lecture 6. cement - aalto · lecture 6. cement ... usually measured indirectly by measuring the...

CIV-E1010 Building Materials Technology (5 cr) (1/17)

Lecture 6. Cement

Prepared by:Fahim Al-Neshawy, D.Sc. (Tech.)Aalto University School of EngineeringDepartment of Civil EngineeringA: P.O.Box 12100, FIN-00076 Aalto, Finland


Table of ContentsLecture 6. Cement ...................................................................................................................................... 1

6.1 Cement history ................................................................................................................................. 3

6.2 Portland cement production ........................................................................................................... 3

6.2.1 Raw materials: .......................................................................................................................... 3

6.2.2 Manufacturing process: ........................................................................................................... 4

6.3 Chemical compounds of Portland cement ..................................................................................... 6

6.4 Fineness of Portland cement .......................................................................................................... 7

6.5 Specific gravity of Portland cement ................................................................................................ 8

6.6 Hydration of Portland cement ........................................................................................................ 9

6.6.1 Structure development in cement paste.............................................................................. 10

6.6.2 Voids in hydrated cement ..................................................................................................... 11

6.6.3 Properties of hydrated cement ............................................................................................. 13

6.7 Cement types and Finnish cements.............................................................................................. 15


6.1 Cement history (1)

Throughout history, cementing materials have played a vital role and were used widely in the ancientworld.

· Lime and clay have been used as cementing material on constructions through manycenturies.

· Romans are commonly given the credit for the development of hydraulic cement, the mostsignificant incorporation of the Roman’s was the use of pozzolan-lime cement by mixingvolcanic ash from the Mt. Vesuvius with lime. Best known surviving example is the Pantheon inRome

· In 1824 Joseph Aspdin from England invented the Portland cement named after the limestonecliffs on the Isle of Portland in England

· The development of the rotary kiln in the late-1900’s and subsequent replacement of statickilns - allowed cement manufacture to become a continuous rather than a batch process

· Portland cement today, as in Aspdin’s time, is a pre-determined and carefully measuredchemical combination of calcium, silica, iron and aluminium, yielded by a complexmanufacturing process, subject to rigorous control and involving a wide range of operations.

· Most recently – the cement industry has focused a good deal of attention on reducing theenvironmental impact of cement production – particularly carbon-dioxide production

6.2 Portland cement production

Cement is the hydraulic binder (hydraulic = hardening when combined with water) which is used toproduce concrete. Cement paste (cement mixed with water) sets and hardens by hydration, both inair and under water. The main base materials for Portland cement, are limestone, marl and clay,which are mixed in defined proportions. This raw mix is burned at about 1450 °C to form clinker whichis later ground to the well-known fineness of cement.

6.2.1 Raw materials:

Table 1. The fundamental chemical compounds to produce cement clinker.

ChemicalComponents Typical Raw Materials Formula Shorthand form % by weight

Lime or Calciumoxide

Limestone (CaCO3), chalk,shells, shale or calcareous

rockCaO C 60 – 67%

Silica sand(SiO2), shale, clay orargillaceous rock SiO2 S 17 – 25%

1 Cement history. Online at: http://www.understanding-cement.com/history.html


Aluminabauxite, recycled

aluminum,clay

Al2O3 A 3 - 8%

Iron clay, iron ore, scrap ironand fly ash

Fe2O3 F 0.5 – 6.0%

SulfateGypsum, CaSO4.2H20found together with

limestoneSO3 Ŝ 0.5 – 1.3%

Water H2O H

6.2.2 Manufacturing process:

Manufacturing process of cement include three steps:

1. Mixing and crushing of raw materialsa. Dry processb. Wet process

2. Burning3. Grinding

(1.a) Mixing and crushing of raw materials - Dry process:

· In the dry process calcareous material such as lime stone (calcium carbonate) and argillaceousmaterial such as clay are ground separately to fine powder in the absence of water and thenare mixed together in the desired proportions.

· Water is then added to it for getting thick paste and then its cakes are formed, dried and burntin kilns.

· Dry process is usually used when raw materials are very strong and hard.· In the dry process, the raw materials are changed to powdered form in the absence of water.· About 75% of cement is produced using the dry process

(1.b) Mixing and crushing of raw materials - Wet process:

· In the wet process, the raw materials are changed to powdered form in the presence of water.· Raw materials are pulverized by using a Ball mill, which is a rotary steel cylinder with hardened

steel balls. When the mill rotates, steel balls pulverize the raw materials which form slurry(liquid mixture). The slurry is then passed into storage tanks, where correct proportioning isdone.

