Settlement

SettlementImmediate settlement Caused by elastic deformation of dry and moist soil without any change in moisture contentPrimary Consolidation Settlement Volume change caused by expulsion of water from voids in saturated cohesive soilsSecondary Consolidation Settlement Volume change after primary consolidation as a result of plastic adjustment of soil matrix

Consolidation SettlementWe will focus on consolidation settlementhh

Consolidation SettlementLets look at how a saturated clay reacts to an applied load, starting at time = 0 (immediately after load was applied). Assuming some clay layer of thickness H with drainage both above and below (sand layers)HvHuvHv=+=+

Consolidation SettlementNow at some time > 0The water slowly is squeezed out of soil and takes the path of least resistancePore pressure is decreasing while the effective stress increasesHvHuvHv=+=+

Consolidation SettlementFinally at time = Pore water is in equilibrium and the soil skeleton is carrying the entire loadThis process will take time weeks, months, even yearsWhy and what might this depend on?HvHuvHv=+=+

Laboratory Consolidation TestIn the lab a soil consolidation test is used to determine settlement characteristics of a soilHv All settlement will occur in voidsHsA = VsHsA = Ws/Gsw Hs = Ws/AGswHv = H Hseo = Vv/Vs = HvA / HsA = Hv/Hseo = void ratio at time 0e = H1/Hse1 = eo e e1 = void ratio at time > 0HsA

Consolidation CurvePlotting e vs. Log p (void ratio on a linear scale vs the load on a log scale)eCr = Recompression Index = Slope of lineCc = Compression Index = Slope of lineCr also (called Cs in book)Log p

Consolidation Curve

Chart1

0.639941875

0.6247816406

0.6023708594

0.5746869531

0.5318428125

0.4665878906

0.3940824219

Log p

Void Ratio - e

Consol Curve

Sheet1

Consolidation Test Data

Ws (g)A (cm2)Gsw

12830.682.751

Hs = Ws / AGsw

e = Hv / Hs

Effective StressFinal Height of specimen after consolidation (cm)Hv = H-Hse

02.5401.0230.674

0.52.4880.9710.640

12.4650.9480.625

22.4310.9140.602

42.3890.8720.575

82.3240.8070.532

162.2250.7080.467

322.1150.5980.394

Sheet1

Log p

Void Ratio - e

Consol Curve

Sheet2

Sheet3

Overconsolidated Normally ConsolidatedOverconsolidated Some past stress was greater than current stressNormally Consolidated Current stress is maxeAt the break in the curve, this value of is called: c The PreConsolidation PressureThis is the max pressure this soil has ever feltLog pc

Overconsolidated Normally ConsolidatedOverconsolidated Some past stress was greater than current stressNormally Consolidated Current stress is maxeLog pOnce c is found from the curveIt is compared to the actual in the field (z)If c= v Normally ConsolidatedIf c > v Overconsolidated ie Sample depth 10, no water table, = 120 pcf, the actual = 1200 psfCompare that to c from consol curve

c

Overconsolidation RatioeLog pcThe OCR is the ratio of past effective stress to present effective stressOCR = c / v

OCR = 1 means what?

v = OC

Finding Pc Casagrandes Method12345

Chart1

0.639941875

0.6247816406

0.6023708594

0.5746869531

0.5318428125

0.4665878906

0.3940824219

Log p

Void Ratio - e

Consol Curve

Sheet1

Consolidation Test Data

Ws (g)A (cm2)Gsw

12830.682.751

Hs = Ws / AGsw

e = Hv / Hs

Effective StressFinal Height of specimen after consolidation (cm)Hv = H-Hse

02.5401.0230.674

0.52.4880.9710.640

12.4650.9480.625

22.4310.9140.602

42.3890.8720.575

82.3240.8070.532

162.2250.7080.467

322.1150.5980.394

Sheet1

Log p

Void Ratio - e

Consol Curve

Sheet2

Sheet3

Calculation of SettlementConsider a layer of clay under an external loadHV = V0-V1 = HA (H-H)A = HAHv=SoilVoidsSolidsV0Vv=eVs=1VoidsSolidsV1Vv=eVs=1Ve = eo-e1We know e=Vv/Vs Also e =Vv/Vs as Vs does not change

Calculation of SettlementV = V0-V1 = HA (H-H)A = HAWe know e = Vv/Vs Also e =Vv/Vs as Vs does not change

Solve for Vv = e VsTherefore V = Vv = HA now HA = e Vs Equation 1Vs = V0 / (1+e0) = AH / (1+e0) Equation 2Solve Both Equations for Vs

Calculation of SettlementHA / e = HA / (1 + e0)We get

H = H e / (1+e0)

The General Settlement Equation

We will show how this is the slope of the consol curve rise / run

Calculation of SettlementNormally Consolidated Soil v= cH = Cc H / (1 + e0) log [(v+ v) / v]eSoil stress due to its own weight is here prior to application of load (OCR = 1)Stress is here after application of loadLog pc

Calculation of SettlementNormally Consolidated SoilH = Cc H / (1 + e0) log [(v+ v) / v]Review this equation It is simply rise / runH / (1 + e0) is from the general settlement eq. derived earlierCc log [(v+ v) / v] is the slope * e

Why?

Calculation of SettlementOver Consolidated Soil If (v+ v) > c

H = Cr H / (1 + e0) log c / v + CcH / (1+e0) log [(v+ v) / c]eSoil stress due to its own weight is here prior to application of load (OCR = 1)Stress is here after application of loadLog pc

Calculation of SettlementOver Consolidated Soil If (v+ v) < c

H = Cr H / (1 + e0) log [(v+ v) / v]eSoil stress due to its own weight is here prior to application of load (OCR = 1)Stress is here after application of loadLog pc

Calculation of SettlementThe text covers several methods for determining the values of Cr and Cc. Take a look at thosezvRecall the plot at leftNow consider a layer of clay to be analyzed for settlementNow look at the settlement equationsGiven an H How do you determine the values of the stresses in that layer?

SettlementLets plot all the stresseszvvcv+ v> c< c

SettlementTo solve any settlement problem with an overconsolidated soil you MUST do this plot (or at least calc the data points) to solvezvvcv+ v> c< c

Settlement

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