1-D Consolidation Test

1
Department of Civil Engineering, IIT Delhi
Submitted By:
Abhinav Kumar
Soil Engineering Lab
REPORT TITLE (09)
1-D Consolidation Test
Disclaimer: This presentation is for educational purposes only. Opinions or points of
view expressed in this presentation represent the view of the presenter, and does not
necessarily represent the official position or policies of IIT Delhi. Nothing in this
presentation constitutes legal advice. The individuals appearing in this presentation, if
any, are depicted for illustrative purposes only and are presumed innocent until proven
guilty in a court of law. Under no circumstance shall we have any liability to you for any
loss or damage of any kind incurred as a result of the use of the data or reliance on any
information provided. Your use of the document and your reliance on any information is
solely at your own risk

2
Objective: Determination of consolidation properties (like CV, CC, CS, t90, mv, av) of the given soil
specimen (Dhanauri Clay) by conducting one-dimensional consolidation test using fixed ring type
setup.
Apparatus:
1. Soil specimen with consolidation setup
2. Steel ball
3. Dial gauge (for displacement measurement)
4. Water reservoir (to keep soil specimen saturated)
5. Loads (for application of vertical stress)
6. Consolidation ring (used for extracting undisturbed soil sample)
Consolidation Ring Porous Stones
Consolidation Ring
Collar
Cell Base
Clamping Screw
Steel Ball
Consolidation Setup
Loading Cap

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Testing methods and Procedures:
Sample Preparation (Remoulded sample):
The sample was prepared using water sedimentation method to ensure 100% saturation.
Theoretical Background:
The gradual process which involves, simultaneously, a slow escape of water and a gradual compression,
and which will be shown later to involve also a gradual pressure adjustment, is called consolidation. It is
merely compression under a steady static pressure where the soil particles attain a closer packing due to
sliding and rolling of particles as water escapes from the voids.
When a compressive load is applied to soil mass, a decrease in its volume takes place, the decrease in
volume of soil mass under stress is known as compression and the property of soil mass pertaining to its
tendency to decrease in volume under pressure is known as compressibility. In a saturated soil mass having
its void filled with incompressible water, decrease in volume or compression can take place when water is
expelled out of the voids. Such a compression resulting from a long-time static load and the consequent
escape of pore water is termed as consolidation. Then the load is applied on the saturated soil mass, the
entire load is carried by pore water in the beginning. As the water begins escaping from the voids, the
hydrostatic pressure in water gets gradually dissipated and the load is shifted to the soil particles which
increases effective stress on them, as a result the soil mass decrease in volume. The rate of escape of water
depends on the permeability of the soil.
Specimen kept in polybag to
prevent loss of moisture content
Soil Specimen prepared by
Wet Sedimentation Method
Sample preparation by Wire Saw
Cutting

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Terzaghi’s Theory of Consolidation:
The assumptions considered to establish the basic relationship are as follows:
• Soil is homogenous, isotropic and fully saturated.
• Soil grains and water in the voids are incompressible.
• Permeability remains constant during the entire period of
consolidation.
• Darcy’s law is valid throughout the consolidation process.
• Soil is laterally confined.
• Compression and fluid flow are only in axial direction.
• Time lag in consolidation is entirely due to the low
permeability of soil.
• Unique relationship (Linear) is assumed between void ratio
and the effective stress, and this remains constant during
the load increment.
The equilibrium of an element at a depth z from its top at time t is
being considered and using Darcy’s law, the following differential
equation has been derived for one-dimensional consolidation:
where, u is the excess hydro-static pressure and cv is coefficient of consolidation.
The solution of this differential equation is obtained through Fourier series and separation of variable
method. Depending upon the boundary conditions,
t = 0, u = u0 , for any value of z (u0 is initial hydrostatic pressure)
t = ∞, u = 0 , for any value of z
z = 0, u = 0 , for any value of t
z = H (=2d), u = 0 , for any value of t
The solution of this equation is:
Where, Tv is time factor and directly proportional to elapse time for consolidation = cvt/d2
. Its value will be
different for different drainage conditions.

