thermal integrity analysis of concrete bridge foundations
TRANSCRIPT
Civil & Environmental EngineeringCivil & Environmental Engineering
Thermal Integrity Analysis of Concrete Bridge Foundations
Using COMSOL Multiphysicsยฎ Software
Kevin R. Johnson, Ph.D.
Outline
โข Concrete Heat of Hydration
โข Thermal Integrity Profiling
โข Governing Equations
โข COMSOLยฎ Model
โข Case Study
โข Conclusions
Background
๐ช ๐บ๐ฏ๐
๐ช๐๐บ
๐ช๐๐บ๐ช๐๐จ
๐ช๐๐จ๐ญ ๐ฏ๐๐ถ
Portland
Cement Water
Hardened
Cement
Heat
Cement hydration is a highly exothermic process
Example: Hoover Dam
Built 1932 - 1935
More than 5 million yd3 of concrete
Equivalent to 2 lane road coast to coast
(w/sidewalks)
600 miles of 1โ steel cooling tubes
100 yr estimated cooling
Drilled Shafts
โข Cast-in-place
concrete deep
foundations
โข 3 โ 30 ft. diameter
โข Up to 300 ft. deep
โข Group or mono-shaft
foundations
Background
Why Test Shaft Integrity?
Thermal Integrity Profiling (TIP)
Yield plot converted to
effective diameter
Yield plot converted to
effective diameter
Measured temperature profile
q= ๐(๐, ๐ป)
๐ = ๐(๐, ๐ป)
๐ = ๐๐๐๐๐
๐ช๐ = ๐(๐, ๐ป)
Semi-Infinite
Medium
๐๐๐๐๐๐๐๐๐๐๐ช๐,๐๐๐๐
๐
๐๐๐๐๐ป
๐๐+๐
๐๐๐๐๐ป
๐๐+๐
๐๐๐๐๐ป
๐๐+ ๐ = ๐๐ช๐
๐๐ป
๐๐
T = temperature
t = time
xyz = rectangular coordinates
k = thermal conductivity
ฯ = density
Cp = specific heat
q = rate of heat generation
Governing Equations
General Heat Equation
๐ก๐ = ๐ธ๐๐ข๐๐ฃ๐๐๐๐๐ก ๐ด๐๐ =
0
๐ก
๐โ๐ธ๐๐ 1๐โ1๐๐ โ ฮ๐ก
๐ผ = ๐๐๐๐๐๐ ๐๐ โ๐ฆ๐๐๐๐ก๐๐๐ =๐ป(๐ก)
๐ป๐ข= ๐ผ๐ข โ exp โ
๐
๐ก๐
๐ฝ
The ฮฑ-ฮฒ-ฯ Model
๐ธ๐ = ๐ด๐๐ก๐๐ฃ๐๐ก๐๐๐ ๐ธ๐๐๐๐๐ฆ
๐๐ = ๐ ๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐ก๐ข๐๐
๐ = ๐๐๐ก๐ข๐๐๐ ๐บ๐๐ ๐ถ๐๐๐ ๐ก๐๐๐ก
๐ผ๐ข๐ฝ๐= ๐โ๐๐๐ ๐๐๐๐๐๐๐ก๐๐๐
๐ป๐ข = ๐๐๐ก๐๐ ๐ด๐ฃ๐๐๐๐๐๐๐ ๐ป๐๐๐ก
Concrete Heat Generation
(Schindler & Folliard, 2002)
COMSOLยฎ Model
Geometry
Governing
equations can be
applied to 2-D or
3-D geometries
๐ผ๐ข = ๐( ๐ค๐๐ , ๐ถ4๐ด๐น,๐๐2๐๐๐ , ๐น๐ด,๐๐ ๐ )
๐ฝ = ๐(๐ถ3๐ด, ๐๐๐๐,๐๐ ๐ )