· Proper composition of raw materials can be ensured by using wet process than dry process.Corrected slurry is then fed into rotary kiln for burning.

· Wet process is generally used when raw materials are soft because complete mixing is notpossible unless water is added.

· About 25% of cement is produced using the dry process.


Figure 1. Typical steps of the Portland cement manufacturing process (2).

2 Michael S. Mamlouk and John P. Zaniewski, (2011). Materials for Civil and Construction Engineers, 3rd Edition: Chapter 6- PORTLAND CEMENT, MIXING WATER, AND ADMIXTURES


(2) Burning:

Corrected slurry is feed to rotary kiln, which is about 1.5 m in diameter and 15 m in length andtemperature arrangement is up to 1500-1650 οC. At this temperature slurry losses moisture andforms into small lumps, after that changes to clinkers. Clinkers are cooled in another inclined tubesimilar to kiln but of lesser length

(3) Grinding:

Grinding is the final process where clinker is grinded, it is first cooled down to atmospherictemperature. Grinding of clinker is done in large tube mills. After proper grinding gypsum (Calciumsulphate Ca SO4) in the ratio of 01-04 % is added for controlling the setting time of cement.

Finally, fine ground cement is stored in storage tanks from where it is drawn for packing.

6.3 Chemical compounds of Portland cement

The proportions of the chemical compounds of cement vary in the various Portland cements. Table 2presents the composition and percentage of found compounds for Portland cement.

Table 2. Chemical compounds of cement clinker.

Compound Formula Shorthandform

% byweight Properties of cement compounds

Alite or tricalciumsilicate Ca3SiO4 C3S 50 - 70%

· C3S Hardens rapidly and largely responsible forinitial set & early strength

· The increase in percentage of C3S compoundwill cause the early strength of Portland cementto be higher.

· A bigger percentage of C3S compound willproduces higher heat of hydration and accountsfor faster gain in strength.

Belite ordicalcium silicate Ca2SiO5 C2S 15 - 30%

· C2S hydrates and hardens slowly.· It is largely responsible for strength gain after

one week.· Responsible for long term strength

Tricalciumaluminate Ca3Al2O6 C3A 5 - 10%

· C3A is the first compound to hydrate· C3A liberates a lot of heat during the early

stages of hydration, but has little strengthcontribution.

· Gypsum slows down the hydration rate of C3A.· Cement low in C3A is sulfate resistant.

Tetracalciumaluminoferrite Ca4Al2Fe2O10 C4AF 5-15%

· Assist in the manufacture of Portland Cementby allowing lower clinkering temperature.

· Also act as a filler· Contributes very little strength of concrete

even though it hydrates very rapidly.· Also responsible for grey colour of Ordinary

Portland Cement


Sodium oxide Na2O N0.5 - 1.3%

Potassium oxide K2O KGypsum CaSO4.2H2O CSH2

6.4 Fineness of Portland cement

o Most of the cement particles have a size of between 2 and 80 μm.o The surface area per unit weight values of most cements in common use range from

about 300 to 400 m2/kg.o The fineness of cement affects the rate of hydration and thus the rate of strength gaino Greater fineness increases the surface available for hydration, causing greater early

strength and more rapid generation of heato The coarser cement will result in higher ultimate strength and lower early strength gain

of mortar

Fineness of cement is usually measured indirectly by measuring the surface area with the Blaine airpermeability apparatus (ASTM C204) or the Wagner turbidimeter apparatus (ASTM C115).

Figure 2. Blaine test apparatus (3).

In the Blaine test (Figure 2), the surface area of the cement particles in is determined by measuringthe air permeability of a cement sample and relating it to the air permeability of a standard material.The Wagner turbidimeter determines the surface area by measuring the rate of sedimentation of

3 http://www.thecementgrindingoffice.com/blaine.html


cement suspended in kerosene. The finer the cement particles, the slower the sedimentation. Boththe Blaine and Wagner tests are indirect measurements of surface area and use somewhat differentmeasurement principles. Therefore, tests on a single sample of cement will produce different results.Fineness can also be measured by determining the percent passing the 0.045 mm sieve (No. 325)(ASTM C430).

