lecture 5 - willkommen an der fh münster€¦ · lecture 5 • intrinsic cracks early...

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Lecture 5 Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage Concrete corrosion/deterioration acid solution sulfate swell Statistic „light“ ⓒJMR 09 Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

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Page 1: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Lecture 5• Intrinsic cracks

early chemical/plastic shrinkagedrying shrinkagecarbonation shrinkage

• Concrete corrosion/deteriorationacid solutionsulfate swell

• Statistic „light“ⓒJMR 09Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Page 2: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

hydratization of cement

• In concrete with quartzitic aggregatesvolume changes can only happen in the cement paste

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 3: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

hydration of cement

hydratization of cement

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

plastic hardenedUnstable structure

Base structure Solid structure

Pore volume

Long fibre

Short fibre

Hydration time Minutes hours days

volume

Source: Zementtaschenbuch 2008

CSH =calcium-silicate-hydrates

ⓒJMR 09

Page 4: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

hydratization of clincergrain

Dry milled grain after watercontact fully hydrated

Source: Zementtaschenbuch 2008

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 5: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

hydratization of cement

Scanning electron microscope (SEM) picture 3 hours hydratization needles of primary CSH and

short columns of ettringitAssessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Source: Zementtaschenbuch 2008

Page 6: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

hydratization of cement

SEM 24 hours of hydratization CA(OH)2 CSH

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Source: Zementtaschenbuch 2008

Page 7: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

hydratization of cement

SEM 28 days of hydratization CA(OH)2 CSH

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Page 8: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Cement phases

SEM Ettringite-needles

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 9: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Volumes in hardened cement paste

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Source: Zementtaschenbuch 2008

Capillary voids

Solid cementpaste

airvoids

Unhydratedcement

Water/cement-ratio

Page 10: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Volume changes

• chemical volume decrease• Early“primary“capillary volume decrease

„plastic shrinkage“• Drying shrinkage• Carbonatization shrinkage

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 11: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Chemical Volume decrease

• Chemical connection of water to cementparticles decreases volume of cementpaste by 8% .

• As aggregates confine the deformationa linear shrinkage of concrete of -0,1Common Strength) up to -0,25 (highstrength) is the result

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Source: Zementtaschenbuch 2008

Page 12: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Early shrinkage

• Caused by capillary stresses(water absorbed by porous aggregates or evaporating water)

• Cracks after less than 24 hours• Without curing up to 4mm/m

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 13: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Typical crack pattern plastic shrinkage

ⓒJMR 09Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Initial movement

after few hours

Page 14: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Typical crack pattern plastic shrinkage

ⓒJMR 09Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Initial movement

after few hours

Page 15: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Early shrinkage

Surface of a oncrete parking slab day after concreting

Page 16: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Early shrinkage

Drilled cores from the parkdeck, cracks fom surface ending in the center

Page 17: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

What can you do against early shrinkage ?

Keep the water in the concrete

secondary compaction in plastic status (1….2 hours after mixing)

Page 18: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Shrinkage

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Cementclass climate

Chemical Shrinkage Drying shrinkage

Page 19: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Shrinkage

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Source: Zementtaschenbuch 2008

Total shrinkage for 2 concretes

Age in days

Drying at 80% RF from day 15

Cement type32,5R or 42,5 N

mm/m

FAQ: How big is the drying shrinkage for common concrete

Page 20: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Typical crack pattern (clay)

ⓒJMR 09Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Primary, secondary and tertiary crack systems

Page 21: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Deformation without confinement

confined

unconfined

Stress with confinement

Page 22: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Stress by confined deformation

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Rough stress/crack width estimation:0,4 mm/m total shrinkage, ultimate tensile deformation of concrete 0,1…0,2 mm/mcalculated with Hooke equation σ=εE E ca 30.000MPa

σ=0,2x10-3x 30.000 Mpa = 6 MpaThis exceeds the tensile strength of normal concreteand leads to crackscracks release the stress, crack width = shrinkage deformation

confined

Page 23: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Typical crack pattern (clay)

ⓒJMR 09Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Confined deformation (here by friction) lead to stress

Omnidirectional stresses lead to „craquelee pattern“

Page 24: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Typical crack pattern (asphalt)

ⓒJMR 09Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

p

st

Page 25: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Typical crack pattern drying shrinkage

ⓒJMR 09Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Page 26: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Shrinkage cracks in concrete

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 27: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Weakest lineShrinkage causes cracking

Page 28: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

ⓒJMR 09Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

What can you do against drying shrinkage?Nothing, it will happen!Which structures are effected, how to avoid these cracks?Critical are geometric forms witha big surface:Roads, foundation slabs, storey slabs

Page 29: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Which structures are effected, how to avoid these cracks?

