Issue 41

A. Mardaliazad et alii, Frattura ed Integrità Strutturale, 41 (2017) 504-523; DOI: 10.3221/IGF-ESIS.41.62 515 sandstones. However, this automatic method was used initially within this study due to the overwhelming number of input parameters which are difficult to obtain from current resources. Apart from the numerical results which are obtained directly from the automatic mode, LS-DYNA also generates all the input parameters automatically and writes them into the “MESSAG” file. Therefore, some of these parameters (i.e. the b-parameters) can be used in addition to the other parameters provided for the users by other resources. Previous studies [36, 37] showed that the mechanical behaviour of Berea sandstone is expected to be very similar to the Pietra Serena. Since the experimental data related to the triaxial compression test of Pietra Serena sandstone is not available (which is required for calibrating the i a - parameters), it was decided to use the experimental data of the Berea sandstone for the calibration the KCC material model. The initial input parameters used for the automatic mode were obtained from [38] and reported in Tab. 3. Density, RO [ton/mm 3 ] Poisson ratio, PR UCS, A0 [MPa] NOUT RSIZE UCF 2.00e-9 0.34 -62.00 2.00 0.03937 145.00 Table 3: The experimental data of Berea sandstone provided for the automatic mode. The parameters RSIZE and UCF are unit conversion factors and the NOUT is called the “output selector for effective plastic strain”. According to [39], when NOUT=2, the quantity labelled as “plastic strain” by LS-PrePost is actually the quantity that describes the “scaled damage measure, δ” which varies from zero to two. When the amount of δ is still lower than one, the elements of the part modelled by the KCC, don’t reach the yield limit. When this amount is equal to two, the corresponding elements meet the residual failure level. Only at the automatic mode of MAT_072R3 keyword (when a maximum of six parameters are defined) the A0 parameter must be defined as a negative number to represent the unconfined compression strength. For instance, the -62 in Tab. 3, means the UCS is considered equal to 62 [MPa]. Tab. 4 expresses the results obtained from the automatic input generation mode of MAT_072R3, after performing the initial simulation, which were also used at the full input calibration mode. B1 B2 B3 ω S λ E drop LOC-WIDTH 1.1 1.35 1.15 0.5 100 1.00 1.35 Table 4 : The results obtained from the automatic input generation mode of MAT_072R3. Where, the parameters ω, E drop and LOC-WIDTH are the frictional dilatancy, post peak dilatancy and three times of the maximum aggregate diameter, respectively. Almost all of the EOS tabular data obtained from the automatic input generation mode, were also used for the full input calibration mode. Only the “Pressure02” parameter from EOS keyword was changed to 26.1 [MPa] to reach the same bulk modulus (and accordingly the elastic behaviour) as the Berea sandstone. The tensile strength parameter was investigated in another recent study by the same authors [37] where the Brazilian tensile test was performed on Pietra Serena and the tensile strength was determined as 5.81 [MPa]. The pairs of η - λ parameters were changed to the values reported in [40]. A new set of i a - parameters were computed by the least square curve fitting method from the experimental triaxial compression tests [20]. These experimental data which were performed at four different confining pressure levels are reported in [41]. The i a - parameters are reported in Tab. 5 (note that the A0 parameter here is a positive value). A0 [MPa] A1 [MPa] A2 A0Y [MPa] A1Y [MPa] A2Y A1F [MPa] A2F 34.458 0.65629 0.00097 21.621 1.11569 0.00251 0.7563 0.00097 Table 5 : The a i -parameters experimental of Berea sandstone provided for the full input mode. Extended (Linear) Drucker-Prager model This is an advanced material model implemented by ABAQUS, which is based on the conventional Drucker-Prager constitutive law. There are three forms of the extended Drucker-Prager material model developed in ABAQUS which are the linear, the hyperbolic and the general exponential forms [30]. Within this research work, the linear form of this model was investigated. The linear Drucker-Prager (LDP) model consists of a pressure-dependent three-invariant failure surface which obtains the opportunity of having the non-circular yield surface (unlike the conventional Drucker-Prager) in the