Identification of Constitutive Parameters for Coupled Thermo-Hydro ...

Identification of Constitutive Parameters for Coupled 

Thermo-Hydro-Mechanical Model of Unsaturated Expansive Soil 

via Back Analysis 

Tom Schanz (a) , Maria Datcheva (b) , and Long Nguyen Tuan (a) 

(a) Chair for Foundation Engineering, Soil- and Rock Mechanics 

Ruhr-Universität Bochum, Germany 

(b) Institute of Mechanics, Bulgarian Academy of Sciences 

ICIP Hong Kong – December 13-17, 2010 

Schanz, Datcheva, and Nguyen Tuan Identification of Parameters for THM Model of Unsaturated Soil via Back Analysis 1 / 23

Thermo-Hydro-Mechanical (THM) Experiment 

Numerical Simulation Framework 

Process of Identification of Const. Parameters 

Conclusions 

Motivation - Nuclear Waste Repository 

Rock 

Container 

Repository design (Gorleben working model) 

Nuclear waste repository 

BUFFER 

Radioactive waste 





Conclusions 

Motivation - THM Behavior 

heat 

Idealization of in-situ conditions 

buffer 

waste 

Radio 

nuclide 

water 

Problem approach 

T = 25 o C 

Water 

Heat 

T = 80 o C 

T = T (t) 

s = s (t) 

σ ∗ = σ*(t) 


Outline 




Conclusions 

1 THM Experiment 

2 Numerical Simulation Framework 

Balance Equations Used 

Constitutive Equations and Parameters 

3 Process of Identification of Constitutive Parameters 

Sensitivity Analysis 

Optimization Algorithm 

Assessment of the Quality of the Optimized Parameters 

Assessment of the Goodness of the Fit 

4 Conclusions 





Conclusions 

THM Column Experiment 

THM experimental apparatus 





Conclusions 

Hydration Test Simulation 

Geometry and discretization 

Schanz, Datcheva, and Nguyen Tuan Identification of Parameters for THM Model of Unsaturated Soil via Back Analysis 6 / 23 

P1 

P2 

P3 

P4

Heating Test Simulation 




Conclusions 

Geometry and discretization 


P1 

P2 

P3 

P4 

25°C 

80°C

Balance Equations 




Conclusions 


Constitutive Equations 

Mass balance of water 

∂ 

w θl Slφ + θ 

∂t 

w g Sg φ + ∇ · j w l + jw 

w 

g = f 

Momentum balance for the medium 

Internal energy balance for the medium 

∇ · σ + b = 0 

∂ 

∂t (Esρs (1 − φ) + ElρlSlφ) + ∇ · (ic + jEs + jEl) = f Q 

θ w 

l , θw g = volumetric mass of water and gas 

j w 

l , jwg 

= total flux of water, gas 

σ = stress tensor 

Es , El , = internal energy in each phase 

ρs , ρl = density of each phase 

f Q = external energy supply 

f w = external supply of water 

φ = porosity 

b = vector of body forces 

ic = energy flux due to conduction 

jEs, jEl = advective fluxes of energy by mass 

motions 






Conclusions 




∂ 


∂t 

w g Sg φ + ∇ · jw l + jw 

w 

g = f 



∇ · σ + b = 0 

∂ 


θ w 


j w 

l , jwg 







φ = porosity 




motions 






Conclusions 




∂ 


∂t 

w g Sg φ + ∇ · jw l + jw 

w 

g = f 



∇ · σ + b = 0 

∂ 


θ w 


j w 

l , jwg 







φ = porosity 




motions 





Conclusions 

Constitutive equations and parameters 



VARIABLES CONSTITUTIVE EQ. NOTATION 

liquid and gas advective flux 

Constitutive relations 

Darcy's law ql, qg 

vapour and air non-advective 

fluxes 

Fick's law ig w , il a 

conductive heat flux Fourier's law ic 

Liquid phase degree of 

saturation 

Retention curve Sl, Sg 

Stress tensor 

Mechanical constitutive 

model ( modified BBM) 

σ 

A vector of 17 mechanical parameters: 

{Mj } = {kio, kso, αss , αi , αsp, pref , α0, λ(0), r, β, k, ps0, p c , M, α, eo, p ∗ 

o } 

A vector of 4 hydraulic parameters: 

