REQUIRED: Calculate the total consolidation settlement in the CL layers due to the addition of the 10 ft of fill.

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1 Geotechnical Engineering Research Laboratory One University Avenue Edward L. Hajduk, D.Eng, PE Lecturer Lowell, Massachusetts Tel: (978) Fax: (978) web site: DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING SOIL MECHANICS Assignment #6: Consolidation Settlement. PROBLEM #1: Boring B-1 and Soil Unit Weight Summary (see Assignment Handout). 10 ft of fill (SP or SM) to the top of the site with a unit weight of 120 pcf. 1D Consolidation Test Results (see Assignment Handout). REQUIRED: Calculate the total consolidation settlement in the CL layers due to the addition of the 10 ft of fill. SOLUTION: Determine in-situ effective stresses with depth. Only need to calculate to 2 nd CL Layer. See Figure A. Figure A. Total, Effective, and Pore Water Pressures with Depth Assignment 6 Solution Page 1 of 4

2 Determine σ due to Planned Fill: σ = (Height of Planned Fill)(γ fill ) = (10 ft)(120 pcf) = 1,200 psf. Calculate Change in Void Ratio ( e) or Vertical Strain (ε v ) due to Planned Fill: For 1 st CL layer: σ' middle of layer = 1,135 psf (see Figure A). σ = 1,200 psf. σ' vf = 2,335 psf. See Figure B For 2 nd CL layer: σ' middle of layer = 2085 psf (see Figure A). σ = 1,200 psf. σ' vf = 3,285 psf. See Figure B for ε v determination. Settlement due to Primary Consolidation = S p = Hε v = H( e/1+e o ) Determine e and ε v from Figure B. For 1 st CL Layer: S p = H( e/1+e o ) = 15ft(0.025/(1+0.51)) = 0.248ft = 2.98 inches For 2 nd CL Layer: S p = H(ε v ) = 15ft(0.012) = 0.18ft = 2.16 inches S p,total = S p,layer1 + S p,layer2 = 2.98 inches inches = 5.14 inches = 5¼ inches S p,total = 5¼ inches PROBLEM #2: GIVEN: Footings shown in Figure 3. Working loads of 300 kips for the columns and 15 kips per linear foot for the wall loads. Total settlements due to primary consolidation cannot be more than 1 inch, and differential settlement (i.e. the settlement difference between the column and wall footings) cannot be more than ½ inch. COLUMN FTG WALL FTG NEW GND SURFACE 5 ft 5 ft 5 ft 10 ft x 10 ft Figure 3. Planned Shallow Foundation Dimensions for Project Site #2 (NTS) Assignment 6 Solution Page 2 of 7

3 Figure B. e and ε v Determinations from 1D Consolidation Test Data Assignment 6 Solution Page 3 of 7

4 PROBLEM 2 (continued) REQUIRED: Calculate the consolidation settlement for these proposed footings. Evaluate if the settlement criteria are met or exceeded. SOLUTION: Assume that consolidation from 6 ft of fill has occurred. Therefore, σ' vo = σ' vf from Problem #1. The new soil profile and total stress, pore pressure, and effective stress calculations are shown in Figure C. Figure C. Total, Effective, and Pore Water Pressures with σ' vo and σ' f vs. Depth. Determine σ due to footings. The 2:1 Method is used in this solution for the column footing and Boussinesq is used for the strip footing. Note the following: 1. The 2 nd CL layer is 35ft (3.5B) from the bottom of the column and strip footings. Therefore, no significant stress (i.e. σ will be insignificant in this layer due to Assignment 6 Solution Page 4 of 7

5 either footing). Therefore, no significant settlement will occur in the 2 nd CL layer due to the column (or strip) footing. The upper CL layer is divided into three (3) sub layers to calculate settlement. These sub layers in depth from the ground surface are from (1) 20-22ft, (2) 22-25ft, and (3) 25-35ft. The average σ' vo, σ, and σ' vf were calculated for these layers (rounded to the nearest 5 psf) for the column footing are presented in Figure C. Table A summaries the calculations for the change in stress due to the column footing. Table A. σ' Calculations for the Strip Footing. Sub Layer Depth 1 (ft) σ/q 2 σ' 3 (psf) 1 16 (3.2B) (3.7B) (5B) NOTES: 1. Depth below strip footing. 2. See Boussinesq Chart in Lecture Notes. 3. Calculated from q = 3,000 psf. Calculate Change in Void Ratio ( e) due to column and strip loading: For the column footing: Layer 1: σ' middle of layer = 2025 psf (see Figure C). σ' vf = 2465 psf. See Figure E Layer 2: σ' middle of layer = 2140 psf (see Figure C). σ' vf = 2510 psf. See Figure E Layer 3: σ' middle of layer = 2450 psf (see Figure C). σ' vf = 2695 psf. See Figure E For the strip footing: Layer 1: σ' middle of layer = 2025 psf (see Figure C). σ' vf = 2595 psf. See Figure F Layer 2: σ' middle of layer = 2140 psf (see Figure C). σ' vf = 2650 psf. See Figure F Layer 3: σ' middle of layer = 2450 psf (see Figure C). σ' vf = 2840 psf. See Figure F Assignment 6 Solution Page 5 of 7

6 Figure E. e Determinations from 1D Consolidation Test Data (Column Footing). Figure F. e Determinations from 1D Consolidation Test Data (Strip Footing) Assignment 6 Solution Page 6 of 7

7 Settlement due to Primary Consolidation = S p = H( e/1+e o ) For the Column Footing: For Layer 1: S p = H( e/1+e o ) = 2ft(0.010/(1+0.51)) = 0.013ft For Layer 2: S p = H( e/1+e o ) = 3ft(0.007/(1+0.51)) = 0.014ft For Layer 3: S p = H( e/1+e o ) = 10ft(0.006/(1+0.51)) = 0.040ft S p,column = S p,layer1 + S p,layer2 + S p,layer3 = 0.067ft = 0.8 inches = 1 inch For the Strip Footing: For Layer 1: S p = H( e/1+e o ) = 2ft(0.010/(1+0.51)) = 0.013ft For Layer 2: S p = H( e/1+e o ) = 3ft(0.007/(1+0.51)) = 0.014ft For Layer 3: S p = H( e/1+e o ) = 10ft(0.007/(1+0.51)) = 0.046ft S p,strip = S p,layer1 + S p,layer2 + S p,layer3 = 0.073ft = 0.88 inches = 1 inch Differential Settlement = S p,column S p,strip = 0 inches. Therefore, Settlement Criteria are MET (S p,column = 1 inch, differential settlement < ½ inch). PROBLEM #3: What affect (if any) would decreasing the column footing depth have on the consolidation settlement? What affect (if any) would increasing the column footing depth have on the consolidation settlement? Explain you answer using the relevant concepts in sufficient detail that a non-engineer can understand your answer. SOLUTION: Decreasing Column Footing Depth results in decreased σ in CL layers, thereby less settlement would occur. Simplified: Higher footing, less stress, less settlement. Increasing Column Footing Depth results in increased σ in CL layers, thereby more settlement would occur. Simplified: Lower footing, increased stress, more settlement Assignment 6 Solution Page 7 of 7