MICROSTRUCTURE BASED LIFE-CYCLE ASSESSMENT AND DURABILITY DESIGN OF CONCRETE BRIDGES
Koichi Maekawa, Benny Suryanto, Chikako Fujiyama, and Nobuhiro Chijiwa
Department of Civil Engineering, The University of Tokyo, Japan
Abstract Moisture and cracks are the two scourges of structural concrete, and understanding the
interactions between the two is the key to determine long-term durability performances. This paper firstly deals with moisture migration and its volume change with creep in four in-service PC bridge viaducts that are experiencing excessive deflections by using a-3D integrated micro-material-structural modeling. It is found that moisture-migration related deflections driven by the capillary surface tension and disjoining pressures in micro pores account for 25 to 45% of the macroscopic deflections. These apparent kinematics can be approximated by adding the moisture-related time-dependent deflections to the mechanistic-induced creep by external loads. This paper then deals with water-crack interaction in RC bridge decks under moving loads. It is found that the water presence on the upper deck parts, when subjected to high-speed traffics, can shorten the deck fatigue life by one-and-a-half order of life-span. This reduction in life is due to high water pressure developing over a large numbers of wheel passages as well as the reduced shear transfer along crack planes.
1. INTRODUCTION
Currently, a large numbers of worldwide bridges are under severe deterioration. This accounts for approximately 25% of the total RC bridges [1] in Japan, and approximately 15-42% of national or all roads in Europe [2]. Concerns over durability grow as serviceability is seriously affected for a safe transportation.
Cracking appears to be the most prevalent factor that haunts reinforced concrete durability. RC bridge decks are particularly susceptible to cracking. Due to wheel load movement, surface cracks may form, existing cracks may propagateeither open or close and slip and become the driving factor for fatigue damage accumulation. Internal cracks, due to wheel movement, can also play a latent role for RC deck deterioration. At the beginning stage of deterioration, these cracks are invisible from the outside and cannot be easily detected, but they may propagate and become the trigger of potholes and spalling of concrete cover.
Water is another prevalent factor of destructive mechanisms. As water exists between crack planes, high water pressure may develop when subjected to high-speed traffic [3]. This
Second International Conference on Microstructural-related Durability of Cementitious Composites, 11-13 April 2012, Amsterdam, The Netherlands
phenomenon was experimentally and analytically found to worsen the fatigue life [4,5]. Not only has the presence at a crack, the migration of water in concrete micro pore structures also been recently found to affect the serviceability of PC bridges. While water migration inside the concrete pores is obviously at a slow rate, it is found to be responsible for a significant portion of the excessive deflections observed in a numbers of PC bridges [6,7].
While cracks and water are clearly two interlinking scourges of concrete bridges, engineers have approached these problems separately. From a material engineer's standpoint, it is of interest to develop a concrete with a good crack control [8]. When realized into bridge decks, the material has, however, met limited success, possibly due to the snowball effects of water [9] and shear at cracks [10]. From a structural engineer's viewpoint, it is of interest to use post-tension forces; in one hand to satisfy structural requirement, and in other hand to keep the concrete always in un-cracked states. The water-induced time-dependent behaviours, if not carefully anticipated in design, may become the critical limit-state for long-term serviceability as currently seen in a number of PC bridges worldwide [11,12,13]. Clearly, water-crack interaction is truly complex, involving circumstances at various scales from micro- concrete pore to macro- structural scales.
Given the complexity of the problems at hand, the authors has been developing a multi-scale, multi-chemo-physics analysis of structural concrete, namely DuCOM-COM3 [14]. This platform is used herein to predict the serviceability of PC-RC bridges in practice. Life assessment of bridge decks under moving loads are also carried out to investigate the effects of water-crack interaction based upon the coupled micro-macro durability mechanism.
2. ANALYSIS PLATFORMS: DUCOM AND COM3
DuCOM-COM3 is a multi-scale analysis platform that links DuCOM [15] and COM3 [16]. DuCOM is a micro-durability platform, capable of simulating cement hydration, micro-pore structure and mass transport in concrete ranging from nm to μm scales, while COM3 is a 3D meso-scale platform to handle mechanistic actions for structural concrete ranging from mm to meter scales, with in-depth considerations of time-dependent, cyclic and fatigue behaviours of un-cracked and cracked concrete.
