MICROSTRUCTURE BASED LIFE-CYCLE ASSESSMENT AND DURABILITY DESIGN...

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


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 1-2

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


pores

rc

dV/d log r

log r

gel

Liquid transport

Vapor transport

Condensed water


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 1-2

1

3 2

Plane 2-3



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


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


416 177 684 1036 1.0400W FA CA Adm

-

T(oC) RH (%)

Remark


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 (%)


W FA CA Adm

Assumed the same as that used in the Tsukiyono

T(oC) RH (%)

Remark


416 177 684 1036 1.0400W FA CA Adm

-

T(oC) RH (%)

Remark


400 152 645 1217 1.0000W FA CA Adm

-

T(oC) RH (%)

Remark


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


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)

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lect

ion fro

m the

com

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tion (m

m)

1 10 100 1000 10000 100000

0

-50

-100

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Expected in design

Measured

Analysis

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lect

ion fro

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m)

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-60

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Expected in design

Measured

Analysis

Elapsed time (day)

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lect

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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

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-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

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-200

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Expected in design

Measured

Analysis

Elapsed time (day)

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lect

ion fro

m the

com

ple

tion (m

m)

1 10 100 1000 10000 100000

0

-100

-200

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-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)

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lect

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1 10 100 1000 10000 100000

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-40

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Mechanics contribution(Case II)


Cases I and II

Added

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m)

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Full Analysis

Mechanics (Case II)


Cases I and II Added

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Full Analysis

Mechanics (Case II)



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Full Analysis

Mechanics contribution

(Case II)



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Full Analysis


(Case II)



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Full Analysis


(Case II)



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Full Analysis


(Case II)



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Fukutani Bridge Urado Bridge

Konaru BridgeTsukiyono Bridge


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


‐‐‐(1)




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)


x1

nS

S

pnS

Sp,1 x1nSfg1 x1nS1

viscosity

gravityforce





p,1 + fg1 1/w1,t + f (u1,tt + w1,tt /n)



‐‐‐(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


t :time


t :time


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 *



Concretefc nn )1(


Saturated concrete



....(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


‐‐‐(1)




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


‐‐‐(1)




fc nn )1(

ifiijij wgu )(,

(1) Equilibrium in direction x1

Dynamic equilibrium equations for fluid materials in the skeleton


x1

nS

S

pnS

Sp,1 x1nSfg1 x1nS1

viscosity

gravityforce





p,1 + fg1 1/w1,t + f (u1,tt + w1,tt /n)



‐‐‐(6)

‐‐‐(2)


x1

nS

S

pnS

Sp,1 x1nSfg1 x1nS1

viscosity

gravityforce





p,1 + fg1 1/w1,t + f (u1,tt + w1,tt /n)



‐‐‐(6)

‐‐‐(2)n

wuU i

ii

ii

ifiifi wnwgup 1/)(,

11,1

12,2

13,3


t :time


11,1

12,2

13,3


t :time


t :time


pijijij *



Concretefc nn )1(


Saturated concrete



....(1b, cracked)

concreteskeleton

pore water

pijijij *



Concretefc nn )1(


Saturated concrete



....(1b, cracked)

concreteskeleton

pore water


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


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


[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).


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