๐ = ๐(๐ถ3๐, ๐๐2๐, ๐๐๐๐, ๐น๐ด,๐๐ ๐ , ๐ด๐ถ๐ถ๐ )
๐ป๐ข = ๐(๐ถ3๐, ๐ถ2๐, ๐ถ3๐ด, ๐ถ4๐ด๐น, ๐๐3, ๐น๐๐๐ ๐ถ๐๐,๐๐๐)
๐ธ๐ = ๐(๐ถ3๐ด, ๐ถ4๐ด๐น, ๐๐3, ๐๐2๐๐๐ , ๐น๐๐๐๐๐๐ ๐ , ๐น๐ด, ๐๐๐๐, ๐๐น,๐๐ ๐ , ๐ด๐ถ๐ถ๐ )
Empirical correlations used to estimate ฮฑ-ฮฒ-ฯ model parameters:
(Schindler, 2005; Ge, 2006; Poole, 2007)
COMSOLยฎ Model
Materials - Concrete
๐ = ๐๐๐ ๐. ๐๐ โ ๐. ๐๐๐ถ
๐ช๐ =๐
๐๐พ๐๐ถ๐ช๐๐๐ +๐พ๐ ๐ โ ๐ถ ๐ช๐ +๐พ๐๐ช๐ +๐พ๐๐ช๐
๐๐ข๐ = 2 โ 3๐
๐ โ ๐พ
๐ถ๐๐๐ = 8.4๐ + 339
COMSOLยฎ Model
Materials - Concrete
ฯ= ๐พ๐ +๐พ๐ +๐พ๐
โข Density
โข Thermal Conductivity
โข Specific Heat
(Schindler, 2002)
(Arya, 2001)(Incropera and
Dewitt, 2002)
COMSOLยฎ Model
Materials - Soil
Dry
Soil Thermal Properties
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
The
rmal
Co
nd
uct
ivit
y (W
/m/K
)
Dry Density (kg/m3)
COMSOLยฎ Model
Physics โ Heat Transfer in Solids
Initial Values
Soil Domain = Ambient soil temperature
Concrete Domain = Ambient air temperature
Boundary Condition
Constant temperature at soil domain edge
Heat Source
Concrete: q= ๐ฏ๐๐
๐๐
๐ท ๐ท
๐๐๐๐ฌ๐
๐น
๐
๐ป๐โ๐
๐ป๐
COMSOLยฎ Model
Physics โ Coefficient Form PDEs
๐ธ๐๐ข๐๐ฃ๐๐๐๐๐ก ๐ด๐๐, ๐ก๐ =
0
๐ก
๐โ๐ธ๐๐ 1๐โ1๐๐ โ ฮ๐ก
๐ท๐๐๐๐๐ ๐๐ ๐ป๐ฆ๐๐๐๐ก๐๐๐, ๐ผ =๐ป(๐ก)
๐ป๐ข= ๐ผ๐ข โ exp โ
๐
๐ก๐
๐ฝ
PDE 1:
โข Note: Initial values ๐ก๐ = 1 and ๐๐ก๐
๐๐ก= 1
PDE 2:
COMSOLยฎ Model
Solver Configuration
Time Dependent Solver with segregated steps:
โข Step 1: Equivalent age, te
โข Step 2: Degree of hydration, ฮฑ
โข Step 3: Temperature, T
COMSOLยฎ Model
Results
Radial heat distribution is
bell shaped with peak
temperatures occurring at
the center of shaft and
radiating outwards into
the surrounding soil.
COMSOLยฎ Model
Results
32
33
34
35
36
37
38
39
40
41
42
60 80 100 120 140
Dep
th (
ft)
Temperature (oF)
Model
Hyperbolic Fit
Bottom of Shaft
Model results also show that
the longitudinal temperature
distributions in a shaft can be
closely approximated by a
hyperbolic tangent function.
