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

{ { Soil Settlement: Stotal = Se + Sc Total Soil Settlement = Elastic Settlement + Consolidation Settlement Stotal = Se + Sc { 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) Elastic settlement occurs in sandy, silty, and clayey soils. By: Kamal Tawfiq, Ph.D., P.E.

Consolidation Settlement (Time Dependent Settlement) By: Kamal Tawfiq, Ph.D., P.E. Consolidation Settlement (Time Dependent Settlement) * 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. SConsolidation = Sprimary + Ssecondary 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) Water Table (W.T.) Expulsion of the water 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 (Du) will reduce, and the void ratio (e) of the soil matrix will reduce too. Water Voids Solids

Elastic Settlement Se = (1 - μs) α Se = (1 - μs) α Es 2 Es Bqo (corner of the flexible foundation) 2 Es Bqo Se = (1 - μs) α 2 (center of the flexible foundation) 1 p Where α = [ ln ( √1 + m2 + m / √1 + m2 - m ) + m. ln ( √1 + m2 + 1 / √1 + m2 - 1 ) m = B/L B = width of foundation L = length of foundation By: Kamal Tawfiq, Ph.D., P.E.

Se = α, αav, αr 3.0 2.5 α αav αr 2.0 1.5 For circular foundation α = 1 Bqo (1 - μs) α Es Se = 3.0 2.5 α αav αr 2.0 α, αav, αr 1.5 For circular foundation α = 1 αav = 0.85 αr = 0.88 1.0 3.0 1 2 3 4 5 6 7 8 9 10 L / B Values of α, αav, and αr 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, μs = 0.5). Referring to Figure 1 for notations, this equation can be written as Se = A1 A2 qoB/Es where A1 is a function H/B and L/B, and is a function of Df/B. Christian and Carrier (1978) have modified the values of A1 and A2 to some extent, and these are presented in Figure 2. 2.0 L/B = ∞ 1.0 L/B = 10 1.5 5 A2 0.9 A1 1.0 2 Square Circle 0.5 0.8 5 10 15 20 Df/B 0.1 1 10 100 1000 H /B Values of A1 and A2 for elastic settlement calculation (after Christian and Carrier, 1978) By: Kamal Tawfiq, Ph.D., P.E.

Elastic Settlement Using the Strain Influence Factor: [Schmertman & Hartman Method (1978)] Se = C1 C2 ( q - q) ∑ (Iz / Es ) Δz where Is = strain influence factor C1 = a correction factor for the depth of foundation embedment = 1 - 0.5 [q / (q - q)] C2 = 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 Df The variation of the strain influence factor with depth below the foundation is shown in Figure 1. Note that, for square or circular foundations, Iz = 0.1 at z = 0 Iz = 0.5 at z = 0.5B Iz = 0 at z = 2B Similarly, for foundations with L/B ≥ 10 Iz = 0.2 at z = 0 Iz = 0.5 at z = B Iz = 0 at z = 4B Example: B x L q Df q = γ Df Iz Es ΔZ1 ΔZ2 Is3 ΔZ3 s3 Average Is Average Es ΔZ4 Depth, z

Dp Dp Dp Dp Dp Dp DH = CS H 1 + eO P0 Po + DP log ( )

DH = log ( ) + CS H 1 + eO PC Po C C H Po + DP log ( ) Dp2 Dp2 Dp2 Dp

Dp2 Dp2 Dp2 Dp Dp2 CS H Po + DP DH = log ( ) 2 1 + eO Po