④ ε gS
Ee
Ec
kslL
kslS
ki
C c
C gL
C gS
① ε e
② ε c
③ ε gL
⑤ ε l
Hardened cement paste
Capillary water10-6 - 10-8 m
Gel water (large)r > 10-9 m
Gel water (small)
Interlayer water
Capillarypores
CSH grain
Inner
Unhydratedcement
r < 10-9 m
~ 10-10 m
product
Outer product
Inner product
Unhydrated core
Outer product
Inner product
Unhydrated core
Multi-component hydration heat model
Microstructure development model
rc
dV/d log r
log r
gel
Liquid transport
Vapor transport
Condensed water
Trapped water in inkbottle
pores
rc
dV/d log r
log r
gel
Liquid transport
Vapor transport
Condensed water
Trapped water in inkbottle
pores
Moisture transfer and equilibrium model
Solidification theory for cement paste
COM3
Two-phase Model
Cement Paste
Vag AggregateVcp
Capillaries, gel, and interlayerdr
r
ro
RepresentativeCSH grain
Outer productsdensity at r
particle radius
Mean separation
max
m
Matrix micro pore structure
dr
r
r=r(r)
Concrete
Multi-scale, time-dependent, and fatigue models for uncracked and cracked concrete
Early age Matured age
Hydration progresses
Water seepage
Ave
rage tensile
stre
ss
Average tensile strainAve
rage tensile
stre
ss
Average tensile strain
Com
pre
ssiv
e s
tress
Compressive strain
Com
pre
ssiv
e s
tress
Compressive strain
Sh
ear
stre
ssS
hea
r st
ress
1
3 2
Plane 2-3
Plane 1-3Decomposition into sub-planes of
non-orthogonal multi-directional cracks
Plane 1-2
1
3 2
Plane 2-3
Plane 1-3Decomposition into sub-planes of
non-orthogonal multi-directional cracks
Plane 1-2
Biot’s theorem
Anisotropic waterflow
+ =
Structure of cracks
Isotropic waterflow
Pore water inside concrete skeletonTime-dependent constitutive models
Multi-directional cracks
DuCOMthermo-hygro
④ ε gS
Ee
Ec
kslL
kslS
ki
C c
C gL
C gS
① ε e
② ε c
③ ε gL
⑤ ε l
Hardened cement paste
Capillary water10-6 - 10-8 m
Gel water (large)r > 10-9 m
Gel water (small)
Interlayer water
Capillarypores
CSH grain
Inner
Unhydratedcement
r < 10-9 m
~ 10-10 m
product
Outer product
Inner product
Unhydrated core
Outer product
Inner product
Unhydrated core
Multi-component hydration heat model
Microstructure development model
rc
dV/d log r
log r
gel
Liquid transport
Vapor transport
Condensed water
Trapped water in inkbottle
pores
rc
dV/d log r
log r
gel
Liquid transport
Vapor transport
Condensed water
Trapped water in inkbottle
pores
Moisture transfer and equilibrium model
Solidification theory for cement paste
COM3
Two-phase Model
Cement Paste
Vag AggregateVcp
Capillaries, gel, and interlayerdr
r
ro
RepresentativeCSH grain
Outer productsdensity at r
particle radius
Mean separation
max
m
Matrix micro pore structureMatrix micro pore structure
dr
r
r=r(r)
Concrete
Multi-scale, time-dependent, and fatigue models for uncracked and cracked concrete
Early age Matured age
Hydration progresses
Water seepageWater seepage
Ave
rage tensile
stre
ss
Average tensile strainAve
rage tensile
stre
ss
Average tensile strain
Com
pre
ssiv
e s
tress
Compressive strain
Com
pre
ssiv
e s
tress
Compressive strain
Sh
ear
stre
ssS
hea
r st
ress
1
3 2
Plane 2-3
Plane 1-3Decomposition into sub-planes of
non-orthogonal multi-directional cracks
Plane 1-2
1
3 2
Plane 2-3
Plane 1-3Decomposition into sub-planes of
non-orthogonal multi-directional cracks
Plane 1-2
Biot’s theorem
Anisotropic waterflow
+ =
Structure of cracks
Isotropic waterflow
Pore water inside concrete skeletonTime-dependent constitutive models
Multi-directional cracks
DuCOMthermo-hygro
Figure 2: Schematic illustration of DuCOM and COM3
If one intention is to trace the change in concrete material properties, to consider the effects of ambient conditions, and to take these effects into account for predicting the response of structural concrete, DuCOM-COM3 might be the practical choice to date. If the intention is to
Second International Conference on Microstructural-related Durability of Cementitious Composites, 11-13 April 2012, Amsterdam, The Netherlands
trace the time-dependent responses of RC structures under short-term dynamic, long-term sustained and fatigue loading conditions, with little impacts from ambient actions, the single task based code COM3 is recommended for simplicity. Recently, Maekawa and Fujiyama [3] incorporated the meso-scale model of water inside cracks. Here, the anisotropic nature of water motion through crack planes is treated with the multi-directional crack concepts, making it appealing for studying water-concrete interaction in a detailed manner.
3. LONG-TERM DEFLECTION SIMULATIONS OF PC BRIDGES
In this section, emphasis is given to the superiority of the integrated DuCOM-COM3 analysis not only in predicting the deflection of long-span prestressed concrete bridges, but also in explaining two primary factors triggering the excessive deflections: mechanically- and thermodynamically-induced components in time.
