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Non-dimensional parameters

Stability of Composite River Banks - continued. b. H. 5.0.  = 0. . 1.0. Non-dimensional parameters. Factor of safety in shear (F ss ). F ss = 5  A. Stability of Composite River Banks - continued. b. H. 5.0. Increasing values of B. . 1.0. Non-dimensional parameters.

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Non-dimensional parameters

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  1. Stability of Composite River Banks - continued b H 5.0  = 0  1.0 Non-dimensional parameters Factor of safety in shear (Fss) Fss = 5  A

  2. Stability of Composite River Banks - continued b H 5.0 Increasing values of B  1.0 Non-dimensional parameters Factor of safety in tension (Fst)

  3. Stability of Composite River Banks - continued b H 5.0 Increasing values of B  1.0 Non-dimensional parameters Factor of safety in beam mode of failure (Fsb)

  4. t - tensile strength • - unit weight • r - ratio of tensile to compressive strength. • based on Thorne and Tovey (1981) m H b Example 1: Overhang b = 0.1m; H = 0.4m initially  =1 and B = 0.25 Fss / A = 5.0 Fsb / A = 3.64 Fst / A =  >> beam mode of failure most likely

  5. Example 2:   = 18 kN m-3 i.e. fully saturated ’ = 8 kN m-3 A becomes 10 and stress point plots at 0.1 stress point moves down > TWICE AS STABLE If t = 8 kPa and  = 16 kN m-3 A = 5 (partially saturated) so Fsb = 5 x 3.64 = 18.2 > VERY STABLE As stage falls, full saturated unit weight acts i.e.  = 18 kN m-3 A becomes 4.44 and stress point plots at 0.23

  6. Example 3: Further erosion of overhang while submerged if b = 0.2 > B = 0.5 Y axis value corresponding to  =1 and B = 0.5 for beam is 1.82 A = 5, so Fsb = 1.82 * 5 = 9.1 As stage falls, A falls (buoyancy effect is removed) i.e. fully saturated block acts as before > stress point moves up to 0.23 as before then falls to 0.2 on partial desiccation A now becomes 2.5 stress point moves to 0.4 (i.e. 1/2.5) Desiccation crack forms 0.1m:  =0.75 Stress point moves to left at y = 0.4 to  =0.75.

  7. Failure occurs when stress point crosses relevant B line in either beam, tension or shear. In this example a beam failure occurs when  =0.48. • t - tensile strength • - unit weight • r - ratio of tensile to compressive strength. • based on Thorne and Tovey (1981) m H b

  8. Example 4: B = 0.3 What is effect as desiccation crack grows?

  9. t - tensile strength • - unit weight • r - ratio of tensile to compressive strength. • based on Thorne and Tovey (1981) m H b Example 1: Overhang b = 0.1m; H = 0.4m initially  =1 and B = 0.25 Fss / A = 5.0 Fsb / A = 3.64 Fst / A =  >> beam mode of failure most likely

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