水泥基复合材料多尺度模拟
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5
c 1 vs 1 wp / p
3.3Extended modeling of temperaturedependent moisture transport equilibrium
❖ The purpose of this part is to quantify the temperature sensitivity of the state and transport of moisture in nano-meter to micro-meter to scale pores , both experimentally and theoretically , and to enhance a system for internal moisture in motion
interlayer
l
Micro-pore structures
Gel pore
g(r) g
Capillary pore
(r) The total porosity distribution
c (r)
c
Interlayer porosity
Gel porosity distribution
The total gel porosity
the total degree of saturation Stotal is calculated as follow
Stotal
cp Scp gl Sgl lr cp gl lr
Slr
φ is the capillary porosity cp
φ is the gel porosity gl
J (Dppl DTT )
Moisture for bothe vapor and liquid water Dp is moisture conductivity with respect to the pore presure gradient Dt is moisture conductivity with respect to the temperature gradient
t
t
l 1.54 108 T 3 1.85105 T 2 6.65103 T +2.47 10-1
θw is the mass of moisture in a unit volume of concrete
J is moisture flux
Q is the sink term corresponding to water consumption due to hydration
Temperature effect on internal
Mix proporition of concrete paste specimen
水灰比（%）
单位质量（kg/m3）
水
水泥
50
520
1040
367
734
石灰粉 405 1080
温度（℃） 20 40 60
温度（℃） 20 40 60
Wetting conditions in the experiment
W/C : 0.46
W/C : 0.25
0.00
-4
-9
-8
-7
-6
-5
-4
Log (r [m])
Outline of the pore structure development computation
Cluster Expansion Model
The particle growth Volume and weight of
Capillary porosity distribution The total capillary porosity
(r) l g (r) c (r)
(r) l gVg cVc
R-R distribution function：
V 1 exp(Br) dV Br exp(Br)d ln r
60.00
Measured value Proposed equation (273<T[K]<373)
280 300 320 340 360
Temperature [K]
(a) density of water
55.00
380
260
280 300 320 340 360 380
Temperature [K]
qv
D0 (T )
rc
1
dV N
k
v
Dvv
Nk
lm 2(r ta )
J (Dppl DTT )
D0 (T1) ( T1 )3/2 ( D,T 2 )
D0 (T2 ) T2
D ,T 1
(1)
ΩD is
the collision integeral at temperature T or 1
3 Micro-pore structure formation and moisture transport
Luo Mian 2011.9.30
Contents
4
3.1 Basic modeling of micropore structure development
Goal: predict the micro-pore structure with time
(r) l g 1 exp Bgr c 1 expBcr
Porosity distribution dV/d ln r
0.25
0.20
Young mortar all = 15 %
0.15 0.10 0.05
W/C Ratio
0.25 0.45 0.65
0.00 -9
-8
-7
-6
-5
Log (r [m])
Degree of saturation
1.0
20C
0.8
60C
0.6 W/C50%
Drying path
0.4
0.2
Wetting path
0
0.2
0.4
0.6
0.8
1.0
Relative humidity
Moisture mass loss [g/cm3]
0.20
Experiment (60ºC)
(c) viscosity of water
Equilibrium between liquid and vapor phase of water under arbitrary temperatures
Pl 2
r
(T ) 2.66104 T 2 3.17 103 T 9.46101
RT
相对湿度（%） 40，55，70，85 40，55，70，85
持续时间（天） 7 7
30，60，90
7，14，28
Drying conditions in the experiment
相对湿度（%）
持续时间（天）
30，60，90 60 30，60，90
7，28，60 7，14，28 7，14，28，60
Porosity distribution dV/d ln r
0.20 0.15
Mature mortar 0.25 = 60 % 0.45 = 85 % 0.65 = 95 %
V : Porosity function
0.10 0.05
Measured porosity distributions of 7 day cured mortars
Density of liquid water [g/cm3]
1.02
Surface tension 103 [N/m]
80.00
1.00 0.98 0.96 0.94
260
75.00
70.00
65.00
Measured value Proposed equation (273<T[K]<373)
ch 0.28
1: Unhydrated core
l (twsl gvs ) / 2
2: Inner products
3: CSH grains
4: Capillary pores 5: Gel pores
6
v 6: Interlayer porosity
g
s ch
l
4
CSH size scale
(b) surface tension
Viscosity of liquid water 10-3 [Pa.s]
2.00
Measured value
1.50
Proposed equation
(273<T[K]<373)
1.00
0.50
0.00 260
280
300
320
340
360
380
Temperature [K]
(r) l g 1 exp Bgr c 1 expBcr
We need to know the 5 parameters
l g c
Original particle boundary
Particle size scale
Macroscopic volumetric
1
23
balance of hydration products
inner products outer products
Total surface area (/m3) capillary pores gel (CSH internal)
Hydration Degree of Matrix
Volumetric Balance
Bulk porosity of capillaries gel and interlayer
B parameters
Matrix micro pore structure
(r) i 1 expBir
The authors subdivide the overall cementitious micro-pore structures into three basic components：
These rsults idicate that the most important issue for future consideration is an oppropriate expression of moisture equilibrium based on a microscopic viewpoint.
