The University of Toledo
Soil Mechanics Laboratory
1
Consolidation Test
Introduction
All soils are compressible so deformation will occur whenever stress is applied to soils. Soil
minerals and water are both incompressible. Therefore, when saturated soils are loaded, the load
first acts on the pore water causing pore water pressures that are in excess of the hydrostatic
pressures. The excess pore water pressures are largest near the application of load and decrease
with distance from the loading. The variations in excess pore water pressure cause total head
gradients in the soil which, according to Darcy’s Law, will induce water to flow from locations
of high total head to low total head. The excess pore water pressures dissipate as water flows
from the soil and, to compensate for the applied stress, the stress is transferred to the soil
minerals resulting in higher effective soil stress. The flow of water from the soil also causes
reductions in the soil volume and settlements at the ground surface. Fine-grained soils have very
low permeability so they can require substantial periods of time before the excess pore water
pressures fully dissipate. This process of time-dependent settlement is referred to as
consolidation. Terzaghi’s theory for one-dimensional consolidation provided the means to
calculate the total amount of consolidation settlement and the consolidation settlement rate. In
practice, engineers obtain representative soil samples, conduct consolidation tests and use
Terzaghi’s consolidation theory to predict the total settlement and time rate of settlement for
embankments and foundations.
Apparatus
1. Water content tare and oven.
2. Consolidometer with porous stone in base, rigid consolidation ring and load cap with
porous stone.
3. Load device with lever arm
Procedure
A.
Sample Preparation (several days before test)
Moist fine-grained soil from the laboratory was placed in the consolidation ring and
statically compacted using several layers. Excess soil from the top of the ring was
carefully trimmed level with the top of the ring.
B.
Test Preparation (several days before test)
1) The height, diameter and mass of the consolidation ring were measured. The initial wet
mass of the soil sample and ring and the height of the soil sample were measured. The
trimmings were used for a water content determination.
1
ASTM D 2435-96
Consolidation - 1
2) The test specimen in the consolidation ring was placed in the consolidometer and the
consolidometer was placed in the loading device. The deformation gage was adjusted
and an initial reading obtained. Loads were applied and removed incrementally in order
to preconsolidate the test specimen. Water was added to the consolidometer periodically
to saturate the soil.
C.
Consolidation Test
1) Apply increments of total stress to the soil specimen. The duration of each increment
should be sufficient to define the characteristic curve obtained by a graph of deformation
versus either the square root of time or the log of time.
2) The standard loading schedule is determined using a load increment ratio (LIR) of one,
obtained by doubling the total stress on the soil. The load values should be 17.1, 34.2,
68.3, 136.7, 273.3, 546.7 kPa.
3) For each load increment, record the dial readings at time intervals of approximately 0.09,
0.25, 0.49, 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100 minutes to obtain the deformations, d.
4) After completion of all load increments, remove the soil from the consolidometer and
determine the final water content.
Calculations
Calculations for the soil mass-volume, time-deformation and load-deformations properties
are given in the equations and tables that follow.
Mass-Volume Properties:
ρd =
ρ
(1)
1+ w
MS =
Mt
1+ w
(2)
Hs =
Ms
Vs
=
A
ρs ⋅ A
(3)
S =
Vw
Mw / ρw
=
× 100%
Vv
A⋅ Hv
(4)
Consolidation - 2
Table 1 – Consolidation Test, Initial and Final Data
Consolidation Test
Soil Description
Mass Density of Solids, ρs (g/cm3)
Ring Height (cm)
Ring Diameter (cm)
Area of Soil, A
Lever Arm Ratio (LAR)
Initial Dial Reading (mm)
Group _________ Date __________
1.905
6.35
31.67
(cm2)
11.03
0.000
Initial Conditions
Height of Soil Sample, Ht (cm) 1.905
Volume of Soil (cm3) 60.33
Mass of Wet Soil + Ring (g)
Mass of Ring (g)
Mass of Wet Soil, Mt (g)
0.003167
(m2)
Final Conditions
Mass of Tare + Wet Soil (g)
Mass of Tare + Dry Soil (g)
Mass of Tare (g)
Mass of Soil (g)
Mass of Water (g)
Water Content, w (%)
Wet Density, ρ (g/cm3)
Dry Density, ρd (g/cm3)
Mass of Dry Soil, Ms (g)
Mass of Water, Mw = Mt - Ms (g)
Equivalent Height of Solids, Hs (cm)
Height of Voids, Hv = Ht - Hs (cm)
Void Ratio, e = (Hv / Hs)
Degree of Saturation, S (%)
(=eo)
Vertical Stress Calculation:
P = ( Mass in kg ⋅ 9.81 m / sec 2 ) ⋅ LAR
σv =
P
P
=
(1000 N/kN) ⋅ A
A
(kg ⋅ m/sec 2 = N)
(kN/m 2 = kPa)
Consolidation - 3
(5)
(6)
Time-Deformation Calculations:
d = (Dial Reading - Initial Dial Reading) X 0.0002 cm/division
(7)
Deformation-Time Data Collection:
Deformation-Time data is recorded and entered into an MS Spreadsheet file as shown in
Table 2.
Table 2 - Deformation-Time Data
Date
Time
Mass, M (kg)
Force, P (N)
0.0
Stress (kPa)
0.0
Elapsed
Time
(min)
Dial
Reading
(Div.)
