Critical state approach and equivalent granular state theory for predicting the undrained cyclic and monotonic behaviour of non-plastic silty sands

Recent earthquake events revealed that liquefaction of silty sands remains an unsolved issue, even after decades of investigations. Difficulties in the prediction of the undrained cyclic response of silty sands arise from combined effects of various factors affecting the behaviour such as fines content, gradation, particle shape, plasticity of fines, initial static shear stress, and so on. This study attempts mainly to quantify the effect of an initial static shear stress through undrained cyclic simple shear tests on sand mixed with non-plastic fines dug up from Ticino river, Italy. The cyclic behaviours and the liquefaction resistance of silty sands were investigated in the framework of critical state soil mechanics. A cyclic simple shear tests programme was accomplished, covering different fines content fc, initial void ratios e0, initial vertical effective stresses s'v0 and initial static shear stress ratios (factor α). In the present study undrained monotonic triaxial tests conducted in a previous study on the same materials were also reinterpreted to enable further characterisation and analysis. Four typical cyclic failure patterns were identified and discussed. They were found dependent on the initial state of the specimens and cyclic loading characteristics. The undrained cyclic test results were interpreted using different measures of the initial state density. When a constant void ratio e was considered, the addition of fines to the Ticino sand caused more contractive behaviour and lower liquefaction resistance up to a threshold fines content fthre. When the equivalent granular void ratio e* was used instead, similar cyclic resistances ratios for the Ticino sand-silt mixtures were found, regardless of fines content and global void ratio. This aim was reached by introducing in the relationship defining e*, a parameter b termed the fines influence factor which quantifies the fraction of fines particles that participates actively in the force transmission chains between grains within the mixture. The value of b was determined to be different according to whether it is evaluated by back analysis conducted on the undrained cyclic resistance of the mixtures (bCRR) or on their critical state lines in e-log(p') plane (bCSL). Correlations between the fines influence factor b with material properties were proposed to simplify the use of the equivalent granular void ratio approach in practical applications. To take into account the combined effect of void ratio, initial vertical stress and fines content, different initial state indices, defined in the frame of the critical state theory, were used and unique correlations were obtained between the undrained monotonic and cyclic behaviours of the investigated mixtures and the aforementioned state indexes. Unique correlations continued to be found even in tests in which an initial static shear stress was applied. Among these state indexes the state parameter Ψ and the equivalent granular state parameter Ψ* provided the more reliable correlations with the undrained response of silty sands. This allowed the conclusion that they can be used effectively for describing the main features of the undrained monotonic and cyclic behaviour of the non-plastic silty sands regardless of fines content (lower than the threshold value), stress level and density. However the equivalent granular state parameter Ψ* has the advantage that it can be assessed referring to an unique critical state line (EG-CSL) without the need to perform several sets of triaxial tests, each one for a given value of fc. A further advantage resides in the fact that this unique EG-CSL can be legitimately assumed to coincide with the CSL of the clean sand. Finally, the pore pressure generated in the cyclic tests was investigated and it was found to be significantly influenced by the initial static shear stress. For this reason, a cyclic pore pressure generation model was proposed capable to predict the residual excess pore pressure rise of non-plastic silty sands under various initial static shear stress conditions.