M4B: A Tool for the Multiphysics Analysis of the ...
Transcript of M4B: A Tool for the Multiphysics Analysis of the ...
M4B: A Tool for the Multiphysics
Analysis of the Deformational
Behaviour of Soils and its Interaction
with Building Foundations
Dr. Juan Alonso. Environmental Engineering
Group. University of Castilla la Mancha
Introduction
HydraulicEquations
EnergyEquations
ChemicalEquations
MechanicalEquations
M4B
CO
MSO
L M
ULT
IPH
YSI
CS
Introduction
Liquid
Gas
Reactive solids
Inert Solid
Water+dissolvedspecies
Water+air
Minerals subjectedto dissolution/precipitation
reactions
Solid skeleton
Phases Components
HYDRAULIC EQUATIONS
0)( WWWW
qv ρmDt
mDs
S
W
GG
W
LL
W SnSnm
W
G
W
rW )( GvL
L
LLL
WW
DnSzgPk
K
q
RT
PW VW
G W
0
VV HPP
RT
sWH
L
W
exp
• Water mass balance
• Water content
• Mass water flux
• Vapour density
• Vapour pressure
HEAT EQUATIONS
Q
E ft
E
l
GLS EEEE TncE SSS 1
TnScE L
W
L
W
LL
nSlnTScE G
W
GG
W
G
W
GG
GLSE lllil C
T T-iC
nS
G
nS
L
n
SLL
11 sSS nE vlS 1
sLL EE vqlW
LL
sGG EE vqlW
GG
• Energy Conservation Equation • Internal Energy
• Heat Flux
• Advection• Conduction
EQUATIONS
MIN
isiMIN
iMIN
MIN
iiLiiL
Rmt
m
RRnSt
CnS
v
j
,
,
)( MkCCT a
ii
N
i
ikk ,...,11
Mk
RnSt
CCnSiLi
a
iiLN
i
ik
,...,1
01
j
01
i
N
i
ik R
Mkt
TnSi
N
i
ikkL ,...,10
1
j
01
i
N
i
iCz
CONSERVED
SUBSTANCES
H+, CO32-, SO4
2-, Ca2+, Mg2+, Na+,
K+, Cl-
SPECIES
HCO3-, OH-, H2CO3, HSO4
-,
H2SO4, CaHCO3+, CaCO3,
CaHSO4+, CaSO4, CaOH+,
MgHCO3+, MgCO3, MgSO4,
MgOH+, NaHCO3, NaCO3-,
NaSO4-, NaOH, KOH, H+, CO3
2-,
SO42-, Ca2+, Mg2+, Na+, K+, Cl-
iiLi
W
i CDnSC qj
• Electroneutrality condition
• Conservation of individual species • Conservation of conserved substances
• Conservation of conserved substances
• Massic flux of individual species
EQUATIONSNombre Fórmula log k Base de datos Reacción
Anhidrita* Ca(SO4) -4.440 ANDRA Ca(SO4) Ca+2 + SO4-2
Antarcticita CaCl2:6H2O 3.940 ANDRA CaCl2:6H2O Ca+2 + 2Cl- + 6H2O
Aragonito CaCO3 -8.310 ANDRA CaCO3 Ca+2 + CO3-2
Arcanita K2SO4 -1.850 ANDRA K2SO4 2K+ + SO4-2
Artinita Mg2(CO3)(OH)2:3H2O 9.810 ANDRA Mg2(CO3)(OH)2:3H2O 2Mg+2 - 2H+ + CO3-2 + 5H2O
Basanita CaSO4:0.5H2O -3.920 ANDRA CaSO4:0.5H2O Ca+2 + SO4-2 + 0.5H2O
Bischofita MgCl2:6H2O 4.460 ANDRA MgCl2:6H2O Mg+2 + 2Cl- + 6H2O
