Center for

By-Products

Utilization

CONCRETE DURABILITY AS INFLUENCED

BY DENSITY AND/OR POROSITY

By Tarun R. Naik

Report No. CBU-1997-27

May 1997

Presented and Published at the Cement and Concrete Institute of Mexico Symposium "World of

Concrete - Mexico", Guadalajara, Mexico, June 4-7, 1997.

Department of Civil Engineering and Mechanics

College of Engineering and Applied Science

THE UNIVERSITY OF WISCONSIN - MILWAUKEE

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CONCRETE DURABILITY AS INFLUENCED BY DENSITY AND/OR POROSITY

By

Tarun R. Naik

ABSTRACT

The presence of capillary pores and air voids influences concrete permeability to a large

extent. Concrete density is inversely proportional to its porosity. The ingress of aggressive

agents into the pore structure is responsible for various durability problems in concrete structures.

Therefore, a durable concrete should have low permeability. Permeability of concrete increases

with the increase in porosity of concrete. Various factors such as water to cementitious materials

ratio, degree of hydration, air content, consolidation, mineral admixtures, aggregates, reaction

between aggregate and cement paste, pozzolanic admixture, etc., affect concrete porosity.

The effects of these factors on concrete porosity and density are discussed in this paper.

Previous investigations relating concrete porosity to permeability, and other durability-related

properties are also briefly addressed. Theoretical and empirical models representing relation

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between porosity and concrete strength properties

are described.

INTRODUCTION

Concrete density depends upon volume fractions of constituent materials and their

densities, and the volume of voids present in the concrete. Concrete can be divided into two

major phases at a macroscopic level; these are coarse aggregates and matrix (i.e., mortar,

hydrated cement paste and sand). Each of these phases is also a composite material. The

region between the aggregates (coarse or fine) and hydrated cement paste (hcp) is more

porous than the hcp; and, it can be considered as a third phase at a microscopic level.

The aggregate phase is largely responsible for the unit weight and dimensional stability

of concrete. These properties are dictated by bulk density and strength of the aggregate.

The volume, size, and distribution of pores present in the aggregate control

these properties to a large extent. In order to produce dense concrete, the porosity of the

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aggregate should be kept low. The shapes and sizes of the aggregate can also influence

concrete properties. Classification of aggregates is done according to size, bulk density, or

source. The coarse aggregates are composed of particles greater than 4.75 mm, and fine

aggregates contain particles of less than 4.75 mm. Based on bulk density, coarse aggregates

are classified into three categories: normal weight aggregate (1520 to 1680 kg/m3), lightweight

(1120 kg/m3), and heavyweight (above 2080 kg/m3).

Coarse aggregates are relatively more impermeable than the hydrated cement paste.

The hcp is composed of solids and voids. The major solids are crystals of calcium silicate

hydrates (C-S-H), calcium hydroxide (Ca(OH)2), calcium sulfoaluminates (C6AS3H32), and

unhydrated portland cement clinker grain. The volume occupied by these crystals varies from

50 to 60% for C-S-H, 20 to 25% for Ca(OH)2, and 15 to 20% for calcium sulfoaluminates

of total volumes of solids in a completely hydrated cement paste (Mehta 1986).

The C-S-H crystals (C-S-H gel), being the major component of solids, play a great

role in influencing concrete properties. The solid-to-solid distance between the C-S-H layer

(gel pore) is found to vary between 5 to 25 A (1 A = 10-5 mm). Due to their size and very

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low interconnectivity, these pores are relatively impermeable to water. However, water removal

from these pores can influence drying shrinkage and creep behavior of concrete

(Mehta 1986). Compared to C-S-H crystals, greater pore sizes are observed between the

solid of Ca(OH)2 and calcium sulfoaluminate crystals.

Capillary voids, voids created by water particles movements and space not occupied

by solid components, are known to make a major contribution to porosity of the concrete.