the law of mass conservation governing the balance in a system
w div( J ( w,T , w, T )) Q 0
t
the potential term for moisture in a porous material
w (l S )
ln
pvap p
Vl Pl
（273<T<373）
Pl
lRT
Mw
ln
pvap p
d ln p Hvap dT RT 2
Pl
lRT
Mw
ln
pvap p
Biblioteka Baidu
pvap p exp( plMw ) p0 exp{( Hvap )( 1 1 )}exp( plMw )
lRT
R T T0
lRT
Modeling of moisture flux
T 2
ql
l 2 50
rc
(
0
rdV )2 Pl
KlPl
(2)
i
exp(
Ge RT
)
i 3.38108 T 4 4.63105 T 3 2.37 102 T 2 5.45 T 4.70 102
J (Dvv KlPl KTT )
Dv
( v
Pl
Pl
v
T
T
)
KlPl
KT T
(Dv
φ is the interlayer porosity lr
S is the degree of saturation of capillary pores cp
S is the degree of saturation of gel pores gl
S is the the degree of saturation of interlayer pores lr
Experiment (20ºC)
0.15
Analysis (60ºC)
0.10
0.05 0
Analysis (20ºC)
W/C50%, 4*4*16[cm] 20ºC, 60%RH
10
20
30
40
Drying time [days]
Computed moisture isotherm
Moisture loss behaviors at 20°C and 60°C
v
Pl
Kl )Pl
(Dv
v
T
KT )T
(DpPl DT T )
Calculation of the degree of saturation in a porous system
Multi-scale modeling of moisture existing in capillary, gel and interlayer pores.
c 1 vs 1 wp / p
3.3Extended modeling of temperaturedependent moisture transport equilibrium
❖ The purpose of this part is to quantify the temperature sensitivity of the state and transport of moisture in nano-meter to micro-meter to scale pores , both experimentally and theoretically , and to enhance a system for internal moisture in motion
interlayer
l
Micro-pore structures
Gel pore
g(r) g
Capillary pore
(r) The total porosity distribution
c (r)
c
Interlayer porosity
Gel porosity distribution
The total gel porosity
the total degree of saturation Stotal is calculated as follow
Stotal
cp Scp gl Sgl lr cp gl lr
Slr
φ is the capillary porosity cp
φ is the gel porosity gl
J (Dppl DTT )
Moisture for bothe vapor and liquid water Dp is moisture conductivity with respect to the pore presure gradient Dt is moisture conductivity with respect to the temperature gradient
t
t
l 1.54 108 T 3 1.85105 T 2 6.65103 T +2.47 10-1
θw is the mass of moisture in a unit volume of concrete
J is moisture flux
Q is the sink term corresponding to water consumption due to hydration
Temperature effect on internal
Mix proporition of concrete paste specimen
水灰比（%）
单位质量（kg/m3）
水
水泥
50
520
1040
367
734
石灰粉 405 1080
温度（℃） 20 40 60
温度（℃） 20 40 60
Wetting conditions in the experiment
W/C : 0.46
W/C : 0.25
0.00
-4
-9
-8
-7
-6
-5
-4
Log (r [m])
Outline of the pore structure development computation
Cluster Expansion Model
The particle growth Volume and weight of
Capillary porosity distribution The total capillary porosity
(r) l g (r) c (r)
(r) l gVg cVc
R-R distribution function：
V 1 exp(Br) dV Br exp(Br)d ln r
60.00
Measured value Proposed equation (273<T[K]<373)
280 300 320 340 360
Temperature [K]
(a) density of water
55.00
380
260
280 300 320 340 360 380
Temperature [K]
qv
D0 (T )
rc
1
dV N
k
v
Dvv
Nk
lm 2(r ta )
J (Dppl DTT )
D0 (T1) ( T1 )3/2 ( D,T 2 )
D0 (T2 ) T2
D ,T 1
(1)
ΩD is
the collision integeral at temperature T or 1
3 Micro-pore structure formation and moisture transport
Luo Mian 2011.9.30
Contents
4
3.1 Basic modeling of micropore structure development
