![Page 1: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/1.jpg)
Kevin MacDonald, P.E., PhD, FACIMary Vancura, P.E., PhD
Beton Consulting Engineerswww.betonconsultingeng.com
1
![Page 2: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/2.jpg)
2
![Page 3: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/3.jpg)
Corrosion Prevention is Easy a. To prevent corrosion:
Change the material Change the environment Isolate the material and the environment
If these don’t work, see a.
3
![Page 4: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/4.jpg)
![Page 5: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/5.jpg)
5
![Page 6: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/6.jpg)
But will it be durable?
6
![Page 7: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/7.jpg)
Sometimes it is and sometimes its not…..
7
![Page 8: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/8.jpg)
Pantheon
8
![Page 9: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/9.jpg)
9
![Page 10: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/10.jpg)
![Page 11: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/11.jpg)
![Page 12: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/12.jpg)
![Page 13: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/13.jpg)
13
![Page 14: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/14.jpg)
Current Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water-cementitious material ratio—
0.45 Slump Aggregates are sound, clean, durable, and well
graded Adequate air void system for freeze-thaw
climates Proper proportioning, mixing, placing, finishing,
and curing
14
![Page 15: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/15.jpg)
15
![Page 16: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/16.jpg)
Column on Gardiner Expressway 1992 MacDonald
16
![Page 17: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/17.jpg)
17
![Page 18: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/18.jpg)
Evolution of Structural Engineering Elasticity
Plasticity
Finite Element
18
![Page 19: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/19.jpg)
What is lifetime? Until the chloride threshold is reached? (0.2% weight
of cement a commonly used value) Until corrosion potential indicates corrosion Until Staining? Cracking? Spalling? Collapse due to loss of section?
19
![Page 20: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/20.jpg)
Tutti Model
20
![Page 21: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/21.jpg)
Fick’s Law Type Diffusion
erfc(x) = 1-erf(x)
21
![Page 22: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/22.jpg)
Clear Cover
Sorption ZoneDiffusion Zone
22
![Page 23: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/23.jpg)
Clear Cover
Sorption ZoneDiffusion Zone
23
![Page 24: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/24.jpg)
Cracking Restrained shrinkage Loading
Shrinkage is a function of aggregate stiffness and water content (NOT w/cm)
0.04 – low shrinkage ASTM C157 – approximately 250 lb / yd3
Model needs to take into account the probability of cracking and related damage
24
![Page 25: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/25.jpg)
Correcting for Cracks Pacheco, CTL Group
𝐷𝐷𝑐𝑐𝑐𝑐 = 𝐷𝐷01− 𝑤𝑤
𝑤𝑤𝑙𝑙𝑙𝑙𝑙𝑙
MacDonald, 2003𝐷𝐷𝑐𝑐𝑐𝑐 = 𝐷𝐷0 + 𝑤𝑤𝑙𝑙𝑙𝑙𝑛𝑛𝐷𝐷0
Where w = crack width, n is a function of binder composition, l is the specific length of crack in m/m2
25
![Page 26: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/26.jpg)
A. Djerbi et al. / Cement and Concrete Research 38 (2008) 877–883 26
![Page 27: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/27.jpg)
Reliability
Strength analogy
A probability of failure has to be tolerated 10 percent is normal in Concrete Design
27
![Page 28: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/28.jpg)
Reliability Pr = Ps + βσ Ps is the specified design value Pr is the trial batch mean value required, β is the reliability factor and σ the standard deviation. The reliability factor is negative where failure is a
higher than specified value (such as water:cementratio) and positive when failure is a lower than specified value (such as strength).
28
![Page 29: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/29.jpg)
Modifying the EnvironmentControlling mass transfer
Sorption Diffusion (pore size and number) Cracking
This is done with mix design and a focus on tests other than slump, air, and freeze/thaw testing. RCP tests are marginal Diffusion Coefficient (ASTM C1556, NTBuild 492) Bulk Conductivity (Resistivity (ASTM C1760)
29
![Page 30: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/30.jpg)
Concrete Mixture Modification to get Desired Diffusion Properties Ternary Blends can give strength and high resistance
to penetration Mix 1 100% OPC Mix 2 40% Cement, 42% Slag, 18% Ash Mix 3 15% Cement, 67%Slag, 18% Ash
30
![Page 31: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/31.jpg)
Mixture Proportioning and Adjustment
31
![Page 32: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/32.jpg)
32
![Page 33: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/33.jpg)
5000 psi SCC w 40 percent OPC
6500 psi concrete 70 percent OPC
4000 psi concrete 18 percent OPC
5000 psi SCC w 40 percent OPC
33
![Page 34: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/34.jpg)
0
2000
4000
6000
8000
10000
12000
0 20 40 60 80 100
Strength,
psi
Time, Days
Footing
Shaft
Pier
Superstructure
34
![Page 35: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/35.jpg)
D = 8100 k - 9.2R² = 0.843
0
20
40
60
80
100
120
140
160
180
0 0.005 0.01 0.015 0.02 0.025
D, x
10-1
3 m
2 /se
c
Conductivity, ohms-1 m-1
MacDonald 199735
![Page 36: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/36.jpg)
Decay values – measurement f ’c 𝑡𝑡2 = f ′c(𝑡𝑡𝑙) 𝑡𝑡1
𝑡𝑡2
𝑚𝑚
𝐷𝐷 𝑡𝑡2 = 𝐷𝐷(𝑡𝑡𝑙) 𝑡𝑡1𝑡𝑡2
𝑚𝑚
k 𝑡𝑡2 = k(𝑡𝑡𝑙) 𝑡𝑡1𝑡𝑡2
𝑚𝑚
It’s the same m value, as it is a result of the reduction in porosity with hydration.
