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1
University of Sulaimani
College of Engineering
Civil Engineering Department
(Soil Mechanics Lab)
Name of the Test: Unconfined compression test
Test No. :
Students Name:
1- Raz Azad Abdullah
2- Zhyar Abu-Bakr
3- Rawezh Saady
Group & Sub-Group: A1-A6
Date of the Test: 30-4-2019
2
Introduction:
The unconfined compression test is by far the most popular method of soil shear
testing because it is one of the fastest and cheapest methods of measuring shear
strength. The method is used primarily for saturated, cohesive soils recovered from
thin-walled sampling tubes. The unconfined compression test is inappropriate for
dry sands or crumbly clays because the materials would fall apart without some
land of lateral confinement.
Unconfined Compression Test is a special type of Unconsolidated – Un drained
(UU) test that is commonly used for clay specimens. It is special case of a tri axial
compression test.
This test may be conducted onundisturbed or remolded cohesive soils. It cannot be
conducted on coarse-grained soils such as sands and gravels as these cannot stand
without lateral support. Also the test is essentially a quick or Un drained one
because it is assumed that there is no loss of moisture during the test, which is
performed fairly fast.
3
Purpose of the Test:
The purpose of this laboratory test is to determine the unconfined compressive
strength of a cohesive soil sample. We will measure this with the unconfined
compression test, which is an unconsolidated un drained (UU or Q-type) test where
the lateral confining pressure is equal to zero (atmospheric pressure).
For soils, the un drained shear strength is necessary for the determination of the
bearing capacity of foundations, dams, etc.
The undrained shear strength of clays is commonly determined from an
unconfined compression test. The undrained shear strength of a cohesive soil is
equal to one half the unconfined compressive strength (qu) when the soil is under
the f = 0 condition (f = the angle of internal friction). The most critical condition
for the soil usually occurs immediately after construction, which represents
undrained conditions, when the undrained shear strength is basically equal to the
cohesion (c).
Equipment:
1. Unconfined Compression testing device.
2. Specimen trimmer and accessories (if undistributed field specimen is used) .
3. Harvard miniature compaction device and accessories (if specimen is to be
molded for class room work).
4. Scale
5. Balance, sensitive to 0.1g.
6. Oven
7. Porcelain evaporating dish.
4
Procedure:
1. The first step in the procedureis to examine the loading frame. Turn the crank
and learn how to read the load and deformation dial gages. Determine the
calibration constantfor the proving ring and the units of the deformation dial
gauge.
2. We will be shearing the samples at a strain rate of 1% per minute. From the
length of your soil sample, determine the deformation at 1% strain. Depending on
the units of the vertical deformation dial gauge (usually 0.001 inches or 0.0001
inches), determine the number of dial divisions per 1 strain- Practice turning the
crank at his number of dial divisions/minute. It is important that the soil sample not
be sheared faster than this specified rate
3. Measure the initial height and diameter of the soil sample with calipers. It is
unlikely that the sample will be a perfect right cylinder. Therefore, it will be
necessary to find the average height and diameter by taking several measurements
in different places along the soil sample. The measurements should be taken by
more than one member of a lab team to be sure that the calipers are read correctly.
If you have any questions about how to take measurements with calipers, ask the
laboratory instructor for instruction.
4. Record the weight of the soil sample and determine the total (moist) unit
weight.
5. Place the soil sample in the loading frame, seat the proving ring and zero the
dials.
6. During this lab you will record the load applied at specified strain values. It is
recommended that readings be taken at strains of 0,0.1,0.2, 0.5, 1,2,3,4,5,6,8, 10,
5
12 14, 16, 18 and 20 percent. You should prerecord the vertical deformation dial
readings at these strain values. With the measured initial height of sample (H0), the
desired percent strain (ε) and the initial dial reading (S0), calculate the dial
readings.