3.1 Modeling Four old PC bridges in Japan are modelled: Tsukiyono, Konaru, Fukatani, and Urado
Bridges. Figure 2 shows the dimensions of each bridge. They all have a hollow-shape girder, with a varying depth. In the analysis, these bridges were modelled as a statically determinate cantilever, representing the girder above the support to the hinge at the centre span, with no exception to Fukatani Bridge, which the centre hinge was connected after ten years.
Figure 2: Details of the targeted bridges
Elevation View Cross-section View and Properties
5800 22752275
10650
150150
5500
350
600
300
800
300 80
2000
7750 2000500 400250
5800 22752275
10650
150150
5500
350
600
300
800
300 80
2000
7750 2000500 400250306,80084,50084,50068,400 68,400
306,80084,50084,50068,400 68,400
Hinge
42,500
5,50
0
2,0
00
Hinge
42,500
5,50
0
2,0
00
115,000
11,833
3,845
115,000
11,833
3,845
90
0
7,3004,200
1,000
320
20
0
5,3
00
2,0
00
6,500 400400
27
0
230
90
0
7,3004,200
1,000
320
20
0
5,3
00
2,0
00
6,500 400400
27
0
230
6,000 2,6502,650
3,5
00
1,5
00
500
500350
400
300
8,000 400400 2,000750
6,000 2,6502,650
3,5
00
1,5
00
500
500350
400
300
8,000 400400 2,000750
6,000 1,2501,250
6,800850
250
150
500
1,5
00
3,84
511
,833
250
450
850
6,000 1,2501,250
6,800850
250
150
500
1,5
00
3,84
511
,833
250
450
850
Tsukiyono Bridge
Konaru Bridge
Fukutani Bridge
Urado Bridge
Note: All dimensions in mm.
59,500
1,500
3,500
59,500
1,500
3,500
5,300
50,700
2,0005,300
50,700
2,000
C
-123 7088
5.227 62.572.3
3.326.5 6679
6.127.2 5979
Mix proportions (kg/m3)
423 165 639 1108 1.0575
440 167 629 1099 1.1000
W FA CA AdmSummer
Other seasons
T(oC) RH (%)
CMix proportions (kg/m3)
W FA CA Adm
Assumed the same as that used in the Tsukiyono
T(oC) RH (%)
Remark
CMix proportions (kg/m3)
416 177 684 1036 1.0400W FA CA Adm
-
T(oC) RH (%)
Remark
CMix proportions (kg/m3)
400 152 645 1217 1.0000W FA CA Adm
-
T(oC) RH (%)
Remark
Elevation View Cross-section View and Properties
5800 22752275
10650
150150
5500
350
600
300
800
300 80
2000
7750 2000500 400250
5800 22752275
10650
150150
5500
350
600
300
800
300 80
2000
7750 2000500 400250306,80084,50084,50068,400 68,400
306,80084,50084,50068,400 68,400
Hinge
42,500
5,50
0
2,0
00
Hinge
42,500
5,50
0
2,0
00
115,000
11,833
3,845
115,000
11,833
3,845
90
0
7,3004,200
1,000
320
20
0
5,3
00
2,0
00
6,500 400400
27
0
230
90
0
7,3004,200
1,000
320
20
0
5,3
00
2,0
00
6,500 400400
27
0
230
6,000 2,6502,650
3,5
00
1,5
00
500
500350
400
300
8,000 400400 2,000750
6,000 2,6502,650
3,5
00
1,5
00
500
500350
400
300
8,000 400400 2,000750
6,000 1,2501,250
6,800850
250
150
500
1,5
00
3,84
511
,833
250
450
850
6,000 1,2501,250
6,800850
250
150
500
1,5
00
3,84
511
,833
250
450
850
Tsukiyono Bridge
Konaru Bridge
Fukutani Bridge
Urado Bridge
Note: All dimensions in mm.
59,500
1,500
3,500
59,500
1,500
3,500
5,300
50,700
2,0005,300
50,700
2,000
C
-123 7088
5.227 62.572.3
3.326.5 6679
6.127.2 5979
Mix proportions (kg/m3)
423 165 639 1108 1.0575
440 167 629 1099 1.1000
W FA CA AdmSummer
Other seasons
T(oC) RH (%)
CMix proportions (kg/m3)
W FA CA Adm
Assumed the same as that used in the Tsukiyono
T(oC) RH (%)
Remark
CMix proportions (kg/m3)
416 177 684 1036 1.0400W FA CA Adm
-
T(oC) RH (%)
Remark
CMix proportions (kg/m3)
400 152 645 1217 1.0000W FA CA Adm
-
T(oC) RH (%)
Remark
Second International Conference on Microstructural-related Durability of Cementitious Composites, 11-13 April 2012, Amsterdam, The Netherlands
Tsukiyono Bridge Konaru Bridge Fukutani Bridge Urado Bridge Tsukiyono Bridge Konaru Bridge Fukutani Bridge Urado Bridge Tsukiyono Bridge Konaru Bridge Fukutani Bridge Urado Bridge Figure 3: Discretization of the targeted bridges, showing only a half model
Figure 3 shows the computer model representing the bridges. The element size near the structural surface exposed to ambient atmospheres was set in the order of mm-scale due to high gradients of the local moisture and the pore water pressure at early ages. The element length along the longitudinal direction was taken as 0.5-1.5m. For this flexure-dominant mode, the selected sizes were confirmed to be efficient, satisfying thermodynamics and mechanistic requirements. The monthly average temperature and humidity were considered to occur at inside and outside surfaces of the girders, except for the outmost top surface in which moisture migration was considered not to occur due to the presence of pavement.