36
![Page 37: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/37.jpg)
Prescription vs. Performance US lagging behind Europe / Canada in code
development I.e. CSA A23.1 class C1 exposure Economic advantage of “how” is removed Innovation is stifled Often meeting the prescription can result in
undesirable, unintended consequences
37
![Page 38: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/38.jpg)
ACI-318-14
38
![Page 39: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/39.jpg)
Clear Cover
Sorption ZoneDiffusion Zone
39
![Page 40: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/40.jpg)
ACI 365.1R (2000)40
![Page 41: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/41.jpg)
41
ACI-318-14
![Page 42: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/42.jpg)
Mix Number
Exposure Class Cement Slag Flyash
Silica Fume
w/c ratio
Total PozzolanFlyash
TotalPozzolan
1 C2,F3 40% 42% 18% 0% 0.45 60% Meet Fail
2 C2,F3 40% 42% 18% 0% 0.45 60% Meet Fail
3 C2,F3 15% 67% 18% 0% 0.45 85% Meet Fail
4 C2,F3 15% 67% 18% 0% 0.45 85% Meet Fail
5 C2,F3 60% 0% 30% 4% 0.35 34% Fail Meet
6 C2,F3 60% 0% 30% 4% 0.35 34% Fail Meet
7 C2,F3 29% 43% 29% 0% 0.36 71% Fail Fail
8 C2,F3 33% 50% 17% 0% 0.35 67% Meet Fail
42
![Page 43: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/43.jpg)
Mix Number
Exposure Class
C157 Drying Shrinkage,
percent
RCP, C passed -28 days
RCP, C passed -56 days
ASTM C666 RetainedDurability
ASTM C1556,m2/sec x10-12
1 C2,F3 -0.028 1097 380 94 0.17
2 C2,F3 -0.029 918 523 76 0.9
3 C2,F3 -0.024 291 177 90 0.15
4 C2,F3 -0.025 386 232 85 0.60
5 C2,F3 -0.026 548 366 98 1.2
6 C2,F3 -0.028 750 530 85 2.4
7 C2,F3 -0.025 442 300 100 0.5
8 C2,F3 -0.026 340 225 100 0.08
43
![Page 44: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/44.jpg)
Conclusions Concrete is rapidly changing – codes are not (cannot) The code already restricts durability - A model code as a companion to ACI 318 and the
Bridge design code is required now
44
![Page 45: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/45.jpg)
Questions Thank you for your time and attention!
45
![Page 46: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/46.jpg)
SuperstructureChloride Freeze ThawScalingCreep and Shrinkage
Piers Mass ConcreteFreeze-Thaw ExposureChlorides
Footing Mass ConcreteFreeze-Thaw ExposureChlorides
ShaftsConsolidationFreeze ThawChlorides / Permeability
46
![Page 47: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/47.jpg)
Strength Gain
010002000300040005000600070008000
0 10 20 30 40 50 60
Time, Days
Stre
ngth
, psi
123
47
![Page 48: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/48.jpg)
1177
756
190
1372
783722
743
347105
0
200
400
600
800
1000
1200
1400
1600
0 20 40 60 80 100
RC
P, C
Time, Days
Superstructure Footing / Shaft Pier
48
![Page 49: Kevin MacDonald, P.E., PhD, FACI · PDF fileCurrent Approach to Concrete Durability Minimum cement content (i.e. 650 lbs, 720 ls) Maximum water -cementitious material ratio — 0.45](https://reader031.vdocuments.us/reader031/viewer/2022030509/5ab8223c7f8b9a28468c7a87/html5/thumbnails/49.jpg)
Figure 4.3 Relationship between D28 and w/cm for concrete at 20oC
1E-12
1E-11
1E-10
0.2 0.3 0.4 0.5 0.6 0.7 0.8
w/cm
Diff
usio
n C
oeffi
cien
t (m
2 /s) Frederiksen et al, 1997
Tang and Sorensen, 1998
Stanish, 2000
Steen, 1995
Sandberg et al, 1996
Sandberg and Tang, 1994D 28 = 10(-12.06 + 2.40(w/cm ))
r 2 = 0.719
MacDonald 1999
49