Bishwajit Bhattacharjee
Emeritus Professor
Civil Engineering Department
IIT Delhi

Early Stage
Strength of concrete as a structural material is of paramount importance as it is the property that governs the performance against both natural and anthropogenic forces. A general definition of concrete would be: concrete is a material consisting of particulate natural material bonded with some cementing material. Hence, general concrete as a structural material is in use for many years almost from early historical time or even pre-historic time. The binder however has changed over period of time. In recent times various cementing i.e., binder materials are used with desirable modifications to satisfy desired performance requirements. Modern day concrete is very versatile and thus can best be represented through a diagram as shown in Fig. 1. Similarly performance of concrete can be again represented in a 3D representation shown in Fig. 2. Design of material system with composition shown in Fig. 1 is expected to be as per performance requirement shown in Fig. 2. This is shown in Fig. 3.

Although concept of the material concrete is very old, the concrete material science is barely 100 years old initiating with Duff Abram postulating the concept of strength- water to cement ratio (W/C) law[1]. Not only that, Abram could also obtain strength as high as 276 MPa for paste at a W/C of 0.08 with pressure application[2]. Nevertheless, in practice cube compressive strength of concrete rarely exceeded 50MPa till 1970[2]. The water requirement of concrete for workability (mould-ability) constrained the reduction of W/C below a point. This stage can referred as early stage of concrete strength.

Micro-Structure And Strength
Concrete as a particulate system is schematically shown in Fig. 4. Strength of the material is the ability to withstand applied load (force) without failure or significant plastic deformation. This property is ascertained by tests on samples. In case of concrete the strength is conveniently tested on cube or cylindrical samples. Failure means separation of particle/material or fracture. Bonds between particles resist this separation. Pushing particles from all sides does not cause separation, but pull does. Such particulate system thus can resist tri-axial compression very well as deformation or dislocation of the particles is obstructed by other incompressible particles as shown in Fig. 5. On the other hand uniaxial pull results in separation of material by fracture as shown in Fig. 6. Bond between CaO-SiO₂ -H₂O i.e., C-S-H is covalent bond while bond between layers of C-S-H is weak van der Waals bond. Van der Waals bond is mechanically very weak and elastically deformable, also results in poor conductivity of material. However that between aggregate and cement paste is simply mechanical and only through frictional force that exists between rough surfaces. Thus, concrete is relatively easily separable by pull than it is deformable to a significant extent by push from all directions, i.e., tri-axial compression. In case of uniaxial compression, tension along direction normal to applied compression, due to Poisson’s effect causes separation and crack parallel to compressive stress. Poisson’s ratio being order of 20% of compression, it takes a while to develop sufficient tension along normal direction. That is the reason why bonded particulate system such as concrete is strong in compression than tension. Further the material failure is brittle in tension as fracture and failure occurs instantaneously as pull exceeds the limit of resistance. Bonding energy can be calculated theoretically. Thus force that one bond can withstand and number of bonds per unit area is known, the tensile stress required at failure can be estimated. Strength estimated on the basis of the above bonding energy for paste alone is a gross over estimate and can be 10 to 1000 times more than that actually realized under tension[3]. This is because of flaws in the material structure; for concrete; these flaws are inherent pores or spaces occupied by air in the material system[3] and can be understood by having a close look in to the microstructure of the OPC paste.

Several microstructure models for hydrated OPC paste were proposed from observations with various analytical techniques.Most accepted model postulate layered sheet like structure for C-S-H which is gelatinous, i.e., having a gel structure. The layers of C-S-H are bonded through van der Walls bond and have inter layer space filled with gel water. This space represents the gel porosity and is estimated to be typically 28%. The thickness of the inter layer space estimated using adsorption isotherms and BET method is 15 Å, after Powers and Brownyard[3]. Powers also identified presence of capillary pores having larger sizes i.e., the empty spaces left behind by unreacted water upon evaporation. Powers’ works were mostly reported in late 1940 to 1960 [3].