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Drainage Paths:
It is maximum distance that water has to travel before reaching free drainage conditions.
Single Drainage or Half-Closed Layer:
Drainage will occur from one side (top in below figure) and other will remain impervious. The value of d
(drainage path) is equal to thickness of layer.
Double Drainage or Open Layer:
Drainage will occur from both sides. The value of d (drainage path) is equal to half the thickness of layer.
Limitations of Theory:
The presence of air may affect the results abruptly.
Permeability decreases as consolidation progresses due to increase in the effective stress.
Darcy’s law is not valid at very low hydraulic gradients.
In the field, consolidation is 3-D not 1-D.
The relationship between void ratio and effective stress is not linear.
Determination of coefficient of consolidation (Cv):
1. Casagrande Method (log(t) method)
2. Taylor Method (√t method)

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Settlement curve (oedometer test at each pressure/load):
Casagrade method: t50 (U = 50%)
Tayor method: t90(U = 90%)
U = Degree of consolidation
T = Time factor
Ht = Depth of the sample
Coefficient of consolidation (cv) can be determined using above equation.
Coefficient of compressibility (av ) can be obtained by using void ratio versus effective stress relationship.
where, mv is coefficient of volume compressibility and e0 is initial void ratio.
where, γw is unit weight of water and k is permeability of soil specimen.

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Settlement calculations:
Compressibility parameters Cc & Cr are used in settlement calculations. Cc is the slope of loading curve and
Cr or Cs is the slope of unloading curve.
where Si is immediate settlement and Sc is settlement due to consolidation, which can
be obtained by oedometer test. St is total settlement and U is degree of consolidation.
Settlement for NC soil
Settlement for OC soil
Calculations:
1. Height of solids (HS) is calculated from the equation
HS = WS/(GS.γw.A)
2. Void ratio. Voids ratio at the end of various pressures are calculated from equation
e = (H – HS)/HS
3. Coefficient of consolidation. The Coefficient of consolidation at each pressures increment is calculated
by using the following equations:
i. Cv = 0.197 d2
/t50 (Log fitting method; Casagrande Method)
ii. Cv = 0.848 d2
t90 (Square fitting method; Taylor Method)
In the log fitting method, a plot is made between dial readings and logarithmic of time at constant load,
and the time corresponding to 50% consolidation is determined.
In the square root fitting method, a plot is made between dial readings and square root of time at constant
load, and the time corresponding to 90% consolidation is determined. The values of Cv are recorded.
4. Compression Index. To determine the compression index, a plot of voids ratio (e) Vs log(t) is made. The
virgin compression curve would be a straight line and the slope of this line would give the compression
index Cc.
5. Coefficient of compressibility. It is calculated as follows av = 0.435 Cc/(Avg. pressure) for the increment
where Cc = Coefficient of compressibility
Or, av can be also obtained by using void ratio versus pressure curve, which will be a function of pressure.
6. Coefficient of permeability. It is calculated as follows
k = Cv.av .γw /(1+eo).

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Data Table
Table I: Data Sheet for Consolidation Test: Time‐ Displacement Relationship
Ring Height(H1) (i) 21.10 (ii) 21.27 (iii) 20.94; Average = 21.103 mm
Ring Dia (i) 60.15 (ii) 60.41 (iii) 60.37; Average = 60.31 mm
Area of Ring = 2856.73 mm2
Volume of Ring = 60285.48 mm3
LC of Dial Gauge = 0.01mm
Initial Height of Specimen,H0 = 21.10 mm Water Content = 27 %
Empty Weight of Ring = 208.78 gm Height of Solid Hs= Ws/(G*γw*A)
Wet Sample + Ring= 326.94 gm Specific Gravity = 2.65
Dry Sample + Ring = 301.50 gm
Height of Solid Hs = 1.238 cm
LOADING STAGE
0.05 kg/cm2
, Normal Load
Time t (min) √t
Vertical Dial
gauge Reading
Compression (mm)
Height of the
specimen, H (cm)
0.00 0.00 7.900 0.000 2.0000
0.25 0.50 7.880 0.020 1.9980
1.00 1.00 7.870 0.010 1.9970
2.25 1.50 7.860 0.010 1.9960
4.00 2.00 7.855 0.005 1.9955
6.25 2.50 7.850 0.005 1.9950
9.00 3.00 7.850 0.000 1.9950
12.25 3.50 7.845 0.005 1.9945
16.00 4.00 7.845 0.000 1.9945
25.00 5.00 7.840 0.005 1.9940
36.00 6.00 7.840 0.000 1.9940
49.00 7.00 7.840 0.000 1.9940
64.00 8.00 7.835 0.005 1.9935
81.00 9.00 7.830 0.005 1.9930
100.00 10.00 7.830 0.000 1.9930
1440.00 37.95 7.810 0.020 1.9910

