Lateral Earth Pressure - Elements of Soil Mechanics - page 198

the Culmann line construction. Besides being able to cope with irregular soil surfaces the method can
also deal with irregular combinations of uniform and line loads.
The procedure is to select a series of trial wedges and find the one that exerts the greatest thrust on
the wall. A wedge is acted upon by three forces:
W, the weight of the wedge;
P a , the reaction from the wall;
R, the reaction on the plane of failure.
At failure, the reaction on the failure plane will be inclined at maximum obliquity, φ ′ , to the normal to the
plane. If the angle of wall friction is δ then the reaction from the wall will be inclined at δ to the normal
to the wall ( δ cannot be greater than φ ′ ). As active pressures are being developed the wedge is tending
to move downwards, and both R and P a will consequently be on the downward sides of the normals (Fig.
7.14b ). W is of known magnitude (area ABD × unit weight) and direction (vertical) and R and P a are both
of known direction, so the triangle of forces can be completed and the magnitude of P a found (Fig. 7.14c ).
The value of the angle of wall friction, δ , can be obtained from tests, but if test values are not available
δ is usually assumed as 0.5 to 0.75 φ ′ .
In Fig. 7.16, the total thrust on the wall due to earth pressure is to be evaluated, four trial wedges
having been selected with failure surfaces BC, BD, BE and BF. At some point along each failure surface a
line normal to it is drawn, after which a second line is constructed at φ ′ to the normal. The resulting
four lines give the lines of action of the reactions on each of the trial planes of failure. The direction of
the wall reaction is similarly obtained by drawing a line normal to the wall and then another line at angle
δ to it.
The weight of each trial slice is next obtained, and starting at a point X, these weights are set off verti-
cally upwards as points d 1 , d 2 , etc. such that Xd 1 represents the weight of slice 1 to some scale, Xd 2
represents the weight of slice 2 + slice 1, and so on.
A separate triangle of forces is now completed for each of the four wedges, the directions of the cor-
responding reaction on the failure plane and of P a being obtained from the space diagram. The point of
Fig. 7.16 Culmann line construction for a cohesionless soil.