In the meantime Kantro and Copeland, almost during the same period as mentioned above, reported the results of an experimental study for over 13 years, to establish the chemically combined water with major compounds of cement. The equation 1 below and Table 1 outline these findings [3].

Wₙ is the chemically combined water, compound quantities are C₃ S, C₂ S, etc., a₁ a₂ a₃ a₄ are amount of water bound to each major compound of cement and were determined experimentally and the results are shown in Table 1. Based on this finding and assuming a typical composition of cement with 48 % C3 S, 25 % C2 S, 11 % C3 A and 9% C4AF, the chemically combined water at complete hydration for cement works out to be approximately 0.23 gm chemically combined water, per gm of cement[3]. Further Powers and Brownyard also estimated the density of hydration products, i.e. C-S-H gel and Ca(OH)₂ as hydration products by using helium pycnometry. Based on density of hydration product and mass of hydration product based equations for total porosity, gel porosity and capillary porosity are proposed by Powers and are given in equation 2 to equation 4.

It is evident that the OPC paste is porous, and the pores constitutes the inherent flaw in the solid system that results in discrepancy between theoretically estimated tensile strength and that actually realized for material like particulate composite such as OPC paste.

The fact that actual tensile strength and theoretically estimated strength differs signifcantly for brittle materials such as glass, with the former being much lower than the later one, was explained by Griffith in 1920s with his fracture concept. Fracture of material results in creation of new surfaces, i.e., interface between solid and a fluid, usually air. Creation of every such interfacial surface requires energy to overcome cohesive forces that hold the material together, less, the adhesive forces exerted by other phase, namely air. Hence surface energy must be supplied during fracture to create new surface. The applied strain energy is the supplier of this energy. For flaw less homogeneous this energy causing fracture would be large, but practical material such as glass with blow holes, or cement paste/concrete with pores, the energy required would be relatively less as stress concentration at the tip of the flaw may intensify the strain energy supply at such location triggering fracture at lower average stress. This concept had been applied to explain fracture of plain concrete by Glucklich in 1960s[3]. The fracture may be initiated around multiple pores. However, several authors also worked on fracture of concrete around a notch in 1960s and used linear elastic fracture mechanics (LEFM) concepts and hence stress intensity factor and fracture energy were applied to model crack propa-gation from an existing crack tip at relatively macro level. For micro level inherent pores and Griffith’s concept holds good for understanding the approximate behaviour. Thus strain energy release rate is equated to rate of required surface energy for creating new surface with respect to pore size to obtain critical tensile stress required for fracture. Since failure under uniaxial compression is due to tension along a direction normal to compression direction, as shown in Fig. 7, thus compressive strength can be related to a pore size parameter, surface energy required and elastic modulus etc.

Griffith considered closed form solution by Inglis for stress field around an elliptic hole in a solid plate. The elastic strain energy decrease due to such a hole was considered and the rate of decrease with half crack length c shown in Fig. 7 is derived. The strain energy U from the solution is U=(πc² σ² )/E; while for 2c crack width and for two new surfaces the total surface energy required S is = 4cγ; γ is the surface energy per unit area, equating dU/dc=dS/dc yields, critical tensile stress at failure as given in equation 5[2,3]

*Fig. 7: Induced Tension along Normal Direction to Applied Uniaxial Compression [3]*

The 'c' can be considered as representing the equivalent pore radius in an un-cracked paste or concrete. The equivalent E and γ for the material would depend upon porosity. Thus strength of material like concrete depends upon elastic modulus and surface energy of skeleton, besides, porosity and a representative pore size. The porosity and pore size are again functions of W/C. The equivalent E and γ would also depend upon proportion of un-hydrated cement, aggregate volume and their mineralogical characteristics and also on proportion of hydration product etc. This concept is extended to concrete compressive strength through a semi empirical model as explained later.