7. Readings of force (F) are taken from the proving ring dial gauge and the stress
applied to the ends of the sample (01, or major principal stress)
Because the soil sample height decreases during shear and the volume of the
sample remains constant, the cross sectional area must increase. For a saturated
soil that undergoes no volume change during shear (no flow of water into or out of
the sample), the equivalent or average area (A) at any strain (e) is computed from
the initial area (Ac) and the assumption that volume is conserved:
Shear the sample at a strain rate of 1% per minute. Typically, the sample fails in
one of two ways. In stiffer clays, a distinct failure plane forms. For this type of
failure, it is likely that the point of failure will be indicated by the measurement of
a peak and then a decrease in load. If this is the case, continue to take four or five
readings past the point of failure. (Caution: before you stop shearing the sample, be
sure that the sample has failed.) A "barreling" failure is more typical for softer
clays. In this type of failure, a distinct failure plane doesn'tform, rather the sample
bulges in the middle The unconfined compressive strength (qu) is the maximum
value σ1, which may or may not coincide with the maximum force measurement
(depending on the area correction).It is also equal to the diameter of Mohr's circle
as indicated in Fig. 1. The undrained shear strength (qu) is typically taken as the
maximum shear stress.
6
9. When your lab team has completed the experiment, dismantle the loading frame
and measure the water content of the soil sample. It is recommended that you
reduce the data for this test during the lab period.
7
Calculation:
*Vertical strain:
ε =
𝛥 𝐿
𝐿
Where:
L = Original specimen length = 86mm
Δ L = total vertical deformation of the specimen.
Δ L(mm) = Deformation reading * calibration factor for the dial gage
Calibration factor for the dial gage = 0.01 mm
 First Reading:
Δ L= 25 * 0.01 = 0.25mm
ε =
0.25
86
= 0.002906977
 Second Reading:
Δ L=50*0.01=0.5mm
ε =
0.5
86
= 0.005813953
- So on the same procedureis followed for the other readings.
8
*Vertical Load on the specimen:
Load (KN) =Proving Ring reading * calibration factor
Calibration factor= 0.0064 div/KN
 First Reading:
= 2 * 0.0064=0.0128 KN
=12.8N
 Second Reading:
=3 * 0.0064 = 0.0192KN
=19.2N
- So on the same procedureis followed for the other readings.
*CorrectedArea of the specimen:
Ac =
𝐴𝑜
(1−𝜀 )
Where:
Ao = Initial Area of the cross section of the specimen=𝜋/4 ∗ 𝐷2
𝜋
4
∗ 38 2= 1134.114948mm2
 First Reading:
Ac =
1134.114948
(1−0.002906977 )
= 1137.421406 mm2
 Second Reading:
Ac =
1134.114948
(1− 0.005813953)
= 1140.747199mm2
- So on the same procedureis followed for the other readings.
9
*Stress (σ):
σ =
𝐿𝑜𝑎𝑑(𝐾𝑁)
𝐴𝑐(𝑚𝑚2)
 First Reading:
σ =
0.0128
1137.421406
= 1.12535 * 10-5 KN/mm2
= 11.2535248 kpa
 Second Reading:
σ =
0.0192
1140.747199
= 1.68311 * 10-5 KN/mm2
=16.83107354 kpa
- So on the same procedureis followed for the other readings.
*WaterContent:
W (%)=
(𝑊𝑡.𝑤𝑒𝑡 𝑠𝑜𝑖𝑙−𝑊𝑡.𝑑𝑟𝑦 𝑠𝑜𝑖𝑙)
𝑊𝑡.𝑑𝑟𝑦 𝑠𝑜𝑖𝑙
Wt. wet soil = Wt.(wet soil+can) – Wt. Can
= 287.65 - 99.13 = 188.52g
Wt. dry soil = Wt.(dry soil+can) – Wt. Can
= 250.96 - 99.13 = 151.83g
Water Content (%) =
188.52−151.83
151.83
* 100 = 24.165%
10
Deformation Reading Proving Ring reading Load(N) delta L(mm) strain corrected area(mm²) stress(kpa)
25 2 12.8 0.25 0.002906977 1137.421406 11.2535248
50 3 19.2 0.5 0.005813953 1140.747199 16.83107354
75 7 44.8 0.75 0.00872093 1144.092499 39.15767304
100 11 70.4 1 0.011627907 1147.457477 61.3530361
125 12.5 80 1.25 0.014534884 1150.842307 69.51430227
150 15 96 1.5 0.01744186 1154.247166 83.1710944
175 11.1 71.04 1.75 0.020348837 1157.672232 61.36451929
200 17.5 112 2 0.023255814 1161.117685 96.45878403
225 19 121.6 2.25 0.026162791 1164.583708 104.4149933
250 20 128 2.5 0.029069767 1168.070485 109.5824281
275 20.5 131.2 2.75 0.031976744 1171.578205 111.9856954
300 21 134.4 3 0.034883721 1175.107055 114.3725582
