Settlement types, definitions, and general equation

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Excessive foundation settlements can impair the serviceability and even the safety of a structure. Settlements are due to either volume change or distortion of the soil and can take place immediately or over a time that could be measured in years. Immediate settlements are estimated using equations from elasticity theory, while long-term settlements are calculated using the concepts of consolidation. An essential design step consists of the comparison of these estimates with the stipulated tolerable settlements: A well-designed foundation will settle less than what is deemed tolerable.


Concepts and Formulas

Deformation in soils

1. All soils deform when stress is changed (given time). Deformation may be immediate and/or may take a long time to occur. 

2. Types of deformation:



General equation for total settlement: St= Si+ Sc+ Ss+ Sm


St = total settlement 
Si = immediate settlement 

Immediate settlement results from distortion of soil mass caused by a change in total stress. Si is zero for true one-dimensional compression but is not zero for two or three-dimensional compression 

Sc = settlement from primary compression 

Primary compression results from changes in effective stress and is time-dependent

Ss = settlement from secondary compression

Secondary compression (volumetric “creep”) occurs with time at constant effective stress 

Sm= settlement induced by changes in moisture condition (wetting or drying) 

Expansive soils are susceptible to swell and shrinkage. All soils may be collapsible under certain conditions, so the potential for settlement from collapse should always be considered. 

1.  Saturated inorganic silts and clays: Sc usually dominates, some Si and some Ss
2.  Granular soils and partially saturated clays: Si dominates, some Ss
3.  Highly organic soils and peats: Si and Ss, some Sc (may be insignificant) 



Compression : distortion and changes in volume occurring as a result of imposed stresses but not those accompanying failure 

a. Distortion of soil mass - change in shape of soil mass without a change in volume 
b. Change in shape or fracturing of particles - generally not a significant component of total settlement 
c. Reorientation and movement of particles 

Consolidation : a special case of compression in which the soil is saturated and fine-grained, and the changes in volume are time-dependent and occur when water is expelled from the voids 

Settlement : a decrease in elevation experienced on or within a soil as a result of compression 

Heave : an increase in elevation experienced on or within a soil as a result of decompression 

One-dimensional compression : all volume change occurs only in one direction (usually the direction of applied stress). For the situations we will consider, volume change is assumed to occur only in the vertical direction. 

Swell : an increase in volume that occurs when an expansive soil gets wetter

Collapse : a decrease in volume that occurs when a soil gets wetter 

Shrinkage : a decrease in volume that occurs when a soil dries out 


General Equation

Generally, total settlement is equal to the integration of vertical strain over the depth of influence below the bearing level:

S=int_{z_{f}=0}^{z_{f}=z_{f0}}varepsilon _{v}dz


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