The size of capillary voids is much larger at the interfacial zone (i.e., the region at the interface

of the aggregate and the hcp) compared to the bulk cement paste. The size of capillary voids

can range from 10 to 50 nm (1 nm = 10-6 mm) in low water to cementitious materials ratio

pastes while for high water to cementitious materials ratio paste, capillary pores are relatively

larger (up to 3 to 5 μm). Additional concrete porosity results from both entrapped and entrained

air voids. Entrapped air voids (as large as 3 mm) are larger in size compared to entrained

air, 50 to 200 μm, (1 μm = 0.001 mm). The dimensional ranges of solids and voids are

shown in Fig. 1.

Both capillary voids and air voids influence concrete impermeability and strength to a

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large extent. Fluids can flow more easily through large capillary pores and air voids compared

to gel pores found in the solid crystals. The voids/flaws present in the concrete reduces the

mechanical strength of the concrete due to the stress concentration effects. Thus, porosity

of concrete composed of large pores has detrimental effects on both impermeability and strength

of the concrete.

Concrete durability-related properties are known to be negatively affected due to

expansions that result from factors such as freezing and thawing actions, alkali-aggregate

reactions, sulfate attack, corrosion of the reinforcement, etc. Such expansions depend, to a

large extent, upon ingress of water, gases, and aggressive chemicals into the concrete;

which, in turn, depend upon permeability (which depend upon porosity). Therefore,

permeability of concrete can be used as a measure of concrete durability. Thus, porosity affects

can be related to concrete durability.

FACTORS AFFECTING CONCRETE POROSITY/DENSITY

For given constituent materials, the porosity of the hcp depends upon several factors

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including the following:

1. Water to cementitious materials ratio.

2. Degree of hydration.

3. Air content.

4. Consolidation.

5. Admixtures.

6. Aggregates.

7. Reaction between aggregate and cement paste.

8. Mixture proportioning.

Water to Cementitious Materials Ratio

For a given cementitious material content of a concrete mixture, the space occupied

by the hydration product increases with increasing water content. However, the volume of the

hydration product will remain constant irrespective of the water content of the mixture at a

particular degree of hydration. Consequently, unfilled spaces, i.e., gel pores and capillary voids,

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will increase with the increase in water to cementitious materials ratio. Therefore, an increase

in water to cementitious materials ratio will cause an increase in porosity and a decrease in

density of concrete.

In a freshly mixed concrete, water films are formed around the aggregate. As a result,

a higher water to cementitious materials ratio is present in the interface region compared to

the bulk cement paste. This condition also favors formation of larger crystals of calcium

hydroxide and ettringite. This results in a higher porosity and lower density in the interface

region relative to the bulk cement paste. Also, in such regions, the crystals of Ca(OH)2 tend

to form oriented layers, with the C-axis perpendicular to the aggregate surface. A general

schematic description of the interfacial zone formation is depicted in Fig. 2.

Degree of Hydration

The degree of hydration increases with age. Both gel pores and capillary pores volume

and pore size decrease with an increase in the degree of hydration due to the formation of

increased amounts of hydration products. This leads to improved (i.e., denser) microstructure

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of the concrete. In order to obtain improved internal structure of concrete, adequate curing

conditions should be maintained. A combination of relative humidity, time, and temperature

should be selected so as to obtain denser microstructure and to avoid microcracking of concrete.

Air Content

In order to ensure freezing and thawing durability of concrete, adequate entrained air

voids are provided. An increase in air content (either entrained or entrapped) causes increase

in porosity and decrease in concrete density and mechanical properties (Naik, et al. 1997).

Consolidation

Compaction of freshly mixed concrete allows elimination of entrapped air pockets and

placement of concrete at a low water to cementitious materials ratio. Compaction/consolidation

also decreases capillary pores. Consequently, proper compaction causes reduction in porosity

and increase in density. This effect is more pronounced in the interface region where packing

of cement particles is inefficient.

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Admixtures

Inclusion of reactive pozzolanic additives such as fly ash, slag, silica fume, natural

pozzolans, and rice husk ash improves concrete microstructure. This happens due to the

densification of the microstructure that occurs as a result of the production of pozzolanic C-S-H.

