Lecture 2 - S4 Stresses Changes Due to Surface Loads(v o...

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S4 Stresses Changes Due to Surface Loads ( Δσ v ) o Stresses within a soil mass will change as a result of surface loads. The change in total stress spreads and diminishes with distance from the load. Equations and charts are available to calculate both the vertical and horizontal stress change ( Δσ v and Δσ h ). o If for some reason the complete total stress at a point is required, then add the geostatic stress, σ v or σ h , to the load-induced stress change, Δσ v or Δσ h . o We are normally most interested in vertical stress increases due to surface compression loads. (As a rule, we assume that soil cannot withstand tension stresses.) o Often we need to know Δσ v to determine how much a structure will settle. (remember the CEG4011 consolidation test??) o To find Δσ v must first define : o size and shape of building foundation o loads supported by building foundation o location of interest within soil mass o Most solutions are based on elasticity theory assuming a homogeneous, isotropic, elastic, half-space. o Note that soil is seldom homogeneous, only approximately isotropic, and elastic only at small loads (<10-20% of the failure stress). But, we have no simple alternatives, and experimental results agree reasonably well. The above assumptions are only a first order approximation, but this approximation is often adequate. o With the above assumptions, the vertical stress increase is independent of the elastic constants: Young’s Modulus (E) and Poisson’s Ratio ( v h or ε Δ ε Δ = ν μ ). However, the horizontal stress is not. o Before looking at the various stress calculation methods, using your intuition what do you think will cause the greater stress increase at point P in the example below? (These footings have the same average contact pressure, q.) σ V due to soil self weight (geostatic) Δσ V due to building (surcharge) P Clay Sand 10 ft x 10 ft 20 ft 5000 tons 50 tons P 100 ft x 100 ft P C L C L q = ? Δσ vA = ? Δσ vB = ?
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S5 Pyramid Approximation For Surface Loads: The “2:1 method “ used for “back of the envelope” solutions (seen on the PE exam). o
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Lecture 2 - S4 Stresses Changes Due to Surface Loads(v o...

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