Research on water transport in loading-damaged …...Tensi l e Loadi ng Ⅱ-Ⅱ 100 100...

Solution of water transport in concrete/damaged concrete

Research on water transport in

loading-damaged concrete

Dalian University of Technology

Licheng WANG Dr.

Dalian University of Technology, Dalian China


Contents

� The fundamental equation of unsaturated flow

� Theoretical and numerical solutions


� Experiment for capillary absorption of damaged

concrete

� Results and conclusions


Extended Darcy’s Law Mass Conservation Law

Introduction--- unsaturated flow within concrete

Description of unsaturated flow in cement-based materials


Richard’s Equation

+∂∂

∂∂

=∂∂

)()( θθ

θθ

Kx

Dxt

D(θθθθ) is the hydraulic diffusivity function . K(θθθθ) is the hydraulic conductivity .

( )Dt x x

θ θθ

∂ ∂ ∂ = ∂ ∂ ∂

Diffusion-like

-K(θθθθ)


As to the Richard’s Equation:

+∂∂

∂∂

=∂∂

)()( θθ

θθ

Kx

Dxt

Here, θ is the normalized water content,

which can be written as θ=(Θ - Θi)/( Θs -

Θ ), in which Θ is the volumetric water

Θi

xSealed

Water front


Capillary water transport process

Θi), in which Θ is the volumetric water

content under any state, and ranges

between the initial and saturated water

content, Θi and Θs respectively. Water

Water front


Semi-theoretical solution of Richard’s Equation

�The root expression: ,)(),( ξθ αΦ= ttxβξ xt=

where α and β are the unknown exponents to be determined.

�The Richard’s Equation will become:

( ) ( )

Φ+Φ

Φ=Φ

+Φ +−+ αβααββξα tKtd

tDd

td )(12


( ) ( )

Φ+Φ=+Φ +−+ αβααβ

ξξξβξα tKt

dtD

dt

d

)(12

It should meet:

D (θ) =D0θ n

K(θ)=KSθ l[1-(1- θ1/m)m]2

where D0 and n are empirically-

fitted constants, KS is the

conventional saturated conductivity.l=0.5

m=0.5


� The final expression of simplified partial differential equation (PDE) as an ordinary differential equation (ODE):

Φ′+

ΦΦ=

Φ+Φ λ

ξξξβξα s

n Kd

dD

d

d

d

d0

�The finite-difference method is applied to this ODE and the time

item t is taken the forward difference; the spatial item x is taken


item t is taken the forward difference; the spatial item x is taken

the centered difference.

�The full implicit difference scheme can be written as:

,i

k

ii

k

ii

k

ii hcba =++ ++

++−

1

1

11

1 θθθ i=1, 2, … , N-1

Here ai, bi and ci are the diagonal elements of the coefficient matrix respectively

and hi correspond to the element of column vector related to the forward step

results.


( ) ( )x

KK

x

D

x

D

xt

k

n

k

n

k

n

k

n

k

n

k

n

k

n

k

n

k

n

k

n

∆

−−

∆

−−

∆

−

∆=

∆

− −++−

+−

++++

+

2

1 11

1

1

1

2/1

11

12/1

1 θθθθθθ

n

k

nn

k

nn

k

nn hcba =++ ++

++−

1

1

11

1 θθθ ，，，，n=2, … , N-1；；；；k=1, 2, …, M-1.


=

×

−

+

+−

+

+

−−−

n

n

k

n

k

n

k

k

nn

nnn

h

h

h

h

ba

cba

cba

cb

1

2

1

1

1

1

1

2

1

1

111

222

11

.

.

.

.

.

.

....