A vector of 4 thermal parameters: 

Total 25 parameters summarized in vector: 

{Hj } = {P0, λ, φ0, ko} 

{Tj } = {τ, D, λsat, λdry } 

{xj } = {Hj , Tj , Mj } 


Concept 




Conclusions 

Forward calculation 

Solver 

Code-Bright (UPC) 

experimental 

data 

Constant volume swelling THM column 

Test- Heating test and hydration test 

Laboratory of Soil Mechanics - RUB 





Coupled THM model 

Two stress variables thermo-elasto-plastic model 

TEP model (UPC) 

Sensitivity 

analysis 

Optimization 

Solver 

varo 2 pt 

Parameter 

select 

Calibrated 

model 

verification validation 


Basic formulas 




Conclusions 

1 – Scaled sensitivity (SS) 

SSi,j = 





 

∂yi . ∂xj 

xj 

yi 

2 – Composite scaled sensitivity (CSS) 

 

1 N 

CSSj = 

N 

3 – Factor (γj ) 

γj = 

i=1 

SS 2 

i,j 

CSSj 

max{CSSj} 

- The vector of parameters: {xj } = {Hj , Tj , Mj } 

- Vector of model response: {yi } = {Sl , T , σyy } 






Conclusions 


SSi,j = 





 

∂yi . ∂xj 

xj 

yi 


 

1 N 

CSSj = 

N 


γj = 

i=1 

SS 2 

i,j 

CSSj 

max{CSSj} 








Conclusions 


SSi,j = 





 

∂yi . ∂xj 

xj 

yi 


 

1 N 

CSSj = 

N 


γj = 

i=1 

SS 2 

i,j 

CSSj 

max{CSSj} 







Conclusions 

Sensitivity Analysis: Results for Hydration Test 

Lambda 





γ calculated at the initial time step t0, 50% of total time interval – t50, and 

100% of total time interval – t100. 

Reference porosity 

1.0 

0.8 

0.6 

0.4 

0.2 

0.0 

P_0 

t0 

t50 

t100 

Intrinsic perm. 

Alpha_sp 

beta 

Alpha_i 

γ for Degree of Saturation γ for Vertical Stress 

Reference porosity 

1.0 

0.8 

0.6 

0.4 

0.2 

0.0 

Alpha_ss 

Intrinsic perm. 


t0 

t50 

t100 

K_so 

K_io




Conclusions 

Sensitivity Analysis: Results for Heating Test 

P_0 

Lamda retention 

Phi_ref 

1.0 

0.8 

0.6 

0.4 

0.2 

0.0 

t0 

t50 

t100 

Diffusion coef. 





k_ref Lamda_sat 

Lamda_dry 

THM Model 

γ for Degree of Saturation γ for Temperature 

Phi_ref 

1.0 

0.8 

0.6 

0.4 

0.2 

0.0 

t0 

t50 

t100 

k_ref 






Conclusions 

Sensitivity Analysis: Results for Heating Test 

Alpha_sp 

Alpha_i 

Alpha_ss 

Alpha_0 

K_so 

Phi_ref 

1.0 

0.8 

0.6 

0.4 

0.2 

0.0 





K_io 

k_ref 

γ for Vertical Stress 

THM Model 

t0 

t50 

t100 


Lamda_sat 

Lamda_dry 





Conclusions 

Optimization Algorithms: Objective Functions 

n 1 calc meas 

F = ∑ y − y i i wi 

n i= 

1 

Method Pros Cons 

Stochastic 

Methods 

Gradient 

based 

Simplex 

based 

Population 

based 

Usage of 

several data series 

very robust, stable, 

global search 

fast, each step gives a 

better solution 

more robust than 

gradient 





Fˆ = ∑ωk 

Fk 

very slow, “crude 

search” 

non robust, local search, 

slow for high dimensions 

very unstable (failed 

calls) 

local search, sometimes 

unstable 

robust, fast, stable local search 


k




Conclusions 

Optimization Algorithms: Direct Approach 

F → Minimum 

∆F= |F − F 

Niteration = Nmax prev | ≤ ɛI 

F≤ ɛII 

Start: 

guess of 

parameter values 

Nonlinear optimization 

technique -- downhill simplex 

method 

Optimization 

algorithm: 

