  This work proposes the Least Squares with Virtual Displacements (LSVD) method
to obtain the shear strength of n soil samples for the cohesionless,
frictionless and mixed resistance conditions. Finding a common tangent line of
more than two samples may not have an exact solution, especially if there are
measurement errors. LSVD is an iterative method to find the best common tangent
line or function to the n soil samples. There are soils that can be modeled
with a linear failure envelope but the LSVD can be formulated in different
forms, adapting itself to other criterion too, like the logarithmic failure
envelope. The tested data is analyzed with LSVD and compared between other
commonly used methods, like p-q method and CTPAC. The soils' samples were
subjected to random noise to simulate errors from measurements to study the
method's results. Also with that analysis a common reference point can be found
to compare the methods given that all of them take different points of the Mohr
Circles.