θθ

θθ


Comparison between the numerical solution considering gravity effect

and the horizontal absorption test data (neglecting the gravity):


Water reservoir

Mortar sample

Moving direction


Experimental test for capillary sorptivity in unloaded

concrete subjected different loading level

Experimental Program

Procedures


Mixture Proportions Specimen Geometry Loading damage Absorption test


MaterialsComposition proportions

(kg/mm3)

Cement 410

Mixture proportion of concrete (w/c=0.5)


Coarse aggregate 1195.95

Fine aggregate 589.05

Water 205

w/c 0.5

Water Reducer 0.2% of the amount of cement


Specimen geometry and loading mechanism

Compressi ve Loadi ng

St rai n GageT

M

Ⅱ Ⅱ

Ⅰ Ⅰ

Tensi l e Loadi ng

Ⅱ-Ⅱ

100

100

-Ⅰ Ⅰ


Ⅰ Ⅰ

M

B

1 2

St eel Bar

Hi gh St r engt hened Bol t150

100

Ⅱ-Ⅱ


Load

level

f/fc(%)

Loading path

Compression Tension

0 — — — —

Loading design


70Sustained for

10min

repeated for

25 times

Sustained for

10min

repeated for

25 times

80Sustained for

10min

repeated for

25 times

Sustained for

10min

repeated for

25 times

90Sustained for

10min—(crushed)

Sustained for

10min

repeated for

25 times


Water absorption test device

Cumulative water absorption test setup

The di r ect i on of

wat er i nj ect i on

Concr et e speci men

Ti ght en bol t


Val ve

wat er i nj ect i on

Suppor t f r ame

The bot t om of

t he speci men

Rubber r i ng f or seal i ng

Ti ght en bol t

Di r ect i on of wat er descendi ng



Photo of the water absorption device


Results

Cumulative water content test under different load level

Sustained compressive loading Sustained tensile loading



Repeated compressive loading Repeated tensile loading



Sorptivity obtained from the first linear part



Sorptivity obtained from the second linear part



Comparison of the sorptivity obtained from the two stages

YC YF


LC LF


Without loading

Prediction of the water content distribution

Load level=70%


Load level of 90%


Conclusions

For short time absorption, For short time absorption, the gravity of water may have the gravity of water may have

marginal effect on the moisture distributionmarginal effect on the moisture distribution. This result . This result

mainly depends on the magnitude of saturated conductivity mainly depends on the magnitude of saturated conductivity KKSS. .

1

2 LoadingLoading--induced damage will accelerate the water absorption induced damage will accelerate the water absorption


2 LoadingLoading--induced damage will accelerate the water absorption induced damage will accelerate the water absorption

speed because of the change of microstructures of concrete. speed because of the change of microstructures of concrete.

For the range of loadingFor the range of loading--levels studied in this work (higher than levels studied in this work (higher than

70% of strength),70% of strength), varying loading level has a small influence varying loading level has a small influence

on the sorptivity because the microcracks within concrete on the sorptivity because the microcracks within concrete

are partially colosed due to unloading.are partially colosed due to unloading.

3


Published papers relating to the project in the

past year� 1. Licheng Wang and Tamon Ueda. Mesoscale modeling of water penetration into concrete

by capillary absorption. Ocean Engineering, 2011, 38(4): 519-528.

� 2. Licheng Wang and Tamon Ueda. Mesoscale simulation of chloride diffusion in concrete

considering the binding capacity and concentration dependence. Computers and Concrete,

2011, 8(2): 125-142.


� 3. Licheng Wang and Tamon Ueda. Mesoscale modelling of the chloride diffusion in cracks

and cracked concrete. Journal of the Advanced Concrete Technology, 2011, 9(3) : 241-

249.

� 4. Wang Li-cheng and Li Shu-hong. Numerical solutions for capillary absorption by

cementitious materials. Applied Mechanics and Materials, 2011, Vols. 94-96: 1560-1563.

� 5. Licheng Wang. Prediction of Chloride Ingress into Concrete by Capillary Absorption.

Advanced Materials Research, 2011, Vols. 163-167, 3210-3213.


Thank you for your attention.


Research on water transport in loading-damaged …...Tensi l e Loadi ng Ⅱ-Ⅱ 100 100...

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Transcript of Research on water transport in loading-damaged …...Tensi l e Loadi ng Ⅱ-Ⅱ 100 100...