Definition
serviceability limit state caused by qw,net
- can be more critical then bearing capacity
Settlement types
Differential
- Rigid body tilt/rotation
* more noticeable in tall buildings and affects lifts
and escalators
- relative displacements that lead to structural damage
Total
- can damage services into the structure but no damage to the building itself
What clay settlements
- Undrained is distortion with no change in volume (rho_u)
- Consolidation has a decrease in volume due to water drainage (rho_c)
-Secondary small and therefore often neglected (rho_s)
Sand settlements
- Secondary settlements
- Immediate settlements
Estimating settlements
- Divide soil into dz thick slices
- Split since soil stiffness increases with depth while change in stress decreacs with depth - Find the change in strain for each, a function of change in stress and soil stiffness
- Find the extension in each layer and sum
Elasticity Theory Assumptions
Assumptions
- Linear elastic
- Isotropic
- Homogeneous
- Semi-inifinite half spcae
- Not used for settlements since soils nonlinearity makes the lineasr elastic assumption invalid but for change in stress
Elastic Theory Soil Properties
- Young modulus
- Poissons ratio
- Shear modulus (G) with G=G’ since water can carry shear also G decreases with shearing
- Bulk modulus (K)
Boussinesq
Gives solution for a point load applied at the surface, independent of v and soil stiffness
delta sigma = (3Qz^3)/(2(pi)R^5)
Change in stress for a udl
delta sigma = q.Ir, found by integrating the point load solution
- q=qnet
- Ir is the influence coefficient and found through the Fadum Chart which gives delta sigma under the corner of rectangular foundation
- Superposition applies
- Leads to the plots for continuous stress change under the foundations
- Square: 0.4q @ B with 0.2q @1.5B
- Strip: 0.4q @1.5B and 0.2q just before 3B
Limitations of Elastic Theory for Settlements
- Soil is nonlinear since stiffness decreases with strain and increases with depth therefore its not possible to get a suitable estimate for E/v for use in elastic theory
- Inaccurate calculations of horizontal stress which affects vertical displacements along with the vertical stress
1D method for consolidation assumptions
- epsilon_h = 0, therefore 1d vertical consolidation
- Gives settlement for drained conditions since in undrainded conditions there is no change in volume epsilon_vol = 0 so epsilon_v must also be zero for epsilon_h = 0
1D method for consolidation calulation approaches
- Use the Oedometer test to relate sigma_v’ and epsilon_v since the test gives void ratio:
delta epsilon_v = delta e/1+e0
- Use the known mv which varries between stress ranges
mv = delat epsilon_v/delta sigma_v’
1D method for consolidation limitations
- Correct method for OC clays but the main error comes from overestimating mv which is usually the case for oedometer tests but can be corrected using factors
1D method for consolidation calc steps
- Divide domain into layers
- Get the original sigma_v’ at the layer midpoint
- Get the dhange in sigma_v’ at the midpoint
- Use the stress range to get epsilon using either approach
rho_c = sum(epsilon.H)
Rate of consolidation
t = Tv.d^2/cv, the time to reach the average degree of consolidation
-Tv varries with U=rho_c_T/rho+c_inf
-cv = K/mv.gamma
Why settlement in sands
-Large settlements are due to cyclic loading, seepage or erosion not monotonic increace of stress with depth
-Usually occur in loose or very loose sands or sands high in organic content
-Dont usually cause structural damage since they occur early in the construction process
Sand settlement calculations
Hard to get sand strength from insitu tests therefore correction factors are usually applied
-Schmertmann uses CPT and corrects for depth and creep
- Berland and Burbidge method uses SPT and is based on the statistical analysis of 200 settlement cases