Advent Of Admixtures And Strength
During early 1960s synthetic polymers made inroads in to many domestic and industrial applications. Consequently more efficient water reducing agents were introduced through their synthesis. Sulphonated Melamine Formaldehyde (SMF) and Sulphonated Naphthalene Formaldehyde (SNF) condensates started to be used as water reducing agent (WRA). These WRAs are of larger molecular size, compared to ligno-sulphonates derived from natural plant sources and obtained from paper industry. Hence, enabled the SNF and SMF to be absorbed at higher doses by cementitious system compared to ligno-sulphonates. Higher dose means more electro-static dispersion of cement particle and reduction in water demand for a given plasticity. Hence W/C could be lowered to attain higher strength than before.

Driven by the environmental concern and cost reduction of cement, utilities of pozzolans as partial replacement of OPC clinker in cement was rediscovered in 1960s. Fly ash (FA) a pozzolana, ground granulated blast furnace slag (GGBFS) etc. were used as mineral admixtures. They did not enhance the achieved strength but expected to provide denser microstructure of hardened paste by converting Calcium Hydroxide (CH) to C-S-H gel, thus their use can enhance the long term performance.

Major breakthrough in strength came through another pozzolana, i.e., silica fume (SF) also known as condensed micro silica. Invention of solid state devices such as transistor, IC etc., and development of semiconductor technology in 1950 and 1960 onwards led to high demand of silicon that is the cheapest semiconductor element. This production of silicon metal and Ferro-silicon metals produced SF as a by-product. Quartz is heated to about 2200°C to obtain silicon metal. The fume produced in the process when condensed results in, up to 95% pure silica of very high fineness. This material has the characteristics of very high pozzolanicity and pore-filling ability in hydrated OPC paste. Simultaneous development of graft polymer resulted in development poly carboxylate ether (PC) based combed polymer structure that can enhance the dispersion of cemetitious particle by steric effects. Suitable radical were grafted to long chain system to enable the combed structure and due to higher dispersion, water demand could be reduced further. These two developments together with application of packing concepts from powder technology led to development of High Strength Concrete (HSC), Reactive Powder Concrete (RPC), Macro Defect Free (MDF), Densified with Small Particles (DSP), Ultra High strength (UHSC) or Ultra High Performance Concrete (UHPC) etc. All these developments can be attributed to chemical and mineral admixtures. All these developments towards concrete strength was realized in 1980s.

Factors Effecting Strength: Current State Of Understanding
Current state of strength achievable for reactive powder concrete a is shown in Table 2 [3]. The ultra-high strength/performance concrete 200 grade, similar to RPC with fibre reinforcement for enhancing ductility and capability to arrest crack, have been used successfully in pre-tensioned structural elements. Other high strength cement based composites such as Engineered Cement Composite (ECC) have been also used for structural and non-structural industrial usage. However, understanding with respect to normal concrete and factors affecting strength still seems to be lagging behind. The clarity with respect to effect of W/C is somewhat there, but there is sufficient ambiguity about other factors affecting strength. For example, at macro level, there are infinite numbers of strength against W/C curves for normal strength concrete in DOE guide lines in UK. Every curve represent a specific concrete at a given age. These curves can be expressed through equation 6, in terms of strength f₀.₅ for W/C=0.5. It implies that aggregate, cement etc. all have a role in strength.

The equations are obtained through regression in two stages, first linear equation involving lnf and W/C were fitted to estimate slope lnK2 and intercept lnK1 for all the curves provided in the reference literature[4]. The values of ƒ₀.₅ at W/C =0.5, for every curve were also obtained. The nature of relationship between K₁ and ƒ₀.₅ and that for K₂ and ƒ₀.₅ were examined and then related to ƒ0.5 through appropriate linear fit. The coefficient of correlation in all cases was mostly more than 0.9.

Microstructure based understanding of strength of cement based materials can be elucidated following the concept expressed in equation 5. An extension of equation 5 to concrete material which is inherently porous with pores ranging over a wide range of sizes with verities of shapes and configuration etc. can be represented approximately through the equation 7 [5].

