Issue 50

G. Belokas, Frattura ed Integrità Strutturale, 50 (2019) 354-369; DOI: 10.3221/IGF-ESIS.50.30 361 where: 2 2 2 2 ( 1) 1 ( 1) / ( 1) )         b b b b ,    3/2 2 2 3 2 ( 1) 1 1 ( a 1 t n )              b b b b (24) 1 – / ( ) ( ) 2      sin cos c a (25) 2 1 ) 2(/ ( )     c a sin cos    (26) Next, the above equations are applied to laboratory results from the Herakleion marl (see Table 3, data from [12]), with 27 specimens and 9 samples (3 specimens per sample). Treating each specimen separately (i.e. sample size n =27), the best estimates of a and b constants of Eq.(6) are determined from the linear regression (Eqs.( 8,9)), which gives a m =229.6 kPa and b m =3.02553. Applying these values into Eqs.(20,19) we get the best estimates c m =66.0 kPa and (tan φ ) m =0.58225. The FORM (by application of Eqs.(23,22,15,14)) gives the corresponding uncertainties SE c = u c =15.5 kPa and SE tanφ = u tanφ =0.0347. A t- student distribution for n -2 dof (Eqs.(16,17)) to account for the error propagation leads to the characteristic values c k1 = 39.60 kPa and (tan φ ) k1 =0.52297. The best estimate of the mean failure envelope, as well as the estimated characteristic en- velopes are represented in Fig.5, in which figure the characteristic 2 and 3 envelopes are explained later in the same section. It is evident from Fig.5 that characteristic 1 can be indeed considered as a conservative estimate of the mean failure envelope. Sample ΓΣ2 (5m) Γ1 (2m) Γ1 (3.5m) ΓΣ13 (17m) Γ1 (18m) σ 3 (kPa) 117.72 155.98 219.74 62 110 304 95 158 383 110.85 200.12 245.25 104 210 427 σ 1 (kPa) 448.32 591.54 736.73 375 606 1488 475 506 1383 593.51 884.86 1044.77 514 785 1339 s (kPa) 283 374 478 219 358 896 285 332 883 352 542 645 309 498 883 t (kPa) 165 218 258 157 248 592 190 174 500 241 342 400 205 288 456 Table 3.1 : Typical triaxial compression data from Herakleion marl ([12]). Sample Γ1 (6m) ΓΣ2 (9m) ΓΣ13 (24m) Γ3 (12.5m) σ 3 (kPa) 79 146 265 119.68 258.98 346.29 73.57 141.26 162.85 52 139 222 σ 1 (kPa) 365 618 997 640.59 1056.54 1339.07 429.68 587.62 750.47 672 819 1004 s (kPa) 222 382 631 380 658 843 252 364 457 362 479 613 t (kPa) 143 236 366 260 399 496 178 223 294 310 340 391 Table 3.2 : Typical triaxial compression data from Herakleion marl ([12]). 0 200 400 600 0 200 400 600 800 1000 1200 1400 1600 σ 3 (kPa) σ 1 (kPa) Experimental results Best estimate Characteristic 1 (FORM) Characteristic 2 (envelope for p>5%) Characteristic 2 (linear regression) Figure 5 : Statistical evaluation of the experimental results of Table 3.