W/C > 0.4 is commonly usedW/C 0.2 is chemically needed,

there is enough water, ifthere is no evaporation.Reduce evaporation by -paraffinspray „antisol“ (used on concrete roads)-cover with polymer foil-cure with waterspray

Page 30: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Joints to avoid cracks

• Roads in Germanyno reinforcement, joints cut at 5m distance with steel bar „dowel shift elements“

Cuts made after 6 to 20 hours after placing the concrete to enforce cracking at this place

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 31: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Joints to avoid cracks

• Joint distance 4 to 6 m

Concrete wall on thickfoundation concrete slab(perfect confinement at wall toe)

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 32: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Stress by hydratization temperature rise

Concrete temperature

stress

Fully confinedAssessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

compressiontension

ca 15K

crack

hours

time

Page 33: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Avoid thermal cracks

Page 34: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Avoid thermal cracks

Page 35: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Avoid thermal cracks

Page 36: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Avoid thermal cracks

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

To get the settlement before connecting tubes to container, container was filled with water (T ca 12 C)

Page 37: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Cooling by coldwater, if T-difference >15K

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Avoid thermal cracks

Page 38: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Avoid thermal cracksThermal expansion of roof

Page 39: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Avoid thermal cracks

Thermal expansion of roof shifts the walls

Page 40: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Avoid thermal cracks, but there isalso a defect sewage piping

Page 41: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Lecture 5 Conclusion• Cement hydratization causes volume

decrease (early plastic shrinkage)• Water evaporation of concrete causes

drying shrinkage• Hydratization increases temperature of

concrete, temperature differences cause deformation

• Confined deformation create stress and cracks

ⓒJMR 09Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Page 42: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Concrete Corrosion/deterioration1 Solution of cement paste by acids2 Swelling by sulfates, reacting with alkalines

(Ca(OH)2 +SO4-- >CaSO4

Gipsum: CaSO4 x 2 H2OEttringite: CaSO4 x 16 H2O Thaumasite: CaSO4 x 32 H2O Cristals in voids/pores expand> tensile failureof hardened cement paste

3 Aggregate-alkali-reaction (only with amorphous silicium acid SiO2)Carbonatisation is no corrosion/deterioration!!

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 43: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Concrete Deterioration

• Concrete Deterioration is in humid climates not the main reason for reinforced concrete problems

• Concrete Corrosion may be relevant for foundations (acids or sulfate in soil)or in wastewater collecting pipes with microbial amplification of chemical attack

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 44: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Sulfate attack, type of degradation

Sewagewater

Concrepipe

Sulfobacter create a lower pH-value(higher concentration)than sewage water

Sulfates react with alcaline parts of cement pastecreating more volume

Page 45: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Sulfate attack, solutions

Sewagewater

Concretepipe

Low alcali, high sulfate resistant cement (NA, HS)

pozzolans need CaOH2

Page 46: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Clinker content of Cement EN197

Portland cement CEM I >95%

Composite cement CEM II >65%

Composite cement CEM III >15%low heat, low alcali, high sulfate resistance

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 47: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Pozzolanic reaction

Blast furnace slag

Clinker

Fly ashMikrosilicaTrass Limestone-

Quartz-flour

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Hydrauliclime

Page 48: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Filler functionFly ash av. size 10..30µm,Blaine 6200cm2/gmicrosilica av. size 1..3µm,Blaine 2200.000cm2/g

Page 49: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Concrete Corrosion Situation Riyadh / Jeddah

• The climate is too dry for carbonatisation (above soil)

• Main problem: sulfate salt creating swelling new minerals:„ettringite, the concrete cancer“increasing salt concentration by evaporation

ⓒJMR 09Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Page 50: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

What is the water consumption of Riyadh?How many cars can pass a bridge?how many people a Airbus 380 can carry?Each German drinks 80 l coffee per year!A car in Germany rides 13.000 km/year!What is the concrete strength of Gammarat bridge?How can you know?

By representative samples and

Page 51: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Statistic fast food: normal distribution, mean, std.deviation

ⓒJMR 09Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009

Page 52: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Statistic fast food: same average, different std dev

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Page 53: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Statistic fast food: how to calculate a Quantile/Fractile

Q%= mean ± k std. deviationk for large number, 5%=1.645,single sided only –ks

fc,5% = 24-1.645×3.21 =18.72 MPa

FAQ: How calculate a Quantil?

Page 54: Lecture 5 - Willkommen an der FH Münster€¦ · Lecture 5 • Intrinsic cracks early chemical/plastic shrinkage drying shrinkage carbonation shrinkage ... -->CaSO 4 Gipsum: CaSO

Assessment and Repair of Concrete structures Riyadh,Jeddah.Tabouk, may 2009 ⓒJMR 09

Statistic fast food: same quantile, different mean&std dev

5%-Quantile means 5% of production may be worse