Your mention of 'mud' suggests that there is water present. The coefficients of friction given in textbooks are usually for dry conditions. The presence of water trapped below a foundation in a mud or clay can make large differences to coefficient of friction and you should try to control or make allowance for any pore water pressures.
The term "mud mat" does not refer to concrete in its wet, plastic state. Rather, it refers to a slab on grade (usually unreinforced, low strength, 2-3 inches thick) used to produce a clean, uniform working surface so the foundation work does not occur in the mud. It is also called by other names, including "rat slab" and "mud slab".
Surely a concrete base is unlikely to slide on a 'mud mat' (I think that also is known as 'blinding concrete' ?).
If the foundation soil is sufficiently soft to require a mud mat, then the concrete base is much more likely to slide TOGETHER WITH THE MUD MAT, on the underlying soil. Thus the controlling coefficient of friction depends on the soil properties.
