Most landscape models to date have utilized very simple assumptions regarding regolith development due to weathering.  Most models assume that 1) Slopes retain a regolith cover at all times , and either 2) that the rate of mass movement is independent of regolith thickness (most movement occurs in the near-surface part of the regolith), or 3) that regolith thickness is spatially and temporally uniform.  In this case the thickness of the regolith does not have to be explicitly modeled.  Slopes with a regolith cover are often called transport-limited slopes because the rate of erosion is limited by  the rate of removal of regolith by mass wasting or water erosion.
In more general models the regolith is idealized as a single layer of uniform properties, which increases in thickness through time if no erosion occurs.  The simplest model is one in which the rate of weathering decreases exponentially with regolith thickness (zs-zb) [formula on left].  A few studies have shown that regolith thickness increases less than linearly with time (e.g., studies of soil thickness on glacial moraines of different age).  Physical weathering is often modeled by this equation, with the decrease in weathering rate with depth being due to decreasing frequency of frost action, wetting and drying, or whatever other process dominates.  Gilbert (1887) suggested that chemical weathering rates exhibit a peak at a finite regolith thickness due to a more consistent  moisture supply.  The equation on the right is one possible function showing a peaked relationship.  In addition, vegetation and microorganism activity associated with the presence of a regolith can enhance weathering rates when a regolith cover is present.  Ahnert (1964) and Carson and Kirkby (1971) were pioneers in using this type of approach.
More explicit treatment of regolith layering and mechanical properties could be used in specialized modeling.
If the erosion rate exceeds the maximum possible weathering rate, bedrock would become exposed and other physical and chemical weathering processes, as listed above, would fragment the exposed rock such that mass wasting and water erosion could remove the weathered material.  Bedrock slopes are commonly called weathering-limited slopes (Carson and Kirkby, 1971).