The live load was not considered but just self-weight was considered. The prestressing forces were simulated by applying pre-strains to the tendon elements that were anchored to the concrete two weeks after concrete casting at once. In analysis, this was considered as the time that the deflection started to progress, as opposed to the time at completion of one-span construction (about six months). A time step of 0.01 day and 25 days are considered at early ages and after a couple of months (when local moisture gradients had stabilized), respectively.
3.2 Analysis Results Figure 4 shows the comparisons of the measured, design- and analysis- predicted
deflections of the bridges. As seen, the analysis reasonably estimates the measured deflections, while the design code predictions give significant underestimations except for Urado Bridge, in which the design creep coefficient was set about 60% higher. The fluctuations seen in the analysis-predicted deflections are caused by temperature and humidity seasonal variations.
3.3 The roles of thermo-hygro and mechanistic creeps To develop a better understanding of the mechanisms affecting excessive deflections
observed, three parametric analyses are made; Case I: full exposure to ambient atmosphere and no loads, Case II: consider self-weight and external loads, but no internal driving forces provoked by concrete drying in the concrete, and Case III: consider all interactions. Thus, Cases I, II, and III represent the thermo-hygro, mechanistic, and apparent creeps, respectively. The ambient temperature and RH are maintained at 15.8oC and 67%, respectively.
Figure 6 shows the parametric analysis results. The contribution of the thermo-hygral deflection (Case I) is notable of about 25-45% of the total deflection. Clearly, full consideration of moisture transport in small concrete pores is critical. Furthermore, it is interesting to consistently observe that the deflections of Case III is similar to that of Cases I and II added together, although each of them is highly nonlinear with regard to thermodynamic states of moisture. Thanks to the stress level that is within the serviceability
Second International Conference on Microstructural-related Durability of Cementitious Composites, 11-13 April 2012, Amsterdam, The Netherlands
Expected in design
Measured
Analysis
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-50
-100
-150
-200
-250
Expected in design
Measured
Analysis
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-50
-100
-150
-200
-250
Expected in design
Measured
Analysis
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-30
-60
-90
-120
-150
Expected in design
Measured
Analysis
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-30
-60
-90
-120
-150
limit state that made this summation is possible. This finding provides a great deal of valuable information that can be used to benchmark practical measures on the deflection of PC bridges.
Figure 4: Comparison of predicted and observed long-term deflections of the four bridges
Figure 5: Importance of thermo-hygro and mechanistic creeps to the apparent deflection
4. THE FATIGUE LIFE OF BRIDGE DECKS UNDER WET CONDITIONS
The COM3 incorporated the meso-scale pore-water model [3] is used to study the effects of water-crack interaction on bridge decks under moving loads.