Case Study
Drilled Shaft
Upper Diam. (cased) = 54โ
Lower Diam. (uncased) = 48โ
Change in soil strata (and
construction procedure) at 12ft
depth caused unexpected
anomaly in thermal profile.
Case Study
Model data vs. Measured data
50
70
90
110
130
150
170
0 3 6 9 12 15 18 21 24
Tem
per
atu
re (
oF)
Time (hrs)
Measured
Model
-5
0
5
10
15
20
25
30
35
60 110 160
Dep
th (
ft)
Temperature (oF)
Wire 1Wire 2Wire 3Wire 4Wire 5AverageModel
TOS
BOC
BOS
Conclusions
โข The use of COMSOLยฎ numerical modeling has been shown to be an
effective tool in simulating concrete hydration behavior and an aid
Thermal Integrity Profiling of drilled shafts.
โข Modeled parametric studies provide insight to general thermal
relationships in foundations.
โข 3-D models used for advanced analysis of shafts with anomalies.
โข The same governing equations and COMSOLยฎ applications can used
for analyses where excess temperature control to prevent thermal
stress cracking is a concern.
References
Anderson, Byron (2011). "Thermal Integrity Profiling Instrumentation Development". Masterโs Thesis, University
of South Florida. http://scholarcommons.usf.edu/etd/2987
ASTM Standard D7949-14, โStandard Test Methods for Thermal Integrity Profiling of Concrete Deep
Foundations,โ ASTM International, West Conshohocken, PA
Arya, S. Pal. (2001). Introduction to Micrometeorology. 2nd Edition. San Diego, CA. Academic Press. p.48.
Bogue, Robert (1947). โThe Chemistry of Portland Cementโ. Reinhold Publishing Corp.
Folliard, K.J., Juenger, M., Schindler, A., Riding, K., Poole, J., Kallivokas, L.F., Slatnick, S., Whigham, J.,
Meadows, J.L. (2008). Prediction Model for Concrete Behavior (Final Report). Austin, TX. Center for
Transportation Research. The University of Austin at Texas. FHWA/TX-08/0-4563-1.
Ge, Zhing. (2005). โPredicting temperature and strength development of the field concreteโ. Doctoral Dissertation,
Iowa State University. UMI No. 3200417.
Incropera, Frank P., and Dewitt, David P. (2007). Fundamentals of Heat and Mass Transfer. 6th Edition. New York,
NY. John Wiley & Sons.
Johnson, Kevin R. (2016). โAnalyzing thermal integrity profiling data for drilled shaft evaluationโ. DFI Journal โ
The Journal of the Deep Foundations Institute. Vol 10, No. 1, May 2016. pp. 25-33.
References
Mullins, Gray (2010). โThermal Integrity Profiling of Drilled Shaftsโ. DFI Journal โ The Journal of the Deep
Foundations Institute. Vol.4, No. 2 December 2010. pp. 54-64.
Mullins, G., and Winters, D. (2012). โThermal Integrity Profiling of Concrete Deep Foundationsโ. Slideshow
presented at the Association of Drilled Shaft Contractors Expo 2012, San Antonio, TX, March 14-17.
Pauly, Nicole M. (2010). โThermal Conductivity of Soils from the Analysis of Boring Logs.โ Masterโs Thesis,
University of South Florida, Department of Civil and Environmental Engineering.
Poole, Jonathan L. (2007). โModeling Temperature Sensitivity and Heat Evolution of Concreteโ. Doctoral
Dissertation, University of Texas at Austin. UMI No. 3285913.
Schindler, A.K. and Folliard, K.J. (2002) Temperature Control During Construction to Improve the Long Term
Performance of Portland Cement Concrete Pavements. Austin, TX. Center for Transportation Research. The
University of Texas at Austin.
Schindler, A.K. and Folliard, K.J. (2005). โHeat of Hydration Models for Cementitious Materialsโ. Technical
Paper, ACI Materials Journal, V. 102, No. 1, January-February 2005.
Questions?