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0.5 kg/cm2
, Normal Load
Time t (min) √t
Vertical Dial
gauge Reading
Compression (mm)
Height of the
specimen, H (cm)
0.00 0.00 7.810 0.000 1.9910
0.25 0.50 7.690 0.120 1.9790
1.00 1.00 7.625 0.065 1.9725
2.25 1.50 7.580 0.045 1.9680
4.00 2.00 7.570 0.010 1.9670
6.25 2.50 7.560 0.010 1.9660
9.00 3.00 7.555 0.005 1.9655
12.25 3.50 7.550 0.005 1.9650
16.00 4.00 7.545 0.005 1.9645
25.00 5.00 7.535 0.010 1.9635
36.00 6.00 7.530 0.005 1.9630
49.00 7.00 7.525 0.005 1.9625
64.00 8.00 7.520 0.005 1.9620
81.00 9.00 7.515 0.005 1.9615
100.00 10.00 7.510 0.005 1.9610
1440.00 37.95 7.480 0.030 1.9580
1.0 kg/cm2
, Normal Load
Time t (min) √t
Vertical Dial
gauge Reading
Compression(mm)
Height of the
specimen, H (cm)
0.00 0.00 7.480 0.000 1.958
0.25 0.50 7.280 0.200 1.938
1.00 1.00 7.210 0.070 1.931
2.25 1.50 7.190 0.020 1.929
4.00 2.00 7.170 0.020 1.927
6.25 2.50 7.160 0.010 1.926
9.00 3.00 7.150 0.010 1.925
12.25 3.50 7.140 0.010 1.924
16.00 4.00 7.130 0.010 1.923
25.00 5.00 7.120 0.010 1.922
36.00 6.00 7.110 0.010 1.921
49.00 7.00 7.100 0.010 1.920
64.00 8.00 7.095 0.005 1.920
81.00 9.00 7.085 0.010 1.919
100.00 10.00 7.080 0.005 1.918
1440.00 37.95 7.050 0.030 1.915

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2.0 kg/cm2
, Normal Load
Time t (min) √t
Vertical Dial
gauge Reading
Compression(mm)
Height of the
specimen, H (cm)
0.00 0.00 7.050 0.000 1.9150
0.25 0.50 6.780 0.270 1.8880
1.00 1.00 6.710 0.070 1.8810
2.25 1.50 6.675 0.035 1.8775
4.00 2.00 6.660 0.015 1.8760
6.25 2.50 6.640 0.020 1.8740
9.00 3.00 6.630 0.010 1.8730
12.25 3.50 6.620 0.010 1.8720
16.00 4.00 6.615 0.005 1.8715
25.00 5.00 6.605 0.010 1.8705
36.00 6.00 6.595 0.010 1.8695
49.00 7.00 6.590 0.005 1.8690
64.00 8.00 6.580 0.010 1.8680
81.00 9.00 6.570 0.010 1.8670
100.00 10.00 6.570 0.000 1.8670
1440.00 37.95 6.520 0.050 1.8620
4.0 kg/cm2
, Normal Load
Time t (min) √t
Vertical Dial
gauge Reading
Compression(mm)
Height of the
specimen, H (cm)
0.00 0.00 6.520 0.000 1.862
0.25 0.50 6.130 0.390 1.823
1.00 1.00 6.040 0.090 1.814
2.25 1.50 6.010 0.030 1.811
4.00 2.00 5.990 0.020 1.809
6.25 2.50 5.980 0.010 1.808
9.00 3.00 5.970 0.010 1.807
12.25 3.50 5.960 0.010 1.806
16.00 4.00 5.950 0.010 1.805
25.00 5.00 5.940 0.010 1.804
36.00 6.00 5.930 0.010 1.803
49.00 7.00 5.920 0.010 1.802
64.00 8.00 5.910 0.010 1.801
81.00 9.00 5.900 0.010 1.800
100.00 10.00 5.890 0.010 1.799
1440.00 37.95 5.830 0.060 1.793

