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FRICTION CIRCLE METHOD COLUMAN’S AND COLOUMB’S THEORY SYABILITY OF SLOPES FRICTION CIRCLE METHOD COLUMAN’S AND COLOUMB’S THEORY

Stability of Slopes

z σz σ τ B A D C Normal and tangential stresses are, σ and τ b b cos i τ is tangential stress acting along plane CD, tries to slide the soil i σ Where as stress τf is resisting the slide of plane CD C τ Factor of Safety

Stability Number We have Factor of Safety for cohesive soils as We know Substituting

Stability of Slopes Stability of finite Slopes can be analyzed by following methods Swedish circle method Friction circle method Bishop’s method

O r C B r W A b b Total Driving Force is W1 W2 W3 W4 N1 W5 W1 W6 T1 W7

To find out Σ N and Σ T following rectangles are drawn b b

P Q Factor of Safety Curve Critical Circle point Least Factor of Safety Q

FRICTION CIRCLE METHOD This method also assumes the failure surface as the arc of a circle. In this method a concentric circle with P as center and “r sinφ” as radius is drawn. When a tangent is drawn to this circle which will cut the failure circle at an Obliquity φ. Other way, if a line is drawn at an obliquity angle φ, from failure surface representing reaction Δ R, then this line will be tangent to the small circle drawn at P This small circle is known as “Friction Circle”

Consider a slope ABC, and a slip surface AC which is a part of a circle with radius “r” Draw a line F1E1 which is tangent to the circle and cuts failure surface at angle φ. F2 F2 G P G r sin φ F1 F1 B C Friction Circle φ E2 φ A E1 Similarly draw line F2E2

R Tangent to friction circle In order to know magnitude of and R, force triangle is drawn as shown. R W In this force polygon (triangle) W is known to us and hence and R can be calculated. Then Factor of Safety is calculated as Parallel to chord AC Where C is cohesive strength and Cm is Mobilised cohesive strength

Area of N-Rectangles = 14.4sq cm In order to find the factor of safety of d/s-slope of an earth dam, during steady seepage , the section of the dam was drawn to a scale of 1 cm = 4 cm, and the following result obtained on a critical sip circle. Area of N-Rectangles = 14.4sq cm Area of T-Rectangles = 6.4sq cm Area of U-Rectangles = 6.9sq cm Length of Arc = 12.6 cm Laboratory test results have furnished angle of resistance as 26 degrees and 19.5kN/m2 for cohesion. Determine the factor of safety of the slope. Unit weight of soil = 19 kN/m3

Scale 1 cm = 4 cm, i.e x= 4

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