The discussion above mentions the slope of an embankment which should be directly related to the stability of the strata that was excavated. Staying in the southeast of England, the Chalk is a soft rock (hit it with a hammer and most of the time you will get a thud rather than a ringing sound). Yet it will stand up with remarkable stability due to the interlocking nature of the component micro fossils. The White Cliffs of Dover are still there after 10,000 years.
When the M40 was excavated through the Chilterns many were surprised to see the Chalk left as a near vertical cliff. Although some degradation has taken place, the cutting is still there today. When I used to take the train from Southampton to London in the 1960s I remember the chalk cliffs at Micheldever Station where the LSWR had created sidings. They are still there today.
Move to Wales and the cutting at Talerddig had near vertical walls between hard rock. Still standing!
The worst case for modellers will be soft clays prone to earth movements. Low angle embankments take up space that we often don't have. Some of these have become news in recent years - the Harbury landslip being an economic disaster for the Chiltern Line. A whole new science has developed around such problems and there is debate as to how best to prevent landslips.
Here is a good link (there are many more images on line):
Harbury Tunnel landslide: an update from Network Rail
Incidentally, the Harbury line was designed under the management of I K Brunel. He also managed the similar cutting at Mickleton Tunnel on the Cotswold Line. Those were early days, though, when "Geotechnics" didn't exist as a university degree course.