Lecture 1 and 2

# Lecture 1 and 2 - S1 SUBSURFACE STRESSES Internal Stress...

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S1 SUBSURFACE STRESSES: Internal Stress Within the Soil Mass Geostatic Stresses (due to the soil’s own weight ) Review concept of stress at a point (P): o Unit Weights: γ w = unit weight of water γ m = moist unit weight of unsaturated soil γ sat = unit weight of saturated soil γ = “effective” unit weight of soil = ( γ sat - γ w ) if soil saturated = γ m if soil not saturated = γ b , “buoyant” unit weight of soil o Total Vertical Stress: γ = σ i i v z use γ m or γ sat as appropriate (= σ z ) o Pore Water Pressure: w w z u γ = (hydrostatic - no flow) (u 0 initial condition) or p w h u γ = (general, h p = pressure head from flow net) o Vertical Effective Stress: u ' v v - σ = σ granular contact stress o Horizontal Effective Stress: v h ' K ' σ = σ K = coefficient of lateral stress, often K 0 (K relates effective stresses) o Total Horizontal Stress: u ' h h + σ = σ o These self-weight stresses ( σ v , σ v , σ h , σ h ) are called geostatic stresses o For a level surface there are no shear forces induced by the geostatic stresses, and therefore they are also principal stresses : h 3 v 1 and σ = σ σ = σ o Karl Terzaghi’s principle of effective stress ( σ σ or ' ) governs most soil behavior (probably the most important point in this class). Examples: Pressure on a retaining wall depends on stress due to soil weight P γ 1 γ 2 σ h = σ h + u z 1 z 2 σ v = σ v + u z w σ h Shear strength, τ , of soil depends on cohesion and σ n due to soil weight σ n τ = c + σ n tan φ failure surface

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S2 Geostatic Stress Example 1 Determine the total horizontal stress at point P: at point P: σ v = γ i i z = 6’ (100 pcf) + 4’ (118 pcf) + 6’ (126 pcf) + 4’ (120 pcf) = 600 psf + 472 psf + 756 psf + 480 psf = 2308 psf u = 14’ (62.4 pcf) = 874 psf σ v = ( σ v – u) = 2308 psf - 874 psf = 1434 psf σ h = K σ ' v = 0.5 (1434 psf) = 717 psf σ h = ( σ h + u) = 717 psf + 874 psf = 1591 psf = 1591 psf x (0.04788 kN/m 2 / 1 psf) = 76.18 kN/m 2 (kPa) (see conversion factors in Appendix A of Das) Sand γ m = 100 pcf, K = 0.4 Sand γ sat = 118 pcf, K = 0.4 Clay γ sat = 126 pcf, K = 0.6 Clay γ sat = 120 pcf, K = 0.5 P 6’ 4’ 6’ 8’ 4’
S3 Geostatic Stress Example 2 What happens when the GWT (ground water table) rises? Look at a sample profile: Conclusion: Effective stress decreases as GWT rises, but stabilizes once the GWT is above the soil surface. (Note that effective stress increases as the GWT is lowered!) σ

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Lecture 1 and 2 - S1 SUBSURFACE STRESSES Internal Stress...

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