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Foundation Settlement By Kamal Tawfiq, Ph.D., P.E. Fall 2001. Bearing Capacity of Layered Clay Soils. Caly ϕ 1 = 0 c 1 = ✓. D f. B. q u. Z. Caly ϕ 2 = 0 c 2 = ✓. Cylindrical Failure Surface. By: Kamal Tawfiq, Ph.D., P.E. N c. 10. 0.1. Z/B = 0. 0.2. 8. 0.3. 0.4. 6.
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Foundation Settlement By Kamal Tawfiq, Ph.D., P.E. Fall 2001
Bearing Capacity of Layered Clay Soils Caly ϕ1 = 0 c1 = ✓ Df B qu Z Caly ϕ2 = 0 c2 = ✓ Cylindrical Failure Surface By: Kamal Tawfiq, Ph.D., P.E.
Nc 10 0.1 Z/B = 0 0.2 8 0.3 0.4 6 0.5 1.5 0.75 1.0 4 0.25 0.5 Z/B = 0 2 0 0.4 0.8 1.2 1.6 2.0 C2 / C1 Bearing capacity on layered clay soils (ϕ = 0) By: Kamal Tawfiq, Ph.D., P.E.
Qu Bearing Capacity of Layered Soils Df B Sand ϕ = ✓ c = 0 H Sand ϕ = ✓ c = 0 Caly ϕ = 0 c = ✓ Caly ϕ = 0 c = ✓ Foundation on sand layer overlying soft caly By: Kamal Tawfiq, Ph.D., P.E.
Values of Ks ___________________________ Friction Angle of Sand, ϕ (deg) Ks ___________________________ 20 1.89 25 2.22 30 3.06 35 4.45 40 6.95 45 11.12 50 19.15 By: Kamal Tawfiq, Ph.D., P.E.
Foundation Settlement: Total Foundation Settlement = Elastic Settlement + Consolidation Settlement Stotal = Se + Sc { Foundation 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.
Water Table (W.T.) Expulsion of the water Water Voids Solids 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) By: Kamal Tawfiq, Ph.D., P.E.
Elastic Settlement 2 Se = Bqo (1 - μs) α (corner of the flexible foundation) 2 Es 2 Se = Bqo (1 - μs) α (center of the flexible foundation) Es Where α = 1/π [ 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 = Bqo (1 - μs) α E 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 Foundations on Saturated Clay Janbu, Bjerrum, and Kjaernsli (1956) proposed an equation for evaluation of the average elastic settlement of flixable 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 = ∞ L/B = 10 1.0 1.5 5 A2 0.9 A1 1.0 2 Square Circle 0.5 0.8 5 20 10 15 0 Df/B 0 1 10 100 1000 0.1 H /B Values of A1 nd A2 for elastic settlement calculation (after Christian and Carrier, 1978) By: Kamal Tawfiq, Ph.D., P.E.
1.0 A2 0.9 0.8 5 10 15 20 0 Df/B Values of A1 nd 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)] 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 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 Example: B x L q Df Iz q = γ Df Es ΔZ1 ΔZ2 Is3 ΔZ3 Es3 Average Is Average Es ΔZ4 Depth, z By: Kamal Tawfiq, Ph.D., P.E.