A generalized equation pore size distribution also have been proposed as given below in equation 8, through which the pore size (radius) r and corresponding fractional volume of pore V is expressed in terms of porosity p, median or mean distribution radius rₘ and dispersion coefficient d [6-8]. The mean distribution radius and porosity are related to strength of paste, mortar and concrete etc., following Griffith’s fracture theory and the concept of the equation is explained later.

The rₘ is related to W/C, mean cement particle size D and age t as demonstrated trough geometric modelling. The equations for rₘ with these factors are given in equations 9.

In above equations, the constants a₁ a₂ a₃ and a₄ are 1184.6, -161.7, 123.0 and -7.4 respectively for OPC paste.

For fly ash admixed paste, mortar etc. similar relationship can also be obtained[9], e.g., for fly ash mortar gel porosity is related to water to binder ratio is as follows:

Where, the constants k₁ , k₂ , k₃ , k₄ and k₅ are 600.72, -270.73, 257.44, -23.56, and -30.82 respectively for cement fly ash mortar. The above expression is obtained after removing few extreme data and the corresponding coefficient of determinations was 73%. Capillary pores in fy ash mortar tend to get segmented early and pore entry radius vanishes.

Thus insight in to strength versus water to cement or water to binder ratio can be better obtained through pore size characteristics. The uniaxial compressive strength of cement based composite including concrete is governed by tensile failure along the direction normal to compressive load, induced owing to Poisson’s effect as shown in figures Fig. 6 and Fig. 7. Hence extending the idea illustrated in equation 7, the compressive strength σc can be expressed as given in equation 10 [5].

The K in equation 10, accounts for a factor relating compressive strength to tensile strength depending upon method of tests, elastic modulus and surface energy of pore free solids, which includes solid phase of aggregates, un-hydrated cement and products of hydration. Recent studies on elastic modulus of solid phases through nano-indentation technique and molecular dynamics simulation could throw light on elastic modulus of un-hydrated cement clinker (UHC), CH and C-S-H gel in both as inner product (IP) and outer products (OP). The elastic modulus of compounds of cement ranges around 137GPa, that of CH is about 35 GPa and; for C-S-H these values are 26-32 GPa and 13-26 GPa respectively are the ranges for IP and OP respectively[10-12]. Elastic modulus for aggregates may range around 100 GPa. The elastic modulus of pore free solid composite consisting of UHC play a major role in strength. Complete hydration is possible at infinite age only above W/C greater than 0.36 as at lower W/C, space available for hydration product is insuficient to accommodate hydration product having specific volume higher than clinker. Thus at W/C lower than 0.36 not only capillary porosity is small for enhancing the strength, but also the contribution of un-hydrated clinker towards elastic modulus leads to higher strength. Modelling for both elastic modulus and surface energy of the composite pore free solid consisting of UHC, CH, IP, OP and aggregate is yet to be accomplished and is a current research challenge.

A case study on effect on cement strength on concrete strength is presented as follows to demonstrate the role of 53 grade vis-à-vis lower cement strength (grade) on in-situ strength of concrete. The case relates to the concrete in the pre-stressed box girder of an important flyover in Delhi[13]. OPC 53 grade as per IS 12269:1987 was specified as the cement for casting of the precast box girder for construction. The cement used satisfied the requirement of strength at the 7 day age. To meet the dead line for completion of the project, the owner agency allowed casting prior to attainment of 28 day age of the standard mortar cubes. However, a few mortar cube sample strengths, representing the cement strength, fell below the required grade strength of 53 MPa and attained only 47 MPa, thus satisfied the 43 grade requirement but failed to satisfy the 53-grade requirement. Apprehensions were expressed post completion of the project, with respect to deviations from contract specifications and confirmation was desired through an investigation. The grade of cement in an existing concrete cannot be conclusively identified with sufficient reliability within acceptable range of accuracy. Following investigation strategy was proposed to the owner agency.

