Line surcharge

Vertical infinitely long line loading f acting on the ground surface parallel with structure leads to a triangular increment of active earth pressure applied to the structure over a given segment h_f  – see figure:

Diagram of increment of active earth pressure due to vertical

line loading acting on ground surface

Action of the line surcharge is deterimened such that two lines are drawn from the point of application following angles φ and ϑ_a (corresponding to the critical slip surface), which is provided by:

where:	φ	-	angle of internal friction of soil
	ε	-	angle derived from the following formulas

where:	β	-	slope inclination
	φ	-	angle of internal friction of soil
	δ	-	angle of friction structure - soil
	α	-	back face inclination of the structure
	c	-	cohesion of soil
	γ	-	unit weight of soil
	h	-	assumed depth

For non-homogeneous soil and inclination of ground surface β smaller than the angle of internal friction of the soil φ the value of the angle ε is given by: 

where:	β	-	slope inclination
	φ	-	angle of internal friction of soil
	δ	-	angle of friction structure - soil
	α	-	back face inclination of the structure

The resultant of the increment of active earth pressure due to line loading f is provided by:

where:	ϑa	-	angle of critical slip plane
	φ	-	angle of internal friction of soil
	δ	-	angle of friction structure - soil
	f	-	magnitude of line surcharge

For non-homogeneous soils the program proceeds as follows.