PSI - Issue 10

G. Belokas / Procedia Structural Integrity 10 (2018) 120–128 G. Belokas / Structural Integrity Procedia 00 (2018) 000 – 000

124

5

Table 1. Typical triaxial compression data from Herakleion marl (Tsiambaos (1988)). Sample ΓΣ2 (5 m) Γ 1 (2 m) Γ 1 (3.5 m)

ΓΣ 13 (17 m)

Γ 1 (18 m)

σ 3 (kPa) σ 1 (kPa) s (kPa)

117.7 448.3

156.0 591.5

219.7

62 110

304

95 158

383

110.9 593.5

200.1 884.9

245.3

104 514 309 205

210

427

736.7 375 606 1488 475 506 1383

1044.8

785 1339

283 165

374 218

478 219 358 258 157 248

896 285 332 592 190 174

883 500

352 241

542 342

645 400

498 288

883 456

t (kPa)

Table 1 (continued). Typical triaxial compression data from Herakleion marl (Tsiambaos (1988)). Sample Γ1 (6 m) ΓΣ2 (9 m) ΓΣ 13 (24 m)

Γ 3 (12.5 m)

σ 3 (kPa) σ 1 (kPa) s (kPa) t (kPa)

79 146 265 119.68

258.98

346.29

73.57 141.26 162.85

52 139

222

365 618 997 640.59 1056.54 1339.07 429.68 587.62 750.47 672 819 1004

222 382 631 143 236 366

380 260

658 399

843 496

252 178

364 223

457 362 479 294 310 340

613 391

Table 2. Mohr – Coulomb failure criterion constants for each sample.

Mean

ΓΣ2 (5 m) 40.99

Γ1 (2 m) 22.34

Γ1 (3.5 m)

ΓΣ13 (17 m)

Γ1 (18 m)

Γ1 (6 m) 29.69

ΓΣ2 (9 m) 76.83

ΓΣ13 (24 m)

Γ3 (12.5 m) 201.58 0.34038

Sample

c (kPa)

64.34

21.24

60.41

77.75

48.20

tan φ φ ( ο )

0.59415

0.53191

0.83698

0.64201

0.64099

0.4862

0.64606

0.59134

0.63149

30.42

28.01

39.93

32.70

32.66

25.93

32.86

30.60

32.27

18.78

600

Experimental results

Best estimate

400

Characteristic 1 (FORM) Characteristic 2 (envelope for p>5%) Characteristic 2 (linear regression)

σ 3 (kPa)

200

0

0

200 400 600 800 1000 1200 1400 1600

σ 1 (kPa)

Fig. 3. Statistical evaluation of the experimental results of Table 1.

5. Alternatives for the statistical measures and the characteristic envelope

Alternatively, for the characteristic envelope we can apply a t-student distribution into the y ( x ) estimate (i.e. the predicted σ 1 for given σ 3 , given by Eq.(19)) for a p =5% probability (i.e. t p,n-2 =1.70814) and n -2 dof. Fig.3 shows the characteristic envelope from Eq.(19) for a p =5%, which is non – linear (characteristic 2). By linear regression, this characteristic envelope leads to characteristic values a k =190.36 kPa and b k =2.92550 for Eq.(19) and then c k2 =55.6 kPa and (tan φ ) k2 =0.56287 for the Mohr – Coulomb failure criterion (Fig.3, characteristic 2 – linear regression). Note that this approach does not take into account the error propagation to calculate the uncertainties.

  

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1 

  

n

n

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



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2

2

3  a b t    m m n

n

1

 

  

1 

 j

 

(19)





i

2

3

3

3

3



n

2





j

i

1

1



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