1. Soil Settlement By Kamal Tawfiq, Ph.D., P.E., F.ASCE Fall 2010

2. Soil Settlement: Total Soil Settlement = Elastic Settlement + Consolidation Settlement S total = S e + S c Load Type (Rigid; Flexible) Elastic Settlement or Immediate Settlement depends on Settlement Location (Center or Corner) { Theory of Elasticity Elastic Settlement Time Depended Elastic Settlement (Schmertman & Hartman Method (1978) { By: Kamal Tawfiq, Ph.D., P.E. Elastic settlement occurs in sandy, silty, and clayey soils.

3. Water Water Table (W.T.) Voids Solids Expulsion of the water Consolidation Settlement (Time Dependent Settlement) By: Kamal Tawfiq, Ph.D., P.E. * Consolidation settlement occurs in cohesive soils due to the expulsion of the water from the voids. * Because of the soil permeability the rate of settlement may varied from soil to another. * Also the variation in the rate of consolidation settlement depends on the boundary conditions. S Consolidation = S primary + S secondary Primary Consolidation Volume change is due to reduction in pore water pressure Secondary Consolidation Volume change is due to the rearrangement of the soil particles (No pore water pressure change, Δu = 0, occurs after the primary consolidation) When the water in the voids starts to flow out of the soil matrix due to consolidation of the clay layer. Consequently, the excess pore water pressure (  u) will reduce, and the void ratio (e) of the soil matrix will reduce too.

4. Elastic Settlement S e = (1 - μ s ) α 2 2 (corner of the flexible foundation) S e = (1 - μ s ) α 2 (center of the flexible foundation) By: Kamal Tawfiq, Ph.D., P.E. Where α = [ ln ( √1 + m 2 + m / √1 + m 2 - m ) + m. ln ( √1 + m 2 + 1 / √1 + m 2 - 1 ) m = B/L B = width of foundation L = length of foundation 1  EsEs Bq o EsEs

5. By: Kamal Tawfiq, Ph.D., P.E. 3.0 2.5 2.0 1.5 1.0 L / B 3.0 28435671091 α, α av, α r α α av αrαr For circular foundation α = 1 α av = 0.85 α r = 0.88 Values of α, α av, and α r Bq o (1 - μ s ) α EsEs S e =

6. By: Kamal Tawfiq, Ph.D., P.E. Elastic Settlement of Foundation on Saturated Clay Janbu, Bjerrum, and Kjaernsli (1956) proposed an equation for evaluation of the average elastic settlement of flexible foundations on saturated clay soils (Poisson’s ratio, μ s = 0.5). Referring to Figure 1 for notations, this equation can be written as S e = A 1 A 2 q o B/E s where A 1 is a function H/B and L/B, and is a function of D f /B. Christian and Carrier (1978) have modified the values of A 1 and A 2 to some extent, and these are presented in Figure 2. 1.0 5 0.8 0.9 0 D f /B 20 1510 A2A2 L/B = ∞ Square L/B = 10 Circle 2 5 2.0 1.5 0 10 0.5 1.0 1 0.1 1001000 H /B A1A1 Values of A1 and A2 for elastic settlement calculation (after Christian and Carrier, 1978)

7. Elastic Settlement Using the Strain Influence Factor: [Schmertman & Hartman Method (1978)] Example: B x L Es DfDf IzIz Depth, z q = γ D f ΔZ 1 q ΔZ 2 ΔZ 3 ΔZ 4 s3 I s3 Average I s Average E s The variation of the strain influence factor with depth below the foundation is shown in Figure 1. Note that, for square or circular foundations, I z = 0.1 at z = 0 I z = 0.5 at z = 0.5B I z = 0 at z = 2B Similarly, for foundations with L/B ≥ 10 I z = 0.2 at z = 0 I z = 0.5 at z = B I z = 0 at z = 4B Se = C 1 C 2 ( q - q) ∑ (I z / E s ) Δz where I s = strain influence factor C 1 = a correction factor for the depth of foundation embedment = 1 - 0.5 [q / (q - q)] C 2 = a correction factor to account for creep in soil = 1 + 0.2 log (time in years /0.1) q = stress at the level of the foundation q = overburden pressure = γ D f

11.  = C S H 1 + e O P0P0 P o +  P log ( ) pp pp pp pp pp pp

12. pp pp p2p2 p2p2 p2p2 pp pp  = log ( ) + C S H 1 + e O PCPC PoPo C C H 1 + e O PCPC P o +  P log ( )

13. pp p2p2 p2p2 p2p2 p2p2  = log C S H 1 + e O PoPo P o +  P ( ) 2