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Increment of earth pressure due to horizontal surcharge

Infinitely long distributed load f acting horizontally the on the ground surface leads to a triangular increment of active earth pressure applied to the structure over a given segment hf - see figure:

Diagram of increment of active earth pressure due to horizontal distributed load acting on ground surface

Range of the earth pressure contribution is determined by two lines drawn from the end points of the distributed load with angle φ and angle ϑa (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 between structure and 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 between structure and soil

α

-

back face inclination of the structure

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

where:

ϑa

-

angle of critical slip plane

φ

-

angle of internal friction of soil

δ

-

angle of friction between structure and soil

f

-

magnitude of line surcharge

For non-homogeneous soils the program proceeds as follows.