The implication of non-compliance of the cement grade on the final product structure and its safety depends upon the material concrete used in its casting. Hence concrete in the girders deemed to satisfy all specifications with respect to quality of ingredients and final product concrete itself, was compared with the doubtful ones. The ones satisfying requirement was called Concrete B. Concrete B is deemed to satisfy all the properties requirement envisaged in the design including those required for adequate safety of the structure. The one not-satisfying requirement was designated as Concrete A. It may be noted that both the concretes A and B were acceptable as per cube test results criteria for 28 day strength. However, in-situ properties are more reliable for post construction safety evaluation. Since the structure was already functional, restriction on number cores to be drilled was imposed. It was proposed that investigation would be completed with limited number of cores as well as with limited number of semi-destructive tests without compromising with the accuracy of analysis. Strategy is to establish whether Concrete A is at-least as good as the Concrete B with respect to its quality and strength and if so, the Concrete A can be also considered to be satisfying all requirements which are prerequisite for safety of the structure in spite of the cement being one grade lower. Thus, the proposed strategy was to test the hypothesis that surface hardness (i.e. Rebound Number), soundness and solidity of the concrete as determined through ultrasonic pulse velocity test and in-situ strength of the Concrete A is as good as Concrete B, and if so, the failure of cement to satisfy grade strength requirement has no bearing on strength and safety performance concrete in the structure. The Non Destructive Tests those are carried out at site, namely: a) Rebound Hammer test and b) Ultra Sonic Pulse Velocity Test (USPV). (c) Pull out (CAPO) test and laboratory test of concrete cores drilled from the site.

Concrete strength and quality varies widely within a member, as comparison is desired, therefore, same relative position within the member had been chosen for all the segments/elements as far as possible [14], with regards to Concrete A and Concrete B. This is done, so that the effect of variation in the concrete due to variation of locations within the member is similar for both Concrete A and Concrete B. Thus variation of location within member would aect the comparison only insignificantly. From practical consideration of non-availability at the site due to traffic disruption, the deck concrete has been kept out of this investigation. The number of location chosen in the web in Concrete A is nearly same as those chosen for Concrete B. Similarly number of locations chosen in the soft slab of the segments of Concrete A is nearly same as that chosen for Concrete B. In both cases segments have been chosen randomly covering most of the deck as far as possible.

The appropriate number of test (sample) is determined based on desired accuracy and cost[15]. The number of test required for a desired degree of accuracy can be calculated using Stein’s formula[15, 16]. According to Steins formula the number of tests 'n' required for a given type of test is given by n=(t×s/SE)2 . Where s is the sample standard deviation, SE is the sampling error and t is student’s t value for a particular confidence level desired. In this formula SE is expressed in absolute value. Expressing SE as a fraction of true value the formula can be rewritten as n= (t C.V/ SE)2 . Where C.V is the coefficient of variation and SE is the sampling error expressed as a fraction of true value. The estimate of true value is the mean. Assuming the mean in-situ cube strength of the cube to be about 50 MPa (M45 grade; note: in-situ strength is lower than standard cube strength) and a level of control being normal to very good, the coecient of variation is 10% [14]. For in-situ tests on concrete the desired sampling error is assumed to be 10 % of the mean with a confidence level of 99% for estimating the number of test required for a given test type. Thus the numbers of test required were calculated as follows. Consider the C.V that is based on sample size, then for small sample size, conservative value of t as 3.5. Corresponding n is then, (3.5×0.1/0.10)2 =13. Thus, sample size greater than 13 would ensure an accuracy better than 10%. In this investigation the sample size adopted for CAPO test is 18-20 each for both Concrete A and Concrete B. Nine to ten segments have been chosen randomly and also depending upon access at site as mentioned earlier for both Concrete A and Concrete B. At each segment CAPO tests were carried out at two locations, rebound hammer test was carried out at three locations and USPV test was carried out four to eight locations. In this way 38 CAPO test results, 57 rebound hammer results and 112 USPV values were obtained. In addition 14 cores were also drilled with 8 and 6 belonging to Concrete A and Concrete B respectively. The cores were drilled at locations close to respective CAPO locations so that correlation of estimated in-situ strength from CAPO test can be verified with estimated in-situ strength obtained from core test for improving the confidence on the inferences.

