Crib wall stability (Coulomb) calculator

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Worked example — results

• ✓ Sliding FS ≥ 1.5
• ✓ Overturning FS ≥ 2.0
• ✓ Resultant within middle third
• ✓ Toe pressure ≤ allowable

Method, formulas and assumptions

• Wall friction δ = 2φ′/3 = 2*30/3 = 20 °
• Back inclination θ = −ω (leaning into fill) = -10 = -10 °
• Coulomb Ka = COS(RADIANS(30--10))^2/(COS(RADIANS(-10))^2*COS(RADIANS(-10+20))*(1+SQRT(SIN(RADIANS(30+20))*SIN(RADIANS(30))/(COS(RADIANS(-10+20))*COS(RADIANS(-10)))))^2) = 0.23169
• Thrust ½KaγH² + KaqH = 0.5*0.23169*19*4^2+0.23169*5*4 = 39.851 kN/m
• Horizontal component = 39.851*COS(RADIANS(20+-10)) = 39.246 kN/m
• Vertical component = 39.851*SIN(RADIANS(20+-10)) = 6.9201 kN/m
• Wall weight γc·B·H = 19*1.6*4 = 121.6 kN/m
• Weight lever about toe B/2 + (H/2)tanω = 1.6/2+4/2*TAN(RADIANS(10)) = 1.1527 m
• Thrust lever (vertical part) B + (H/3)tanω = 1.6+4/3*TAN(RADIANS(10)) = 1.8351 m
• Thrust height (combined) = (0.5*0.23169*19*4^2*4/3+0.23169*5*4*4/2)/39.851 = 1.4109 m
• Base normal force = 121.6+6.9201 = 128.52 kN/m
• Resultant from toe = (121.6*1.1527+6.9201*1.8351-39.246*1.4109)/128.52 = 0.75857 m
• Eccentricity B/2 − x = 1.6/2-0.75857 = 0.041427 m
• Toe pressure N/B(1 + 6e/B) = 128.52/1.6*(1+6*ABS(0.041427)/1.6) = 92.804 kPa
• Limit: B/6 = 1.6/6 = 0.26667 m
• Check: |e| = ABS(0.041427) = 0.041427 m
• Overturning FS = (121.6*1.1527+6.9201*1.8351)/(39.246*1.4109) = 2.7607
• Sliding FS (W + Pv)tan δb/Ph = (121.6+6.9201)*TAN(RADIANS(30))/39.246 = 1.8907
• Global (deep-seated) stability and internal crib member strength must be checked separately; batter of 1:4 to 1:6 is typical for concrete cribs.

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