Bloedita* Na2Mg(SO4)2:4H2O -2.350 ANDRA Na2Mg(SO4)2:4H2O Mg+2 + 2Na+ + 2SO4
-2 + 4H2O
Brucita Mg(OH)2 17.100 ANDRA Mg(OH)2 Mg+2 - 2H+ + 2H2O
Burkeita Na6(CO3)(SO4)2 -0.770 ANDRA Na6(CO3)(SO4)2 6Na+ + CO3
-2 + 2SO4-2
Ca2Cl2(OH)2:H2O(s) Ca2Cl2(OH)2:H2O 26.530 ANDRA Ca2Cl2(OH)2:H2O 2Ca+2 - 2H+ + 2Cl- + 3H2O
Ca4Cl2(OH)6:13H2O(s) Ca4Cl2(OH)6:13H2O 68.730 ANDRA Ca4Cl2(OH)6:13H2O 4Ca+2 - 6H+ + 2Cl- + 19H2O
CaCl2:2H2O(cr) CaCl2:2H2O 7.950 ANDRA CaCl2:2H2O Ca+2 + 2Cl- + 2H2O
CaCl2:4H2O(cr) CaCl2:4H2O 5.350 ANDRA CaCl2:4H2O Ca+2 + 2Cl- + 4H2O
CaCl2:H2O(s) CaCl2:H2O 7.850 ANDRA CaCl2:H2O Ca+2 + 2Cl- + H2O
CaCO3:H2O(s) CaCO3:H2O -7.600 ANDRA CaCO3:H2O Ca+2 + CO3-2 + H2O
Calcita* CaCO3 -8.480 ANDRA CaCO3 Ca+2 + CO3-2
CaMg3(CO3)4(s)/Huntita CaMg3(CO3)4 -30.810 ANDRA CaMg3(CO3)4 Ca+2 + 3Mg+2 + 4CO3-2
Carnalita KMgCl3:6H2O 4.330 ANDRA KMgCl3:6H2O Mg+2 + K+ + 3Cl- + 6H2O
Dolomita* CaMg(CO3)2 -17.120 ANDRA CaMg(CO3)2 Ca+2 + Mg+2 + 2CO3-2
Epsomita* Mg(SO4):7H2O -1.880 ANDRA Mg(SO4):7H2O Mg+2 + SO4-2 + 7H2O
Gaylussita CaNa2(CO3)2:5H2O -9.430 ANDRA CaNa2(CO3)2:5H2O Ca+2 + 2Na+ + 2CO3-2 + 5H2O
….
EQUATIONS
0TOT zgσ
mσσ P TOT
),max( LG PPP
PmCHS dddddd el εεεεεDσ
ds
Psd
atm
SS
ε
i
MIN
i
i
CH
V RWd i
i
ε
n
i
iiic
MIN
iK
IAPk
WR
1
1
i
i
MIN
i
i
sS RWn
Dt
nDi
11
v
• Equilibrium equation
• Constitutive stresses
• Incremental stresses
• Porosity variations
• Strain component due to suctionchanges
• Strain component due to dissolution/precipitation
• Dissolution/precipitation rates
Example Model. Excavation and gypsumdissolution
Parameter Value
s , soil density 2650 kgm-3
ks, bulk modulus
related to suction
changes
-0.02 MPa-1
, coefficient
related to crystal
growth pressure
1
Elastic modulus 17 MPa
Poisson
coefficient0.3
Initial porosity, n 0.4
Intrinsic
permeability, KL
1.00 x 10-17 m2
Initial gypsum
content20 %
Initial sulphate
concentration0.002 mol l-1
Initial calcium
concentration0.014 mol l-1
kc 3.4 x 10-04 kgm-2s-1
Excavation
12
3
Dissolution
Section forces
M4B: A Tool for the Multiphysics
Analysis of the Deformational
Behaviour of Soils and its Interaction
with Building Foundations
Dr. Juan Alonso. Environmental Engineering
Group. University of Castilla la Mancha