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CALIBRATION OF MODIFIED CAM CLAY MODEL WITH USE OF LOADING PATH METHOD AND GENETIC ALGORITHMS
Magdalena KOWALSKA
Department of GeotechnicsFaculty of Civil Engineering
Silesian University of TechnologyGliwice, POLAND
2
PRESENTATION PLAN
1. Calibration
2. Loading Path Method
3. Case Study
4. Conclusions
3
1. CALIBRATION
CALIBRATION= evaluation of appropriate values for
parameters so that the simulatedstress-strain relationship of soil ispossibly consistent with thebehaviour observed in field orlaboratory test.
4
1. CALIBRATION
7E*, m, f, g, ν, c, φ2005
Coulomb-Mohr/Fahey-Carter
nonlin. elastic / perfectly plastic
5M, G, l, k, N1965ModifiedCam-Clay
elasto-plastic+ isotr. harden.
4E, ν, c, φXVIIICoulomb-Mohr
elasto-perfectly-plastic
2E, νXVIIHooke's lawelastic isotropic
No.parametersyearnametype
5
2. LOADING PATH METHOD
1. Select representative point2. Evaluation of in situ conditions3. Theoretical loading path (FEM)4. Undisturbed soil sample5. TX test: loading path →
experimental response path6. Theoretical response path7. Optimization → set of parameters
6
peat, dark brown
clay, gray
silt, grayfine/medium sand, gray
clayey aggradate mud, gray light brown
2.20
3.40
4.40
5.10
3. CASE STUDY3.1. Subsoil investigation
MAN trucks factory in Niepołomice
7M = 1.0, λ = 0.15, κ = 0.02, ν = 0.3, e0 = 0.9, γ = 18 kN/m3
600 kPaZ_SOIL.PC v.6.27Modified Cam Clay
siltclaysiltcl. sand
f. sand
5.0 m 5.0
m
164
3. CASE STUDY3.2. Model
8
3. CASE STUDY3.3. Stress path
0
40
80
120
160
0 40 80 120 160 200 240 280p' [kPa]
q [kPa]
point 164 CSL K0 line YS
9
3. CASE STUDY3.4. Triaxial test
Bishop & Wesley’s apparatusPolish Academy of Sciences
10
3. CASE STUDY3.4. Triaxial test
0
100
200
300
400
500
600
0 100 200 300 400 p' [kPa]
q' [kPa]
controlled pathsimple shearingCSL
11
3. CASE STUDY3.4. Triaxial test
controlled pathsimple shearing
-5
0
5
10
15
-5 0 5 10 15 20 25
εs [%]
εv [%]
12
3. CASE STUDY3.5. Theoretical response
Modified Cam Clay
MATLAB 6.1
Genetic Algorithms
13
3. CASE STUDY3.6. Genetic Algorithm
fitness function
minn
FF
n
i
2
ev
ei,v
ti,v
2
es
ei,s
ti,s
→
∑⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛
εΔ
ε−ε+⎟
⎟⎠
⎞⎜⎜⎝
⎛
εΔ
ε−ε
=
where:Δεx = max(εx
e)-min(εxe)
xt, xe – theoretical & experimental valuesn – number of points
14
3. CASE STUDY3.6. Genetic Algorithm
0
100
200
300
400
500
600
0 100 200 300 400 p' [kPa]
q' [kPa]
segment I
segment II
segment III
15
3. CASE STUDY3.6. Genetic Algorithm
9 different cases were analysed:A. strain path εs-εv
B. compressibilty characteristic p’- εv
C. shearing characteristic q’-εs
a. controlled stress path with shearing(segm. I+II+III)
b. controlled stress path (segm. I+II)c. controlled stress path inside the YS
(segm, I)Named: Aa, Ba, Ca, Ab,…, Cc
16
(*) – the concrete value independent on the FF
( ) – with a trend in FF minimizing
3. CASE STUDY3.7. Estimation of parameters