4.1 Modeling of water-crack interaction from mm scale Water in nano-scale pores in concrete composites before cracking behaves in an isotropic
manner, and thereafter in anisotropic owing to its crack orientation. Before concrete cracking, relative motion of the vapour and condensed water inside micro pores is computed based on DuCOM scheme with the moisture equilibrium and the flux modeling. After cracking, the
Expected in design
Midspan hinge was rigidlyconnected for bridge strengthening
(assuming midspanhinge always exists)
Measured
Analysis
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-30
-60
-90
-120
-150
Expected in design
Midspan hinge was rigidlyconnected for bridge strengthening
(assuming midspanhinge always exists)
Measured
Analysis
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-30
-60
-90
-120
-150
Expected in design
Measured
Analysis
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-100
-200
-300
-400
Expected in design
Measured
Analysis
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-100
-200
-300
-400
Konaru Bridge
Fukutani Bridge
Urado Bridge
Tsukiyono Bridge
Full Analysis
Mechanics contribution(Case II)
Thermo-hygralcontribution (Case I)
Cases I and II
Added
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-20
-40
-60
-100
-80
-120Full Analysis
Mechanics contribution(Case II)
Thermo-hygralcontribution (Case I)
Cases I and II
Added
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-20
-40
-60
-100
-80
-120
Full Analysis
Mechanics (Case II)
Thermo-hygralcontribution (Case I)
Cases I and II Added
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-100
-200
-300
-400
Full Analysis
Mechanics (Case II)
Thermo-hygralcontribution (Case I)
Cases I and II Added
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-100
-200
-300
-400
Full Analysis
Mechanics contribution
(Case II)
Thermo-hygralcontribution (Case I)
Cases I and II Added
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-25
-50
-75
-100
Full Analysis
Mechanics contribution
(Case II)
Thermo-hygralcontribution (Case I)
Cases I and II Added
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-25
-50
-75
-100
Full Analysis
Mechanics contribution
(Case II)
Thermo-hygralcontribution (Case I)
Cases I and II Added
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-50
-100
-150
-200
Full Analysis
Mechanics contribution
(Case II)
Thermo-hygralcontribution (Case I)
Cases I and II Added
Elapsed time (day)
Def
lect
ion fro
m the
com
ple
tion (m
m)
1 10 100 1000 10000 100000
0
-50
-100
-150
-200
Fukutani Bridge Urado Bridge
Konaru BridgeTsukiyono Bridge
Second International Conference on Microstructural-related Durability of Cementitious Composites, 11-13 April 2012, Amsterdam, The Netherlands
authors assume that the meso-scale pore water pressure acts perpendicular to the crack plane(s). Figure 6 provides a schematic illustration of the modelling.
Figure 6: General scheme of solid-crack-water interaction
The water-concrete interaction is taken into account by satisfying dynamic equilibrium of the two. It is considered that the kinematics of the two phases can interact to produce dragging forces that can be related to the permeability of pore water in concrete pores and in each crack direction. The stiffness of pore water under compression is considered to be linear and based on the value under atmospheric pressure of 0.1 MPa.
The pore water pressure can be both positive and negative, depending on the extent of crack opening/closure under repetitive loading. When the water pressure drops below the vapor pressure, cavitation process may occur, turning the liquid water into vapor. Noted that the occurrence of cavitation in general RC elements has never been reported in the civil engineering literature and the model is developed to cover all possible events of mechanics.
4.2 Bridge deck model The details and dimensions of the reinforced concrete decks tested by Matsui [5] were used
to define the geometry of a hypothetical deck model. Taking advantage of the symmetry, only one half of the hypothetical deck was modelled, resulting into the dimensions of 1000×3000×190 mm (see Fig. 7). This deck model was divided into 20, 10, and 5 elements along the longitudinal, transverse, and vertical directions, respectively. All reinforcements were considered in a smeared manner. The deck was supported vertically along its one longitudinal and two transverse edges. Over 1800-mm of the free edge, a 80-kN rolling wheel load was applied by simultaneous loading and unloading two adjacent and previous two nodes at every four loading steps. The magnitude of the load applied corresponds to about 43% of the static punching shear capacity.