Principle of the Blaine method:

· The principle of air permeability method is to determine the time taken for a fixed quantity ofair to flow through a compacted cement bed of specified dimension and porosity.

· Under standard conditions, the specific surface area of cement is proportional to the squareroot of time T.

· Where T is the time for given quantity of air to flow through the compacted cement bed.· The number and size range of individual pores in the specified bed are determined by the

cement particle size distribution, which also determined the time for the specified air flow.· This method is comparative and therefore a reference sample of known specific surface area is

required to calibrate the apparatus.

6.5 Specific gravity of Portland cement

Specific gravity: the specific gravity of Portland cement is generally around 3.15.

The specific gravity is defined as the ratio between the weight of a given volume of material andweight of an equal volume of water. To determine the specific gravity of cement, kerosene whichdoes not recent with cement is used.

Figure 3. Apparatus of measuring the specific gravity of Portland cement - Le Chaterlier”s flask andkerosene (free from water).

· Le Chaterlier”s flask, is made of thin glass having a bulb at the bottom. The capacity of thebulb is nearly 250 ml. The bulb is 7.8 cm in mean diameter. The stem is graduated inmillimeters.


· Test procedure:(i) The flask is dried carefully and filled with kerosene or naphtha to a point on the stem

between zero and 1 ml.(ii) The level of the liquid in the flask is record as initial reading (V1, ml).

(iii) A weighted quantity of cement (W = about 60 gm) is placed into the flask so that levelof kerosene rise to about 22 ml mark, care being taken to avoid splashing and to seethat cement does not adhere to the sides of the above the liquid.

(iv) After placing all the cement to the flask, roll the flask gently in an inclined position toexpel air until no further air bubble rises to the surface of the liquid.

(v) The new liquid level is marked as final reading (V2, ml).

6.6 Hydration of Portland cement

Hydration is the general term used to describe the chemical reaction that takes place betweencement powder and water.

Figure 4. Hydration of Portland cement (4).

The cement hydration stages as shown in Figure 4 are:

Stage 1:

o Heat of wetting or initial hydrolysis C3A and C3S Hydration.

4 http://matse1.matse.illinois.edu/concrete/prin.html

ℎ = −

ℎ = ( − ) ℎ

=ℎ

ℎ = −

(1)


o 7 to 15 min after mixing.o Stage 1 is brief because of the rapid formation of an amorphous layer of hydration product

around the cement particles, which separates them from the pore solution and preventsfurther rapid dissolution.

Stage 2:

o Dormant (induction) period related to initial set.o is a 1-2 hour period of inactivity that separates the initial short breakout of reaction that

occurs when cement and water first come into contact from the main hydration period thatleads to set

o During this period, the concrete is in a plastic state which allows the concrete to betransported and placed without any major difficulty.

Stage 3:

o Accelerated reaction of the hydration products.o That determine the rate of hardening and final set.

Stage 4:

o Decelerates formation of hydration products and determines the rate of early strength gain.o Completely diffusion dependent reaction

Stage 5:

o Steady state - constant rate of reaction (12-24 hours) - steady formation of hydrationproducts.

o Temperature has little effect on hydration at this point

6.6.1 Structure development in cement paste

The sequential development of the structure in a cement paste is summarized in Table 3.

a) The process begins immediately after water is added to the cement.b) In less than 10 minutes, the water becomes highly alkaline. As the cement particles hydrate,

the volume of the cement particle reduces, increasing the space between the particles. Duringthe early stages of hydration, weak bonds can form, particularly from the hydrated.

c) Further hydration stiffens the mix and begins locking the structure of the material in place.d) Final set occurs when the C-S-H phase has developed a rigid structure, all components of the

paste lock into place and the spacing between grains increases as the grains are consumed byhydration

e) The cement paste continues hardening and gains strength as hydration continues Hardeningdevelops rapidly at early ages and continues, as long as unhydrated cement particles and freewater exist. However, the rate of hardening decreases with time.


Table 3. Development of structure in the cement paste (2).

Phase Phase name Description

(a) Initial C-S-Hphase

The C - S -H phase is initially formed.C3A forms a gel fastest.

