower w/c
Higher cement content
Supplementary cementitious materials
Smaller Maximum size of aggregate
Reactive dolomitic aggregate
Lightweight aggregate
Extended moist curing

17. FAILURE MODES IN CONCRETE
With a material such as concrete, which contains void spaces of various size and shape in the matrix and microcracks at the transition zone between the matrix and coarse aggregates, the failure modes under stress are very complex and vary with the type of stress.
Under uniaxial tension, relatively less energy is need for the initiation and growth of cracks in the matrix. Rapid propagation and inter-linkage of the crack system, consisting or preexisting cracks at the transition zone and newly formed cracks in the matrix, account for the brittle failure.

18. In compression, the failure mode is less brittle because considerably more energy is needed to form and to extend cracks in the matrix. It is generally agreed that in a uniaxial compression test on medium-or low-strength concrete, no cracks are initiated in the matrix up to about 50 percent of the failure stress; at this stage a stable system of cracks, called shear-bond cracks, already exists in the vicinity of coarse aggregate.
At higher stress levels, cracks are initiated within the matrix; their number and size increases progressively with increasing stress levels.
The cracks in the matrix and the transition zone (shear-bond cracks) eventually join up, and generally a failure surface develops at about 20 to 30 from the direction of the load, as shown in Fig.

19. Compressive Strength and Factors Affecting It
Characteristics and proportions of materials
Curing conditions
Testing parameters

20. Effect of Mix Proportions
Water to cement ratio
Abrams’ water to cement ratio
fc = k1/(k2w/c)
where w/c represents the water/cement ratio of the concrete mixture and k1 and k2 are empirical constants.

21. Affect of Water Cement Ratio

22. Effect of water/cement on the compressive strength
Influence of the water-cement ratio and moist curing age on concrete strength.
Compressive strength of concrete is a function of the water-cement ratio and
the degree of cement hydration. At a given temperature of hydration, the degree
of hydration is time dependent and so is the strength.

23. Effect of air-entrainment
Influence of the water-cement ratio, entrained air and cement content on concrete strength.
At a given w/c ratio or cement content, entrained air generally reduces the strength of concrete.

24. Effect of Cement type

25. Effect of Mix Proportions
Aggregate
It is true that aggregate strength is usually not a factor in normal strength concrete because, with the exception of lightweight aggregate, the aggregate particles is several times stronger than the matrix and the interfacial transition zone in the concrete.
There are, however, aggregate characteristics other than strength, such as
Maximum Size, Shape, Surface Texture, Grading
Mineralogical Composition
which are known to affect concrete strength in varying degrees.

26. Effect of max. aggregate size
Influence of the aggregate size and the water-cement ratio on concrete strength
at 28 days of age.
Generally, the compressive strength of high strength (i.e. low w/c ratio) concrete is adversely affected by increasing the size of aggregate. The aggregate size does not seem to have much effect on the strength in the case of low strength or hıgh w/c ratıo concrete.

27. Curing Conditions
The term of curing of concrete involves a combination of conditions that promote the cement hydration, namely,
time
temperature
humidity
conditions immediately after the placement of a concrete mixture into formwork.
Hydration can proceed satisfactorily only under conditions of saturation; it almost stops when the vapor pressure of water in capillaries falls below 80% of the saturation humudity.

28. Strength evolution with time
ACI Committee 209 recommends the following relationship for moist-cured concrete made with normal Portland cement (ASTM Type I)
For concrete specimens cured at 20 oC, the CEB-FIP Models Code (1990) suggests the following relationship:

29. Humidity
Great importance of moist curing.

30. Effect Temperature
With moist-cured concrete the influence of temperature on strength depends on the time –temperature history of casting and curing. This can be illustrated with the help of three cases:
Cast and cured at the same temperature
Cast at different temperature but cured at the normal temperature
Cast at normal temperature but cured at different temperatures.

31. Influence of Casting and Curing Temperature on Concrete Strength

32. Influence of Casting and Curing Temperature on Concrete Strength
From microscopic studies, many researchers have concluded that, with low temperature casting,
a relatively more uniform microstructure of the hydrated cement paste (especially the pore size
distribution) accounts for the higher strength.

