Random-effects regression model for shear wave velocity as a function of standard penetration test resistance, vertical effective stress, fines content, and plasticity index

A random effect regression model is used to formulate a unified equation and estimate shear wave velocity (Vs). Standard penetration test (SPT) number, effective overburden pressure, plasticity index, and the fines content (Fc) are used as input parameters. First, a fixed model regression is used to obtain the regression parameters. SPT number and shear wave velocity are measured at 2 m intervals up to a depth of 10 m, for 71 boreholes, distributed evenly in Urmia city. Plasticity index and fines content are evaluated from laboratory tests that were performed on 355 samples obtained from the 71 boreholes (i.e., 5 samples from each borehole). Statistical analysis performed on the fixed effect model showed the need for examining the random effects arising from variable SPT test conditions in each borehole. A mixed effect regression model is employed to investigate such effects. The distribution of residuals is found to satisfy the normality criteria for the mixed effect model. A strong fit for the model is obtained, and through statistical evidence, it is implied that the proposed model is practical. The model's most prominent feature is the capability of unifying different soil types via the incorporation of plasticity index and fines content as inputs.