Two parameters are considered: wheel-load movement speeds (77 and 0.77 km/h) and water saturation conditions (completely saturated over the whole deck thickness, fully saturated only over the two upper elements, fully saturated over the two lower elements, and
Dynamic equilibrium equations for a saturated skeleton
11,1 12,2 13,3 g1 nsu1,tt nfu1 w1/n,tt
11,1 12,2 13,3 g1 u1,tt f w1,tt
1j,j g1 u1,tt f w1,tt
‐‐‐(1)
Summation convention
(2) Generalization for each coordinate axis
ij,j g1 ui,tt f wi,tt ‐‐‐(5)
fc nn )1(
ifiijij wgu )(,
(1) Equilibrium in direction x111,1 12,2 13,3 g1 nsu1,tt nfu1 w1/n,tt
11,1 12,2 13,3 g1 u1,tt f w1,tt
1j,j g1 u1,tt f w1,tt
‐‐‐(1)
Summation convention
(2) Generalization for each coordinate axis
ij,j g1 ui,tt f wi,tt ‐‐‐(5)
fc nn )1(
ifiijij wgu )(,
(1) Equilibrium in direction x1
Dynamic equilibrium equations for fluid materials in the skeleton
a) porous area b) normal to plane x2‐x3c) gravity forced) permeability
x1
nS
S
pnS
Sp,1 x1nSfg1 x1nS1
viscosity
gravityforce
viscosity(p+dp/dx1 x1)nS
(1) Viscosity ‐‐‐ resistant force exerted by contact with skeletonFrom simple assumption; without any acceleration (static movement)p,1 w1,t
p,1 x1nS 1/w1,t x1nS multiplied by “‐1/ x1nS”
(2) Dynamic equilibrium
p,1 + fg1 1/w1,t + f (u1,tt + w1,tt /n)
p,i = f (ui,tt ‐ gi) + f wi,tt /n + 1/wi,t
pressure gravity viscosity mass x acceleration=force
‐‐‐(6)
‐‐‐(2)
a) porous area b) normal to plane x2‐x3c) gravity forced) permeability
x1
nS
S
pnS
Sp,1 x1nSfg1 x1nS1
viscosity
gravityforce
viscosity(p+dp/dx1 x1)nS
(1) Viscosity ‐‐‐ resistant force exerted by contact with skeletonFrom simple assumption; without any acceleration (static movement)p,1 w1,t
p,1 x1nS 1/w1,t x1nS multiplied by “‐1/ x1nS”
(2) Dynamic equilibrium
p,1 + fg1 1/w1,t + f (u1,tt + w1,tt /n)
p,i = f (ui,tt ‐ gi) + f wi,tt /n + 1/wi,t
pressure gravity viscosity mass x acceleration=force
‐‐‐(6)
‐‐‐(2)n
wuU i
ii
ii
ifiifi wnwgup 1/)(,
11,1
12,2
13,3
g1nsu1,ttnfu1 w1/n,tt
t :time
a) normal to plane x2‐x3b) normal to plane x3‐x1c) normal to plane x1‐x2d) gravity forcee) mass of skeletonf) acceleration of skeletong) mass of waterh) acceleration of water
11,1
12,2
13,3
g1nsu1,ttnfu1 w1/n,tt
t :time
a) normal to plane x2‐x3b) normal to plane x3‐x1c) normal to plane x1‐x2d) gravity forcee) mass of skeletonf) acceleration of skeletong) mass of waterh) acceleration of water
t :time
a) normal to plane x2‐x3b) normal to plane x3‐x1c) normal to plane x1‐x2d) gravity forcee) mass of skeletonf) acceleration of skeletong) mass of waterh) acceleration of water
pijijij *
The affinity: Porous material (skeleton) with waterSoil Soil skeleton
Volume: (1‐n)VDensity: sDisplacement: uiPore waterVolume: nVDensity: fDisplacement: ui +wi/n
Concretefc nn )1(
Biot’s theorem: pliijijij *
Saturated concrete
pijijij *Total stress:
…………....(1a, uncracked)
....(1b, cracked)
concreteskeleton
pore water
pijijij *
The affinity: Porous material (skeleton) with waterSoil Soil skeleton
Volume: (1‐n)VDensity: sDisplacement: uiPore waterVolume: nVDensity: fDisplacement: ui +wi/n
Concretefc nn )1(
Biot’s theorem: pliijijij *
Saturated concrete
pijijij *Total stress:
…………....(1a, uncracked)
....(1b, cracked)
concreteskeleton
pore water
Dynamic equilibrium equations for a saturated skeleton
11,1 12,2 13,3 g1 nsu1,tt nfu1 w1/n,tt
11,1 12,2 13,3 g1 u1,tt f w1,tt
1j,j g1 u1,tt f w1,tt
‐‐‐(1)
Summation convention
(2) Generalization for each coordinate axis
ij,j g1 ui,tt f wi,tt ‐‐‐(5)
fc nn )1(
ifiijij wgu )(,
(1) Equilibrium in direction x111,1 12,2 13,3 g1 nsu1,tt nfu1 w1/n,tt
11,1 12,2 13,3 g1 u1,tt f w1,tt
1j,j g1 u1,tt f w1,tt
‐‐‐(1)
Summation convention
(2) Generalization for each coordinate axis
ij,j g1 ui,tt f wi,tt ‐‐‐(5)
fc nn )1(
ifiijij wgu )(,
(1) Equilibrium in direction x1
Dynamic equilibrium equations for fluid materials in the skeleton
a) porous area b) normal to plane x2‐x3c) gravity forced) permeability
x1
nS
S
pnS
Sp,1 x1nSfg1 x1nS1
viscosity
gravityforce
viscosity(p+dp/dx1 x1)nS
(1) Viscosity ‐‐‐ resistant force exerted by contact with skeletonFrom simple assumption; without any acceleration (static movement)p,1 w1,t
p,1 x1nS 1/w1,t x1nS multiplied by “‐1/ x1nS”
(2) Dynamic equilibrium
p,1 + fg1 1/w1,t + f (u1,tt + w1,tt /n)
p,i = f (ui,tt ‐ gi) + f wi,tt /n + 1/wi,t
pressure gravity viscosity mass x acceleration=force
‐‐‐(6)
‐‐‐(2)
a) porous area b) normal to plane x2‐x3c) gravity forced) permeability
x1
nS
S
pnS
Sp,1 x1nSfg1 x1nS1
viscosity
gravityforce
viscosity(p+dp/dx1 x1)nS
(1) Viscosity ‐‐‐ resistant force exerted by contact with skeletonFrom simple assumption; without any acceleration (static movement)p,1 w1,t
p,1 x1nS 1/w1,t x1nS multiplied by “‐1/ x1nS”
(2) Dynamic equilibrium
p,1 + fg1 1/w1,t + f (u1,tt + w1,tt /n)
p,i = f (ui,tt ‐ gi) + f wi,tt /n + 1/wi,t
pressure gravity viscosity mass x acceleration=force
‐‐‐(6)
‐‐‐(2)n