(b)Forming ofgels

The volume of cement grain decreases asa gel forms at the surface.Cement grains are still able to moveindependently, but as hydration grows,weak interlocking begins.Part of the cement is in a thixotropicstate; vibration can break the weakbonds.

(c)

Initial set—developmentof weakskeleton

The initial set occurs with thedevelopment of a weak skeleton inwhich cement grains are held in place.

(d)

Final set—developmentof rigidskeleton

Final set occurs as the skeleton becomesrigid, cement particles are locked inplace, and spacing between cementgrains increases due to the volumereduction of the grains.

(e) Hardening.Spaces between the cement grains arefilled with hydration products as cementpaste develops strength and durability.

6.6.2 Voids in hydrated cement

Due to the random growth of the crystals and the different types of crystals, voids are left in the pastestructure as the cement hydrates. Concrete strength, durability, and volume stability are greatlyinfluenced by voids. Two types of voids are formed during hydration:


a) the interlayer hydration space,b) capillary voids.

Figure 5. Simplified scheme of hydrated cement paste microstructure.

Interlayer hydration space

o Interlayer hydration space occurs between the layers in the C-S-H.o The space thickness is between 0.5 nm and 2.5 nm, which is too small to affect the strength.o It can contribute 28% to the porosity of the paste.o Water in the interparticle space is strongly held by hydrogen bonds, but can be removed when

humidity is less than 11%, resulting in considerable shrinkage.o The finest pores, ranging from approximately 10 nm to 0.5nm, are called gel pores since they

constitute the internal porosity of the C-S-H gel phase

Capillary voids

o Capillary voids are the result of the hydrated cement paste having a lower bulk specific gravitythan the cement particles.

o The amount and size of capillary voids depends on the initial separation of the cementparticles, which is largely controlled by the ratio of water to cement paste.


o For a highly hydrated cement paste in which a minimum amount of water was used, thecapillary voids will be on the order of 10 nm to 50 nm.

o A poorly hydrated cement produced with excess water can have capillary voids on the order of3 μm to 5 μm

o Capillary voids greater than 50 nm decrease strength and increase permeability.o Removal of water from capillary voids greater than 50 nm does not cause shrinkage, whereas

removal of water from the smaller voids causes shrinkage.

Trapped air (Air vopids)

o In addition to the interlayer space and capillary voids, air can be trapped in the cement pasteduring mixing.

o The trapped air reduces strength and increases permeability.o However, well-distributed, minute air bubbles can greatly increase the durability of the

cement paste.o Admixtures are widely used to entrain air into the cement paste.

6.6.3 Properties of hydrated cement

Properties of the hydrated cement are evaluated with either cement paste (water and cement) ormortar (paste and sand).

6.6.3.1 Setting

Setting refers to the stiffening of the cement paste or the change from a plastic state to a solid state.Setting is usually described by two levels: initial set and final set. The initial and final sets are based onmeasurements by either the Vicat apparatus or the Gillmore needles, see Figure 6.

The Vicat test (Figure 6 a)

· Requires that a sample of cement paste be prepared, using the amount of water required fornormal consistency according to a specified procedure.

· The 1 mm diameter needle is allowed to penetrate the paste for 30 seconds and the amountof penetration is measured.

· The penetration process is repeated every 15 minutes (every 10 minutes for Type III cement)until a penetration of 25 mm or less is obtained.

· By interpolation, the time when a penetration of 25 mm occurs is determined and recorded asthe initial set time.

· The final set time is when the needle does not penetrate visibly into the paste.· The initial setting time given by Vicat needle for Portland cement ≥ 45 minutes· The final setting time given by Vicat needle for Portland cement ≤ 375 minutes· The Vicat needle test is more common and tends to give shorter times than the Gillmore

needle test.


The Gillmore test (Figure 6 b)

· Requires that a sample of cement paste of normal consistency be prepared.· A pat with a flat top is molded, and the initial Gillmore needle is applied lightly to its surface.· The application process is repeated until the pat stand the force of the needle without

appreciable indentation (hole), and the elapsed time is recorded as the initial set time.· This process is then repeated with the final Gillmore needle and the final set time is recorded.· The initial setting time given by Gillmore needle for Portland cement ≥ 60 minutes· The final setting time given by Gillmore needle for Portland cement ≤ 600 minutes

Due to the differences in the test apparatuses and procedures, the Vicat and Gillmore tests producedifferent results for a single sample of material.