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8.0 kg/cm2
, Normal Load
Time t (min) √t
Vertical Dial
gauge Reading
Compression(mm)
Height of the
specimen, H (cm)
0.00 0.00 5.830 0.000 1.7930
0.25 0.50 5.450 0.380 1.7550
1.00 1.00 5.350 0.100 1.7450
2.25 1.50 5.320 0.030 1.7420
4.00 2.00 5.300 0.020 1.7400
6.25 2.50 5.280 0.020 1.7380
9.00 3.00 5.270 0.010 1.7370
12.25 3.50 5.260 0.010 1.7360
16.00 4.00 5.250 0.010 1.7350
25.00 5.00 5.240 0.010 1.7340
36.00 6.00 5.220 0.020 1.7320
49.00 7.00 5.215 0.005 1.7315
64.00 8.00 5.200 0.015 1.7300
81.00 9.00 5.200 0.000 1.7300
100.00 10.00 5.195 0.005 1.7295
1440.00 37.95 5.120 0.075 1.7220

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UNLOADING STAGE
Pressure Decreased in
kg/cm2
8.0 to 4.0 4.0 to 2.0 2.0 to 1.0 1.0 to 0.5 0.5 to 0.1 0.1 to 0.0
Elapsed
Time (min)
√t (min) Dial Gauge Readings
0 0 5.13 5.19 5.29 5.40 5.54 5.83
10.0 3.162 5.19 5.29 5.40 5.54 5.82 6.04
20.0 4.472 5.19 5.29 5.40 5.54 5.83 6.06
Void
Ratio
(e)
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.01 0.1 1 10
e-logp
Loading Stage
Unloading Stage
Pre-consolidation
Pressure
log (p)

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Cc/Cs Ratio
FINAL TABLE
Normal
Stress
σ
kg/cm2
Initial
DG
Reading
(mm)
Final DG
Reading
(mm)
Compression
ΔH (mm)
Height of
Specimen
H (cm)
Void Ratio e
= (H‐ Hs)/Hs
Δe Δσ
av
cm²/kg
mv
(cm²/kg)
x10-2
t90
(min)
Havg
Cv
(cm²/ sec)
x10¯4
0.848xHavg/t90
Cc Cs
0.05 7.90 7.81 0.09 1.991 0.608 2.25
0.18 0.034
0.50 7.81 7.48 0.33 1.958 0.582 0.026 0.45 0.0578 3.6521 3.24 0.987 43.07
1.00 7.48 7.05 0.43 1.915 0.550 0.032 0.50 0.0640 4.1290 4.00 0.968 34.21
2.00 7.05 6.52 0.53 1.862 0.504 0.046 1.00 0.0460 3.0585 4.84 0.944 27.57
4.00 6.52 5.83 0.69 1.793 0.448 0.056 2.00 0.0280 1.9337 6.25 0.913 20.66
8.00 5.83 5.12 0.71 1.722 0.390 0.058 4.00 0.0145 1.0431 7.84 0.878 15.84
4.00 5.12 5.19 0.07 1.729 0.397 0.007 4.00 0.0018
2.00 5.19 5.29 0.10 1.739 0.404 0.007 2.00 0.0035
1.00 5.29 5.40 0.11 1.750 0.414 0.010 1.00 0.0100
0.50 5.40 5.54 0.14 1.764 0.425 0.011 0.50 0.0220
0.05 5.54 5.68 0.14 1.778 0.436 0.011 0.45 0.0244
Pre-consolidation Stress
1.10 kg/cm²
110kPa
Cc 0.180
Cs 0.034
Ratio Cc/Cs 5.294 O.K.

