I think that Govind is right, particularly if the calcium carbonate has surface of weakness through which the slip surface can follow to cause instability.
The presents of calcite on a shear surface in weathered mudrocks increases the residual strength significantly above that that would be measured if it were not present because the calcite particles act like silt or sand mixed with the clay. see for example Hawkins and McDonald in Geotechnique 1992. This is important where there has already been a landslide and remedial measured are to be designed.
Where no shear surface is present the intact material behaviour will also be influenced by the calcite depending on its proportion and whether it is bonding the particles or simply acting as an unbound granular material.