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Introduction

Because soil is used to bear loads in civil engineering, determining the compressibility of a soil is

important. It can be determined by applying loading to a soil and measuring how much the soil deformed

over a period of time with various magnitudes of loads. This test is usually performed on clay, however,

in this laboratory, coarse sand is used.

The sample will be placed in a metal ring and the deformation will be calculated versus the load rather

than the time to demonstrate the drainage effects of the soil.

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Sample Calculations

To determine the initial height of the specimen, the distance from the top of the sand to the top of the cell

ring, Hr is subtracted from the height of the rings. Hd.

=== 63.22.270 dr HHH

24.57mm

The vertical displacement is simply the value obtained from the dial gage.

The height of the specimen after loading and unloading can be calculated by subtracting the vertical

displacement from the initial height of the specimen.

426.24144.57.240 === HHH

mm

The height of the solids is defined by the following equation:

=

===

3

2

2

981066.206362.4

)81.916114(.

m

Nm

s

mkg

AG

mg

AG

WH

wsws

ss

19.05 mm

Where Hs is the height of the solids, Ws is the weight of the solids, A is the area of the oedometer cell, Cs

is the specific gravity of the soil, yw is the unit weight of water, m is the mass of the soil, and g is the

acceleration due to gravity.

The height of the voids can be calculated by subtracting the height of the solids from the height of the soil

specimen, H.

== sv HHH

24.426 19.05 = 5.376 mm

The void ratio, e, of the soil sample can be computed by dividing the height of the voids by the height of

the solids.

===

05.19

376.5

s

v

H

He

.2822

The compression index can be found by plotting the void ratio versus the vertical stress on a logarithmic

scale and finding the slope of the linear portion of the graph. Using the information from the graph and

the following equation, the compression index, Cc, can be determined.

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0507.)120/480log(

225.256.

)/log( 12

12=

=

=

kPakPa

eeCc

E1 and e2 are two void ratios and s1 and s2 are the corresponding stresses.

The coefficient of consolidation, Cv, can be calculated for a consolidation test with a one load increment

using the square root of time method. Deformation of the sample is plotted against the square root of

time, and graphic constructions are added to determine t90.

Using the plot, t90 is approximately 3.24. Using the table in Fundamentals of Geotechnical Engineering,

T90 is .848.

=+

=+

=4

74.19838.22

4

0 ininHHH

f

dr

10.28 in

min/65.27

28.10

)24.3(848.

2

2

9090

mmc

c

H

tcT

v

v

dr

v

=

===

==mm

cmmmcv

100

1

sec60

min1

min65.27

2

.0046 cm2/sec

To find T50, the now known cv value can be plugged into the previous equation.

dayst

t

mm

t

H

tcT

dr

v

23.5

sec452579

)1028.10(

0046.197.

50

50

2

50

2

5050

=

=

===

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Results

Table 4.1 Raw Data

Mass Stressdialreading displacement Height

Height ofVoids Void Ratio

[kg] [kPa] [mm] [mm] [mm] [mm] [%]

1 30 0.144 0.144 24.426 5.376 0.282

2 60 0.382 0.382 24.188 5.138 0.270

4 120 0.596 0.596 23.974 4.924 0.258

2 60 0.562 0.562 24.008 4.958 0.260

1 30 0.508 0.508 24.062 5.012 0.263

2 60 0.55 0.55 24.02 4.97 0.261

4 120 0.652 0.652 23.918 4.868 0.256

8 240 0.916 0.916 23.654 4.604 0.242

16 480 1.234 1.234 23.336 4.286 0.225

Figure 4.1 Void Ratio versus log-stress

Table 4.2 Coefficient of Compression

Cc 0.0507

Figure 4.2 Square Root of Time Fitting Method

Table 4.3 Coefficient of Consolidation and t50

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Hdr 10.28 mm

Cv 0.004 cm2/sec

t90 3.24 min

t50 5.23 days

Analysis

With the compression index being small, the soil will work well for the materials needed for the dam

project. This soil will not compress much with respect to the load that it will have to withstand. Even

after loading and unloading, the settlement was minimal. From figure 4.1 it can be seen that the

displacement is minimal in relation to the stress that is applied. The consolidation index was found usingthe data from the loading versus time. The graph turned out as expected.

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References

University of Minnesota, Civil Engineering, 2008, 1D Compression. Pages 35-38, Soils ! Laboratory

Manual.

Das, Braja M. Fundamentals of Geotechnical Engineering. Toronto, Ontario, Canada. Nelson, 2005.

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Soil Mechanics

Department of Civil Engineering

University of Minnesota

Minneapolis, MN

55455

Date

Geoproject Incorporated

2300 Arapahoe Avenue

Minneapolis, MN 55455

Dear Dr. Bojan Guzina,

This letter is in response to your request for the compression index of the sand and the coefficient of

consolidation for the clay that could be used in the proposed earth dam project.

In order to determine the compression index, an ELE Oedometer was used to calculate the displacement

in relation to the load. To determine the coefficient of consolidation, the square root of time method wasused.

The compression index was found to be 0.0507. The coefficient of consolidation was found to be 0.004

cm2/sec. If a 70kPa surcharge load is applied to the sand, the maximum displacement is 1.234 mm,

which is less than the allowable 10 mm deformation. The time to reach 50% consolidation in the clay, or

t50, is 5.23 days. Because the life of the dam is 5 years, it is important that the soil be able to withstand

the loading without too much displacement. To determine if the rate of settlement of the clay is sufficient

for this project, the

From these results, it can be determined that the sand would be sufficient to use in the dam project. The

compression index is small meaning that the soil will be able to withhold a large amount of stress withoutdeforming too much. The consolidation test was performed to determine the coefficient of consolidation.

The value determined in this lab is reasonable.

It was our pleasure to work with you and your associates on this matter and we look forward to the

further design of this project.

Sincerely,

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XXXXXX