Geotechnical Engineering Research Laboratory One University Avenue Lowell, Massachusetts 01854 Edward L. Hajduk, D.Eng, PE Lecturer PA105D Tel: (978) 934 2621 Fax: (978) 934 3052 e mail: Edward_Hajduk@uml.edu web site: htt://faculty.uml.edu/ehajduk DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING 14.330 OIL MECHANIC Exam #2: Consolidation. Questions (3 Points Each - 30 Points Total): 1. Describe the rocess of rimary consolidation in your own words. Primary consolidation is volume change in saturated soils caused by the exulsion of ore water from loading. 2. Your lab manager has given you the results of a 1D consolidation test on a clay samle taken at a deth of 75 ft below the existing ground surface. The maximum ast ressure from the 1D consolidation test is 4,000 sf. You have calculated the current insitu vertical effective stress to be 2,750 sf. What is the overconsolidation ratio for this samle? OCR = Maximum Past Pressure/Current Effective tress OCR = ' vm /' o = 4,000 sf/2,750 sf = 1.45 3. Relate excess ore ressure buildu and dissiation to degree of consolidation. Write any relevant equation(s) and detail the variables. U u o u e u o Where: U = Degree of Consolidation u o = Initial Excess Pore Pressure (at t=0) u e = Excess Pore Pressure at any time t. 1 u e u o 4. Determine the exected settlement of a ML soil layer when the average degree of consolidation is 67%. You have calculated the settlement due to rimary consolidation to be 7¾ inches. U t 0.67 1 x 5.19inches 5 4 x _ inches 7.75inches inches
5. Exlain, in your own words, the concet of surcharging. Relate your answer to relevant 1D consolidation rinciles. urcharging reduces the time required to reach a desired settlement due to structural loading by using additional weight. 6. A standie in a CH layer you are monitoring during a surcharge rogram is measuring a total head 4 ft above hydrostatic conditions. Two months ago, the contractor laced 5 ft of fill ( = 110 cf) on the site. What is the degree of consolidation for the CH soil layer? U u o u u o e 1 u u e o 1 lb 4 ft(62.4 ) 3 ft lb 5 ft(110 ) 3 ft 0.546 55% 7. Relate settlement due to rimary consolidation to void ratio. Write any relevant equation(s) and detail the variables. Where: H v e H 1 e = ettlement due to Primary Consolidation H = Height of oil Layer v = Vertical train e = Change in Void Ratio e o = Initial Void Ratio 8. Describe the variable H dr in your own words. What would H dr be for a MH layer that is 21 ft thick that is sandwiched between an CL layer (k CL << k MH ) on the to and a P layer on the bottom? H dr is the height of the maximum drainage ath (i.e. the longest distance it takes water to drain from the soil mass). H dr = 21 ft for one way drainage in this roblem. o 14.330 2012 Exam 2 olution Page 2 of 10
9. Relate the degree of consolidation to time from loading for 1D consolidation. Write any relevant equation(s) and detail the variables. Where: t ( H dr ) c v 2 T v t = Time to Consolidation T v = Time Factor (Dimensionless). Related to U. c v = Coefficient of Consolidation H dr = Height of Drainage Path 10. Relate void ratio to strain for 1D consolidation. Write any relevant equation(s) and detail the variables. Where: v e 1 e o v = Vertical train e = Change in Void Ratio e o = Initial Void Ratio 14.330 2012 Exam 2 olution Page 3 of 10
PROBLEM: (1 15 oints, 2-25 oints, 3 20 oints, 4 10 oints) NOTICE: You must detail your answers (i.e. show your work) for these four roblems for full credit. You may use the back of the age as well if additional worksace is needed. Additional aer is available uon request. Reference the roblem number if you use the back of the ages or additional age(s). 1. You have been given the results of a recent geotechnical exloration for a local roject. The groundwater table at the time of exloration was 4 ft from the existing ground surface, which is also the interface for the M and CH soil layers. Figure A rovides the soil rofile at the time of testing. From the rovided information, calculate total stress, ore ressure, and effective stress to a deth of 20 ft and lot them on the rovided grahs. You must label numbers on the grahs for full credit. Figure A. oil Profile for Problem 1. 14.330 2012 Exam 2 olution Page 4 of 10