Figure 6. Measuring cement setting times. a) Vicat set time apparatus and b) Gillmore set timeapparatus.


6.6.3.2 Soundness

· Soundness of the cement paste refers to itsability to retain its volume after setting.

· Expansion after setting, caused by delayed orslow hydration or other reactions, could resultif the cement is unsound.

· The autoclave expansion test (Figure 6.7) isused to check the soundness of the cementpaste.

· In this test, cement paste bars are subjected toheat and high pressure, and the amount ofexpansion is measured. ASTM C150 limitsautoclave expansion to 0.8%.

Figure 7. Cement autoclave expansionapparatus.

6.6.3.3 Compressive strength of mortar

Compressive strength of mortar is measured by preparing 50-mm cubes and subjecting them tocompression. The mortar is prepared with cement, water, and standard sand. Minimum compressivestrength values are specified by ASTM C150 for different cement types at different ages. Thecompressive strength of mortar cubes is proportional to the compressive strength of concretecylinders. However, the compressive strength of the concrete cannot be predicted accurately frommortar cube strength, since the concrete strength is also affected by the aggregate characteristics, theconcrete mixing, and the construction procedures.

6.7 Cement types and Finnish cements

In Europe, cements are covered by the standard EN 197-1 (composition, specifications and conformitycriteria) (5). The standard divides the common cements into 5 main types (6), as follows:

Table 4. Designation, notation, ans composition of main types of common cement (EN 197-1).

Notation Type Composition (%, by mass)Clinker (%) Other main constituent rather than clinker

CEM I Portland cement 95 - 100 -

CEM II Portland Compositecements 65-94 Up to 35% of an addition (different sub-classification,

see Table 6CEM III Blast furnace cement 5-64 36 – 95% blast furnace slag

CEM IV Pozzolan cement 45-89 11 – 65% of pozzolanic materials (of one type ormixture of several types)

CEM V Composite cement 20-64 Mixture of: 18 - 50% of blast furnace slag and 18 – 50%of natural pozzolan and/or fly ash.

5 EN 197-1: Cement. Composition, specifications and conformity criteria for common cements6 http://www.finnsementti.fi/en/cement/quality/cement-standard


In accordance with EN 197-1, cement is also categorized by strength class as well as cement type, andthese categories are shown in Table 5, where there are minimum limits to early-age strength andlimits for 28-day strength.

Table 5. Requirements for standard strength and early strength

Strengthclass

Compressive strength [MPa]Initial setting time

[min]Early strength Standard strength2 days 7 days 28 days

32,5 N - ≤16,0 ≥ 32,5 ≤ 52,5 ≥ 7532,5 R ≥ 10,0 -42,5 N ≥ 10,0 -

≥ 42,5 ≤ 62,5 ≥ 6042,5 R ≥ 20,0 -52,5 N ≥ 20,0 -

≥ 52,5 - ≥ 4552,5 R ≥ 30,0 -

Table 6. Common cement products according to EN 197-1:2000

1 The silica dust content is limited to 10 %.2 Total organic carbon (TOC) must not exceed 0.2 % by weight.3 Total organic carbon (TOC) must not exceed 0.5 % by weight.

Natural Artificial Highsilica

Highlime

K S D1 P Q V W T L2 LL3

CEM I Portland cement CEM I 95-100 - - - - - - - - - 0-5CEM II/A-S 80-94 6-20 - - - - - - - - 0-5CEM II/B-S 65-79 21-35 - - - - - - - - 0-5

Portland silicadust cement

CEM II/A-D 90-94 - 6-10 - - - - - - - 0-5

CEM II/A-P 80-94 - - 6-20 - - - - - - 0-5CEM II/B-P 65-79 - - 21-35 - - - - - - 0-5CEM II/A-Q 80-94 - - - 6-20 - - - - - 0-5CEM II/B-Q 65-79 - - - 21-35 - - - - - 0-5CEM II/A-V 80-94 - - - - 6-20 - - - - 0-5CEM II/B-V 65-79 - - - - 21-35 - - - - 0-5CEM II/A-W 80-94 - - - - - 6-20 - - - 0-5CEM II/B-W 65-79 - - - - - 21-35 - - - 0-5CEM II/A-T 80-94 - - - - - - 6-20 - - 0-5CEM II/B-T 65-79 - - - - - - 21-35 - - 0-5CEM II/A-L 80-94 - - - - - - - 6-20 - 0-5CEM II/B-L 65-79 - - - - - - - 21-35 - 0-5CEM II/A-LL 80-94 - - - - - - - - 6-20 0-5CEM II/B-LL 65-79 - - - - - - - - 21-35 0-5CEM II/A-M 80-94 0-5

