From Coulomb’s theory, Karl Culmann (1866) devised his own Culmann’s Graphical Method for calculating earth pressure. According to Coulomb’s wedge theory, Culmann’s method allows us to graphically calculate the magnitude of the earth pressure and locate the most dangerous rupture surface.
This method has more general application than Poncelet’s and is, in fact, a simplified version of the more general trial wedge method. It is suitable for any form of ground surface, various forms of surcharge loads, and layered backfill with different unit weights for different layers.
The measures or steps in the procedure of culmann’s method are as follows :
Procedure of Culmann’s Method
- To scale, draw the retaining wall AB.
- BD is the φ-line.
- A line BL is drawn at an angle of 0 with line BD, resulting in Ψ= α – δ.
- The weight (W) of the failure wedge ABF (γ. ABF) is calculated using a failure surface BF which is totally assumed.
- BP = W is obtained by plotting the weight (W) along BD.
- To intersect the failure surfaces BF and Q, a line PQ is drawn from point P parallel to BL.
- The magnitude of Pa needed to maintain equilibrium for the presumed failure plane is represented by the length PQ.
- The process is replicated with several different failure planes BF₂, BF₁, BF₃, etc. As a result, the points Q², Q¹, Q³ and so on are obtained.
- A smooth curve is drawn joining points Q², Q, Q¹, Q³ etc. This curve is called Culmann’s Line.
- A line XY (dotted) tangential to the culmann line and parallel to BD is drawn. The point of tangency is designated by the letter T.
- Drawing a line TO from T on BD and parallel to BL measures the magnitude of largest value of Pₐ. It’s the same as the coulomb’s pressure (Pₐ).
- The failure plane actually passes through point T (dotted).
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Also Read : California Bearing Ratio Test【CBR Test】of Soil
Problems Based on Culmann’s Graphical Method
Example :
The following data was available for a retaining wall system :
Wall Height = 7 m
Backfill Properties, γ𝒹 = 16 kN/m², φ = 35°
Wall Friction Angle = δ = 20°
Backfill Slope = 1:10
Back of the wall is inclined at 20° to the vertical.
Determine the magnitude of active earth pressure by Culmann’s Graphical Method.
Solution :
Trial Pressure lines BC₁, BF₂, BF₃, etc are drawn by making AC₁ = C₁C₂ = C₂C₃ etc = 2 cm.
The length of perpendicular from B to backfill surface is 8.2 m.
The area of wedges BAC₁, BAC₂, BAC₃ = ½ (base length AC or AC₂ or AC₃, etc) * 8.2 cm
The weight of the wedges in above per unit length of wall may be found out by multiplying the area by the unit weight of the soil.
The weights of wedges BAC₁, BAC₂, etc are respectively plotted as BD₁, BD₂, etc on the φ-line using the scale 1 cm = 100 kN.
Lines drawn parallel to the pressure line from points D₁, D₂, D₃, etc meet the trial rupture lines BC₁, BC₂, etc at points E₁, E₂, E₃, etc respectively.
Pressure locus is drawn passing through the points E₁, E₂, E₃, etc.
Line ZZ is drawn tangential to the pressure locus at a point at which this is parallel to the φ-line. This point coincides with point E₃.
E₃D₃ gives the active earth pressure, Pₐ = 180 kN/m on the length of the wall.
BC₃ is the critical rupture line.