The use of pozzolanic additives is essential for densification of the interface region, in

production of high-strength and/or high-performance concretes. Use of high-range water-

reducing admixture (HRWRA), also called superplasticizer, results in the production of the

desired consistency of the concrete at a low water to cementitious materials ratio for a given

water content. This causes reduction in the amount and size of gel and capillary pores. As

a result, a denser concrete microstructure is produced, which in turn, improves concrete strength

and impermeability. Therefore, HRWRA is needed in production of high-quality, high-strength,

and/or high-performance concretes.

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Aggregates

The size and shape of coarse aggregates can affect concrete microstructure to a large

extent. In general, an increase in the maximum size of aggregate or amount of flat particles

tends to increase the amount of water in the vicinity of the aggregate. As a result, the water

distribution in the mortar matrix becomes non-uniform. This occurs due to bleeding and the

wall effects around aggregates that prevent packing of cement grains of large size (10 μm

or more). Therefore, shape, size, and amount of flat aggregates permitted should be judiciously

selected to avoid increase in porosity or decrease in density of concrete.

Reaction between Aggregate and Cement Paste

Chemical composition of the aggregate can influence the porosity of the interface region

(Bentur and Odler 1996). When the aggregate (e.g., calcite and dolomite) reacts with the

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cement paste, formation of compounds such as carboaluminates or calcium carbonate-calcium

hydroxide complex occurs in the interface region. This can result in increased density and

decreased porosity of the interfacial region of concrete.

Effect of Mixture Proportioning

The mixture proportioning plays a significant role in packing of cement particles near

the interface region. In general, a low water to cementitious materials ratio and a high

aggregate/cement ratio promotes packing of cement particles in the interfacial region (Scrivener

and Pratt 1996). Improved packing results in decreased porosity of concrete and increased

density of concrete.

PREVIOUS INVESTIGATIONS

In accordance with ACI Committee 201, durability of concrete is defined as its ability

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to resistant weathering action, chemical attack, abrasion, or any other process of deterioration.

This means that a durable concrete will maintain its original form, quality, and serviceability

when exposed to various environmental conditions. The movement of water or other fluids

through concrete can carry aggressive agents which create various types of durability problems

for concrete construction. In fact, permeability controls the rate at which aggressive agents

such as gases (CO2, SO2, etc.) and liquids (acid rain, sea water, sulfate rich water, salt-bearing

snow/water, groundwater, etc.) can penetrate into concrete. Therefore, in order to avoid

permeation of these agents, permeability of concrete must be reduced by decreasing porosity

and/or increasing density of the concrete.

Effect of Porosity on Concrete Permeability

In general, permeability decreases with an increase in porosity up to a certain level,

and then the influence of porosity on permeability is negligible. A strong correlation between

porosity and permeability is reported by a number of investigators (Powers, et al. 1954; Naik,

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et al. 1993; Naik, et al. 1996; Mehta 1986; Massazza 1996). Researchers (Powers, et al.

1959; Costa and Massazza 1985) have indicated that when volume fraction of porosity is less

than 35%, the permeability becomes negligible. The same trend was also observed by Mehta

(1986) at a porosity of 30%. This may be attributed to the fact that at a low porosity, there

is a large reduction in size and amount of capillary pores, and interconnection between them.

Concrete porosity is maximum at the interfacial region of concrete (Fig. 2) A relation between

permeability and capillary porosity is presented in Fig.3.

A variation in paste permeability and porosity with time is shown in Fig. 4. A large

number of studies (Ozyldirin and Halstead 1988; Naik, et al. 1992; Thomas and Mathews 1992;

Torii and Kawamura 1992; Naik, et al. 1993; Bilodeau, et al. 1994; Naik, et al. 1996) have

reported decreases in permeability of concrete due to inclusion of pozzolanic admixtures. The

decrease in permeability was attributed to improvement in the concrete microstructure,

especially in the transition zone.

