The recent development of robust and accurate numerical methods capable of simulating the complex coupled deformation and flow processes occurring in the soil around a penetrating object, such as the PFEM, allows to analyse in great detail the evolution of deformation, stress and pore pressure fields occurring in the soil during a cone penetration test with measurement of pore pressures (CPTu test). The focus of the present work is in the study of the effects that the large deformations induced by the cone penetration may have on the fabric and interparticle bonding in natural structured soils, and, in turns, in the conventional interpretation of the test results in terms of cone tip resistance. To this end, a series of CPTu tests in a saturated soil mass were simulated with the PFEM code G-PFEM, adopting for the soil a finite deformation, hyperelastic-plastic model - the FDMilan model - based on the multiplicative split of the deformation gradient and equipped with non-local hardening laws. The model was calibrated from the available experimental data on Osaka clay, a soft heavily structured natural clay. The PFEM simulations were capable of capturing: i) the destructuration associated with the extreme plastic deformations which develop around the cone tip; ii) the space and time evolution of pore water pressure as the cone tip advances; iii) the effect of the initial structure on predicted values of cone tip resistance, and iv) the effects of the assumed internal length scale on the localized deformation pattern. The conventional interpretation of CPTu test results in presence of significant destructuration effect may lead to a significant underestimation of the apparent undrained strength and of the overconsolidation ratio of the deposit.