Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 497

Line Load

A railway track or a long wall of building or a loaded wharf near a waterfront structure will

constitute a line load if it runs parallel to the length of a retaining wall.

Culmann’s graphical method may be adapted to take into account the effect of such a

line load on the lateral earth pressure on the retaining wall, as illustrated in Fig. 13.38.

H

f

B

(+)fd

y-line

G G^1

G¢

F 1

F

W¢

q¢

F¢

A b

l C C¢

q¢

Modified Culmann curve

Culmann curve

FnFn

f-line

Without line load

Ground line

a

Fig. 13.38 Effect of line load on lateral earth pressure
Let AB represent the wall face and let the backfill surface or ground line be inclined to
the horizontal at an angle β. Draw the φ-line and ψ-line through the heel, B, of the wall as
shown. Using the Culmann’s graphical method and ignoring the presence of the line load,
obtain the Culmann’s curve BFF 1 Fn, the maximum ordinate GF and the failure plane BFC.
Let the weight of the wedge ABC′ be W′, C′ being the point of application of the line load. This
is represented by BG 1 along the φ-line. F 1 is the corresponding point on the Culmann-curve
ignoring the line load. If the line load is also included, the weight of the wedge ABC′ will be (W′

• q′). Letting BG′ represent this increased weight, G′F′ is drawn parallel to the ψ-line to meet
  BC′ in F′. For all other wedges considered to the right of the line load, the load q′ should be
  included and the points on the Culmann-curve obtained. The ‘modified’ Culmann-curve ob-
  tained in this manner includes the effect of the line load. There is an abrupt increase in the
  lateral pressure, the increase being proportional to q′. If G′F′ or any other ordinate of the
  modified Culmann-curve is greater than GF, failure will not occur along BF′C′, but will occur
  along BF′C′ if G′F′ is the maximum ordinate, of the modified Culmann-curve. If GF is still the
  maximum ordinate, it means that there is no influence of the line load on the active thrust, Pa.

If G′F′ is the maximum ordinate, the increase in thrust is (G′F′ – GF), or say ∆Pa.

(Invariably, the maximum ordinate of the modified Culmann-curve will be G′F′ indicating

failure along BF 1 F′C′, passing through the line load).

This increase in thrust ∆Pa may be obtained for several different locations of the line

load, as illustrated in Fig. 13.39.

First, the Culmann-curve BFFn is obtained ignoring the line load. Next, the modified

Culmann-curve BF 1 F′F 2 is obtained considering, the line load and adding q′ to the weight of

every wedge. The intercepts GF and G′F′ are obtained by drawing tangents parallel to the φ-

line to the Culmann-curve and the modified Culmann-curve, respectively, these giving the

greatest thrusts without and with the line load. IF the tangent to the Culmann-curve at F is