wuU i
ii
ii
ifiifi wnwgup 1/)(,
11,1
12,2
13,3
g1nsu1,ttnfu1 w1/n,tt
t :time
a) normal to plane x2‐x3b) normal to plane x3‐x1c) normal to plane x1‐x2d) gravity forcee) mass of skeletonf) acceleration of skeletong) mass of waterh) acceleration of water
11,1
12,2
13,3
g1nsu1,ttnfu1 w1/n,tt
t :time
a) normal to plane x2‐x3b) normal to plane x3‐x1c) normal to plane x1‐x2d) gravity forcee) mass of skeletonf) acceleration of skeletong) mass of waterh) acceleration of water
t :time
a) normal to plane x2‐x3b) normal to plane x3‐x1c) normal to plane x1‐x2d) gravity forcee) mass of skeletonf) acceleration of skeletong) mass of waterh) acceleration of water
pijijij *
The affinity: Porous material (skeleton) with waterSoil Soil skeleton
Volume: (1‐n)VDensity: sDisplacement: uiPore waterVolume: nVDensity: fDisplacement: ui +wi/n
Concretefc nn )1(
Biot’s theorem: pliijijij *
Saturated concrete
pijijij *Total stress:
…………....(1a, uncracked)
....(1b, cracked)
concreteskeleton
pore water
pijijij *
The affinity: Porous material (skeleton) with waterSoil Soil skeleton
Volume: (1‐n)VDensity: sDisplacement: uiPore waterVolume: nVDensity: fDisplacement: ui +wi/n
Concretefc nn )1(
Biot’s theorem: pliijijij *
Saturated concrete
pijijij *Total stress:
…………....(1a, uncracked)
....(1b, cracked)
concreteskeleton
pore water
Second International Conference on Microstructural-related Durability of Cementitious Composites, 11-13 April 2012, Amsterdam, The Netherlands
completely dry). Water-concrete interaction in the saturated elements is represented by overlapping the standard RC elements with the pore water elements.
Figure 7: Details of the bridge deck of interest
The constitutive laws of cracked concrete [14] are used, with an explicit consideration of the effects of moisture on the damage evolution of crack shear-transfer. To clarify the impact of pore water pressure and the corresponding concrete fracture and damage, the specified concrete tensile strength is used rather than a custom-based value.
4.3 Parametric analysis The progress of the mid-span deflection of each deck is shown in Figure 8. For a reference,
the fatigue life obtained from Case DF (dry, high-speed) is indicated in dotted lines. High-speed wheel movement (F series) is observed to appreciably shortens fatigue life
when the upper parts of the deck are wet (Cases A and U). The negative effects of high-speed wheel movement is particularly seen when only the upper parts of the deck are wet (Case U). High-speed wheel movement does not have appreciable influence the fatigue life under dry condition (Case D). As high-speed traffic loading does really occur in reality, the worsening effects of water that may easily be accumulated at bridge deck surface must be anticipated. Waterconcrete interaction causes the responses of RC bridge decks to be rate-dependent.
Shown in Fig. 9 is the plot of water pore pressure versus concrete principal strains monitored from one representative element under the wheel passage. High-speed wheel load movement is seen to keep high water pressure to develop over a large number of passages and to result in a rapid increase of concrete principal strain from the early numbers of passage (Cases AF and UF). Since concrete principal strain is a direct measure on concrete damage, it is clear that it is the high water pressure that is responsible for the reduced fatigue life of bridge decks under wet conditions as seen in Cases AF and UF.
Finally, the authors direct their attentions to the pore water pressure at the bottom surface of the deck center span, where negative water pressure is evident. High-speed traffic is again seen to have a significant role as it brings the water pressure close to vapor pressure, implying the cavitation like processthe water inside concrete pores changes phases from a liquid to a vapor. The models employed have not yet consider the negative effects of this phenomenon.
Completely dry
Completely wetAF
AS
UF
US
BF~BSDF
DS
2
4
6
8
2
4
6
8
01 100 10000 10000000.01 1 100 10000 1000000
F: 77 km/h; S: 0.77 km/h
Numbers of passage
Mid
span
dis
pla
cem
ent
(mm
)
wet
wet
DF
DF
DF
DF
Completely dry
Completely wetAF
AS
UF
US
BF~BSDF
DS
2
4
6
8
2
4
6
8
01 100 10000 10000000.01 1 100 10000 1000000
F: 77 km/h; S: 0.77 km/h
Numbers of passage
Mid
span
dis
pla
cem
ent
(mm
)
wet
wetwet
DFDF
DFDF
DFDF
DFDF
.fy = 295 MPa; Es=21104 MPa All dimensions in mm. X
ZLoad
Y
Unload
3000
1000
190
X
ZLoad
Y
Unload
3000
1000
190
Location Longitudinal Transverse Top D16-200 D16-260 Bottom D16-100 D16-130
'cf = 24 MPa; Ec=2.5104 MPa
Second International Conference on Microstructural-related Durability of Cementitious Composites, 11-13 April 2012, Amsterdam, The Netherlands
Figure 8: Progress of mid-span deflections versus number of passage.