By
Date
Time
Mass, M (kg)
Force, P (N)
0.0
Stress (kPa)
0.0
d
(cm)
Square
Root
of Time
Elapsed
Time
(min)
0
0.0000
0.0
0.09
0.0000
0.25
0.49
1
2
4
9
16
25
36
49
64
81
100
d
(cm)
Square
Root
of Time
0
0.0000
0.0
0.3
0.09
0.0000
0.3
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5
0.7
1.0
1.4
2.0
3.0
4.0
0.25
0.49
1
2
4
9
16
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.5
0.7
1.0
1.4
2.0
3.0
4.0
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
5.0
6.0
7.0
8.0
9.0
10.0
25
36
49
64
81
100
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
5.0
6.0
7.0
8.0
9.0
10.0
Consolidation - 4
Dial
Reading
(Div.)
By
The coefficient of consolidation is computed for each load increment using the following
equations and the graphs of deformation versus the square root of time.
cv =
T90 H dr2
t 90
(8)
Where T90 = dimensionless time factor for 90% primary consolidation = 0.848;
Hdr = length of the longest drainage path, Hd50, at 50 % primary consolidation;
t90 = time at 90% primary consolidation.
Hdr and Hd50 must be computed for each load increment since the height of the soil sample is
continuously changing. The consolidation test is conducted with porous stones on the top of
and below the soil sample. Therefore, the longest drainage path for a load increment is equal to
one half of the average sample height.
To determine the t90, d50 and d100, it is necessary to graph deformation versus the square
root of time for each load increment. The following steps are required for 90 % primary
consolidation (from ASTM D2435).
1)
Draw a straight line through the points representing the initial readings that exhibit a
straight line trend. Extrapolate that line back to t = 0 and obtain the deformation
ordinate,d0 (y-axis) representing 0% primary consolidation.
2)
Draw a second straight line through the 0% ordinate so that the abscissa (x-axis) of this
line is 1.15 times the abscissa of the first straight line through the data. The intersection
of this second line with the deformation-square root of time curve is the deformation, d90,
and time, t90, corresponding to 90% primary consolidation.
3)
The deformation at 100% consolidation, d100, is 1/9 more than the difference in
deformation between 0 and 90 % consolidation. The time of primary consolidation, t100,
may be taken at the intersection of the deformation-square root of time curve and this
deformation ordinate. The deformation, d50, corresponding to 50% consolidation is equal
to the deformation at 5/9 of the difference between 0 and 90 % consolidation. d50 is used
to compute the average sample height, Hd50, (Initial Sample Height – d50). Hdr is
computed using the following equation.
Hdr = (Initial Sample Height – d50) / 2 = Hd50 / 2
Consolidation - 5
(9)
Load-Deformation Properties:
The load-deformation properties are obtained from the graph of void ratio (e100) versus
log of vertical effective stress. The void ratio is computed using Equation 10. The other
computations can be obtained using the table and graphs below.
e100 =
Hv
Hs
(10)
Where e100 = void ratio at 100% primary consolidation and Hv is computed using d100.
Results
The required graphs can be obtained using the figures provided in the spreadsheet program.
Conclusions
Determine the preconsolidation stress using the Casagrande method.
Determine the compression index, Cc.
σ v = ________ kPa
Consolidation Test
Deformation, d (cm)
0.010
0.012
t90 =
min
0.014
0.016
d0 =
.
d90 =
.
d50 =
.
d100 =
.
0.018
0.020
0.022
0.024
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
1/2
Square Root of Time (min )
8.0
Figure 1 – Void Ratio Vs. Square Root of Time
Consolidation - 6
9.0
10.0
Table 3 - Consolidation Test Summary Table
Effective Stress (kPa)
Deformation, d100 (cm)
Final Sample Height (cm)
Height of Voids, Hv, (cm)
Void Ratio, e100
d50 (cm)
Hdr (cm)
t90, min
cv, cm2/min
Void Ratio, e100
Consolidation Test
Void Ratio vs. Log of Effective Stress
1.00
10.00
100.00
Effective Stress, kPa
Figure 2 – Void Ratio Vs. Effective Stress
Consolidation - 7
1000.00
Porous
Stone
Consolidometer
Top Ring
Rigid Ring
Loading Cap
Picture 1 – Consolidometer
Load Device
with Lever Arm
Consolidation Weights
Picture 2 – Consolidation Test Load Device
Consolidation - 8
Appendix
Sample Calculations for Consolidation Test
Mass-Volume Properties:
ρd =
ρ
(1)
1+ w
MS =
Mt
1+ w
(2)
Hs =
Ms
Vs
=
A
ρs ⋅ A
(3)
S =
Vw
Mw / ρw
=
× 100%
Vv
A⋅ Hv
(4)
Time-Deformation Calculations:
P = ( Mass in kg ⋅ 9.81 m / sec 2 ) ⋅ LAR
σv =
P
P
=
(1000 N/kN) ⋅ A
A
d = (Dial Reading - Initial Dial Reading) X 0.000254 cm/division
cv =
T90 H dr2
t 90
(5)
(6)
(7)
(8)
Hdr = (Initial Sample Height – d50) / 2
(9)
Load-Deformation Properties:
e100 =
Hv
Hs
(10)
Consolidation - 9