The ordinate cm-bm (parallel to BE) at the point where the tangent parallel to BD touches the curve

The shortest distance from B to the curve

H/3 above the base, inclined at delta to the wall normal

H/2 above the base, horizontally

2081 Bhadra · 4 marks

Culmann's method, active, cohesionless

Short answer

Draw wall, φ-line BD, pressure line BE at ψ=θ−δ. From heel draw trial planes, compute wedge weights W=γA. Plot W on BD, draw lines parallel to BE to intersect planes, forming the Culmann curve. Tangent parallel to BD gives maximum ordinate Pa, acting at H/3, inclined at δ to the wall normal.

Explain with neat sketch the step by step procedure for Culmann's graphical method of active earth pressure without surcharge load for cohesionless soil.

Culmann's graphical method for active thrust on a wall with a cohesionless backfill and no surcharge:

Draw the wall $AB$ and the backfill surface to scale and mark the heel $B$ .
Draw the $\phi$ -line $BD$ from $B$ at angle $\phi$ to the horizontal.
Draw the pressure line $BE$ from $B$ making angle $\psi = \theta-\delta$ with $BD$ ( $\theta$ = wall back angle with horizontal, $\delta$ = wall friction).
Draw trial failure planes $BC_1, BC_2, BC_3,\dots$ from $B$ to the ground surface.
Find the area of each wedge $ABC_i$ and its weight $W_i = \gamma\times\text{area}$ per metre run.
To a suitable scale, mark $W_1, W_2, W_3,\dots$ on $BD$ as $b_1, b_2, b_3,\dots$
From each $b_i$ draw a line parallel to $BE$ to meet $BC_i$ at $c_i$ .
Join $c_1, c_2, c_3,\dots$ with a smooth curve (Culmann curve).
Draw a tangent to the curve parallel to $BD$ ; let it touch at $c_m$ .
Draw $c_m b_m$ parallel to $BE$ to meet $BD$ . Its length, converted by the force scale, is the active thrust $P_a$ . $BC_m$ is the critical failure plane.
$P_a$ acts at $H/3$ above the base of the wall, inclined at $\delta$ to the wall normal.

    A |\                      ground
      |  \_____________________ C1 C2 Cm C3
      |     curve ..  .
      |        ..  /
    B +---b1--b2--bm--b3--> D   (phi from horizontal)
          BE at psi from BD, weights on BD

✓ Answer checked by Claude Sonnet 5.5

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