Incorporation of reactive pozzolans such as fly ash, natural pozzolans, silica fume,

and rice husk fly ash causes both grain and pore refinements. This occurs primarily due to

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production of pozzolanic C-S-H and efficient packing of cementitous materials particles, leading

to improved concrete microstructure. An increase in reactive mineral admixture may or may

not decrease total porosity. But it decreases the fraction of total capillary pores with increased

discontinuity between pores (Young 1988; Marsh, et al. 1985; Moukwa 1993)

Due to slow pozzolanic reaction of many fly ashes, a greater curing time is required

for fly ash concrete compared to concrete without fly ash. The beneficial effects of curing

temperature on the pozzolanic reactions of fly ash and slag has been observed in the past

(Naik, et al. 1993; Naik, et al. 1994 a,b,c) In general, concrete permeability decreases with

increasing strength (Fig. 5). Naik, et al. (1996) reported optimum cement replacement with

fly ash in the range of 35 to 55% with respect to air, water, and chloride permeabilities. At

a very high replacement of cement with fly ash, concrete microstructure was adversely affected

due to the dilution effects. Silica fume is a more efficient pozzolanic material than natural

pozzolans or fly ash. Consequently, lower amounts of silica fume can be used to obtain the

beneficial effects of pozzolanic reactions (Naik, et al. 1994c ); however, at a possibly increased

cost of the

concrete. An optimum dosage of silica fume should range between 5-10% of the total

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cementitious materials for improving concrete impermeability with favorable economics.

The use of chemical admixture in cement-based materials results in changes

in pore size distribution (Manmohan and Mehta 1981; Young 1988). Generally, addition of

high-range water-reducing admixture (HRWRA) reduces water demand for a given consistency

of fresh concrete. This, in turn, reduces size of capillary pores and total porosity of the concrete.

Consequently, permeability of superplasticized concrete is lower compared to

unsuperplasticized

concrete. The incorporation of calcium chloride enhances amount of fine capillary pores in

cement paste (Manmohan and Mehta 1981). This causes reduction in permeability of cement-

paste.

Other Durability-Related Properties

A few investigations have attempted to establish a relation between porosity, strength,

and durability-related properties. Brunauer (1965) observed a non-linear relationship between

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compressive strength and density (Fig. 6). In general, as expected, compressive strength

increased with density. A linear relation between compressive strength and log of porosity

has been reported for up to 700 MPa of cement pastes (Fig.7). One percent increase in

porosity causes a reduction in concrete strength in the 5 - 6% range (Massazza 1996).

Due to relatively high porosity of the interfacial zone compared to other regions, it

becomes a weak link in the concrete structure. As a result, concrete strength and

durability-related properties are dictated by the properties of the interface region to a marked

extent. In order to improve concrete durability, it is essential to improve strength and durability

of the interfacial region. In general, attempts have been made to improve properties of the

interfacial region through the use of mineral additives and chemical admixtures. Recent

investigations

(Naik, et al. 1994 a,b; Gjorv 1994) have shown reduction in the size of interface through the

use of mineral additives and HRWRA at a very low water to cementitious materials ratio.

A special class of concrete, called high-performance concrete (HPC), is proportioned

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to eliminate the negative effects of the interfacial regions. This type of concrete is made with

very high quality constituent materials, and requires special mixture proportioning and production

technique. A number of investigations by Naik and his co-workers (Brand 1992; Patel 1992;

Naik, et al. 1994 a,b,c; Olson 1994; Beffel 1995) and others (Aitcin, et al. 1987; De Larrand,

et al. 1990; 1987; Gjorv 1994) have been directed toward development of HPCs for strengths

ranging between 50 and 150 MPa. These concretes have exhibited excellent durability

properties, including high resistance to freezing and thawing, alkali-silica reaction, abrasion,

chloride-ion penetration, etc.

MODELS RELATING STRENGTH PROPERTIES AND POROSITY

It is well accepted that mechanical and elastic properties of solids are adversely affected

by the presence of pores or voids in the materials (Mackenzie 1950; Krstic and Erickson 1987;

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Pani and Niyogi 1987; Wang 1987). Mackenzie (1950) was probably the first to propose

theoretical models for the shear and bulk modulus for solids containing spherical holes.

These models are written as:

V

8) +K (9

G)4 +K (3 5 - 1G = G voo

K) V 3 +G (4

)V - (1KG 4 = K

vo

po

o

where Go and Ko are shear modulus and bulk modulus of porous solids, and G and K refer

to shear and bulk moduli of non-porous solids; and Vvo is the volume fraction of voids present

in the solid.