325 22 140.8 3.25 0.037790698 1178.657227 119.4579703
350 22.1 141.44 3.5 0.040697674 1182.228915 119.6384204
375 22.9 146.56 3.75 0.043604651 1185.822316 123.5935586
400 23 147.2 4 0.046511628 1189.437628 123.7559637
425 23.5 150.4 4.25 0.049418605 1193.075052 126.0608037
450 24 153.6 4.5 0.052325581 1196.734792 128.3492392
475 24 153.6 4.75 0.055232558 1200.417053 127.9555298
500 24.5 156.8 5 0.058139535 1204.122044 130.2193584
525 24.8 158.72 5.25 0.061046512 1207.849976 131.4070482
550 25 160 5.5 0.063953488 1211.601062 132.0566686
575 25.25 161.6 5.75 0.066860465 1215.375521 132.9630203
600 25.25 161.6 6 0.069767442 1219.173569 132.5488053
625 25.25 161.6 6.25 0.072674419 1222.99543 132.1345903
650 25.25 161.6 6.5 0.075581395 1226.841327 131.7203752
675 25.25 161.6 6.75 0.078488372 1230.711489 131.3061602
Table of Results:
From the Graph:
The peak stress from the graph =132.982kpa = qu = unconfined compression
strength.
Cohesion (c) = kpa
11
12
Figures:
- The failure mode of the sample is Plastic Failure, in which the specimen bulges
laterally into a ‘barrel shape’ without splitting .
Figure 1
Figure 2
Figure 1
13
Discussion & Conclusion:
The unconfined compression test is a quick method of determining the value of cu
for a clayey soil. The unconfined strength is given by the relation qu= cu/2, where
qu = unconfined compression strength. For soils, it is necessary for the
determination of the bearing capacity of foundations, dams, etc.
In this experiment the unconfined compression strength resulted to be
(132.982kpa), and the untrained cohesion of the sample is ( ).
In term of consistency our soil consistency is (stiff) because qu= 2777.386I b/ft 2 it
lies in the range of (2000-4000) (Ib/ft2).
The failure mode of the sample is Plastic Failure, in which the specimen bulges
laterally into a ‘barrel shape’ without splitting.
In terms of the shape of the graph the graph started off with almost a liner line until
the point 7 which there is a drop that must not be like that, and this is may be
caused by a wrong reading (human error) or the machine dropped and came back
at that point, the rest values is taken correctly.
There are a number of sources oferror in the unconfined compressiontest. One at
the largest sources is the use of an unrepresentative sample of soil. The soil may be
unrepresentative because it is not the same as, or perhaps even similar to. The bulk
of the soil found in the ground, the sample can also be unrepresentative if it has
been disturbed or changed from its original slate. A common cause for disturbance
is the soil sampling process. Disturbance usually has the effect of lowering the
strength of the soil and reducing the slope of the stress-strain curve, avoid this
problem, another sourceof error is that the soil is not confined during shear but
will be confined in the field if the soil is located at a depth of a few feet or more.
14
The problem is most severe with fissured soils (soils that contain cracks). In the
ground, the cracks are held closed by the confining pressure due to the weight of
soil above it. The soil is much stronger in this state than it is with no confining
pressure in Cohesive soils display a wide array of engineering properties, including
erosion behavior, that are not easily derived from the physical properties of the
soil. For noncohesive soils, the engineering properties, particularly the resistance to
erosion, depend primarily on the soil structure and grain properties. The behavior
of cohesive soils depends not only on these factors but also on the electrochemical
attraction and repulsion characteristics of the soils. Further complicating any
assessment is the possibility that these properties change when samples are
removed from a site for testing or when samples are created in a laboratory. With
respect to laboratory prepared soils, the soil structure may be influenced by the
preparation technique and sequence an unconfined compressiontest.