The test methods and estimation of properties and performance indices were carried out as per national and international standards[17-21].

For brevity, test details are omitted in this discussion and only relevant results and analysis are presented. CAPO test result is an indicator of in-situ compressive strength, however core test provides direct more accurate and reliable indication of strength, but core test were conducted at limited number of sample locations, hence prior to arriving at inferences based on CAPO results a comparison of core test results with CAPO results was carried out through 14 cores. CAPO to Core ratio varied from 0.86 to 1.19 and their average is 0.999. The comparison was appraised with Integrated Absolute Error (IAE). An IEA value of <10%, indicate good correlation between predicted (P) and observed (O) values. P are CAPO predicted and O are Core strength results. The expression for IEA is given in equation 11 and the calculated value in this case is 3.5% indicating CAPO results are sufficiently reliable with reference to core results.

The relative sur face hardness (rebound Number), USPV values and CAPO results of Concrete A vis-a-vis Concrete B were compared using statistically concepts of hypotheses testing concerning two means. The results are summarised in terms of mean standard deviations and sample sizes in Table 3. The unbiased estimate of the mean values µₐ and µ₆ for Concrete A and Concrete B are given by their sampling means Xₐ X₆ The variances of these estimates are the variances of the respective sampling means. The distribution of differences of the two means can be considered and it is known that the mean of the difference is given by µA-µB and the variance of the difference is sum of the variance of two individual distributions; correspondingly one can estimate the test statistic Z given as follows [22] in equation 12. The effect of small sample size is ignored for Rebound and USPV tests, in these cases for calculating the standard deviation as sample sizes are quite large as shown in Table 3.

For CAPO tests sample-size are relatively smaller and effect OF small sample size was not ignored. Value of “t” statistic as given in equation 13 is considered. The standard deviations are also calculated using effect of small sample size.

Where S Xₐ X₆ − is given below and n₁ = 20 and n₂ =18 are the sample size for CAPO test for concrete A and concrete B respectively.

For rebound number, z works out to be 2.11. Critical value of zα from the statistical table for the level of significance, α=0.05 is 1.645 and is smaller than calculated z. Thus, z > z0.05; as shown in Table 3, hence it is concluded that observed difference between the two means is significant, in other words surface hardness of Concrete A is slightly higher than Concrete B. Similarly, for USPV, z works out to be 2.88, and greater than critical value of zα for the level of significance, α=0.05, i.e., 1.645. Thus, z > z0.05; as shown in Table 3, hence it is concluded that observed difference between the two means is significant, in other words soundness of Concrete A is better than Concrete B.

For 5.1; n1 =20; n2 =18; sA=3.6 and sB =5.9, t works out to be 1.02. Critical value of tα from the table for the relevant statistical table level of significance, α=0.025 is 1.96 and is greater than calculated t. Thus, t < tα/2; hence null hypothesis cannot be rejected and it is concluded that observed difference between the two means is not significant, in other words strengths of Concrete A and Concrete B represent the same population therefore are same.

It is inferred therefore that although the cement did not satisfy the grade strength requirement of 53 grade cement, rather satisfied the 43 grade requirement, it is does not have any impact on nal concrete strength and properties. Thus grade of cement has no effect on strength of concrete.

Summary And Conclusions
Chronological evolution of concrete in terms of its strength characteristics is presented in this article. Role of microstructure and its understanding in the context of strength is illustrated. Impact of admixture revolution on evolution of concrete strength is highlighted. Factors effecting strength as understood on present day is discussed at length. Strength of cement is getting undue importance in the concrete strength. Through an in-situ case study results it is demonstrated that strength/grade of cement have insignificant or no effect on strength of concrete in structure.