Several empirical models are available for describing elastic modulus of solids. Most

widely used models are polynomial in form, containing one or more material constants (Krstic

and Erickson 1987; Phani and Niyogi 1987; Wang 1984). A generalized form is expressed

as:

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)] _ + cP + bP + (aP [- exp E = E 32o

where E and Eo are the elastic moduli at porosity P and zero, and a, b, c, are material

constants. Several forms of the above model representing modulus relation with porosity are

summarized by Phani and Niyogi (1987).

Sereda, et al. (1980) reviewed various models that represent relation between strength

and porosity of hardened paste. Three most commonly used regression models (Uchikawa

and Okamura 1993) are:

(1) S = So. (1-P)A (Balsin's formula)

(2) S = So. exp (-BP) (Ryshkewitch's formula)

(3) S = C. ln (Pcr/P) (Schiller's formula)

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Where S = strength; So = strength at zero porosity; P = porosity; Pcr is zero strength

porosity; A,B, and C are regression coefficients.

Akyüz, et al. (1993) developed a mathematical model to relate compressive strength

with porosity or water/cement ratio (W/C). The model is of the form:

})P - (1 - {1 M = f

c + 1 3/2

1’c

1 or

})P - (1 - {1 M = f0.23) -

C

W( + 1

3/2

2’c

2

where M1 and M2 are constants which represent the theoretical compressive strength of concrete

with zero porosity, c is the capillary coefficient, θ1 and θ2 are constants, and P is porosity.

The results of this investigation are depicted in Fig. 8 and 9.

SUMMARY

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Concrete is a hybrid particulate composite material. It is composed of three

major phases: particles (coarse aggregates), matrix (hydrated cement paste (hcp) and sand,

mortar), and the interfacial region between aggregate and the hcp. The aggregates are less

permeable compared to the hcp. The interface region between the hcp and aggregate is more

porous and weak compared to the other two phases. Furthermore, each of these phases at

a microscopic level can be treated as a multiphase material.

Concrete porosity is inversely proportional to its density. Concrete porosity is affected

by a number of parameters, including water to cementitious materials ratio, degree of hydration,

air content, consolidation, admixtures, aggregates, reaction between aggregate and the

hydrated cement paste, mixture proportioning, etc. Of these, the water to cementitious materials

ratio and degrees of hydration (curing) are the most important parameters that affect concrete

porosity and thus concrete density. An increase in water to cementitious materials ratio

increases porosity.

For production of low porosity in concrete, a low water to cementitious materials ratio

with optimum curing is used. An increase in compaction reduces porosity. The size of

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aggregates should be reduced to minimize creation and to decrease the amount and size of

the interfacial region in concrete. The amount of flat aggregate should be minimized/avoided

because it contributes significantly to the amount of weaker interfacial region. The introduction

of pozzolanic additives, such as fly ash, natural pozzolans, slags, rice husk ash, and silica fume,

cause refinement of grain and pore structures, especially in the interfacial region. Concrete

permeability increases with an increase in porosity and decrease with an increase in density.

For achieving high durability, concrete porosity should be kept low so as to reduce its

permeability. A very high impermeable concrete will reduce or eliminate ingress of water and

other aggressive chemicals and gases. This will lead to improved concrete durability due to

avoided expansive reaction that can occur in presence of these aggressive agents. Various

theoretical and empirical models can be used to evaluate the effects of porosity on concrete

strength properties.

