Find: LL laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 19 23 27 30 Find the liquid limit of a soil. [pause] In this problem,

Find: LL laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 19 23 27 30 we’ve been provided laboratory test data from a liquid limit test.

Find: LL wc laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 19 23 27 30 The liquid limit of a soil is the water content which divides the liquid state of a soil from the plastic solid state of the soil.

- + Find: LL SL PL LL wc Increasing water content Brittle Ductile Plastic Liquid Solid Solid Solid SL PL LL Shrinkage Limit Plastic Limit Liquid Limit As the water content of a soil increases,

- + Find: LL SL PL LL wc Increasing water content Brittle Ductile Plastic Liquid Solid Solid Solid SL PL LL Shrinkage Limit Plastic Limit Liquid Limit it moves past the shrinkage limit, from brittle to ductile,

- + Find: LL SL PL LL wc Increasing water content Brittle Ductile Plastic Liquid Solid Solid Solid SL PL LL Shrinkage Limit Plastic Limit Liquid Limit then past the plastic limit, from ductile to plastic,

- + Find: LL SL PL LL wc Increasing water content Brittle Ductile Plastic Liquid Solid Solid Solid SL PL LL Shrinkage Limit Plastic Limit Liquid Limit then past the liquid limit, from plastic to liquid.

- + Find: LL SL PL LL wc Increasing water content Brittle Ductile Plastic Liquid Solid Solid Solid SL PL LL Shrinkage Limit Plastic Limit Liquid Limit For this problem, we’re interested in the liquid limit.

Find: LL wwater wc= wsoil 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 Liquid Plastic Find: LL wwater wc= wsoil laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 We’ll plot the number of turns --- turns

Find: LL wwater wc= wsoil 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 Liquid Plastic Find: LL wwater wc= wsoil laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 of the Casagrande cup on the horizontal axis, using a log scale. turns

Find: LL wwater wc= wsoil 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 Liquid Plastic Find: LL wwater wc= wsoil laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 And the water content of the soil tested, will be plotted on the vertical axis, using a linear scale. turns

Find: LL wwater wc= wsoil 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 Liquid Plastic Find: LL wwater wc= wsoil laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 The laboratory data includes 3 tests, which provide the number of turns, turns

Find: LL wwater wc= wsoil 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 Liquid Plastic Find: LL wwater wc= wsoil laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 and data to be used to determine the water content, for each test. turns

Find: LL wwater wc= wsoil 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 Liquid Plastic Find: LL wwater wc= wsoil laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 The basic procedure is to plot the three points, turns

Find: LL wwater wc= wsoil 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 Liquid Plastic Find: LL wwater wc= wsoil laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 add a line of best fit, turns

Find: LL wwater wc= wsoil 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 Liquid Plastic Find: LL wwater wc= wsoil laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 trace up from 25 turns to the line of best fit, turns 25

Find: LL LL wwater wc= wsoil 14 65.04 78.25 74.58 27 66.21 83.22 79.21 Liquid Plastic Find: LL wwater wc= wsoil laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 then trace over to the water content axis, to find the liquid limit. However we’ll use a second approach --- LL turns 25

Find: LL LL wwater wc= wsoil 14 65.04 78.25 74.58 27 66.21 83.22 79.21 Liquid Plastic Find: LL wwater wc= wsoil laboratory data: # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 wc=A-B * LOG(turns) which uses the equation of the line of best fit to solve for the water content when the number of turns is 25. LL turns 25

Find: LL wwater wc= wsoil 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 Liquid Plastic Find: LL wwater wc= wsoil # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 Before we can plot, we must solve for our water content, turns

Find: LL wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 which we can calculate using the test data. turns

Find: LL wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 For the first test, the values are plugged into the equation, turns

Find: LL wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 and the water content computes to 38.5 percent. turns

Find: LL wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 We also compute the water content for the second test, turns

Find: LL wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% 22.6% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 19 23 27 30 and the third test. turns

Find: LL wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% 22.6% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 40 30 20 25 35 19 23 27 30 So we plot out our data --- turns

Find: LL wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% 22.6% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 40 30 20 25 35 19 23 27 30 one point at a time. turns

Find: LL wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% 22.6% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 40 30 20 25 35 19 23 27 30 --- turns

Find: LL wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% 22.6% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 40 30 20 25 35 19 23 27 30 --- turns

Find: LL wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% 22.6% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc 40 30 20 25 35 19 23 27 30 We draw the line of best fit, turns

Find: LL wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% 22.6% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc=80.4-36.0 * LOG(turns) wc 40 30 20 25 35 19 23 27 30 calculate it’s equation, turns

Find: LL 25 wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% 22.6% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc=80.4-36.0 * LOG(turns) wc 40 30 20 25 35 19 23 27 30 and solve for the water content when the number of turns equals 25. 25 turns

Find: LL 25 30.1% wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% 22.6% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc=80.4-36.0 * LOG(turns) wc 40 30 20 25 35 19 23 27 30 The liquid limit for this sample is 30.1 percent. 30.1% 25 turns

Find: LL 25 30.1% wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% 22.6% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc=80.4-36.0 * LOG(turns) wc 40 30 20 25 35 19 23 27 30 From the possible solutions, 30.1% 25 turns

Find: LL 25 AnswerD 30.1% wwater wdish+wet soil-wdish+dry soil wc= = wsoil wdish+dry soil- wdish wc 38.5% 30.8% 22.6% # of turns Wdish [g] Wdish+wet soil [g] Wdish+dry soil [g] 14 65.04 78.25 74.58 27 66.21 83.22 79.21 37 64.18 80.11 77.17 wc=80.4-36.0 * LOG(turns) wc 40 30 20 25 35 19 23 27 30 the answer is D 30.1% 25 AnswerD turns

( ) ? τ [lb/ft2] γclay=53.1[lb/ft3] Index σ’v = Σ φ γ Δ d ˚ H*C σfinal Find: σ’v ρc d = 30 feet (1+wc)*γw wc+(1/SG) σ’v = Σ φ γ Δ d ˚ d Sand 10 ft γT=100 [lb/ft3] 100 [lb/ft3] φ=α1-α2 10 [ft] 20 ft Clay = γsand dsand +γclay dclay A W S V [ft3] W [lb] 40 ft text wc = 37% ? Δh 20 [ft] τ [lb/ft2] (5 [cm])2 * π/4 ( ) H*C σfinal ρcn= 1+e σinitial log ‘ φ size[mm] % passing 0% 20% 40% 60% 80% 100% 10 1 0.1 0.01 c=0 400 1,400 σ3 Sand σ1