References:
 https://www.cyut.edu.tw/~jrlai/CE7334/Unconfined.pdf
 https://uomustansiriyah.edu.iq/media/lectures/5/5_2018_03_06
!05_25_52_PM.pdf
 Soil mechanic lab manual
 https://www.coursehero.com/file/p7ca30t/Discussion-The-
unconfined-compression-test-is-a-quick-method-of-
determining-the/
15
16

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Uucnt copy

  • 1. 1 University of Sulaimani College of Engineering Civil Engineering Department (Soil Mechanics Lab) Name of the Test: Unconfined compression test Test No. : Students Name: 1- Raz Azad Abdullah 2- Zhyar Abu-Bakr 3- Rawezh Saady Group & Sub-Group: A1-A6 Date of the Test: 30-4-2019
  • 2. 2 Introduction: The unconfined compression test is by far the most popular method of soil shear testing because it is one of the fastest and cheapest methods of measuring shear strength. The method is used primarily for saturated, cohesive soils recovered from thin-walled sampling tubes. The unconfined compression test is inappropriate for dry sands or crumbly clays because the materials would fall apart without some land of lateral confinement. Unconfined Compression Test is a special type of Unconsolidated – Un drained (UU) test that is commonly used for clay specimens. It is special case of a tri axial compression test. This test may be conducted onundisturbed or remolded cohesive soils. It cannot be conducted on coarse-grained soils such as sands and gravels as these cannot stand without lateral support. Also the test is essentially a quick or Un drained one because it is assumed that there is no loss of moisture during the test, which is performed fairly fast.
  • 3. 3 Purpose of the Test: The purpose of this laboratory test is to determine the unconfined compressive strength of a cohesive soil sample. We will measure this with the unconfined compression test, which is an unconsolidated un drained (UU or Q-type) test where the lateral confining pressure is equal to zero (atmospheric pressure). For soils, the un drained shear strength is necessary for the determination of the bearing capacity of foundations, dams, etc. The undrained shear strength of clays is commonly determined from an unconfined compression test. The undrained shear strength of a cohesive soil is equal to one half the unconfined compressive strength (qu) when the soil is under the f = 0 condition (f = the angle of internal friction). The most critical condition for the soil usually occurs immediately after construction, which represents undrained conditions, when the undrained shear strength is basically equal to the cohesion (c). Equipment: 1. Unconfined Compression testing device. 2. Specimen trimmer and accessories (if undistributed field specimen is used) . 3. Harvard miniature compaction device and accessories (if specimen is to be molded for class room work). 4. Scale 5. Balance, sensitive to 0.1g. 6. Oven 7. Porcelain evaporating dish.
  • 4. 4 Procedure: 1. The first step in the procedureis to examine the loading frame. Turn the crank and learn how to read the load and deformation dial gages. Determine the calibration constantfor the proving ring and the units of the deformation dial gauge. 2. We will be shearing the samples at a strain rate of 1% per minute. From the length of your soil sample, determine the deformation at 1% strain. Depending on the units of the vertical deformation dial gauge (usually 0.001 inches or 0.0001 inches), determine the number of dial divisions per 1 strain- Practice turning the crank at his number of dial divisions/minute. It is important that the soil sample not be sheared faster than this specified rate 3. Measure the initial height and diameter of the soil sample with calipers. It is unlikely that the sample will be a perfect right cylinder. Therefore, it will be necessary to find the average height and diameter by taking several measurements in different places along the soil sample. The measurements should be taken by more than one member of a lab team to be sure that the calipers are read correctly. If you have any questions about how to take measurements with calipers, ask the laboratory instructor for instruction. 4. Record the weight of the soil sample and determine the total (moist) unit weight. 5. Place the soil sample in the loading frame, seat the proving ring and zero the dials. 6. During this lab you will record the load applied at specified strain values. It is recommended that readings be taken at strains of 0,0.1,0.2, 0.5, 1,2,3,4,5,6,8, 10,
  • 5. 5 12 14, 16, 18 and 20 percent. You should prerecord the vertical deformation dial readings at these strain values. With the measured initial height of sample (H0), the desired percent strain (ε) and the initial dial reading (S0), calculate the dial readings. 7. Readings of force (F) are taken from the proving ring dial gauge and the stress applied to the ends of the sample (01, or major principal stress) Because the soil sample height decreases during shear and the volume of the sample remains constant, the cross sectional area must increase. For a saturated soil that undergoes no volume change during shear (no flow of water into or out of the sample), the equivalent or average area (A) at any strain (e) is computed from the initial area (Ac) and the assumption that volume is conserved: Shear the sample at a strain rate of 1% per minute. Typically, the sample fails in one of two ways. In stiffer clays, a distinct failure plane forms. For this type of failure, it is likely that the point of failure will be indicated by the measurement of a peak and then a decrease in load. If this is the case, continue to take four or five readings past the point of failure. (Caution: before you stop shearing the sample, be sure that the sample has failed.) A "barreling" failure is more typical for softer clays. In this type of failure, a distinct failure plane doesn'tform, rather the sample bulges in the middle The unconfined compressive strength (qu) is the maximum value σ1, which may or may not coincide with the maximum force measurement (depending on the area correction).It is also equal to the diameter of Mohr's circle as indicated in Fig. 1. The undrained shear strength (qu) is typically taken as the maximum shear stress.