REFERENCES

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Aitcin, P.C., Sarkar, S.L., Regourd, M., and Hornain, H.(1987), "Microstructure of Two-Year-Old Very High Strength (100 MPa) Field Concrete," Proceedings of the Symposium on Utilization of High Strength Concrete, Tapir Publisher, Trondheim, Norway, 1987, pp. 99-109. Akyüz, S., Tasdemir, M. A., and Uyan, M. (1993), “Pore Effects on the Compressive Strength of Concrete,” Proceedings of the International Conference on Concrete 2000: Economic and Durable Construction Through Excellence, R. K. Dir. and M. R. Jones, eds., University of Dundee, Scotland, U.K., Vol. 2, September 7-9, pp. 1408-1416. Beffel, J. (1995), "Curing Temperature Effects on High-Performance Concrete," MS Thesis, University of Wisconsin-Milwaukee. Bentur, A., and Odler, I. (1996), “Development and Nature of Interfacial Microstructure,” RILEM Report 11: Interfacial Zone in Concrete, J. C. Mao, ed., E&FN SPON, London, England, U.K., First Edition, pp. 18-44. Bilodeau, A., Sivasundaram, V., Painter, K. E., and Malhotra, V. M. (1994), “Durability of Concrete Incorporating High Volumes of Fly Ash from Sources in the USA,” ACI Materials Journal, Vol. 91, No. 1, pp. 3-12. Brand, L. (1992), "Shear Strength of Reinforced Concrete Beams for High-Strength Concrete," MS Thesis, University of Wisconsin-Milwaukee. Brunauer, S. (1965), “The Structure of Hardened Portland Cement and Concrete,” Proceedings of the 8th Conference on the Silicate Industry, Budapest, Hungary, June 9-12, pp. 205-230, as reported by Massazza (1996).

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Costa, U., and Massazza, F. (1988), “Permeability and Pore Structure of Cement Pastes,” Proceedings of the Second International Conference on Engineering Materials, Bologna-Modena, Italy, June 19-23, as reported by Massazza (1996). De Larrand, F., Ithurralde, G., Acker, P., and Chavel, D. (1990), "High-Performance Concrete for a Nuclear Containment," Proceedings of the Second Symposium on High-Strength Concrete, SP-121, ACI, Detroit, MI, pp. 5549-5576. Gjorv, O.E. (1994), "High Strength Concrete," In Advances in Concrete Technology, V. M. Malhotra, Ed., CANMET, Ottawa, Canada, pp. 19-82. Krstic, V. D., and Erickson, W. H. (1987), “A Model for the Porosity: Dependence of Young’s Modulus in Brittle Solids Based on Crack Opening Displacement,” Journal of Materials Science, Vol. 22, pp. 2881-2886. Mackenzie, J. K. (1950), “The Elastic Constants of a Solid Containing Spherical Holes,” Proceedings of the Physics Society, December-January, pp. 2-11. Manmohan, D., and Mehta, P.K. (1981), "Influence of Pozzolanic Slag and Chemical Admixtures on Pore Size Distribution and Permeability of Hardened Cement Pastes," Cement, Concrete, and Aggregates, ASTM, Vol. 3, No. 1, 1981, pp. 63-67. Marsh, B.K., Day, R.L., and Bonner, D.G. (1985), "Pore Structure Characteristics Affecting the Permeability of Cement Paste Containing Fly Ash," International Journal of Cement and Concrete Research, Vol. 15, No. 6, Nov. 1985, pp. 1027 - 1038. Massazza, F. (1996), “Action of Environmental Conditions,” RILEM REPORT 11: Interfacial Transition Zone in Concrete, J. C. Maso, ed. E&FN SPON, London, England, U.K., First Edition, pp. 132-149. Mehta, P. K. (1986), Concrete Structures, Properties, and Materials, Prentice-Hall, Inc.,

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Eaglewood Cliff, New Jersey, 450 pages. Moukwa, M. (1993), "Durability of Silica Fume Concrete," In Progress in Cement and Concrete: Mineral Admixture in Cement and Concrete, S.N. Ghosh, et al., eds., ABI Books Pvt. Ltd., New Delhi, India, Vol. 4, pp. 467-493. Naik, T. R., Collins, W. C., Patel, V. M., and Tews, J.H. (1992), “Rapid Chloride Permeability of Concrete Containing Mineral Admixture,” Proceedings of the CBU/CANMET International Symposiums on the Use of Fly Ash, Silica Fume, Slag, and other By-Products in Concrete and Construction Materials, Milwaukee, WI, November 2-4. Naik, T. R., Singh, S. S., and Hossain, M. M. (1993), “Permeability of Concrete Incorporating Large Quantities of Fly Ash,” A final technical report prepared for Electric Power Research Institute, Palo Alto, CA. Naik, T.R., Olson, Jr, W.A., and Singh, S.S. (1994a), "Effects of Temperature on High-Performance Concrete," Presented and Preprint Published at the ACI 1994 International Conference Concrete, Singapore, November. Naik, T.R., Olson, Jr., W.A., and Singh, S.S. (1994b), "Effects of Temperature and Fly Ash on Compressive Strength and Permeability of HPC," Presented at the ACI 1994 International Conference on High Performance Concrete, Singapore, November. Naik, T.R., Olson, Jr., W.A., and Singh, S.S. (1994c), Chloride Permeability of Silica Fume Containing HPC, " Presented at the ACI 1994 International Conference on High Performance Concrete, Singapore, November. Naik, T. R., Singh, S. S., and Hossain, M. M. (1996), “Permeability of High-Strength Concrete Containing Low Cement Factor,” ASCE Journal of Energy Engineering, New York, NY, Vol. 122, No. 1, pp. 21-39.