2.4800.0100.0790.2870.0310.0340.2560.0670.072FF
0.4930.2450.2940.1400.4020.1040.188*0.0330.486ν
0.005*0.0060.0020.007*0.0060.0300.005*0.0540.001κ
0.7170.0690.0671.1520.0120.0990.0280.0590.067λ
0.9810.9581.410*19.4370.6671.414*1.0900.6401.403*M
CcCbCaBcBbBaAcAbAa
Compressib. charact. p-εv
Shearing charact. q-εs
Strain pathεv-εs
a – controlled path + simple shearingb – controlled pathc – controlled path inside YS
17
3. CASE STUDY3.7. Estimation of parameters
2.4800.0100.0790.2870.0310.0340.2560.0670.072FF
0.4930.2450.2940.1400.4020.1040.188*0.0330.486ν
0.005*0.0060.0020.007*0.0060.0300.005*0.0540.001κ
0.7170.0690.0671.1520.0120.0990.0280.0590.067λ
0.9810.9581.410*19.4370.6671.414*1.0900.6401.403*M
CcCbCaBcBbBaAcAbAa
Compressib. charact. p-εv
Shearing charact. q-εs
Strain pathεv-εs
a – controlled path + simple shearingb – controlled pathc – controlled path inside YS
(*) – the concrete value independent on the FF
( ) – with a trend in FF minimizing
0.30
0.02
0.15
1.00
FEM
18
3. CASE STUDY3.7. Estimation of parameters
2.4800.0100.0790.2870.0310.0340.2560.0670.072FF
0.4930.2450.2940.1400.4020.1040.188*0.0330.486ν
0.005*0.0060.0020.007*0.0060.0300.005*0.0540.001κ
0.7170.0690.0671.1520.0120.0990.0280.0590.067λ
0.9810.9581.410*19.4370.6671.414*1.0900.6401.403*M
CcCbCaBcBbBaAcAbAa
Compressib. charact. p-εv
Shearing charact. q-εs
Strain pathεv-εs
a – controlled path + simple shearingb – controlled pathc – controlled path inside YS
(*) – the concrete value independent on the FF
( ) – with a trend in FF minimizing
19experimentaltheoretical
3. CASE STUDY3.7. Estimation of parameters
A. Strain path εv – εs
-5
0
5
10
15
-5 5 15 25 35εs [%]
εv [%]
-2
0
2
4
6
8
-1 0 1 2 3εs [%]
εv [%]
-0,1
-0,05
0
0,05
-0,06 -0,04 -0,02 0 0,02εs [%]
εv [%]
Ab
Aa
Ac
20
3. CASE STUDY3.7. Estimation of parameters
B. Shearing charact.q’–εs
Bb
Ba
Bc0
50
100
150
200
-1 0 1 2 3εs [%]
q' [kPa]
15
20
25
30
35
-0,06 -0,04 -0,02 0 0,02
εs [%]
q' [kPa]
0
200
400
600
-5 0 5 10 15 20 25εs [%]
q' [kPa]
experimentaltheoretical
21
3. CASE STUDY3.7. Estimation of parameters
C. Compressibilty char.p’–εv
Cb
Ca
Cc
-4
0
4
8
12
0 100 200 300 400p' [kPa]
εv [%]
-2
0
2
4
6
8
0 100 200 300
p' [kPa]
εv [%]
-0,1
-0,05
0
0,05
30 35 40 45 50
p' [kPa]
εv [%]
experimentaltheoretical
22
4. CONCLUSIONSIN THE ANALYSED CASE:
The parameters in the optimum set aredifferent than the results of simplelaboratory tests.
It is also different than the one assumedin FEM analysis.
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4. CONCLUSIONS
GENERAL:
Shape of the loading path imposed on a sample and the estimation method havegreat influence on values of parameters.
Modified Cam Clay model is effective for normally consolidated soils. The quality ofmatching is much better in the plasticrange of stress than in the YS interior.
24
THANK YOU FOR YOUR ATTENTION!
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