Figure 9: Pore water pressure and principal concrete strain versus numbers of passage
6. CONCLUSIONS
The integration of thermodynamics and mechanistic models of concrete provides a rational basis regardless of size and time and hence the long-term response of structures.
The migration of water at concrete micro pores is found to contribute appreciably to the long-term structural deflections of four, in-service PC bridges.
High pore water pressure, induced by high-speed traffic, can accelerate concrete damage on bridge deck surfaces. Shorter deck lifespan may result.
REFERENCES
[1] NILIM, '2010 Statistical yearbook of the road', Document No. 645 (2011) H21-59. [2] Daly, A.F., 'Bridge management in Europe (BRIME): modelling of deteriorated structures',
Bridge management 4: inspection, maintenance, assessment and repair (2000) 552-559. [3] Maekawa, K., and Fujiyama, C., 'Rate-dependent model of structural concrete incorporating
kinematics of ambient water', in Proceedings of the CORAN, Portugal, November, 2011 - . [4] Maekawa, K. Gebreyouhannes, E., Mishima, T., and An, X., '3D fatigue simulation of RC slabs
under travelling wheel-type loads', J. of Advanced Concrete Technology 4(3) (2006) 445-457. [5] Matsui, S., 'Fatigue strength of RC-slabs of highway bridge by wheel running machine and
influence of water on fatigue', in Proceedings of Japan Concrete Institute 9(2) (1987) 627-632. [6] Ohno, M., Chijiwa, N., Suryanto, B., and Maekawa, K., 'An investigation into the long-term
deflection of PC viaducts by using 3D multi-scale analysis', J. of Adv. Conc. Tech. (in press). [7] Maekawa, K., Chijiwa, N. and Ishida, T. 'Long-term deformational simulation of PC bridges
based on the thermo-hygro model of micro-pores', Cement&Conc. Res. 41(12) (2011) 1310-1319. [8] Li, V.C., 'On engineered cementitious composites', J. of Adv. Conc. Tech. 1(3) (2003) 215-230. [9] Mitamura, H., 'Development of a high-performance, economical ECC/steel plate deck', Report of
Civil Engineering Research Institute for Cold Regions 130 (2007). [10] Suryanto, B., Nagai, K., and Maekawa, K., 'Bidirectional multiple cracking tests on HPFRCC
plates', ACI Material J. 107(5) (2010) 450-460. [11] Bazant, Z.P., Yu, Q., Li, G.-H., Klein, G. and Kristek, V. 'Excessive deflections of record-span
prestressed box girder', Concrete International 32 (6) (2010) 44-52. [12] Burdet, O., 'Experience in the long-term monitoring of bridges', in Proceedings of the 3rd fib
International Congress, 663, Washington D.C., USA, (2010) 108–113. [13] Hata, Y., Onishi, N. and Watanabe, Y., 'Creep behavior of prestressed concrete bridge over ten
years', in Proc. of FIP symposium, (1993) 305–310. [14] Maekawa, K., Ishida, T. and Kishi, T., 'Multi-scale modeling of structural concrete' (Taylor and
Francis, 2008).
1
-3
-7
-111 100 10000 10000000.01
Numbers of passage
Po
re w
ate
rp
res
su
re (
MP
a)
AS~US
AF~UF
1
-3
-7
-111 100 10000 10000000.01
Numbers of passage
Po
re w
ate
rp
res
su
re (
MP
a)
AS~US
AF~UF 0.0
0.4
0.8
1 100 10000 10000000.01
Numbers of passage
Str
ain
(%
)
AF~UF
AS~US0.0
0.4
0.8
1 100 10000 10000000.01
Numbers of passage
Str
ain
(%
)
AF~UF
AS~US
Second International Conference on Microstructural-related Durability of Cementitious Composites, 11-13 April 2012, Amsterdam, The Netherlands
[15] Maekawa, K., Chaube, R. and Kishi, T., 'Modeling of concrete performance-hydration, microstructure formation and transport' (E&FN Spon, 1999).
[16] Maekawa, K., Pimanmas, A. and Okamura, H., 'Nonlinear mechanics of reinforced concrete' (Spon Press, 2003).
Second International Conference on Microstructural-related Durability of Cementitious Composites, 11-13 April 2012, Amsterdam, The Netherlands