Issue 50

G. Belokas, Frattura ed Integrità Strutturale, 50 (2019) 354-369; DOI: 10.3221/IGF-ESIS.50.30 363 Finally, as it was applied for the direct shear test, a common approach in engineering practice for the estimation of all stat- istical measures of c and tan φ is first to derive the Mohr – Coulomb constants ( c , tan φ ) for each sample separately (see Table 4) and then apply a statistical t-test on each constant independently for n /3-1 dof (where n the complete number of specimens and n /3 the number of specific locations of soil sampling). For the Herakleion marl case the n /3-1=8 dof lead to: a) mean values: c m =64.34kPa, (tan φ ) m =0.59415, b) standard deviation: S d,c =55.69kPa, S d,tanφ =0.13577, c) standard error: Figure 7 : Characteristic and best estimate Mohr – Coulomb failure envelopes superimposed on the Mohr – Coulomb failure envelopes of each sample. Best estimate c m (kPa) (tan φ ) m SE c (kPa) SE tan(φ) a m , b m from linear regression of all σ 1 , σ 3 data points c m , (tan φ ) m from Eqs.(20,19) SE c and SE tanφ from FORM error propagation (this gives characteristic 1) 66.00 0.58225 15.50 0.0347 c m , (tan φ ) m from mean values of Table 4 SE c and SE tanφ from single variable model (this gives characteristic 4) 64.34 0.59415 18.56 0.0423 Table 5 : Mohr – Coulomb failure criterion constants (mean values and uncertainties). Characteristic values c k (kPa) (tan φ ) k Characteristic 1 ( SE from FORM error propagation): c k = c m - t p,n-2 SE c , tan( φ ) k = tan( φ ) m - t p,n-2 SE tan(φ) 39.60 0.52297 Characteristic 2: a k , b k from linear regression on σ 1pred , σ 3 data points ( σ 1pred = a m + σ 3 b m ± t n-2 SE σ1 ) c k , (tan φ ) k from Eqs.(20,19) 55.65 0.56288 Characteristic 3: a k = a m - t p,n-2 SE a , b k = b m - t p,n-2 SE b c k , (tan φ ) k from Eqs.(20,19) 43.43 0.49395 Characteristic 4 ( SE from one variable model, Eq.(4), for c and tan φ ): cm and tanφ from mean values of Table 4 c k = c m - t p,n-2 SE c , tan( φ ) k = tan( φ ) m - t p,n-2 SE tan(φ) 29.82 0.50990 Table 6 : Mohr – Coulomb failure criterion constants (characteristic values).