Goal: predict the micro-pore structure with time
(r) l g 1 exp Bgr c 1 expBcr
Porosity distribution dV/d ln r
0.25
0.20
Young mortar all = 15 %
0.15 0.10 0.05
W/C Ratio
0.25 0.45 0.65
0.00 -9
-8
-7
-6
-5
Log (r [m])
Degree of saturation
1.0
20C
0.8
60C
0.6 W/C50%
Drying path
0.4
0.2
Wetting path
0
0.2
0.4
0.6
0.8
1.0
Relative humidity
Moisture mass loss [g/cm3]
0.20
Experiment (60ºC)
(c) viscosity of water
Equilibrium between liquid and vapor phase of water under arbitrary temperatures
Pl 2
r
(T ) 2.66104 T 2 3.17 103 T 9.46101
RT
相对湿度（%） 40，55，70，85 40，55，70，85
持续时间（天） 7 7
30，60，90
7，14，28
Drying conditions in the experiment
相对湿度（%）
持续时间（天）
30，60，90 60 30，60，90
7，28，60 7，14，28 7，14，28，60
Porosity distribution dV/d ln r
0.20 0.15
Mature mortar 0.25 = 60 % 0.45 = 85 % 0.65 = 95 %
V : Porosity function
0.10 0.05
Measured porosity distributions of 7 day cured mortars
Density of liquid water [g/cm3]
1.02
Surface tension 103 [N/m]
80.00
1.00 0.98 0.96 0.94
260
75.00
70.00
65.00
Measured value Proposed equation (273<T[K]<373)
ch 0.28
1: Unhydrated core
l (twsl gvs ) / 2
2: Inner products
3: CSH grains
4: Capillary pores 5: Gel pores
6
v 6: Interlayer porosity
g
s ch
l
4
CSH size scale
(b) surface tension
Viscosity of liquid water 10-3 [Pa.s]
2.00
Measured value
1.50
Proposed equation
(273<T[K]<373)
1.00
0.50
0.00 260
280
300
320
340
360
380
Temperature [K]
(r) l g 1 exp Bgr c 1 expBcr
We need to know the 5 parameters
l g c
Original particle boundary
Particle size scale
Macroscopic volumetric
1
23
balance of hydration products
inner products outer products
Total surface area (/m3) capillary pores gel (CSH internal)
Hydration Degree of Matrix
Volumetric Balance
Bulk porosity of capillaries gel and interlayer
B parameters
Matrix micro pore structure
(r) i 1 expBir
The authors subdivide the overall cementitious micro-pore structures into three basic components：
These rsults idicate that the most important issue for future consideration is an oppropriate expression of moisture equilibrium based on a microscopic viewpoint.
the law of mass conservation governing the balance in a system
w div( J ( w,T , w, T )) Q 0
t
the potential term for moisture in a porous material
w (l S )
ln
pvap p
Vl Pl
（273<T<373）
Pl
lRT
Mw
ln
pvap p
d ln p Hvap dT RT 2
Pl
lRT
Mw
ln
pvap p
Biblioteka Baidu
pvap p exp( plMw ) p0 exp{( Hvap )( 1 1 )}exp( plMw )
lRT
R T T0
lRT
Modeling of moisture flux
T 2
ql
l 2 50
rc
(
0
rdV )2 Pl
KlPl
(2)
i
exp(
Ge RT
)
i 3.38108 T 4 4.63105 T 3 2.37 102 T 2 5.45 T 4.70 102
J (Dvv KlPl KTT )
Dv
( v
Pl
Pl
v
T
T
)
KlPl
KT T
(Dv
φ is the interlayer porosity lr
S is the degree of saturation of capillary pores cp
S is the degree of saturation of gel pores gl
S is the the degree of saturation of interlayer pores lr
Experiment (20ºC)
0.15
Analysis (60ºC)
0.10
0.05 0
Analysis (20ºC)
W/C50%, 4*4*16[cm] 20ºC, 60%RH
10
20
30
40
Drying time [days]
Computed moisture isotherm
Moisture loss behaviors at 20°C and 60°C
v
Pl
Kl )Pl
(Dv
v
T
KT )T
(DpPl DT T )
Calculation of the degree of saturation in a porous system
Multi-scale modeling of moisture existing in capillary, gel and interlayer pores.