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Primary Consolidation

Courses > Foundation Analysis and Design > Settlement of Shallow Foundations > Primary Consolidation


Introduction on Primary Consolidation :

Primary compression results from changes in effective stress and is time-dependent. For general definitions, remarks and types of settlement refer to Settlement types, definitions, and general equation article.



Concepts and Formulas of Primary Consolidation:

 

Virgin Compression 

Virgin compression occurs when the soil is normally consolidated and the effective vertical stress increases from the beginning to the end of the stress increment being analyzed. For virgin compression, the following equation is the primary consolidation settlement: 

S_c = int_{z=z_f}^{z=z_{f0}} frac{C_c}{1+e_0}Delta(logsigma'_v)dz

for each layer with constant parameters

S_c = frac{C_c}{1+e_0}Delta(logsigma'_v)H_0

In a more familiar way it can be rewritten as:

S_c = frac{C_cH_0}{1+e_0}logfrac{sigma'_{vf}}{sigma'_{v0}}

where 

Cc = virgin compression index

H0 = height of the layer 

e0 = void ratio

subscripts "0" and "f" for vertical stresses mean "initial" and "final", respectively. 

Note! Delta(logsigma'_v) = logsigma'_{vf}-logsigma'_{v0} = logfrac{sigma'_{vf}}{sigma'_{v0}}

 

Decompression (Rebound) 

Decompression (aka rebound or heave) occurs when the soil is either normally consolidated or overconsolidated and the effective vertical stress decreases from the beginning to the end of the stress increment being analyzed 

S_c = int_{z=z_f}^{z=z_{f0}} frac{C_r}{1+e_0}Delta(logsigma'_v)dz

for each layer with constant parameters

S_c = frac{C_r}{1+e_0}Delta(logsigma'_v)H_0

In a more familiar way it can be rewritten as:

S_c = frac{C_rH_0}{1+e_0}logfrac{sigma'_{vf}}{sigma'_{v0}}

where 

Cr = decompression/recompression (rebound/reload) index

H0 = height of the layer 

e0 = void ratio

subscripts "0" and "f" for vertical stresses mean "initial" and "final", respectively. 

Note! Delta(logsigma'_v) = logsigma'_{vf}-logsigma'_{v0} = logfrac{sigma'_{vf}}{sigma'_{v0}}

 

Recompression plus Virgin Compression

Recompression plus virgin compression occurs when the soil is overconsolidated and the effective vertical stress increases from the beginning to the end of the stress increment being analyzed

S_c = int_{z=z_f}^{z=z_{f0}} frac{C_r}{1+e_0}logfrac{sigma'_p}{sigma'_{v0}} + frac{C_c}{1+e_0}logfrac{sigma'_{vf}}{sigma'_p}dz

for each layer with constant parameters

S_c = H_0(frac{C_r}{1+e_0}logfrac{sigma'_p}{sigma'_{v0}} + frac{C_c}{1+e_0}logfrac{sigma'_{vf}}{sigma'_p})

where 

Cc = virgin compression index

Cr = decompression/recompression (rebound/reload) index

H0 = height of the layer 

e0 = void ratio

subscripts "0", "f" and "p" for vertical stresses mean "initial", "final" and "preconsolidation", respectively. 



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