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7.450
7.500
7.550
7.600
7.650
7.700
7.750
7.800
7.850
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Normal Stress: 0.5kg/cm2
√t90 = 1.8
t90 = 3.24
7.800
7.810
7.820
7.830
7.840
7.850
7.860
7.870
7.880
7.890
7.900
7.910
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
Normal Stress: 0.05 kg/cm2
√t90
= 1.5
t90
= 2.25
√t
√t
Dial
Gauge
Reading
Dial
Gauge
Reading

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7.000
7.050
7.100
7.150
7.200
7.250
7.300
7.350
7.400
7.450
7.500
7.550
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
√t90 = 2.0
t90 = 4.00
6.400
6.500
6.600
6.700
6.800
6.900
7.000
7.100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
√t90 = 2.2
t90 = 4.84
√t
√t
Dial
Gauge
Reading
Dial
Gauge
Reading

17
5.70
5.80
5.90
6.00
6.10
6.20
6.30
6.40
6.50
6.60
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
√t90 = 2.5
t90 = 6.25
5.00
5.10
5.20
5.30
5.40
5.50
5.60
5.70
5.80
5.90
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
√t90 = 2.8
t90 = 7.84
√t
√t
Dial
Gauge
Reading
Dial
Gauge
Reading

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Result:
For the given soil sample (Dhanauri Clay):
● Coefficient of Consolidation (Cv) = 2.827 x 10-3
cm2
/sec;(Average value).
● Compression Index (Cc)= 0.18; (from slope of curve plotted between logarithmic of stress v/s void ratio).
● Cs = 0.034
● Coefficient of Compressibility (av) = 0.0272 cm2
/kg; (Average value).
● Coefficient of Volume Compressibility (mv) = 2.763 x 10-2
cm2
/kg; (Average value).
● Cc/Cs = 5.294 (Within the range of 0-10; OK).
● Average value of Coeff. of Permeability (k) = 8.7858 x 10-6
cm/sec.
● Pre-consolidation stress = 110 kPa.
Discussion:
1. From consolidation test, the following information can be determined:
a) Amount of settlement experienced by a soil-structure after load application
b) Rate of consolidation of soil under a normal load
c) Degree of consolidation at any time
d) Pressure void ratio relationship
e) Coefficient of consolidation at various successively increasing pressure
f) Permeability of soil at various stages of loading
g) Compression index of soil
2. The general procedure for laboratory evaluation of consolidation characteristics of soils involves a
one-dimensional consolidation.
This is necessary because of:
• Difficulty of instrumentation for recording volume change and natural strains.
• Complexities in mathematical analysis of three-dimensional consolidation.
3. The underlying assumptions in the derivation of the mathematical equations are as follows:
• The clay layer is homogeneous.
• The clay layer is saturated, the compression of the soil layer is due to the change in volume only,
which in turn, is due to the squeezing out of water from the void spaces.
• Darcy’s law is valid.
• Deformation of soil occurs only in the direction of the load application.
4. Effects of ring friction
• During loading reduce stress acted on the specimen, specimen compresses less.
• During rebound reduce the swelling tendency specimen swell less.
• Flatten the swelling curve at low stress level.
5. Resultant Cv decreases with increasing stress, implying its NC clay.
6. Sample was preserved in polybag to check loss of moisture content.

19
7. While preparing the specimen, attempt has to be made to have the consolidation apparatus
orientated in the same direction in the soil strata.
8. During trimming care should be taken in handling the soil specimen with least pressure.
9. Smaller increments of sequential loading have to be adopted for soft soils.
10. Graphs Plotted:
a) Dial reading VS square root of time.
b) Voids ratio VS logp (average pressure for the increment).
References:
1. IS: 2720 (Part 15) – 1965 (Reaffirmed‐2002),
2. D2435 / D2435M‐11,
3. BS 1377‐6
4. IS: 2-1960

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