  • 6. 6 9. When your lab team has completed the experiment, dismantle the loading frame and measure the water content of the soil sample. It is recommended that you reduce the data for this test during the lab period.
  • 7. 7 Calculation: *Vertical strain: ε = 𝛥 𝐿 𝐿 Where: L = Original specimen length = 86mm Δ L = total vertical deformation of the specimen. Δ L(mm) = Deformation reading * calibration factor for the dial gage Calibration factor for the dial gage = 0.01 mm  First Reading: Δ L= 25 * 0.01 = 0.25mm ε = 0.25 86 = 0.002906977  Second Reading: Δ L=50*0.01=0.5mm ε = 0.5 86 = 0.005813953 - So on the same procedureis followed for the other readings.
  • 8. 8 *Vertical Load on the specimen: Load (KN) =Proving Ring reading * calibration factor Calibration factor= 0.0064 div/KN  First Reading: = 2 * 0.0064=0.0128 KN =12.8N  Second Reading: =3 * 0.0064 = 0.0192KN =19.2N - So on the same procedureis followed for the other readings. *CorrectedArea of the specimen: Ac = 𝐴𝑜 (1−𝜀 ) Where: Ao = Initial Area of the cross section of the specimen=𝜋/4 ∗ 𝐷2 𝜋 4 ∗ 38 2= 1134.114948mm2  First Reading: Ac = 1134.114948 (1−0.002906977 ) = 1137.421406 mm2  Second Reading: Ac = 1134.114948 (1− 0.005813953) = 1140.747199mm2 - So on the same procedureis followed for the other readings.
  • 9. 9 *Stress (σ): σ = 𝐿𝑜𝑎𝑑(𝐾𝑁) 𝐴𝑐(𝑚𝑚2)  First Reading: σ = 0.0128 1137.421406 = 1.12535 * 10-5 KN/mm2 = 11.2535248 kpa  Second Reading: σ = 0.0192 1140.747199 = 1.68311 * 10-5 KN/mm2 =16.83107354 kpa - So on the same procedureis followed for the other readings. *WaterContent: W (%)= (𝑊𝑡.𝑤𝑒𝑡 𝑠𝑜𝑖𝑙−𝑊𝑡.𝑑𝑟𝑦 𝑠𝑜𝑖𝑙) 𝑊𝑡.𝑑𝑟𝑦 𝑠𝑜𝑖𝑙 Wt. wet soil = Wt.(wet soil+can) – Wt. Can = 287.65 - 99.13 = 188.52g Wt. dry soil = Wt.(dry soil+can) – Wt. Can = 250.96 - 99.13 = 151.83g Water Content (%) = 188.52−151.83 151.83 * 100 = 24.165%
  • 10. 10 Deformation Reading Proving Ring reading Load(N) delta L(mm) strain corrected area(mm²) stress(kpa) 25 2 12.8 0.25 0.002906977 1137.421406 11.2535248 50 3 19.2 0.5 0.005813953 1140.747199 16.83107354 75 7 44.8 0.75 0.00872093 1144.092499 39.15767304 100 11 70.4 1 0.011627907 1147.457477 61.3530361 125 12.5 80 1.25 0.014534884 1150.842307 69.51430227 150 15 96 1.5 0.01744186 1154.247166 83.1710944 175 11.1 71.04 1.75 0.020348837 1157.672232 61.36451929 200 17.5 112 2 0.023255814 1161.117685 96.45878403 225 19 121.6 2.25 0.026162791 1164.583708 104.4149933 250 20 128 2.5 0.029069767 1168.070485 109.5824281 275 20.5 131.2 2.75 0.031976744 1171.578205 111.9856954 300 21 134.4 3 0.034883721 1175.107055 114.3725582 325 22 140.8 3.25 0.037790698 1178.657227 119.4579703 350 22.1 141.44 3.5 0.040697674 1182.228915 119.6384204 375 22.9 146.56 3.75 0.043604651 1185.822316 123.5935586 400 23 147.2 4 0.046511628 1189.437628 123.7559637 425 23.5 150.4 4.25 0.049418605 1193.075052 126.0608037 450 24 153.6 4.5 0.052325581 1196.734792 128.3492392 475 24 153.6 4.75 0.055232558 1200.417053 127.9555298 500 24.5 156.8 5 0.058139535 1204.122044 130.2193584 525 24.8 158.72 5.25 0.061046512 1207.849976 131.4070482 550 25 160 5.5 0.063953488 1211.601062 132.0566686 575 25.25 161.6 5.75 0.066860465 1215.375521 132.9630203 600 25.25 161.6 6 0.069767442 1219.173569 132.5488053 625 25.25 161.6 6.25 0.072674419 1222.99543 132.1345903 650 25.25 161.6 6.5 0.075581395 1226.841327 131.7203752 675 25.25 161.6 6.75 0.078488372 1230.711489 131.3061602 Table of Results: From the Graph: The peak stress from the graph =132.982kpa = qu = unconfined compression strength. Cohesion (c) = kpa