Setting parameter 

values 

Calculationof 

deviationbetween 

calculatedvalues 

and measurements 

End: 

Stop criteria satisfied 





With program 

Executionof 

forward calculation 

Extractionof 

relevant 

calculated 

values 





Conclusions 

Back Analysis of Hydration Test 

Degree of saturation 

Vertical stress (Mpa) 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

0 

-0.05 

-0.1 

-0.15 

-0.2 

-0.25 

-0.3 

P1 measurement 



P1 simulation 

P2 simulation 

P3 simulation 

0 100 200 300 400 500 600 700 

Time (h) 

Time (h) 

0 100 200 300 400 500 600 700 


P4 simulation 





Before optimization After optimization 


Vertical stress (MPa) 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

0 100 200 300 400 500 600 700 

0 

-0.05 

-0.1 

-0.15 

-0.2 

-0.25 

-0.3 

Time (h) 

Time (h) 




P1 simulation 

P2 simulation 

P3 simulation 

0 100 200 300 400 500 600 700 

P4 simulation 






Conclusions 

Back Analysis of Heating Test 

Temperature (°C) 


80 

70 

60 

50 

40 

30 

20 

0.8 

0.7 

0.6 

0.5 

0.4 





Before optimization After optimization 

P1 measurement P2 measurement P3 measurement 

P1 simulation P2 simulation P3 simulation 

0 100 200 300 400 500 

Time (h) 




P1 simulation 

P2 simulation 

P3 simulation 

0 100 200 300 400 500 

Time (h) 

Temperature (°C) 


80 

70 

60 

50 

40 

30 

20 

0.8 

0.7 

0.6 

0.5 

0.4 

P1 measurement P2 measurement P3 measurement 

P1 mimulation P2 mimulation P3 simulation 

0 100 200 300 400 500 

Time (h) 




P1 simulation 

P2 simulation 

P3 simulation 

0 100 200 300 400 500 

Time (h) 





Conclusions 

Parameters Identification Algorithm 





Algorithm to identify model parameters based on 

hydration test and heating test 

Numerical Simulation 

Hydration test Heating test 

Optimization 

Optimization 3 Optimization 1 Optimization 2 Optimization 4 

Temperature parameters 

Hydraulic parameters 





Conclusions 






Mean value of gamma values: 

νj = 1 n i=1 n 

γij 

Table: The Quality of the Optimized Parameters 

{y i } k io kso αss α i αsp P 0 λ ko D λ dry λsat 

S (a) 

l 

T (a) 

Stress (a) 

S (b) 

l 

Stress (b) 

{x j } 

0.000 0.000 0.000 0.000 0.000 1.000 0.895 0.118 0.355 0.000 0.000 

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.014 0.059 0.214 1.000 

0.810 0.623 1.000 0.103 0.911 0.000 0.000 0.116 0.478 0.046 0.291 

0.000 0.000 0.000 0.000 0.000 1.000 0.828 0.271 0.000 0.000 0.000 

0.100 0.099 0.182 0.035 1.000 0.000 0.000 0.392 0.000 0.000 0.000 

ν 0.182 0.144 0.236 0.028 0.382 0.400 0.345 0.182 0.178 0.052 0.258 

(a) : Sensitivity of heating test and (b) : Sensitivity of hydration test 





Conclusions 


Mean value: µ = 1 n i=1 

n 

εi 

Standard deviation: σ = 

Skewness: γ1 = µ3 

σ 3 

 

1 n i=1 

n 

(εi − µ) 2 

εi = error between measurement and simulation 






Conclusions 




Conclusions 

1 Two laboratory tests (hydration test and heating test) have 

been simulated 

2 Process for identification of coupled THM model parameters 

was introduced 

3 P0, αsp and λ are the parameters influence the most as 

compared to the other parameters to simulations of two tests 

4 The result of accuracy analysis showed that the fitting of 

heating test independently is the more accurate than the others 

in back analysis. 


Conclusions 




Conclusions 











Conclusions 




Conclusions 











Conclusions 




Conclusions 











GBF Geotechnical Group 




Conclusions 

Thank you for your attention! 

http://www.gbf.rub.de

Identification of Constitutive Parameters for Coupled Thermo-Hydro ...

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