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Olson, J., W.A. (1994), "Temperature Effects on the Permeability of High-Performance Concrete," MS Thesis, University of Wisconsin-Milwaukee. Ozyildirin, E. and Halstead, W. (1988), "Resistance to Chloride Ion Penetration of Concrete Containing Fly Ash, Silica Fume, or Slag," In Permeability of Concrete, ACI SP-108, Detroit Michigan, pp 35-62. Patel, V. (1992) "Full-Scale Beam Tests for Shear Strength of High-Strength Concrete," MS Thesis, University of Wisconsin-Milwaukee. Phani, K. K., and Niyogi, S. K. (1987), “Young Modulus of Porous Brittle Solids,” Journal of Materials Science, pp. 257-263. Powers, T. C., Copeland, L. E., and Mann, H.M. (1959), “Capillary Continuity or Discontinuity in Cement Pastes,” Journal of PCA Research and Development Laboratories, Skokie, IL, Vol. 1, No. 2, pp. 3-4. Powers, T. C., Copeland, L. E., and Hayes, J. C. (1954), “Permeability of Portland Cement Paste,” Journal of the American Concrete Institute, Proceedings, Detroit, MI, Vol. 26, No. 3, pp. 285-298. Roy, D.M., and Gouda, G.R. (1973), "Porosity-Strength Relation in Cementitious Materials with Very High Strengths," Journal of the American Ceramic Society, Vol. 56, No. 10, pp. 549-550. Scrivener, K. L., and Pratt, P. L. (1996), “Characterization of Interfacial Microstructure,” RILEM Report 11: Interfacial Zone in Concrete, J. C. Mao, ed. E&FN SPON, London, England, U.K., First Edition, pp. 1-17.

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Sereda, P.J., Feldman, R.F., and Ramachandran, V.S. (1980), "Structure Formation and Development in Hardened Cement Paste," Proceedings of the 7th International Congress on the Chemistry of Cement, Paris, France, pp. VI-1/3 to 1/44.

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Thomas, M.D.A., and Mathews, J.D. (1992), "The Permeability of Fly Ash Concrete," Materials and Structures, Paris, France, pp. 388-3960. Torri, K., and Kawamura, M. (1992) "Pore Structure and Chloride Permeability of Concrete Containing Fly Ash, Blast-Furnace Slag and Silica Fume," ACI Special Publication SP-132, Detroit, MI, pp. 135-150. Uchikawa, H., and Okanura, T. (1993), "Binary and Ternary Components Blended Cement," In Progress in Cement and Concrete: Mineral Admixtures in Cement and Concrete, S.N. Gosh, et al., Eds., Vol. 4, ABI Books Pvt., Ltd., New Delhi, India, pp. 1-83. Wang, J. C. (1984), “Young’s Modulus of Porous Materials: Part 2. Young’s Modulus of Porous Alumina with Changing Pore Structures,” Journal of Materials Science, Vol. 19, pp. 809-814. Young, J.F., "A Review of the Pore Structure of Cement Paste and Concrete and its Influence on Permeability," In Permeability of Concrete, D. Whiting and A. Walit, Eds., ACI SP-108, Detroit, MI, 1988, pp 1-18.

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