Kamal Tawfiq, Ph.D., P.E., F.ASCE
Soil Settlement By Kamal Tawfiq, Ph.D., P.E., F.ASCE Fall2013 { { 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, u = 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 - s) Se = (1 - s) Es 2 Es Bqo
(corner of the flexible foundation) 2 Es Bqo Se = (1 - s) 2 (center of the flexible foundation) 1 p Where = [ ln ( 1 + m2 + m / 1 + m2 - m) + m. ln ( 1 + m2 + 1 / 1 + m ) m = B/L B = width of foundation L = length of foundation By: Kamal Tawfiq, Ph.D., P.E. Se = , av, r 3.0 2.5 av r 2.0 1.5 For circular foundation = 1
Bqo(1 - s) Es Se = 3.0 2.5 av r 2.0 , av, r 1.5 For circular foundation = 1 av = 0.85 r = 0.88 1.0 3.0 1 2 3 4 5 6 7 8 9 10 L / B Values of , av, and r 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 (Poissons ratio, s = 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. Dp Dp Dp Dp Dp Dp DH = Cc H 1 + eO P0 Po+ DP log ( ) CS H PC C C H Po + DP DH = log ( ) + log ( ) 1 + eO Po 1 + eO PC Dp2 Dp2 Dp2 Dp2 Dp Dp2 CS H Po+ DP DH = log ( ) 2 1 + eO Po Example: Cc = 0.72 Void Ratio (e) Cs = 0.1 Po Log (p) Cc Cs Figure 1
Dr. Kamal Tawfiq Example: Figure 1 G.S. gsand = 96 pcf 3 ft Soil sample was obtained from the clay layer Conductconsolidation test [9 load increments ] Plot evs. log (p)(Figure 2) Determine Compression Index (Cc ) & Swelling Index (Cs) W.T. Sand 4 ft Clay gclay = 110 pcf wc= 0.3 Po 16 ft Soil Sample In the lab and after removing the soil sample from the ground, the stresses on the soil sample= 0 Dp1 Dp2 In the ground, the sample was subjected to geostatic stresses. In the lab and before the consolidation testthe stresses on the sample = 0. During testing, the geostatic stress is gradually recovered eo = 0.795 Dp Dp7 Dp1 Dp9 Cc = 0.72 Cs = 0.1 Stress Increments Void Ratio (e) Cc Cs In the lab the stresses are added to the soil sample Dp9 Po Log (p) Figure 2 5.DeterminePo = 3.(96) + 4.( ) + 8.( ) = lb/ft2 Tangent to point 1 Example: Pc Po Void Ratio (e) Po = Pc Log (p)
Dr. Kamal Tawfiq Tangent to point 1 Example: G.S. gsand = 96 pcf 3 ft W.T. 6. Using Casagrandes Method to determine Pc Pc =800 lb/ft2 Overconsolidation Ratio OCR= = 1 The soil is Normally Consolidated N.C. soil Sand 4 ft gclay = 110 pcf wc= 0.3 Clay Po 16 ft Point of maximum curvature Pc Po Dp1 6 2 X 1 X 4 Void Ratio (e) 5 3 Tangent to point 1 7 Po = Pc Log (p) Casagrandes Method to Determine Preconsolidation Pressure (Pc)
Dr. Kamal Tawfiq Casagrandes Method to Determine Preconsolidation Pressure (Pc) 1 Normally Consolidated Soil Point of maximum curvature 6Intersection of 4 & 5 2 Horizontal line X 1 X 4 divide the angle between 2 & 3 Void Ratio (e) 3 Tangent to point 1 Extend the straight line 7 Po = Pc Log (p) Overconsolidation Ratio OCR= = 1 The soil isNormally Consolidated(N.C.) soil Pc Po Casagrandes Method to Determine Pc 2 Overconsolidated Soil
Dr. Kamal Tawfiq Casagrandes Method to Determine Pc 2 Overconsolidated Soil Point of maximum curvature 6Intersection of 4 & 5 2 Horizontal line X 1 X 4 divide the angle between 2 & 3 Void Ratio (e) 3 Tangent to point 1 5Extend the stright line 7 Po Pc Log (p) Overconsolidation Ratio OCR= > 1 The soil is oversonsolidated (O.C.) soil Pc Po Example: Void Ratio (e) Po Log (p) Building
Dr. Kamal Tawfiq qdesign Example: G.S. gsand = 96 pcf 3 ft W.T. A 150 x 100 building will be constructed at the site. The vertical stress due to the addition of the building qdesign =1000 lb/ft2 The weight of the building Qdesign will be transferred to the mid height of the clay layer Qdesign =15,000,000 lb The added stress at15 from the ground surface is Dp = Sand 4 ft Clay DP1 Po Po 16 ft eo = wc. Gs= 0.3 x 2.65 = 0.795 Dp1 (150+15) x (100+15) 15,000,000 lb Void Ratio (e) DP = lb/ft2 DP+ Po = = lb/ft2 Po Log (p) Example: DH = 1.9 ft Void Ratio (e) Po Log (p) Building
Dr. Kamal Tawfiq Example: qdesign G.S. DP+ Po = = lb/ft2 gsand = 96 pcf 3 ft W.T. Consolidation Settlement DH = log ( ) Cc H 1 + eO Po+ DP Po Sand 4 ft Clay DP1 Po Po 16 ft DH = log ( ) 0.72 x 16 eo = wc. Gs= 0.3 x 2.65 = 0.795 803 DH = 1.9 ft Dp1 DP1 Void Ratio (e) Po Po+ DP Log (p) Demolished Void Ratio (e) Po Log (p)
Dr. Kamal Tawfiq When the building was removed, the soil has become an overconsolidated clay. The rebound has taken placethrough swelling from pint 1 to point 2 qdesign G.S. gsand = 96 pcf 3 ft W.T. Sand 4 ft Clay Po Po 16 ft eo = wc. Gs= 0.3 x 2.65 = 0.795 Dp1 DP1 Void Ratio (e) 2 1 Po Po+ DP Log (p) The soil now is overconsolidated Soil:
Constructing a new building Dr. Kamal Tawfiq Scenario #1 The soil now is overconsolidated Soil: The new building is heavier in weight qdesign G.S. gsand = 96 pcf 3 ft W.T. Sand 4 ft Clay DP2 Po Po 16 ft DH = log( ) + CS H 1 + eO PC Po C C H Po+ DP log ( ) eo = wc. Gs= 0.3 x 2.65 = 0.795 eo =0.61 Dp1 DP2 AssumePo + Dp2 = 2100 psf DP1 Void Ratio (e) 0.1 x 16 ( ) DH = log 803 CS + 0.72 x 16 CC log ( ) 2100 = Po Pc Po+ DP New Building Log (p) The soil now is overconsolidated Soil:
Dr. Kamal Tawfiq qdesign Constructing a new building G.S. Scenario # 2 The soil now is overconsolidated Soil: The new building is lighter in weight gsand = 96 pcf 3 ft W.T. Sand 4 ft Clay DP2 Po Po 16 ft eo = wc. Gs= 0.3 x 2.65 = 0.795 DH = CS H Po+ DP log ( ) 1 + eO P0 Dp1 DP2 eo =0.61 DP1 AssumePo + Dp2 = 1600 psf Void Ratio (e) 0.1 x 16 CS DH = log ( ) 1600 = Po Po+ DP New Building Log (p) Example of Semi-log Scale
Dr. Kamal Tawfiq Example of Semi-log Scale Once you determine Tv use the table shown on the page to determine U% Degree of Consolidation (U%) vs. Time Factor (Tv)