Calculate total, ore ressure, and effective stresses with deth at the following oints shown in Figure A: Point A: Bottom of M Layer and GWT location (4 ft below existing ground surface) Point B: Middle of CH Layer (7 ft below existing ground surface) Point C: Bottom of CH Layer (10 ft below existing ground surface) Point D: Bottom of Given oil Profile (20 ft below existing ground surface) Point A: Use moist unit weight for M: sm = 110 cf. A = sm (4ft) = (110 cf)(4ft) = 440 sf u A = 0 (Above GWT) A = ' A since u A = 0 sf Point B: B = A + AT,CH (3ft) = 440 sf + (115 cf)(3ft) = 785 sf U B = w (3ft) = (62.4 cf)(3ft) = 187 sf = 185 sf ' B = B u B = 785 sf 185 sf = 600 sf Point C: C = B + AT,CH (3ft) = 785 sf + (115 cf)(3ft) = 1130 sf U C = w (6ft) = (62.4 cf)(6ft) = 374 sf = 375 sf ' C = C u C = 1130 sf 375 sf = 755 sf Point D: D = C + AT,P-M (10ft) = 1130 sf + (120cf)(10ft) = 2330 sf u D = w (16ft) = (62.4 cf)(16ft) = 998 sf = 1000 sf ' D = D u D = 2330 sf 1000 sf = 1330 sf 14.330 2012 Exam 2 olution Page 5 of 10
2. For the roject site detailed in Problem 1, six (6) ft of structural fill will be laced on to of the existing ground surface. This fill will have a moist unit weight of 120 cf when roerly comacted to 95% of ATM D1557. Determine the rimary consolidation settlement in the CH layer using the 1D consolidation results rovided in Figure B. Figure B. 1D Consolidation Results for Problem 2. H v (6 ft)(0.012) 0.072 ft 0.864inches 1inch 14.330 2012 Exam 2 olution Page 6 of 10
3. You have been given the deformation with time results for a load increment of a 1D consolidation test. The average height of the samle in the 1D test was 0.375 inches at the time of this load increment. The test results for this load increment are lotted with log time and square root of time in Figure C. Determine the coefficient of consolidation for this soil using the log time method. If you determine the coefficient of consolidation using both methods, you will be graded for the solution of my choosing. However, no additional oints will be awarded for the extra work. ee Figure C for grahical solution to find t 50 from given data. 2 TvHdr To find c v c : v t Remember, dual drainage of 1D Test samle: H dr = 0.5H = 0.5(0.375 in) = 0.1875 in = 0.015625 ft Table 1. ummary of Coefficient of Consolidation Calculations. Method t 50 (min) t 90 (min) T v (Table 7.1, Das FGE 2006) c v (ft²/min) c v (in²/min) Log Time 9.1 NA 0.197 5.29 x 10-6 7.61 x 10-4 Figure C. 1D Consolidation Test Results with Log Time and quare Root of Time. 14.330 2012 Exam 2 olution Page 7 of 10
4. Using the coefficient of consolidation calculated in Problem 3, calculate the times for 67% and 99% consolidation for the CL layer. What will be the soil settlements at these times? Use your value of calculated in Problem 2. 5.2910 3 0.364 5.2910 3 T 50 = 619282 mins = 430.1 days = 61.4 weeks = 1.18 years U 67 t 0.67 x 0.67inches 3 4 x _ inches 1inch inches 1.781 5.2910 3 T 99 = 3030057 mins = 2104 days = 300.6 weeks = 5.76 years U 99 x 1inch t 0.99 x _ inches 1inches 14.330 2012 Exam 2 olution Page 8 of 10
EXTRA CREDIT (5 oints): An eight (8) ft square footing was laced on to of six (6) ft of structural fill for Problem #2. The footing has an allowable load of 128 kis. How long would it take this footing to reach end of rimary consolidation of the CH layer? ame as 99% consolidation in Problem #4 (5.76 years) UEFUL INFORMATION? Table 7.1 (Das FGE 2006). 14.330 2012 Exam 2 olution Page 9 of 10
D Cu D v = ki 60 10 C c q = kia (D30) (D xd 60 2 10 ) H q k E = mc 2 N d Figure 7.27. Das FGE (2006). 14.330 2012 Exam 2 olution Page 10 of 10