Reference

Abrams, D.A. (1919): “Design of Concrete Mixtures”, Structural Materials Research Laboratory, Lewis Institute; Chicago.
Brandt, A. M., (1995) “Cement-Based Composites: Materials, Mechanical Properties and Performance” E & FN SPON.
Soroka, I., (1979) Portland Cement Paste And Concrete, Macmillan Press London.
Neville, A.M. and Brooks, J.J., (1990): “Concrete Technology”, ELBS .1990..
Kumar, R. And Bhattacharjee, B., (2003): Porosity, pore size distribution and in situ strength of concrete. Cement and Concrete Research, Vol. 33(1), pp.155-164.
Patil S.G., and Bhattacharjee, B., (2008): “Size And Volume Relationship Of Pore For Construction Materials”. Jr. of Materials in Civil Engineering, ASCE. Vol 20.No. 6. pp. 410-418.
Kondraivendhan. B and .Bhattacharjee, B.,(2010): “Effect Of Age, W/C Ratio On Size And Dispersion Of Pores In OPC Paste” ACI Materials Journal. Vol 107, No.: 2 pp. 147-154.
Kondraivendhana B. and. Bhattacharjee, B.,(2014): “Prediction Of Strength, Permeability And Hydraulic Diffusivity Of OPC Paste” ACI Materials Journal. Vol 111, No.: 2,. pp.171-178.
Kondraivendhana B, and Bhattacharjee, B., (2013): “Pore Size Distribution Modification Of OPC Paste Through Inclusion Of Fly Ash And Sand” Magazine of Concrete Research, Volume 65, Issue 11, pp. 673 –684.
Veleza, K., Maximiliena, S., Damidotb, D., Fantozzia, G and Sorrentinob, F., (2001): “Determination By Nanoindentation Of Elastic Modulus And Hardness Of Pure Constituents of Portland Cement Clinker”, Cement and Concrete Research, Vol. 31, pp.555-561. 1
Wu, Weidong, Al-Ostaz, Ahmed; Alexander H.-D. Cheng, M.; and Song, C.R., (2011): “Computation of Elastic Properties of Portland Cement Using Molecular Dynamics” Jr. of Nanomechanics and Micromechanics, Vol. 1, pp. 84-90.
Manzano, H., Dolado, J.S. and Ayuela, A., (2009) “Elastic properties of the main species present in Portland cement pastes”, Acta Materialia 57, pp. 1666–1674.
Bhattacarjee, B.(2012): Investigation of Concrete In the Identified Section Of Constructed Elevated road …for grade and quality of Concrete vis-à-vis the concrete in the accepted on through in-situ Testing and analysis. Consultancy Project (CW12106) IIT Delhi.
Bungey, J.H.and Millard,S.G., (1996): “Testing of concrete in structure”, 3rd edition , Chapman & Hall. 1996.
Kay, Ted. ;(1992): Assessment and Renovation of Concrete Structures. Longman Scientific and Technical
Newman, John & Choo, Ban Sang. (2003): “Advanced Concrete Technology-Testing and Quality” Elsevier 2003.
Bureau of Indian Standard, (1992) IS 13311 (PartII) : 1992 Non-Destructive Testing of Concrete- Method of Test. Part II Rebound Hammer.
Bureau of Indian Standard, (1992) IS 13311 (Part 1) : 1992 Non-Destructive Testing of Concrete- Method of Test Part 1 Ultra Sonic Pulse Velocity.
British Standard Institution, (1981) Guide to Assessment of Concrete Strength in Existing Structures BS 6089 :1981
British Standard Institution, (1983). “Method for Determination of Compressive strength of Concrete Cores. BS 1881: part 120 :1981”
British Standard Institution, (2007). “Assessment of in-situ compressive strength in structure and precast concrete components”. BS EN 13791: 2007.
Miller, I and Freund, J.E. “Probability and statistics for engineers” Prentice-Hall of India. 1981

Concrete Strength - Past 100 Years

Properties of Geo Polymer Concrete Behaviour at Elevated Temperatures