The laws of smearing saliva on the ground:
Regarding smearing the saliva on the floor-See “The Laws of Building and Destroying”.
May one smear saliva on a bench? It is permitted according to all.
Why is smearing saliva not forbidden due to the smearing prohibition? It requires analysis why this matter is not forbidden due to the smearing prohibition. One can however say that the smearing prohibition only applies when one’s intent is to smear one item on to another, however here that his intent is that it become completely absorbed into the ground [and not remain at all over the ground] it thus does not contain the smearing prohibition. [See footnote for other opinions]
 SHU”A of Michaber 316/11. In Admur these laws are not found.
 M”A 316/24, Levushei Serud on M”A; M”B 316/49
 M”A 316/24, Levushei Serud on M”A; M”B 49
 However the Elyah Raba learns that according to Rashi/Ran/Tur there is a smearing prohibition involved. The Daas Torah concludes that one may certainly be lenient like the Magen Avraham in a case that one is smearing saliva for one who is sick. To note that this dissenting opinion of the Elyah Raba is not recorded by the M”B.