Dataset of the homonymous paper: a first-of-its-kind database that addresses the size and complexity issues of creating synthetic datasets for nonlinear constitutive modeling of soils by simulating both drained and undrained triaxial tests. Two datasets are provided: the first one considers a nested Latin Hypercube Sampling of input parameters encompassing 2000 soil types, each subjected to 40 initial test configurations, resulting in a total of 160000 triaxial test results (NorSandTXL_H5.zip). The second one considers nested quasi-Monte Carlos sampling techniques (Sobol and Halton) of input parameters encompassing 2048 soil types, each subjected to 42 initial test configurations, resulting in a total of 172032 triaxial test results (NorSand_2048_42_Drained.zip and NorSand_2048_42_Undrained.zip). Each simulation dataset comprises a 4000 by 10 matrix that can be used for general multivariate forecasting benchmarks, in addition to direct geotechnical and soil science applications.