Probabilistic Models for Cyclic Straining of Saturated Clean Sands

A maximum likelihood framework for the probabilistic assessment of postcyclic straining of saturated clean sands is described. Databases consisting of cyclic laboratory test results including maximum shear and postcyclic volumetric strains in conjunction with relative density, number of stress (strain) cycles, and “index” test results were used for the development of probabilistically based postcyclic strain correlations. For this purpose, in addition to the compilation of existing data from literature, a series of stress-controlled cyclic triaxial and simple shear tests were performed on laboratory-constituted saturated clean sand specimens. The variabilities in testing conditions (i.e., type of test, consolidation procedure, confining pressure, rate of loading, etc.) were corrected through a series of correction schemes, the effectiveness of which were later confirmed by the discriminant analyses results. Volumetric and shear strain boundary curves were developed in the cyclic stress ratio versus $N_{1,60,\mathrm{CS}}$ or $q_{c,1}$ domain. In addition to being based on significantly extended and higher quality databases, contrary to the existing judgmentally derived deterministic ones, proposed correlations have formal probabilistic bases, and so provide insight regarding uncertainty of strain predictions or probability of exceeding a target strain value. Probabilistic uses of the proposed correlations were illustrated by three sets of examples. A companion paper applied and calibrated the proposed volumetric strain correlation to semiempirically evaluate postearthquake settlement of level, free-field sites. For the calibration, case history soil profiles, composed of a broad range of sand types and depositional characteristics, shaken by a number of earthquakes, were used. Superior predictions of field settlements by this laboratory data-based cyclic strain assessment approach were concluded to be strongly mutually supportive.