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