# unsat12 - Derivation of Relationships for Volume Change...

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Derivation of Relationships for Volume Change Requirements for Volume Change Theory Representation of deformation behavior requires constitutive equations relating a deformation state variable related to two independent stress state variables. Stress State Variables The required stress state variables are: 1 ) ( σ m - u a ); 2 ) ( u a - u w ); 3 ) ( σ 1 - σ 3 ). where σ m is the mean or average of the three principal stresses. Alternatively, the stress state variable ( σ m - u w ) could be substituted for ( σ m - u a ) above. Proposed constitive equations for the soil structure and water phase are: ) ( ) ( ) ( 3 1 23 22 21 σ d d C du d C du du C V dV a m w a + + = ) ( ) ( ) ( 3 1 13 12 11 d d C du d C du du C V dV a m w a w + + = Unsat12 - 1

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Deformation State Variables The required deformation state variables are: 1) void ratio, e, used to represent the volume change behavior of the soil structure; 2) water content, w, or degree of saturation used to represent the volume change behavior of t h e w a t e r . Constitutive Relationships To define a constitutive relationship, it is necessary to show that a unique surface can be formed when plotting one of the two deformation state parameters against two of the stress state p a r a m e t e r s . For unsaturated soil, it may be possible to obtain unique surfaces for monotonic loading, i. e. for one cycle of either wetting or drying. To verify that uniqueness is valid, soil is tested at various state conditions, including isotropic and anisotropic states of stress.
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## This note was uploaded on 12/12/2011 for the course CIVIL ENGI 7004 taught by Professor Hasan during the Spring '11 term at Auckland.

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unsat12 - Derivation of Relationships for Volume Change...

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