# unsat3 - Stress State Variables Definition Stress variables...

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Stress State Variables Definition Stress variables are used to determine the state of stress in a soil that is then used to model mechanical behavior. These stress state variables cannot be dependent on the properties of the soil. Saturated Soils The primary stress state variable used to characterize saturated soil behavior is the effective stress. σ ' = ( σ - u w ) Example: The shear strength of a saturated soil can be given in terms of the effective stress for a given soil (Mohr- Coulomb). No material properties are required in the expression of effective stress. Unsat3 - 1

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Unsaturated Soils It is not possible to express the effective stress in terms of the pore water pressure (negative) because the pore water is discontinuous and thus does not act throughout the soil. It is more difficult to characterize the behavior of unsaturated soils because both liquid and air phases occur requiring at least two independent stress state variables. Various forms of effective stress equations that include a parameter(s) that is a material property. Examples: σ ' = ( σ - β ' u w ) σ ' = ( σ - u a ) + χ (u a - u w ) σ ' = ( σ + ψ p'') σ ' = ( σ + β p'') σ ' = ( σ - u a ) + χ m (u m - u a ) + χ s (u s - u a ) σ ' = σ + χ m p'' + χ s p'' The problem is that none of the parameters are single-valued. Put another way, it is not possible to express quantitatively the effect of the negative pore water pressure that acts throughout the soil which adds to the soil effective stress. See handout from Lambe and Whitman (1969) Unsat3 - 2
Proposed Solution Two independent stress state variables can be used to characterize unsaturated soil behavior. Examples: 1 ) ( σ - u a ) and (u a - u w ) 2 ) ( σ - u w ) and (u a - u w ) 3 ) ( σ - u a ) and ( σ - u w ) These stress state variables can be used to define constitutive relations to define shear strength and volume change

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Theoretical Treatment of Force Equilibrium at a Point Saturated Soil uses the surface traction forces and the gravitational forces acting on a representative elementary volume. (See Figure 3-2.)
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unsat3 - Stress State Variables Definition Stress variables...

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