33. Influence of Casting and Curing Temperature on Concrete Strength

34. Testing Parameters
The results of concrete strength tests are significantly affected by parameters involving the test specimen and loading conditions. Specimen parameters include the influence of size, geometry, and the moisture state of concrete; loading parameters include stress level and duration, and the rate at which stress is applied.

35. Size effect: Influence of Specimen Diameter on Concrete Strength
Height of cylinder = 2 x diameter
Specimen geometry can affect the laboratory test data on concrete strength. The strength of
cylindrical specimens with a slenderness ratio (H/D) above 2 or a diameter above 30 cm is not much
influenced by the size effects.

36. Effect of Length-Diameter Ratio

37. Effect of Moisture State of Concrete
The standard procedure requires that the specimens
continue to be in a moist condition at the time of testing.
In compression tests it has been observed that air-dried
specimens show 20 to 25% higher strength than
corresponding specimens tested in a saturated
condition. The lower strength of the saturated concrete
is attributed to the disjoining pressure within the cement
paste.

38. Loading Condition
In regard to the effect of loading rate on concrete strength, it is generally reported that the more rapid the rate of loading, the higher the observed strength value.

39. Behavior of Concrete under Various States
Pure compression
Pure tension
Splitting tension
Flexure
Multi-axial stress

40. Compressive Testing brittle stronger in compression
cross-sectional area
cylindrical, cube
ends must be plane & parallel
end restraint apparently higher strength
1) Tensile stresses at the ends of the specimen may cause tensile splitting failure perpendicular to the direction of loading.
2) Barrelling effect changes the length/diameter ratio.

41. The stress level of 75 percent of compressive strength, which represents the onset of unstable
crack propagation, is called critical stress; critical stress also corresponds to the maximum value
of volumetric strain.

42. instantaneous or short-time loading normally used in the laboratory
The ultimate strength of concrete is also affected by the rate of loading. Due to progressive
microcracking at sustained loads, a concrete will fail at a lower stress than that induced by
instantaneous or short-time loading normally used in the laboratory

43. Loaded Compressive Specimen

44. Elastic Properties E = modulus of elasticity = Young’s modulus = slope
Linear Elastic
Nonlinear Elastic
Strain energy per unit volume = area
Stress
(s)
Strain (e) E 1

45. Elastic Properties Poisson’s ratio =- (radial strain/axial strain)
Poisson’s ratio is not generally needed for most concrete design computations, however, it is
needed for structural analysis of tunnels, arch dams, and other statically indeterminate structures.
Poisson’s ratio =- (radial strain/axial strain)

46. Poisson’s Ratio (u) ratio of lateral strain to axial strain
steel 0.28
wood 0.16
granite 0.28
concrete 0.1 to 0.18
rubber 0.50
deformed
axial

47. Pure tension Very difficult test to conduct.
The shape of the stress-strain curve, the elastic modulus, and the Poisson’s ratio of concrete under uniaxial tension are similar to those under uniaxial compression.
The ratio between uniaxial tensile and compressive strengths is generally in the range of 0.07 to 0.11.
Most concrete elements designed under the assumptions that the concrete would resist the compressive but not the tensile stressess.
Direct tension tests of concrete are seldom carried out, mainly because the specimen holding devices introduce secondary stresses that cannot be ignored.

48. Splitting Tension Test – ASTM C496
15 by 30 cm concrete
cylinder
Compared to direct tension test,
the splitting tension test is known to
overestimate the tensile strength of
concrete by 10 to 15 %

49. Flexural Test ASTM C78 150 by 150 by 500 mm concrete beam
Explained in terms of the modulus of rupture (R) = PL/bd2
The results from the modulus of rupture test tend to overestimate the tensile strength of concrete
by 50 to 100%, mainly because the flexure formula assumes a linear stress-stain relationship in
concrete throughout the cross section of the beam. Additionally, in direct tension tests the entire
volume of the specimen is under applied stress, whereas in the flexure test only a small volume of
concrete near the bottom of the specimen is subjected to high stresses.

50. Correlation of Concrete Strengths
Concrete permeability, porosity, and density affect strength.
Concrete is stronger in compression than in tension. Often used with reinforcing steel to carry the tensile load after cracking has occurred.
Concrete strength also depends on the w/c and the degree of hydration. The degree of hydration depends on temperature and moisture of the concrete.

51. Effect of Confinement

52. Interplay of Factors Influencing Concrete Strength