CEM II/B-M 65-79 0-5CEM III/A 35-64 36-65 - - - - - - - - 0-5CEM III/B 20-34 66-80 - - - - - - - - 0-5CEM III/C 5-19 81-95 - - - - - - - - 0-5CEM IV/A 65-89 - - - - 0-5CEM IV/B 45-64 - - - - 0-5CEM V/A 40-64 18-30 - - - - - 0-5CEM V/B 20-39 31-50 - - - - - 0-5

Blast furnacecement

Pozzolancement

Maincementtype

CEM III

CEM IV

CEM V Compositecement

Designation

Portland slagcement

CEM II

Portlandpozzolan cement

Portland fly ashcement

Portland shalecement

Portlandlimestonecement

Portlandcomposite cem.

< -------------------------------------- 6-20 ---------------------------------------->

< -------------------------------------- 21-35 --------------------------------------->

11-3536-5518-3031-50

Cementtype

Major components

Minor

components

Portlandcementclinker

Slag Silicadust

Pozzolanes Fly ashes Burntshale

Limestone


Table 7. Example of the cement naming according to the cement standard SFS-EN 197-1(7).

CEM II/A-LL 42,5 RCEM II A-LL 42,5 R

Cement notation “Type: PortlandComposite Cement”, see Table 4

Main additive of Portland limestonecement is limestone (code LL) a total

of 6–20% (code A), see Table 6.

standard strength ≥ 42.5 MPa and ≤62.5 MPa early strength 2d ≥ 20 MPa,

see Table 5

Finnsementti Oy (8) is a Finnish cement manufacturer since year 1914. Most of the cement needed inFinland is manufactured in Finnsementti’s works in Parainen and Lappeenranta. Finnsementti’scement assortment includes Plus cement, Yleis-(general) cement, Rapid cement, Pika-(quick) cement,Mega cement, SR cement, and Valko-(white) cement.

Plus cement: Normally hardening Portland composite cement, CEM II/B-M (SLL) 42,5N. Plus cement isused in general construction purposes (most buildings, bridges, pavements, precast units, etc). Pluscement includes 15 - 25 % blast furnace slag.

Yleis (General) cement: Normally hardening Portland composite cement, CEM II A-M (SLL) 42,5N.Yleis (General) cement is also used for all general construction purposes. Yleis (General) cementincludes 3 – 14 % blast furnace slag.

Rapid cement: Rapidly hardening Portland composite cement CEM II/A-LL 42,5R. The hardening ratedepends of the cement fineness. The rapid cement is used in rapid construction, cold weatherconcreting and precast concreting. The Rapid cement includes 0 - 5 % blast furnace slag.

Pika (Quick) cement: Very fast hardening Portland cement CEM I 52,5R. Pika-cement is used in rapidconstruction when the form work is removed quickly. Pika-cement is also used for high and ultra-highstrength concretes.

Mega-cement: Fast hardening Portland cement CEM I 42,5R. Mega cement is used in ready mixedconcrete productions and the industrial pre-cast concrete productions.

SR-cement: Sulfate resistance Portland cement CEM I 42,5N SR3. SR-cement is used in structuresexposed to high levels of sulfate ions as: harbors constructions, waste water systems, dams,underground water pipes, foundations, sewers, irrigation canals and treatment plants. it isappropriate cement for using at the structures that require resistance against chemical effects such assea water and sulfate environments

Valko (white) cement: White cement is normally hardening Portland cement CEM I 52,5R. Whitecement is used in architectural works requiring great brightness and artistic finishes, to createmosaics and artificial granite, and for sculptural casts and other applications where white prevails.

7 SFS-EN 197-1 Sementti. Osa 1: Tavallisten sementtien koostumus, laatuvaatimukset ja vaatimustenmukaisuus8 Finnsementti Oy In Englis - http://www.finnsementti.fi/en

lecture 6. cement - aalto · lecture 6. cement ... usually measured indirectly by measuring the...

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