Different experimental and theoretical methods that are used in practice to determine tensile strength of sand and clay in saturated and unsaturated condition.
I didn't hear about "tensile strength of soil " in soil mechanics before, there is "Cohesion" , some types of soil have real cohesion like clay and silt, others have apparent cohesion (due to capillary) like wet fine sand. Soil strength always define by their shear strength.
On other hand, if you mean by "tensile strength of soil " the minimum normal stress at failure, you can calculate it from direct shear test or from tri-axial test.