CEGR 3258: Geotechnical Engineering Lab: Fall 2008

Laboratory Report 4: Consolidation Test (Full Report) References:

o ASTM D2435: “Standard Test Method for One-Dimensional Consolidation Properties of

Soils”.

o Liu and Evett (2008). Soil Properties: Testing, Measurement and Evaluation, 6th

Edition

Introduction:

This test is performed in the laboratory to simulate field consolidation and determine the rate and

amount of volume change that a laterally confined fined-grained soil sample undergoes under the

application of different vertical stresses. From the laboratory data, the dial reading versus time

relationship for each applied vertical stress, and void ratio versus stress relationships can be plotted.

These plots are useful in determining coefficient of consolidation (Cv), the compression index (Cc), the

recompression index (Cr) and the preconsolidation stress (or maximum past stress) ( p) of the soil.

Report

Prepare and submit 2 hard copies of your report on consolidation test in accordance with the format and

guidelines in the CEE manual of Laboratory report.

In your report (body or appendix as appropriate) include:

1. tables of:

Dial reading and time for each vertical stress change

Summary of data analysis: ( , R0, R100, R50, t50, Cv, e, etc)

2. plots of:

Dial reading versus log of time for each stress change

Void ratio (e ) versus log of stress ( ) (consolidation curve)

Coefficient of consolidation (Cv) versus stress ( )

3. determine and present the following:

Initial water content, final water content and initial void ratio (e0)

R0, R50, R100, t50, and the coefficient of consolidation (Cv) using Casagrande’s logarithm

of time fitting method for each stress

Compression index (Cc)

Recompression index (Cr) from the unload-reload cycle, as well as the final unloading of

the Sample. Are the values equal?

Preconsolidation pressure ( p) using Casagrande’s method.

Note: The following pages present method of data reduction and analysis.

Reduction of Consolidation Test Data Last week, Dr. Ogunro said there were 5 terms that we needed to get from the consolidation test:

a) cv b) e0 c) cc d) cr

e) ’p Determine Coefficient of Consolidation, cv

Plot dial gage readings R vs. log time for each load and fit a smooth curve for analysis.

Calculate cv and c using the Casagrande construction:

a) Find R0: choose t1, calculate t2 = t1/4, measure vertical distance “a” on curve from t1 to t2, R0 is distance 2a above R at t1

b) Find R100 at “intersection” of primary and secondary consolidation c) Find R50 by taking average of R0 and R100 d) Calculate cv as shown above using time factor T50

log time, t

R50

R0

R100

t50 t2 t1

a

a

c = - e / log (t4 / t3)

t3 t4

cv = T50 (H/N)2 / t50 = 0.197 (H/2)2 / t50

(N = 2 for double drainage)

Determination of Initial Void Ratio For Specimen, e0 Know from measurements:

o Diameter of specimen (inside diameter of ring) o Height of specimen (height of ring) o Initial mass of specimen (mass of specimen and ring – mass of specimen) o Initial water content of specimen (average of two readings)

Specimen assumed saturated, so Vv = Vw

If you know M and w, w

M wM

w 1and w

w V

w

MV V

So if V = Vv + Vs and v

s

Ve

V, then v

V

Ve

V V, we’ll call this e0.

Reduction of Data and Assembly of Consolidation Curve

In order to determine, these terms, the consolidation curve must be assembled. The

consolidation curve is plotted in terms of effective vertical stress ’v and void ratio e. The effective vertical stress is the stress on the specimen at the completion of the consolidation step. This is the applied stress (2/3 tsf, 8/3 tsf, etc.) The void ratio is the void ratio at the completion of the consolidation step. This is calculated incrementally starting with the initial

voild ratio, determined above. Each consolidation increment will result in a e. This e is

determined using the change in height of the specimen during the increment: H = R100 – R0. In order to make calculation of the void ratio less tedious, a term called the height of solids, Hs is introduced. Consider, if all of the solid particles and water molecules could be magically separated into two distinct phases, much like the phase diagram. During consolidation, the change in volume is only due to the change in water volume, the volume of solids DOES NOT

change. Thus, if v

s

Ve

Vthen v

s

Ve

V. Also consider that the sample is confined inside a

metal ring that does not allow displacement or strain in the horizontal direction. So, if both of

the hypothetical phases have the same crossectional area, A, then e and e can be rewritten: v

s

V

A v

V

sA

He

H and

v

s

V

A v

V

sA

He

H . Since all change in volume is due to change in voids, the

equation is reduced to s

He

H.

M

Ms

Mw

VV

Vs

V

You can get to the same terms using phase diagrams directly:

S

V0

S

V0

0H

H

V

Ve

S

VF

S

VF

FH

H

V

Ve

Subtracting:

SS

V0VF

0FH

ΔH-

H

HH)e(eΔe or Δe-H ΔH

S

Determine Hs Hs comes from the initial conditions.

We know V and we already calculated Vw, so Vs = V – Vw, therefore s

s

VH

A.

Alternately, using the definitions of total volume and void ratio:

VSV VV so )e(1H

H

H1HHH H

0S

S

V

SVSor

0

Se1

HH

Assembling the Consolidation Curve Starting with the initial void ratio, at the end of the first consolidation step, say 2/3 tsf:

’v = 2/3 tsf e2/3 = e0 – e2/3 At the end of the next step, 4/3 tsf

’v = 4/3 tsf e4/3 = e0 – e2/3 – e4/3 or e4/3 = e2/3 – e4/3 and so on.

VV0 = HV0 A

VS = HS A

V = H A

Initial State

Final State

VVF = HVF A

VS = HS A

V = H A

H

Plot the data with effective stress ’v on the horizontal axis (logarithmic scale) and e on the vertical axis. Determination of Compression and Recompression Indices cc and cr The compression and recompression indices are the slopes of the consolidation curve in the compression and recompression zones:

Compression Index CC = - e / log ’V = - e / log ( ’2/ ’1)

Recompression Index CR = - e / log ’V = - e / log ( ’2/ ’1)

e

’v

Recompression Slope CR

Compression Slope Cc

log scale

Determine the Preconsolidation Pressure ’p

Using the consolidation curve already assembled:

e) Find point A – maximum curvature (minimum radius) on reload portion of laboratory curve.

f) Draw horizontal line and tangent to curve at point A g) Bisect angle between horizontal and tangent at point A. h) Extrapolate straight line “virgin curve” to intersect bisector at preconsolidation

pressure ’p

void ratio, e

’v ’p

Virgin Curve

tangent at point A

horizontal

bisector

A