  • 11. 11
  • 12. 12 Figures: - The failure mode of the sample is Plastic Failure, in which the specimen bulges laterally into a ‘barrel shape’ without splitting . Figure 1 Figure 2 Figure 1
  • 13. 13 Discussion & Conclusion: The unconfined compression test is a quick method of determining the value of cu for a clayey soil. The unconfined strength is given by the relation qu= cu/2, where qu = unconfined compression strength. For soils, it is necessary for the determination of the bearing capacity of foundations, dams, etc. In this experiment the unconfined compression strength resulted to be (132.982kpa), and the untrained cohesion of the sample is ( ). In term of consistency our soil consistency is (stiff) because qu= 2777.386I b/ft 2 it lies in the range of (2000-4000) (Ib/ft2). The failure mode of the sample is Plastic Failure, in which the specimen bulges laterally into a ‘barrel shape’ without splitting. In terms of the shape of the graph the graph started off with almost a liner line until the point 7 which there is a drop that must not be like that, and this is may be caused by a wrong reading (human error) or the machine dropped and came back at that point, the rest values is taken correctly. There are a number of sources oferror in the unconfined compressiontest. One at the largest sources is the use of an unrepresentative sample of soil. The soil may be unrepresentative because it is not the same as, or perhaps even similar to. The bulk of the soil found in the ground, the sample can also be unrepresentative if it has been disturbed or changed from its original slate. A common cause for disturbance is the soil sampling process. Disturbance usually has the effect of lowering the strength of the soil and reducing the slope of the stress-strain curve, avoid this problem, another sourceof error is that the soil is not confined during shear but will be confined in the field if the soil is located at a depth of a few feet or more.
  • 14. 14 The problem is most severe with fissured soils (soils that contain cracks). In the ground, the cracks are held closed by the confining pressure due to the weight of soil above it. The soil is much stronger in this state than it is with no confining pressure in Cohesive soils display a wide array of engineering properties, including erosion behavior, that are not easily derived from the physical properties of the soil. For noncohesive soils, the engineering properties, particularly the resistance to erosion, depend primarily on the soil structure and grain properties. The behavior of cohesive soils depends not only on these factors but also on the electrochemical attraction and repulsion characteristics of the soils. Further complicating any assessment is the possibility that these properties change when samples are removed from a site for testing or when samples are created in a laboratory. With respect to laboratory prepared soils, the soil structure may be influenced by the preparation technique and sequence an unconfined compressiontest. References:  https://www.cyut.edu.tw/~jrlai/CE7334/Unconfined.pdf  https://uomustansiriyah.edu.iq/media/lectures/5/5_2018_03_06 !05_25_52_PM.pdf  Soil mechanic lab manual  https://www.coursehero.com/file/p7ca30t/Discussion-The- unconfined-compression-test-is-a-quick-method-of- determining-the/
  • 15. 15
  • 16. 16