Lecture 21 - SL8 Circular Arc Analysis: Assume circular...

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SL8 Circular Arc Analysis: Assume circular failure surface Draw free body force diagram Calculate driving and resisting forces (weight, loads, etc.) Sum moments about center of circle Determine required average shear stress on failure plane o if φ = 0 (clay soils, saturated) then τ = c and independent of σ v o if > 0 (clay-silt-sand mixes) then τ = c + σ tan φ and must calculate σ along failure surface o Repeat the above calculations ( many times ) for different circles to find the circle that develops the most shear stress, τ d , and hence has the lowest safety factor defined as: tan tan FS c c FS tan c tan c FS d d c d d d φ φ = = φ σ + φ σ + = τ τ = φ where c d and φ d refer to the "developed" shear strength required for stability o Note that if the c and φ strength are developed at the same rate then FS = FS c = FS φ o In the absence of external forces (W w , W h and V) the shear strength c d mobilized for a clay with a given combination of slope angle i, slope height H, unit weight γ can be calculated and expressed as a “stability number ” = H c N d S γ = R V F W w W h L 4 L 3 L 2 L 1 c Length of Arc = Δ L W s φ H i
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SL9 o Taylor (1948) provided the figure below for the stability number if φ = 0° and including the possibility that the depth of the failure may be limited by a hard stratum at DH : o Calculate the FS c using N S as follows: FS c = H N c S γ where c = available cohesion N S = stability number required for FS c = 1 (from chart) γ = soil unit weight ( γ m or, if submerged, γ ') H = height of slope (if FS c =1, then H = H cr = critical slope height) FS c = factor of safety with respect to cohesion For i > 53°, use φ = 0° curve in Taylor 2 chart Taylor 1 for φ = 0° Note: Taylor 1 analysis and chart is short term, for total stress. (There is no consideration of seepage forces or effective stresses.)
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SL10 o Taylor (1948) then added the chart below for φ 0. N s in this chart is the stability number required if the friction component, tan φ , is fully mobilized (i.e. FS φ = 1 in the chart): Taylor 2 for φ For φ d = 0 and 1 < D <
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Lecture 21 - SL8 Circular Arc Analysis: Assume circular...

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